22

THE

GENETICAL THEORY OF
NATURAL SELECTION

OXFORD UNIVERSITY PRESS

AMEN HOUSE, E.O. 4

LONDON EDINBURGH GLASGOW

LEIPZIG NEWTOBK TORONTO

MELBOURNE CAPETOWN BOMBAY

CALCUTTA MADRAS SHANGHAI

HUMPHREY MILFORD

PUBLISHER TO THB
UNIVERSITY

NA'

For description of the frontispiece see p. xiii

THE

GENETICAL THEORY OF
NATURAL SELECTION

o

R. A. FISHER, Sc.D., F.R.S.

OXFORD

AT THE CLARENDON PRESS
1930

OH

Printed in Great Britain

TO

MAJOR LEONARD DARWIN

In gratitude for the encouragement,

given to the author, during the last

fifteen years, by discussing many

of the problems dealt with

in this book

PEEFACE

NATURAL Selection is not Evolution. Yet, ever since the two
words have been in common use, the theory of Natural Selection
has been employed as a convenient abbreviation for the theory of
Evolution by means of Natural Selection, put forward by Darwin
and Wallace. This has had the unfortunate consequence that the
theory of Natural Selection itself has scarcely ever, if ever, received
separate consideration. To draw a physical analogy, the laws of con-
duction of heat in solids might be deduced from the principles of
statistical mechanics, yet it would have been an unfortunate limita-
tion, involving probably a great deal of confusion, if statistical
mechanics had only received consideration in connexion with the
conduction of heat. In this case it is clear that the particular physical
phenomena examined are of little theoretical interest compared to
the principle by which they can be elucidated. The overwhelming
importance of evolution to the biological sciences partly explains
why the theory of Natural Selection should have been so fully identi-
fied with its role as an evolutionary agency, as to have suffered neglect
as an independent principle worthy of scientific study.

The other biological theories which have been put forward, either
as auxiliaries, or as the sole means of organic evolution, are not quite
in the same position. For advocates of Natural Selection have not
failed to point out, what was evidently the chief attraction of the
theory to Darwin and Wallace, that it proposes to give an account
of the means of modification in the organic world by reference only
to 'known ', or independently demonstrable, causes. The alternative
theories of modification rely, avowedly, on hypothetical properties
of living matter which are inferred from the facts of evolution them-
selves. Yet, although this distinction has often been made clear, its
logical cogency could never be fully developed in the absence of a
separate investigation of the independently demonstrable modes of
causation which are claimed as its basis. The present book, with all
the limitations of a first attempt, is at least an attempt to consider
the theory of Natural Selection on its own merits.

When the theory was first put forward, by far the va,giipst-
in its"composition was the principle of inheritance. NV^maji nf_
ing*-qr~t;xpeTleiice could deny this principle, vet, at thp. timft. no^
approach could be given to an exact account of its working. That an

viii PREFACE

independent study of Natural Selection is now possible is principally
due to the great advance which our generation has seen in the science
Of genetics, it deserves notice that the first decisive experiments,
which opened out in biology this field of exact study, were due to
a young mathematician, Gregor Mendel, whose statistical interests
extended to the physical and biological sciences. It is well known
that his experiments were ignored, to his intense disappointment,
and it is to be presumed that they were never brought under the
notice of any man whose training qualified him to appreciate their
importance. It is no less remarkable that when, in 1900, the genetic
facts had been rediscovered by De Vries, Tschermak, and Correns, and
the importance of Mendel's work was at last recognized, the principal
opposition should have been encountered from the small group of
mathematical statisticians then engaged in the study of heredity.

The types of mind which result from training in mathematics and
in biology certainly differ profoundly; but the difference does not
seem to lie in the intellectual faculty. It would certainly be a mistake
to say that the manipulation of mathematical symbols requires more
intellect than original thought in biology ; on the contrary, it seems
much more comparable to the manipulation of the microscope and
its appurtenances of stains and fixatives ; whilst original thought in
both spheres represents very similar activities of an identical faculty.
This accords with the view that the intelligence, properly speaking,
is little influenced by the effects of training. What is profoundly
susceptible of training is the imagination, and mathematicians and
biologists seem to differ enormously in the manner in which their
imaginations are employed. Most biologists will probably feel that
this advantage is all on their side. They are introduced early to the
immense variety of living things ; their first dissections, even if only
of the frog or dog fish, open up vistas of amazing complexity and
interest, at the time when the mathematician seems to be dealing
only with the barest abstractions, with lines and points, infinitely
thin laminae, and masses concentrated at ideal centres of gravity.
Perhaps I can best make clear that the mathematician's imagination
also has been trained to some advantage, by quoting a remark
dropped casually by Eddington in a recent book —

' We need scarcely add that the contemplation in natural science of a

wider domain than the actual leads to a far better understanding of the

actual.' (p. 267, The, Nature of the Physical World.)

PREFACE ix

For a mathematician the statement is almost a truism. From a
biologist, speaking of his own subject, it would suggest an extra-
ordinarily wide outlook. No practical biologist interested in
sexual reproduction would be led to work out the detailed con-
sequences experienced by organisms having three or more sexes;
yet what else should he do if he wishes to understand why the sexes
are, in fact, always two ? The ordinary mathematical procedure in
dealing with any actual problem is, after abstracting what are
believed to be the essential elements of the problem, to consider it
as one of a system of possibilities infinitely wider than the actual,
the essential relations of which may be apprehended by generalized
reasoning, and subsumed in general formulae, which may be applied
at will to any particular case considered. Even the word possibilities
in this statement unduly limits the scope of the practical procedures
in which he is trained ; for he is early made familiar with the advan-
tages of imaginary solutions, and can most readily think of a wave, or
an alternating current, in terms of the square root of minus one.
The most serious difficulty to intellectual co-operation would seem
to be removed if it were clearly and universally recognized that the
•' essential difference lies, not in intellectual methods, and still less
in intellectual ability, but in an enormous and specialized extension
of the imaginative faculty, which each has experienced in relation
to the needs of his special subject. I can imagine no more beneficial
change in scientific education than that which would allow each to
appreciate something of the imaginative grandeur of the realms of
thought explored by the other.

In the future, the revolutionary effect of Mendelism will be seen
tg. flow from the particulate character of the hereditary elements.
• On this fact a rational theory of Natural Selection can be based, and
it is, therefore, of enormous importance. : The merit for this discovery
must mainly rest with Mendel, whilst among our countrymen, Bateson
played the leading part in its early advocacy. Unfortunately he was
unprepared to recognize the mathematical or statistical aspects of
biology, and from this and other causes he was not only incapable
of framing an evolutionary theory himself, but entirely failed to see
how Mendelism supplied the missing parts of the structure first
erected by Darwin. His interpretation of Mendelian facts was from
the first too exclusively coloured by his earlier belief in the dis-
continuous origin of specific forms. Though his influence upon

x PREFACE

evolutionary theory was thus chiefly retrogressive, the mighty body
of Mendelian researches throughout the world has evidently out-
grown the fallacies with which it was at first fostered. As a pioneer of
genetics he has done more than enough to expiate the rash polemics
of his early writings.

To treat Natural Selection as an agency based independently on
its own foundations is not to mimimize its importance in the theory
of evolution. On the contrary, as soon as we require to form opinions
by other means than by comparison and analogy, such an indepen-
dent deductive basis becomes a necessity. This necessity is particu-
larly to be noted for mankind ; since we have some knowledge of the
structure of society, of human motives, and of the vital statistics of
this species, the use of the deductive method can supply a more
intimate knowledge of the evolutionary processes than is elsewhere
possible. In addition it will be of importance for our subject to call )
attention to several consequences of the principle of Natural Selection!
which, since they do not consist in the adaptive modification of specific I
forms, have necessarily escaped attention. The genetic phenomena of I
dominance and linkage seem to offer examples of this class, the future '
investigation of which may add greatly to the scope of our subject.

No efforts of mine could avail to make the book easy reading.
I have endeavoured to assist the reader by giving short summaries
at the ends of all chapters, except Chapter IV, which is summarized
conjointly with Chapter V. Those who prefer to do so may regard
Chapter IV as a mathematical appendix to the corresponding part
of the summary. The deductions respecting Man are strictly in-
separable from the more general chapters, but have been placed
together in a group commencing with Chapter VIII. I believe no
one will be surprised that a large number of the points considered
demand a far fuller, more rigorous, and more comprehensive treat-
ment. It seems impossible that full justice should be done to the
subject in this way, until there is built up a tradition of mathematical
work devoted to biological problems, comparable to the researches
upon which a mathematical physicist can draw in the resolution of
special difficulties.

R. A. F.
BOTHAMSTED, June 1929.

CONTENTS

List of Illustrations . . . . . . xiii

I. The Nature of Inheritance - . . . • , 1
The consequences of the handing thnnry. as drawn by Darwin.
Difficulties felt by Darwin. Particulate inheritannft. Conservation of
the variance. Theories of evolution worked by mutations. Is all
inheritance participate ? Nature and frequency of observed mutations.

II. The Fundamental Theorem of Natural Selection . . 22
The life table and the table of reproduction. The Malthusian para-
meter of population increase. Reproductive value. The genetic
element in variance. Natural Selection. The nature of adaptation.
Deterioration of the environment. Changes in population. Summary.

III. The Evolution of Dominance ..... 48
The dominance of wild genes. Modification of the effects of Mendelian
factors. Modifications of the heterozygote. Special applications of

the theory. The process of modification. Inferences from the theory
of the evolution of dominance. Summary.

IV. Variation as determined by Mutation and Selection . 70
The measurement of gene frequency. The chance of survival of an
individual gene; relation to Poisson series. Low mutation rates of
beneficial mutations. Single origins not improbable. Distribution of

gene ratios in factors contributing to the variance. Slight effects
of random survival. The number of the factors contributing to the
variance.

V. Variation &c. (continued) . . . .97

The observed connexion between variability and abundance. Stable
gene ratios. Equilibrium involving two factors. Simple metrical
characters. Meristic characters. Biometrical effects of recent
selection. Summary.

VI. Sexual Reproduction and Sexual Selection . .121

The contrast between sexual and asexual reproduction. The nature
of species. Fission of species. Sexual preference. Sexual selection.
Sex limitation of modifications. Natural Selection and the sex ratio.
Summary.

VII. Mimicry 146

The relation of mimicry theory to the parent theory of Natural
Selection. Theories of Bates and Muller. Supposed statistical limita-
tion of Miillerian theory. Observational basis of mimicry theory.
The evolution of distastefulness. The theory of saltations. Stability
of the gene-ratio. Summary.

xu CONTENTS

VTII. Man and Society 170

On Man, prominence of preliminary studies. The decay of civiliza-
tions. Sociological views. Insect communities. Summary.

IX. The Inheritance of Human Fertility . . . .188
The great variability of human reproduction. The mental and moral
qualities determining reproduction. Direct evidence of the inheritance
of fertility. The evolution of the conscience respecting voluntary re-
production. Analogies of animal instinct and immunity to disease.
Summary.

X. Reproduction in relation to Social Class . . .210
Economic and biological aspects of class distinctions. Defects of
current data. Early investigations. British data. Position in the
U.S.A. Effects of differential fertility. Summary.

XI. Social Selection of Fertility 228

History of the theory. Infertility in all classes, irrespective of its
cause, gains social promotion. Selection the predominant cause of the
inverted birth-rate. The decay of ruling classes. Contrast with
barbarian societies. Heroism and the higher human faculties. The
place of social class in human evolution. Analogy of parasitism
~~^" among ants. Summary.

XII. Conditions of Permanent Civilization . . . 256

Apology. A permanent civilization not necessarily unprogressive.
Redistribution of births. Social promotion of fertility. Inadequacy of
French system. Problem of existing populations. Summary.

Works Cited . 266

Index 269

DESCRIPTION OF COLOURED PLATES
PLATE I

Frontispiece
All the figures are of the natural size.

FIG. 1. Abispa (Monerebia) ephippium, Fab., a common member of the
predominant group of Australian wasps, characterized by a dark
brownish-orange ground-colour and the great size and reduced number
of the black markings. They are mimicked by many other insects of
different groups including bees, flies, moths, and numerous beetles. That
the resemblance may be produced by quite different methods is illus-
trated in Figs. 2 and 3.

FIG. 2. Tragocerus formosus, Pascoe, a Longicorn beetle. Almost the
whole of the mimetic pattern is developed on the elytra or wing-covers
which hide the unwasplike abdomen, shown from above in Fig. 2A.
Free movement of the wings is permitted by an arched excavation in the
side of each wing-cover.

FIG. 3. Esthesis ferrugineus, Macleay. Another Longicorn beetle in which
the mimetic pattern is developed on the abdomen itself ; the wing-covers
are reduced to small rounded scales, thus freeing the wings, but at the
same time exposing the abdomen.

FIG. 4. Heliconius erato erato, Linn., a distasteful tropical American butter-
fly with a conspicuous pattern beautifully mimicked by the day-flying
Hypsid moth represented below.

FIG. 5. Pericopis phyleis, Druce. This moth and its butterfly model were
taken in Peru. The striking mimetic resemblance does not extend to the
antennae, which are threadlike and inconspicuous in the model.

FIG. 6. Methona confusa, Butler, another tropical American butterfly
captured with one of its moth mimics (Fig. 7) in Paraguay. In this
butterfly and its allies, the antennae are rendered conspicuous by
terminal orange knobs, resembled by many of the mimics in different
groups of butterflies and moths.

FIG. 7. Castnialinus, Cramer. The antennal knobs of this day- flying moth,
in spite of the marked resemblance, possess a form quite different from
those of the model, but one characteristic of the Castniidae. This
example of mimetic likeness to a normally inconspicuous feature, here
exceptionally emphasized, may be compared with Figs. 1, lA-3, 3A on
Plate II.

This model and mimic also illustrate, as do Figs. 1-3, the different
methods by which the resemblance may be obtained. The pale trans-
parent areas of the model are produced by the great reduction in the
size of the scales ; in the mimic, without reduction, by their transparency

v DESCRIPTION OF COLOURED PLATES

and by their being set at a different angle so that the light passes between
them. The important mimetic association illustrated by Figs. 6 and 7
includes numerous other species belonging to several distantly related
groups of butterflies and moths, and among these transparency is
attained by various different methods.

PLATE II

Facing p. 156

FIGS. 1-3. The head of the abundant East African Acraeine butterfly
^Acraea zetes acara, Hew., as seen from the front (I), "from above (2) ancr
the side~(3), showing that the palpi, which are inconspicuous in most
butterflies, are a prominent feature with their orange colour displayed
against the black background.

.

FIGS. 1A-3A. Similar aspects of the head of the Nymphaline butterfly
Pseudacraea boisduvali trimenii, Butler, a mimic of A. z. acara and found
in the same part of Africa. It is evident that the resemblance here ex-
tends to the exceptionally emphasized feature, as was observed in the

_ American examples shown in Figs. 6 and 7 of Plate I.

FIG. 4. Danaida tytia, Gray, a conspicuous Oriental Danaine butterfly
taken with its mimic (Fig. 5) in the Darjiling district.

FIG. 5. Papilio agestor, Gray, a swallowtail butterfly mimicking the pattern
of tytia.

FIG. 6. Neptis imitans, Oberth., a Nymphaline butterfly from S. W. China,
mimicking the geographical form of D. tytia which is found in the same
area.

Thus these two butterflies of widely separated groups both mimic this
peculiar Danaine pattern.

The butterflies and moths here represented illustrate by single examples
the widespread mimicry of the chief distasteful families in the tropics — on
Plate I the Ithomiinae (Fig. 6) and Heliconinae (Fig. 4) of the New World ;
on Plate IT, the Danainae (Fig. 5), and Acraeinae (Figs. 1-3) of the Old.

I

THE NATURE OF INHERITANCE

The consequences of the blending theory, as drawn by Darwin. Difficulties felt by
Darwin. Particulate inheritance. Conservation of the variance. Theories of evolution
worked by mutations. Is all inheritance particulate ? Nature and frequency of observed
mutations.

But at present, after drawing up a rough copy on this subject, my conclusion
is that external conditions do extremely little, except in causing mere variability.
This mere variability (causing the child not closely to resemble its parent)
I look at as very different from the formation of a marked variety or new
species. DARWIN, 1856. (Life and Letters, ii, 87.)

As Samuel Butler so truly said : 'To me it seems that the "Origin of
Variation ", whatever it is, is the only true " Origin of Species ".' w. BATESON,
1909.

The consequences of the blending theory

THAT Charles Darwin accepted the fusion or blending theory of
inheritance, just as all men accept many of the undisputed beliefs
of their time, is universally admitted. That his acceptance of this
theory had an important influence on his views respecting variation,
and consequently on the views developed by himself and others on ,
the possible causes of organic evolution, was not, I think, apparent
to himself, nor is it sufficiently appreciated hi our own times. In the
course of the present chapter I hope to make clear the logical con-
sequences of the blending theory, and to show their influence, not
only on the development of Darwin's views, but on the change of
attitude towards these, and other suppositions, necessitated by the
acceptance of the opposite theory of particulate inheritance.

It is of interest that the need for an alternative to blending in-
heritance was certainly felt by Darwin, thqughprobably he never
worked out a distinct idea of a fpartjculate theoryj In_a letterjio
Huxley probably dated hi 1857 pec"** +V ^^^nr^a (More Letters,
vol. i, Letter 57).

Approaching the subject from the side which attracts me most, viz.,
inheritance, I have lately been inclined to speculate, very crudely and
indistinctly, that propagation by true fertilization will turn out to be
a sort of mixture, and not true fusion, of two distinct individuals, or
rather of innumerable individuals, as each parent has its parents and

3653 B

\

/2 THE NATURE OF INHERITANCE

ancestors. I can understand on no other view the way in which crossed
forms go back to so large an extent to ancestral forms. But all this, of
cojirse, is infinitely crude.

The idea apparently was never developed, perhaps owing to the
rush of work which preceded and followed the publication of the
Origin. Certainly he did not perceive that the arguments on varia-
tion in his rough essays of 1842 and 1844, which a year later (1858)
he would be rewriting in the form of the first chapter of the Origin,
would on a participate theory have required him entirely to recast
them. The same views indeed are but little changed when The causes
of variability' came to be discussed in Chapter XXII of Variation of
Animals and Plants published in 1868.

The argument which can be reconstructed from these four sources
may be summarized as follows :

/-f#)-with blending inheritance bisexual reproduction will tend

rapidly to produce uniformity ; ^ V +

(6) if variability persists, causes of new variation must be con-
tinually at work ;

(c) the causes of the great variability of domesticated species, of
all kinds and in all countries, must be sought for in the condi-
tions of domestication ; »^~ «>*•

(d) the only characteristics of domestication sufficiently general
to cover all cases are changed conditions and increase of food ;

(e) some changes of conditions seem to produce definite and
regular effects, e. g. increased food causes (hereditary) increase
in size, but the important effect is an indefinite variability in
all directions, ascribable to a disturbance, by change of condi-
tions, of the regularity of action of the reproductive system ;

(/) wild species also will occasionally, by geological changes, suffer
changed conditions, and occasionally also a temporary increase
in the supply of food; they will therefore, though perhaps
rarely, be caused to vary. If on these occasions no selection is
exerted the variations will neutralize one another by bisexual
reproduction and die away, but if selection is acting, the
variations in the right direction will be accumulated and a per-
*v_manent evolutionary change effected.

To modern readers this will seem a very strange argument with
which to introduce the case for Natural Selection ; all that is gained

THE NATURE OF INHERITANCE 3

by it is the inference that wild as well as domesticated species will at
least occasionally present heritable variability. Yet it is used to
introduce the subject in the two essays and in the Origin. It should
be remembered that, at the time of the essays, Darwin had little
direct evidence on^this point : even in the Origin the second chapter
oif 'Variation under Nature' deals chiefly with natural varieties
sufficiently distinct to be listed by botanists, and these were certainly
regarded by Darwin not as the materials but as the products of
evolution. During the twenty-six years between 1842 and 1868 evi-
dence must have flowed in sufficiently at leastjbo convince him_that
heritable variability was as widespread, though not nearlyas extensive,
inwilcTas injlpmesticated species. Theline of reasoning ui question
seems to have lost its importance sufficiently for him to introduce the
subject in 1868 (Variation, Chapter XXII) with the words 'The sub-
ject is an obscure one ; but it maybe useful to probe our ignorance.'

It is the great charm of the essays that they show the reasons
which led Darwin to his conclusions, whereas the later works often
only give the evidence upon which the reader is to judge of their
truth. The antithesis is not so heterodox as it sounds, for every
active mind will form opinions without direct evidence, else the
evidence too often would never be collected. Impartiality and
scientific discipline come in in submitting the opinions formed to as
much relevant evidence as can be made available. The earlier steps
in the argument set out above appear only in the two essays, while
the conclusions continue almost unchanged up to the Variation of
Animals and Plants. Indeed the first step (a), logically the most
important of all, appears explicitly only in 1842. In 1844 it is clearly
implied by its necessary consequences. I believe its significance for
the argument of the Origin, would scarcely ever be detected from
a study only of that book. The passage in the 1842 MS. is (Founda-
tions, p. 2):

Each parent transmits its peculiarities, therefore if varieties allowed
freely to cross, except by the chance of two characterized by same
peculiarity happening to marry, such varieties will be constantly de-
molished. All bisexual animals must cross, hermaphrodite plants do
cross, it seems very possible that hermaphrodite animals do cross-
conclusion strengthened :

together with a partly illegible passage of uncertain position,

If individuals of two widely different varieties be allowed to cross,

4 THE NATURE OF INHERITANCE

a third race will be formed — a most fertile source of the variation in
domesticated animals. If freely allowed, the characters of pure parents
will be lost, number of races thus [illegible] but differences [ ?] besides
the [illegible]. But if varieties differing in very slight respects be allowed
to cross, such small variation will be destroyed, at least to our senses —
a variation just to be distinguished by long legs will have offspring not
to be so distinguished. Free crossing great agent in producing uni-
formity in any breed.

The proposition is an important one, marking as it does the great
contrast between the blending and the particulate theories of in-
heritance. The following proof establishes it in biometrical terms.

Let x and y represent the deviations in any measurement of the
two parents from the specific mean ; if the measurement is affected
not only by inheritance, but by non-heritable (environmental)
factors also, x and y stand for the heritable part of these deviations.
The amount of variability present in any generation of individuals
will be measured by the variance, defined as the mean value of the
square of x, or of y. In purely blending inheritance the heritable
portions of the deviations of the offspring will be, apart from muta-
tions, equal to %(x + y) ; in the absence of such mutations, therefore,
the variance of the progeny generation will be the mean value of

The mean values of x and y are both zero, since they are both
defined as deviations from the mean of the species ; consequently, in
the absence of selective mating, the mean value of xy is also zero, and
the variance of the progeny generation is found to be exactly half the
variance of the parental generation. More generally the ratio is not £
but \(\ +r), where r is the correlation between x and y. r cannot
exceed unity, else the average value of the positive quantities (x-y}-
would have to be negative, and can only be unity, if they are all zero,
that is, if the size of each individual prescribes exactly the size of its
possible mates. Darwin's 'except by the chance of two individuals
characterized by same peculiarities happening to marry' is his way
of rejecting high correlations as improbable.

The effect of correlation between mates is to hasten, if the correla-
tion is negative, or to retard if positive, the tendency of blending
inheritance to reduce the variance ; such effects are not of importance,
for even if the correlation were as high as 0-5, and mates had to be
as much alike as parent and child usually are, the rate of decay would

THE NATURE OF INHERITANCE 6

be little more than halved. The important consequence of the blend-
ing is that, if not safeguarded by intense marital correlation, the
heritable variance is approximately halved in every generation. To
maintain a stationary variance fresh mutations must be available in
each generation to supply the half of the variance so lost. If vari-
ability persists, as Darwin rightly inferred, causes of new variability
must continually be at work. Almost every individual of each genera-
tion must be a mutant, i. e. must be influenced by such causes, and
moreover must be a mutant in many different characters.

An inevitable inference of the blending theory is that the bulk of
the heritable variance present at any moment is of extremely recent
origin. One hah* is new in each generation, and of the remainder one
half is only one generation older, and so on. Less than one-thousandth
of the variance can be ten generations old; even if by reason of
selective mating we ought to say twenty generations, the general
conclusion is the same ; the variability of domesticated species must
be ascribed by any adherent of the blending theory to the conditions
of domestication as they now exist. If variation is to be used by the
human breeder, or by natural selection, it must be snapped up at
once, soon after the mutation has appeared, and before it has had
time to die away. The following passage from the 1844 essay shows
that Darwin was perfectly clear on this point (pp. 84-6).

Let us then suppose that an organism by some chance (which might
be hardly repeated in 1,000 years) arrives at a modern volcanic island
in process of formation and not fully stocked with the most appropriate
organisms ; the new organism might readily gain a footing, although the
external conditions were considerably different from its native ones.
The effect of this we might expect would influence in some small degree
the size, colour, nature of covering, &c., and from inexplicable influences
even special parts and organs of the body. But we might further (and
this is far more important) expect that the reproductive system would
be affected, as under domesticity, and the structure of the offspring
rendered in some degree plastic. Hence almost every part of the body
would tend to vary from the typical form in slight degrees, and in no
determinate way, and therefore without selection the free crossing of
these small variations (together with the tendency to reversion to the
original form) would constantly be counteracting this unsettling effect
of the extraneous conditions on the reproductive system. Such, I con-
ceive, would be the unimportant result without selection. And here
I must observe that the foregoing remarks are equally applicable to

6 THE NATURE. OF INHERITANCE

that small and admitted amount of variation which has been observed
in some organisms in a state of nature ; as well as to the above hypo-
thetical variation consequent on changes of condition.

Let us now suppose a Being with penetration sufficient to perceive
differences in the outer and innermost organization quite imperceptible
to man, and with forethought extending over future centuries to watch
with unerring care and select for any object the offspring of an organism
produced under the foregoing circumstances ; I can see no conceivable
reason why he could not form a new race (or several were he to separate
the stock of the original organism and work on several islands) adapted
to new ends. As we assume his discrimination, and his forethought, and
his steadiness of object, to be incomparably greater than those qualities
in man, so we may suppose the beauty and complications of the adapta-
tions of the new races and their differences from the original stock to be
greater than in the domestic races produced by man's agency: the
ground-work of his labours we may aid by supposing that the external
conditions of the volcanic island, from its continued emergence, and the
occasional introduction of new immigrants, vary ; and thus to act on the
reproductive system of the organism, on which he is at work, and so keep
its organization somewhat plastic. With time enough, such a Being
might rationally (without some unknown law opposed him) aim at
almost any result.

Difficulties felt by Darwin

The argument based on blending inheritance and its logical con-
sequences, though it certainly represents the general trend of
Darwin's thought upon inheritance and variation, for some years
after he commenced pondering on the theory of Natural Selection,
did not satisfy him completely. Reversion he recognized as a fact
which stood outside his scheme of inheritance, and that he was not
altogether satisfied to regard it as an independent principle is shown
by his letter to Huxley already quoted. By 1857 he was in fact on
the verge of devising a scheme of inheritance which should include
reversion as one of its consequences. The variability of domesticated
races, too, presented a difficulty which, characteristically, did not
escape him. He notes (pp. 77, 78, Foundations) in 1844 that the most
anciently domesticated animals and plants are not less variable, but,
if anything more so, than those more recently domesticated; and
argues that since the supply of food could not have been becoming
much more abundant progressively at all stages of a long history of

THE NATURE OF INHERITANCE 7

domestication, this factor cannot alone account for the great varia-
bility which still persists. The passage runs as follows:

If it be an excess of food, compared with that which the being obtained
in its natural state, the effects continue for an improbably long time ;
during how many ages has wheat been cultivated, and cattle and sheep
reclaimed, and we cannot suppose their amount of food has gone on
increasing, nevertheless these are amongst the most variable of our
domestic productions.

This difficulty offers itself also to the second supposed cause of
variability, namely changed conditions, though here it may be
argued that the conditions of cultivation or nurture of domesticated
species have always been changing more or less rapidly. From a
passage in the Variation of Animals and Plants (p. 301), which runs:

Moreover, it does not appear that a change of climate, whether more
or less genial, is one of the most potent causes of variability; for in
regard to plants Alph. De Candolle, in his Geographic Botanique, re-
peatedly shows that the native country of a plant, where in most cases
it has been longest cultivated, is that where it has yielded the greatest
number of varieties.

it appears that Darwin satisfied himself that the countries in which
animals or plants were first domesticated, were at least as prolific
of new varieties as the countries into which they had been imported,
and it is natural to presume that his inquiries under this head were
in search of evidence bearing upon the effects of changed conditions.
It is not clear that this difficulty was ever completely resolved in
Darwin's mind, but it is clear from many passages that he saw the
necessity of supplementing the original argument by postulating
that the causes of variation which act upon the reproductive system
must be capable of acting in a delayed and cumulative manner so
that variation might still be continued for many subsequent genera-
tions.

Particulate inheritance

It is a remarkable fact that had any thinker in the middle of the
nineteenth century undertaken, as a piece of abstract and theoretical
analysis, the task of constructing a particulate theory of inheritance,
he would have been led, on the basis of a few very simple assump-
tions, to produce a system identical with the modern scheme of
Mendelian or factorial inheritance. The admitted non-inheritance of

8 THE NATURE OF INHERITANCE

scars and mutilations would have prepared him to conceive of the
hereditary nature of an organism as something none the less definite
because possibly represented inexactly by its visible appearance.
Had he assumed that this hereditary nature was completely deter-
mined by the aggregate of the hereditary particles (genes), which
enter into its composition, and at the same time assumed that
organisms of certain possible types of hereditary composition were
capable of breeding true, he would certainly have inferred that each
organism must receive a definite portion of its genes from each parent,
and that consequently it must transmit only a corresponding portion
to each of its offspring.! The simplification that, apart from sex and
possibly other characters related in their inheritance to sex, the
contributions of the two parents were equal, would not have been
confidently assumed without the evidence of reciprocal crosses ; but
our imaginary theorist, having won so far, would scarcely have
failed to imagine a conceptual framework in which each gene had its
proper place or locus, which could be occupied alternatively, had the
parentage been different, by a gene of a different kind. Those
organisms (homozygotes) which received like genes, in any pah* of
corresponding loci, from their two parents, would necessarily hand on
genes of this kind to all of then* offspring alike ; whereas those (hetero-
zygotes) which received from their two parents genes of different
kinds, and would be, in respect of the locus in question, crossbred,
would have, in respect of any particular offspring, an equal chance of
\JTnnFiTnitting either kind. jSChe heterozygote when mated to either
kind of homozygote would produce both heterozygotes and homo-
zygotes in a ratio which, with increasing numbers of offspring, must
tend to equality, while if two heterozygotes were mated, each
homozygous form would be expected to appear in a quarter of the
offspring, the remaining half being heterozygous. It thus appears
that, apart from dominance and linkage, including sex linkage, all
the maui characteristics of the Mendelian system flow from assump-
tions of participate inheritance of the simplest character, and could
have been deduced a priori had any one conceived it possible that
the laws of inheritance could really be simple and definite.

The segregation of single pairs of genes, that is of single factors,
was demonstrated by Mendel in his paper of 1865. In addition Mendel
demonstrated hi his material the fact of dominance, namely that the
heterozygote was not intermediate in appearance, but was almost or

THE NATURE OF INHERITANCE 9

quite indistinguishable from one of the homozygous forms. The fact
of dominance, though of the greatest theoretical interest, is not an
essential feature of the factorial system, and in several important
cases is lacking altogether. Mendel also demonstrated what a theorist
could scarcely have ventured to postulate, that the different factors
examined by him in combination, segregated in the simplest possible
manner, namely independently. It was not till after the rediscovery
of Mendel's laws at the end of the century that cases of linkage were
discovered, in which, for factors in the same linkage group, the pair
of genes received from the same parent are more often than not
handed on together to the same child. The conceptual framework
of loci must therefore be conceived as made of several parts, and
these are now identified, on evidence which appears to be singularly
complete, with the dark-staining bodies or chromosomes which are
to be seen in the nuclei of cells at certain stages of cell division.

The mechanism of particulate inheritance isevidently suitable for
reproducing the phenomenon of reversion, in which an individual
argfandparent or moTc icmotc aiiiiUHtoTrmsome respget

Jawhich it differs^from its parents.^ toT the anSestrali gene combina-
tion may by chance be reproduced. This takes its simplest form when
dominance occurs, for every union of two heterozygotes will then
produce among the offspring some recessives, differing in appearance
from their parents, but probably resembling some grandparent or
ancestor.

Conservation of the variance

It has not been so clearly recognized that particulate inheritance
differs from the blending theory in an even more important fact.
There is no inherent tendency for the variability to diminish. \In
a population breeding at random in which two alternative genes of
any factor, exist in the ratio p to q, the three genotypes will occur in
the ratio p2 : 2pq : q2, and thus ensure that their characteristics will
be represented in fixed proportions of the population, however they
may be combined with characteristics determined by other factors,
provided that the ratio p : q remains unchanged. This ratio will
indeed be liable to slight changes ; first by the chance survival and
reproduction of individuals of the different kinds ; and secondly by
selective survival, by reason of the fact that the genotypes are pro-
bably unequally fitted, at least to a slight extent, to their task of

3653 n

10 THE NATURE" OF INHERITANCE

survival and reproduction. The effect of chance survival is easily
susceptible of calculation, and it appears, as will be demonstrated
more fully (Chapter IV), that in a population of n individuals breed-
ing at random the variance will be halved by this cause acting alone
in 1-4 n generations. Since the number of individuals surviving to
reproduce in each generation must in most species exceed a million,
and in many is at least a million-fold greater, it will be seen that this
cause of the diminution of hereditary variance is exceedingly minute,
when compared to the rate of halving in one or two generations by
blending inheritance.

It will be seen in Chapter IV that selection is a much more impor-
tant agency in keeping the variability of species within limits. But
even relatively intense selection will change the ratio p : q of the
gene frequencies relatively slowly, and no reasonable assumptions
could be made by which the diminution of variance due to selection,
in the total absence of mutations, would be much more than a ten-
thousandth of that ascribable to blending inheritance. The immediate
consequence of this enormous contrast is that the mutation rate
needed to maintain a given amount of variability is, on the particulate
theory, many thousand times smaller than that which is required on
the blending theory. Theories, therefore, which ascribe to agencies
believed to be capable of producing mutations, as was 'use and
disuse' by Darwin, a power of governing the direction in which
evolution is taking place, appear in very different lights, according
as one theory of inheritance, or the other, is accepted. For any
evolutionary tendency which is supposed to act by favouring muta-
tions in one direction rather than another, and a number of such
mechanisms have from time to time been imagined, will lose its force
many thousand-fold, when the particulate theory of inheritance, in
any form, is accepted; whereas the directing power of Natural
Selection, depending as it does on the amount of heritable variance
maintained, is totally uninfluenced by any such change. This con-
sideration, which applies to all such theories alike, is independent of
the fact that a great part of the reason, at least to Darwin, for
ascribing to the environment any considerable influence in the pro-
duction of mutations, is swept away when we are no longer forced to
consider the great variability of domestic species as due to the
comparatively recent influence of their artificial environment.

The striking fact, of which Darwin was well aware, that whole

THE NATURE OF INHERIATNCE 11

brothers and sisters, whose parentage, and consequently whose
entire ancestry is identical, may differ greatly in their hereditary
composition, bears under the two theories two very different inter-
pretations. Under the blending theory it is clear evidence of new
and frequent mutations, governed, as the greater resemblance of
twins suggests, by temporary conditions acting during conception
and gestation. On the particulate theory it is a necessary consequence
of the fact that for every factor a considerable fraction, not often
much less than one half, of the population will be heterozygotes, any
two offspring of which will be equally likely to receive unlike as like
genes from their parents. In view of the close analogy between the
statistical concept of variance and the physical concept of energy,
we may usefully think of the heterozygote as possessing variance in
a potential or latent form, so that instead of being lost when the
homozygous genotypes are mated it is merely stored in a form from
which it will later reappear. A population mated at random immedi-
ately establishes the condition of statistical equilibrium between tfo
latent and the apparent form of variance. The particulate theory of
inheritance resembles the kinetic theory of gases with its perfectly
elastic collisions, whereas the blending theory resembles a theory of
gases with inelastic collisions, and in which some outside agency is
required to be continually at work to keep the particles astir.

The property of the particulate theory of conserving the variance
for an indefinite period explains at once the delayed or cumulative
effect of domestication in increasing the variance of domesticated
species, to which Darwin calls attention. Many of our domesticated
varieties are evidently ill-fitted to survive in the wild condition. The
mutations by which they arose may have been occurring for an
indefinite period prior to domestication without establishing them-
selves, or appreciably affecting the variance, of the wild species. In
domestication, however, not only is the rigour of Natural Selection
relaxed so that mutant types can survive, and each such survival add
something to the store of heritable variance, but novelties of form or
colour, even if semi-monstrous, do undoubtedly attract human
attention and interest, and are valued by man for their peculiarity.
The rapidity with which new variance is accumulated will thus be
enhanced. Without postulating any change in the mutation rates
due to domestication, we should necessarily infer from what is known
of the conditions of domestication that the variation of domesticated

12 THE NATURE OF INHERITANCE

species should be greater than that of similar wild species, and that
this contrast should be greatest with those species most anciently
domesticated. Thus one of the main difficulties felt by Darwin is
resolved by the particulate theory.

Theories of evolution worked by mutations

The theories of evolution which rely upon hypothetical agencies,
capable of modifying the tppqugncy. or direction in which mutations
are taking place, fall intofour classes. In stating these it will be
convenient to use the term 'mutation', to which many meanings have
at different times been assigned, to denote simply the initiation of any
heritable novelty.

(A) It may be supposed, as by Lamarck in the case of animals,
that the mental state, and especially the desires of the organism,
possess the power of producing mutations of such a kind, that these
desires may be more readily gratified in the descendants. This view
postulates (i) that there exists a mechanism by which mutations are
caused, and even designed, in accordance with the condition of the
nervous system, and (ii) that the desires of animals in general are
such that their realization will improve the aptitude of the species
for life in its natural surroundings, and also will maintain or improve
the aptitude of its parts to co-operate with one another, both in
maintaining the vital activity of the adult animal, and in ensuring
its normal embryological development. The desires of animals must,
in fact, be very wisely directed, as well as being effective in provoking
suitable mutations.

(B) A power of adaptation may be widely observed, both among
plants and animals, by which particular organs, such as muscles or
glands, respond by increased activity and increased size, when addi-
tional physiological calls are made upon them. It may be suggested,
as it was by Darwin, that such responses of increased functional
activity induce, or are accompanied by, mutations of a kind tending
to increase the size or activity of the organ in question in future
generations, even if no additional calls were made upon this organ's
activity. This view implies (i) that the power which parts of organisms
possess, of responding adaptively to increased demands upon them,
is not itself a product of evolution, but must be postulated as a
primordial property of living matter : and requires (ii) that a mecha-

THE NATURE OF INHERITANCE 13

nism exists by which the adaptive response shall itself tend to cause,
or be accompanied by, an appropriate mutation.

Both these two suggested means of evolution expressly aim at
explaining, not merely the progressive change of organic beings, but
the aptitude of the organism to its place in nature, and of its parts to
their function in the organism.

(C) It may be supposed that the environment hi which the or-
ganism is placed controls the nature of the mutations which occur
in it, and so directs its evolutionary course ; much as the course of
a projectile is controlled by the field of force in which it flies.

(D) It may be supposed that the mutations which an organism
undergoes are due to an 'inner urge' (not necessarily connected with
its mental state) implanted in its primordial ancestors, which thereby
directs its predestined evolution.

The two last suggestions give no particular assistance towards the
understanding of adaptation, but each contains at least this element
of truth; that however profound our ignorance of the causes of
mutation may be, we cannot but ascribe them, within the order of
Nature as we know it, either to the nature of the organism, or to
that of its surrounding environment, or, more generally, to the niter-
action of the two. What is common, however, to all four of these
suppositions, is that each one postulates that the direction of evo-
lutionary change is governed by the predominant direction in which
mutations are taking place. However reasonable such an assumption
might have seemed when, under the blending theory of inheritance,
every individual was regarded as a mutant, and probably a multiple
mutant, it is impossible to let it pass unquestioned, in face of the
much lower mutation rates appropriate to the particulate theory.

A further hypothetical mechanism, guiding the evolution of the
species according to the direction in which mutations are occur-
ring, was suggested by Weismann. Weismann appreciated much more
thoroughly than many of his contemporaries the efficacy of Natural
Selection, in promoting the adaptation of organisms to the needs of
their lives in their actual habitats. He felt, however, that this action
would be aided in a subordinate degree if the process of mutation
could acquire a kind of momentum, so that a series of mutations
affecting the increase or decrease of a part should continue to occur,
as a consequence of an initial chance tendency towards such increase
or decrease. Such an assumed momentum in the process of mutation

14 THE NATURE OF INHERITANCE

he found useful in two respects : (i) it would enable an assumed minimal
mutation in an advantageous direction to be increased by further
mutations, until it ' attains selection value ' ; (ii) it explains the con-
tinuous decrease of a useless organ, without assuming that each step
of this decrease confers any advantage upon the organism mani-
festing it.

The concept of attaining selection value, which is fairly common
in biological literature, seems to cover two distinct cases. In the first
case we may imagine that, with increasing size, the utility of an
organ shows no increase up to a certain point, but that beyond this
point increasing size is associated with increasing utility. In such
a case, which, in view of the actual variability of every organism,
and of the parts of related organisms, must be regarded as somewhat
ideal, we are really only concerned with the question whether the
actual variability in different members of the species concerned, does
or does not reach as far as the critical point. If it does not do so the
species will not be able to take the advantage offered, simply because
it is not variable enough, and the postulate of an element of momen-
tum in the occurrence of mutations, was certainly not made in
order to allow organisms to be more variable than they would be
without it.

The second meaning, which is also common hi the literature,
depends upon a curious assumption as to the manner in which
selective advantage increases with change of size of the organ upon
which this advantage is dependent ; for it is sometimes assumed that,
while at all sizes an increase of size may be advantageous, this
advantage increases, not continuously, but in a step-like manner ; or
at least that increases below a certain limit produce an advantage
which may be called 'inappreciable', and therefore neglected. Both
the metaphor and the underlying idea appear to be drawn from
psychophysical experience. If we compare two physical sensations
such as those produced by the weights of two objects, then when the
weights are sufficiently nearly equal the subject will often be unable
to distinguish between them, and will judge them equal, whereas
with a greater disparity, a distinct or appreciable difference of weight
is discerned. If, however, the same test is applied to the subject
repeatedly with differences between the weights varying from what is
easily discernible to very much smaller quantities, it is found that
differences in the weights, which would be deemed totally inappreci-

THE NATURE OF INHERITANCE 15

able, yet make a significant and perfectly regular difference to the
frequency with which one is judged heavier than the other. The
discontinuity lies in our interpretation of the sensations, and not in
the sensations themselves. Now, survival value is measured by the

5250

h-

o

Ozoo

CO

,50

H-

o

100
C)

z

ui

§50

O

0

84

88 92 96

WEIGHT TESTED

100 104
IN GRAMS

108

FIG. 1. The frequency with which test objects of different weights are
judged heavier than a standard 100 gram weight. (Urban's data, for a
single subject.) Illustrating the fact that with a sufficient number of
trials, differences in weight, however 'inappreciable', will affect the
frequency of the judgement.

frequency with which certain events, such as death or reproduction,
occur, to different sorts of organisms exposed to the different chances
of the same environment, and, even if we should otherwise be in doubt,
the psychophysical experiments make it perfectly clear that the
selective advantage will increase or decrease continuously, even for
changes much smaller than those appreciable to our own senses, or
to those of the predator or other animal, which may enter into the
biological situation concerned. If a change of 1 mm. has selection
value, a change of 0-1 mm. will usually have a selection value
approximately one-tenth as great, and the change cannot be ignored
because we deem it inappreciable. The rate at which a mutation
increases in numbers at the expense of its allelomorph will indeed
depend on the selective advantage it confers, but the rate at which
a species responds to selection in favour of any increase or decrease
of parts depends on the total heritable variance available, and not

16 THE NATURE -OF INHERITANCE

on whether this is supplied by large or small mutations. There is no

limen of appreciable selection value to be considered.

The remaining advantage which Weismann sought hi postulating
his mechanism of germinal selection was to supply an explanation
of the progressive diminution of useless organs, even when these are
of so trifling a character that the selective advantage of then* sup-
pression is questionable. The subject is an interesting one, and
deserves for its own sake a more extended discussion than would be
suitable in the present book. For our present purpose it will be
sufficient to notice (i) that to assert in any particular case that the
progressive suppression of an organ brings with it no progressive
selective advantage appears to be very far beyond the range of our
actual knowledge. To take a strong case from Weismann — the
receptaculum seminis of an ant is assuredly minute ; but the ant her-
self is not very large, nor are we concerned only with the individual
ant, but with the whole worker population of the nest. As an economic
problem we certainly do not possess the data to decide whether the
suppression of this minute organ would or would not count as an
appreciable factor in the ant polity. Human parallels might be given
hi which the elimination of very minute items of individual waste,
can lend an appreciable support to social institutions which are
certainly not negligible. I do not assert that the suppression of the
receptaculum has been useful to the ant, but that in this as in other
cases, if we pause to give the matter due consideration, it is at once
apparent that we have not the knowledge on which to base any
decided answer, (ii) In the second place Weismann's view that in
the absence of all selection a useless organ might diminish, degenerate,
and finally disappear, by the cumulative action of successive muta-
tions, and especially his view that this is the only type of progressive
change, which could take place by mutations only, without the
guidance of Natural Selection, is fully in accordance with modern
knowledge of the nature of mutations. The special mechanism,
however, by which he sought to explain the successive occurrence of
degenerative mutations must be judged to be superfluous. It is
moreover exposed to the logical objection that the driving force of
his mechanism of germinal selection is an assumed competition for
nutriment between the chromatin elements which represent the
degenerating organ, and those which represent the rest of the body.
The degenerating organ itself is assumed to be so unimportant that

THE NATURE OF INHERITANCE 17

its demands upon the general nutrition of the body are to be neglected ;
and it may well be asked if it is legitimate to bring in, in respect of
the well-nourished germ cell, the factor of nutritional competition
which is to be ignored in the occasionally ill-nourished body.

Is all inheritance particulate ?

The logical case for rejecting the assumption that the direction of
evolutionary change is governed by the direction in which mutations
are taking place, and thereby rejecting the whole group of theories
in which this assumption is implicit, would be incomplete had not
modern researches supplied the answer to two further questions:^
(i) May it not be that in addition to the mechanism of particulate
inheritance, which has been discovered and is being investigated,
there is also, in living organisms, an undiscovered mechanism of
blending inheritance ? (ii) Do the known facts within the particulate
system render a mechanism, which could control the predominant
direction of mutation, inoperative as a means of governing the /
direction of evolutionary change ? **— '

On the first point it should be noted briefly that, whereas at the
beginning of the century there were several outstanding facts of
inheritance which seemed to demand some sort of blending theory,
these have all in the course of research been shown, not only to be
compatible with particulate inheritance, but to reveal positive
indications that such is their nature. The apparent blending in colour
in crosses between white races of man and negroes is compatible
with the view that these races differ in several Mendelian factors,
affecting the pigmentation. Of these some may have intermediate
heterozygotes, and of the remainder in some the darker, and in some
the lighter tint may be dominant. The Mendelian theory is alone
competent to explain the increased variability of the offspring of the
mulattoes.

The biometrical facts as to the inheritance of stature and other
human measurements, though at first regarded as incompatible with
the Mendelian system, have since been shown to be in complete
accordance with it, and to reveal features not easily explicable on any
other view. The approximately normal distribution of the measure-
ments themselves may be deduced from the simple supposition that
the factors affecting human stature are approximately additive in
their effects. The correlations found between relatives of different

3653

18 THE NATURE OF INHERITANCE

degrees of kinship are, within their sampling errors, of the magnitudes
which would be deduced from the assumption that the measurement
is principally determined by inheritance, and that the factors con-
trolling it show, like most Mendelian factors, complete or almost
complete dominance. The presence of dominance is a Mendelian
feature, which is shown in the biometrical data by the well-estab-
lished fact that children of the same parents are, on the average,
somewhat more alike than are parent and offspring.

So far we have merely established the negative fact that there are
no outstanding observations which require a blending system of
inheritance. There is, however, one group of modern researches
which, at least hi the organisms investigated, seems to exclude it,
even as a possibility. In certain organisms which are habitually self-
fertilized, as Johannsen was the first to show with a species of bean,
it is possible to establish so-called pure lines, within which heritable
variability is, apart from exceptional mutations, completely absent.
Within these lines the selection of the largest or the smallest beans,
even where this selection was continued for ten or twenty generations,
constantly produced offspring of the same average size. This size
differed from one line to another, showing that heritable variability
existed abundantly in the species, and among the thousands of beans
examined two distinct mutants were reported. If, however, any
appreciable fraction of the variance in bean size were ascribable to
elements which blend, the mutations necessary to maintain such
heritable variability would, in ten generations, have had time to
supply it almost to its maximum extent, and must inevitably have
been revealed by selection. Experiments of this type seem capable
of excluding the possibility that blending inheritance can account
for any appreciable fraction of the variance observed.

Nature and frequency of observed mutations

The assumption that the direction of evolutionary change is actually
governed by the direction in which mutations are occurring is not
easily compatible with the nature of the numerous mutations whiclj
have now been observed to occur. For the majority of these produce
strikingly disadvantageous deformities, and indeed much the largest
class are actually lethal. If we had to admit, as has been so often
assumed in theory, that these mutations point the direction of
evolution, the evolutionary prospects of the little fruit-fly Drosophila

THE NATURE OF INHERITANCE 19

would be deplorable indeed. Nor is the position apparently different
with man and his domesticated animals and plants ; as may be judged
from the frequency with which striking recessive defects, such as
albinism, deaf-mutism, and feebleness of mind in man, must have
occurred in the comparatively recent past, as mutations. Mutant
defects seem to attack the human eye as much as that of Drosophila,
and in general the mutants which occur in domesticated races are
often monstrous and predominantly defective, whereas we know in
many cases that the evolutionary changes which these creatures have
undergone under human selection have been in the direction of a
manifest improvement.

In addition to the defective mutations, which by their con-
spicuousness attract attention, we may reasonably suppose that
other less obvious mutations are occurring which, at least in certain
surroundings, or in certain genetic combinations, might prove them-
selves to be beneficial. It would be unreasonable, however, to assume
that such mutations appear individually with a frequency much
greater than that which is observed hi the manifest defects. The
frequency of individual mutations in Drosophila is certainly seldom
greater than one in 100,000 individuals, and we may take this figure
to illustrate the inefficacy of any agency, which merely controls the
predominant direction of mutation, to determine the predominant
direction of evolutionary change. For even if selective survival were
totally absent, a lapse of time of the order of 100,000 generations
would be required to produce an important change with respect to *-
the factor concerned, in the heritable nature of the species. Moreover,
if the mutant gene were opposed, even by a very minute selective
disadvantage, the change would be brought to a standstill at a very
early stage. The ideas necessary for a precise examination of the
nature of selective advantage will be developed in Chapter II ; but
it will be readily understood that if we speak of a selective advantage
of one per cent., with the meaning that animals bearing one gene
have an expectation of offspring only one per cent, greater than those
bearing its allelomorph, the selective advantage in question will be
a very minute one; at least in the sense that it would require an
enormous number of experimental animals, and extremely precise
methods of experimentation, to demonstrate so small an effect
experimentally. Such a selective advantage would, however, greatly
modify the genetic constitution of the species, not in 100,000 but in

20 THE NATURE OF INHERITANCE

100 generations. If, moreover, we imagine these two agencies opposed
in their tendencies, so that a mutation which persistently occurs in
one in 100,000 individuals, is persistently opposed by a selective
advantage of only one per cent., it will easily be seen that an
equilibrium will be arrived at when only about one individual in
1,000 of the population will be affected by the mutation. This
equilibrium, moreover, will be stable ; for if we imagine that by some
chance the number of mutants is raised to a higher proportion than
this, the proportion will immediately commence to diminish under
the action of selection, and evolution will proceed in the direction
contrary to the mutation which is occurring, until the proportion of
mutant individuals again reaches its equilibrium value. For muta-
tions to dominate the trend of evolution it is thus necessary to postu-
late mutation rates immensely greater than those which are known
to occur, and of an order of magnitude which, in general, would be
incompatible with particulate inheritance.

Summary

The tacit assumption of the blending theory of inheritance led
Darwin, by a perfectly cogent argument, into a series of speculations,
respecting the causes of variations, and the possible evolutionary
effects of these causes. In particular the blending theory, by the
enormous mutation rates which it requires, led Darwin and others
to attach evolutionary importance to hypothetical agencies which
control the production of mutations. A mechanism (Mendelism) of
particulate inheritance has since been discovered, requiring mutations
to an extent less by many thousandfold. The 'pure line ' experiments
seem to exclude blending inheritance even as a subordinate possibility.
The nature of the mutations observed is not compatible with the
view that evolution is directed by their means, while their observed
frequency of occurrence shows that an agency controlling mutations
would be totally ineffectual in governing the direction of evolutionary
change.

The whole group of theories which ascribe to hypothetical physio
I logical mechanisms, controlling the occurrence of mutations, a power
of directing the course of evolution, must be set aside, once the
blending theory of inheritance is abandoned. The sole surviving

theory is that of Natural Selection, and it would appear impossibl
to avoid the conclusion that if any evolutionary ph

V ---

e
enomenon

THE XATURE OF INHERITANCE 21

appears to be inexplicable on this theory, it must be accepted at
present merely as one of the facts which in the present state of
knowledge seems inexplicable. The investigator who faces this fact,
as an unavoidable inference from what is now known of the nature
of inheritance, will direct his inquiries confidently towards a study
of the selective agencies at work throughout the life history of the
group in their native habitats, rather than to speculations on the
possible causes which influence their mutations. The experimental
study of agencies capable of influencing mutation rates is of the
highest interest for the light which it may throw on the nature of
these changes. We should altogether misinterpret the value of such
researches were we to regard them as revealing the causes of evolu-
tionary modification.

The life table and the table of reproduction. The Malthusian parameter of popu-
lation increase. Reproductive value. The genetic element in variance. Natural Selection.
The nature of adaptation. Deterioration of the environment. Changes in population.
Summary.

One has, however, no business to feel so much surprise at one's ignorance,
when one knows how impossible it is without statistics to conjecture the
duration of life and percentage of deaths to births in mankind. DARWIN,
1845. (Life and Letters, ii, 33.)

In the first place it is said — and I take this point first, because the imputation
is too frequently admitted by Physiologists themselves — that Biology differs
from the Physico-chemical and Mathematical sciences in being 'inexact'.
HUXLEY, 1854.

The life table

IN order to obtain a distinct idea of the application of Natural
Selection to all stages in the life-history of an organism, use may be
made of the ideas developed in the actuarial study of human mor-
tality. These ideas are not in themselves very recondite, but being
associated with the laborious computations and the technical nota-
tion employed in the practical business of life insurance, are not so
familiar as they might be to the majority of biologists. The text-
books on the subject, moreover, are devoted to the chances of death,
and to monetary calculations dependent on these chances, whereas
in biological problems at least equal care and precision of ideas is
requisite with respect to reproduction, and especially to the combined
action of these two agencies in controlling the increase or decrease of
the population.

The object of the present chapter is to combine certain ideas
derivable from a consideration of the rates of death and reproduction
of a population of organisms, with the concepts of the factorial
^scheme of inheritance, so as to state the principle of Natural Selection
in the form of a rigorous mathematical theorem, by which the rate
of improvement of any species of organisms in relation to its environ-
ment is determined by its present condition.

The fundamental apparatus of the actuary's craft is what is known

FUNDAMENTAL THEOREM OF NATURAL SELECTION 23

as a life table. This shows, for each year of age, of the population
considered, the proportion of persons born alive who live to attain
that age. For example, a life table may show that the proportion of
persons living to the age of 20 is 88 per cent., while only 80 per cent.
reach the age of 40. It will be easily inferred that 12 per cent, of
those born alive die in the first 20 years of life, and 8 per cent, in the
second 20 years. The life table is thus equivalent to a statement of
the frequency distribution of the age of death in the population con-
cerned. The amount by which each entry is less than the preceding
entry represents the number of deaths between these limits of age,
and this divided by the number living at the earlier age gives the-.
probability of death within a specified time of those living at that age.
Since the. probability of death changes continuously throughout life,
the death rate at a given age can only be measured consistently by
taking the age interval to be infinitesimal. Consequently if lx is the
number living to age x, the death rate at age x is given by:

1 d d

the logarithm being taken, as in most mathematical representations,
to be on the Natural or Naperian system. The life table thus contains
a statement of the death rates at all ages, and conversely can be
constructed from a knowledge of the course taken by the death rate
throughout lif e. This in fact is the ordinary means of constructing the
life tables in practical use.

It will not be necessary to discuss the technical procedure employed
in the construction of life tables, the various conventions employed
in this form of statement, nor the difficulties which arise in the inter-
pretation of the observational data available in practice for this
purpose. It will be sufficient to state only one point. As in all other
experimental determinations of theoretical values, the accuracy
attainable in practice is limited by the extent of the observations;
the result derived from any finite number of observations will be
liable to an error of random sampling, but this fact does not, in any
degree, render such concepts as death rates or expectations of life
obscure or inexact. These are statements of probabilities, averages
&c., pertaining to the hypothetical population sampled, and depend
jonly upon its nature and circumstances. The inexactitude of our
methods of measurement has no more reason in statistics than it has

24 FUNDAMENTAL THEOREM OF NATURAL SELECTION
in physics to dim our conception of that which we measure. These
conceptions would be equally clear if we were stating the chances of
death of a single individual of unique genetic constitution, or of one
exposed to an altogether transient and exceptional environment.

The table of reproduction

The life table, although itself a very comprehensive statement, is
still inadequate to express fully the relation between an organism and
its environment ; it concerns itself only with the chances or frequency
of death, and not at all with reproduction. To repair this deficiency it
is necessary to introduce a second table giving rates of reproduction
in a manner analogous to the rates of death at each age. Just as a
person alive at the beginning of any infinitesimal age interval dx has
a chance of dying within that interval measured by Pxdx, so the
chance of reproducing within this interval will be represented by bydx,
in which 6^ may be called the rate of reproduction at age x. Again, just
as the chance of a person chosen at birth dying within a specified
interval of age dx is IxV-ydx, so the chance of such a person living to
reproduce in that interval will be lj)xdx.

Owing to bisexual reproduction a convention must be introduced
into the measurement of bx, for each living offspring will be credited
to both parents, and it will seem proper to credit each with one hah*
hi respect of each offspring produced. This convention will evidently
be appropriate for those genes which are not sex-linked (autosomal
genes) for with these the chance of entering into the composition of
each offspring is known to be one hah*. In the case of sex-linked genes
those of the heterogametic parent will be perpetuated or not accord-
ing as the offspring is male or female. These sexes, it is true, will not
be produced in exactly equal numbers, but since both must co-operate
in each act of sexual reproduction, it is clear that the different
frequencies at birth must ultimately be compensated by Sexual
differences hi the rates of death and reproduction, with the result that
the same convention appears hi this case to be equally appropriate.

A similar convention, appropriate in the sense of bringing tne
formal symbolism of the mathematics into harmony with the biologi-
cal facts, may be used with respect to the period of gestation. For it
will happen occasionally that a child is born after the death of its
father. The children born to fathers aged x should in fact be credited
to males aged three-quarters of a year younger. Such corrections are

FUNDAMENTAL THEOREM OF NATURAL SELECTION 25

not a necessity to an exact mathematical representation of the facts,
but are a manifest convenience in simplifying the form of expression ;
thus with mankind we naturally think of the stage in the life -history
as measured in years from birth. With other organisms the variable
x which with man represents this age, may in some cases be more
conveniently used to indicate rather the stage in the life history
irrespective of chronological age, merely to give greater vividness to
the meaning of the symbolism, but without altering the content of
the symbolical statements.

The M althusian parameter of population increase

If we combine the two tables giving the rates of death and repro-
duction, we may, still speaking in terms of human populations, at
once calculate the expectation of offspring of the newly-born child.
For the expectation of offspring in each element of age dx is lxbxdx,
and the sum of these elements over the whole of life will be the
total expectation of offspring. In mathematical terms this is

where the integral is extended from zero, at birth, to infinity, to cover
every possible age at which reproduction might conceivably take
place. If at any age reproduction ceases absolutely, bx will thereafter
be zero and so give automatically the effect of a terminating integral.

The expectation of offspring determines whether in the population
concerned the reproductive rates are more or less than sufficient to
balance the existing death rates. If its value is less than unity the
reproductive rates are insufficient to maintain a stationary popula-
tion, in the sense that any population which constantly maintained
the death and reproduction rates in question would, apart from
temporary fluctuations, certainly ultimately decline in numbers at a
calculable rate. Equally, if it is greater than unity, the population
biologically speaking is more than holding its own, although the
actual number of heads to be counted may be temporarily decreasing.

This consequence will appear most clearly in its quantitative aspect
if we note that corresponding to any system of rates of death and
reproduction, there is only one possible constitution of the population
in respect of age, which will remain unchanged under the action of
this system. For if the age distribution remains unchanged the

3653

E

26 FUNDAMENTAL THEOREM OF NATURAL SELECTION
relative rate of increase or decrease of numbers at all ages must be
the same ; let us represent the relative rate of increase by ra ; which
will also represent a decrease if m is negative. Then, owing to the
constant rates of reproduction, the rate at which births are occurring
at any epoch will increase proportionately to emt. At any particular
epoch, for which we may take t = Q, the rate at which births were
occurring x years ago will be proportional to e~mx, and this is the rate
at which births were occurring at the time persons now of age x were
being born. The number of persons in the infinitesimal age interval
dx will therefore be eTmxlyAx^ for of those born only the fraction lx
survive to this age. The age distribution is therefore determinate if
the number m is uniquely determined. But knowing the numbers
living at each age, and the reproductive rates at each age, the rate at
which births are now occurring can be calculated, and this can be
equated to the known rate of births appropriate to t = 0. In fact, the
contribution to the total rate, of persons in the age interval dx, must
be e~mxlxbxdx, and the aggregate for all ages must be

o

which, when equated to unity, supplies an equation for m, of which
one and only one real solution exists. Since e~mx is less than unity for
all values of a;, if m is positive, and is greater than unity for all values
of x, if m is negative, it is evident that the value of m, which reduces
the integral above expressed to unity, must be positive if the expecta-
tion of offspring exceeds unity, and must be negative if it falls short
of unity.

The number m which satisfies this equation is thus implicit in any
given system of rates of death and reproduction, and measures the
relative rate of increase or decrease of a population when in the steady
state appropriate to any such system. In view of the emphasis laid
by Malthus upon the ' law of geometric increase ' m may appropriately
be termed the Malthusian parameter of population increase. It
evidently supplies in its negative values an equally good measure of
population decrease, and so covers cases to which, in respect of man-
kind, Malthus paid too little attention.

In view of the close analogy between the growth of a population
supposed to follow the law of geometric increase, and the growth of
capital invested at compound interest, it is worth noting that if we

FUNDAMENTAL THEOREM OF NATURAL SELECTION 27
regard the birth of a child as the loaning to him of a life, and the birth
of his offspring as a subsequent repayment of the debt, the method by
which m is calculated shows that it is equivalent to answering the
question — At what rate of interest are the repayments the just
equivalent of the loan ? For the unit investment has an expectation
of a return IJbydx in the time interval dx, and the present value of this
repayment, if m is the rate of interest, is er^ljbyfix ; consequently the
Malthusian parameter of population increase is the rate of interest at
which the present value of the births of offspring to be expected is
equal to unity at the date of birth of their parent. The actual values
of the parameter of population increase, even in sparsely populated
dominions, do not, however, seem to approach in magnitude the rates
of interest earned by money, and negative rates of interest are, I
suppose, unknown to commerce.

Reproductive value

The analogy with money does, however, make clear the argument
for another simple application of the combined death and reproduction
rates. We may ask, not only about the newly born, but about persons
of any chosen age, what is the present value of their future offspring ;
and if present value is calculated at the rate determined as before, the
question has the definite meaning — To what extent will persons of
this age, on the average, contribute to the ancestry of future genera-
tions ? The question is one of some interest, since the direct action of
Natural Selection must be proportional to this contribution. There
will also, no doubt, be indirect effects in cases in which an animal
favours or impedes the survival or reproduction of its
suckling mother assists the survival of her child, as in mankktd~nr
mother past bearing may greatly promote the reproduction of her
children, as a foetus and in less measure a sucking child inhibits
conception, and most strikingly of aJJr-a^~nrthe-sefvices of neuter
insects to their queen. Neverthel^essuch indirect effects will hi very
many cases be unimportant compared to the effects of personal repro-
duction, and by the analogy of compound interest the present value
of the future offspring of persons aged x is easily seen to be

Each age group may in this way be assigned its appropriate

28 FUNDAMENTAL THEOREM OF NATURAL SELECTION
reproductive value. Fig. 2 shows the reproductive value of women
according to age as calculated from the rates of death and reproduc-
tion current in the Commonwealth of Australia about 1911. The
Malthusian parameter was at that time positive, and as judged from

20 30

AGE IN YEARS

Fio. 2. Reproductive value of Australian women.

The reproductive value for female persons calculated from the birth- and death-
rates current in the Commonwealth of Australia about 1911. The Malthusian
parameter is +0-01231 per annum.

female rates was nearly equivalent to 1 J per cent, compound interest ;
the rate would be lower for the men, and for both sexes taken together,
owing to the excess of men in immigration. The reproductive value,
which of course is not to be confused with the reproductive rate,
reaches its maximum at about 18|, in spite of the delay in repro-
duction caused by civilized marriage customs ; indeed it would have
been as early as 16, were it not that a positive rate of interest gives
higher value to the immediate prospect of progeny of an older woman,
compared to the more remote children of a young girl. If this is the

FUNDAMENTAL THEOREM OF NATURAL SELECTION 29

case among a people by no means precocious in reproduction, it would
be surprising if , in a state of society entailing marriage at or soon after
puberty, the age of maximum reproductive value should fall at any
later age than twelve. In the Australian data, the value at birth is
lower, partly by reason of the effect of an increasing population in
setting a lower value upon remote children and partly because of the
risk of death before the reproductive age is reached. The value shown
is probably correct, apart from changes in the rate since 1911, for
such a purpose as assessing how far it is worth while to give assistance
to immigrants in respect of infants (though of course, it takes no
account of the factor of eugenic quality), for such infants will usually
emigrate with their parents ; but it is overvalued from the point of
view of Natural Selection to a considerable extent, owing to the capa-
city of the parents to replace a baby lost during lactation. The
reproductive value of an older woman on the contrary is undervalued
in so far as her relations profit by her earnings or domestic assistance,
and this to a greater extent from the point of view of the Common-
wealth, than from that of Natural Selection. It is probably not without
significance in this connexion that the death rate in Man takes a
course generally inverse to the curve of reproductive value. The
minimum of the death rate curve is at twelve, certainly not far from
the primitive maximum of the reproductive value; it rises more
steeply for infants, and less steeply for the elderly than the curve of
reproductive value falls, points which qualitatively we should antici-
pate, if the incidence of natural death had been to a large extent
moulded by the effects of differential survival.

A property that well illustrates the significance of the method of
valuation, by which, instead of counting all individuals as of equal
value in respect of future population, persons of each age are assigned
an appropriate value vx, is that, whatever may be the age constitution
of a population, its total reproductive value will increase or decrease
according to the correct Malthusian rate m, whereas counting all
heads as equal this is only true in the theoretical case in which the
population is in its steady state. For suppose the number of persons
in the age interval dx is nxdx ; the value of each element of the popula-
tion will be nxvxdx ; in respect of each such group there will be a gain
in value by reproduction at the rate of nxbxv0dx, a loss by death of
nxij,xvxdx, and a loss by depreciation of -^ixdvX) or in all

30 FUNDAMENTAL THEOREM OF NATURAL SELECTION
but by differentiating the equation by which vx is defined, it appears
that

dv 1 ctt - Ze-"1* bv

— - — h - - -- m =

x0

vdx ldx
or that

dvx - HxVydx + bxv0dx =

Consequently the rate of increase in the total value of the population
is m times its actual total value, irrespective of its constitution in
respect of age. A comparison of the total values of the population at
two census epochs thus shows, after allowance for migration, the
genuine biological increase or decrease of the population, which may
be entirely obscured or reversed by the crude comparison of the
number of heads. The population of Great Britain, for example, must
have commenced to decrease biologically at some date obscured by
the war, between 1911 and 1921, but the census of 1921 showed a
nominal increase of some millions, and that of 1931 will, doubtless hi
less degree, certainly indicate a further spurious period of increase,
due to the accumulation of persons at ages at which their reproduc-
tive value is negligible.

The genetic element in variance

Let us now consider the manner in which any quantitative individual
measurement, such as human stature, may depend upon the indi-
vidual genetic constitution. We may imagine, in respect of any pan*
of alternative genes, the population divided into two portions, each
comprising one homozygous type together with hah* of the hetero-
zygotes, which must be divided equally between the two portions. The
difference in average stature between these two groups may then be
termed the average excess (hi stature) associated with the gene sub-
stitution in question. This difference need not be wholly due to the
single gene, by which the groups are distinguished, but possibly also
to other genes statistically associated with it, and having similar
or opposite effects. This definition will appear the more appropriate
if , as is necessary for precision, the population used to determine its
value comprises, not merely the whole of a species in any one genera-
tion attaining maturity, but is conceived to contain all the genetic
combinations possible, with frequencies appropriate to their actual

FUNDAMENTAL THEOREM OF NATURAL SELECTION 31
probabilities of occurrence and. survival, whatever these may be, and
if the average is based upon the statures attained by all these geno-
types in all possible environmental circumstances, with frequencies
appropriate to the actual probabilities of encountering these circum-
stances. The statistical concept of the excess in stature of a given
gene substitution will then be an exact one, not dependent upon
chance as must be any practical estimate of it, but only upon the
genetic nature and environmental circumstances of the species. The
excess in a factor will usually be influenced by the actual frequency
ratio p : q of the alternative genes, and may also be influenced, by
way of departures from random mating, by the varying reactions of
the factor in question with other factors ; it is for this reason that its
value for the purpose of our argument is defined in the precise
statistical manner chosen, rather than in terms of the average sizes
of pure genotypes, as would be appropriate in specifying such a value
in an experimental population, in which mating is under control, and
in which the numbers of the different genotypes examined is at the
choice of the experimenter.

For the same reasons it is also necessary to give a statistical
definition of a second quantity, which may be easily confused with
that just defined, and may often have a nearly equal value, yet which
must be distinguished from it in an accurate argument ; namely the
average effect produced in the population as genetically constituted,
by the substitution of the one type of gene for the other. By what-
ever rules mating, and consequently the frequency of different gene
combinations, may be governed, the substitution of a small propor-
tion of the genes of one kind by the genes of another will produce a
definite proportional effect upon the average stature. The amount of
the difference produced, on the average, in the total stature of the popu-
lation, for each such gene substitution, may be termed the average
effect of such substitution, in centra-distinction to the average excess
as defined above. In human stature, for example, the correlation
found between married persons is sufficient to ensure that each gene
tending to increase the stature must be associated with other genes
having a like effect, to an extent sufficient to make the average
excess associated with each gene substitution exceed its average
effect by about a quarter.

If a is the magnitude of the average excess of any factor, and a the
magnitude of the average effect on the chosen measurement, we shall

32 FUNDAMENTAL THEOREM^OF NATURAL SELECTION
now show that the contribution of that factor to the genetic variance
is represented by the expression pqaa.

The variable measurement will be represented by a;, and the relation
of the quantities a to it may be made more clear by supposing that
for any specific gene constitution we build up an 'expected' value, X,
by adding together appropriate increments, positive or negative,
according to the natures of the genes present. This expected value
will not necessarily represent the real stature, though it may be a
good approximation to it, but its statistical properties will be more
intimately involved in the inheritance of real stature than the
properties of that variate itself. Since we are only concerned with
variation we may take as a primary ingredient of the value of X, the
mean value of a; in the population, and adjust our positive and nega-
tive increments for each factor so that these balance each other when
the whole population is considered. Since the increment for any one
gene will appear p times to that for its alternative gene q times in the
whole population, the two increments must be of opposite sign and in
the ratio q : ( — %>). Moreover, since their difference must be a, the
actual values cannot but be qa and (— pa) respectively.

The value of the average excess a of any gene substitution was
obtained by comparing the average values of the measurement x in
two moieties into which the population can be divided. It is evident
that the values of a will only be properly determined if the same
average difference is maintained in these moieties between the values
of X, or in other words if in each such moiety the sum of the devia-
tions, x-X, is zero. This supplies a criterion mathematically
sufficient to determine the values of a, which represent hi the popula-
tion concerned the average effects of the gene substitutions. It
follows that the sum for the whole population of the product X (x - X)
derived from each individual must be zero, for each entry qa or ( -pa)
in the first term will in the total be multiplied by a zero, and this will
be true of the items contributed by every factor severally. It follows
from this that if X and x are now each measured from the mean of
the population, the variance of X , which is the mean value of Xz, is
equal to the mean value of Xx. Now the mean value of Xx will
involve a for each Mendelian factor ; for X will contain the item qa
in the p individuals of one moiety and ( -pa) in the q individuals of
the other, and since the average values of # in these two moieties
differ by a, the mean value of X x must be the sum for all factors of the

FUNDAMENTAL THEOREM OF NATURAL SELECTION 33
quantities pqaa. Thus the variance of X is shown to be W=2(pqaa)
the summation being taken over all factors, and this quantity we may
distinguish as the genetic variance in the chosen measurement x.
That it is essentially positive, unless the effect of every gene severally
is zero, is shown by its equality with the variance of X. An extension
of this analysis, involving no difference of principle, leads to a
similar expression for cases in which one or more factors have more
than two different genes or allelomorphs present.

The appropriateness of the term genetic variance lies in the fact
that the quantity X is determined solely by the genes present in the
individual, and is built up of the average effects of these genes. It
therefore represents the genetic potentiality of the individual con-
cerned, in the aggregate of the mating possibilities actually open to
him, in the sense that the progeny averages (of x, as well as of X) of
two males mated with an identical series of representative females
will differ by exactly half as much as the genetic potentialities of
their sires differ. Relative genetic values may therefore be determined
experimentally by the diallel method, in which each animal tested is
mated to the same series of animals of the opposite sex, provided
that a large number of offspring can be obtained from each such
mating. Without obtaining individual values, the genetic variance
of the population may be derived from the correlations between
relatives, provided these correlations are accurately obtained. For
this purpose the square of the parental correlation divided by the
grandparental correlation supplies a good estimate of the fraction, of
the total observable variance of the measurement, which may be
regarded as genetic variance.

It is clear that the actual measurements, x, obtained in individuals
may differ from their genetic expectations by reason of fluctuations
due to purely environmental circumstances. It should be noted that
this is not the only cause of difference, for even if environmental
fluctuations were entirely absent, and the actual measurements
therefore determined exactly by the genetic composition, these
measurements, which may be distinguished as genotypic, might still
differ from the genetic values, X. A good example of this is afforded
by dominance, for if dominance is complete the genotypic value of
the heterozygote will be exactly the same as that of the correspond-
ing dominant homozygote, and yet these genotypes differ by a gene
substitution which may materially affect the genetic potentiality

3653 T?

34 FUNDAMENTAL THEOREM. OF NATURAL SELECTION
represented by X, and be reflected in the average measurement of
the offspring. A similar cause of discrepancy occurs when gene
substitutions in different factors are not exactly additive in their
average effects. The genetic variance as here defined is only a portion
of the variance determined genotypically, and this will differ from,
and usually be somewhat less than, the total variance to be observed.
It is consequently not a superfluous refinement to define the purely
genetic element in the variance as it exists objectively, as a statistical
character of the population, different from the variance derived from
the direct measurement of individuals.

Natural Selection

The definitions given above may be applied to any characteristic
whatever; it is of special interest to apply them to the special
characteristic m which measures the relative rate of increase or
decrease. The two groups of individuals bearing alternative genes,
and consequently the genes themselves, will necessarily either have
equal or unequal rates of increase, and the difference between the
appropriate values of m will be represented by a, similarly the
average effect upon m of the gene substitution will be represented
by a. Since m measures fitness to survive by the objective fact of
representation in future generations, the quantity pqaa will represent
the contribution of each factor to the genetic variance in fitness;
the total genetic variance in fitness being the sum of these contribu-
tions, which is necessarily positive, or, in the limiting case, zero.
Moreover, any increase dp in the proportion of one type of gene at the
expense of the other will be accompanied by an increase adp in the
average fitness of the species, where a may of course be negative ;
but the definition of a requires that the ratio p : q must be increasing
in geometrical progression at a rate measured by a, or in mathe-
matical notation that

d /p\

5iosy=a

which may be written

? = a dt,

or dp = pqa dt

whence it follows that,

adp =pqaadt

FUNDAMENTAL THEOREM OF NATOTRAL SELECTION 37
and, taking all factors into consideration, the totar.not a little instruc-

Z(adp) = S(pqaa}dt = Wdt. *ition among the

•Itimately be

If therefore the time element at is positive, the total chaA , ,,

„ -^e should
ness W at is also positive, and indeed the rate of increase in fitnb.

^.es —
to all changes in gene ratio is exactly equal to the genetic variance, , .

fitness W which the population exhibits. We may consequently state '
the fundamental theorem of Natural Selection in the form :

The rate of increase in fitness of any organism at any time is equal
to its genetic variance in fitness at that time.

The rigour of the demonstration requires that the terms employed
should be used strictly as defined ; the ease of its interpretation may
be increased by appropriate conventions of measurement. For
example, the ratio p : q should strictly be evaluated at any instant
by the enumeration, not necessarily of the census population, but of
all individuals having reproductive value, weighted according to the
reproductive value of each.

Since the theorem is exact only for idealized populations, in which
fortuitous fluctuations in genetic composition have been excluded,
it is important to obtain an estimate of the magnitude of the effect
of these fluctuations, or in other words to obtain a standard error
appropriate to the calculated, or expected, rate of increase in
fitness. It will be sufficient for this purpose to consider the special
case of a population mating and reproducing at random. It is
easy to see that if such chance fluctuations cause a difference 8p
between the actual value of p obtained in any generation and that
expected, the variance of Bp will be

??,

2»

where n represents the number breeding in each generation, and In
therefore is the number of genes hi the n individuals which live to
replace them. The variance of the increase in fitness, aBp, due to this
cause, will therefore be

and since, with random mating, the chance fluctuation in the different
gene ratios will be independent, and the values of a and a are no
longer distinct, it follows that, on this condition, the rate of increase

34 FUNDAMENTAL ^HEOREM 'OF NATURAL SELECTION

represented by •£ inured over one generation, will have a standard

the offspring. ^om survival equal to

substitution*-

I IE.

T\J2n

average P
of tb<-

afiere T is the time of a generation. It will usually be convenient for
each organism to measure time in generations, and if this is done it
will be apparent from the large factor 2n in the denominator, that
the random fluctuations in W, even measured over only a single
generation, may be expected to be very small compared to the average
rate of progress. The regularity of the latter is in fact guaranteed by
the same circumstance which makes a statistical assemblage of
particles, such as a bubble of gas obey, without appreciable deviation,
the laws of gases. A visible bubble will indeed contain several
billions of molecules, and this would be a comparatively large number
for an organic population, but the principle ensuring regularity is tne
same. Interpreted exactly, the formula shows that it is only when
the rate of progress, W, when time is measured in generations, is
itself so small as to be comparable to ifn, that the rate of progress
achieved in successive generations is made to be irregular. Even if
an equipoise of this order of exactitude, between the rates of death
and reproduction of different genotypes, were established, it would be
only the rate of progress for spans of a single generation that would
be shown to be irregular, and the deviations from regularity over a
span of 10,000 generations would be just a hundredfold less.

It will be noticed that the fundamental theorem proved above
bears some remarkable resemblances to the .second law_jil thermo-
dynamics. Both are properties of populations, or aggregates, true
irrespective of the nature of the units which compose them ; both are
statistical laws ; each requires the constant increase of a measurable
quantity, in the one case the entropy of a physical system and in the
other the fitness, measured by ra, of a biological population. As in
the physical world we can conceive of theoretical systems hi which
dissipative forces are wholly absent, and in which the entropy con-
sequently remains constant, so we can conceive, though we need not
expect to find, biological populations in which the genetic variance
is absolutely zero, and in which fitness does not increase. Professor
Eddington has recently remarked that ' The law that entropy always
increases — the second law of thermodynamics — holds, I think, the

FUNDAMENTAL THEOREM OF NATURAL SELECTION 37
supreme position among the laws of nature '. It is not a little instruc-
tive that so similar a law should hold the supreme position among the
biological sciences. While it is possible that both may ultimately be
absorbed by some more general principle, for the present we should
note that the laws as they stand present profound differences —
(1) The systems considered in thermodynamics are permanent;
species on the contrary are liable to extinction, although biological
improvement must be expected to occur up to the end of their exis-
tence. (2) Fitness, although measured by a uniform method, is
qualitatively different for every different organism, whereas entropy,
like temperature, is taken to have the same meaning for all physical
systems. (3) Fitness may be increased or decreased by changes in the
environment, without reacting quantitatively upon that environ-
ment. (4) Entropy changes are exceptional in the physical world in
being irreversible, while irreversible evolutionary changes form no
exception among biological phenomena. Finally, (5) entropy changes
lead to a progressive disorganization of the physical world, at least
from the human standpoint of the utilization of energy, while evolu-
tionary changes are generally recognized as producing progressively
higher organization in the organic world.

The statement of the principle of Natural Selection in the form of
a theorem determining the rate of progress of a species in fitness to
survive (this term being used for a well-defined statistical attribute
of the population), together with the relation between this rate of
progress and its standard error, puts us in a position to judge of the
validity of the objection which has been made, that the principle of
Natural Selection depends on a succession of favourable chances. The
objection is more in the nature of an innuendo than of a criticism, for
it depends for its force upon the ambiguity of the word chance, in its
popular uses. The income derived from a Casino by its proprietor
may, in one sense, be said to depend upon a succession of favourable
chances, although the phrase contains a suggestion of improbability
more appropriate to the hopes of the patrons of his establishment. It
is easy without any very profound logical analysis to perceive the
difference between a succession of favourable deviations from the
laws of chance, and on the other hand, the continuous and cumulative
action of these laws. It is on the latter that the principle of Natural
Selection relies.

38 FUNDAMENTAL THEOREM OF NATURAL SELECTION

The nature of adaptation

In order to consider in outline the consequences to the organic world
of the progressive increase of fitness of each species of organism, it is
necessary to consider the abstract nature of the relationship which we
term 'adaptation'. This is the more necessary since any simple
example of adaptation, such as the lengthened neck and legs of the
giraffe as an adaptation to browsing on high levels of foliage, or the
conformity in average tint of an animal to its natural background,
lose, by the very simplicity of statement, a great part of the meaning
which the word really conveys. For the more complex the adaptation,
the more numerous the different features of conformity, the more
essentially adaptive the situation is recognized to be. An organism
is regarded as adapted to a particular situation, or to the totality of
situations which constitute its environment, only in so far as we can
imagine an assemblage of slightly different situations, or environ-
ments, to which the animal would on the whole be less well adapted ;
and equally only in so far as we can imagine an assemblage of slightly
different organic forms, which would be less well adapted to that
environment. This I take to be the meaning which the word is
intended to convey, apart altogether from the question whether
organisms really are adapted to their environments, or whether the
structures and instincts to which the term has been applied are
rightly so described.

The statistical requirements of the situation, in which one thing is
made to conform to another hi a large number of different respects,
may be illustrated geometrically. The degree of conformity may be
represented by the closeness with which a point A approaches a
fixed point 0. In space of three dimensions we can only represent
conformity in three different respects, but even with only these the
general character of the situation may be represented. The possible
positions representing adaptations superior to that represented by
A will be enclosed by a sphere passing through A and centred at O.
If A is shifted through a fixed distance, r, in any direction its transla-
tion will improve the adaptation if it is carried to a point within this
sphere, but will impair it if the new position is outside. If r is very
small it may be perceived that the chances of these two events are
approximately equal, and the chance of an improvement tends to the
limit \ as r tends to zero ; but if r is as great as the diameter of the

FUNDAMENTAL THEOREM OF NATURAL SELECTION 39
sphere or greater, there is no longer any chance whatever of improve-
ment, for all pouits within the sphere are less than this distance from
A. For any value of r between these limits the actual probability of
improvement is

where d is the diameter of the sphere.

The chance of improvement thus decreases steadily from its
limiting value £ when r is zero, to zero when r equals d. Since A in our
representation may signify either the organism or its environment,
we should conclude that a change on either side has, when this change
is extremely minute, an almost equal chance of effecting improvement
or the reverse ; while for greater changes the chance of improvement
diminishes progressively, becoming zero, or at least negligible, for
changes of a sufficiently pronounced character.

The representation in three dimensions is evidently inadequate ; for
even a single organ, in cases in which we know enough to appreciate
the relation between structure and function, as is, broadly speaking,
the case with the eye in vertebrates, often shows this conformity in
many more than three respects. It is of interest therefore, that if in
our geometrical problem the number of dimensions be increased, the
form of the relationship between the magnitude of the change r and
the probability of improvement, tends to a limit which is represented
in Fig. 3. The primary facts of the three dimensional problem are
conserved in that the chance of improvement, for very small displace-
ments tends to the limiting value |, while it falls off rapidly for in-
creasing displacements, attaining exceedingly small values, however,
when the number of dimensions is large, even while r is still small
compared to d.

For any degree of adaptation there will be a standard magnitude
of change, represented by d[\/n, and the probability of improvement
will be determined by the ratio which the particular change considered
bears to this standard magnitude. The higher the adaptation the
smaller will this standard be, and consequently the smaller the prob-
ability that a change of given magnitude shall effect an improvement.
The situation may be expressed otherwise by supposing changes of
a given magnitude to occur at random in all directions, and comparing
the rates of evolutionary progress caused by two opposite selective
agencies, one of which .picks out and accumulates all changes which

40 FUNDAMENTAL THEOREM OF NATURAL SELECTION
increase the adaptation, and another which similarly picks out and
accumulates all which diminish it. For changes very small compared
to the standard, these two agencies will be equally effective, but, even
for changes of only one-tenth of the standard, the destructive selection
is already 28 per cent, more effective than the selection favouring

0 I 2 ,

MAGNITUDE OF CHANGE * df/H.

Fio. 3. The relation between the magnitude of an undirected change and the prob-
ability of improving adaptation, where the number of dimensions (n) is large

00

p = ==. I erV*dt, x = r^/n/d.

x

adaptation. At one hah* the standard it is over three and a hah* times
as powerful, at the standard value itself, at which the probability of
improvement is still, as the diagram shows, nearly one in six, the
selection destroying adaptation is thirteen times as effective as that
building it up, and at twice and three times the standard value the
ratio has risen to the values 236 and 7,852 respectively.

The conformity of these statistical requirements with common
experience will be perceived by comparison with the mechanical
adaptation of an instrument, such as the microscope, when adjusted
for distinct vision. If we imagine a derangement of the system by
moving a little each of the lenses, either longitudinally or transversely,
or by twisting through an angle, by altering the refractive index and
transparency of the different components, or the curvature, or the
polish of the interfaces, it is sufficiently obvious that any large
derangement will have a very small probability of improving the ad-
justment, while in the case of alterations much less than the smallest

FUNDAMENTAL THEOREM OF NATURAL SELECTION 41
of those intentionally effected by the maker or the operator, the chance
of improvement should be almost exactly half.

Deterioration of the environment

If therefore an organism be really in any high degree adapted to the
place it fills in its environment, this adaptation will be constantly
menaced by any undirected agencies liable to cause changes to either
party in the adaptation. The case of large mutations to the organism
may first be considered, since their consequences in this connexion
are of an extremely simple character. A considerable number of such
mutations have now been observed, and these are, I believe, without
exception, either definitely pathological (most often lethal) in their
effects, or with high probability to be regarded as deleterious in the
wild state. This is merely what would be expected on the view, which
was regarded as obvious by the older naturalists, and I believe by all
who have studied wild animals, that organisms in general are, in fact,
marvellously and intricately adapted, both in their internal mecha-
nisms, and in their relations to external nature. Such large mutations
occurring in the natural state would be unfavourable to survival, and
as soon as the numbers affected attain a certain small proportion in
the whole population, an equilibrium must be established in which the
rate of elimination is equal to the rate of mutation. To put the matter
in another way we may say that each mutation of this kind is allowed
£o contribute exactly as much to the genetic variance of fitness in the
species as will provide a rate of improvement equivalent to the rate
of deterioration caused by the continual occurrence of the mutation.
As to the physical environment, geological and climatological
changes must always be slowly in progress, and these, though possibly
beneficial to some few organisms, must as they continue become
harmful to the greater number, for the same reasons as mutations in
the organism itself will generally be harmful. For the majority of
organisms, therefore, the physical environment may be regarded as
constantly deteriorating, whether the climate, for example, is becom-
ing warmer or cooler, moister or drier, and this will tend, in the
majority of species, constantly to lower the average value of m, the
Malthusian parameter of the population increase. Probably more
important than the changes in climate will be the evolutionary
changes in progress in associated organisms. As each organism
increases in fitness, so will its enemies and competitors increase in

3653 Q

42 FUNDAMENTAL THEOREM -OF NATURAL SELECTION

fitness ; and this will have the same effect, perhaps in a much more
important degree, in impairing the environment, from the point of
view of each organism concerned. Against the action of Natural
Selection in constantly increasing the fitness of every organism, at a
rate equal to the genetic variance in fitness which that population
maintains, is to be set off the very considerable item of the deteriora-
tion of its inorganic and organic environment. It is only if the former
of these agencies exceeds the latter that there can be any actual
increase hi population, while in the reverse case the population will
certainly decrease.

Changes in population

An increase in numbers of any organism will impair its environment
in a manner analogous to, and probably more definitely than, an
increase in the numbers or efficiency of its competitors. It is a patent
oversimplification to assert that the environment determines the
numbers of each sort of organism which it will support. The numbers
must indeed be determined by the elastic quality of the resistance
offered to increase in numbers, so that life is made somewhat harder
to each individual when the population is larger, and easier when the
population is smaller. The balance left over when from the rate of
increase hi the mean value of m produced by Natural Selection, is
deducted the rate of decrease due to deterioration in environment,
results not in an increase in the average value of m, for this average
value cannot greatly exceed zero, but principally in a steady increase
in population.

The situation is represented by the differential equation

dM M

^r + -c = w-D •

in which M is the mean of the Malthusian parameter, C is a constant
expressing the relation between fitness and population increase, and
defined as the increase hi the natural logarithm of the population,
supposed stationary at each stage, produced by unit increase in the
value of M , W is the rate of actual increase in fitness determined by
natural selection, and D is the rate of loss due to the deterioration of
the environment. If C, W and D are constant the equation has the
solution

FUNDAMENTAL THEOREM OF NATURAL SELECTION 43
in which A is an arbitrary constant, dependent upon the initial
conditions. C has the physical dimensions of time, and may therefore
be reckoned in years or generations, and the equation shows that if
C, W, and D remain constant for any length of time much greater
than C, the value of M will approach to the constant value given by

W-D

M =

C

In this steady state the whole of the organism's advantage or dis-
advantage will be compensated by change in population, and not at
all by change in the value of M.

A word should perhaps be said as to the form of statement of
selection theory which ascribes the 'struggle for existence' to the
excessive production of offspring, supposedly to be observed through-
out organic nature. If the numbers of a species are adjusted to that
level at which each adult produces on the average just two offspring
which attain the adult state, then, if there is any mortality whatever
in the previous life stages, either through inorganic causes, or by
reason of predators and parasites, it necessarily follows that young
must be produced in excess of the parental numbers. If the mortality
is high, then the ratio of this excess will be large. Having realized
this situation, if we now imagine an ideal world in which all these
offspring attain maturity and breed, it is obvious that in such a world
the numbers of the species considered will increase without limit. It
is usually added, though this is logically irrelevant, that the increase
will be in geometrical progression. We may in this sense speak of the
production of offspring as 'excessive', and the geometrical rate of
increase with its impressive picture of over-population, has been
widely represented as a logical basis of the argument for natural
selection. However, it should be remembered that the production of
offspring is only excessive in relation to an imaginary world, and the
'high geometrical rate of increase' is only attained by abolishing a
real death rate, while retaining a real rate of reproduction. There is
something like a relic of creationist philosophy in arguing from the
observation, let us say, that a cod spawns a million eggs, that there-
fore its offspring are subject to Natural Selection ; and it has the
disadvantage of excluding fecundity from the class of characteristics
of which we may attempt to appreciate the aptitude. It would be
instructive to know not only by what physiological mechanism a just

44 FUNDAMENTAL THEOREM OF NATURAL SELECTION
apportionment is made between the nutriment devoted to the gonads
and that devoted to the rest of the parental organism, but also what
circumstances in the life-history and environment would render
profitable the diversion of a greater or lesser share of the available
resources towards reproduction. The historical fact that both Darwin
and Wallace were led through reading Malthus's essay on population
to appreciate the efficacy of selection, though extremely instructive
as to the philosophy of their age, should no longer constrain us to
confuse the consequences of that principle with its foundations.

It will have been apparent in the earlier sections of this chapter
that the actuarial information necessary for the calculation of the
genetic changes actually hi progress in a population of organisms, will
always be lacking ; if only because the number of different genotypes
for each of which the Malthusian parameter is required will often,
perhaps always, exceed the number of organisms in the population,
in addition to the fact that this parameter is very imperfectly known
even in human population aggregates, for which vital statistics are
in some degree available. If, however, we are content to consider not
in full detail exactly what changes are in progress, but quite broadly
to what extent an organism is holding its own in the economy of
nature, it is only necessary to determine the numerical values of the
four quantities W, D, C, and M , which enter into the equation of
population growth. Our ignorance as to these is, of course, profound,
but, regarding the problem in this limited aspect, it is by no means
obvious, with respect to organisms of sufficient importance to deserve
detailed study, that it could not largely be removed by systematic
and well-directed observations. The quantity C, for example, which
is a period of time, measuring the facility with which, with increased
fitness, the population is allowed to increase, must be intimately
related to the course of population increase or decrease, with which
the numbers of an organism exposed to new influences, approach an
equilibrium value, which over short periods may be regarded as
stationary. An organism introduced into a new environment, to
which it is well suited, will increase in numbers rapidly for a compara-
tively few years, and somewhat rapidly attain its equilibrium density.
The same must be true of the decrease of a population exposed by
man to new causes of destruction. In these cases it is probable
that the process of attaining equilibrium is sufficiently rapid for the
changes due to organic evolution, and the natural deterioration of

FUNDAMENTAL THEOREM OF NATURAL SELECTION 46
the environment, to be neglected, and further changes in the extent of
human intervention could, for experimental purposes, be suspended
locally. In such cases, at their simplest, the course of population
change would be represented by the equation M — Ae-t/C, or, since
M is the relative or logarithmic growth rate of the population, by
logN = logiVo —ACe~llG , where N is the size or density of the popula-
tion, and NQ the steady value to which it is tending. Observations of
N will then determine, at least approximately, the value of the time
constant C. It should be noticed that for such comparatively large
changes of population density as could be measured with sufficient
precision, important changes will often take place in the numbers of
associated organisms. The simple relation obtained above will only
be satisfactory if these associated changes take place rapidly in
comparison to the change we are studying. Otherwise it would be
necessary to take account by direct observation of the changes in
numbers of at least the more important of the associated organisms,
and so to determine the constants of the more complex system of
differential equations by which their interactions may be represented.
With respect to the other constants, the practical difficulties appear
to be greater, though, seeing how little attention in general has been
paid to the quantitative study of organisms in their natural habitats,
it would be rash to assume that their determination is beyond human
endeavour. Though it would be out of place here to outline a pro-
gramme of research, it is perhaps worth while to indicate a few
possibilities. The density of populations of animals and plants may
be studied in relation to the climatic and other environmental factors
of their habitats. Knowledge of this kind, even if only approximately
complete, would indicate to what extent physical changes now in
progress can be improving or impairing the environment. If the
constant C is also known, these effects may be translated directly
into terms of fitness. In certain cases, such as the slow changes in
composition of plant associations, the value of M might be directly
determined, and in conjunction with more or less trustworthy deter-
minations of C and D, this would lead to a more or less exact estimate
of the evolutionary factor W. The direct determination of the latter
quantity would seem to require a complete genealogy of the species
for several generations, and this will only be possible in Man. More-
over, owing to the rapid changes which man is making in his environ-
ment, it may be foreseen that human genealogies on a national or

46 FUNDAMENTAL THEOREM .OF NATURAL SELECTION
international scale, such as has been undertaken in Sweden, while
throwing an immense amount of light on the current conditions of
human reproduction and survival, will offer special difficulties in the
determination and interpretation of the evolutionary value W.

Summary

The vital statistics of an organism in relation to its environment
provide a means of determining a measure of the relative growth-rate
of the population, which may be termed the Malthusian parameter of
population increase, and provide also a measure of the reproductive
values of individuals at all ages or stages of their life-history. The
Malthusian parameter will in general be different for each different
genotype, and will measure the fitness to survive of each.

The variation in a population of any individual measurement is
specified quantitatively by its variance, and of this, taking account
of the genetic composition of all possible individuals, a definite
amount may be recognized as genetic variance.

The rate of increase of fitness of any species is equal to the genetic
variance in fitness, and the standard error of this rate of progress even
over a single generation, will (unless the latter is so exceedingly
minute as to be comparable, when time is measured in generations,
to the reciprocal of the number of organisms in the population) be
small compared to the rate of progress.

Adaptation, in the sense of conformity in many particulars between
two complex entities, may be shown, by making use of the geometrical
properties of space of many dimensions, to imply a statistical situa-
tion in which the probability, of a change of given magnitude effect-
ing an improvement, decreases from its limiting value of one hah*, as
the magnitude of the change is increased. The intensity of adapta-
tion is inversely proportional to a standard magnitude of change for
which this probability is constant. Thus the larger the change, or
the more intense the adaptation, the smaller will be the chance of
improvement.

Against the rate of progress in fitness must be set off, if the organism
is, properly speaking, highly adapted to its place in nature, deteriora-
tion due to undirected changes either in the organism, or in its
environment. The former, typified by the pathological mutations
observed by geneticists, annul their influence by calling into existence
an equivalent amount of genetic variance. The latter, which are

FUNDAMENTAL THEOREM OF NATURAL SELECTION 47
due to geological and climatological changes on the one hand, and to
changes in the organic environment, including the improvement of
enemies and competitors, on the other, may be in effect either greater
or less than the improvement due to Natural Selection.

Any net advantage gained by an organism will be conserved in the
form of an increase in population, rather than in an increase in the
average Malthusian parameter, which is kept by this adjustment
always near to zero.

Although it appears impossible to conceive that the detailed action
of Natural Selection could ever be brought completely within human
knowledge, direct observational methods may yet determine the
numerical values which condition the survival and progress of par-
ticular species.

ni

THE EVOLUTION OF DOMINANCE

The dominance of wild genes. Modification of the effects of Mendelian factors. Modi-
fication of the heterozygote. Special applications of the theory. The process of modi-
fication. Inferences from the theory of the evolution of dominance. Summary.

The very object of hypothesis is to inquire whether a real cause has not had
a under operation than there is any direct evidence for. ROBERTSON SMITH.

The dominance of wild genes

IT has been seen in Chapter I that it is scarcely possible, in the light
of the particulate nature of inheritance, to ascribe to mutations any
importance in determining the direction of evolutionary change;
their importance in evolution lies in playing the very different role
of maintaining the stock of genetic variance at a certain level, which
level in its turn is a factor in determining the speed, though not the
direction, of evolutionary progress. Before attempting to consider hi
detail the relations between the amount of the stock of genetic
variability in a species, the rates of mutation, and the size of the
population, as will be done in Chapter IV, it is necessary to examine,
as far as the present state of the evidence allows, into the character
of the genetic changes known as mutations.

It will certainly be felt by some, especially by those to whom the
relevant evidence is still to a large extent unfamiliar, that at the
present time it is altogether premature to put forward, as a basis for
further argument, a theory of the evolution of dominance ; seeing that,
until quite recently, dominance was accepted by geneticists as an
unexplained fact which, in our ignorance of its causes, could be
dismissed as without theoretical importance. Nevertheless, it would
scarcely have been defensible to develop a theory of the role of
mutations in evolution, without regard to the cases of mutations
actually observed. A study of these changes reveals a body of
evidence, concordant so far as it goes, though far less complete than
it will doubtless soon become, now that attention has been drawn to
the subject ; it will scarcely be thought wrong, therefore, to put
before the reader both the salient points of the evidence, and my
inferences from them. The statement of the evidence is entirely
provisional, and will, I hope, before long be largely superseded by
more direct and complete observation ; whilst my theory will, I be-

THE EVOLUTION OF DOMINANCE 49

lieve, appear under examination to be at present sufficiently well
founded to serve as a guide to the direction of our further inquiries.
The validity of later Chapters will not be impugned, though their
relevance will be, if I am wrong hi the inferences drawn in this
Chapter.

The term mutation has been applied to a number of different kinds
of intracellular events, having in common the production of heritable
novelties. Cases are known of the doubling of the entire chromosome
outfit, the doubling of single chromosomes, and of parts of chromo-
somes ; in other cases a part of a chromosome appears to be trans-
located from its habitual site and attached to some other chromo-
some ; and these are all mutations in the wide and primitive meaning
of the term. Nevertheless, the evolutionary possibilities of these
kinds of change are evidently extremely limited compared to those
of the type of change to which the term gene-mutation is applied.
This consists in a change in a single hereditary particle, or gene, into
a gene of a new type, occupying the same locus in the germinal
structure. The grosser forms of mutation may indeed play a special
evolutionary role in supplying a mechanism of reproductive incom-
patibility, which may be of importance when physiological isolation
is hi question, but only hi very special cases could they contribute
appreciably to the genetic diversity of an interbreeding population.

With respect to any pah- of alternative or allelomorphic genes,
the one may be distinguished from the other in four different respects,
which, in order to examine their relationships, it is important to
keep conceptually distinct. We may distinguish (a) the rarer from
the more common, (6) the less advantageous from the more advan-
tageous, (c) the mutant gene from the relatively primitive gene from
which it arose, and finally (d) the recessive gene from the dominant.
It is only when these four means of contrast are kept distinct that we
can appreciate the associations between them which arise from
different causes.

In connexion with the nature of adaptation it has been seen that
mutant genes will more often than not be disadvantageous, and that
this will be most conspicuously the case with the factors having a large
effect, and which consequently are more easily detected and studied.
Distinctions (6) and (c) are thus closely associated. Moreover, hi a
freely mixing population, but not in an aggregate of genotypes kept
as separate breeds, the less advantageous genes will tend to become

3653 TT

50 THE EVOLUTION OF DOMINANCE

the rarer, and if this tendency is checked at any point by occasional
mutations, such mutant and less advantageous genes will at the same
time generally be the rarer. Finally, if we suppose provisionally that
the invent genes are dominant just as often as they are recessive,
sttection will be far more severe in eliminating the disadvantageous
dominants than in eliminating the disadvantageous recessives. This
may be seen most easily by considering cases of equal rarity of the
two types. If 1 gene in 100 represents a dominant defect, each
10,000 of the population will contain on the average 199 defectives,
exposed to unfavourable selection, whereas if 1 gene in 100 represents
a recessive defect, the defect will appear on the average in only 1 in
10,000. Consequently, the rare recessive is much sheltered from the
action of selection, and in such a population we might expect to find
many cases of rare recessive defects (a, b, d), and but few rare
dominant defects. The fact that the rare recessives exposed by
inbreeding prove themselves to be defective does not then demon-
strate that mutant defects are generally recessive. On the other hand,
if evolution had proceeded by steps comparable in size with the effects
of factors which it is convenient to study, one might expect to find
among the rare recessives a few primitive genes superseded in the
bulk of the population by more advantageous genes which had arisen
from them by mutation. Such cases appear to be entirely unknown;
we may interpret this as indicating either that the evolutionary steps
are not ordinarily so large as the effects of the factors which we can
study, or that the mutant gene is rarely or never completely domi-
nant to its predecessor. Since I believe both statements to be true,
it is not permissible to use this observation to prove either.

Among species of plants propagated, like sweet peas, in distinct
varieties, genetical analysis shows that the genes which on morpho-
logical grounds must be regarded as mutants, are, in an immense
preponderance, recessives. In sweet peas complete recessiveness
seems to be the invariable rule, as judged from the fifteen or twenty
factors so far successfully elucidated. In the majority of such cases
the occurrence of the mutation has not itself been observed, but the
mutant gene is recognized as such by producing effects unknown
in the older varieties, or wild prototypes. This is very substantial
and extensive evidence of the tendency of mutant genes to be
recessive, for dominant mutants would be as eagerly seized upon
and perpetuated as novelties, and would be more quickly detected

THE EVOLUTION OF DOMINANCE 51

than are recessives. The greater ease of detection is especially to be
emphasized in the case of Man, where the recognition of a rare
as due to a single Mendelian factor depends upon genealc
evidence; for the simplest pedigree, such as is a? <ost always a li-
able, will reveal the character of a dominant defect, while the colla-'
tion of the statistical evidence of extensive pedigree collections is
usually necessary to demonstrate the Mendelian character of a
simple recessive. For example, the Mendelian character even of
albinism in Man has been disputed. In consequence of this difficulty
it is probable that more dominant defects are known in Man than
recessives, although there can be no doubt that the great bulk of
human defects, physical and mental, are, as in other animals, recessive.
This view is confirmed by the fact that sex-linked mutants, which
a priori in an organism with 24 pairs of chromosomes should be
a small minority, are prominent in the list of human defects ; here
the recessives are nearly as easily detected as dominants, and all
known cases are recessive. Further, in the case of so-called dominant
defects in Man we only know that the heterozygote differs from the
normal; we cannot ordinarily know what is the appearance of the
homozygote mutant, or even if it is viable.

The imposing body of genetical researches devoted to the fruit-fly,
Drosophila, in this as in other genetical questions has supplied the
most decisive evidence. Something like 500 mutants have been
actually observed in cultures of this fly, and, setting aside the large
class of lethals, and all those which produce no visible effect, there
remain 221 cases in which we can classify the mutation as Recessive,
Intermediate, or, as it is usually called, Incompletely Dominant, or
finally completely Dominant. The table shows the distribution into
these three classes, respectively for the autosomal and the sex -linked
mutations.

TABLE 1.

Completely

Recessive. Intermediate. Dominant. Total.
Autosomal .130 9 0 139

Sex-linked .78 4 0 82

The classification has been compiled from the magnificent article
on Drosophila in Bibliographica Genetica. In several individual
instances my classification may be mistaken, either because the
observations are affected by some uncertainty, or because they are
not in every case explicitly stated. No one will doubt the extreme

62 THE EVOLUTION OF DOMINANCE

thoroughness with wnich the genetics of this fly has been investigated ;
it is, however, perhaps worth mentioning that whereas recessives
are so^xtfhmon that the loss of one without investigation would seem
1M>J0eat tragedy, mutations which can be 'used as a dominant ', that
i*' AC Intermediates, are of the greatest service to further research,
find are much valued. They are, moreover, exposed to detection
immediately upon their occurrence, whereas recessives are only
noticed when they appear as homozygotes. For both reasons the
proportion of recessives, high as it is, is likely to be an underestimate
of the actual frequency of occurrence.

Lethal factors, which have been excluded from the enumeration
set out above, provide independent though slightly equivocal con-
firmation of the same conclusion. The majority of so-called dominants
are lethal in the homozygous condition, and must for this reason be
properly classed as Intermediate. It is more remarkable that recessive
lethals, which can produce no visible changes, were soon discovered
by their effect in disturbing the frequency ratios of other factors, and
especially of sex. It has since been demonstrated that both in normal
conditions, and when mutations are artificially stimulated by X-rays,
the recessive lethals are by far the most frequent class of mutation.
Something like two per cent, of untreated fruit-flies must be mutants
for some recessive lethal, and the frequency of mutations of this
class must be quite tenfold that of all visible mutations. Whereas,
among the latter, one in seventeen has been classed as inter-
mediate in respect of dominance, the proportion must be even lower
among lethals, unless indeed some of the obscure, though probably
large, class of mutants which are lethal when heterozygous, be counted
as dominant.

The pronounced tendency of the mutant gene to be recessive, to
the gene of wild type from which it arises, calls for explanation, and
there is fortunately an important group of observations available, to
show that in this connexion we should stress the prevalence in the
wild state of the dominant gene, rather than its relation of predecessor
to the mutant which arises from it. Numerous cases are now known
in which several different mutations have occurred to the same gene,
and each of the mutant types can replace each other, and the wild
type, in the same locus. In rodents, for example, several members of
the albino series of genes have been found, ranging in effect from
a slight dilution of pigmentation to its complete suppression. Using

THE EVOLUTION OF DOMINANCE 53

a set of five such alternative genes in the cavy or guinea pig} Sewall
Wright has formed all of the fifteen possible combin^.ions five
homozygous and ten heterozygous, which a set of five
make possible. These he has examined in sufficient
determine the average, and normal variation in depth of pigment
both of the areas which range from black through sepia to %ite
and those which range from red through yellow. The four he«»T«o_
zygous forms containing the wild type gene are indistinguishable .>
depth of pigment from the homozygous wild type, from which all the
other four homozygotes differ considerably. The remaining six
heterozygous forms, which contain no gene of the wild type, all are
clearly intermediate in both colours between the two homozygotes
for the genes which they contain. This case, remarkable for the
thoroughness with which it has been examined, is by no means
exceptional. A number of similar series have been found in Droso-
phila, and the rule that the wild type gene dominates all others, but
that these others show no mutual dominance, is stated as general by
Morgan, Bridges, and Sturtevant.

The exceptional position in respect to dominance of the genes of
the wild type among their allelomorphs is not owing to their
being the originals from which the others arose by mutation, for one
mutant allelomorph has been observed to arise from another, and
mutant genes to mutate back to the wild type. We are driven
therefore to see in dominance a characteristic proper, not to the pre-
decessor as opposed to the successor in a series of mutational changes,
but to the prevalent wild type as opposed to its unsuccessful com-
petitors. Moreover, unless we are to abandon altogether the evolu-
tionary conception of the modification of species by the occasional
substitution of one gene for the predecessor from which it arose, the
existence of the rule which gives genetical dominance to genes of the
prevalent wild type requires that the successful new gene should in
some way become dominant to its competitors, and if back mutations
occur, to its predecessor also. The means by which this can occur are
of special interest in the theory of Natural Selection, for they reveal
an effect of selection which has nothing to do with its well-understood
action in fitting a species to its place in nature. As has been indicated
in Chapter II, it is scarcely possible to imagine a problem more intri-
cate, or requiring so inconceivably detailed a knowledge of the
bionomic situation, as that of tracing the net gam in fitness of any

54 THI EVOLUTION OF DOMINANCE

particular gentfic change. Our knowledge in this respect, while
sufficient to enable us to appreciate the adaptive significance of the
differences is organization which distinguish whole orders or families,
is almost- AVays inadequate to put a similar interpretation on specific
differer-es, and still more on intraspecific variation. This circum-
stance which has been felt as a difficulty to the theory of Natural
by writers such as Bateson (1894) and Robson (1927),
admitting of notable exceptions, such as external colour, and
espcially the mimetic patterns of butterflies, does yet give an added
interest to a case in which our quantitative information, while far
from exact, is yet substantial and approximate.

Modification of the effects of Mendelian factors

The fashion of speaking of a given factor, or gene substitution, as
causing a given somatic change, which was prevalent among the
earlier geneticists, has largely given way to a realization that the
change, although genetically determined, may be influenced or
governed either by the environment in which the substitution is
examined, or by the other elements in the genetic composition. Cases
were fairly early noticed hi which a factor, B, produced an effect
when a second factor, A, was represented by its recessive gene, but
not when the dominant gene was present. Factor A was then said
to be epistatic to factor B, or more recently B would be said to be
a specific modifier of A. There are other cases in which neither A
nor B produce any effect when the other is recessive, in which cases
we speak of the two factors as complementary ; again neither may
produce any effect if the other is dominant, when we speak of the
two factors as duplicate. These are evidently only particular examples
of the more general fact that the visible effect of a gene substitution
depends both on the gene substitution itself and on the genetic
complex, or organism, in which this gene substitution is made. We
may perhaps find a form of words which reduces to a minimum the
discrepancy between the complexity of the actual relationships, and
the simplicity of those presupposed by ordinary grammatical forms,
by speaking of the observed somatic change as the reaction of the
organism to the gene substitution in question. We should then at
least avoid any impression of vagueness or contradiction if differently
constituted organisms should be found to react differently. It is,
once the matter is viewed thus, far from inconceivable that an

THE EVOLUTION OF DOMINANCE 55

organism should evolve, if so required, in such a way as to modify its
reaction to any particular gene substitution.

There are several cases in which such modification has been
observed to occur in experimental stocks. It has been rather fre-
quently observed, when a new and sharply distinct mutant in Droso-
phila has been put aside to breed in stock bottles for some genera-
tions, that when it is required again for use, the mutant form appears
to be appreciably less distinct from the wild type than it had at first
seemed. The reality of this tendency to revert to the wild form, as
well as its cause, has been demonstrated in several cases by the
simple but crucial experiment of mating the modified mutants to
unrelated wild stock, and, from the hybrid, extracting the mutant
form by inbreeding. The mutant form so recovered is found to have
regained much of its original intensity; and thus shows that the
modification has not been due to any change in the mutant gene, but
to a change in the genetic complex of the organism with which it
reacts. This change is now open to a simple explanation. The flies
from which the stock was formed were variable in genetic qualities
which affected the violence of their reaction to the mutant gene. In
the competitive conditions of the stock bottle those hereditary units
which favoured a mild reaction produced flies less defective than
their competitors, and the selection of these modifying factors rapidly
modified the average intensity of the reaction to the mutant gene,
and consequently its average divergence in appearance from the
wild fly. A similar case of the partial recovery of a mutation in the
nasturtium, handicapped by partial sterility, has been observed by
Professor Weiss ; and Mr. E. B. Ford informs me that the mutant types
found in the shrimp, Gammarus chevreuxi, have frequently made in
culture a noticeable improvement in viability. The effect of preserving
a mutation in a number of individuals breeding preferentially from
the least defective, is thus to modify the organism in such a way as
to mitigate the disadvantageous effects of the mutation. It is not
only the frequency of a gene, but the reaction of the organism to it,
which is at the mercy of Natural Selection. To understand the effect
of a gene on members of a given population, that is, the reaction of
such organisms to it, we must consider what part that gene has
played in their ancestry.

The great majority, if not all, of the mutations which we can hope
to observe in experimental culture must, unless these mutations can

66 THE EVOLUTION OF DOMINANCE

be ascribed to our cultural methods, have occurred in the history of
the species in enormous numbers : many of the Drosophila mutations
have occurred repeatedly in culture, and, large as the numbers
observed have been, they are trifling compared to the total ancestry
of any individual wild fly. Our knowledge of the frequency of
individual mutations is at present slender; but it is sufficient to
establish that many mutations must occur with a frequency of 1 in
100,000, or 1 in 1,000,000; and, indeed, the probability of mutations
much rarer than this appearing in cultures is extremely small. We
have, of course, no direct knowledge of the mutation rates prevalent
in nature, but what has been discovered so far of the causes affecting
mutation rate gives no ground for supposing that they are lower than
in the laboratory. As to the extent of the ancestry of an individual
fly over which a given mutation has been liable to occur, we have
good grounds for assuming that it may often be longer than the
separate existence of specific types ; for different species of Drosophila
have shown several mutations which can be identified by hybridi-
zation. Beyond this, direct tests of identity fail us ; but it is not an
unreasonable conjecture that such a mutation as albinism, which
appears in mammals of the most diverse orders, has been occurring
in the ancestry of the group from its earliest beginnings. On the
other hand, as will be seen below, we have reason for believing that,
with the evolution of new species, new mutations do sometimes
commence to occur, or at least to occur with appreciable frequency.

Modification of the heterozygote

When an unfavourable mutation persists in occurring in every
generation once, let us say, in each million chromosomes, it will, of
course, be kept rare by selection; but it will, on the other hand,
affect many individuals who are potential ancestors of future genera-
tions, in addition to those who are actually mutants. An important
consequence of its rarity is that both these classes will be hetero-
zygotes far more frequently than they will be homozygotes. If p is
the relative frequency in the population of mutant to wild-type genes,
the three classes of individuals, non-mutant, heterozygote and
homozygous mutant will appear in the ratio 1 : 2p : p2, so that even
if p were as large as one-thousandth, the heterozygotes would be
2,000 times as numerous as the mutant homozygotes. A consequence
of this is that, so long as the heterozygote differs from the wild type

THE EVOLUTION OF DOMINANCE 57

appreciably in fitness to survive, the relative numbers of the three
classes will be determined, for a given mutation rate, by the selective
disadvantage of the heterozygote, and to no appreciable extent by
the selective disadvantage, or even complete lethality, of the mutant
homozygote.

For our present purpose we take as the relative fitness of the
heterozygote, denoted by v, the ratio which the average number of
offspring of this type bears to the average from non-mutant indivi-
duals. Then it is easy to see that the fraction p will be diminished in
each generation by the quantity p(l -v) and, so long as p is small,
will be augmented by the quantity k representing the actual muta-
tion rate. An equilibrium will therefore be established between the
agencies of mutation and selection when

p(l -v) = k.

If, to take one extreme, v is a small fraction, then p is little greater
than k, little greater, for example, than 1 in 1,000,000, and at this
extreme the heterozygotes will occur 2,000,000 times as frequently
as the mutant homozygotes. If v is £, p will be twice k, and the
heterozygotes will still be a million times the more frequent. If on
the other hand the viability and general fitness of the heterozygoted
are so good that it is only at a 1 per cent, disadvantage, and v — 0-99,
the heterozygotes will still be 20,000 times the more frequent.

These very high ratios justify the conclusion that if the heterozygote
is at any appreciable disadvantage compared to the wild type, it will
be so enormously more frequent than the homozygote that any
selection of modifiers which is in progress will be determined by the
reaction of the heterozygote.

Two other circumstances serve to increase the disproportion of the
selective effects. In the first place, the efficacy of the selection in
modifying the characteristics of the species depends not only upon
the frequency of the individuals selected, but upon their chance of
leaving a remote posterity. In fact we need to evaluate not the
relative numbers of the two types in any one generation, but the
proportions they represent of the total ancestry of a distant sub-
sequent generation. Evidently, if, as is to be anticipated, the viability
of the homozygous mutant is lower than that of the heterozygote,
the latter will count for more in future generations, and even if
the two types had equal viability, the heterozygote is still at an

3653 T

58 THE EVOLUTION OF DOMINANCE

advantage, for mated with wild type only half his offspring will be
heterozygous, while in a similar case all the offspring of the homo-
zygote will be equally handicapped.

This point becomes of importance with sex-linked factors, where the
mutant type males and the heterozygous females do not differ greatly
in frequency, but may differ greatly in viability, with the result that
the latter may occur much more frequently in the ancestry of the
existing wild population.

In the second place, on any biochemical view of the intracellular
activity of the genes, it is difficult not to admit the probability that
the heterozygote may be inherently more modifiable than are the
two homozygotes, especially in respect to the differences which
distinguish these last ; for in modifying the effect of the homozygote
we must imagine the modifying gene to take part in some reaction
which accentuates or inhibits the effect in question, while in the
heterozygote the original ingredients are already present for all that
normally takes place in the two corresponding homozygotes. The
future examination of the instances cited below in which modifica-
tion appears to be demonstrable should make much clearer than it
now is how much weight should be given to this consideration.

The fraction of the ancestry of future generations, ascribable to
heterozygotes, though greatly exceeding that due to mutant homo-
zygotes, is still absolutely small. We may obtain the proportion
ascribable to a single heterozygote, compared to a non-mutant, by
equating it to half the proportion ascribable to its probable offspring :
thus if the proportions due to heterozygotes and non-mutants are as
x : 1 we shall have

or x = ~v

v

X =

2-v '
and, since the proportion of the population which is heterozygous is

2k
1-v'

their proportionate contribution to remote future generations is
found to be

THE EVOLUTION OF DOMINANCE 59

This quantity which, when the mutation rate (k) is 1 in 1,000,000,
rises to about 1 in 5,000 if v is 0-99, represents the rate of progress in
the modification of the heterozygote, compared to the rate of progress
which would be effected by selection "of the same intensity, acting
upon a population entirely composed of heterozygotes. In the case
of homozygotes the progress made by the Natural Selection of
modifying factors has been shown to be far from negligible, even
over short periods of observation, and under the serious restriction
that the supply of modificatory variance is limited by the small
number of the original stock. In considering the modification due
to the selection of heterozygotes hi nature, we may fairly assume that
these are at least as liable to genetic modification as are homozygous
mutants, and that a selection acting only on 1 in five or ten thousand
of the population will have no appreciable influence in reducing the
variance available.

Special applications of the theory

An extremely interesting case showing the modification of the
heterozygote so far as to be indistinguishable from the non-mutant,
that is of the acquisition of complete dominance by the wild type gene,
has been brought to my notice by Mr. J. B. Hutchinson from the
work of Dr. C. S. Harland on the genetics of the cotton plant. The
several species of new-world cottons can be freely intercrossed and
yield fertile offspring. One of these, the Sea Island cotton, has
repeatedly produced a mutant form known as Crinkled Dwarf, which
in that species is completely recessive. It appears to be identical with
a similar mutant known as Wrinkled Leaf, appearing in some nearly
related forms grown in Egypt, but so far as is known none of the other
American species throw this mutant. In the course of Dr. Harland's
experiments the Crinkled Dwarf mutation of Sea Island was crossed
with two other new-world species, Upland and Peruvian. The out-
standing results of the cross were the same in both cases. The
heterozygote was found to be slightly affected by the mutant
character, thus indicating, even at this stage, some incompleteness of
dominance. The most remarkable effects, however, were produced
in the second generation, derived from the heterozygote by self-
fertilization. In this we should expect a quarter of the offspring to
be Crinkled Dwarf, a half to be heterozygote, and a quarter to be
non-mutant. The homozygous forms appeared as expected, but were

60 THE EVOLUTION OF DOMINANCE

connected by a practically continuous series of intermediate types.
The heterozygotes in fact showed dominance of all grades. It is
evident that the Sea Island cotton differed from the other new-world
species in a number of modifying factors affecting the development
and appearance of the heterozygote, the combined effect of which
hi the Sea Island species is to render the heterozygote normal in
appearance. In this case the complete modification in the reaction
of the organism to the mutant gene must have been brought about
since the separation of this species from its new -world congeners;
the whole process of evolution from the first appearance of the
mutation, at least with appreciable frequency, must therefore have
been comparatively rapid. When the mutation rate has been deter-
mined this case should afford a useful guide to the extent of the
analogous events which we should expect to have taken place in
other species.

A group of facts of very particular interest in this connexion is
presented by domestic poultry. Crosses between the different breeds
show that a number of the distinctive breed characteristics are due
to simple Mendelian factors. In a number of cases, however, it is the
fancy breed character, and not the character of the wild Gallus
bankiva, which is found to be dominant. There must be a dozen or
more factors of this kind ; three are known which affect the conforma-
tion of the comb ; one produces a crest ; there is a dominant white
which inhibits pigment formation in the plumage; and others
influencing the colour or pattern of the feathers, or the colour of the
shanks. Domestic poultry show also mutants of the kinds familiar in
other organisms, recessives and lethal 'dominants', but they are
peculiar in this surprising group of factors which are non-lethal and
dominant to the wild type. It is noteworthy that none of these
factors originated in a recorded mutant and that their effects, while
presumably they would be deleterious in the wild environment, are
not pathological in the sense of impairing the vitality of the birds as
domestic poultry. They are all, in fact, definite breed characteristics.
Other birds bred in captivity seem to have thrown mutants only of
the ordinary recessive kind, such as cinnamon canaries, or yellow
budgerigars ; and for each of these reasons we should be led to seek
for an explanation of the peculiarity of the domestic fowl rather in
the conditions of its domestication than in the nature or environment
of the wild species. In the former there seems to be one very striking

THE EVOLUTION OF DOMINANCE 61

circumstance which throws light on the dominant characters of the
domestic breed.

The wild jungle fowl is common in many parts of India, and it has
frequently been observed that the wild cocks mate, when opportunity
is afforded, with the hens of domestic flocks. If this is so down to the
present day, we may infer that it has been so since the earliest stages
of domestication, and indeed that it was the prevalent condition
throughout the period, probably a long one, when the fowl was only
kept by jungle tribes. I do not postulate that the cocks were not
kept ; for they may have been valued for cock-fighting as early as the
hens for egg -production ; moreover, some of the factors concerned are
sex -linked, and would only show dominance in the cock ; but it is pro-
bable, and indeed almost impossible to dispute, that for long ages the
domestic flocks were continually liable to be sired by wild birds . In the
case of most domestic animals and plants, recessive mutations, when
they appear, will immediately breed true, and man's curiosity and love
of novelty have thus repeatedly led him to perpetuate forms which, as
often as they appear in a state of nature, are eliminated by Natural
Selection. On crossing with the wild form such recessive characters
disappear and seem to be lost, and if such crossing is at all frequent,
the only mutations which could lead to constant breed characteristics
would be those that were not completely recessive. With these some
of the chicks would always show the breed characteristic, and a con-
tinued selection or preservation of the valued types would retain their
character in the breed. Moreover, since these types are only to be
retained by selection, it is certain that selection would favour those
individuals in which the mutant characteristic reached the most
pronounced development. Man, in fact, whenever his broods con-
sisted half of heterozygotes and half of wild-type fowls, if he valued
the heterozygote characteristics, and therefore selected them rather
than the others, would also, necessarily, at the same time select those
heterozygotes in which the mutant gene was least recessive or most
dominant.

It will be noticed that on this view of the origin of some of the
breed characteristics of the domestic fowl, we have an explanation of
two distinct peculiarities which these characters exhibit; namely
both the high proportion of mutant characters which are not recessive
to the wild type; and of the high degree in which dominance is
developed, at least in certain breed crosses. It is important, too, in

62 THE EVOLUTION OF DOMINANCE

this connexion, that other crosses are known in the case of several
of these factors, in which dominance appears to be incomplete.
A full and satisfactory examination of such cases would seem to be
possible only by introducing the mutant gene, and very little else,
into breeds in which this gene is unknown ; for dominance can only
properly be examined if the two homozygotes and the heterozygote
have, in other respects, a similar genetic composition. It may be
mentioned that my inference concerning the modification of domi-
nance in mutant factors in the fowl, is open to the crucial test of intro-
ducing one or more of these dominants into a genuinely wild strain
of jungle fowl. If my inference is correct, the mutant would then be
found to be clearly intermediate, and not either completely dominant
or completely recessive. Through the kindness of the Zoological
Society of London, and the generosity of Mr. Spedan Lewis, it has
been possible to start this experiment ; the result cannot, of course,
be known for several years.

The process of modification

The case of fowls confirms, so far as it goes, the other evidence avail-
able as to the speed with which dominance may be modified ; for in
this case, although the whole process has perhaps occupied no more
than a thousand generations, the effective selection is applied, not
to a population containing only one heterozygote in 10,000 or so,
but to broods half of which are heterozygotes ; and moreover in
which ex hypothesi it is the heterozygotes rather than the wild type
that are chosen to continue the breed. Evolution under such human
selection should, therefore, take place many thousand times more
rapidly than the corresponding evolution of recessiveness in nature.

As to the speed of the latter process, the principal unknown
element for a mutation of given viability (v) and mutation rate (k)
is the quantity of modificatory variance available to influence the
heterozygote. This will presumably tend nearly to zero as v tends to
unity, but its relation to v for values differing considerably from unity
will be somewhat different according to the different views which we
may form as to the manner in which the modification is brought about.
In the case of homozygotes we must suppose that the modifying
factors, by intensifying the appropriate developmental reactions,
succeed, in effect, in remedying the situation which arises at that
stage at which defective development is initiated. This may also be

THE EVOLUTION OF DOMINANCE 63

true of heterozygotes, and, if the greater part of the modificatory
variance available is of this sort, we should expect its magnitude,
ceteris paribus, to depend only upon v, and consequently that all
mutations would follow one another along the same path towards

4321
TIME IN ARBITRARY UNITS

FIG. 4. The relation between the severity of the handicap imposed by a mutation,
and the time needed to repair the defect by the selection of modifiers, supposing the
variance of v to be proportional to v (1-v).

normality at speeds proportional to their mutation rates, but other-
wise dependent only on the stage which they have at any moment
reached. Such a view is illustrated in Fig. 4.

On the other hand it does not seem, in the present state of know-
ledge, improbable that the greater part of the variance may be due
to a cause special to heterozygotes; namely the varying extent to
which one or other of the homologous genes may be allowed to take
part in the nuclear reactions for which they are responsible. On this
view the amount of variance available would depend, not only on the
viability actually attained, but upon its original value ; being, for
heterozygotes of the same viability, greater for mutations having the
larger effect. We should then obtain such a series of trajectories as is
illustrated in Fig. 5.

In either case the final stages of approach to normality will be the
most rapid, and a mutation which makes a bad start may have made
but little progress by the time other mutations, which have occurred
no more frequently, have attained complete normality. We should
of course expect to find most cases at the stages where progress is

64 THE EVOLUTION OF DOMINANCE

slowest, and a comparatively large accumulation in any stationary
condition. The relatively rare 'dominant' mutants of Dros&phila
may be regarded either as comparatively new mutations, or more
probably, as regards the greater number of them, as mutations in

TIME

3 2

IN ARBITRARY UNITS

FIG. 5. Trajectories of improvement of the heterozygote, on the supposition that the
modificatory variance depends also on the magnitude of the unmodified effect.

which the heterozygote has been throughout its history so severely
handicapped, that little progress has been made. The greater number
of observed mutations are found, as would be expected, in the resting
stage of complete recessiveness, and in the case of the lethals, whose
condition should be absolutely stationary, the number accumulated
is enormous. With non-lethal mutants, after the heterozygote has
become, within a very minute difference in viability, equivalent to the
wild type, a process of modification of the homozygote may be
expected to commence ; and this for the same level of viability, should,
on the view that the homozygote is not much less modifiable than the
heterozygote, be comparable in speed with the modification of the
latter. The second process would, apart from any difference of
modifiability, presumably be appreciably slower than the first, for
the homozygote may be expected to be initially much the more
heavily handicapped, though its viability may have been, incident-
ally, considerably improved during the process of modification of the
heterozygote. Nevertheless, we must be prepared to admit that in-
numerable mutations may have occurred in the past, of which even
the homozygote has become to all appearances normal, and which

THE EVOLUTION OF DOMINANCE 85

consequently leave no trace for genetic research to reveal. There
appears to be no reason, however, why such factors should not func-
tion in special cases in modifying the effects of rare mutants.

A case of interest in this connexion is presented by the two factors
forked and semiforked in Drosophila melanogaster. Forked is a sex-
linked recessive mutant, in which the bristles of the head, thorax, and
scutellum are shortened, twisted and heavier in appearance, than in
the wild fly. Since the factor is sex-linked, dominance can only
appear in the female, and ordinary females heterozygous for forked
have bristles indistinguishable from those of wild flies. In the course
of Dr. Lancefield's experiments with this factor in 1918, however,
the gene semif orked was discovered ; this gene has no distinguishable
effect upon the homozygous forked females, or upon the forked males ;
it produces, but rarely, a slight shortening of the bristles in normal
flies, but heterozygous females are modified by it into clear inter-
mediates. Semif orked thus acts as a modifier of dominance in forked,
having biochemical effects similar to those factors by the selection of
which, on the view here put forward, its dominance has been acquired.
It is, however, scarcely probable that semiforked is actually one of
these factors, for it is itself a recessive, as judged by its interaction
with heterozygous forked. It may, on the other hand, well be an old
mutation which has reached a stage in modification at which even
when homozygous it exerts scarcely any effect.

Inferences from the theory of the evolution of dominance

One inference that may fairly be drawn from the foregoing con-
siderations is that the widely observed fact that mutations are usually
recessive should not lead us to assume that this is true of mutations
of a beneficial or neutral character. On the contrary, we have reason
to believe that it is confined to a class of mutation which persistently
recurs, with a mutation rate not greatly less than one in a million,
and which has been eliminated with equal persistence by Natural
Selection for many thousands, or possibly millions of generations.
This class of mutation is, and will perhaps always be, of the greatest
value to the plant-breeder and the geneticist, for it supplies them with
their most prized variants, but we have no right on this account to
suppose that it has any special importance in evolution. With
mutations not of this class we have no reason to expect dominance in
either direction. A priori it would be reasonable to suppose that at

66) THE EVOLUTION OF DOMINANCE

the first appearance of a mutation, the reaction of the heterozygote
would be controlled equally by the chemical activity of the two
homologous genes, and that this would generally, though not neces-
sarily in every individual case, lead to a heterozygote somatically
intermediate between the two homozygotes. We should of course not
expect all quantitative differences to be numerically equal, for these
depend upon our methods of measurement, and to take a simple
analogy, the removal of hah* the pigment from a black structure
might well be judged to produce less effect than the removal of the
remainder. To postulate equal functional importance of the two
homologous genes is therefore not to deny the possibility of all
appearance of dominance, but that a general intermediacy of charac-
ter, such as that to which attention has already been called in
heterozygotes between different mutants of the same gene, should be
the prevalent condition. The change brought about in a species by
the acquisition of a favourable mutation will thus generally take
place by two not very unequal steps taken successively in the same
direction. It is interesting that this situation bears some slight
resemblance to the successive mutations in the same direction,
imagined by Weismann.

The case of the evolution of dominance serves to illustrate two
features of Natural Selection which, in spite of the efforts of Darwin,
still constitute a difficulty to the understanding of the theory, when
the latter is illustrated by the active care of the human breeder in
selecting his stock. These are the absence of any intention by nature
to improve the race, and the fact that all modifications which tend
to increase representation in future generations, however indirectly
they may seem to act, and with whatever difficulty their action may
be recognized, are ipso facto, naturally selected. The acquirement of
dominance to harmful mutants cannot properly be said to improve
the species, for its consequence is that the harmful genes are con-
cealed and allowed to increase. There is some analogy here with
Darwin's theory of sexual selection in so far as this is applied to
characters of no use to the organism in relation to its environment
or to other organisms, and to qualities which do not assist the sexes
to discover and unite with one another, but only to qualities which
are preferred by the opposite sex. Even in such cases, however,
sexual selection does give a real advantage to one hah* of the species
in relation to one situation of their life-history, while in the selection

r

THE EVOLUTION OF DOMINANCE 67

of dominance the genetic modification of the whole species results in
the structural modification of an incomparably smaller fraction. If
we adopt Darwin's analogy of a human or super-human breeder
scrutinizing every individual for the possibility of some direct or
indirect advantage, the case of the evolution of dominance shows
well how meticulous we must imagine such scrutiny to be.

We have seen in the previous chapter, in general terms, that the
difficulty of effecting any improvement in an organism depends on
the extent or degree to which it is adapted to its natural situation.
The difficulties which Natural Selection has to overcome are in this
sense of its own creating, for the more powerfully it acts the more
minute and intricate will be the alterations upon which further
improvements depend. The fact that organisms do not change
rapidly might in theory be interpreted as due either to the feebleness
of selection or to the intensity of adaptation, including the com-
plexity of the relations between the organism and its surroundings.
We have no direct measure of either value, and the point at issue
can only be expressed in concrete terms in relation to some definite
change, real or imaginary, in some particular organism. For this
purpose the recessive mutations seem to supply what is wanted, and
the reader who accepts the conclusions of this chapter will perceive
that any maladaptation of the same order of magnitude as these,
and equally capable of modification, would be remedied by Natural
Selection some ten or hundred thousand times more rapidly than
dominance has actually been acquired. To take a more real case, in-
stead of imagining that a whole species were suddenly changed so as
to be as ill-adapted to its conditions as our familiar mutants, if we
suppose that the organic or inorganic environment of the species were
to change suddenly, or that a colony of the species were to find itself
in surroundings to which it was equally ill-adapted, we have equal
reason to suppose that the evolution of adaptive characters would
proceed at the same rate. It might indeed be said that each mutation
is such an experiment in little.

With regard to the precision with which adaptation is in fact
effected we must be careful to remember that all of the heterozygotes
of the different recessive mutations, including, apparently, thousands
of recessive lethals, are genetically different. However indistinguish-
able the end products may be, these are produced by different
developmental processes, even if the ultimate differences are only

68 THE EVOLUTION OF DOMINANCE

intracellular reactions. The fact that they are much alike can only
be interpreted as showing that likeness of this degree is requisite,
even for such approximately normal adaptation as is required of
a rather rare heterozygote. If any appreciable diversity of form were
possible within the range of such approximately equal adaptation
we should surely find it among this multitude of heterozygotes.
Since any differences which may exist between them are certainly
extremely minute we have here a clear indication of the closeness
with which any tolerably successful individual must approach the
specific type, and an upper limit of the magnitude of the differences,
which have a reasonable chance of effecting improvement.

Summary

Examination of the incidence of dominance in mutations observed
to occur, and of other genes which must be regarded as mutants,
shows that in the majority of cases the wild gene is dominant to the
mutant genes, while in a minority of cases dominance is incomplete.
Different mutations of the same wild genes show mutually on the
other hand a regular absence of dominance. If the substitution of
mutant for primitive genes has played any part in evolution these
observations require that the wild allelomorphs must become dominant
to their unsuccessful competitors.

The incidence of heterozygotes of each mutant among the ancestry
of the wild population is, if we may rely upon observed mutation
rates to be of the right order of magnitude, sufficient to account for
the evolution of dominance by the selection of modifying factors.
This process is extremely slow, since the proportion of the popula-
tion effectively exposed to selection is only about 1 in 10,000 or
100,000.

A case has been found in Cotton in which apparently complete
dominance has been acquired by the one of a group of nearly related
species, which shows the corresponding mutation; the anomalous
occurrence of dominance in domestic poultry may be interpreted at>
due to the effects of human selection in flocks liable to be sired by
wild birds.

The theory of the evolution of dominance thus accounts for a con-
siderable body of facts which have received so far no alternative
explanation. If it is accepted it appears to throw considerable light

THE EVOLUTION OF DOMINANCE 69

upon the nature of mutations, and on the intensity of adaptation;
in particular the closeness of the convergence of very numerous
heterozygous genotypes indicates somewhat forcibly that adaptive
significance, sufficient to govern evolutionary change, is to be found
in differences of much less than specific value.

IV

VARIATION AS DETERMINED BY MUTATION
AND SELECTION

The measurement of gene frequency. The chance of survival of an individual gene ;
relation to Poisson series. Low mutation rates of beneficial mutations. Single origins
not improbable. Distribution of gene ratios in factors contributing to the variance.
Slight effects of random survival. The number of the factors contributing to the vari-
ance. Chapter V. The observed connexion between variability and abundance. Stable
gene ratios. Equilibrium involving two factors. Simple metrical characters. Meristic
characters. Biometrical effects of recent selection. Summary.

There was a first occurrence, once for all,
Of everything that had not yet occurred.

SOPHOCLES.

The measurement of gene frequency

IN Chapter II considerable emphasis was laid on the fact that the
heritable variance displayed by any interbreeding group of organisms
has no inherent tendency to diminish by interbreeding, provided
that the variance is due to differences between particulate genes,
which segregate intact from all the genetic combinations into which
they may enter. In such a system any changes in variability which
may be in progress must be ascribed to changes in frequency, in-
cluding origination and extinction, of the different kinds of genes.
In the present chapter we have to inquire into the causes which
determine the degree of variability manifested, or in other words,
into the level of variability at which the origination and extinction
of genes are equally frequent.

It will be sufficient to treat in detail the case of dimorphic factors,
that is of loci to occupy which there are only two kinds of genes
available. It seems probable that the cases in which there are three
or more different kinds of genes present are in most species in a small
minority, and contribute inappreciably to the variance. However
this may be, then- explicit treatment would seem merely to complicate
the statement of the argument, and to elaborate the necessary nota-
tion, without introducing any new principle. In considering di-
morphic factors we shall be concerned with the relative frequency of
only two kinds of genes, which we have represented in previous
chapters by the ratio p : q, and with the causes by which their

VARIATION BY MUTATION AND SELECTION 71

frequencies are modified. It is therefore of some importance to
adopt an appropriate scale on which such changes of the frequency
ratio may be numerically measured. It would of course be possible
to adopt a percentage scale for such measurement, to distinguish
factors according to the percentages of the loci available occupied
by the two types of genes. We should thus distinguish factors in
which each type of gene occupied 50 per cent, of the loci available,
from factors in which the more numerous type of gene occupied
60 or 90 or 99 per cent., and discuss with what frequency factors
might be expected to he in the regions bounded by these values;
what proportions of the factors, that is to say, should be expected
to have their more numerous gene occupying between 50 and 60 per
cent, of the loci, what proportion between 60 and 70 per cent, and
so on. In cases where dominance has been developed we might ask
the same questions respecting the frequency not of the more frequent,
but of the dominant gene ; and would thus distinguish cases in which
from 20 to 30 per cent, of the genes were dominants, from cases in
which the proportion lay between 70 and 80 per cent. For all purposes
of this kind, however, in view of the actual relationships to be dis-
cussed it is more useful to use a scale on which the ratio between the
two frequencies increases in geometric progression. Starting from the
case in which the two frequencies are equal and each gene occupies
50 per cent, of the available loci, we should then regard the frequency
ratios 2:1,4:1,8:1,16:1 and so on, as equal steps of increasing
frequency, although the corresponding percentages are 66-7, 80-0,
88-9, 94-1. Such a scale is symmetrical. If we step off in the opposite
direction we shall arrive at the frequency ratios 1 : 2, 1 : 4, 1 : 8,
1 : 16 with the complementary percentages. Mathematically the
scale we have chosen is equivalent to measuring the frequency ratio
by the variate

z = log- =

If the logarithms are taken to the base 2, our steps will be each of
unit length, while if we use, as is mathematically more convenient,
natural or Naperian logarithms, the steps, while still being of equal
length, will be about 0-7 of a unit. The two practical advantages of
the use of the logarithmic scale for the frequency ratios of a dimorphic
factor are, firstly, that it enables an adequate distinction to be drawn
between the very high frequency ratios such as a thousand million to

72 VARIATION AS DETERMINED BY

one, which can occur in the genes of numerous species, and more
moderate frequency ratios such as 1,000 to 1 which are almost
indistinguishable from them on a percentage scale; and secondly,
that the effects of selection in modifying the gene frequencies are,
on the logarithmic scale, exhibited with the utmost simplicity,
namely by changes of position with velocities that are uniform and
proportional only to the intensity of selection.

For factors which are not sex-linked, each individual will contain
two genes like or unlike each other. If every individual in a species
is thus enumerated, and counted as two, the maximum attainable
frequency ratio will be effectively the ratio which twice the number
of individuals in the species bears to unity. The range of possible
frequency ratios on the logarithmic scale thus depends on the number
of individuals in the species, and it is easy to see that it is increased
by 2 log 10, or 4-6, if the population in the species is increased tenfold.
For example, a species of 10,000,000,000 individuals will give a range
of values from about - 23-7 to + 23-7. Of this range about 5 units
at either end represent cases hi which the less frequent gene exists in
only about 100 or less distinct individuals, or to be more exact, since
1 individual can contain 2 such genes, in about 100 homologous loci.
In these regions it is clear that the rarer gene is, relatively speaking,
in some danger of extinction, and the absolute length of these regions
on our scale will not depend on the number of individuals in the species.
Between these two extreme regions lies a central region in which
both genes are comparatively numerous, at least in the sense that
neither of them will exist in less than 100 individuals. It is the length
of this central or safe region which depends on the magnitude of the
population of the species. For 10,000,000,000 it is about 37 units in
length, for 100,000,000 it has only about 28 units. The logarithmic
scale thus affords a simple demonstration of the important bearing
which population size has on the conservation of variance.

In the hypothetical enumeration of the genes of the population
considered in the last paragraph, no account was taken of the age
or reproductive value of the individuals enumerated. If account is
taken of these there is no limit to the magnitude of the frequency
ratio attainable in either direction, but the distinction between the
relative insecurity of the rarer gene in the extreme regions, and its
relative security in the central region, is still valid. This statement
is based on the circumstance that a gene which exists in a dozen

MUTATION AND SELECTION 73

individuals who, in the sense of Chapter II have low reproductive
value, is in at least as much danger of extinction as one existing in a
single individual whose reproductive value is equivalent to that of the
twelve others put together. For mature forms the probability of sur-
vival must be nearly equivalent. If, however, the reproductive value
we are considering is supplied entirely by immature or larval forms,
normally liable to great mortality, the chance of extinction for a
given amount of reproductive value may be considerably enhanced.
It is therefore convenient to exclude the immature forms altogether
from discussion, and to consider the results of enumeration in which
individuals are only counted when they attain to the beginning of
the reproductive stage of their hie history. We shall count each
generation near the maximum of its reproductive value, and when its
numbers are least. The magnitude of the population of a species can
then be conceived, not by the analogy of a census enumeration, in
which individuals of all ages are counted, down to an arbitrary legal
minimum at birth, but as the number of individuals of each genera-
tion who attain to the reproductive stage. In species having several
generations in the year, the numbers of which are also much affected
by the annual cycle, it is probable that the conclusions to be drawn
as to the effects of population size, will be most nearly applicable to
the normal annual minimum of numbers.

The chance of survival of an individual gene

An individual gene carried by an organism which is mature, but has
not reproduced, will reappear in the next generation in a certain
number 0, 1, 2, 3 etc. of individuals or homologous loci. With bisexual
organisms these must of course be separate individuals, but where
self-fertilization is possible the same gene may be received by the
same individual offspring in each of its two parental gametes, and if
such an individual survives to maturity our original gene will thus
be doubly represented. In general we shall be concerned with the
total number of representations, although it will be convenient to
speak as though these were always in different individuals. The
probabilities that of the offspring receiving the gene, 0, 1, 2 ...
attain maturity will be denoted by

Po> PvP2> »

where, since one of these contingencies must happen,

PO+PI+PZ + = !

74 VARIATION AS DETERMINED BY

In order to consider the chances in future generations we shall first
calculate the appropriate frequencies for the case in which our gene
is already represented in r individuals . In order to do this concisely
we consider the mathematical function

This function evidently increases with x from p0, when x = 0, to
unity when x = 1. Moreover, if the r individuals reproduce inde-
pendently, the chance of extinction in one generation will be pTQ.
The chance of representation by only a single gene will be

IP**?*

and in general the chance of leaving s genes will be the coefficient of
Xs in the expansion of

(/(*))'.

Now, starting with a single gene, the chance of leaving r in the second
generation is pr, and the chance that these leave s in the third
generation will be the coefficient of x1 in

Pr(f(*)Y'

It follows that the total chance of leaving s in the third generation,
irrespective of the number of representatives hi the second generation,
will be the coefficient of x* in

or, in fact, in

/(/(*))•

This new function, which is the same function of f(x) as f(x) is of x,
therefore takes the place of f(x) when we wish to consider the lapse,
not of one but of two generations, and it will be evident that for
three generations we have only to use f{f(f(x))}, and so on for as
many generations as required.

There are good grounds for supposing that if, as has been suggested,
enumeration is confined to the condition of early maturity the
function f(x) will always have, to a good approximation, the same
mathematical form. If we consider, for example, any organism capable
of giving rise to a considerable number of progeny, such as a cross-
pollinated cereal plant, it appears that each sexually mature indi-
vidual is the mother of a considerable number, let us say 40, mature
grams, and the father, on the average, of an equal number. Into each

MUTATION AND SELECTION 75

of these grains any particular gene has an independent probability of
one half of entering. But since, of these grains only 2, on an average,
will be represented in next year's crop by mature plants the chance
of both entering into the grain and of surviving in it is only 1 in 80.
The probabilities therefore of the gene reappearing in the following
year in 0, 1, 2 ... individuals will be the coefficients of a0, x1, x2, . . .
in the expansion

/79 1
(,80 + 80

so

These coefficients are already very close to the terms of the
Poisson series.

,-,)

i liil

' '2'6'24J

1 1

<rr />— A I

*• 1'2!'3!'

and would become identical with them if the arbitrary number 80
were increased indefinitely. The departure from the Poisson series
is in fact ascribable to artificial assumptions which for simplicity
have been allowed to enter into the calculation. We have arbitrarily
assumed that each plant produces the same number of grams,
whereas in reality this number will be variable. The number of pollen
grains also from each plant which enter into perfect seeds will vary,
and the effect of this variability will be to change the distribution
very slightly in the direction of the limiting Poisson distribution. In
fact it is probable that in so far as the binomial distribution obtained
above differs from the limiting form, it differs in the wrong direction,
for the variability in the number of grains on different plants seems
to be slightly greater than what is required in a perfect Poisson series.
The general character of the Poisson series which makes it appro-
priate to our problem is that it arises when a great number of indi-
viduals enjoy each a small independent chance of success; if the
number of individuals and the chance of each are such that on the
average c succeed, then the numbers actually succeeding in different
trials will be distributed according to the series

- - \

}C'2P3!' /'

and this may generally be regarded as a good approximation to the
chances of individual gametes produced by a single mature individual.

76 VARIATION AS DETERMINED BY

If the gene confers no selective advantage or disadvantage, c will
be equal to unity ; the values of p0, plt p2 . . . will be given by the
Poisson series

ill! \

2!' 3!' ' ' i

and the function f(x) takes the form

or

f(x) - e*-
TABLE 2.

Number

of
Generations.

Probability of Extinction.

Difference.

Probability of Survival.

No
Advantage.

1 per cent.
Advantage.

No
Advantage.

1 per cent.
Advantage.

1

0-3679

0-3642

0-0037

0-6321

0-6358

3

0-6259

0-6197

0-0062

0-3741

0-3803

7

0-7905

0-7825

0-0080

0-2095

0-2175

15

0-8873

0-8783

0-0090

0-1127

0-1217

31

0-9411

0-9313

0-0098

0-0589

0-0687

63

0-9698

0-9591

0-0107

0-0302

0-0409

127

0.9847

0-9729

0-0118

0-0153

0-0271

Limit

1-0000

0-9803

0-0197

0-0000

0-0197

Moreover if the gene in question is increasing in frequency in each
generation in the ratio c : 1, we shall have similarly

f(x) = c^-W.

Having obtained these forms for f(x) we may trace the survival,
multiplication or extinction of the descendants of single individual
genes, by a mere repetition of the process of substituting f(x) for x.
Table 2 shows in the first column the number of generations which
have elapsed from the starting-point, these numbers having been
chosen so as to follow the course of the changes over a large number of
generations, in a moderately compact table. These changes are most
rapid at first, so that we have chosen successive steps of 1, 2, 4, 8
generations and tabulated the conditions reached after the total
expiration of 1, 3, 7, 15, 31, 63 and 127 generations. The second
column shows the probability of extinction, at each stage, for genes
having no selective advantage or disadvantage. The numbers may
also be read, ignoring the decimal point, as the number of cases out of

MUTATION AND SELECTION 77

.10,000 in which the descendants of the original gene will have
become extinct. The proportion of extinctions in the early genera-
tions is extremely high, nearly 3 in 8 are extinguished in the first
generation, and of the remaining 5, 2 have failed by the third genera-
tion. In 15 generations nearly 8 out of 9 will have failed. As we
proceed extinctions become very much rarer, only 2-87 per cent,
are lost between the 31st and the 63rd generation, and only 1-49 per
cent, between the 63rd and the 127th when there are still 1-53 per
cent, surviving. The survivals may best be followed hi the 5th
column, in which it will be seen that with the steps we have chosen,
the number of survivors tends increasingly closely to be halved at
each step ; in fact when n is large the chance of survival for n genera-
tions is very nearly 2jn.

For comparison the corresponding figures have been tabulated in
adjacent columns for genes for which c = 1-01, and which con-
sequently enjoy an advantage of 1 per cent. ; the differences are
shown in the 4th column. It will be seen that the selective advantage
amounts ultimately, in the limit when n is increased indefinitely, to
survival in just less than 2 per cent, of the cases originally started,
and of this advantage very little is gained in the early stages where
extinction is rapid. Of 10,000 mutations enjoying a 1 per cent,
selective advantage, and which have already reached the stage of
existence in one sexually mature individual, 3,642 will fail to transmit
the advantageous gene to any descendant, whereas with no selective
advantage whatever, only 3,679 will so fail. Even after 31 genera-
tions the number surviving out of 10,000 will be only 687 against an
expectation of 589 where no selective advantage is enjoyed. The fact
is, that a selective advantage of the order of 1 per cent., though
amply powerful enough to bring about its evolutionary consequences
with the utmost regularity and precision when numbers of individuals
of the order if 1,000,000 are affected, is almost inoperative in com-
parison to random or chance survival, when only a few individuals
are in question. A mutation, even if favourable, will have only a very
small chance of establishing itself in the species if it occurs once only.
If its selective advantage is only 1 per cent, it may well have to occur
50 times, but scarcely in mature individuals as many as 250 times,
before it establishes itself in a sufficient number of individuals for its
future prospects to be secure.

The fact that a mutation conferring an advantage of 1 per cent.

78 VARIATION AS DETERMINED BY

in survival has itself a chance of about 1 in 50 of establishing itself
and sweeping over the entire species, shows that such mutations
cannot occur with any great total frequency before this event is
realized, or at least rendered certain, by the initial success of one of
their number. The odds are over 100 to 1 against the first 250
mutations of such a favourable type all perishing. Consequently
the success of such a mutation must become established at a time
when the mutation rate of the mutation in question is extremely low,
for in a species in which 1,000,000,000 come in each generation to
maturity, a mutation rate of 1 in a thousand million will produce one
mutant in every generation, and thus establish the superiority of the
new type in less than 250 generations, and quite probably hi less than
10, from the first occurrence of the mutation ; whereas, if the new
mutation started with the more familiar mutation rate of 1 in
1,000,000 the whole business would be settled, with a considerable
margin to spare, in the first generation. It is to be presumed that
mutation rates, like the other characteristics of organisms, change
only gradually in the course of evolution; whereas, however, the
mutation rate of an unfavourable mutation will be allowed to
increase up to 1 in 1,000,000 or even higher, without appreciably
affecting the character of the species, favourable mutations can
scarcely be permitted to continue occurring for long, even at rates
1,000-fold less, and we cannot exclude the possibility that a pro-
portion of the favourable mutations that occur and are ultimately
adopted, may have mutation rates so low that they occur sporadic-
ally, perhaps once only in thousands of generations. A quantitative
comparison of the mutation rates current in homologous mutations
in different allied species might well throw light on the difficult
question as to how rapidly mutation rates should be thought of as
increasing or decreasing.

When there is no selective advantage or disadvantage, the fraction
of cases in which extinction has not taken place after n generations
is, as has been seen, approximately 2/n. It follows, since in the
absence of selection the expectation hi any future generation is equal
to the number now living, that the average number of individuals
in which these surviving genes will each be represented, is \n. This
number will, however, vary greatly in different cases and it is of
some interest to obtain the actual form of its distribution.

This can be done by observing that, if the frequency with which

MUTATION AND SELECTION 79

each number occurs is the coefficient of the corresponding power in
the expansion of

*(*),

then substituting e* for x, we have in <f> the generating function of
the moments of the distribution. Now to advance one generation
is to substitute

e*"1 for x

or e**-1 for e*

or e'-l for t ;

if therefore ^ fa, fat . . . are the moments, about zero as origin, of
the distribution in the earlier generation, those in the latter generation
will be the coefficients of t in the expansion of

in powers of t ; and if these are denoted by ^{, p,'z, fj,'3, ... we have
the relations

th. = Pi

and so on.

Since all the moments are initially unity it is easy to see from these
that fa will increase proportionately to n, ^ to nz, /n4 to n*, etc. when
n is large. Moreover, since in general

the coefficient of n?-1 in ^tp is %p times the coefficient of nP~z in /i^_j ;
starting therefore with /^ = 1 we find

to a first approximation, when n is large.

Knowing the moments we may now infer the actual form of the

80 VARIATION AS DETERMINED BY

distribution, for the moments we have obtained will be reproduced
if the probability of exceeding x individuals is

e-2x/n

An inference of some interest is that hi the absence of favourable
selection, the number of individuals having a gene derived from a
single mutation cannot greatly exceed the number of generations
since its occurrence. Actually, the chance is less than 1 in 1,000
that x should exceed 3£w. If, therefore, a mutant form exists in as
many as 1,000 million individuals in each generation, we may be
confident either that its numbers have been increased, at least up to
a certain point, by selection, which is a relatively rapid process, or
by recurrent mutation unopposed by selection, which must usually
be a much slower process, or if we must suppose that it has originated
in a single act of mutation and owes its present numbers to chance
increases, that the process has been going on for at least 280 million
generations, which makes it much the slowest and, for such high
numbers, the least probable process of all.

A similar investigation of the distribution of the numbers, attained
by the descendants of individual genes enjoying a small selective
advantage, shows that the ultimate form of the distribution is the
same in this case also. The probability of exceeding the number x
after n generations may now be written

e-2(c-l)zc~n

showing of course that, as c exceeds unity, the numbers are certain
to exceed any specified value of x in a sufficiently great number of
generations.

The formula should represent the distribution correctly so long as

cn

is still a small fraction of the number of individuals in the species,
but it evidently represents only the distribution of the numbers
derived from mutations all of which occur in the same generation.
This is an artificial and unnecessary limitation, since, as we have seen,
with advantageous mutations those which occur earliest will first
have an opportunity of establishing themselves, and will, after com-
paratively few trials, preclude the necessity for further mutations of

MUTATION AND SELECTION 8l

the same sort. We must suppose that when favourable mutations
occur they have seldom occurred before, and that their mutation rate
is generally increasing. As to the nature of such increase we have no
direct knowledge, but if it is dependent upon a change in the geno-
typic constitution of the species we must suppose it to be gradual,
and since negative mutation rates are meaningless the simplest possible
assumption is that the relative rate of increase per generation may
be represented by a small number k, so that the mutation rate
increases by the factor ek in each generation.

On this assumption the number of mutations which at any stage
are already represented in more than x individuals, will be pro-
portional to

which turns out, when x is sufficiently large for (c-l)x to be as
great as 4 or 5, and large compared to k/logc— 1, to be very nearly
proportional to

y, — fc/IOgC

In this formula we may recognize the element log c, which is the
amount by which the mutant gene avails to increase the Malthusian
parameter of Chapter II, or approximately the selective advantage,
0-01, of our numerical illustrations. It measures the relative rate of
increase of frequency of the gene in question, just as k measures that
of its mutation rate. If it be supposed that the mutation rate depends
wholly upon the presence of certain groups of genotypes, we must
suppose k and log c to be quantities of the same kind, and of the
same order of magnitude, but not necessarily approximately equal.
If we consider that, of the gene substitutions capable of influencing
any particular mutation rate, some may be progressing in one
direction and some in the other, and that in general the increases in
mutation frequency due to the increasing frequency of some geno-
types, will be partly compensated by the disappearance of other
genotypes in which the mutation also occurs, it appears probable
that k must very frequently be the smaller quantity. If we confine
attention to mutations possessing a selective advantage of just 1 per
cent., this amounts to saying that when such mutations just begin
to occur, the mutation rate is not increasing so rapidly as to double

3653 JUT

82 VARIATION AS DETERMINED BY

or treble itself within 100 generations, while not excluding the
possibility that the increase in this period should be 10 per cent, or so.
The practical consequence which follows if the ratio k/log c is small
is that, of the mutant genes which ultimately pervade the species
a large proportion are derived from that one individual mutation
which first has the good fortune to establish itself in appreciable
numbers, while only a negligible fraction can be contributed by the
aggregate of all similar mutations which achieve a less or later success.
Whereas if kjlog c were large the mutant genes would be derived,
though in unequal numbers, from a large number of separate muta-
tions, no one of which would contribute a large fraction of the total.

It should be noticed that in respect to the initial stages in which
survival is determined, c is the absolute rate of multiplication of the
mutant type, and only approximately to be equated to its selective
advantage over other genotypes. The difference becomes plain if
we consider not, as hitherto, a stationary population, but one in-
creasing or decreasing in numbers. In an increasing population
mutations possessing no selective advantage, or indeed mutations
at a selective disadvantage, provided this is less than the rate of
increase of the species as a whole, will have a finite chance of avoiding
extinction; while with a declining population, even mutations
possessing a slight selective advantage, if this is less than the rate of
decrease of the species, will be in a worse position than neutral muta-
tions in a species of stationary size. In consequence growing popula-
tions receive greater accessions to their variability than stationary
populations, while declining populations receive less; and if the
intensity of selective actions is the same in both cases, we may expect
growing populations to grow more variable, and declining populations
to become less so by a process which is distinct from the effect of
population size itself upon variability. In part at least the effect of
increase will anticipate the consequences of the effect of size, for it
will be shown that with larger populations statistical equilibrium
will be established with a larger variance, and the direct effect of
increasing population will be to increase the variance without waiting
for the slower process of the establishment of a statistical equilibrium
to show its effects.

The scope of this cause is limited by the actual rates of increase or
decrease of natural populations, and I suppose that such changes are
seldom so great as an increase of one-hundredfold in 10,000 genera-

MUTATION AND SELECTION 83

tions, or about 1 in 2,000 in each generation over such a period.
How important may be the contribution of mutations conferring an
advantage or disadvantage of less than 1 in 2,000 is quite uncertain.
It must certainly be greatest where adaptation, in the sense developed
in Chapter II, is most intense, and it would at least be premature to
assume that such minute changes are generally either rare, or without
substantial evolutionary effects, although such may in fact be the
case.

The distribution of gene ratio in factors contributing
to the variance

We are now in a position to consider the relationships which must
exist between the genetic variability maintained in a species, and the
frequency of occurrence of mutations. The fundamental theorem
proved in Chapter II will have prepared us to find that the variance
maintained in fitness to survive must be ultimately connected with
the frequency of occurrence of favourable mutations ; although a por-
tion of it is generated by the occurrence of persistent unfavourable
mutations of the kind considered in Chapter III, and is effective only
in continually freeing the species from these defects. Such persistent
unfavourable mutations will also contribute to the variance main-
tained in all other measurable characters, and further contributions
must be supplied by those cases in which the gene ratio is in stable
equilibrium under selective influences, to be considered more fully in
Chapter V, and by cases in which the advantages of a character in one
region or station occupied by the species are counteracted by dis-
advantages in alternative situations, a case the evolutionary con-
sequences of which will be considered in Chapter VI. Our immediate
purpose is to discuss the maintenance by mutations of that more
elusive and fluid portion of the variance which is maintained by
favourable mutations, and by those having a selective advantage or
disadvantage so small that it may be neglected. Part of our problem
will be to determine how small such selective advantage or disadvan-
tage must be. The favourable mutations must, as was shown in
Chapter II, be generally exceedingly minute in their somatic effects,
and as we have seen in this chapter they must individually possess
mutation rates so low that we are in fact confronted not with a calcu-
lable stream of mutations of each type, but with individual and
sporadic occurrences. Mutations having nearly neutral effect might

84 VARIATION AS DETERMINED BY

on the contrary have time to attain considerable mutation rates, for
even if the rates were high, some million generations or more would be
required to establish the new type, and this would give time for the
mutation rate to rise from its initial inappreciable value. Apart from
this slight difference the two cases may be treated together.

To distinguish the parts played by the different elements of the
problem we need only consider three cases. First the distribution of
gene ratio when, in the absence of selection or mutation, the variance
is gradually decaying through the random extinction of genes. Next,
the distribution when the variance is maintained by new mutations
uninfluenced by selection ; and finally the distributions appropriate to
slight selective advantage or disadvantage.

The most powerful method of treating the first two of these
problems is that of obtaining a functional equation for the series of
terminal frequencies. If the number of individuals breeding in each
generation is n, a large number of many millions or thousands of
millions, the possible values of the gene frequency p are l/2n, 2/2n,
.... ; these possible values are very numerous, and in the greater
part of its range of distribution we may conveniently consider p as
a continuous variate. At the extremes, however, a more exact treat-
ment will be necessary, and here we shall make the simplifying
assumption that the form of the terminal distribution, when statistical
equilibrium is established, is not affected by the size of the population.

If now 6l5 62> &3> ..... stand for the frequencies at the values
p = l/2n, 2/2n, 3/2n, ..... '.we may define a function

<f> (x) = b±x + b2xz +

and the conditions of statistical equilibrium will yield a functional
equation, the solution of which will give the frequencies 6X, 62, 63,
..... , and therefore the distribution of the gene ratio. In the case of
extinction without mutation, we may, in particular, ask what values
the coefficients 6 must have in order that just one gene shall be ex-
terminated in each generation. The sum of the values of these co-
efficients will then give the number of factors contributing to the
variance, and from this we can determine the relation between the
variance and its rate of decrease by random extinction.

If extermination takes place at the rate of one gene in each genera-
tion, we may suppose that hah* of these consist of cases in which the
number of genes present is reduced from 1, 2, 3, .... to 0, and hah*

MUTATION AND SELECTION 85

to cases in which it is increased from 2n - 1, 2n - 2, 2n — 3, ..... to
2n. Genes represented in 0 individuals will of course supply the co-
efficient of #° in <f>, so that after one generation the function <f> repre-
senting the distribution at one terminal must be increased by £.

But in one generation we have already seen that <f>(x) will be
replaced by

consequently the equation to be satisfied by $ is

To facilitate the solution of functional equations of this sort, it is
necessary to consider a function uv of an argument v such that

Uv+, = e""-1.

If this equation is satisfied by any function /(v), it will evidently
also be satisfied by F(v) =f(v + k), consequently we may assign
arbitrarily the value u0 = 0, from which uv, if v is any positive
integer, may be obtained by direct substitution. In practice values of
u for non integral v are obtained by interpolating in the series of
integral values, at about v — 20, and calculating lower values from
the interpolates by means of the relation

We may now write the functional equation for <j> in the form

^ (uv+i) ~<f> (uv) =$>

from which it appears that <f> must be the same function of x as %v is of
u. The initial frequencies will therefore be obtained from the differen-
tial coefficients of v with respect to u at u = 0, while the law of
frequencies for larger values of p will be inferred from the behaviour
of the function v as u tends to unity.
Now, putting

1

«% • — •

V V 1 9

l-uv'
we have the recurrence formula

1 1 1

y+l ~~ 1-e-1/"" * 2 12 vv 720 v3'
so that as v tends to infinity, u must tend to unity, and vv to

2 e

where the numerical value of c is found to be about 0-899144. The

86 VARIATION AS DETERMINED BY

result shows that \v(\-u) tends to unity with u, and therefore that
the frequency at p = r/2n tends to unity as r is increased.
Moreover it follows that

1 1 ,

2 v = v- -logv-c'

where c' tends to about 1-014649 as v tends to infinity, consequently

U

tends to about - 0-014649 when u = 1. Apart from this finite portion
of the frequency, the distribution is therefore given by the expansion
in a Maclaurin series of

Js IT /i \

l-x 6
5 11 17

and the coefficients of this series may be taken as a second approxima-
tion to the frequencies of factors, the rarer genes in which appear in

1, 2, 3, loci.

The actual values of the earlier coefficients may be obtained, though
with decreasing precision by tabulating the function uv ; these are
shown in Table 3.

TABLE 3.
Terminal frequencies of factors suffering extinction.

Second Actual

Approximation. frequency. Difference.

1 0-833333 0-818203 -0-015131

0-916667 0-916762 +0-000096

0-944444 0-944923 +0-000479

0-958333 0-958266 -0-000067

0-966667 0-966634 -0-000033

0-972222 0-972225 +0-000003

from which it appears that nearly the whole of the small discrepancy
0-014649 is accounted for by the first few terms, and that thereafter
the frequency is well represented by the values 1 - 1/6 r. The terminal
frequencies are shown in Fig. 6.

The total number of factors in such a distribution may now be
estimated to be

2 In - ^ (y + log 2 n) - 0-014649J

MUTATION AND SELECTION 87

where y is Euler's constant 0-577216. The remainder of this expres-
sion may be neglected in comparison with 2n, so that the solution
attained shows a decay of variance of only one part in 2n in each
generation.

i-o

i-o

I 23456789

FIG. 6. Frequencies with which factors are represented by 1, 2, 3, ... genes in the
whole population, in the case of steady extinction without mutation. The upper line
represents unit frequency at each value, which is approached for the higher values.
Random survival will exterminate genes at the rate of one in every two generations,
while leaving the distribution exhibited unchanged.

This is an extremely slow rate of decay ; if the variance of species
could be imagined to be ascribable to factors unaffected by selection,
and if no new mutations occurred, the variance would decay ex-
ponentially so as to be reduced after r generations hi the ratio

e-r,'2n

it would therefore halve its value in 2n log 2, or about l'4n generations.
No result could bring out more forcibly the contrast between the
conservation of the variance in particulate inheritance, and its dissi-
pation in inheritance conforming to the blending theory.

In a previous attack on this problem I was led by an erroneous
method to the correct distribution for the factors contributing to the
variance in a state of steady decay, but gave the time of relaxation as
4n instead of 2n generations. Professor Sewall Wright of Chicago,
who had arrived by an independent method at the correct result,
drew my attention to the discrepancy and has thus led me to a more
exact examination of the whole problem.

The extremely slow rate of the natural decay of the variance is due
to the fact that the great majority of factors possess gene ratios

88 VARIATION AS DETERMINED BY

which are not extremely unequal. The distribution of z for this case
is shown in Fig. 7, where it will be seen that for nearly all factors z
lies between +6, and therefore that the rarer genes scarcely ever
occupy less than 1/400 of the loci available, and thus are hi little
danger of extinction.

-2 o

VALUES OF

FIG. 7. Distribution of the measure of gene-ratio z, when the variance is in a state
of steady decay, with neither mutations nor selection. The time of relaxation is now
twice as many generations as the number of parents in each generation.

The method first developed has certain advantages for examining
the frequency distribution in the central region. If 6 is any measure
of gene frequency, the frequency in any differential element dd, may
be represented by ydd, and the condition of statistical equilibrium
may be put in the form of a differential equation for the unknown
function y. Using the variate defined by

cos 6 = l-2p

where 6 is an angle in radian measure, which increases from o to -n as p
increases from 0 to 1, 1 obtained in 1922 the equation, like that of the
conduction of heat,

dy J_e%

dr " 4n 86*

which with the solution y = sin 0, leads to a condition of steady decay
with tune of relaxation equal to 4w. generations. The correct differen-
tial equation is, however,

By Id, 1 82y

which while admitting the same solution yields the correct time of
relaxation.

MUTATION AND SELECTION 89

In the second case to be considered, in which the variance main-
tained is in statistical equilibrium with a constant supply of fresh
mutations, we may apply this method at once by putting Byfdr = 0.
Integrating the right hand side we obtain

|| +ycot9 = A,
where A is some constant, whence

o

— (ysinfl) = 4sin0,

y sin 6 = -A cos 6 + B,
y = B cosec 6 - A cot 6.

The symmetrical solution makes y proportional to cosec 6. In the
variatez this is a flat-topped distribution, all equal intervals dz being
equally probable, at least in the central portion for which alone the
differential equation is valid. Since when 6 = rr, cosec 6 + cot 6 = 0
we may consider also the solution

y = B (cosec 6 + cot 0)

appropriate to the case in which all mutations are taken to occur
at 6 = 0.

In either case the integral over the whole range is infinite, owing to
the rapid increase of y at 0 = 0. It does not follow that the total
number of factors is infinite, for it is exactly in this region that the
differential equation is invalid. In terms of p the frequency element
(cosec 6 + cot 6) is equivalent to

2qdp _ dp
~2pq ' ~p

so that the unsymmetrical solution obtained is one in which the
frequency at p = r[2n is proportional to I//', at least when r is large.
The total frequency will then evidently involve log (2n), but to
determine its value the examination of the terminal conditions is in
this case essential.

If <f>(x) again represent the function, the coefficients of the expansion
of which in powers of x are the frequencies maintained at p = l/2w,
2/2/t, . . , by a single mutation in each generation, the functional
equation for <f> is now

f(tf>-») -*(*)*!-*,
in which equation the left hand side represents the change in <f>(x) due

3653

90 VARIATION AS DETERMINED BY

to random reproduction for one generation, while the effect of a single
mutation must be to increase the coefficient of x by unity, and to
reduce the absolute term (z°) by unity. To solve the equation we may
again utilize the device of writing uv for x, and obtain the equation

^K*.i)-^K) = 1-«V
Now, from the equation

«rtl = *«*-!,

it appears on differentiating with respect to v, that

or that log u'v+1 - log u'v = uv - 1 .

Hence the equation for <f>, may be written

<t> («H-I) - ^ W = ~ (log W'H-I - log O

an equation which is satisfied if <f>(uv) differs from - log u'-, by a con-
stant. The constant part of (f>(x), representing the frequency of the
factors not represented in any individual is of course arbitrary, and on
the convention that <f> (0) = 0, we have the solution

(f>(uv) =logu'0 -logu'v

or, if v stands for the differential coefficient of v with respect to u

4(u) =logv'-logv;
= logv' -0-492502
this being an empirical evaluation of the constant term.

Now as u approaches unity, we have seen that v increases pro-
portionately to 2/(l -u), and therefore log v' tends to equality with
log 2-2 log (1 -u) ', apart from a finite discrepancy in the terminal
frequencies, and frequencies will be given by the coefficients of the
expansion

-21og(l-aO =

so that the frequency at p = r}2n approaches 2/r as r is increased, in
accordance with the solution found from the differential equation.
The first few actual coefficients are :

TABLE 4.
Terminal frequencies for factors maintained by mutations.

Approximation.

Actual.

Excess.

1

2-000000

2-240917

+0-240917

2

1-000000

0-953776

-0-046224

3

0-666667

0-671864

+0-005197

4

0-600000

0-601096

+0-001096

6

0-400000

0-399762

-0-000238

MUTATION AND SELECTION 91

The total number of factors maintained in the population by one
new mutation in each generation will be the sum of the 2n first co-
efficients of the expansion of <f> (x), or

2(y + log 2n) + 0-200645.
For values of n from a million to a billion, the following table shows

2-0

•2-0

I I I I I I I

Fid. 8. Frequencies with which factors are represented by 1, 2, 3, ... genes in the
whole population, in the case when the variation is maintained by fresh mutations at a
constant level. For one new mutation in each generation the frequency for r genes is
nearly 2/r.

the number of factors contributing to the specific variance for each
one occurring per generation :

TABLE 5.
n. Number of factors.

106

107

108

109

1010

1011

10ia

30-4
35-0
38-6
44-2
48-8
53-4
58-0

Fig. 8 shows the distribution of the terminal frequencies. It will be
observed that a considerable ' head ' of new mutations is needed to
maintain even low frequencies at the central values. The number
of these central values is, however, so great that the numbers
maintained even by only a single mutation in each generation are, as
table 5 shows, considerable, and practically proportionate to the
range in the values of z possible for a population of given size.

92 VARIATION AS DETERMINED BY

If the frequency of a gene is favoured by selection so that log p/q
is increased in each generation by an amount a supposed small, then
in one generation

8p = apq
and

80 = a^/pq = \ a sin 6.

The effect of selection is thus to produce a flux \ay sin 6, and our
differential equation takes the form

For statistical equilibrium, maintained by mutations, we now require
that

8y

-£ + y cot 6-2 any sin 6 = A

od

which may be put in the form

o

—

ee

or ys\nde*ancoa0 = \Asui6

performing the integration, this leads to

(y = cosec 6) (— + Be~2 an cos * J

The value of the flux

1 1 1 dy A

- ay sin 0 y cot 0 £- = —

O *^ yl <wt ** >4 JM Q L) >4 JM

Z 471 471 OV 471

is \a times the coefficient of cosec 0.

The solution appropriate to a supply of mutations at the rate of one
in each generation having each a small selective advantage a, must
be equal to 4 cosec 0 at 0 = 0, while at 0 = TT where no mutations are
occurring, it must be proportional to sin 0. The appropriate form is

4 COSeC 0 fj_ ^a.a+.e.ft].

l_e-4«» I j '

for which the frequency in the range dp is

2dp l-e-4"™
~^q~ i -e-4an

When q = 1 this evidently gives a terminal distribution similar to

MUTATION AND SELECTION 93

that given by mutations without selective advantage, while when q
tends to zero, we have

8 an

_ e-4on

dp,

appropriate to extinction without mutation, the rate of extinction
being 2 a/(l - e~*an), which must represent the probability of ultimate
success to a mutation with small selective advantage a. When a = 0,
this probability tends to the limiting value 1/2 n, which is the prob-
ability of success of a mutation without selective advantage, and is
not effectively increased so long as 4 aw is a small quantity ; if 4 an is
neither large nor small the full formula is required, but if 4 aw is large,
the exponential factor is negligible, and the probability of success is
given very nearly by 2 a. The frequency distribution in this case is
represented by

pq

in which the second term is only appreciable for small values of q, where
a constant frequency San dp, or 4 a in each possible value of p is
maintained, as is appropriate to the extinctionof 2 a in each generation.

The differential equation is valid for values of a which make an
large, but requires that a2n should be small. The exact treatment of
selection rates less extremely small than those here dealt with, would
evidently involve much more complex expressions, but would not
probably differ essentially from that appropriate to very small
selections.

The corresponding selection for the equally important case of
mutations with a small selective disadvantage, may be found by
changing the sign of a. The chance of success is now always less than
Ij2n, being

2a
e^n-\ '

and is in all cases negligible. The distribution has a frequency in the
range dp

2dp e4ana - 1

pq e*an — 1
which, when an is large, is simply

2dp

—£• e~
pq

Aanv

94 VARIATION AS DETERMINED BY

giving a total number of factors nearly 2 log (l/2a), so long as 4 aw is
large, for each such mutant per generation.

Thus disadvantageous mutations, unlike those which are advan-
tageous, or practically neutral (an small) maintain no more factors
contributing to the variance of numerous species than of rare species.
The calculations refer, of course, to the variation maintained by a fixed
number of mutations, and take no account of the fact that in abun-
dant species there will be many more individuals in which mutations
may occur, in each generation.

The analysis shows how very minute must be the selective intensity
acting on a factor, before we can count it as neutral either for the pur-
pose of evaluating the probability of a sporadic mutation establishing
itself in a species, or in considering the relation between mutation rate
and the variance maintained. In either case we are concerned with
the product an found by multiplying the selective advantage by the
number breeding in each generation. In respect of survival small
deviations of this quantity from zero exert a considerable effect, the
chance of survival, for example, is increased more than fiftyfold as
an increases from - 1 to +1. The contribution to the variance is less
sensitive, since this depends little on the terminal frequencies and
principally on the central frequencies; broadly speaking neutral
mutations contribute half as much to maintaining the variance as is
contributed by those with a substantial selective advantage. If an
is - 2-5 the contribution is a tenth, while at + 2-5 it is nine-tenths of
the full value. Evidently in a population of a thousand million, only
those gene contrasts, which possess an equipoise of advantage within
at most a few parts in a thousand million, can be regarded as neutral.
The distribution for favourable mutations from these minute ad-
vantages up to advantages a millionfold greater must be all very
similar, the probability of falling in equal ranges dz being nearly con-
stant over the whole range of possible values. Disadvantageous
mutations are confined to smaller and smaller values of the gene
ratio as the disadvantage increases, until while the disadvantage is
still very minute, the only appreciable contribution will be that made
by mutations having appreciable or high mutation rates.

Although for the same number of neutral or beneficial mutations
per generation, abundant species will maintain a larger number of
factors contributing to the variance, than will rarer species, yet this
is due principally to the greater range of the values of z available. The

MUTATION AND SELECTION 95

additional factors will then have somewhat extreme gene ratios, and
will therefore contribute little to the measurable variance. The great
contrast between abundant and rare species lies in the number of
individuals available in each generation as possible mutants. The
actual number of mutations in each generation must therefore be
proportional to the population of the species. With mutations having
appreciable mutation rates, this makes no difference, for these will
reach an equilibrium with counterselection at the same proportional
incidence. The importance of the contrast lies with the extremely
rare mutations, in which the number of new mutations occurring
must increase proportionately to the number of individuals available.
It is to this class, as has been shown, that the beneficial mutations
must be confined, and the advantage of the more abundant species in
this respect is especially conspicuous.

The very small range of selective intensity in which a factor may be
regarded as effectively neutral suggests that such a condition must in
general be extremely transient. The slow changes which must always
be in progress, altering the genetic constitution and environmental
conditions of each species, must also alter the selective advantage of
each gene contrast. Slow as such changes in selective advantage must
undoubtedly be, the zone separating genes possessing a definite
selective advantage from those suffering a definite selective dis-
advantage is so narrow, of the order of the reciprocal of the breeding
population, that it must be crossed somewhat rapidly. Each success-
ful gene which spreads through the species, must in some measure
alter the selective advantage or disadvantage of many other genes.
It will thus affect the rates at which these other genes are increasing
or decreasing, and so the rate of change of its own selective advantage.
The general statistical consequence is that any gene which increases
in numbers, whether this increase is due to a selective advantage, an
increased mutation rate, or to any other cause, such as a succession
of favourable seasons, will so react upon the genetic constitution of
the species, as to accelerate its increase of selective advantage if this
is increasing, or to retard its decrease if it is decreasing. To put
matter in another way, each gene is constantly tending to create /
genetic situations favourable to its own survival, so that an increase C
in numbers due to any cause will in its turn react favourably upon the
selective advantage which it enjoys.

It is perhaps worth while at this point to consider the immense

96 VARIATION BY MUTATION AND SELECTION

diversity of the genetic variability available in a species which
segregates even for only 100 different factors. The total number of
true-breeding genotypes into which these can be combined is 2100,
which would require 31 figures in the decimal notation. The number
including heterozygotes would require 48 figures. A population of
a thousand million or a billion individuals can thus only exhibit the
most insignificant fraction of the possible combinations, even if no
two individuals are genetically alike. Although the combinations
which occur are in all only a minute fraction of those which might
with equal probability have occurred, and which may occur, for
example, in the next generation, there is beyond these a great
unexplored region of combinations none of which can be expected to
occur unless the system of gene ratios is continuously modified in the
right direction. There are, moreover, millions of different directions
in which such modification may take place, so that without the
occurrence of further mutations all ordinary species must already
possess within themselves the potentialities of the most varied
evolutionary modifications. It has often been remarked, and truly,
that without mutation evolutionary progress, whatever direction it
may take, will ultimately come to a standstill for lack of further
possible improvements. It has not so often been realized how very
far most existing species must be from such a state of stagnation, or
how easily with no more than one hundred factors a species may be
modified to a condition considerably outside the range of its previous
variation, and this in a large number of different characteristics.

VARIATION AS DETERMINED BY MUTATION
AND SELECTION (continued)

The observed connexion between variability and abundance. Stable gene ratios.
Equilibrium involving two factors. Simple metrical characters. Meristic characters.
Biometrical effects of recent selection. Summary.

The observed connexion between variability and abundance

IN the second chapter of the Origin of Species Darwin summarizes
a study of the causes of variability, based upon a statistical investiga-
tion of the number of well-marked varieties recorded in different
species of plants. He was, perhaps unfortunately, dissuaded from
publishing his actual tabulations, but gained the concurrence of
Hooker to the general conclusions that ' Wide ranging, much diffused,"1
and common species vary most'. Darwin was concerned to show
that it was not merely that wide ranging forms give rise to local
varieties in reaction to different inorganic and organic environments,
but also that, 'In any limited country, the species which are most
common, that is, abound most in individuals, and the species which
are most widely diffused within their own country (and this is a
different consideration from wide range, and to a certain extent from
commonness), oftenest give rise to varieties sufficiently well marked
to have been recorded in botanical works'.

A few years ago it was my privilege to make a statistical investiga-
tion of the extensive observations of Mr. E. B. Ford upon the vari-
ability of the wing colour in a number of species of night-flying moths.
For thirty-five species the tints were sufficiently comparable to be
represented on a single colour scale, and for these the observations,
which included over 5,000 individuals, offered an exceptionally fine
opportunity of examining the association between abundance and
variability. It is essential in such an investigation to eliminate any
tendency for one group of species to appear more variable than
another owing to the peculiarities inherent in an arbitrary scale of
tints. The data, however, were sufficiently copious to make it possible
to eliminate this source of error, and after making the necessary
allowances, it appeared that, in both sexes, the ten species classed as
'abundant' or 'very common' exceeded in variance the thirteen

3653 Q

98 VARIATION AS DETERMINED BY

species which were less than common by between 70 and 80 per cent,
the twelve 'common' species being in both cases of intermediate
variability.

Because many other factors besides numbers must influence the
variability, and particularly because the precision of any classifica-
tion of abundance must be exceedingly low, it is essential to base such
comparisons upon as large a number of species as is possible, and this
seems to be an important cause of the present lack of satisfactory
data bearing upon the variability of species. The differences observed
among the moths were, however, sufficiently substantial to be
statistically significant, even in comparison with the large differences
in variability found within each class. It may be mentioned that the
same data showed in fact a larger variability in the species with the
widest geographical ranges, as contrasted with less widespread
species, although the differences in this comparison cannot claim to
be statistically established. There is no reason, however, to believe
that an increase of numbers by increase of range is less effective hi
increasing variability than would be the same increase of numbers
due to greater density of population, for the numerical ratio of species
classed by entomologists as abundant and rare respectively must be
much greater than is ordinarily the ratio of the areas occupied by
different species.

The theoretical deduction that the actual number of a species is
an important factor in determining the amount of variance which it
displays, thus seems to be justified by such observations as are at
present available. Its principal consequence for evolutionary theory
seems to be that already inferred by Darwin, that abundant species
will, ceteris paribus, make the most rapid evolutionary progress, and
will tend to supplant less abundant groups with which they come
into competition. We may infer that in the ordinary condition of the
earth's inhabitants a large number of less abundant species will be
decreasing in numbers, while a smaller number of more abundant
species will be increasing — the number of species being maintained
^. by fission of the more abundant, and especially of the more wide-
spread species, a subject which will be considered in the next chapter.
It may be noted, however, that whereas an increase in fitness when
invested in an increase in numbers in the manner described in
Chapter II, is now seen to bear a substantial rate of interest in laying
the foundations of sufficiently rapid further improvement, the process

MUTATION AND SELECTION 99

of fission, while yielding doubtless an immediate adaptive advantage,
yet entails a certain loss in the degree of variability which the divided
parts can severally maintain. There is thus in the continuous elimina-
tion of the smaller specific groups a natural check set to the excessive
comminution of species, which would ensue upon specialization in
the direction of minutely differentiated aptitudes.

Among the factors which influence the relationship between f
variation and selection may be mentioned the tendency of like to '
mate with like, known as homogamy. Among the higher animals we
have no certain knowledge of this save in the case of man, but this
can scarcely detract from the value of the human evidence, since its
occurrence is contrary to popular opinion, and not sufficiently
explained by any circumstance of social organization. In collections
of human measurements the resemblance between married persons
is rather a conspicuous feature. Its principal biometric effects seem
to be to increase the genetic variance produced by a given number of
Mendelian factors with given gene ratios, and so to increase in a
fixed proportion the intensity of the selection to which each is exposed.
The effect of selection in human stature is increased in this way by
more than 20 per cent. It is therefore potentially an important agent '
in promoting evolutionary change. Its causes are quite uncertain.
It has been suggested that fertility depends in some measure upon
the constitutional similarity of the mates, but evidence for this is
lacking in the case of man and the higher animals, and I know of
no serious attempt to demonstrate the truth or falsity of the sugges-
tion. It is at least equally possible that the standards of sexual
preference are slightly modified by individual size, and on this view
the causes of homogamy can scarcely be distinguished from those
which, in sexual preference, to be considered in Chapter VI, produce
direct selective effects.

Stable gene ratios

We have hitherto considered only those factors which contribute to
the genetic variance in fitness to survive and progress. There remain
to be considered those factors in which one gene has a selective
advantage only until a certain gene-ratio is established, while for
higher ratios it is at a selective disadvantage. In such cases the gene
ratio will be stable at the limiting value, for the selection in action
will tend to restore it to this value whenever it happens to be

100 VARIATION AS DETERMINED BY

disturbed from it in either direction. At this value the effect of the
gene substitution upon survival will be zero, and consequently no con-
tribution will be made to the genetic variance in fitness, although the
genetic variance in other measurable characters may be augmented
by such factors. These cases have a special importance owing to the
principle that factors will be found most frequently when their rate of
change in gene ratio is least. In consequence of this, if their stability
could be assumed to be absolutely permanent, such cases would have
been accumulating in each species since its earliest beginnings; in
fact, however, the conditions of stability must themselves be transient
during the course of evolutionary change, and we can only be sure
that cases of such gene stability must exist with a frequency quite
disproportionate to the probability of occurrence of the conditions on
which the stability is based.

A single factor may be hi stable equilibrium under selection if the
heterozygote has a selective advantage over both homozygotes. For
if we suppose the three phases of the factor to appear in any genera-
tion in the ratio pz : 2pq : q2, and that their relative selective
advantages are respectively in the ratio a : b : c, then the three
phases hi this generation will reproduce in the ratio ap2 : 2bpq : cq2,
where the absolute magnitudes of the quantities a, b, c are a matter
of indifference, only their ratios being required. If equilibrium in the
gene ratio is established this ratio will be the same in those which
reproduce as it was in the preceding generation, and therefore,

p _ ap2 + bpq
q ~ bpq+cq2 '
whence it appears that

ap + bq = bp + cq.
Subtracting each of these from b (p + q) we obtain

p(b-a) = q(b-c),
or

p b-c

q ~ b-a

There is therefore always a real ratio of equilibrium if b - a and
b-c are either both positive or both negative ; that is, if the hetero-
zygote is either better or worse adapted than both the homozygotes.
A priori we should judge either condition to be exceptional; they
will not, however, be found in nature equally infrequently, for when

MUTATION AND SELECTION 101

6 is less than a and c the equilibrium is unstable and there will be no
tendency for such cases to accumulate, whereas if 6 exceeds a and c
the equilibrium is stable and such cases will therefore persist until
the stability is upset.

To demonstrate the condition for stability it is sufficient to observe
that the ratio

bpq + cq2
may be written

p (ap + cq) +pq (b - c)
q (ap + cq) +pq (b - a)

which lies between the ratios p : q and (6 -c) : (6 -a), if 6 exceeds
a and c, but not if b - c and b -a are negative.

In organisms capable both of self- and of cross-fertilization, the
situation in which the heterozygote has a selective advantage tends
to give the offspring by cross-fertilization a higher reproductive value
than offspring by self-fertilization, and therefore to make it worth a
somewhat greater expenditure ; for in a population mating at random,
such as is assumed above, the reproductive values of the three geno-
types will be simply in the ratio a : b : c. Hence for the genotype of
the first kind the average value of its offspring will be pa +qb, if it is
cross-fertilized at random, against a if it is self-fertilized. For the
heterozygote we find \ (pa + b+qc) for cross-fertilization, against
J (a + 26 + c) for self-fertilization. The average advantages in the
two homozygous phases are thus q (b - a) and p (b -c) respectively,
while in the heterozygote it is I (p - q) (a - c). Remembering that
the frequencies with which these three phases occur are in the ratio
p2 : 2pq : qz we find for the average loss of value hi self-fertilization

= %pq(2b-a-c).

Now according to our previous solution, equilibrium will be
established when

b -c b -a

2b-a-c 2b-a-c

and if we are to interpreted, and c as proportionate contributions to
the ancestry of future generations we must have also

pza + 2pqb+q*c = 1,

102 VARIATION AS DETERMINED BY

in which, if we substitute for p and q, we shall find the relation

bz-ac = 26-a-c.

Using these relations, we may express the average loss of value of the
offspring, caused by self-fertilization, as a homogeneous expression in
a, b, and c only, hi the form

(6-q)(6-c)
2(62-oc)

Thus, for example, if for any factor a, 6, and c were in the ratio
5 : 6 : 4 a stable genetic situation would be established hi which the
products of self-fertilization would be worth, in respect of their
prospects of contributing to future generations, just ^ less than the
average products of cross-fertilization. Any other factors of the
same kind, which might happen to be present, would of course add
to the advantage of cross-fertilization. The formula, however, given
above, is that appropriate to organisms in which cross-fertilization
is the rule, for if self-fertilization is much practised the reproductive
values of the three phases will be hi a higher ratio than their selective
factors for a single generation.

Equilibrium involving two factors

Two factors, the alternative genes hi which may be represented by
A, a and.B, 6 will maintain each other mutually hi genetic equilibrium,
if the selective advantage of A over a is reversible when B is substitu-
ted for b, or vice versa. Without attempting to specify the exact
selective advantage enjoyed by each of the nine genotypes we may
specify the type of selection under consideration by saying that A is
advantageous in the presence of B but disadvantageous hi the
presence of 6, and that B is advantageous in the presence of A but
disadvantageous in the presence of a. Equally of course in this
statement we might transpose the words advantageous and dis-
advantageous.

Equilibrium in such a system evidently implies that the increase
in the frequency of A which takes place in the presence of B shall be
exactly counterbalanced by its decrease in the presence of 6; and
that the increase in B which takes place in the presence of A shall be
exactly counterbalanced by its decrease in the presence of a. But it
is important to notice that the equilibrium of the frequencies of the
gametic combinations AB, Ab, aB, ab requires a third condition of

MUTATION AND SELECTION 103

equilibrium. By the conditions of our problem, two of these, which
we have chosen to be AB and ab, are favoured by Natural Selection,
and increase in their zygotic stages, while the opposite pair .46 andal?
decrease. The adjustment of the ratio between the frequencies of
these two pairs of gametic types must take place by recombination
in those individuals which are heterozygotes for both factors . Of these
so-called double heterozygotes some arise by the union of the gametic
types AB and ab, and in these the effect of recombination is to
diminish the frequencies of these two types. This effect will be
partially counteracted by recombination in heterozygotes of the
second kind, arising from the union of Ab and aB ; and, if the net
effect of recombination is to decrease the frequencies of AB and ab,
it is obvious that double heterozygotes derived from gametes of these
kinds must be the more numerous.

The inequality in the frequencies of the two kinds of double
heterozygotes in the case we are considering has an important con-
sequence; for whenever the two factors considered happen to be
located in the same chromosome the frequency of recombination will
depend upon crossing over, which is known to be much affected by
the genetic differences between different strains. Moreover in the
more numerous kind of double heterozygote recombination results in
the substitution of the less favoured gametic combinations for the
more favoured combinations, and consequently in a reduction in
reproductive value, and this will not be completely balanced by the
increase in reproductive value due to recombination in the less
numerous kind of double heterozygote. Consequently the presence
of pairs of factors in the same chromosome, the selective advantage
of each of which reverses that of the other, will always tend to
diminish recombination, and therefore to increase the intensity of
linkage in the chromosomes of that species. This tendency is always
in the same direction, and although the type of factorial interaction
from which it arises may be rare, yet owing to the stability of the
gene-ratios which it induces, we may anticipate that such cases will
be found present at any one time with a frequency quite dispro-
portionate to their rate of occurrence.

The discovery of an agency which tends constantly to increase the
intensity of linkage, naturally stimulates inquiry as to the existence
of other agencies having an opposite effect, and under the combined
action of which, with that already discussed, linkage intensity could

104 VARIATION AS DETERMINED BY

have become adjusted to its observed value. Such an agency appears
to be at hand in the constant spread of advantageous mutations
through the populations in which they occur. For, unless advan-
tageous mutations occur so seldom that each has had time to become
predominant before the next appears, they can only come to be
simultaneously in the same gamete by means of recombination. If
two advantageous mutations, which happen to be located in homo-
logous chromosomes, are spreading simultaneously through the same
species, we may look forward to a future epoch in which every
gamete will contain both advantageous mutants, and these will have
been derived in lineal succession, either from gametes of the same
kind or, ultimately, from individuals in which recombination has
taken place. Such individuals, we may infer, will have been, for this
reason, somewhat better represented in future generations than the
remainder, in which recombination frequency must have been, on the
average, lower. It is apparent that for this process to have been an
effective check upon the constant tendency to increase the intensity
of linkage, the stream of favourable mutations must be an abundant
one. There seems, however, to be no evidence against the view that
even in every chromosome of most species numerous favourable
mutations are at any one time always to be found, each as it increases
in frequency, adding, perhaps only a trifle, to the perfection of its
internal or external adaptation. If the need of combining these
advantages is in reality the effective check to linkage intensity, it
may prove possible, as data become more abundant, to gauge in
this way, at least roughly, the relative rates of improvement in
different species.

Simple metrical characters

Characters which can be specified by a single measurement, such as
human stature, the length of an individual bone or tooth, etc., have
a special importance owing to the fact that they can be studied
relatively easily by direct biometrical methods. As has been pointed
out in Chapter II the idea of adaptation cannot be applied with its
full force to such simple characters, considered in isolation ; but each
may nevertheless be supposed to possess an optimum value hi relation
to the existing state of the organism and its environment, which we
may regard as nearly coincident with the mean value exhibited by
the species. That this must be so is evident from the extreme

MUTATION AND SELECTION 105

rapidity with which such measurements are modified when selection
is directed to this end. For example, it appears from the observed
average statures of the offspring of parents of different heights that
no extreme selection would be needed to increase or decrease the
stature of a human population by one inch in each generation, and
even with the long generations of Man, such a rate of change would
transcend the largest observed racial differences, within a short
historical period.

If we consider any factor which affects such a measurement, and
of which the other effects, if any, have no appreciable influence on
survival, it is evident that the stability of its gene ratio requires
separate consideration. For it would seem at first sight, if dominance
were absent or incomplete, and in consequence the heterozygote were
intermediate between the two homozygotes, that selection favouring
intermediate values would tend to favour the heterozygotes, and in
consequence induce very generally the condition of stability which
has been considered. If this were so we should be faced with two
somewhat alarming conclusions, (i) that by the accumulation in
conditions of stability of a large number of factors with intermediate
heterozygotes, the metrical characters should indicate in their bio-
metrical properties a general absence of dominance, whereas, as has
been already mentioned (p. 18) the body of human measurements
available give clear indications to the contrary, (ii) that the action of
selection in favouring the intermediate values would have the effect,
by preventing the extinction of all variant types of progressively
increasing the variance of the character in question, and consequently
of making the intermediate values progressively rarer.

The recognition that the specific mean adjusts itself rapidly to the
optimum size, however, makes the problem an essentially different
one from that already considered, for the selective advantage of the
heterozygote is dependent upon the average deviation of this geno-
type from the optimum, and this will vary as the gene ratio changes.
If i, j, k represent the deviations of the average values of these geno-
types from the mean, the effect of selection will be equivalent to
eliminating small fractions of each genotype proportional to i2,j2, and
&2. If the three g^uptypes are in the proportion p2 : 2pq : q2, the
ratios by which the two alternative genes are reduced will be pro-
portional to

and pj2 + qk2,

106 VARIATION AS DETERMINED BY

and the gene ratio will only be in equilibrium if these two quantities

are equal. Further from the definition of the mean, we have

p*i + 2pqj + q*k = 0.

If we use the latter equation to eliminate the deviations i, j, k,
replacing them by a single ratio, defined as

a _ i-j

/O-*'

and which depends only on the degree in which dominance is ex-
hibited in the factor in question, we find that this ratio is connected
with the ratio p : q, when the condition of equilibrium is established,
by the equation

p(l-2p*)a* + 2pq(q-p)aft-q(l-2q*)ft2 = 0.

This expression is symmetrical if p and q, a and 8 are interchanged,
the value on the left being proportional to the rate of decrease of
z(= log p- log q).

From the signs of the three terms it appears that one real positive
solution exists, if q exceeds p, only if q does not exceed \ \/2 ; moreover
since the expression is positive if ft = 0, while if a = $ it is reduced to

which is still positive, it follows that if q exceeds p, so must ft exceed a,
when equilibrium is attained. The more dominant gene must be the
less frequent.

If any equilibrium were stable then the expression must increase
as p is increased ; its differential coefficient with respect to p is

(1 - 6^2) a2 + (1 - Qpq) 2aft + (1 - 602) ft2,
or

(a+ft)2-6(pa+qft)2.

Now a + jS is arbitrary, and may be taken like p +q to be unity,
then since

2 (pa+qft) = (p+q) (a+ft) + (p-q) (a- ft)

it follows that pa + qft cannot be less than £, for we have shown that
when q exceeds p, then ft exceeds a. Consequently the differential
coefficient at any position of equilibrium is less than

V -i .

MUTATION AND SELECTION 107

and is always negative. The conditions of equilibrium are always
unstable. Whichever gene is at less than its equilibrium frequency
will tend to be further diminished by selection.

All mutations therefore affecting such a character, unless they
possess countervailing advantages hi other respects, will be initially
disadvantageous, and we may conceive of each coming to an equi-
librium at which the mutation rate is just balanced by the counter-
selection to which it is exposed. This situation resembles that of
intrinsically disadvantageous mutations considered in Chapter III,
but differs from it in that for sufficiently high mutation rates the
mutant gene will now pass the point of maximum resistance, and,
when it attains sufficient frequency, will be thereafter actually
assisted by selection. The mutation rates required to bring this
about depend on (i) the magnitude of the effect produced by the
factor, i. e. the metrical difference between the two homozygotes,
represented by a, (ii) the total variance of the species in the measure-
ment in question, represented by a2, (iii) the intensity of selection
in favour of the optimum measurement ; this may be measured by
1/T2, where r2 is a quantity of the same dimensions as a2, which
vanishes for infinitely intense selection, and would be infinitely great
if all values of the measurement were equally satisfactory.

In the absence of dominance the maximum resistance is encountered
when p = J, and this is overcome if the mutation rate, k, exceeds

64(a2+r2)

a full discussion of the situation would require an examination of the
effect of selection upon the variance, for if selection is intense and r2
small, it is probable that a2 will become small also ; for the present
we may note that the contribution of the factor in question to the
total variance will be at most a2/8. If therefore the effect of the factor
is so small that it will contribute at most one part in 100,000 to the
total variance, a mutation rate of the order of one in a million might
well effect its gradual establishment. Such would be the situation of
factors affecting human stature by about one-fortieth of an inch.
Factors having less effect than this might establish a mutant form
at lower mutation rates, in each case the more easily, the more lax
is the preferential survival of the medium sizes.

Mutant genes with greater effect or lower mutation rates will be

108 VARIATION AS DETERMINED BY

hung up at all values up to p = 0-25. Now at this value the mean lies
midway between the average values of the heterozygote and the non-
mutant homozygote; consequently at and below this value the
heterozygote might with advantage more nearly resemble the non-
mutant homozygote. There will, therefore, always be a tendency,
analogous to that discussed in Chapter III, for the non-mutant
gene to become dominant, by the modification of the heterozygote
towards greater resemblance with it. Dominance should then be
developed against mutations in whichever direction they appear ; thus
we may expect to find in such characters mutant genes of which
the tendency is either to increase or to decrease the measurement,
indiscriminately recessive. The fact that the offspring of crosses
between races exhibiting differences in metrical characters are usually
intermediate is one which might have been inferred from this bilateral
tendency towards the development of dominance.

The development of dominance inevitably reacts upon the con-
ditions of equilibrium; for complete dominance, for example, the
maximum counterselection is met with at^> = 0-5, and the mutation
rate necessary to establish the mutant gene is four times as great
as the value found for factors without dominance. The condition
necessary for dominance to increase is that the heterozygote shall be
on the opposite side of the mean to the non-mutant homozygote.
For any particular degree of dominance, that is for any particular
value of a, dominance will increase so long as

«<«!.
ft p*

With sufficient time, therefore, dominance will increase, and the
value of /? dimmish, until these two values are equal. The simul-
taneous variation of the two ratios p : q and a : j8 will be made more
clear by the aid of the diagram (Fig. 9) on which the curve AXZB
represents the series of possible conditions hi which there is no
further tendency to modify the degree of dominance, and at different
points along which factors may be maintained by appropriate muta-
tion rates. On the same diagram the line EA YC is drawn through
the points at which maximum counterselection is met with for
different values of a. A mutation commencing without dominance
will start from 0, and as its gene frequency increases, move along
the line OE, until it reaches some point on this line at which the

MUTATION AND SELECTION 109

mutation rate is balanced by counterselection. At this stage, and
indeed during its progress towards this stage, selection will tend to
render the mutant gene recessive and the representative point will
pass along a line below EZ to come to rest on the limiting line ZB,
at all points of which, as appears from the diagram a exceeds 0-95.

i-o

0-9

0-8

0-7

op-6

LL.

o

120-5

D

0-3

0-2

0-1

-o

:- G

4 -5 -6

VALUES OF <x

1-0

FIG. 9. The relations between frequency, mutation rate, and degree of dominance,
in a factor having simple metrical effect only. For detailed explanation see text.

At any stage an alteration in the mutation rate will move the
representative point upwards or downwards on the diagram accord-
ing as the mutation rate is increased or diminished, but it is clear
that a factor left without change in the area AEOB will gravitate
to the appropriate level on the line XB. In the same way any factor
displaced to a point in the area XDB will experience selection in the
direction of a diminution of dominance, for with these the displace-
ment of the heterozygote from the mean of the species is in the same

110 VARIATION AS DETERMINED BY

direction as that of the non-mutant homozygote and selection will
favour any tendency to diminish this deviation. Such a path is
represented by OZ. From the position of the point X it will be seen
that this process cannot reduce the value of a below about 0-79
unless the critical line AC is crossed. Factors held in equilibrium
will thus tend to retain at least this degree of dominance, even if their
mutation rate is very nearly sufficient to overcome all opposition.
Finally a factor placed in the region CYXD will, if the conditions
remain unchanged, diminish its dominance until it meets the line AC,
at which the effect of counterselection is a maximum and beyond
which it grows weaker instead of stronger, when the frequency of the
mutant gene is increased. The course of such factors is, with some
vicissitudes, similar to that of factors which, combining the advan-
tages of a high mutation rate and a very small measurable effect,
never encounter sufficient opposition to check their progress. The
lowest mutation rate which could maintain the factor on such a path
is very nearly double that initially required for a factor without
dominance to pass at E, and is represented by the line DXY sepa-
rating the factors which will pass AC from those which will be hung
up on the line XZB.

We are in the dark as to the frequencies with which different
mutations will attain the different stages indicated in the diagram.
The greater part of the area represented could, however, only come
to be occupied by mutations which fail by but little from passing
through unopposed. Mutations having a comparatively large effect
and possibly many others with less effect, combined with low muta-
tion rates, may be expected to be checked at low values of p and to
gravitate to points near B on the line ZB, where it will be observed
that dominance, while still slightly incomplete, attains a very pro-
nounced development.

A second peculiarity of metrical factors, and one which may be of
more consequence, is that, of any two genes having similar effect,
that is both increasing or both diminishing the measurement, each
will be most advantageous or least disadvantageous, in the absence
of the other. The preceding analysis has shown that this interaction
does not lead to stability of the gene ratios, comparable to that
discussed on p. 102 ; nevertheless the interaction must have exactly
analogous effects in favouring genotypes which exhibit close linkage.
Gametic combinations hi which the different factorial effects are well

MUTATION AND SELECTION 111

balanced and tend to a measurement of medium length, must be
continually favoured by selection at the expense of ill-balanced
combinations determining the production of very large or very small
values. The numbers of the latter will therefore require on the average
to be continually replenished by recombination, with the result that
crossing-over must, so far as these factors are concerned, tend to
lower the average reproductive value of the offspring.

It will now be clear in what way we should imagine the average
value of the measurements to be modified by selection whenever
such modification happens to be advantageous. If the optimum
value is increased all genes, the effect of which in contrast to their
existing allelomorphs is a metrical increase, will be immediately, or at
least rapidly, increased in frequency. In the case of those factors,
the effects of which upon survival can be completely expressed in
terms of their effect upon the measurement in question, the effects of
such a change of frequency will be in some cases permanent and in
others temporary. Some genes previously opposed by selection will
be shifted to frequencies at which they are favoured, and these may
increase to such an extent during the period of selection that when
this dies away they may still be favoured. Their subsequent progress
will thus tend to increase the value of the measurement even after it
has attained the new optimum. The same applies to mutant genes
the frequency of which is increased past the point of maximum
counterselection, into a region in which selection, while still opposing
mutation, is insufficient to check their increase. In other cases the
increase or decrease in frequency produced by temporary selection,
is itself only temporary, and these, when the new optimum is attained,
will tend to revert to their previous frequencies, tending incidentally
by so doing, to make the specific mean revert somewhat from the
new optimum. The system resembles one in which a tensile force is
capable of producing both elastic and permanent strain, and in
which the permanent deformations always tend to relieve the elastic
forces which are set up.

Meristic characters

In his search for evidences of discontinuous variation Bateson paid
considerable attention to variations in the number of similar parts
occurring, like vertebrae, in series. Apart from abnormalities in
development, variation in such characters is bound to be discon-

112 VARIATION AS DETERMINED BY

tinuous, the variate exhibited by any one individual being necessarily
one of the series of whole numbers. There is no reason, however, to
suppose that the discontinuity so produced is in any way connected
with the discontinuity of the genetic particles in Mendelian inheri-
tance. On the contrary, it would be equally reasonable to suppose
a priori, that the actual number exhibited is but the somatic expres-
sion, to the nearest whole number, of an underlying physiological
variate influenced, like a simple measurement, by both environ-
mental and genetic causes. That this is the true view must now be
regarded as established in several important cases.

The series of frequencies with which different vertebra numbers
occur bear a striking superficial resemblance to the series obtained
when a normally distributed variate is grouped in equal but some-
what large intervals of its value ; as if, for example, human stature
were recorded in a large number of individuals, to the nearest
multiple of three inches. The impression of similarity is increased if
instead of observations upon single individuals, we consider the
simultaneous distribution of a number of pairs of parents and off-
spring, for in this case the average value of the meristic variate in
a group of offspring obtained from parents with the same value, is
found to increase quantitatively from group to group in a manner
exactly similar to that observed with simple measurements.

The actual proof that each individual possesses, in respect of a
character showing meristic variation, a definite genotypic or genetic
value, which differs from the corresponding values of other individuals
by amounts which are not integers, but fractions differing significantly
from integers, can, as Schmidt has shown, be supplied by two methods
of experimentation. With organisms capable of self-fertilization, or
vegetative reproduction, it may be possible to establish pure lines of
individuals genotypically identical, and a direct comparison can thus
be made between the averages of large numbers of individuals of two
or more different lines, developed in the same environment. Alterna-
tively with organisms capable of giving a sufficient number of off-
spring at a single mating, a series of males may be bred, each to every
one of a series of females. By comparing the averages of these
progenies Schmidt determined the differences between the under-
lying genetic values of parents of the same sex, with sufficient pre-
cision to show that these differences could not possibly be integral.

If we regard such a variate as vertebra number as the somatic

MUTATION AND SELECTION 113

expression of an underlying genotypic variate having continuous
variation, the striking constancy of such meristic characters in large
groups of related organisms evidently requires a special explanation.
This constancy is made no less remarkable by its exceptions. Among
the great diversity of forms developed among the mammalia, almost
all have constantly seven neck vertebrae, yet two of the sloths have
six and nine neck vertebrae respectively. A similar situation in
fishes, in which several families with various vertebra numbers have
apparently developed at different times, from a group of families in
which 24 vertebrae appear to be invariable, has been felt by Tate
Regan to present such a difficulty to the theory of Natural Selection,
that he is willing to fall back upon the supposed effects of changed
conditions in producing mutations as an alternative explanation.
What prospect there is of such an agency, if its existence could be
demonstrated, aiding us in understanding this particular problem
seems at present uncertain. It is therefore the more important to
examine whether known causes are really as ineffective as has been
thought in bringing about the observed effects.

In groups in which all or nearly all the individuals have the same
vertebra number two views are possible ; (i) that there is no genetic
variability, and (ii) that neither genetic variability, nor the varia-
bility of the developmental environment, is sufficient to produce
frequent departures from the central integer. The first view may be
set aside, not only because different species do certainly differ in the
number of then* vertebrae, but also because, hi the light of the argu-
ment of the last chapter, a mutant gene affecting the underlying
variate, unless it have other effects, will be exempt from selection,
at least so long as the vertebra number is actually constant. Con-
sequently, any mutations of this kind which have occurred in the
past must accumulate in such species.

If we take the second view, heritable individual variation exists in
respect of the tendency to produce a given number of vertebrae, and
the species is therefore potentially plastic in this respect. Supposing
the mean of this distribution to coincide with the modal integer, the
frequency of values other than this integer may be easily calculated
from the standard deviation of the distribution ; for example, if the
standard deviation is £ of a unit, about three exceptions are to be
expected among a thousand individuals, for £ of a unit only sixty-
three in a million, for ^ of a unit only one in two million, and so on.

3683

114 VARIATION AS DETERMINED BY

Very extensive counts would therefore be required to exclude varia-
tion of these amounts, which would nevertheless be sufficient to permit
of an evolutionary change in vertebra number, if at any time this
became advantageous.

The evolutionary fact, which on this view requires a special ex-
planation, is that in large groups of organisms with widely diverse
adaptations, it has so seldom been found advantageous to make such
a change, for in this the meristic variates offer a very striking con-
trast to the metrical variates. The integral numbers appear to be
possessed of a special kind of stability favouring a conservative
tendency in evolution, which is not to be found in the simple measure-
ments. It is possible that the explanation of this tendency lies in
the simple fact that the intercalation or omission of a member of
a series of structures requires a corresponding modification of a
number of associated organs, such as attached muscles, nerves, blood-
vessels, etc. ; and that even in cases where there is a slight advantage
to be gained by a complete reorganization on the basis of an increased
number of vertebrae, it may well be that such advantage is less than
the disadvantage suffered initially owing to the disorganization of
associated structures in any individuals which happen to have the
higher number. Even if the associated structures were morpho-
logically complete, it is not certain that all quantitative physiological
adjustments will be perfectly co-ordinated. The argument is a special
case of a more general one to the effect that in any highly adapted
organism the probability of advantage through any considerable
evolutionary step (saltation) rapidly becomes infinitesimal as the
step is increased in magnitude.

The liability to maladjustment should of course be least in species
showing considerable variability, such as the eel, in which we may
expect the developmental processes to be carried through nearly
perfectly whatever the actual number of vertebrae laid down. It
should be greatest where the meristic variate is most constant, and
where the capacity of the developmental mechanisms for dealing
with other numbers has not been subjected to selection in previous
generations. In these, however, the rarity of the exceptions precludes
the possibility of demonstrating any associated signs of abnormal
development. An intermediate case, for which some data are avail-
able, is afforded by the herring. Ford and Bull have studied the
occurrence of fused and abnormal vertebrae in this fish. Out of

MUTATION AND SELECTION 116

nearly 7,000 skeletons examined 95 were found to contain abnormal
or multiple structures. If each element in these structures is counted
as a whole vertebra it is found that the mean vertebra number of the
abnormal skeletons is 55-82, which exceeds the mean value for normal
skeletons by only 0-03. Although the mean values are thus brought
into close agreement the variability of the abnormal skeletons is very
much greater than that of the normal. In other words the extreme
vertebra numbers 53 and 58 show the highest percentages of abnormal
skeletons, the median vertebra numbers 55 and 56, which contain
nearly 90 per cent, of the fish, show the lowest percentages, while the
intermediate numbers 54 and 57 show intermediate percentages
abnormal. The actual percentages obtained from Ford and Bull's
data are as follows :

TABLE 6.

Vertebra number.

53 54 55 56 57 58

Per cent, abnormal . . 45-5 4-1 1-2 1-1 2-6 10-0
Percentage frequency . 0-08 1-06 28-36 61-30 8-91 0-29

It will be observed that the fish with the rarer vertebra numbers
show a very pronounced liability to develop abnormal structures. If
such a tendency is general in the case of unwonted meristic variations,
as seems on general grounds to be extremely probable, any meristic
variation from the existing standard must in general encounter
appreciable counter selection, and could scarcely establish itself
unless the increased number conferred advantages which could be
obtained in no other way.

If we are right in referring the conservative tendency, which is
observed to hold in meristic matters, to the liability to disorganiza-
tion consequent upon a sudden change, it follows that this tendency
must be in at least partial abeyance at periods in which the associated
structures, or their relationships to the vertebrae are, for other reasons,
in a state of reorganization. Such a pronounced change in the
structure and movements of the body as must have been required
in the adoption of the habits of the flat fish, or in the musculature of
the neck by the inverted position of the sloth, may thus have afforded
a temporary opportunity for a form of variability always present,
though constantly kept in subjection, to produce for once an evolu-
tionary modification.

116 VARIATION AS DETERMINED BY

Biometrical effects of recent selection

The immediate effect of selection in either direction is to change the
average value of the metrical or meristic variate, as the case may be.
Such an effect can only be detected if successive average values can
be determined, as is the case with some palaeontological material.
A further effect may be anticipated in a slight reduction of the
variance, by the elimination of factors previously contributing to it ;
this effect will be extremely small, and would in any case give no
indication as to whether the selection had favoured an increase or
decrease in size. Among the third degree functions of the measure-
ments there should, however, be traces of recent selection, which
would differ according to the direction in which the selection has
been applied. For a selection in favour of increased size would only
temporarily displace recessive genes having a dwarfing effect, and
these should remain in the species during such a process. On the
other hand a recessive gene, the effect of which is to increase the
metrical character, would have a chance during such a process of
becoming established throughout the species, by the extinction of its
allelomorph. Consequently after such selection has been long in
action the recessive genes should more frequently tend to diminish
than to increase the character studied. Equally when, as in the
development of toy breeds of dogs, selection has favoured diminished
size, we should expect to find an excess of recessives tending to
increase the average dimensions.

The biometrical detection and measurement of any prevalence of
dominance in one direction over that in the other would certainly
require very ample material, but apart from this the necessary
calculations appear to be straightforward. The simplest method,
that of measuring the asymmetry of the frequency distribution by
means of the third moment, will encounter some difficulties of
interpretation owing to the effects of environmental variations ; for
this reason it may be inferior to the study of the asymmetry of large
fraternities derived from different pairs of parents. The most direct
investigation would be rendered possible by considering in con-
junction the measurements of father, mother, and offspring, and
expressing the regression of the size of the offspring upon the sizes of
the two parents in a regression formula of the form

ax + by-cxy

MUTATION AND SELECTION 117

in which, x and y are the parental measurements, and a, 6, c the
coefficients to be determined from the data. Selection for increased
size will then tend to produce positive values of c, or in general to
increase its value algebraically, while selection in the opposite
direction will tend to decrease it, and to produce negative values.

Summary

In the two preceding chapters an attempt has been made to check
the adequacy of the genetic theory of Natural Selection by a detailed
examination of the method by which on this view new genes arise,
prevail, or become extinct, and in particular new gene contrasts, or
Mendelian factors, become temporarily or permanently established
as contributors to that stock of organic variability from which the
rate of progress of species has been shown to depend.

The examination of the important problem of the survival of
individual genes is much simplified by the fact that so long as few are
in existence all other effects are unimportant compared with the
fortuitous element in the survival and reproduction of their bearers.
In many important cases the survival for a single generation may be
represented by a function simply related to the Poisson series, and
in many other cases by the substitution for a generation of the
appropriate biological cycle the same formulae will supply an excellent
approximation.

Although initially subject to the full force of random survival,
beneficial mutations have a finite probability, simply related to the
benefit which they confer, of establishing themselves as permanent
in the heredity of the species. They can, therefore, have occurred but
a small number of times before this event is rendered practically
certain. The mutation rates during their period of trial must
therefore be generally exceedingly minute, and it must frequently
happen that nearly the whole of the individual genes that ultimately
pervade the species will have been derived by descent from a single
such mutant.

An examination of the statistical equilibrium established between
new mutations and the causes of the extinction of genes, shows that
advantageous mutations, at all levels of advantage, resemble neutral
mutations in the distribution of gene ratios established, the frequency
being equal in all equal intervals of the variate z, in which it is con-
venient to measure variations hi gene ratio. The range of z is longer

118 VARIATION AS DETERMINED BY

in abundant than in rare species, and for this reason the number of
factorial differences maintained in an abundant species bears a higher
ratio to the rate of occurrence of new mutations than does the
number maintained in rare species. The range of selective advantage
which may be regarded as effectively neutral is, however, extremely
minute, being inversely proportional to the population of the species.
Since it is scarcely credible that such a perfect equipoise of selective
advantage could be maintained during the course of evolutionary
change, random survival, while the dominant consideration in respect
to the survival of individual genes, is of merely academic interest in
respect to the variance maintained in the species, which must be
mainly supplied by definitely advantageous mutations. In particular
the rate of decay of variance due to random extinction in the total
absence of mutations is shown to be of the most trifling importance.
There are, on the theory here developed, the strongest theoretical
grounds for concluding that the more numerous species must ceteris
paribus tend to be the more variable, though the rate at which
variability should increase in relation to increased numbers can, it
would seem, only be established by direct observation. The relation-
ship between abundance and variability has been confirmed by a
fine body of observations on moths, but deserves extensive investiga-
tion in other groups. An evolutionary consequence of some im-
portance is that in general a smaller number of large species must
be increasing in numbers at the expense of a larger number of small
species, the continuous extinction of the latter setting a natural check
to the excessive subdivision of species which would ensue upon a too
fine and detailed specialization.

Of great importance for our subject is the occurrence, even when
due to exceptional circumstances, of gene ratios which are stable
under selective influences; since factors of this kind cannot be
eliminated unless and until, hi the process of evolutionary change,
the stability is upset. The simplest type of these occurs when the
heterozygote of a single factor is favoured by selection at the expense
of both homozygotes. It is shown that in this case an equilibrium
always exists and is always stable, whereas in the opposite case the
equilibrium is unstable, and the less numerous gene will be con-
tinuously eliminated until its extinction. The accumulation of
factors in which the heterozygote is favoured will give a constant
average advantage to cross- over self-fertilization, in the sense that

MUTATION AND SELECTION 119

the progeny by cross-fertilization has a higher average reproductive
value, and is worth more to produce, than the progeny by self-
fertilization. The development of separate sexes in motile animals
and of the many devices to ensure cross-pollination in plants, though
not the origin of sexual reproduction itself, seems to be ascribable to
the small constant individual advantages due to the favouring of the
heterozygote ; at least if we include in this phrase the constant
tendency of the heterozygote to resemble the more favourable
homozygous form, examined in Chapter III.

Other types of stable equilibrium may be established by the inter-
action of two or more factors. The importance of this group of cases
lies in their constant tendency, whenever two such factors are in the
same linkage group, for the linkage between them to be increased.
The same consequence ensues, without the establishment of stable
equilibrium, when two factors of such a group both modify the
magnitude of any simple physical measurement, and have no other
effects of importance to survival. There is thus shown to be an
agency constantly favouring closer linkage between factors of the
same group, and since linkage values are eminently liable to selective
modification, and are not, in most species investigated, such as to
preclude frequent crossing over, it is an inevitable inference that
some other cause must induce an equally powerful selection in favour
of crossing over. While the mathematical difficulties of an exact
investigation are worthy of a far more extended treatment, it is
suggested that such an agency may be found in the advantage of
combining different advantageous mutations, which, unless they
occur consecutively, can only be done by recombination. It seems
probable that in order to exert a perceptible influence upon linkage
the stream of favourable mutations would need to be a consider-
able one, and that with further extensions of our knowledge in
this direction it may prove possible, by this means, to gauge its
magnitude.

Mutations whose effect is produced only upon simple metrical
characters will, unless their effects are very minute, be exposed to
counter-selection, and the mutant gene, whether its effect be positive
or negative, will tend to become recessive. Dominance in such cases
should be incomplete, though in most factors exposed long to counter-
selection the heterozygote should differ from the non-mutant
homozygote by less than 1/20 of the difference between the homozy-

120 VARIATION BY MUTATION AND SELECTION

gotes. The evidence of dominance observed in metrical characters is
thus in full accord with the analytic theory.

Meristic variation is, in those cases which have been investigated,
certainly due to an underlying quantitative variate. Specific modifica-
tion in such characters is, however, constantly opposed by selection,
arising by the interaction of co-ordinated structures. The striking
conservatism manifested by large groups of organisms in meristic
characters is thus rendered intelligible, while the possibility of their
modification at any time, during the reorganization of the relation-
ships and attachments of associated structures, is constantly main-
tained. Such anomalies as occur in the numerical variations in the
neck vertebrae of mammals may be cited as illustrating both sides
of the working of this principle.

VI
SEXUAL REPRODUCTION AND SEXUAL SELECTION

The contrast between sexual and asexual reproduction. The nature of species. Fission
of species. Sexual preference. Sexual selection. Sex limitation of modifications. Natural
Selection and the sex ratio. Summary.

To all who are engaged in Psyche's task, of sorting out the seeds of good
from the seeds of evil, I dedicate this discourse. FKASER.

The contrast between sexual and asexual reproduction

A GROUP of organisms in which sexual reproduction was entirely
unknown might none the less evolve under the action of natural
selection. This condition cannot, I believe, be ascribed with certainty
to any known group. Yet, since it is impossible to draw any sharp
distinction within a whole series of asexual processes, from individual
growth at the one extreme, through the regeneration of injured or
lost parts, to vegetative reproduction by budding ; it is tempting to
believe that asexual reproduction was the primitive condition of
living matter, and that the sexual reproduction of the predominant
types of organisms is a development of some special value to the
organisms which employ it. In such an asexual group, systematic
classification would not be impossible, for groups of related forms
would exist which had arisen by divergence from a common ancestor.
Species, properly speaking, we could scarcely expect to find, for each
individual genotype would have an equal right to be regarded as
specifically distinct, and no natural groups would exist bound to-
gether like species by a constant interchange of their germ-plasm.

The groups most nearly corresponding to species would be those
adapted to fill so similar a place in nature that any one individual
could replace another, or more explicitly that an evolutionary im-
provement in any one individual threatens the existence of the
descendants of all the others. Within such a group the increase in
numbers of the more favoured types would be balanced by the
continual extinction of lines less fitted to survive, so that, just as,
looking backward, we could trace the ancestry of the whole group
back to a single individual progenitor, so, looking forward at any
stage, we can foresee the time when the whole group then living will
be the descendants of one particular individual of the existing
population. If we consider the prospect of a beneficial mutation

3653

122 SEXUAL REPRODUCTION AND SEXUAL SELECTION
occurring at any instant, ultimately prevailing throughout the
whole group, and so leading to evolutionary progress, it is clear that
its prospect of doing so will depend upon its chance of falling, out of
the whole population, upon the one individual whose descendants are
destined ultimately to survive. At first sight this chance appears to
be extremely small ; but we must take account of the fact that in so
far as the mutation is beneficial, its occurrence will increase the
prospect of the individual, in which it occurs, proving ultimately
victorious. In the limiting case in which the benefit derived from the
new mutation tends to zero the chance of success is evidently only
one in as many individuals as there are in the competing group. If
on the other hand the benefit is appreciable, the chance of success
will certainly be greater than this by an amount which now depends
on the amount of heritable diversity in the group, and on the prospect
of the occurrence of other beneficial mutations, before the replace-
ment of the original population by the improved type has been
completed. If the total rate of mutations is so small that the usual
condition of the group is one of genetic uniformity, any advantageous
mutation may be expected to prevail, provided it survives the
chances of accidental death during the initial period in which it is
represented by only one or few individuals. These chances, which are
effectively the same with asexual or with sexual reproduction, have
been considered in an earlier chapter (IV).

The evolutionary progress of an asexual group thus presents the
dilemma that it can only utilize all those beneficial mutations which
occur, and survive the dangers of the initial period, if the rate of
occurrence of mutations is so low that the population of competing
organisms is normally in a state of genetic uniformity, and in such
a state evolutionary progress will necessarily be almost at a standstill ;
whereas if on the contrary the mutation rates, both of beneficial and
of deleterious mutations, are high enough to maintain any consider-
able genetic diversity, it will only be the best adapted genotypes
which can become the ancestors of future generations, and the bene- ^
ficial mutations which occur will have only the minutest chance of
not appearing in types of organisms so inferior to some of their
competitors, that their offspring will certainly be supplanted by
those of the latter. Between these two extremes there will doubtless
be an optimum degree of mutability, dependent on the proportion of
beneficial to deleterious mutations, and therefore on the aptitude of

SEXUAL REPRODUCTION AND SEXUAL SELECTION 123
the group to its place in nature ; but it is not difficult to see that the
rate of progress, supposing that the optimum mutability were
established, would still be very inferior to that of a sexual organism
placed in the same circumstances.

The argument developed above as to the rate of evolutionary
progress of a group of asexual organisms may be applied to the
evolutionary progress in any one particular locus, in a species of
sexual organisms, if we suppose that changes of several different kinds
may take place in an homologous set of genes. The comparative
rates of progress of sexual and asexual groups occupying the same
place in nature, and at the moment equally adapted to that place,
are therefore dependent upon the number of different loci in the
sexual species, the genes in which are freely interchangeable in the
course of descent. From what is known of the higher animals this
number must be at least several thousands; but even a sexual
organism with only two genes would apparently possess a manifest
advantage over its asexual competitor, not necessarily from any
physiological benefit derived from sexual union, but from an approxi-
mate doubling of the rate with which it could respond to Natural
Selection. On this view, although asexual reproduction might be
largely or even exclusively adopted by particular species of sexual
groups, the only groups in which we should expect sexual reproduc-
tion never to have been developed, would be those, if such exist, of
so simple a character that their genetic constitution consisted of
a single gene.

The nature of species

From genetic studies in the higher organisms it may be inferred, that
whereas genetic diversity may exist, perhaps in hundreds of different
loci, yet in the great majority of loci the normal condition is one of
genetic uniformity. Unless this were so the concept of the wild type
gene would be an indefinite one. Cases are indeed known, as in the
agouti locus in mice, in which more than one kind of wild gene have
been found, these being both dominant to their other non-lethal
allelomorphs; but numerous as are the loci in which such genetic
diversity must exist, we have some reason to suppose that they form
a very small minority of all the loci, and that the great majority
exhibit, within the species, substantially that complete uniformity,
which has been shown to be necessary, if full advantage is to be taken

124 SEXUAL REPRODUCTION AND SEXUAL SELECTION
of the chances of favourable mutations. In many loci the whole of
the existing genes in the species must be the lineal descendants of
a single favourable mutation.

The intimate manner hi which the whole body of individuals of
a single species are bound together by sexual reproduction has been
lost sight of by some writers. Apart from the intervention of geo-
graphical barriers so recently that the races separated are not yet
regarded as specifically distinct, the ancestry of each single individual,
if carried back only for a hundred generations, must embrace
practically all of the earlier period who have contributed appreciably
to the ancestry of the present population. If we carry the survey
back for 200, 1,000, or 10,000 generations, which are relatively short
periods hi the history of most species, it is evident that the community
of ancestry must be even more complete. The genetical identity in
the majority of loci, which underlies the genetic variability presented
by most species, seems to supply the systematist with the true basis
of his concepts of specific identity or diversity. In his Contributions
to the Study of Variation, W. Bateson frequently hints at an argument,
which evidently influenced him profoundly, to the effect that the
discontinuity to be observed between different species must have
owed its origin to discontinuities occurring in the evolution of each.
His argument, so far as it can be traced from a work, which owed its
influence to the acuteness less of its reasoning than of its sarcasm,
would seem to be correct for purely asexual organisms, for in these it
is possible to regard each individual, and not merely each specific
type, as the last member of a series, the continuity or discontinuity
of which might be judged by the differences which occur between
parent and offspring ; and so to argue that these provide an explana-
tion of the diversity of distinct strains. In sexual organisms this
argument breaks down, for each individual is not the final member
of a single series, but of converging lines of descent which ramify
comparatively rapidly throughout the entire specific group. The
variations which exist within a species are like the differences in
colour between different threads which have crossed and recrossed
each other a thousand times hi the weaving a single uniform fabric.

The effective identity of the remote ancestry of all existing
members of a single sexual species may be seen hi another way, which
in particular cases should be capable of some quantitative refinement.
Of the heritable variance hi any character in each generation a

SEXUAL REPRODUCTION AND SEXUAL SELECTION 125
is due to the hereditary differences in their parents, while the
- remainder, including nearly all differences between whole brothers
^and sisters, is due to genetic segregation. These portions are not very
unequal; the correlations observed in human statistics show that
segregation must account for a little more than two-fifths, and the
hereditary differences of the parents for nearly three-fifths of the
whole. These hereditary differences are in their turn, if we go back
a second generation, due partly to segregation and partly to heredi-
tary differences in the grandparents. As we look farther and farther
back, the proportion of the existing variance ascribable to differences
of ancestry becomes rapidly smaller and smaller ; taking the fraction
due to segregation as only f in each generation, the fraction due to
differences of ancestry 10 generations back is only about one part in
160 while at 30 generations it is less than one in four millions. It is
only the geographical and other barriers to sexual intercourse between
different races, factors admittedly similar to those which condition
the development of incipient species as geographical races, which
prevent the whole of mankind from having had, apart from theJast-
thousand years, a practically identical ancestry. The ancestry of
members of the same nation can differ little beyond the last 500 years ;
at 2,000 years the only differences that would seem to remain would
be those between distinct ethnographic races ; these, or at least some
of the elements of these, may indeed be extremely ancient ; but this
could only be the case if for long ages the diffusion of blood between
the separated groups was almost non-existent.

Fission of species

The close genetic ties which bind species together into single bodies
bring into relief the problem of their fission — a problem which in-
volves complexities akin to those that arise in the discussion of the
fission of the heavenly bodies, for the attempt to trace the course of
events through intermediate states of instability, seems to require
in both cases a more detailed knowledge than does the study of
stable states. In many cases without doubt the establishment of
complete or almost complete geographical isolation has at once
settled the line of fission; the two separated moieties thereafter
evolving as separate species, in almost complete independence, in
somewhat different habitats, until such time as the morphological
differences between them entitle them to 'specific rank'. It would,

126 SEXUAL REPRODUCTION AND SEXUAL SELECTION
however, be contrary to the weightiest opinions to postulate that
specific differentiation had always been brought about by geographic
isolation almost complete in degree. In many cases it may safely be
asserted that no geographic isolation at all can be postulated, although
this view should not be taken as asserting that the habitat of any
species is so uniformly favourable, both to the maintenance of
population, and to migration, that no 'lines of weakness' exist,
which, if fission is in any case imminent, will determine the most
probable geographic lines of division. It is, of course, characteristic
of unstable states that minimal causes can at such times produce dis-
proportionate effects; in discussing the possibility of the fission of
species without geographic isolation, it will therefore be sufficient if
we can give a clear idea of the nature of the causes which condition
genetic instability.

Any environmental heterogeneity which requires special adapta-
tions, which are either irreconcileable or difficult to reconcile, will
exert upon the cohesive power of the species a certain stress. This
stress will be least when closely related individuals are exposed to the
environmental differences, and vanishes absolutely if every individual
has an equal chance of encountering either of two contrasted environ-
mental situations, or each of a graded series of such situations. It is
greatest when associated with circumstances unfavourable to sexual
union, of which the most conspicuous is geographical distance,
though others, such as earliness or lateness in seasonal reproduction,
may in many cases be important. I do not know any such circum-
stance, which, in the genetical situation produced, differs essentially
from geographical distance, in terms of which, therefore, it is con-
venient to develop the theory.

We may consider the case of a species subjected to different con-
ditions of survival and reproduction at opposite ends of its geo-
graphical range. Certain of the genes which exist as alternatives will
be favoured at one extreme, and will tend there to increase, while at
the other extreme they will be disadvantageous and tend to diminish
in frequency, the intermediate region being divisible into a series of
zones in which the advantage increases, from a negative value at one
extreme, through zero at a region in which the selective advantage
is exactly balanced, to a certain positive advantage at the other
extreme. A condition of genetic equilibrium is therefore only
established if the increase in frequency in the favourable region and

SEXUAL REPRODUCTION AND SEXUAL SELECTION 127
the decrease in frequency in the unfavourable region, not only
balance each other quantitatively, but are each equal to the rate at
which genes diffuse by migration and sexual union, from the one
region to the other. This rate must itself be determined, apart from
migratory or sedentary habits of the species, by the length of each
zone across which diffusion occurs, by the density of population
along it, and finally by the gradient in the frequency ratio between
the gene and its allelomorph as we pass across it. So long as a sufficient
gradient can be maintained, accompanied by an active diffusion of
germinal material, so long the local varieties, although, possibly,
distinct differences between them may be detected, will have no
tendency to increase these differences in respect of the frequency of
the genes in which they differ, and will be connected by all grades of
intermediate types of population.

The longer such an equilibrium is maintained the more numerous
will the genetic differences between the types inhabiting extreme
regions tend to become, for the situation allows of the extinction of
neither the gene favoured locally nor its allelomorph favoured else-
where, and all new mutations appearing in the intermediate zone which
are advantageous at one extreme but disadvantageous at the other
will have a chance of being added to the factors in which they differ.
In addition to those genes which are selected differentially by the
contrasted environments, we must moreover add those, the selective
advantage or disadvantage of which is conditioned by the genotype
hi which they occur, and which will therefore possess differential
survival value, owing not directly to the contrast in environments,
but indirectly to the genotypic contrast which these environments
induce. The process so far sketched contains no novel features, it
allows of the differentiation of local races under natural selection,
and shows that this differentiation must, if the conditions of diffusion
are constant, be progressive. It involves no tendency to break the
stream of diffusion, or consequently to diminish in degree the unity
of ancestry which the species possesses. It is analogous to the stretch-
ing of a material body under stress, not to its rupture.

There are, however, some groups of heritable variations which will
influence diffusion. In the case we are considering in which the cause
of isolation is geographical distance, the instincts governing the
movements of migration, or the means adopted for dispersal or fixa-
tion, will influence the frequency with which the descendants of an

128 SEXUAL REPRODUCTION AND SEXUAL SELECTION
organism, originating in one region, find themselves surrounded by
the environment prevailing in another. _Thfi-_CQnstant elimination
in each extreme region of the genes which diffuse to it from the other,
must involve incidentally the elimination of those types of individuals
which are most apt so to diffuse. If it is admitted that an aquatic
organism adapted to a low level of salinity will acquire, under Natural
Selection, instincts of migration, or means of dispersal, which
minimize its chances of being carried out to sea, it will be seen that
selection of the same nature must act gradually and progressively to
minimize the diffusion of germ plasm between regions requiring
different specialized aptitudes. The effect of such a progressive
diminution in the tendency to diffusion will be progressively to
steepen the gradient of gene frequency at the places where it is
highest, until a line of distinction is produced, across which there is
a relatively sharp contrast in the genetic composition of the species.
Diffusion across this line is now more than ever disadvantageous, and
its progressive diminution, while leaving possibly for long a zone of
individuals of intermediate type, will allow the two main bodies of
the species to evolve almost in complete independence.

In cases in which the cause of genetic isolation is not merely geo-
graphical distance, but a diversity among different members of the
species in their habitats or life history, in connexion with which
different genetic modifications are advantageous; the isolation will
of course not be increased by the differential modification of the
instincts of migration, or the means of dispersal ; but by whatever
type of hereditary modification will minimize the tendency for
germinal elements, appropriate to one form of life, to be diffused
among individuals living the other form, and among them con-
sequently eliminated.

The power of the means of dispersal alone, without the necessity
for selective discrimination in either region, is excellently illustrated
by the theory, due to Ray Lankester, which satisfactorily accounts
for the diminution or loss of functional eyes by the inhabitants of
dark caverns. Ray Lankester pointed out that the possession of the
visual apparatus is not merely useless to such animals but, by favour-
ing their migration towards sources of light, will constantly eliminate
them from the body of cave inhabitants, equally effectively whether
they survive or perish in their new environment. Those which remain
therefore to breed in the cavern are liable to selection in each genera-

SEXUAL REPRODUCTION AND SEXUAL SELECTION 129
tion for their insensibility to visual stimuli. It should be noted that
with such very restricted habitats migrational selection of this sort
might attain to very high intensity and in consequence produce
correspondingly rapid evolutionary effects.

Sexual preference

A means of genetic isolation which is of special importance in that it
is applicable equally to geographical and to other cases is one, which
for want of a better term, we may consider under the heading of
reproductive or sexual preference.

The success of an organism in leaving a numerous posterity is not
measured only by the number of its surviving offspring, but also by
the quality or probable success of these offspring. It is therefore
a matter of importance which particular individual of those available
is to be their other parent. With the higher animals means of dis-
crimination exist in the inspection of the possible mate, for in large
groups the sense organs are certainly sufficiently well developed to
discriminate individual differences. It is possible therefore that the
emotional reactions aroused by different individuals of the opposite
sex will, as in man, be not all alike, and at the least that individuals
of either sex will be less easily induced to pair with some partners
than with others. With plants an analogous means of discrimination
seems to exist in the differential growth rate of different kinds of
pollen in penetrating the same style.

An excellent summary of recently established facts in this field
has been given by D. F. Jones (Selective Fertilization, University of
Chicago, 1928). Cases are known in maize in which discrimination is
exercised against pollen bearing certain deleterious mutant factors,
and in one case in Oenothera against ovules bearing a certain lethal
factor. In these reactions both the genotype of the mother plant and
that of the pollen are exposed to selection, and it is this that serves
to explain the remarkable fact established by Jones' own observations
with maize, that pollen applied in mixtures is on the whole less
effective the greater the genetic diversity between the seed parents
and the pollen parent. Such a generalized tendency towards homo-
gamy, which is perhaps especially manifest in maize owing to the
enormous number of recessive defects, which by continued cross
pollination have accumulated in that plant, would, however, be far
less effective in promoting the fission of species than would the selec-

130 SEXUAL REPRODUCTION AND SEXUAL SELECTION

tion of discriminative tendencies specially directed towards that end,
such as must occur, as will be explained more fully below, in a group
constantly invaded by the diffusion of unfavourable genes.

In general the conditions upon which discrimination, when possible,
carTusefuIIy be exercised seem to be (i) that the acceptance of one
mate precludes the effective acceptance of alternative mates, and
(ii) that the rejection of an offer will be followed by other offers,
either certainly, or with such high probability, that the risk of tjheir
non-occurrence shall be smaller than the probable advantage to be
gained by the choice of a mate. The first condition is satisfied by the
females of most species, and in a considerable number of cases by
the males also. In other cases, while it would be a serious error for the
male to pursue an already fertilized female, it would seem that any
opportunity of effective mating could be taken with advantage. The
second condition is most evidently satisfied when members of the
selected sex are in a considerable majority at the time of mating.

The grossest blunder in sexual preference, which we can conceive
of an animal making, would be to mate with a species different from
its own and with which the hybrids are either infertile or, through the
mixture of instincts and other attributes appropriate to different
courses of life, at so serious a disadvantage as to leave no descendants.
In the higher animals both sexes seem to be congenitally adapted to
avoid this blunder and from the comparative rarity of natural
hybridization among plants, save in certain genera where specific dis-
tinctness may have broken down through maladaptation in this very
respect, we may infer the normal prevalence of mechanisms effective
in minimizing the probability of impregnation by foreign pollen. It
is therefore to be inferred that in the higher animals the nervous
system is congenitally so constructed, that the responses normal to
an association with a mate of its own species are, in fact, usually
inhibited by the differences which it observes in the appearance or
behaviour of a member of another species. Exactly what differences in
the sensory stimuli determine this difference in response it is of course
impossible to say, but it is no conjecture that a discriminative
mechanism exists, variations in which will be capable of giving rise to
a similar discrimination within its own species, should such dis-
crimination become at any time advantageous.

A typical situation in which such discrimination will possess
a definite advantage to members of both sexes must arise whenever

SEXUAL REPRODUCTION AND SEXUAL SELECTION 131
a species occupying a continuous range is in process of fission into
two daughter species, differentially adapted to different parts of that
range ; for in either of the extreme parts certain relatively disadvan-
tageous characters will constantly appear in a certain fixed proportion
of the individuals in each generation, by reason of the diffusion of
the genes responsible for them from other parts of the range. The
individuals so characterized will be definitely less well adapted to the
situation in which they find themselves than their competitors ; and
in so far as they are recognizably so, owing, for example, to differences
in tint, their presence will give rise to a selective process favouring a
sexual preference of the group in which they live. Individuals in each
region most readily attracted to or excited by mates of the type there
favoured, in contrast to possible mates of the opposite type, will, in
fact, be the better represented in future generations, and both the
discrimination and the preference will thereby be enhanced. It
appears certainly possible that an evolution of sexual preference due
to this cause would establish an effective isolation between two
differentiated parts of a species, even when geographical and other
factors were least favourable to such separation.

Sexual selection

The theory put forward by Darwin to account for the evolution of
secondary sexual characters involves two rather distinct principles.
In one group of cases, common among mammals, the males, especially
when polygamous, do battle for the possession of the females. That
the selection of sires so established is competent to account for the
evolution, both of special weapons such as antlers, and of great
pugnacity in the breeding season, there are, I believe, few who doubt,
especially since the investigation of the influence of the sex hormones
has shown how genetic modifications of the whole species can be
made to manifest themselves hi one sex only, and has thereby
removed the only difficulty which might have been felt with respect
to Darwin's theory.

For the second class of cases, for which the amazing development
of the plumage in male pheasants may be taken as typical, Darwin
put forward the bold hypothesis that these extraordinary develop-
ments are due to the cumulative action of sexual preference exerted
by the females at the time of mating. The two classes of cases were
grouped together by Darwin as having in common the important

132 SEXUAL REPRODUCTION AND SEXUAL SELECTION
element of competition, involving opportunities for mutual inter-
ference and obstruction, the competition being confined to members
of a single sex. To some other naturalists the distinction between the
two types has seemed more important than this common element,
especially the fact that the second type of explanation involves the
will or choice of the female. A. R. Wallace accepted without hesita-
tion the influence of mutual combats of the males in the evolution
of sex-limited weapons, but rejected altogether the element of female
choice in the evolution of sex-limited ornaments.

It has been pointed out in Chapter II that a detailed knowledge
of the action of Natural Selection would require an accurate evalua-
tion of the rates of death and reproduction of the species at all ages,
and of the effects of all the possible genetic substitutions upon these
rates. The distinction between one kind of selection and another
would seem to require information in one respect infinitely more
detailed, for we should require to know not the gross rates of death
and reproduction only, but the nature and frequency of all the
bionomic situations in which these events occur. The classification
of causes of death required by law is sufficiently complex, and would
require very extensive medical knowledge if full justice were to be
done to it in every case. Even qualified medical men, however, are
not required to specify the sociological causes of birth. In pointing
out the immense complexity of the problem of discriminating to
which possible means of selection a known evolutionary change is to
be ascribed, or of allotting to several different means their share in
producing the effect, I should not like to be taken to be throwing
doubt on the value of such distinctions as can be made among the
different bionomic situations in which selection can be effected. The
morphological phenomena may be so striking, the life-history and
instincts may have been so fully studied in the native habitat, that
a mind fully stored with all the analogies within its field of study may
be led to perceive that one explanation only, out of those which are
offered, carries with it a convincing weight of evidence. Every case
must, I conceive, be so studied and judged upon by persons acquainted
with the details of the case, and even so in the vast majority of
cases the evidence will be too scanty to be decisive. It would accord
ill with the scope of this book (and with the pretensions of its author)
to attempt such a decision in any particular case. There does seem
room, however, for a more accurate examination of the validity of the

SEXUAL REPRODUCTION AND SEXUAL SELECTION 133
various types of argument which have been used, and which must be
used if any interpretation at all is to be put upon the evidence, than
seems hitherto to have been attempted.

It is certain that some will feel that such an abstract form of
treatment does injury to the interest of the subject. On the other
hand I am confident that many engaged in the actual work of
observation and classification would welcome any serious attempt
to establish impartial principles of interpretation. The need is
greatest in a subject, in which generalizations embodying large
numbers of observational facts are of such high value, that in con-
troversy mere citations of fresh facts seem sometimes to be invested
with a logical force, which they do not really possess ; it is possible
thus for even the fairest minded of men, when thoroughly convinced
of the correctness of his own interpretation, in which conviction he
may be fully justified, to use in its support arguments which, had he
been in real doubt, he could scarcely have employed. To take but
a single instance of a most innocent lapse of logic in discussions of
sexual selection; it was pointed out by Wallace that very many
species which are conspicuously or brilliantly coloured, and in which
the females are coloured either exactly like the males, or, when
differently coloured are equally conspicuous, either nest hi concealed
situations such as holes in the ground or in trees, or build a domed or
covered nest so as completely to conceal the sitting bird. In this con-
cealment Wallace perceived an explanation of the lack of protective
coloration in the female. To the objection, which seems to have
originated with the Duke of Argyll, that a large domed nest is more
conspicuous to an enemy than a smaller open nest, Wallace replied
that as a matter of fact they do protect from attack, for hawks or
crows do not pluck such nests to pieces. Darwin, on the other hand,
believed that there was much truth in the Duke of Argyll's remark,
especially in respect to all tree-haunting carnivorous animals. It will
be noticed that neither controversialist seems to perceive that the
issue is not concerned with the advantages or disadvantages of covered
nests, or that, however disadvantageous these nests may be supposed
to be, they nevertheless do fulfil the conditions required by Wallace
of precluding the selection during brooding of protective colours in
the female, by the action of predators to which brooding females
might otherwise have been visible.

A much more serious error, which has not been without echoes in

134 SEXUAL REPRODUCTION AND SEXUAL SELECTION
biological opinion, was made by Wallace in arguing that the effect of
selection in the adult is diminished by a large mortality at earlier
stages (Darwinism, p. 296).

In butterflies the weeding out by natural selection takes place to an
enormous extent in the egg, larva, and pupa states ; and perhaps not
more than one in a hundred of the eggs laid produces a perfect insect
which lives to breed. Here, then, the impotence of female selection, if
it exists, must be complete; for, unless the most brilliantly coloured
males are those which produce the best protected eggs, larvae, and
pupae, and unless the particular eggs, larvae, and pupae, which are able
to survive, are those which produce the most brilliantly coloured butter-
flies, any choice the female might make must be completely swamped.
If, on the other hand, there is this correlation between colour develop-
ment and perfect adaptation at all stages, then this development will
necessarily proceed by the agency of natural selection and the general
laws which determine the production of colour and of ornamental
appendages.

It should be observed that if one mature form has an advantage
over another, represented by a greater expectation of offspring, this
advantage is in no way diminished by the incidence of mortality in
the immature stages of development, provided there is no association
between mature and immature characters. The immature mortality
might be a thousandfold greater, as indeed it is if we take account of
the mortality of gametes, without exerting the slightest influence
upon the efficacy of the selection of the mature form. Moreover,
Wallace himself attached great importance to other selective effects
exerted upon mature butterflies as is shown by his treatment of
protective resemblance on page 207 of the same work. It cannot
therefore have been the cogency of the argument he uses which
determined Wallace's opinion, but rather the firmness of his con-
viction that the aesthetic faculties were a part of the ' spiritual nature '
conferred upon mankind alone by a supernatural act, which supplies
an explanation of the looseness of his argument.

The two fundamental conditions which must be fulfilled if an
evolutionary change is to be ascribed to sexual selection are (i) the
existence of sexual preference at least in one sex, and (ii) bionomic
conditions in which such preference shall confer a reproductive
advantage. In cases where the two conditions can be satisfied, the
existence of special structures, which on morphological grounds may
be judged to be efficacipus as ornaments, but to serve no other useful

SEXUAL REPRODUCTION AND SEXUAL SELECTION 135
purpose, combined with ecological evidence that the structures are
at their fullest development in the mating season, and are then
paraded conspicuously, provides evidence of the same kind as, in
other cases, is deemed conclusive as to the evolutionary significance
of bodily structures.

With respect to sexual preference, the direct evidence of its
existence in animals other than man is, and perhaps always will be,
meagre. The extreme oddity of the preferences reported of individual
birds in captivity suggests that their mentality is sometimes deranged,
at least in respect of sexual preference, by the artificial conditions,
and show no more that an effective nervous mechanism does in fact
exist, which responds differently to different suitors. The only point
of value, which it would seem might be determined by such observa-
tions, is the extent to which different hen birds concur in then-
preferences among the cocks. Since, I suppose, only one choice could
be confidently observedin each season, sucha test could onlybeapplied
with sufficient numbers to polygamous birds ; among these, however,
it should be possible to demonstrate it with certainty, if an order of
preference exists.

The strongest argument adduced by Darwin in respect to birds in
the wild state must certainly be given now a different interpretation.
He gives numerous cases in which when one of a pair of birds is shot
its place is found almost immediately to be taken by another of the
same sex, whether male or female. He concludes that, surprising as
it may seem, many birds of both sexes remain unpaired, and also —
and here only we part company with him — this, because they cannot
find a mate to please them. If this were the true explanation it would
indicate sexual preferences so powerful as to inhibit mating altogether
in a considerable proportion of birds, and such intensity of preference
could scarcely be maintained in a species unless the advantage to the
prospects of the progeny due to the possibility of gaining a very
superior mate were larger than the certain loss of an entire breeding
season. As will be seen, it is difficult to assign in most cases a rational
basis for so great an advantage. On the other hand the researches of
H. E. Howard upon Territory in Bird Life provide a very simple and
adequate explanation of the fact observed. On this view the birds
which remain unmated do so because they are not in possession of
a breeding territory where they can nest unmolested, but are ready
to mate at once with a widow or widower left in possession of this

136 SEXUAL REPRODUCTION AND SEXUAL SELECTION

coveted property. I do not know, however, how much evidence there
is for asserting that it is always the widowed bird and a new mate,
rather than a new pair, which is found in possession of the vacant
territory. The adoption of existing young suggests that sometimes
at least it is the former.

If instead of regarding the existence of sexual preference as a basic
fact to be established only by direct observation, we consider that
the tastes of organisms, like their organs and faculties, must be
regarded as the products of evolutionary change, governed by the
relative advantage which such tastes may confer, it appears, as has
been shown in a previous section, that occasions may be not in-
frequent when a sexual preference of a particular kind may confer
a selective advantage, and therefore become established in the species.
Whenever appreciable differences exist in a species, which are in fact
correlated with selective advantage, there will be a tendency to select
also those individuals of the opposite sex which most clearly dis-
criminate the difference to be observed, and which most decidedly
prefer the more advantageous type. Sexual preference originating in
this way may or may not confer any direct advantage upon the
individuals selected, and so hasten the effect of the Natural Selection
in progress. It may therefore be far more widespread than the
occurrence of striking secondary sexual characters.

Certain remarkable consequences do, however, follow if some
sexual preferences of this kind, determined, for example, by a
plumage character, are developed in a species in which the preferences
of one sex, in particular the female, have a great influence on the
number of offspring left by individual males. In such cases the
modification of the plumage character in the cock proceeds under
Jbwo selective influences (i) an initial advantage not due to sexual
preference, which advantage may be quite inconsiderable hi magni-
tude, and (ii) an additional advantage conferred by female prefer-
ence, which will be proportional to the intensity of this preference.
The intensity of preference will itself be increased by selection so long
as the sons of hens exercising the preference most decidedly have any
advantage over the sons of other hens, whether this be due to the first
or to the second cause. The importance of this situation lies in the
fact that the further development of the plumage character will still
proceed, by reason of the advantage gained in sexual selection, even
after it has passed the point in development at which its advantage

SEXUAL REPRODUCTION AND SEXUAL SELECTION 137
in Natural Selection has ceased. The selective agencies other than
sexual preference may be opposed to further development, and yet
the further development will proceed, so long as the disadvantage
is more than counterbalanced by the advantage in sexual selection.
Moreover, as long as there is a net advantage in favour of further
plumage development, there will also be a net advantage in favour of
giving to it a more decided preference.

The two characteristics affected by such a process, namely plumage
development in the male, and sexual preference for such develop-
ments in the female, must thus advance together, and so long as the
process is unchecked by severe counterselection, will advance with
ever-increasing speed. In the total absence of such checks, it is easy
to see that the speed of development will be proportional to the
development already attained, which will therefore increase with
time exponentially, or in geometric progression. There is thus in any
bionomic situation, in which sexual selection is capable of conferring
a great reproductive advantage, the potentiality of a runaway
process, which, however small the beginnings from which it arose,
must, unless checked, produce great effects, and in the later stages
with great rapidity.

Such a process must soon run against some check. Two such are
obvious. If carried far enough, it is evident that sufficiently severe
counterselection in favour of less ornamented males will be encoun-
tered to balance the advantage of sexual preference; at this point
both plumage elaboration and the increase in female preference will
be brought to a standstill, and a condition of relative stability will
be attained. It will be more effective still if the disadvantage to the
males of their sexual ornaments so diminishes their numbers surviving
to the breeding season, relative to the females, as to cut at the root of
the process, by diminishing the reproductive advantage to be con-
ferred by female preference. It is important to notice that the condi-
tion of relative stability brought about by these or other means, will
be of far longer duration than the process in which the ornaments are
evolved. In most existing species the runaway process must have
been already checked, and we should expect that the more extra-
ordinary developments of sexual plumage were not due like most
characters to a long and even course of evolutionary progress, but
to sudden spurts of change. The theory does not enable us to
predict the outcome of such an episode, but points to a great

3653 T

138 SEXUAL REPRODUCTION AND SEXUAL SELECTION
advantage being conferred by sexual preference as its underlying
condition.

Exactly in what way the males which most effectually attract the
attention and interest of the females gain thereby a reproductive
advantage is a much more difficult question, since polygamy is not
nearly so widespread as sex-limited ornaments, and the theory of
sexual selection therefore requires that some reproductive advantage
should be conferred also in certain monogamous birds. Darwin's
theory on this point is exceedingly subtle. He supposes in effect that
there is a positive correlation in the females between the earliness
with which they are ready to breed, and the numbers of offspring
they rear, variations in both these variates being associated, as
Darwin suggests, with a higher nutritional condition. Whether this
is so in fact it is difficult to say, but it should be noted that the
dates of the breeding phenomena of a species could only be stabilized
if birds congenitally prone to breed early did not for this reason
produce more offspring. The correlation required by Darwin's theory
must be due solely to non-hereditary causes, such as chance varia-
tions of nutrition might supply. Whether or not there is such a
correlation, it would seem no easy matter to demonstrate.

There does seem, however, to be one advantage enjoyed by the
males mated earliest in any one district, and which therefore might
be conferred by sexual preference ; namely, that due to mortality
during the breeding season. The death rates of animals are often
surprisingly high, and a death rate of only one per cent, per week
would give a considerable advantage to the earlier mated males, even
if the chances of survival of his offspring were unfavourably affected
by his death.

A second circumstance in which sexual preference must afford
some reproductive advantage is in the remating of birds widowed
during the breeding season ; it appears certain that an abundance of
unmated birds are usually at hand to take advantage of such a situa-
tion, and the choice among these gives to those preferred a reproduc--
tive advantage, equally in the case of both sexes. To judge, however,
of the relative efficacy of the different possible situations in which
sexual preference may confer a reproductive advantage, detailed
ecological knowledge is required.

The possibility should perhaps be borne in mind in such studies
that the most finely adorned males gain some reproductive advantage

SEXUAL REPRODUCTION AND SEXUAL SELECTION 139
without the intervention of female preference, in a manner analogous
to that in which advantage is conferred by special weapons. The
establishment of territorial rights involves frequent disputes, but
these are by no means all mortal combats ; the most numerous, and
from our point of view, therefore, the most important cases are those
in which there is no fight at all, and in which the intruding male is so
strongly impressed or intimidated by the appearance of his antagonist
as not to risk the damage of a conflict. As a propagandist the cock
behaves as though he knew that it was as advantageous to impress
the males as the females of his species, and a sprightly bearing with
fine feathers and triumphant song are quite as well adapted for war-
propaganda as for courtship.

The selective action here considered combines the characteristics
of the two classes to which Darwin applied the term sexual selection,
namely the evolution of special weapons by combats between rival
males, and the evolution of adornments which attract or excite the
female. An appearance of strength and pugnacity is analogous to
the possession of these qualities in producing the same effect ; but the
effect is produced in a different way, and in particular, as in the case
of attractive ornaments, by the emotional reaction of other members
of the species. It involves in fact closely similar mental problems to
those raised by the existence of sexual preference. One difference
should be noted ; in the case of attractive ornaments the evolutionary
effect upon the female is to fit her to appreciate more and more highly
the display offered, while the evolutionary reaction of war paint upon
those whom it is intended to impress should be to make them less and
less receptive to all impressions save those arising from genuine
prowess. Male ornaments acquired in this way might be striking, but
could scarcely ever become extravagant.

Sex limitation of modifications

A difficulty which was regarded rather seriously during the develop-
ment of the theory of sexual selection is implicit in the limitations
of many of the structures ascribable to sex-limited selection, to the
particular sex on which the selection acts. The difficulty lay in how
far selection acting on only one sex ought to be expected to affect
the characters of both sexes, and whether a mutation originally
affecting the development of both sexes could be confined to one
sex only, by counter-selection on the other sex.

140 SEXUAL REPRODUCTION AND SEXUAL SELECTION

Of the large mutational changes chiefly available for genetic study
the great majority manifest themselves equally in the two sexes ; in
an important minority the effect is either unequal in the two sexes or
strictly limited to one sex. In birds and mammals a clearly under-
stood mechanism of sexual differentiation lies in the internal secre-
tions of the gonads, which are sexually differentiated, and possibly hi
a sexual differentiation of other internal secretions. It is a natural
inference that a proportion of the mutations which occur affecting any
given structure will be, from the first, sex limited in their appearance,
and, if they produce their effect only in conjunction with the internal
secretions of the sexual glands of one sex, their appearance will be
delayed to the adult stage like the other signs of sexual maturity.
This proportion may be as low as that observed in the genetic
mutations, and indeed the only reason for thinking that it may be
higher is that these somewhat violent changes may perhaps be
expected to be produced by deviations occurring at an early stage
of development, while the slighter changes to which progress by
Natural Selection must chiefly be due may more frequently be
initiated at later developmental stages.

Whatever the frequency, however, of sex limitation, it may fairly
be inferred that selection acting upon one sex only, would, in the
complete absence of counter-selection in the other sex, lead to an
evolutionary modification not very unequal in the two sexes. Well-
marked sexual differentiation must on this view be ascribed to a con-
dition in which the selective agencies acting on the two sexes oppose
each others influence. On the view that both sexes are in most
species highly adapted to their place in nature, this situation will be
readily brought about by the selection of modifications in one sex
only, for these, in so far as they are not sex-limited, will be accom-
panied by changes in the opposite sex, which, on the assumption of
high adaptation, will generally be disadvantageous and therefore
opposed by selective agencies. Without the assumption of high
adaptation, opposition between the actions of selection on the two
sexes must be fortuitous and rare, and it is by no means clear how the
widespread occurrence of sex -limited modification can on this view
be explained.

Since the whole body of genetic evidence seems to favour, and
even to require, the view that organisms are in general extremely
closely adapted to their situations, we need only consider the

SEXUAL REPRODUCTION AND SEXUAL SELECTION 141
consequences of this view. Selection applied to particular qualities
in one sex only will then tend, in the first instance, to modify this
sex slightly more than the other. The opposite sex will only be
modified so far as to bring into play agencies exerting selection, in
the opposite direction, and with equal intensity. The advantage of
protective coloration, stressed by Wallace, is of obvious importance
in this connexion. From this point, which must be reached relatively
rapidly, onwards, the selective advantage of a mutation in respect of
the selective activity under consideration, will not depend at all upon
the average of its effects in the two sexes, but only upon the difference
between these effects. If it enhances the sexual contrast and makes
the two sexes less alike, it will be favoured by selection, and will have
therefore a definite probability of contributing its quotum towards the
building up of sexual differentiation. If on the contrary its effect would
have been to render the sexes more alike, it will be rejected by the
selection in progress. In this, the more prolonged evolutionary phase,
it should be noted that any effect which the new mutations may have
upon both sexes equally, or, hi fact, the average of their effects upon
the two sexes, will be immediately neutralized by a change of frequency
in those factors which, without being sex limited, influence the
development of the organ in question.

Besides the mutations, the effects of which are conditioned by the
sexual secretions, an important class of mutations are those which
influence the nature of these secretions themselves ; for in the con-
dition of sexually opposed selections, any modification of these
secretions, which, without impairing their normal action, enhances or
increases the range of their developmental effects will thus afford
a further means of increasing sexual differentiation. In this way it is
by no means a supposition to be excluded as impossible that a
character at first manifested equally by the two sexes should, by the
action of natural selection, later become sex-limited in its appearance.

Natural Selection and the sex -ratio

The problem of the influence of Natural Selection on the sex-ratio
may be most exactly examined by the aid of the concept of reproduc-
tive value developed in Chapter II. As is well known, Darwin expressly
reserved this problem for the future as being too intricate to admit
of any immediate solution. (Descent of Man, p. 399).

142 SEXUAL REPRODUCTION AND SEXUAL SELECTION

In no case, as far as we can see, would an inherited tendency to
produce both sexes in equal numbers or to produce one sex in excess,
be a direct advantage or disadvantage to certain individuals more than
to others ; for instance, an individual with a tendency to produce more
males than females would not succeed better in the battle for life than
an individual with an opposite tendency ; and therefore a tendency of
this kind could not be gained through natural selection. Nevertheless,
there are certain animals (for instance, fishes and cinipedes) in which
two or more males appear to be necessary for the fertilization of the
female; and the males accordingly largely preponderate, but it is by
no means obvious how this male-producing tendency could have been
acquired. I formerly thought that when a tendency to produce the two
sexes in equal numbers was advantageous to the species, it would follow
from natural selection, but I now see that the whole problem is so
intricate that it is safer to leave its solution for the future.

In organisms of all kinds the young are launched upon their careers
endowed with a certain amount of biological capital derived from
their parents. This varies enormously in amount in different species,
but, in all, there has been, before the offspring is able to lead an
independent existence, a certain expenditure of nutriment in addition,
almost universally, to some expenditure of time or activity, which
the parents are induced by their instincts to make for the advantage
of their young. Let us consider the reproductive value of these off-
spring at the moment when this parental expenditure on their behalf
has just ceased. If we consider the aggregate of an entire generation
of such offspring it is clear that the total reproductive value of the
males in this group is exactly equal to the total value of all the
females, because each sex must supply half the ancestry of all future
generations of the species. From this it follows that the sex ratio will
so adjust itself, under the influence of Natural Selection, that the total
parental expenditure incurred in respect of children of each sex, shall
be equal ; for if this were not so and the total expenditure incurred
in producing males, for instance, were less than the total expenditure
incurred in producing females, then since the total reproductive value
of the males is equal to that of the females, it would follow that those
parents, the innate tendencies of which caused them to produce
males in excess, would, for the same expenditure, produce a greater
amount of reproductive value ; and in consequence would be the
progenitors of a larger fraction of future generations than would
parents having a congenital bias towards the production of females.

SEXUAL REPRODUCTION AND SEXUAL SELECTION 143
Selection would thus raise the sex-ratio until the expenditure upon
males became equal to that upon females. If, for example, as in man,
the males suffered a heavier mortality during the period of parental
expenditure, this would cause them to be more expensive to produce,
for, for every hundred males successfully produced expenditure
has been incurred, not only for these during their whole period of
dependance but for a certain number of others who have perished
prematurely before incurring the full complement of expenditure. The
average expenditure is therefore greater for each boy reared, but less
for each boy born, than it is for girls at the corresponding stages, and
we may therefore infer that the condition toward which Natural
Selection will tend will be one in which boys are the more numerous
at birth, but become less numerous, owing to their higher death-rate,
before the end of the period of parental expenditure. The actual
sex-ratio in man seems to fulfil these conditions somewhat closely,
especially if we make allowance for the large recent diminution in the
deaths of infants and children ; and since this adjustment is brought
about by a somewhat large inequality in the sex ratio at conception,
for which no a priori reason can be given, it is difficult to avoid the
conclusion that the sex-ratio has really been adjusted by these means.
The sex-ratio at the end of the period of expenditure thus depends
upon differential mortality during that period, and if there are any
such differences, upon the differential demands which the young of
such species make during their period of dependency ; it will not be
influenced by differential mortality during a self -supporting period ;
the relative numbers of the sexes attaining maturity may thus be
influenced without compensation, by differential mortality during the
period intervening between the period of dependence and the attain-
ment of maturity. Any great differential mortality in this period
will, however, tend to be checked by Natural Selection, owing to the
fact that the total reproductive value of either sex, being, during this
period, equal to that of the other, whichever is the scarcer, will be the
more valuable, and consequently a more intense selection will be
exerted in favour of all modifications tending towards its preservation.
The numbers attaining sexual maturity may thus become unequal if
sexual differentiation in form or habits is for other reasons advan-
tageous, but any great and persistent inequality between the sexes
at maturity should be found to be accompanied by sexual differentia-
tions, having a very decided bionomic value.

144 SEXUAL REPRODUCTION AND SEXUAL SELECTION

Summary

A consequence of sexual reproduction which seems to be of funda-
mental importance to evolutionary theory is that advantageous
changes in different structural elements of the germ plasm can be
taken advantage of independently ; whereas with asexual organisms
either the genetic uniformity of the whole group must be such that
evolutionary progress is greatly retarded, or if there is considerable
genetic diversity, many beneficial changes will be lost through
occurring in individuals destined to leave no ultimate descendants
in the species. In consequence an organism sexually reproduced can
respond so much more rapidly to whatever selection is in action, that
if placed in competition on equal terms with an asexual organism
similar in all other respects, the latter would certainly be replaced by
the former.

In order to take full advantage of the possible occurrence of
advantageous mutations, mutation rates must be generally so low
that hi the great majority of loci the homologous genes throughout
a single species are almost completely identical, and this is the con-
dition which we appear to find in the higher organisms. With sexual
reproduction species are not arbitrary taxonomic units such as they
would be with asexual reproduction only, but are bound together
by sharing a very complete community of ancestry, if we look back
only a hundred generations. The bulk of intraspecific variance apart
from the differences between geographic races, in which some degree
of isolation has taken effect, must be ascribed to segregation during
comparatively few generations in the immediate past.

Selection acting differently on different parts of a species, whether
or not these parts are distinguished geographically, will induce
distinctions between them in the frequency with which different
genes or gene combinations occur, without necessarily impairing the
unity of the species. An element of instability will, however, be
introduced in such cases, by genetic modifications affecting the
frequency of germinal interchange between the parts ; and this,
under sufficiently intense selection, will lead to the fission of species,
even in the absence of geographical or other barriers to intercourse.

An important means of fission, particularly applicable to the
higher animals, lies in the possibility of differential sexual response to
differently characterized suitors. Circumstances favourable to the

SEXUAL REPRODUCTION AND SEXUAL SELECTION 145
fission of species into parts adapted to different habitats will also be
favourable to the development both of discrimination and of sexual
preference.

The main postulate of Darwin's theory of sexual selection, namely
the exercise of sexual preference, will thus tend to be satisfied by the
effects of previous selection. We may infer that the rudiments of
an aesthetic faculty so developed thus pervade entire classes,
whether or not this faculty is in fact afforded opportunities of in-
ducing evolutionary change. In species so situated that the reproduc-
tive success of one sex depends greatly upon winning the favour of
the other, as appears evidently to be the case with many polygamous
birds, sexual selection will itself act by increasing the intensity of
the preference to which it is due, with the consequence that both the
feature preferred and the intensity of preference will be augmented
together with ever-increasing velocity, causing a great and rapid
evolution of certain conspicuous characteristics, until the process
can be arrested by the direct or indirect effects of Natural Selection.

Consideration of the mechanism of sex-limited hormones, by which
the secondary sexual characteristics of mammals and birds are
largely controlled, shows that sexual differentiation may be increased
or diminished by the action of Natural Selection, either through the
occurrence of mutations sex-limited in effect, or through a modifica-
tion of the hormone mechanism. It is thus not impossible that
a mutant form, at first manifested equally by both sexes, should later,
under the action of selection, become confined to one sex only. The
question of the ratio of the sexes at maturity has not the same
importance for sexual selection as was formerly thought, at least in
species in which the number of breeding pairs is limited by the alloca-
tion of territory. It is shown that the action of Natural Selection will
tend to equalize the parental expenditure devoted to the production
of the two sexes ; at the same time an understanding of the situations
created by territory will probably reveal more than one way in which
sexual preference gives an effective advantage in reproduction.

VII
MIMICRY

The relation of mimicry theory to the parent theory of Natural Selection. Theories of
Bates and Miiller. Supposed statistical limitation of Mullerian theory. Observational
basis of mimicry theory. The evolution of distastefulness. The theory of saltations.
Stability of the gene-ratio. Summary.

// our object is to ascertain how living things have become what they are . . . ,
a solution can never be attained unless the details of the selective process are
studied at least as fully and thoroughly as the material which is subjected to
selection. POUI/TON, 1908.

THERE are three respects in which the theory of mimicry is of great
importance to the student of Natural Selection. In the first place a
great array of striking facts is by its means rendered intelligible under
the heading of a single principle ; that principle being the selective
action of a single definite factor, usually predatism, in an insect's
environment, upon a single set of characters, coloration, patterning,
attitude at rest, mode of flight, observable in the insect itself. In our
ordinary state of ignorance as to the lives of wild creatures it is rare
to be able to particularize, as can be done in this case, either the
incidence of an environmental factor, or the peculiar benefits of an
observed morphological or physiological characteristic.

Secondly, as has been mentioned on page 54, it is of special impor-
tance to be able to demonstrate, in any extensive group of cases, the
adaptive significance of the characteristics of species. For while it
may be true, as has been urged by Robson, that even a minute
morphological examination of the differences distinguishing closely
related species, is not usually capable of revealing to us their adaptive
significance hi relation to their natural habitats, there can be no
doubt that the study of mimicry has shown in numerous instances
the particular environmental factor to which are to be ascribed
certain characteristics distinctive of nearly related species, sub-,
species, and even of local varieties.

Thirdly, it is a matter of historical interest that the theory of
mimicry, as the greatest post-Darwinian application of Natural
Selection, played an especially important part towards the end of the
nineteenth and the beginning of the twentieth century (when the
concentration of biological effort in the museums and laboratories

MIMICRY 147

was beginning to render the conclusions of the field naturalists of an
earlier generation in part unintelligible), by calling constant attention
to the importance of ecological observations for the interpretation of
the material gathered in the great museums.

It will be clearly understood, from the argument of Chapter I, that
in the opinion of the author the bearings of genetical discoveries, and
in particular of the Mendelian scheme of inheritance, upon evolu-
tionary theory, is quite other than, and indeed opposite to, that
which the pioneers of Mendelism originally took it to be. These were
already, at the time of the rediscovery of Mendel's work, in the full
current of that movement of evolutionary thought, which in the
nineties of the last century had set in in favour of discontinuous origin
for specific forms. It was natural enough therefore that the discon-
tinuous elements in Mendelism should, without sufficiently critical
scrutiny, have been interpreted as affording decisive evidence in
favour of this view. Nowhere perhaps in biology has this current of
opinion introduced such serious discrepancies, as in the interpretation
of mimetic resemblance.

Theories of Bates and Miiller

The theory of Bates, put forward in 1861, implies no more than
is readily understood from the term mimicry; namely that certain
palatable forms, which Bates observed especially among butterflies,
being preyed upon by insect-eating birds, are so placed that it is
advantageous for them to be mistaken for other objects, especially
less palatable forms, which they somewhat resemble ; and that the
selective advantage so conferred upon those individuals in whom the
resemblance is most complete, has led these species to become more
and more perfect mimics of other species inhabiting the same district,
relatively immune to attack, and therefore appropriate models. This
theory depends on the errors of the predators, but on errors of the
senses only, not of the judgement. The choice of food made by the
bird may be made by instinct, perfect, though latent, in the egg, or
may be the result of experience. In the latter case no account is
taken of the stages during which the experience is gathered, but only
of the final stage when the education is complete and a correct judge-
ment as to diet finally formed. The eye may still be deceived; it
is the essence of Bates 's theory that it should be exposed to decep-
tion ; but errors of judgement have no place in the theory.

148 MIMICRY

Whether it be supposed to be fixed by heredity, or to be open to
modification by experience, the judgement of the predator does impose
one limitation upon Bates 's theory. If hereditary it must have been
moulded by Natural Selection, as a system of food preferences ad-
vantageous to the species, and could not long continue to apply to
those particular situations in which the loss due to rejecting mimics
actually outweighed the advantage of rejecting the models. The same
consequence follows, only more immediately, if individual experience
is the basis of the judgement formed. It must be assumed, therefore,
that the mimics are sufficiently rare, or the models sufficiently
noxious, for it to be advantageous for the predator to reject the
models, together with a certain proportion of deceptive mimics, on
those occasions on which a discriminative rejection is practised ; or
alternatively, to assume that the state of affairs observed is a transient
one, pending a more perfect adaptation of the predator's instincts. In
point of fact the conclusion was early drawn by Bates, and widely
accepted, that the mimic must be a comparatively rare species, gain-
ing its advantage through resemblance to a highly protected and
abundant species inhabiting the same region.

A limitation of a similar kind, but of a somewhat different specifica-
tion, is imposed by the reaction of the model. The resemblance which
is favourable to the mimic will be for the same reason disadvantageous
to the model. An individual of the model species may suffer from
being mistaken for a mimic, and as the probability of this is least
when the resemblance is least, selection will tend to modify the model
so as to render it different from the mimic as conspicuously as possible.
This situation is not essentially different from that which gives rise
to warning colours generally, for to be recognized as unpalatable
is equivalent to avoiding confusion with palatable species. Close
Batesian mimicry can therefore only be established if the rate of
modification of the model has been less than that of the mimic, and
this may be taken, in terms of the predominant factors of the situa-
tion, to imply that the selective advantage conferred on the individual
mimic, exceeds the selective disadvantage suffered by the individual
model. Disparity in numbers is as useful in ensuring the fulfilment
of this condition as it is in satisfying that imposed by the feeding
proclivities of the predator.

The observation, which was familiar to Bates, of the close super-
ficial resemblance between very abundant, and apparently equally

MIMICRY 149

protected, species, led Miiller eighteen years later to formulate what
has been called the Miillerian, as opposed to the Batesian, theory of
mimicry, a term which it is still convenient to apply, although, as
Professor__PouJtoji. has pointed out, the term mimicry should in
strictness be confined to the theory of Bates. Miiller's theory involves,
more than does that of Bates, a consideration of the ecological
situation in which the destruction of butterflies by birds actually
occurs. He^ points out that young birds, at least, do in fact learn
much by experience, and that during this process of self education
in what is and what is not good to eat, the total destruction suffered
by two unpalatable species will be diminished and ultimately halved,
if they come gradually to resemble one another so closely that the
lesson of avoidance learnt from the one will be equally applicable to
jEhe otherr~An extension of-the notion of education in this argument
was pointed out in 1915 by C. F. M. Swynnerton, who, on the basis
of very detailed observations, together with extensive experiments,
on the preferences of insect-eating birds, considers that, owing to a
partial failure of visual memory, the process of education is continued
throughout life by encountering, without necessarily attacking, the
aposematic types ; and that the greater the numbers showing a given
warning colour, the more frequently is the memory reinforced, and,
in consequence, actually fewer mistaken attacks are made.

The Batesian mimic gains its advantage at the expense of the
predator which it deceives, and of the model whose life it endangers.
In the Miillerian system both species alike are mimic and model, each
reaps an advantage of the same kind, and both co-operate to confer
an advantage upon the predator by simplifying its education. The
predator which requires to frustrate the wiles of a Batesian mimic
should develop a keen and sceptical discrimination ; while he will best
take advantage of the Miillerian situation by generalization, and
reasoning from analogy. The predator will tend to co-operate with
both kinds of prey to establish the Miillerian relationship, which is
to the advantage of all three, while model and predator will both
tend to diminish the advantage of the Batesian mimic, the first by
directly diminishing the resemblance, the other by modification of
feeding habits and by increasingly keen discrimination. The last
tendency, while diminishing the advantage of resemblance of any
given degree, will, however, tend to increase the degree of resemblance
actually attained.

150 MIMICRY

Supposed statistical limitation of Miillerian theory

It has been seen that the reactions of model and predator impose
a statistical limitation upon the theory of Bates, of which the prin-
cipal observable factor is the relative abundance of the species. It
has been supposed, and the supposition has been frequently repeated,
that a similar limitation inheres in the theory of Miiller. In 1908
G. A. K. Marshall suggested that, for arithmetical reasons, of two
equally unpalatable species inhabiting the same region the less
numerous will tend to resemble the more numerous, while the more
numerous will not reciprocate this tendency. Marshall does not
suggest that the more numerous will tend to decrease the resemblance.
The general purport of his paper is to emphasize the Batesian as
opposed to the Miillerian factor in resemblance, and that principally
for reasons other than that under discussion. The frequent repetition
of his statistical argument gives this point a special importance,
and it will be examined here since it is eminently of the type to
which mathematical reasoning should be able to supply a decisive
answer.

When no question of degree is introduced into the discussion
nothing is clearer than the distinction between the Batesian and the
Miillerian factors. If, however, we take into consideration that
butterflies may exist in all degrees of palatability, and that avoidance
or acceptance by the predator must depend greatly upon its appetite,
there is some danger that the distinctness of the evolutionary ten-
dencies pointed out by these two authors may be lost in the com-
plexity of the actual biological facts. This is necessarily the case in
the discussion of separate aspects of Natural Selection. An evolu-
tionary tendency is perceived intuitively, and expressed in terms
which simplify, and therefore necessarily falsify, the actual biological
facts. The only reality which stands behind such abstract theories is,
in each case, the aggregate of all the incidents of a particular kind,
which can occur from moment to moment to members of a species in
the course of their life-histories.

In order to show how these incidents may be specified let us
imagine three species, occupying the same region, of which A is
highly unpalatable, B less so, while C is free from objectionable
qualities. Then all possible situations may be exhaustively classified
as follows (I, II, III, IV), in which, however, the alternative reasons

MIMICRY 151

given for the occurrence of any situation (a, b, c), are by no means
exhaustive, but might conceivably be much elaborated by detailed
biological observations.

I. A, B, and C all liable to attack.

II. B and C liable to attack, but not A.

(a) A bird which, either by inheritance or sufficient experience,
prefers B to A is ready to attack an object recognized as B and not
to attack an object recognized as A.

(6) A bird has attacked A and found it to be unpalatable, but has
not yet had sufficiently impressed upon its mind the unpalatable
qualities of B.

III. A and C liable to attack, but not B.

(c) A bird has attacked B and found it to be unpalatable, but has
not yet had sufficiently impressed upon its mind the unpalatable
qualities of A.

IV. C only liable to attack.

In situation I, mimetic resemblance is without effect, while in
situation IV, C would gain by being mistaken for A or B, and A or B
would lose by being mistaken for C. C might, therefore, if the former
effect were to exceed the latter, become a Batesian mimic of A or B,
while, on the contrary, A and B would gain by emphasizing their
distinctive colouring, if so they could diminish the danger of confusion
with C. Similarly, in situation II, A loses by being mistaken for B,
and B gams by being mistaken for A ; while in situation III the reverse
is the case ; both A and B will seem, therefore, to be acted upon by
opposing tendencies, one tending towards similarity, and the other
towards dissimilarity. It is only when the situations are analysed
into their suggested causes that it is possible to indicate the resultant
effect.

For this purpose we distinguish the ' Batesian situation ' II (a), from
the 'Mullerian situations' 11(6) and III(c), recognizing that this
classification need not be exhaustive. It is then seen that Batesian
situations are to be distinguished by (i) depending upon differences
of palatability and (ii) producing a 'Batesian tendency' for B to
approach A and for A to recede from B. While the Miillerian situa-
tions (6) and (c) do not depend upon any difference of palatability,
but are taken to occur whenever both species are, on occasion,
deemed inferior to some alternative food.

152 MIMICRY

In the occurrence of situation II in which a bird will attack one
form, but will not attack the other, the difference between the action
of the Mullerian and the Batesian factor could only be discerned by
an observer who knew whether the bird's judgement, admittedly
right, was founded upon sufficient or insufficient experience. If the
experience is sufficient the bird would never prefer A to B (situation
III), consequently he would create only Batesian situations; while
if his experience is insufficient we must admit that it might have led
him to create situation III, and that even when he creates situation
II, that situation is none the less Mullerian. As a Batesian agent a
bird is always right in his judgement ; as a Mullerian agent he may be
right, but in view of his inexperience, he has no right to be right. If
the bird, as is usually the case with man, has only partially satis-
factory grounds for his judgement, he may in the same act be both a
Batesian and a Mullerian agent. It is only in the statistical aggregates
formed by all occasions of the two appropriate kinds that the two
evolutionary tendencies are completely distinct. Further study and
thought devoted to the habits of wild animals may thus enable other
tendencies to be recognized.

It is not, however, obvious from the analysis developed above that
the net effect of (6) and (c) will be to cause a mutual, though possibly
unequal, approach between the two species, such as Miiller inferred.
It is Marshall's contention that when the unpalatability is equal, the
less numerous species will be attracted by the greater, but the greater
will not be attracted by the less. Marshall does not fail to draw from
this conclusion a very important consequence, for, as he points out,
his premises lead to the inevitable result that, when a mimetic
similarity is once effected, the larger species will have gained the
smaller share, but still a share, of advantage from the association, and
one might be inclined to argue from this that the larger species also
will be led to approach this more advantageous condition. The far-
reaching conclusion is drawn that such an argument is not valid,
unless a continuous path from the first state to the second can be
shown to exist, such that the advantage increases for each step
along the path. Such a restriction, if necessary, would throw upon
the selectionist an onus of detailed demonstration, which his op-
ponent might increase indefinitely by challenging the details with
increasing minuteness. Even if the case of Mullerian mimicry were
not in itself of sufficient importance, it would be essential to examine

MIMICRY 153

in some detail the particular case in which the argument from ulti-
mate advantage is believed to lead to an erroneous conclusion.

Marshall's argument is essentially as follows: if A and B are two
equally distasteful species, of which B is the less numerous, then, in
the absence of mistakes due to the resemblance of the two species, the
young birds will take a proportionately heavier toll of B than of A,
before they have all learnt their lesson ; consequently any mutant of
A which resembles B will suffer more than the non-mutant type, and
in consequence will be eliminated. It will be seen that the mutant is
supposed to lose the whole of the advantage of the warning colour A,
and in return to receive only the less advantage of the warning colour
B, and this argument is indeed conclusive in showing that a mutation,
which leaps clear outside the protective influence of its type, will
suffer heavily for its rashness, even if, miraculously enough, its leap
lands it in the heart of the protective influence of a less numerous
aposeme. But what of a less violent mutation ? Is it possible to gain
some of the advantage of resembling B without losing the whole of
the advantage of resembling A ? Is it even possible that increased
shelter from aposeme B will more than counterbalance the loss from
decreased shelter from aposeme A? In his answer to Marshall's
argument Dixey puts forward a directly opposite supposition, namely
that a mutant of appearance intermediate between A and B, would
gain the full advantage of both resemblances. In fact, whereas
Marshall assumes that the whole of the advantage of resembling A
is lost before any of the advantage of resembling B is gained, Dixey
assumes, on the contrary, that the whole of the advantage of re-
sembling B may be gained before any advantage of resembling A is
lost. Both are clearly extreme assumptions; neither can be true
generally, and since the two assumptions lead to opposite conclusions
it would seem, so far as these arguments carry us, that we are faced
with a balance of forces of unknown magnitude, and can neither
assert that the Miillerian principle will work, nor that it will fail.

There remains the argument upon which Muller relied, that the
final condition of close resemblance being beneficial to both species,
both will therefore tend to approach this advantageous condition.
Marshall challenges the legitimacy of this argument, his reason being
the powerful one that he has disproved the conclusion hi a particular
instance ; as we have seen, however, Marshall's argument in the
chosen instance is indecisive, and the general argument from the

3653 Y

164 MIMICRY

advantage of the final state is in a position to reassert its claims. If
it is conclusive, however, it should be possible to devise a form of
argument which shall show unequivocally, on the agreed postulates,
that the admitted Miillerian situation will in fact produce a Miillerian
evolutionary tendency affecting both species concerned.

Such an argument may, I suggest, be constructed by comparing
the fate of any deviation from the type A, not with the average of
that type, but with an equally conspicuous but opposite deviation.
It will be admitted that variations of the species A, whether due to
mutation or to Mendelian recombination, will be equally frequent in
the direction of B as in the opposite direction; we may, therefore,
without error, consider such variations to occur in pairs comprising
variations of equal magnitude, but in opposite directions.

Since they are of equal magnitude they will lose (if anything)
equally by failing to be recognized as typically A, but if either, or
both, are ever mistaken for species B, the greater benefit will certainly
be reaped by the variation in the direction of B. Since the whole
species may be regarded as made up of such pairs of variations, and
since in every pair selection favours the one more like B, if either is
favoured, the net resultant must be a modification in the direction
of species B.

It will be seen that the condition for the existence of a mimetic
tendency is that in a certain proportion of the situations in which A
is liable to, but B is immune against attack, members of species A
should, through their similarity to B, actually escape attack. This is
somewhat different from the condition arrived at by Professor H. H.
Turner, in his appendix to Poulton's Memoir on Mimicry in the
Butterflies of Fiji, 1924, who speaks of an actual overlap of the varia-
tions of the two species as the condition for the efficacy of Miiller's
statistical argument. The possibility of error on the part of the
predator seems an essential feature in mimicry theory, and allowance
can be made for it in Turner's treatment, provided we interpret his
distribution curves as referring, not to the objective variability of the
species, but to the (probably much greater) variability of the preda-
tor's subjective impressions, influenced as these must often be by
inattention or haste, and by deceptive or insufficient illumination —
in fact, by whatever circumstances conduce to error, human or avian.
It is rather remarkable that, on a subject so remote from direct
evidence as the subjective impressions of birds, we should possess

MIMICRY 156

three good reasons for assuming an approximately normal distribu-
tion : (a) that the reasons for which this distribution is chosen as the
'normal law of errors' can scarcely be confined to mankind, (6) that
the objective variability of a measurable character due either to
Mendelian segregation, or to environmental fluctuations, is usually
closely normal, and (c) that the resultant compounded of two indepen-
dent distributions is necessarily more normal than one, and possibly
than both of its components.

The argument developed above may assuredly be refuted by dis-
proving any of the biological factors assumed in the discussion. If it
were proved that situations never in fact arise in which a member of
A would survive if mistaken for B, but would perish if not so mistaken,
that no predator learns by experience or is ever influenced by mimetic
resemblances, or that such variations of A as do favour the resem-
blance are not heritable, then the Miillerian theory of mimicry
would fail as an explanation of the resemblances observed. The sole
point established by the above reasoning is that if these biological
factors are admitted the resulting evolutionary tendency cannot be
confined to the less numerous of two species. The efficiency of
Miillerian selection will doubtless be greater (ceteris paribus) with the
smaller species, but the supposed statistical objection to the Miillerian
attraction of a larger species (or group) by a smaller is wholly fictitious.

Observational basis of mimicry theory

Though it would be beyond the scope of this book to attempt even
a general survey of the biological facts connected with mimicry ; it is
necessary to give a very concise summary of the kinds of observational
data which suffice to put the theory beyond doubt as the only satis-
fying explanation.

The number of species involved, among the insects alone, is so
great that in the majority of individual cases many classes of appro-
priate observations are lacking, and the probable explanation must
therefore be judged from incomplete evidence, in the light of cases of
which more is known.

The biological reasons upon which the conclusive cases are based
have been developed with conspicuous success by Poulton, whose line
of argument I can do little more than summarize, and to whose
labours and inspiration the great mass of facts now accumulated is
principally due.

156 MIMICRY

(i) Mimetic resemblances bear the hallmark of adaptation in the
multiplicity of the simultaneous modifications to which they are due.
This feature, as was pointed out in Chapter II, cannot be simply
exemplified, since the essence of adaptation lies in its complexity.
Mimetic resemblances involve colour, pattern, form, posture, move-
ment and sometimes also sound ; and many of these items, if analysed,
are themselves highly complex. Natural Selection is the only means
known to biology by which complex adaptations of structure to
function can be brought about.

(ii) In addition to showing adaptation, mimetic resemblances mani-
fest a further characteristic of Natural Selection, in the variety of
methods by which the same end is attained. This characteristic,
analogous to opportunism in human devices, seems to deserve more
attention than it has generally received. For the mechanisms of
living bodies seem to be built up far less than might be expected by
a human inventor, on simple and effective mechanical, physical, or
chemical principles. On the contrary every property of the behaviour
of matter, however odd and extraneous it may seem, seems to have
been pounced upon as soon as it happened to produce a desirable
effect. In the case of mimicry Poulton mentions four distinct means
used by different species of imitating the superficial appearance of an
ant, and in a single mimicry group finds five different methods of giving
an appearance of transparency to the wings of moths and butterflies.

In addition to these two features characteristic of Natural Selection
generally, three classes of facts are available to establish the particu-
lar requirements of mimicry theory.

(iii) Mimetic resemblances in general are not to be explained by
systematic affinity. Striking cases occur between different classes of
animals. Wheeler describes a case of tactile mimicry in which a mite
imposes upon the instincts of certain blind ants, by mimicking with
its anterior legs those movements of the antennae, by means of which
ants obtain food one from the other. Obviously the more closely
allied are the organisms which show resemblance, the more frequently
are homologous parts utilized in its elaboration, and the more care
is needed to demonstrate that a superficial resemblance has been
imposed upon or has prevented an initial divergence in appearance.

(iv) Mimetic resemblances are not accompanied by such additional
similarities as do not aid in the production, or strengthening, of a
superficial likeness.

PLATE II

ALL THE FIGURES ABE OF THE NATURAL SIZE

FIGS. 1-3. The head of the abundant East African Acraeine butterfly
Acraea zetes acara, Hew., as seen from the front (1), from above (2) and
the side (3), showing that the palpi, which are inconspicuous in most
butterflies, are a prominent feature with their orange colour displayed
against the black background.

FIGS. 1A-3A. Similar aspects of the head of the Nymphaline butterfly
Pseudacraea boisduvali trimenii, Butler, a mimic oiA.z. acara and found
in the same part of Africa. It is evident that the resemblance here ex-
tends to the exceptionally emphasized feature, as was observed in the
American examples shown in Figs. 6 and 7 of Plate I.

FIG. 4. Danaida tytia, Gray, a conspicuous Oriental Danaine butterfly
taken with its mimic (Fig. 5) in the Darjiling district.

FIG. 5. Papilio agestor, Gray, a swallowtail butterfly mimicking the pattern
of tytia.

FIG. 6. Neptis imitans, Oberth., a Nymphaline butterfly from S. W.China,
mimicking the geographical form of D. tytia which is found in the same
area.

Thus these two butterflies of widely separated groups both mimic this
peculiar Danaine pattern.

The butterflies and moths here represented illustrate by single examples
the widespread mimicry of the chief distasteful families in the tropics — on
Plate I the Ithomiinae (Fig. 6) and Heliconinae (Fig. 4) of the New World ;
on Plate II, the Danainae (Fig. 5), and Acraeinae (Figs. 1-3) of che Old.

OFT.

PLATE II. MODELS AND MIMICS IN AFRICAN (Figs. l-3a) AND
ORIENTAL (Figs. 4-6) INSECTS

PLATE I. MODELS AND MIMICS IN AUSTRALIAN (Figs. 1-3) AND
TROPICAL AMERICAN (Figs. 4-7) INSECTS

MIMICRY 167

(v) Mimetic resemblances occur between species inhabiting the
same region, appearing at the same seasons and hours, and having
frequently been captured flying together.

It should be added that it is not necessary, in order to establish the
mimetic character of a resemblance, that all of these five classes of
evidence should be available. Evidence under class (i) alone may be
sufficiently strong to exclude all reasonable doubt. Although that
under (iii), (iv), and (v) is of great value as independent corroboration,
no one item of it is necessarily present in all mimetic examples. The
importance of the facts grouped under (ii) lies not in their value as
evidence for individual cases, but in the comparative and systematic
survey of the phenomenon of mimicry as a whole.

Plates I and II, from examples chosen by Professor Poulton, will
serve to exemplify the kinds of superficial similarities, which form
the observational basis of the theory. While these are sufficient to
illustrate some characteristics of the evidence, familiarity with the
living animal and its ecological associates is of special importance in
these studies.

To distinguish whether an observed resemblance is to be ascribed
to the Batesian or to the Miillerian evolutionary tendencies, or to
both acting simultaneously, or, as in the case of the ant parasites
mentioned above, to some distinct type of selective action, appears
to be a much more difficult matter. Although Miillerian selection,
unlike that of Bates, causes a mutual approach of the two species ;
we can scarcely expect that their modifications will be sufficiently
nearly equal, save in a small minority of cases, for both to be made
apparent by comparison with related species. In the majority of
cases modification will be manifest on phylogenetic grounds only in
those species which have become most rapidly modified. The criterion
of palatability seems even more difficult to apply ; for though the
principle of Bates is excluded when two species are actually equally
acceptable or unacceptable, to demonstrate such equality with
sufficient precision to exclude differential predatism, and to demon-
strate it with respect to the effectual predatory population, would
seem to require both natural knowledge and experimental refinement
which we do not at present possess. It is perhaps from the lack of
more clearly decisive means of discrimination, that reliance has been
placed upon observations of relative abundance, which, though
clearly relevant to the problem, are not in themselves sufficient to

168 MIMICRY

supply a final test. Batesian mimicry by a more numerous of a less
numerous form, cannot be excluded as impossible on purely theor-
etical grounds ; for if the model were extremely noxious or the mimic
a not particularly valuable source of food, the motive for avoidance
may be but little diminished by the increase of the mimic. Moreover
it is not so much abundance relative to the entomological collector,
as abundance relative to selective agents of unknown species, and
whose habits and times of feeding are therefore also unknown, which
has to be considered, when this argument is used to exclude the
Batesian principle. Equally, demonstrable differences in palatability
do not, as has been seen, serve to exclude the Miillerian factor, the
potency of which appears to be manifest when similar warning
patterns are adopted by a group of several different and remotely
related species in the same district.

A distinction between the kind of resemblance attained by the
Batesian and Miillerian factors might be theoretically inferred in
cases in which the group of predators is confronted with only one or
the other type of resemblance. Since the Batesian resemblance is
deceptive, it should extend to every observable character, at least
in so far that no conspicuous differences remain by which the mimic
might be distinguished from the model. This is not a necessity for the
warning colours developed by Miillerian selection ; for these it might
suffice that a single conspicuous character should induce the predator
to classify the object viewed as unpalatable. Thus conspicuously
different insects may enjoy the advantages of Mullerian selection
provided they display in common any one conspicuous feature, where-
as Batesian mimics should show at least some resemblance to their
models in all features.

The evolution of distastefulness

An important question raised by both the Batesian and the Mullerian
theories of mimicry concerns the process by which nauseous flavours,
as a means of defence, have been evolved. Most other means of
defence such as stings, or disagreeable secretions and odours, are
explicable by increasing the chance of life of the individuals in which
they are best developed, or of the social community to which they
belong. With distastefulness, however, although it is obviously
capable of giving protection to the species as a whole, through its
effect upon the instinctive or acquired responses of predators, yet since

MIMICRY 159

any individual tasted would seem almost bound to perish, it is difficult
to perceive how individual increments of the distasteful quality,
beyond the average level of the species, could confer any individual
advantage.

The gregarious habit of certain larvae supplies a possible solution
of the problem, if we are willing to accept the view that the distasteful
quality of the imago, which warning colours are so well adapted to
advertise, is itself merely a by-product due to the persistence of
nauseous substances acquired through the protection afforded to the
larva. For, although with the adult insect the effect of increased
distastefulness upon the actions of the predator will be merely to
make that individual predator avoid all members of the persecuted
species, and so, unless the individual attacked possibly survives, to
confer no advantage upon its genotype, with gregarious larvae the
effect will certainly be to give the increased protection especially to
one particular group of larvae, probably brothers and sisters of the
individual attacked. The_sglectiye potency of the avoidance of
brothers will erf course be only hah* as grea^ aq j| thp. individual itself

is to be set the fact that it applies to the

whole of a possibly numerous brood. There is thus no doubt of the
real efficacy of this form of selection, though it may well be doubted
if all cases of insect distastefulness can be explained by the same
principle.

Professor Poulton has informed me that distasteful and warningly
coloured insects, even butterflies, have such tough and flexible bodies
that they can survive experimental tasting without serious injury.
Without the weight of his authority I should not have dared to
suppose that distasteful flavours in the body fluids could have been
evolved by the differential survival of individuals in such an ordeal.
The effect of selection on gregarious larvae, while not excluding
individual selection of the imago, provides an alternative which will
certainly be effective in a usefully large class of cases.

The institution of well defined feeding territories among many
birds in the breeding season makes it possible to extend the effect
produced on gregarious larvae to other cases in which the larvae,
while not gregarious in the sense of swarming on the same plant, are
yet distributed in an area which ordinarily falls within the feeding
territory of a single pair. The selective effect in such cases will be
diluted in so far as larvae of other broods may fall within the same

160 MIMICRY

territory, and will share in the advantage or disadvantage occasioned
by the high or low development of distastefulness of any larvae
tasted within this area. Such dilution will certainly make slower the
evolution of distastefulness, its speed, if we oversimplif y the problem
by supposing that a number of broods chosen at random share a
common reputation, being inversely proportional to the number of
broods ; dilution of a selective effect, should, however, not be confused
with a counteracting tendency, which might bring progress to a
standstill. The laying habits of several moths with conspicuous,
though scattered, larvae deserve attention in this respect.

The view that nauseous flavours have generally been acquired by the
effects of selection acting upon related larvae living in propinquity,
implies that gregariousness, or equivalent habits, were formerly used
by species which are now distasteful, though it does not imply that
species with distasteful and even conspicuous larvae should neces-
sarily have retained the gregarious habit ; for the advantages of this
habit, among which we may surmise (i) the reduced exposure of the
female during oviposition, and (ii) in the case of distasteful and
conspicuous larvae the advantage of increased protection from
predators, will not always counterbalance the disadvantage some-
times entailed by a depletion of the food-supply. We may, however,
fairly infer that if gregarious or equivalent habits are a necessary
condition for the development of protective flavours, and if the
possession of such flavours gives an added advantage, both to the
gregarious habit, and to conspicuous coloration, then some associa-
tion should be observable in nature between the conspicuousness of
the larvae, and the habit of laying the whole brood either in great
numbers on a single plant, or on neighbouring plants. The subject
is one on which a comprehensive summary of the biological facts is
much to be desired. I am indebted to Professor Poulton and Dr
A. D. Imms for the following instances.

The Buff-tip moth Zygaera bucephala is distasteful alike as larva,
pupa, and imago. The caterpillar is conspicuously yellow and black .
and strikingly gregarious, the pupa is brown and buried, though
equally distasteful, and the perfect moth is a beautiful example of
cryptic coloration. Since the distastefulness is thus only advertised
in the larval stage it may well have been developed by selection in
this stage only, a process certainly facilitated by its gregarious habits.
The Gothic moth, Mania typica is also unpalatable at all stages ; in

MIMICRY 161

this case the larvae are not conspicuous, but feed when small in
companies on the under sides of leaves.

The hairy rather brightly coloured caterpillars of Onethocampa
processioned live in communal webs. When they have eaten the
foliage enclosed in the web they march out in large 'processions', and
seek out a site for a new web. When older they sally out at dusk and
break into small parties to feed, returning to the communal web
before daylight; they seem instinctively to avoid solitude as if it
were a danger. These caterpillars exhibit a number of features, the
web, the avoidance of daylight, and the fear of solitude, each of
which may be interpreted as affording some measure of protection
against different predators.

Conspicuous larvae of butterflies and moths are generally grega-
rious though not always so. An apparent exception is afforded by
the Magpie moth Abraxas grossulariata of which the larvae feed
separately ; the eggs, however, are laid in groups, and the larvae are
numerous on the same bush, or on adjacent bushes. Anosia plexippus
however, scatters her eggs, although she has solitary, inedible, con-
spicuous, larvae. This is probably true of many Danaines.

True gregariousness seems to be characteristic of distasteful species
which fly over considerable distances, while those with sluggish
females may have scattered, though not widely scattered larvae.

An instructive case is afforded by the Peacock and Tortoise-shell
butterflies, Vanessa, and related genera. These are swift fliers, and
their larvae might, therefore, be widely scattered. In the true genus
Vanessa the larvae are conspicuous, and the eggs are laid in batches,
whereas in the Painted Lady Cynthia cardui, and the Red Admiral
Pyrameis atalanta, formerly placed in Vanessa, the larvae are partly
concealed and the eggs are laid singly.

Larvae of many Chrysomelid beetles are gregarious, and some of
these at least are notably distasteful.

Of Saw-fly larvae Cameron says those 'which give out secretions
or fetid odours are gregarious, several feeding on the same leaf, often
ranged in a row with their bodies stuck out in the air. They have
nearly always bright colours'. The advantage of gregariousness in
strengthening these means of defence is obvious; they may be
regarded as developments of the passive defence afforded by nauseous
flavours, and it is in the initial stages of this development that the
gregarious habit seems to supply the condition for effective selection.

3653 v-

162 MIMICRY

In general it may be said that the observational facts in this field
are consistent with, and lend some support to the view, that, whereas
offensive flavours supply the condition for the evolutionary develop-
ment of warning colours, and presumably also of warning odours, the
condition for the evolutionary development of offensive flavours,
which may equally characterize all stages of the life history, is to be
found in the gregariousness or propinquity of larvae of the same
brood, and therefore of somewhat highly correlated genetic constitu-
tion. A much wider knowledge of the observational facts than the
author possesses would, however, be needed, before it could be as-
serted that no alternative view would suffice to explain the evolution
of distastefulness, as a means of defence.

The principle deduced in this section of the selective advantage
shared by a group of relatives, owing to the individual qualities of one
of the group, who enjoys no personal selective advantage, is analogous
to the situation which arises in human communities, in the tribal
state of organization, in the selection of the group of qualities which
may be summed up as heroism. The ideal of heroism has been
developed among such peoples considerably beyond the optimum of
personal advantage, and its evolution is only to be explained, in
terms of known causes, by the advantage which it confers, by repute
and prestige, upon the kindred of the hero. The human situation,
which will be analysed in more detail in Chapter XI is, however,
certainly complicated by sexual selection, of which there is no
evidence in the case of the evolution of distasteful qualities in insects.

The theory of saltations

In his book on Mimicry in Butterflies, 1915, Punnett repeats Mar-
shall's argument, and concludes without reservation that Mullerian
mimicry of a less numerous by a more numerous species is excluded
by it. At first sight the argument appears irrelevant to Punnett's
mam contention of the inadequacy of Natural Selection to produce
adaptations, for he evidently, unlike Marshall, would reject also both
Batesian mimicry, and the Mullerian mimicry of the more numerous
by the less numerous species. Nevertheless, it would not be altogether
fair to regard Punnett's citation of Marshall's argument as a merely
extraneous addition to his indictment, such as by arousing suspicion
of error, though on an irrelevant issue, might serve to secure a verdict
on the main count; on the contrary, Marshall's argument plays a

MIMICRY 163

small yet essential part in his destructive argument derived from
mimicry rings. The case of two presumably palatable female types
each quite unlike the corresponding males, which males are unlike
each other, is chosen to illustrate this difficulty. The two females
show an apparent mimetic resemblance to three other butterflies,
two regarded as definitely unpalatable and the third as doubtfully so.
Assuming that the non-mimetic males represent the former appear-
ance of the two mimetic females, it is asked how the latter have come
to resemble the distasteful members of the ring. Granted that these
models might once have been not unlike in appearance to one of these
males it can scarcely be assumed that they ever resembled both,
either simultaneously or consecutively ; but unless such a resemblance
formerly existed a gradual mimetic evolution is precluded, and we
should be forced to admit that the mimetic females arose as sports or
saltations totally unlike their mothers.

It will be seen that for Punnett's argument on this important
point, the gradual and mutual convergence of two or more different
warning colours must be wholly excluded, for if the possibility of such
aprocess is admitted, the difficulty of imagining a continuous sequence
of changes entirely disappears, while on the contrary the assumption
of discontinuity becomes a burden upon the theory, involving as it
does the definite improbability of hitting off a good resemblance at
one shot. Consequently Marshall's argument, which Punnett seems
to have taken as reimposing all the limitations of the Batesian
situation, plays an essential part in the argument in favour of salta-
tions ; so essential indeed that it seems impossible to repair the breach
made by its removal.

The case for saltations as presented by Punnett was not entirely
negative and destructive in character; it embodied one (then)
recently discovered fact of considerable interest, namely that the
differences between the three forms of the trimorphic female of
Papilio polytes could be ascribed to two Mendelian factors, both
limited in their obvious effects to the female sex, and one apparently
necessary for the manifestation of the second.

This fact is of importance as indicating the mechanism by which
a clear polymorphism is maintained ; it shows that polymorphism in
this case, and probably in similar cases, is dependent on one or more
Mendelian factors the function of which is to switch on one or other
of the possible alternatives, just as the more widespread dimorphism

164 MIMICRY

of sex is also dependent upon the Mendelian mechanism. In some
groups, e. g. Drosophila and Man, a whole chromosome is utilized hi
the process of sex determination, in some fishes, on the contrary,
crossing over has been found to occur between the ' sex-chromosomes '
in the heterogametic sex, whether male as hi Lebistes, or female as
in Platypoecilus ; in fishes it appears that we ought more properly to
speak of the sex-gene rather than the sex-chromosome as the agent
of sex determination. The passage from the one condition to the
other, by the cessation of crossing over, presents no inherent diffi-
culties, especially as Mendelian factors are known which expedite or
inhibit crossing over. The reason for such a change is not so obvious,
but since both systems are found still in use, it is probable that each
has, upon particular conditions, its own advantages.

The core of Punnett's argument in favour of the production of
mimetic forms by saltations lies in the Mendelian behaviour of the
polymorphic females, for it is argued that these Mendelian factors
must have arisen originally as mutations, and seeing that the different
forms demonstrably differ by only single factor differences, these
types must have sprung into existence each at a single leap. Con-
vincing as this argument at first sight seems, we should, nevertheless,
at once recognize our fallacy if we argued that because the sex
difference in the fish Lebistes is apparently determined by a single
factor, therefore a female fish of that genus, with the appropriate
adaptations of her sex had arisen by a single saltation from a male of
the same species ! Or vice versa. In this case we are freed even from
the necessity of rejecting the supposed saltation as improbable, for
since the reproduction of the species requires the co-operation of both
sexes, we may be certain that the origin of the sex factor antedated
the evolution of separate sexes, and has presumably persisted, in
its function of switch, unchanged during the whole course of the
evolutionary development of these two types.

The example of sex emphasizes strongly the fact, which is becoming
more and more appreciated as genetical research is more applied to
complex and practical problems, that it is the function of a Mendelian
factor to decide between two (or more) alternatives, but that these
alternatives may each be modified hi the course of evolutionary
development, so that the morphological contrast determined by the
factor at a late stage may be quite unlike that which it determined
at its first appearance. The inference, therefore, that because a single

MIMICRY 165

factor determines the difference between a mimetic and a male-like
form in P. polytes, therefore the mimetic form arose fully developed
by a single mutation, is one that cannot fairly be drawn ; it requires, in
fact, the gratuitous assumption that no evolutionary change has taken
place in either of the two alternative forms since the dimorphism
was first established.

Certain genetical experiments have demonstrated that genetic
changes of the kind here considered are compatible with a purely
Mendelian scheme of inheritance. In rats, the hooded (black and
white) pattern is a simple recessive to the 'self' or 'solid' coloration ;
the case is probably parallel to the 'Dutch' pattern in rabbits, and
the 'recessive pied' in mice. In studying variations in the hooded
pattern Castle found that by selection it was easy to obtain strains
of hooded rats which were almost entirely black, and other strains
almost entirely white, and equally, of course, a large number of
stable patterns of an intermediate character. All these types of
'hooded' behaved, as before selection, as simply recessive to self-
colour. Two possible explanations were put forward; the first pos-
sibility was that the modification produced by selection lay in the
hooded gene, that, in fact, selection had sorted out from a large
number of slightly differing allelomorphs, those favouring much or
little pigmentation, and consequently that the surviving hooded
genes were different from those prevalent before selection. The
second possibility was that the hooded gene was invariable in charac-
ter, but that the pigmented area depended also on the co-operation
of other genes, so-called modifying factors, and that the change in the
hooded pattern was the result of selection among the alternatives
presented by these modifiers, of those types which developed larger
or smaller pigmented areas respectively. A crucial experiment was
devised to decide between these possibilities. Rats of both selected
lines were bred back to unselected selfs, the young were inbred, and
the hooded pattern was recovered in the grandchildren ; if the modi-
fication had taken place in the hooded gene the recovered hooded
rats would have received fully modified hooded genes, and must have
been as dark, or as light, as the hooded line from which they were
obtained ; but, if other factors were responsible, the hooded grand-
children would have received these equally from their self and from
their hooded grand-parents, and would consequently be less extremely
dark or light than the latter. The second alternative was proved to

166 MIMICRY

be correct, the modification being readily transmitted by self rats
which contained no hooded gene. The gene, then, may be taken to be
uninfluenced by selection, but its external effect may be influenced,
apparently to any extent, by means of the selection of modifying
factors.

Unless these analogies are wholly misleading, we should suppose
that the factors H and R which Fryer found to determine the
differences between the polymorphic forms of P. polytes, each arose
suddenly by a mutation, and that the new genes so produced have
been entirely unmodified since their first appearances. On the other
hand, we should see no reason whatever on genetic grounds to believe
that the combination HHrr on its first appearance at all closely
resembled the modern form polytes, or was an effective mimic of P.
aristolochiae ; nor that the combination HHRR resembled the modern
form romulus, or was an effective mimic of P. hector. The gradual
evolution of such mimetic resemblances is just what we should expect
if the modifying factors, which always seem to be available in abun-
dance, were subjected to the selection of birds or other predators.

Stability of the gene -ratio

It should be emphasized that there is nothing in the argument
developed above which helps to explain polymorphism itself. The
phenomenon is sufficiently uncommon to suggest that it must always
owe its origin to some rather special circumstances; however, the
Mendelian character of the phenomenon does suggest one short step
in the direction of a solution, namely, that the underlying condition
for its development is that the proportionate numbers of the genes
of some Mendelian factor, having a f airly marked effect, should be in
stable equilibrium, such as that considered in Chapter V.

Stabilizing selection can scarcely be other than exceptional, yet it
may be expected to arise in several ways. A Batesian mimic, for
example, will receive less protection, the more numerous it is in
comparison with its model ; a dimorphic Batesian mimic will therefore
adjust the numbers of its two forms, if these are dependent upon a
single Mendelian factor, until they receive equal protection; any
increase in the numbers of one form at the expense of the other would
diminish the advantage of the former and increase that of the latter,
thus producing a selective action tending to restore the original
proportion. A mimic, owing its advantage to Miillerian situations

MIMICRY 167

only, should not be dimorphic unless additional causes of stability
are at work, for apart from these the selection produces an unstable
equilibrium, from which the ratio will continue to depart until one
or other type is exterminated.

A second form of stabilizing action is found in reproductive
selection. The stable ratio of the sexes is clearly due to this cause, as
is that of the thrum-eyed and pin-eyed primroses. It is interesting to
note that Fryer, in his breeding experiments with Papilio polytes
observed numerous cases of sterile unions, which suggested to him
the possible existence of 'illegitimate' pairings. One of the simplest
possibilities of this type is a merely greater fertility of the hetero-
zygous as compared to the homozygous condition.

It should perhaps be noted that Gerould's work, on the dominant
white observed in the female of several species of Colias, also reveals
som^ peculiar features suggestive of a stability mechanism governing
the yellow-white gene-ratio. Gerould reports that great difficulties
were encountered in obtaining the homozygous white types, these
difficulties being evidently connected with the occurrence of a closely
linked lethal factor. When pure white broods had been obtained,
from a strain apparently freed from the lethal, the failure of the males
to mate caused the introduction of wild males, and these were found
to bring in the lethal factor. The fact that this particular lethal is
apparently not rare in nature, although we should expect it to die out
somewhat rapidly, suggests that a stabilizing system must be present.
The genetic complexities are not fully elucidated, for certain types
of mating seem regularly to give an abnormal sex-ratio (3 ? : 2 <J).
It is interesting in connexion with the modifying effects of selection,
that Gerould notes the occurrence of a fluctuating tinge of yellow
on the wing of the genetically white female, and ascribes its variability
to secondary factors.

Both the white form in Colias and the two mimetic forms of
polytes are confined to the females, and in both sexes the mutant
form is dominant to the older gene from which it presumably arose.
This circumstance, together with the probability in both cases of
stability of the gene ratio, suggests that the mutant form enjoys a
selective advantage, and has for this reason been acquired by the
heterozygote, and that the selective disadvantage of the mutant gene
is confined to the reproductive factor of genetic lethality or sterility
associated with the mutant homozygote. In the case of the mimetic

168 MIMICRY

forms of P. polytes, their selective advantage had already been
inferred by students of mimicry, though whether the white Cclias can
be brought under the same principle appears to be doubtful. If,
however, this surmise as to the causes of genetic stability should be
proved correct, these and analogous cases should provide an unex-
ampled opportunity of actually assessing the magnitude of a particu-
lar selective agency in nature. For reproductive causes of selection,
especially if dependent on absolute sterility or lethality, should be
capable of experimental demonstration and measurement, and their
selective efficacy can be calculated from the frequencies with which
the alternative genes, or gene combinations, are found in nature.
They should then form a measurable standard to which the efficacy
of mimetic selection, against which they must be balanced, can be
equated, and even its local variation examined. The importance of
such a direct determination need scarcely be emphasized; the
hindrances to free reproduction in these groups have appeared
hitherto merely as an obstacle impeding the Mendelian analysis of the
polymorphic forms; it is much to be hoped that, in view of the
application outlined above, their elucidation may, in future studies,
be made a principal object of research.

Whatever be the cause to which a factor owes its stability, any
species in which a stable factor occurs will be potentially dimorphic,
and permanently so unless in changed conditions the stability can be
upset. If, in this condition, selection favours different modifications
of the two genotypes, it is clear that it may become adaptively
dimorphic by the cumulative selection of modifying factors, without
alteration of the single-factor mechanism by which the dimorphism
is maintained.

Summary

The theory of mimicry is of special interest for the student of Natural
Selection, as affording examples of the adaptive significance of speci-
fic and varietal differences, and by reason of the great disparity
between the views formed by the pioneers of Mendelism and those of
selectionists.

The theory of Bates involves errors only of the senses of the
predator; it is subject to limitations imposed by the evolutionary
reactions of both predator and model. The theory of Muller involves
errors both of the senses and of the judgement ; the predator and both

MIMICRY 169

species of prey are all subject to evolutionary tendencies favourable
to Miillerian mimicry.

The statistical limitation of Miillerian mimicry put forward by
Marshall is based on insecure reasoning, and on examination is found
to be wholly imaginary.

The observational bases for mimicry theory may be analysed into
five distinctive categories, two of which are characteristic of Natural
Selection generally. Although full evidence is available only for a
very small minority of the cases suspected, the concurrence of
independent classes of observations puts the well-investigated cases
beyond possibility of doubt.

The evolution of distastefulness presents a special problem, which
may find its solution in the protection afforded by special distaste-
fulness among gregarious larvae to members of the same brood.

The tendency of Miillerian selection to cause the gradual and
mutual approach of different warning patterns supplies an explana-
tion of the difficulty felt by Punnett with respect to mimicry rings.
His further argument from the Mendelian character of polymorphic
mimics that these mimics arose as such by single saltations, overlooks
the effects of other factors in modifying the forms determined by the
original mutations.

Mendelian polymorphism normally implies a stable gene-ratio in
the determining factor. If the mechanism of stability involves, as one
may suspect in Papilio polytes and Colias, an element of sterility or
lethality balanced against an element of bionomic advantage, it
should be possible by analysing the mechanism of stability to
evaluate the intensity of selective advantage experienced in nature
by the favoured types.

3663

VIII
MAN AND SOCIETY

On Man, prominence of preliminary studies. The decay of civilizations. Sociological
views. Insect communities. Summary.

. . . and if her wretched captives could not solve and interpret these riddles,
she with great cruelty fell upon them, in their hesitation and confusion, and
tore them to pieces. BACON (Sphinx or Science).

On Man

THE earlier discussions of Man in connexion with evolutionary
theory were principally devoted to the establishment of two points.
First, that man, like the other animals, owed his origin to an evolu-
tionary process governed by natural law ; and next that those mental
and moral qualities most peculiar to mankind were analogous, in their
nature, to the mental and moral qualities of animals ; and in their
mode of inheritance, to the characters of the human and animal body.
However necessarily the second conclusion may seem to follow from
the first on any unified view of organic nature, the fact that man's
traditional opinion of himself constituted the mam difficulty to such
a unified view caused the researches, which have led to the final accept-
ance of Darwin's conclusion on this matter, to follow two paths,
distinct in subject and method, which may be typified by the labours
of Huxley and of Galton. The similarity of the human to other animal
bodies must have been obvious from the earliest times. On the
crudest scientific classification, he must be placed as one of a particular
order of mammals. An enormous mass of investigation of the form,
development, and workings of his body, is found to be consonant in
every detail with the view that he is an old world monkey, most
closely allied to the tailless apes.

The minuteness with which this subject has been examined would
scarcely have been necessary, from the evolutionary standpoint, but
for the difficulties presented by the human mind. These difficulties
are of two kinds. The first flows from the great development of the
human mind compared with the minds of other animals of which we
know enough to make any safe comparison. The second is that
we have an ulterior view or consciousness of the human mind, and
find in it qualities of great consequence or value to ourselves, which,
so long as we remain men, must appear to us immensely superior

MAN AND SOCIETY 171

to anything else in organic nature. Without this second factor,
I cannot think that the mere difference in degree of development
would have occasioned any popular difficulty in accepting the
scientific standpoint. Many animals show great development of
particular organs, without leading to any popular misapprehension
of their natural affinities. The trunk of an elephant is, regarded
merely as a structural development, at least as remarkable as the human
brain, though it happens to be less important to us.

Unfortunately for the general adoption of such an objective view
of things human, as is necessary for the scientific understanding of
human affairs, it is often felt to be derogatory to human nature, and
especially to such attributes as man most highly values — as if I had
said that the human brain was not more important than the trunk of
an elephant, or as if I had said that it ought not to be more important to
us, if only we were as rational as we should be. These statements would
be unnecessarily provocative : in addition they are scientifically void.
And lest there should be any doubt upon a matter, which does not in
the least concern science, I may add that, being a man myself, I have
never had the least doubt as to the importance of the human race, of
their mental and moral characteristics, and in particular of human
intellect, honour, love, generosity and saintliness, wherever these
precious qualities may be recognized. The supreme value which, I
feel, ought to be attached to these several aspects of human excel-
lence, appears to provide no good reason for asserting, as is some-
times done, with a petulant indignation not unmixed with spiritual
arrogance, that such a low matter as natural causation cannot be of
importance to these sublime things. On the contrary, it introduces
the strongest motive for striving to know, as accurately and distinctly
as possible, in what ways natural causes have acted in their evolu-
tionary upbuilding, and do now act in making them more or less
abundant.

This reasonable, and I believe inevitable, consideration has been
too frequently neglected by writers on both sides of the controversy.
Some seem certainly to have thought that the replacement, by
rational, of sentimental or superstitious beliefs, on matters of fact,
could be paralleled, and as it seemed completed, by the establish-
ment of moral and aesthetic valuations upon an exclusively scien-
tific basis. Others, whose attitude can be explained, rather than
excused, by obscurantist opposition, would seem to have developed

172 MAN AND SOCIETY

a positive dislike for the higher qualities of the human consciousness,
at least for controversial purposes, and to delight in assimilating the
poetic and religious aspirations of mankind to whatever unedifying
proclivities may happen to have a similar physiological basis. It
seems to be not uncommon for medical students, who have learnt
something of the psychological effects of the sex hormones, to feel
that the poetic emotions, which the rest of mankind associate with
sexual love, are thereby discredited. And, although this may be
dismissed as an extreme and juvenile aberration, men are in general
somewhat reluctant to give up the early accepted dogma that what-
ever is noblest in their nature must be due to causes, and even arise
by processes, which in themselves possess the same value. Perhaps
the basis of this dogma, which seems to be, in itself, indefensible,
may be found in the aristocratic tradition by which men were valued
at least as highly for their ancestry as for their personal qualities.
Whatever may be its cause, the intellectual efforts made by a man
such as Wallace, to avoid ascribing the higher human faculties to
natural causation, should warn us of a source of error so powerful
that it might perhaps have permanently incapacitated mankind from
furthering the development of what he values most.

The conscious and active being is concerned with himself habitually
as an original cause. If he considers the natural causes which have
brought himself into existence his perspective is inverted, and his
intuitions fail him. It is readily to be understood that differences in
behaviour, whether due to conscious deliberation or to impulsive
reaction, do in fact determine differences in the rates of death and
reproduction. Nor can we doubt that these differences in behaviour
flow from personal individuality in the constitution of the mind,
without which all men would act alike and the concept of voluntary
action would be an illusion. It is true that this concept implies that
we take circumstances into consideration and act, or refrain from
acting, accordingly ; but also more emphatically that we weigh the
circumstances, and that others in like case might have acted differ-
ently. Apparent as is this aspect of voluntary action it is a remark-
able fact that many, who would find no difficulty in conceiving the
involuntary reactions of mankind to be modified by a selective
process, yet find a difficulty in applying the same argument to matters
involving voluntary choice. I suspect the reason to be that voluntary
choice is open to modification, apart from other circumstances, by

MAN AND SOCIETY 173

persuasion, and that the importance of the effects achieved by this
means sometimes prevent us from perceiving very striking contrasts
in the ease with which persuasion is effected.

The supreme inner arbiter of our choice in matters of right and
wrong we call our conscience. We do not regard our consciences as
open to outside persuasion, and from this point of view they must be
regarded as wholly innate. We do, however, show some ambiguity in
the extent to which we recognize their individuality. Emphatically
your conscience is not my conscience ; yet we are sometimes tempted
to be so uncharitable as to imply that, apart from hypocrisy or an
acquired callousness or blindness towards their own better nature,
others would assuredly comply with our own standards. From the
standpoint of selection it is a matter of indifference whether we
regard mankind as differing in their very consciences, or merely in
their reactions to their inward monitor. Since, however, each man is
aware only of his own conscience I shall be content, in what follows,
to take the former view.

However obvious it may seem to some, it is certainly necessary to
insist upon the point that the systematic position of mankind and the
demonstrated inheritance of the mental and moral qualities do not
exhaust the evolutionary interest of the human species. On the
contrary, these are only preliminary inquiries designed to examine
whether man, and if so, whether man in all his aspects, falls within
the scope of a naturalistic theory of evolution. They are preliminaries
to our interest in the evolutionary history and destiny of mankind,
a subject the interest of which seems to have been very inadequately
explored. An animal which in its comparatively recent history has
undergone profound changes in its habitat, diet, and habitual posture,
should, for these reasons alone, be of sufficient interest to the evolu-
tionist. If we add the development of a social organization un-
paralleled within its own class, the use of artificially constructed
implements, and a means of expressing and recording its experiences
and ideas, it is obvious that to the non-human observer mankind
would present a number of highly interesting evolutionary inquiries
and would raise questions not easily to be answered only by the use
of comparisons and analogies.

Most modern writers on genetics seem, with respect to man, to fall
into two opposite, but equally unsatisfactory, attitudes. A minority
appear to fear that the purity of their subject, as an abstract science,

174 MAN AND SOCIETY

would be contaminated were it applied to the species to which they
themselves belong ; and although, perhaps, interested in the practical
improvement of domesticated animals and plants, are careful, if any
point in human genetics has to be mentioned, to dissociate themselves
from any suggestion that it also may have practically important
consequences. A larger, and more enterprising school, fully imbued
with a sense of the universal applicability of genetic knowledge,
recognize in mankind a useful field for its exploitation. They are
more ready, and are perhaps better prepared, to appreciate the
similarities of human inheritance to that of Drosophila or Maize, than
they are to appreciate the special problems which the evolution of
man in society presents ; and will sum up the human problem in a
cursory, and even superficial, chapter at the end of an elaborate, and
often admirable exposition of modern inheritance discoveries. While
genetic knowledge is essential for the clarity it introduces into the
subject, the causes of the evolutionary changes in progress can only be
resolved by an appeal to sociological, and even historical facts. These
should at least be sufficiently available to reveal the more powerful
agencies at work in the modification of mankind.

The decay of civilizations

The decay and fall of civilizations, including not only the historic
examples of the Graeco-Roman and Islamic civilizations, but also
those of prehistoric times, which have been shown to have preceded
them, offers to the sociologist a very special and definite problem — so
sharply indeed that its existence appears to challenge any claim we
dare make to understand the nature and workings of human society.

To be used properly the term civilization must be applied not
merely to those societies the institutions of which we see reason to
admire, but to designate the aggregate of all the social adaptations
appropriate to the permanent existence of a dense population. In
general form these adaptations have a universal character. In all
societies which we call civilized, the personal understandings, which
a man can form with a small circle of immediate acquaintances, are
supplemented by a vastly more numerous system of conventional
understandings, which establishes his customary relations, his rights
and his obligations, with regard to the entire society of which he is
a member. He is thus free to devote himself to productive labour
even of a highly specialized character, with confidence that the pro-

MAN AND SOCIETY 175

duction of his primary necessities, the protection of his possessions
from violence, and even the satisfaction of his moral and intellectual
needs, will be undertaken by the labours of others, who make of such
tasks their special occupations. The specialization of occupations,
involving the customary acceptance of a conventional standard of
exchange, the maintenance of public order, and the national organiza-
tion of military preparations, are thus the universal characteristics of
the civilized in contradistinction to the uncivilized societies of man-
kind. It is a matter of experience, which no one thinks of denying,
that such an organization does in fact enable a given area to support
a much larger population, and that at a higher level of material and
intellectual well-being, than the uncivilized peoples who could
alternatively occupy the same territory.

Such a civilized society, once organized and established, how is it
possible to imagine that it should fail in competition with its un-
civilized neighbours ? The latter occupy their territory more sparsely,
they lack moreover the organized central government which could
mobilize to advantage their scanty numbers. On the contrary, our
experience of uncivilized populations shows them to be divided by
hereditary enmities and petty jealousies, which should make their
union, even upon a question of the simplest national interest, almost
an impossibility. Industrial organization gives to civilized peoples,
in antiquity as well as in our own times, the advantage of superior
weapons; while the habits of co-operative labour enable them to
adopt a more regular, co-ordinated, and effective system of military
tactics. Above all, the superior knowledge which a civilized people
can, and does indeed, continually accumulate, should enable them to
act generally with superior information, with a surer foresight of the
consequences of their collective action, and with the capacity to
profit by experience, and to improve their methods if their first
attempts should prove to be unfortunate. Bearing in mind the
unquestionable advantages of superior knowledge, of co-ordinated
efforts and of industrial skill, should we not confidently anticipate,
if we were ignorant of the actual history of our planet, that the
history of civilization would consist of an unbroken series of triumphs ;
and that once the germ of an organized society had made its appear-
ance, in Babylonia, perhaps, or in Egypt, it would be only a question
of time for every country in the world to be in turn absorbed and
organized by the Babylonian, or Egyptian, civilization ?

176 MAN AND SOCIETY

The indications which we possess of the earlier civilizations, as well
as the plain narrative of the historic period, differ remarkably from
the rational anticipation deduced above. We see, indeed, a certain
tenuous continuity hi many elements of traditional civilization which
are handed on from one social group to another, as these hi turn
become civilized. But this circumstance seldom even obscures the
contrasts between the social groups, involving differences between
the territory, language, religion, and race, associated with the highest
civilization at different epochs. These contrasts are obviously
associated, in the case of each great change, with the violent irruption
of some new people of uncivilized origin. The experiment of becoming
civilized has, hi fact, been performed repeatedly, by peoples of very
different races, nearly always, perhaps, with some aid from the
traditional ideas of peoples previously civilized, but developing their
national and industrial organizations by their own progressive
powers; and in all cases without exception, if we set aside the in-
complete experiment of our own civilization, after a period of glory
and domination accompanied by notable contributions to the sciences
and the arts, they have failed, not only to maintain their national
superiority, but even to establish a permanent mediocrity among the
nations of the globe, and in many cases have left no other record of
their existence than that which we owe to the labours of archaeologists.

Before considering those causes which I propose to assign both to
the phenomenon in general, and to its more salient characteristics,
hi the course of the succeeding chapters on Man, it is as well to give
some attention to the preliminary question: Of what sort should be an
explanation which we should regard as adequate ? It is easy to find
among the peoples of antiquity institutions disagreeable enough to
our modern feelings, it is easy to criticize their educational ideas, or
the forms of government which they have successively adopted;
above all it is easy to find fault with their ignorance of economic law,
and to ascribe to their mistakes in this domain the same civil and
political misfortunes, which we anticipate equally from the parallel
errors of our political opponents ! Such arguments are not only
inconclusive from our ignorance of the laws of causation upon
which they rely, they are also demonstrably insufficient to meet the
requirements of our special problem. For, hi the first place, our
knowledge of the earlier stages of the history of great peoples shows
us customs no less repulsive, manners no less licentious, a neglect of

MAN AND SOCIETY 177

education at least equally pronounced, and ignorance of economic law
as absolute as any which can be ascribed to their civilized successors.
In the second place, moreover, in a period of national decay it would
be unreasonable to expect that any aspect of national life, political,
religious, intellectual, or economic, should remain in a healthy and
flourishing condition, or that the misfortunes of the times will escape
the complaints of observant contemporaries. That the condition of
agriculture, for example, was unsatisfactory in the later Roman
empire, though a legitimate inference from the state of that society,
fails to constitute in any useful sense an explanation of its progressive
decay. Peoples in the prime of their powers appear to find no diffi-
culty in making good use of very inferior natural resources, and adapt
their national organization with complete success to much more
violent changes than those which, can be adduced to explain the
misfortunes of the later stages of their civilization.

A physician observing a number of patients to sicken and die in
similar though not identical conditions, and with similar though not
identical symptoms, would surely make an initial error if he did not
seek for a single common cause of the disorder. The complexity of
the symptoms, and of the disturbances of the various organs of the
body, should not lead him to assume that the original cause, or the
appropriate remedial measures, must be equally complex. Is this
not because the physician assumes that the workings of the body,
though immensely complex, are self-regulatory and capable of a
normal corrective response to all ordinary disturbances ; while only
a small number of disturbances of an exceptional kind meet with no
effective response and cause severe illness ? It is impossible to doubt
that we have equally a right to expect self -regulatory power in human
societies. If not, we should be led to predict that such societies should
break down under the influence of any of the innumerable accidents
to which they are exposed. Uncivilized societies of various kinds have
adapted themselves to every climate, from the Arctic, to the forests
and deserts of the Tropics. They share the territories of the most
savage or poisonous animals, and often long withstand without dis-
ruption the assaults of most implacable human enemies. Social
progress has not been arrested by the introduction of new weapons,
of alcohol, or of opium, or even of infanticide ; yet these introductions
might each of them seem to threaten the existence of the race. That
civilized men, possessed of more effective appliances, with access to

178 MAN AND SOCIETY

more knowledge, and organized for the most detailed co-operation,
should prove themselves incapable of effective response to any distur-
bance of their social organization, surely demands some very special
explanation.

Sociological views

A philosophical view of history, which has attained to great popu-
larity in several continental countries, regards the rise as well as the
fall of civilizations as but the successive phases of a cycle of growth
and decay, which, it is supposed, repeats itself, and will repeat itself
endlessly, throughout human history. So long as we aim at no more
than an effective generalized description of the phenomena there is
much to be said for considering the phases of rise and development of
the great civilizations in conjunction with the phases of their decay
and collapse. It is a real advantage that the parallelisms between the
earlier phases of different cultures should be recognized, and that
their relations hi time to recognizably parallel later phases should be
established as accurately as possible. Generalized description should,
however, never be regarded as an aim in itself. It is at best a means
towards apprehending the causal processes which have given rise to
the phenomena observed. Beyond a certain point it can only be
pursued at the cost of omitting or ignoring real discrepancies of detail,
which, if the causes were understood, might be details of great con-
sequence. Alternatively, somewhat different states and events are
subsumed under generalized and abstract terms, which, the more
they are made comprehensive tend to possess the less real and defin-
able content. Finally, any purely descriptive general picture of
events in time is in its nature fatalistic and allows no place for
intelligent and corrective intervention.

The early evolutionary speculations of the Greeks had this fatal-
istic and sterile character, for the lack of any clearly understood mode
of causation, which could bring about the modification of living
organisms. It is characteristic of the scientific attitude of the middle
of the nineteenth century that the evolutionary theories of earlier
generations excited little interest in the absence of a satisfactory
explanation capable of expressing the means of modification in terms
of known causes. Even Darwin and Wallace, although Darwin at
least was in possession of much indirect evidence, did not put forward
their evolutionary theories until each had satisfied himself that, in

MAN AND SOCIETY 179

the struggle for existence, natural selection did provide the efficient
cause. With a clear grasp of scientific principle, which is not always
sufficiently appreciated, it is evident that they felt that the mere
historical fact of descent with modification, however great its
popular interest, could not usefully be discussed prior to the establish-
ment of the means by which such modification may be brought about.
Once the nexus of detailed causation was established, evolution
became not merely History, but Science. Evidently, the more special
and peculiar is the case considered, the less can descriptive analogy
be relied updn, and the more essential is a knowledge of the laws of
causation.

In the descriptive study of the rise and decay of human civiliza-
tions the closest analogy which is found with any process capable of
scientific study is that with the growth and death of the individual
organism. In both, it may be said, we find, in regular sequence, a
period of developmental vigour and superfluous vitality with the
acquisition of new powers, a period of maturity with substantial
achievement, a period of stagnation in which the organism or the
society can do little more than hold its own, and a period of decay
followed sooner or later by dissolution. The moment we attempt,
however, to interpret this generalized description in terms of known
causes, the analogy is seen to be as false as it well could be. The
' youthful ' peoples whom we see at the dawn of their civilized history
have already behind them a social history far longer than the
civilized period before them. They have not just been begotten from
elements secreted by previous civilizations, elements which might
be supposed to carry the hereditary determiners of the cycle of
changes to be enacted. The healthy society may be said to grow and
to assimilate; it cannot be said to reproduce itself. And without
reproduction there is no terminus a quo for the sequence of growth and
death. Societies are potentially immortal, bearing within themselves
the power continually to replace every living element in their structure.
The phenomenon of senescence from which the whole analogy arose
is only observed in societies which have for some little time enjoyed
that closely co-operative structure which we call civilization.

If we set aside the purely descriptive point of view, it is apparent
that, in associating the rise and growth of civilizations in a single
sequence with their decay and fall, the nature of the problem has
only been obscured. Obviously the phenomena of decadence can only

180 MAN AND SOCIETY

be presented after a certain level of success has already been achieved.
But, whereas the decay of civilizations presents an abrupt and un-
expected problem, the advantages to be reaped from the progressive
adoption of those phases of culture which we call civilized are, to all,
obvious and familiar. Consequently, while a solution of the problem
presented by decadence in terms of the detailed sociological reactions
to which it is due, would doubtless throw light on sociological causa-
tion in general, and consequently on the characteristics of the earlier
as well as of the later phases of civilized society, the mere fact that
a society, as it acquires the arts and organization of civilized life,
simultaneously experiences a great accession of prosperity and power,
is itself due to causes which are perfectly familiar and fully under-
stood. These advantages would be even further enhanced and pro-
longed, if, as it was formerly thought could be safely assumed, life
in the civilized condition, as hi the barbaric state, favoured the sur-
vival and reproduction of those human types who could most
effectively promote the prosperity of their society, and who on the
other hand were most apt temperamentally to appreciate and exploit
its advantages. The evolution of man from savagery, through bar-
barism to a final highly civilized condition might then be regarded, as
by Herbert Spencer, as forming a continuous and inevitable process
of human advancement. In the light of this highly rational optimism
the failure of high civilizations in the past appears as a single and
formidable problem.

Insect communities

The only animal societies hi which co-operation is sufficiently highly
developed to justify comparison with civilized men are those of the
social insects. In these, specialization for the performance of various
tasks such as defence, building, direct social services for the benefit
of the rising generation, and the collection or cultivation of food, is
sufficiently clearly developed; nevertheless, although social Me has
appeared independently in several distinct groups, all alike present
the same initial difficulty to comparison with human societies, in
that, in addition to showing such specialization in behaviour or
capacity as is necessary for organized co-operation, all display an
apparently superfluous specialization in reproduction. A single queen
termite, to take an extreme example, is said to maintain the wastage
among a whole society of many millions of workers, by producing

MAN AND SOCIETY 181

continuously an egg every few seconds. In general, the vast majority
of a community of social insects take no part in reproduction ; and
while it cannot be denied that some small economic advantage
accompanies this, like other specializations for the division of labour,
yet the danger to the community of entrusting its future existence to
a single life is obvious and serious. In this respect the insect society
more resembles a single animal body than a human society, for
although many tissues are capable by cell division of the replacement
of damaged parts, yet the reproduction of the whole organism is con-
fined to specialized reproductive tissue, whilst the remainder of the
body with its various co-operative functions, co-operating with but
taking no part in reproduction, is in this respect analogous to the body
of sterile workers which constitutes the bulk of the hive. It is of some
interest to follow out the effects of the system of reproduction
adopted by the social insects in contrast to the individualistic system
of reproduction in human societies.

Human communities show the same kind of genetic variation as
is shown by the species as a whole ; individuals are fitted for their
various special tasks, partly by direct and deliberate selection, partly
by indirect selection via social class, and partly by special education,
including in that term not only paid instruction in youth, but also
experience gained in practice. The different tissues of a metazoan
body, are, it seems, normally identical genetically, and owe the
differences which they exhibit entirely to differences in the influences
to which they are exposed from other developing tissues. The
different offspring of a single queen cannot be genetically identical,
for the factors in which their mother is heterozygous must segregate,
so that in each such factor offspring of the two kinds are produced in
equal numbers. Such genetic variability, however, must be different
in each different society, and seems not to be utilized in producing
polymorphism among the workers, or even between the sterile and
the reproductive types. Although the subject is very obscure, the
predominant weight of opinion appears to favour the view of Wheeler
that the principle controlling influence is exercised through the
quantity of food supplied to the larvae during development. The
mechanism by which polymorphism is produced is thus very different
from the simple Mendelian mechanism found in the polymorphic
butterflies, and one far more appropriate to the needs of social in-
sects. At the same time it should be noticed, as with polymorphic

182 MAN AND SOCIETY

butterflies, that the particular mechanism employed to secure poly-
morphism throws no light whatever upon the adaptive and evolu-
tionary significance of the polymorphism itself. The manner in which
developmental changes are modified by restricted nutrition is a
variable equally exposed to selective action as the manner in which a
wing pattern is modified by a particular Mendelian mutant. The
selection in this case must act exclusively upon the reproductive
insects via the prosperity of the society from which they arise ; and
although the effect of such selection may be to modify only the
sterile workers, this presents no more difficulty than that a selection
acting exclusively upon the gametes of a sheep, via the observable
characteristics of the animal which bears*them, should modify the
nature of its wool.

Although real genetic differences must exist among the sterile
workers of the same society, these differences are without selective
effects. The relative frequencies with which the different genotypes
appear among the offspring of a single queen must be presumed to
remain constant during her reproductive period, and the selection of
males and females for reproduction depends only on then* individual
qualities, and the aggregate quality of the communities from which
they arise. On the contrary, the genotypic differences which char-
acterize the individuals of societies practising individualistic repro-
duction are exposed through their differential rates of death and
reproduction to an intra-communal selection capable of modifying
indefinitely the genotypic composition of the body politic. Among a
group of small independent competing tribes the elimination of tribes
containing an undue proportion of the socially incompetent, and their
replacement by branches of the more successful tribes, may serve
materially to maintain the average standard of competence appro-
priate to that state of society. Even hi such a state of society intra-
communal selection will undoubtedly be at work, and the larger the
social group becomes the greater is the importance of the intra-com-
munal element. Consequently, from the earliest times of which we have
knowledge, the hereditary proclivities, which undoubtedly form the
basis of man's fitness for social life, are found to be supplemented by
an economic system, which, diverse as are the opinions which different
writers have formed about it, appears to the writer to be one of the
unconscious triumphs of early human organization.

The basis of the economic system consists in the free interchange

MAN AND SOCIETY 183

of goods or services between different individuals whenever such
interchange appears to both parties to be advantageous. It is essential
to the freedom of such agreements that the arbitrary coercion of one
individual by another shall be prohibited, while, on the other hand,
the coercive enforcement of obligations freely undertaken shall be
supported by the public power. It is equally essential that the private
possession of property, representing, as in this system it must do, the
accumulation of services already performed to other members of the
society, and the effective means of calling upon equivalent return
services in the future, shall be rigorously protected. In the theory of
this system each individual is induced, by enlightened self-interest,
to exert himself actively in whatever ways may be serviceable to
others, and to discover by his ingenuity new ways or improved
methods of making himself valuable to the commonwealth. Such
individuals as succeed best in performing valuable services will receive
the highest rewards, including, in an important degree, the power
to direct the services of others in whatever ways seem to them most
advantageous. Those, on the contrary, who fail most completely to
perform socially advantageous actions have the least claim upon the
wealth and amenities of the community. In theory they may perish of
starvation, or may become indebted up to the amount of the entire
potential services of the remainder of their lives, or of the lives of
their children.

It need scarcely be said that this economic system has never
formed the exclusive basis of social co-operation in man. It has
at most been partially established in compromise with social instincts
already in being, founded during the existence of less closely co-
operative societies. Nevertheless, it bears a sufficient resemblance,
both to the theory of rationalistic economists, and to the practice of
various ancient civilizations, to indicate that we have presented, in
an abstract and ideal form, a real and effective factor in human social
organization. The biological importance of this factor lies in the
safeguard which it appears to provide that intra-communal selection
in human societies shall not favour the multiplication of unproductive
or parasitic types, at the expense of those who exert themselves
successfully for the common good. On the contrary, it seems to insure
that those who produce the best goods or provide the most valuable
services shall be continually augmented in each succeeding generation,
while those who, by capacity or disposition are unable to produce

184 MAN AND SOCIETY

goods equivalent to what they consume, shall be continually elimi-
nated. Nor is this beneficial selection confined to individuals in their
capacity of producers. In consumption and distribution an equally
beneficial selection would seem to be in progress. The individual who,
by reason of his imperfect instincts, is tempted to expend his re-
sources in ways which are not to his biological advantage, the indivi-
dual who from prejudice favours a bad market, or who is tempera-
mentally incompetent in striking a bargain, is equally at an economic
and, it would seem, at a selective, disadvantage. This selection of
the consumer provides in an important respect the theoretical com-
pletion of the individualistic economic system, for it supplies a means
by which the opportunities of gaining wealth by the provision of
illusorv benefits, shall become ever narrower, until all substantial

V

sources of profit are confined to the provision of real public benefits. The
population produced by such a system should become ingenious and
energetic industrialists, shrewd and keen in the assessment of social
value, and with standards of well-being perfectly attuned to their
biological and reproductive interests. To complete the picture, at
the expense of anticipating a little a subsequent argument, our
economic Utopians must be endowed with consciences which recog-
nize the possession of wealth, at least as a means to reproduction, as
the highest good, and its pursuit as the synthesis of all virtuous
endeavour. To them the wealthy man would enjoy not only the
rewards, but also the proofs of his own virtue, and that of his forbears ;
he would be in some sort a saint, to co-operate in whose virtuous
proceedings would be a supreme felicity. Upon such men, no public
honour could be bestowed more noble than a direct cash payment,
and to purchase other honours for money would seem not so much
corrupt as insane. Charity, hi the sense of the uneconomic relief of
poverty, would evidently be a vicious weakness, although there would
be some virtue in shrewdly backing for mutual advantage the capable,
but accidentally unfortunate.

If in practice man's sociological development had indeed taken
this turn it might have been said that man, by individualizing
property, had found the appropriate social concomitant for his in-
dividualistic habit in reproduction ; that he had established a type of
society unattainable by any order of insects, for lack of an intellectual
equipment adequate to deal, with the necessary justice and con-
sistency, with disputed ownership or contractual obligations — for

MAN AND SOCIETY 185

lack, in fact, of judges and lawyers ; and that for this reason the only
means open to them, to avoid the disastrous consequences of intra-
communal selection, lay in the complete elimination of competition
between reproductive members of the same society, by the concentra-
tion of the whole duty of reproduction upon a single individual. As the
matter stands, however, it appears that even if an insect community
had achieved some efficacious system of instincts, which would
produce the economic effects of personal ownership, its difficulties
would not necessarily have been at an end ; for the instinctive feelings
and prejudices of social man do not seem at all to have developed in
the direction of a more strictly economic and less ' sentimental ' basis for
social institutions. Whether an imaginary insect could, and whether
man himself can, overcome the further sociological difficulty which
has arisen can only be decided when that difficulty has been more
thoroughly examined. The important point for the present chapter
is that the difficulties that man has encountered and, at most,
partially overcome, have been evaded in all orders of social insects,
by forming the community from the offspring of a single individual.
The primary evolutionary process for us to notice here is the enor-
mous, though doubtless gradual, increase in individual fertility in
insects. As was remarked in Chapter II, the importance of Natural
Selection in moulding fertility to its optimum value has been obscured
by the importance attached, by early evolutionary writers, to a ' high
rate of increase ' as the primary driving force of Natural Selection
itself. When, on the contrary, we regard fertility as a secondary
phenomenon, determined by Natural Selection, it becomes important
to consider what circumstances influence the level of fertility which
is, in any particular case, optimal. In this connexion Major Leonard
Darwin has pointed out that the principal importance should be given
to the factor of parental care, including in that term all expenditure
in the form of nutriment, effort, or exposure to danger, incurred in
the production and nurture of the young. In organisms in which
that degree of parental expenditure, which yields the highest pro-
portionate probability of survival, is large compared to the resources
available, the optimal fertility will be relatively low. Any circum-
stance which materially lightens the burden on the parent will
necessarily have an immediate effect in favouring survival ; it is
more important that it will usually lower the optimal expendi-
ture, and consequently tend to raise the level of fertility. Major

3653

186 MAN AND SOCIETY

Darwin illustrates this principle by the example of the parasitic
cuckoos, which have found a way to relieve themselves of a great part
of the parental burden borne by other birds, and have, in fact,
acquired a considerably greater fecundity than their non-parasitic
allies. The social insects offer an even more striking example of the
same principle. As soon as the young adults of any incipient social
form took either to performing the preparatory labour for reproduc-
tion, or to tending the young, before they had themselves commenced
to reproduce, the balance of selective advantage would have been
shifted towards favouring the fertility of the foundress of the colony,
and favouring equally the development of the organs and instincts
of workers rather than of queens among her earlier, and possibly less
well nourished, offspring. The enormous development of fertility
alongside extensive sterility in all groups of social insects shows
how powerful is the action of selection in modifying this particular
character. In the following chapter (IX) the hereditary factors which
influence fertility in Man will be discussed, and it will be seen that the
selective modification of these factors is as important, though in a
very different way, to the evolution of human as to that of the insect
societies.

Summary

The earlier evolutionary work on Man was naturally directed to-
wards establishing the two preliminary points, (i) that Man like other
animals has arisen by an evolutionary process, (ii) that the mental
and moral qualities of Man are equally with the physical qualities
the result of natural causation. The difficulty felt by Man in re-
adjusting his traditional opinion about himself has required that
these two points should have been established with considerable
cogency.

A naturalistic view of Man provides no means of putting on
an objective basis those mental valuations, moral and aesthetic, to
which Man attaches such high importance ; it cannot, therefore, be
used to throw doubt upon these valuations. The high human value
of the moral attributes does, however, invest their natural causation
with a special importance.

Among the problems presented by the social evolution of Man the
most conspicuous is that of the decay and ruin of all civilizations
previous to our own, in spite of their having had every reason to

MAN AND SOCIETY 187

anticipate continued success and advancement. The purely descrip-
tive treatment of the rise and fall of civilizations is inadequate
without an examination of the operative causes to which changes in
social structure are due.

In the animal kingdom the only societies which bear comparison with
human civilization are those of the social insects, and these all differ
from human societies in the striking feature of reproductive specializa-
tion. This has the effect of eliminating intra-communal selection as
an evolutionary process, so that the dangers to which society is
exposed from this source are special to Man. Human societies from
very early times have adopted an economic system of individualizing
property which might have been expected to control intra-communal
selection along socially advantageous lines. The logical effects to be
anticipated have, however, not been realized.

The specialization of reproduction in insect communities has been
possible owing to the efficacy of selection in modifying fertility. The
inheritance of fertility will be seen to be equally influential, though in
a very different way, in the evolution of human societies.

IX

THE INHERITANCE OF HUMAN FERTILITY

The great variability of human reproduction. The mental and moral qualities de-
termining reproduction. Direct evidence of the inheritance of fertility. The evolution
of the conscience respecting voluntary reproduction. Analogies of animal instinct and
immunity to disease. Summary.

Or who is he so fond wiU be the tomb
Of his self-love, to stop posterity ? SHAKESPEARE.

The great variability of human reproduction

THE existence of statistical data for civilized man might suggest that
these should provide an opportunity for evaluating, in this species,
the probabilities of any individual leaving 0, 1, 2, ... offspring,
according to the chances of his life as considered in Chapter IV. The
case of man will be shown to differ from that of most other organisms,
in the high relative importance of differences in fertility and in the
comparative unimportance of the differences of mortality between
birth and the reproductive period. In view of these characteristics
of mankind it would be of very special interest to be able to evaluate,
even approximately, the magnitude of the effects of the chance
element hi causing variation in the numbers of children actually born.
Two special obstacles must be encountered in such an attempt, which
in the present state of our knowledge can be at best only partially
overcome. In the first place the actual variation in the number of
children born, let us say, to a group of women at the end of their
reproductive period, cannot, with the faintest show of reason, be
ascribed wholly to chance. In this respect probably mankind, hi the
civilized condition, differs materially from all other organisms except
the social insects. For unless the rates of reproductive selection in
these other organisms are materially higher than we have had reason
to suppose, the chance factor must, as was seen in Chapter IV, be
the dominant one in individual survival, contributing in fact nearly
the whole of the individual variance. In man, on the other hand, we
must be prepared to ascribe to differences in individual temperament
and disposition an amount of the variance almost as great as that
ascribable to chance, and therefore of an altogether different order
of magnitude from the reproductive selections to be anticipated in
other organisms.

THE INHERITANCE OF HUMAN FERTILITY 189

If we cannot evaluate the chance component of the variance
by equating it to the total, the alternative method of evaluating
it a priori, as due to the successive occurrence of independent
events, is rendered, at best, extremely uncertain by the long duration
and persistence of human purpose. The occurrences of successive
children are not independent events in so far as they are conditioned
by the married or unmarried state of their parents, although that
state may be held to be influenced, though in a very minor degree, by
a genuinely fortuitous element. A complete statistical statement of
the birth-rates of the married and unmarried at each age, of the
frequency with which the unmarried become married, and the married
become unmarried by widowhood or divorce, would still afford no
direct measure of the extent to which different members of an un-
differentiated group, would differ in their number of children. The
process of calculation which takes not only the successive births but
also marriages, as conditioning the probability of births, as a series of
events occurring independently with the appropriate frequencies, seems
to err as much in ascribing marriage wholly to chance, as does the
simpler method of calculation in which the effect of marriage is ignored.

A. 0. Powys (Biometrika, IV. 238) gives the number of children born
to 10,276 married women dying aged 46 or over in New South Wales
from 1898-1902. The number of children varies from 0 to 30, and the
number of women recorded at each value are given in Table 7. The
average number of children was 6-19, and if the data had represented
women of equal natural fertility exposed throughout their lives to
equal risk of maternity the variance would certainly be somewhat less
than the average number. Actually the variance is 16-18, or consider-
ably more than double the greatest amount ascribable to pure chance.

TABLE 7.

No. of
children.

Frequency.

No. of
children.

Frequency.

No. of

children.

Frequency.

0

1,110

11

568

22

1

1

533

12

422

23

—

2

581

13

226

24

1

3

644

14

129

25

—

4

702

15

57

26

—

5

813

16

39

27

—

6

855

17

12

28

—

7

976

18

5

29

—

8

963

19

2

30

1

9

847

20

2

10

786

21

1

Frequency total 10,276.

190 THE INHERITANCE OF HUMAN FERTILITY

A great part of the variance must certainly be ascribed to age at
marriage. Yet the variance still exceeds the mean very strikingly if
data are chosen which should minimize this factor. A group of
2,322 wives married before 20 years of age, and living with their
husbands at the time of the Census (1901) 25-30 years later, are
distributed as in Table 8.

TABLE 8.

No. of No. of No. of

children. Frequency. children. Frequency. children. Frequency.

0 44 7 167 14 77

1 41 8 237 15 46

2 63 9 272 16 19

3 65 10 333 17 9

4 83 11 271 18 6

5 105 12 208 19 3

6 141 13 131 20 1

Frequency total 2322

The mean number of children for this group of women, for whom
the chosen conditions are especially favourable to fertility, is 8-83,
but the variance is still as high as 12-43.

From these examples, and indeed from any series of similar data, it
is evident, that while an exact evaluation of the chance factor in
reproduction is not possible, yet there clearly exist, both in the age
at marriage, and in fertility during marriage, causes of variation so
great as to be comparable with the chance factor itself.

The extraordinary variation in fertility in Man has been noticed
in a somewhat different manner by Dr. D. Heron, using material
provided by the deaths (30,285 males and 21,892 females) recorded
in the Commonwealth of Australia for 1912. Heron finds that hah*
of the total number of children come from families of 8 or more,
which are supplied by only one-ninth of the men or one-seventh of the
women of the previous generation. It would be an overstatement to
suggest that the whole of this differential reproduction is selective ;
a substantial portion of it is certainly due to chance, but on no theory
does it seem possible to deny that an equally substantial portion is
due to a genuine differential fertility, natural or artificial, among the
various types which compose the human population.

The mental and moral qualities determining reproduction

Whereas the part played by chance in producing variations in the
rate of reproduction is elusive and difficult to evaluate, that part,

THE INHERITANCE OF HUMAN FERTILITY 191

which is due to constitutional and therefore hereditary differences in
temperament, is manifest to all. When we consider the causes which
normally lead to the production of children, the occasions upon which
individual temperament is liable to exert a decisive influence will be
seen to be very numerous. A considerable percentage of persons of
both sexes never marry: the age of marriage is very variable, and
with women especially the effect of age is very great: according to
the Australian figures of 1911 the maximum rate of reproduction for
married women occurs at 18, and at 31 has fallen to half the maxi-
mum value. A bride of 30 may expect but 38 per cent, of the family
she would have borne had she married at 20, and by 35 the number
is further reduced by one-half, and is a little less than 19 per cent.
With men the potentiality of fatherhood is usually retained to a
considerable age, nevertheless the age at marriage is still very
influential, since the most frequent age for the brides increases
steadily with the age of the bridegroom. For bridegrooms of from
34 to 44 years of age, brides of the most frequent age are very
regularly ten years junior to their mates. Using the age of their wives
as a basis for calculation, men marrying at 40 to 44 may be expected
to have only two-fifths of the number of children of men marrying
20 years earlier.

The choice between celibacy and marriage, and if marriage be
decided upon, between the precipitation and the postponement of
the union, is in modern societies very much a matter of temperament.
Some men are little charmed by female society, others of a more
sociable disposition seem for long unsuited to a permanent alliance :
in all normal men the primary impulses of sex appear to be suffi-
ciently developed, but in civilized circumstances the strength of this
impulse is not directly exerted towards the conjugal condition: in
many men it is overcome by prudence and self denial, in others it is
dissipated in unproductive channels. The various privileges and
obligations of marriage appeal very differently to different natures :
patience, caution, and a strong sense of financial responsibility often
postpone, or prevent the initiation of desirable matches: confident,
passionate, and impulsive natures marry in circumstances which
would awake in the prudent the gravest misgivings. The influence of
the innate disposition in this matter is increased in our own times by
the absence of any strong social opinion which might regulate the
erring fancy of the individual, and by the conditions of urban life

192 THE INHERITANCE OF HUMAN FERTILITY

which set no limit to the variety of acquaintance. Upon considera-
tion it would seem that while to the individual, fortuitous circum-
stances may seem to be of much importance, their influence is easily
exaggerated even in determining the individual destiny. The man
who from an early disappointment condemns himself to celibacy,
is less the victim of misfortune than of his own temperament, as is
the unwary youth who becomes the lifelong victim of an unfortunate
entanglement. In each case temperament largely determines how the
chances of life are taken, and in the aggregate of sufficient numbers
the chance element is wholly negligible.

The initiative in respect of marriage is conventionally regarded as
confined to men, while the factors which determine celibacy or age
at marriage in the case of women are conditioned by the character
and frequency of the offers they receive. Even if this distinction
were absolute in practice, it would be difficult not to admit that
temperamental differences in young women do in fact exert the
predominant influence upon their respective probabilities of marriage
within, say, the next five years. To this probability other hereditary
characteristics will also contribute, in so far as they control beauty,
health or traits of character favoured by suitors. In point of fact,
however, the distinction between the sexes in this matter is far from
absolute and the probability of marriage in either sex is much in-
fluenced by the characters, which, on a conventional basis, have been
ascribed to the other.

Besides these causes of varying fertility, which act through the
incidence of the social state of marriage or celibacy, there exist in
civilized and savage life, and have existed from the most ancient
tunes, a number of practices by which the increase of population is
artificially restricted. Infanticide, feticide or abortion, and the pre-
vention of conception, have all been or are now being practised among
every considerable body of people: to these should be added such
practices as prostitution the use of which attains the same purpose by
competing with instead of corrupting the conjugal condition.

The extent to which infanticide is and has been practised may be
appreciated by a perusal of the masterly section which Westermarck
devotes to the subject. Among uncivilized peoples, though not
universal, it is commonly customary, and frequently compulsory.
Though forbidden by Buddhism and Taoism it is frequent in China.
Among the pre-Islamic Arabs it seems to have been usual and

THE INHERITANCE OF HUMAN FERTILITY 193

approved: it is repeatedly condemned in the Koran. It is not
mentioned in the Hebrew Scriptures, and may have been unknown
to the early Jews. In India where it was forbidden by the laws of
Manu, the Rajputs are said to have been particularly addicted to the
practice, for which, however, priestly absolution was obtained. In
Ancient Greece the practice of exposing healthy infants, though
hardly approved, was tolerated, except at Thebes where it was
a capital crime. In Rome, though the destruction of deformed infants
was enjoined, the murder, and the less decisive act of exposure, of
healthy infants was contrary to the prevailing moral standards.

Of those factors affecting the fertility of married persons in our
own civilization, by far the chief importance must be given to the
prevention of conception. At the present time there can be no doubt
of the wide prevalence of birth limitation among married couples in
Europe and America. It is earnestly urged hi certain restricted circles,
that only by the adoption of these methods can private indigence and
public scarcity be prevented, and their use is put forward not only
as a blessing but as a duty. Public opinion, however, so far as one
can gauge it upon a topic, which, however prominently discussed
is essentially private, appears to resemble that of Pliny respecting
feticide, that it is a venial offence and one that is frequently excusable.
' The great fertility of some women ', says Puny, ' may require such
a licence '. It is important to observe that deliberate contraceptive
practices are confidently supposed to be the most important causes,
not only of the general decline of the birth-rate in recent decades, but
especially of the diminished fertility of the upper classes.

In the practice of, or abstention from, contraception, tempera-
mental differences, including the attitude towards sexual morality
generally, are particularly pronounced. This is evident, if only from
the various grounds on which this practice is advocated. It is certain
that, to some, the freedom from individual liability to the natural
consequences of sexual intercourse is a most attractive feature, and
that a radical alteration of the accepted attitude towards sexual
morality, including the abandonment of the conventional abstinence
of the unmarried, would be welcomed. To others, again, who are
totally averse from sexual anarchy, a genuine appeal is made through
the intensity of the parental instincts ; for the prospect of endowing
or educating the earlier children may be reasonably held to be
impaired by later arrivals. The sentiment that the beneficent effects

3653 c c

194 THE INHERITANCE OF HUMAN FERTILITY

of parental companionship also gains strength by being concentrated
on a few, should perhaps be classed among the excuses, rather than
the reasons, for family limitation. Yet even the excuses are instruc-
tive from the enormous variability of the emotional response which
they evoke. The majority I suspect, even of those that practise it,
regard contraception with some degree of reluctance or aversion, but
according to the strength of this feeling may be induced to overcome
it by a greater or less intensity of economic pressure. Others, again,
would certainly feel themselves disgraced if they were to allow
economic motives to curtail in any degree the natural fruit of their
marriage.

If we consider the immense variety of the temperamental reactions
of mankind toward the two predominant factors determining fertility,
on the one hand marriage, and on the other the restricted or un-
restricted production of children by married couples, it will not be
surprising that, as has been seen, an exceptionally great variability
ascribable to these two causes should appear in the statistics of
civilized peoples ; and that the genotypic differences in reproduction
outweigh any genotypic differences which it would be reasonable to
anticipate hi mortality, the more especially since the incidence of
mortality among civilized peoples has been much diminished by the
advances which have been made in public and private hygiene. In
respect to mortality it is necessary to note that only deaths prior to,
and in less degree during, the reproductive period, have any selective
influence, and that these are already a minority of all deaths. The
diagram in Chapter II showing the reproductive value of women
according to age gives a fair idea of the importance in this respect of
the death-rate at different ages. Even the highest death-rate hi this
period, that in the first year of life, must be quite unimportant
compared with slight differences in reproduction ; for the infantile
death-rate has been reduced in our country to about seven per cent,
of the births, and even a doubling of this rate would make only about
a third as much difference to survival as an increase in the family
from three children to four.

Direct evidence of the inheritance of fertility

Great as the contribution of fortuitous circumstances to the observed
variance in individual reproduction undoubtedly is, it is none the less
possible to obtain direct evidence of the importance of hereditary

THE INHERITANCE OF HUMAN FERTILITY 195

causes, by comparing the number of children born to individuals
with the number born to their parents. As a biometrical variate the
number of children born to an individual is peculiar in several respects.
It is, like the meristic variates, discontinuous and confined to the
positive whole numbers, while unlike most of these, the frequencies
begin abruptly at zero. Moreover, where reproduction is governed by
the civil institution of marriage, the variate will usually be the same
for a man and for his wife, and cannot be properly regarded as
distinctive of either individually. It is obvious too that where a con-
siderable fraction of the variance is contributed by chance causes,
the variance of any group of individuals will be inflated in com-
parison with the covariances between related groups, with the result
that all correlations observable will be much diluted in comparison
with those to be found between metrical characters. Rather numerous
groups must therefore be studied if clear results are to be obtained.
From the data given by Pearson of the numbers of children born
to mothers and daughters, in a thousand cases extracted from the
British Peerage, the average number of children born to the daughter
is found to increase according to the size of the family to which she
belongs, from 2-97 from families of 1, to 6-44for families of 12 or more,
in accordance with the following table :

Number of
children
born to
mother.

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15

TABLE

9.

Total number

Number of
cases.

of children
born to
daughters.

35

104

67

237

111

249

136

464

138

550

132

513

114

448

87

354

74

313

50

219

24

191

9U2
1 f 3'

3J

122

99"]

"Lia.

20 J

Average
children

per
daughter.

.6-44

It will be seen from the averages, which are charted hi Fig. 10, that
apart from the inevitable irregularities due to limited numbers, there

196 THE INHERITANCE OF HUMAN FERTILITY

is a consistent increase in the number of children born to the daughters,
as the size of the family is increased, from which they were derived.
On the average an increase of one in the mother's family is followed
by an increase of 0-21 in that of the daughter, and although this is

I6

<

LU

I

_

O

LU
M

O

O

o

o

o

o

o

I I I

I 2 3 4 5 6 7 8 9 10 II IE 13 14 15

SIZE OF MOTHER'S FAMILY v
35 67 III 136 138 132 114 87 74 50 24 32

NUMBER OF FAMILIES

FIG. 10. Average number of children born to peeresses, according to the size of the
families of their mother.

less than one-half of what we should obtain in comparing the metrical
variates of individual parents and children, when these variates are
almost exclusively determined by hereditary causes, yet the value
which emerges from the data is more than six times its standard error,
and is unquestionably significant of a tendency for the size of a
daughter's family to resemble that of her mother in its deviation,
whether positive or negative, from the current average of her
generation.

It would be important to ascertain to what extent, if at all, this

THE INHERITANCE OF HUMAN FERTILITY 197

resemblance could be ascribed to a traditional continuity, whether in
religious doctrine, moral environment, or social ideas. We could only
adopt this explanation, to the exclusion of organic inheritance, by
assuming that individuals are not influenced in assimilating such

o

d

f^\

o

o

o o

2 3 4 5 6 7 8 9 10 il 12 13 14 15 16 17 18 19 20 21
SIZE OF GRANDMOTHER'S FAMILY ,

67 91 118 123 125 102 99 98 72 41 28 36

NUMBER OF FAMILIES

FIG. 11. Average number of children born to granddaughters, according to the
number born to their paternal grandmothers.

ideas, or in putting them into practice, in any degree by heritable
traits of character, and this is disproved by the obvious differences
observable in members of the same family. It is moreover far from
obvious, in considering the causes which might influence a young
girl's ideas on this subject, that the environment of a large family
would favour a higher degree of fertility than that of a small one.
The example of a mother must act both by suggestion and by
counter suggestion, and it would seem hazardous to assume that girls
are more strongly influenced, in practice, by a consciousness of the
special advantages of their home environment, than by a conscious-
ness of its special disabilities.

However this may be, we possess in the relationship between the
fertility of granddaughters and that of their paternal grandmothers,
an unequivocal confirmation of the view that the relationship
observed between mother and daughter is essentially one of organic

198 THE INHERITANCE OF HUMAN FERTILITY

inheritance. For a corresponding table shows that the regression of
the granddaughter's fertility on that of the grandmother's is 0-1065,
almost exactly half of that found for the influence of the mother.
An effect due wholly to organic inheritance should approximately
be halved in each generation, apart from any strong tendency
towards homogamy, and although the grandparental effect especially,
though statistically significant, is subject to somewhat large sampling
errors, its coincidence with the expected value undoubtedly points to
organic inheritance as responsible, at least, for the greater part of the
correlations observed.

It is instructive to put this agreement in another way. In the table
between mother and daughter, the covariance1 between the two
fertilities is 20-9 per cent, of the variance observed hi the fertility of
the daughters. In characters almost wholly determined by inheritance,
the covariance should be almost hah* of the variance, and we may
thus make the estimate that 41-8 per cent, of the observed variance
in fertility is ascribable to heritable causes. In Chapter II it was
pointed out that a good estimate of the genetic element in the variance
of any character could be obtained by dividing the square of the
correlation between parent and child, by the correlation between
grandparent and grandchild. In the present instance this gives us
(0-2096)2 + 0-1 123 or 39-1 per cent. Both methods of calculation
therefore agree in ascribing about 40 per cent, of the observed
variance to heritable causes, and this estimate, when we consider the
enormous predominance of the random element hi individual survival
obtained in the discussion in Chapter IV, shows that the heritable
factors influencing human fertility must exert a selective effect of
quite exceptional magnitude.

We may express the selective intensities thus indicated in the
units we have used hitherto to express differences in the Malthusian
parameters, namely per cent, per generation, by recognizing that
the genetic variance arrived at hi the preceding paragraph is in actual
magnitude 3-042 units, corresponding to a standard deviation, due to
hereditary causes only, of 1-745 children per family. Since the average
number of children born to the daughters is 3-923, individuals or
stocks differing from the average by no more than the standard
deviation, in opposite directions, will have families in the ratio
5-668 : 2-178. If the generations are of equal length, we may obtain
1 The mean product of the deviations from the means.

THE INHERITANCE OF HUMAN FERTILITY 199

the selective advantage of the more fertile over the less fertile groups,
by finding the difference between the natural logarithms of these two
numbers. This difference is 0-9564, indicating that the selective
advantage produced by variations (of by no means exceptional
magnitude) in innate fertility, amounts to over 95 per cent, in each
generation. In this form the statement of the intensity of selection
is comparable to the selection of the order of one per cent, which it
has hitherto been found convenient to consider hi exemplifying the
numerical effects of selections of determinate intensity.

The evolution of the conscience respecting voluntary
reproduction

The calculations of the last section indicate that among our con-
temporaries, at least, differences in heritable disposition play so
large a part in the determination of fertility, that somewhat large
modifications of temperament must be brought about by reproductive
selection within a span of ten generations, that is within a relatively
short historical period. We have seen that by no means extreme
genotypes have rates of reproduction in a ratio higher than 2 to 1,
and if for simplicity we imagine a population consisting of two strains,
which, having equal mortality, differ only to this extent in fertility,
it is easy to see that the numbers of one type relative to that of the
other will, in ten generations, be increased over a thousandfold. To
put the matter in another light, if at the beginning of the period the
population consisted of 97 per cent, of the less fertile and 3 per cent,
of the more fertile strain, in 5 generations the 2 strains are brought
to an equality, and in 5 more their situations are reversed, so that
the less fertile strain is represented by 3 and the more fertile by
97 per cent, of the population. Civilized man, in fact, judging by the
fertility statistics of our own time, is apparently subjected to a
selective process of an intensity approaching a hundredfold the
intensities we can expect to find among wild animals, with the
possible exception of groups which have suffered a recent and
profound change in their environment. We may therefore anticipate
that a correspondingly rapid evolution has taken place within
historical times in the appropriate mental attributes.

As is well known, the practice of infanticide is somewhat widespread
among uncivilized peoples. If we consider the perils of savage Me,
and the extreme hardships to which uncivilized peoples are from
time to time exposed, it would, I believe, be a mistake to regard this

200 THE INHERITANCE OF HUMAN FERTILITY

practice as altogether a maladaptation. Wherever the mortality in
infancy and childhood is extremely high, the reproductive value, in
the sense of Chapter II, of a new-born infant, must be small compared
to that of a young and fertile woman. In times of famine, or of
urgently enforced migration, an attempt to spare the life of the child
would not only be often unsuccessful, but would certainly endanger
the more valuable life of its mother. The act of infanticide, however
offensive to civilized feelings, has, in these circumstances, a certain
natural propriety, and it is not surprising that it should often be
regarded as a moral action and be, to some extent, compulsory. The
motive may be regarded as economic ; but since among peoples with
whom the accumulation of property is at a minimum, foresight as to
future resources is only felt under urgent stress, their motives can
scarcely be called prudential. Among settled peoples, on the con-
trary, prudence and the accumulation of property begin to play an
essential role, while the immediate effect of increasing prosperity,
by diminishing the selective importance of the death-rate, is to
enhance that of the rate of reproduction. It is not surprising therefore
that the religions of all civilized peoples, without exception, should
expressly condemn infanticide, although in several cases, such as the
peoples of Northern Europe and the pre-Islamic Arabs, we know it
to have been the practice of then* barbarous ancestors.

It is evident that the natural instincts of the father and mother
must offer some resistance to the practice of infanticide, even when
it is performed under the pressure of need. Moreover, we cannot
doubt that savages, like civilized people, differ among themselves in
their degree of callousness or sensibility. The feeling of aversion and
repugnance to the cruel act must be more strongly developed in some
parents than in others, and since infanticide is always to some extent
at the discretion of the parents, it cannot be doubted that the former
allow a larger number of offspring to live. In this way there is
a natural tendency, wherever infanticide is practised without the
pressure of the severest hardship, to strengthen the feelings of tender-
ness and compassion towards the newly born child, by the natural
elimination of those who are the most willing to murder their offspring,
for the sake of an easier or a freer life.

Amongst wholly savage peoples, although infanticide is not usually
regarded as wrong, it is probably not practised more frequently than
is on the whole racially advantageous. If however, in the course of

THE INHERITANCE OF HUMAN FERTILITY 201

time, a people, with feelings in this matter appropriate to the condi-
tion of extreme savagery, came to be placed in conditions in which
the accumulation of property is not only possible, but is the natural
aim of the more ambitious, the temptation to infanticide will be more
uniformly insistent, and the corresponding selection of the moral
instincts which resist this temptation, will be correspondingly severe.
If we accept the view that all long civilized peoples have been purged
of their more callous or murderous elements by passing through this
period of severe selection, we shall be in a position to realize why
it is that the consciences of civilized peoples, as expressed in their
religious teaching, should so unhesitatingly condemn infanticide.

An interesting example of such a transitional period is supplied by
the Arabs. The extreme hardship of the life of the desert Bedouin
must have presented many occasions in which infanticide was,
not merely economically, but biologically advantageous. Property
existed, but was principally tribal, and tribal feeling is evident in the
restriction of infanticide to female children. In the pre-Islamic period
we hear of reluctant parents being urged to kill their baby daughters
for the sake of their tribe. In the little trading centres the conditions
of life were doubtless much ameliorated, and the possession of
property was certainly largely individualized, though moral opinion
was doubtless dominated by the Bedouin tradition. The Koraish, the
tribe of Muhammad, seems to have been in possession of Mecca for
about five generations before his birth. At that time it is evident that
the public conscience was beginning to rebel against the usages of
their ancestors, from the importance which his little band of prose-
lytes attached to abstaining from infanticide. It is abjured in one of
the few clauses of the 'First Homage', and is repeatedly forbidden
in the Koran. One of the first acts of Muhammad, after his conquest
of Mecca, was to obtain an oath of abstinence from infanticide from
the Meccan women. To avoid the misapprehension that this doctrine
was connected with the military ambitions of the Moslem state, it
should be noted that the ' First Homage ' was taken before Muham-
mad's flight from Mecca, at a time when the idea of upholding their
faith by force of arms was entirely remote from the minds of the
faithful.

If it be conceded that the selective effect of infanticide has been
gradually to extinguish those hereditary types of temperament which
are least unwilling to conform to this savage custom, a similar selec-

3653

202 THE INHERITANCE OF HUMAN FERTILITY

tive effect is to be expected from the equivalent act of feticide or
abortion, whenever from prudential motives this practice has become
sufficiently common. The history of the evolution of moral opinion
in ancient Greece and Rome, during a period when feticide was very
widely practised, is therefore of considerable interest. It is fortunate
that an examination of the historical evidence relevant to the theories
under discussion does not require a detailed knowledge of the practice
of peoples at different epochs, but of the prevailing moral opinion as
to what is right and what is reprehensible. An investigation into
practice would be a matter of the greatest difficulty, as is evident from
our ignorance of the current practices of our own time. The practice
of different individuals at any one time is, moreover, certainly far
more variable than their moral opinions, which are usually held in
common to a rather remarkable degree. The majority of those who
do what is thought to be wrong certainly do so without departing far,
in their moral opinions, from the rest of the society to which they
belong. We can seldom indeed find distinct differences of moral
opinion, even between the protagonists in religious controversy. If,
therefore, we find pronouncements upon social practices in the
writings of moral philosophers of high repute in their own generation,
we are on very safe ground in inferring that their expressed opinions
on these subjects were not shocking to any considerable body of their
contemporaries, but, on the contrary, were nicely designed to express
the common ground of thoughtful and high-minded opinion in their
own time.

In the fourth and fifth centuries B.C. no opprobium seems to have
been attached to the practice of feticide. We find high-minded men
of the greatest moral weight commending its utility. Plato advocates
it principally for eugenic, Aristotle for economic motives, much as
high-minded men of our own day may be found to advocate more
modern methods of birth limitation. A few centuries later a some-
what changed outlook is unmistakable. Polybius, in whose time, in
the second century B.C., the increase of the custom had led to an
evident depopulation, regards this as a political evil, and evidently
felt that the rich, at least, should be blamed as unpatriotic. 'For this
evil grew upon us rapidly, and without attracting attention, by our
men becoming perverted to a passion for show and money and the
pleasures of an idle life, and accordingly either not marrying at all,
or, if they did marry, refusing to rear the children that were born,

THE INHERITANCE OF HUMAN FERTILITY 203

or at most one or two out of a number, for the sake of leaving them
well off or bringing them up in extravagant luxury.' He believes that
this should be changed, ' by the men themselves if possible changing
their objects of ambition ; or, if that cannot be done, by passing laws
for the preservation of infants'. In the first century A.D. Pliny, whom
we have already quoted, is almost apologetic, but evidently broad-
minded. Seneca is more severe. Writing in praise of his mother
Helvia he specially mentions her virtue in never having committed
feticide, an act which he evidently reckons among the follies and vices
of the fashionable world. We may see by these instances, and by
many other less direct indications, that a profound change had taken
place in the public conscience of the Roman Empire before its con-
version to Christianity. A few centuries later, what had seemed
patriotic and high-minded to Plato and Aristotle, a venial offence
and a fashionable folly to Pliny and Seneca, was anathematized as a
damnable sin by the Christian fathers, such as Tertullian, and was
made a capital offence in the laws of Valentinian.

Since the change in moral opinion with respect to feticide, together
with associated changes in sexual morality, took place over a period
during which the ancient world experienced the religious revolution
of conversion to Christianity, and since these concurrent changes were
ultimately connected causally, it is important to avoid the mis-
apprehension that the change in moral feeling, with which we are
concerned, was derived as a consequence from the acceptance of
Christian doctrine. It would, I believe, be a fundamental mistake to
imagine that the moral attitude of any religious community is to any
important extent deducible from the intellectual conceptions of their
theology (however much preachers make it their business so to
deduce it), and still more to suppose that official doctrine is not itself
largely moulded by the state of the popular conscience. The facts
available to guide us in the present case are :

(i) The progressive change of moral opinion among pagan writers
from Plato to the jurist Julius Paulus, who, about the beginning of
the third century A.D. , stated the opinion that the exposure of children
was morally, though not legally, equivalent to murder, and expressed
strong disapproval of the practice of feticide. The opinion of these
writers, who either knew nothing of Christianity, or rejected its
doctrine, cannot easily be ascribed to the state of Christian feeling
upon the subject.

204 THE INHERITANCE OF HUMAN FERTILITY

(ii) Our earliest authentic source of Christian doctrine, the story
as told in the Gospels, teaches an attitude of gentleness, forbearance
and self-sacrifice which has ever since been regarded as ideally Chris-
tian. It contains, however, no condemnation of feticide ; and cannot
even be regarded as the source of the theological doctrine of the
damnation of unbaptized infants, even if born dead, which un-
doubtedly at a later date exerted an important influence in crystalliz-
ing Christian opinion upon this subject. It cannot easily be argued
that, while not specifically condemning feticide, the gentle and
humane character of the Gospel teaching in reality determined the
later attitude of the church, for there is nothing gentle or humane
in the doctrine we have quoted, and the early Christian legislation
against sexual offences certainly seems to err on the side of excessive
ferocity. On a statute of Constantine Gibbon remarks :

The successful ravisher was punished with death; and as if simple
death were inadequate to the enormity of his guilt he was either burnt
alive, or torn in pieces by wild beasts in the amphitheatre. The virgin's
declaration that she had been carried away with her own consent,
instead of saving her lover, exposed her to share his fate. The slaves,
whether male or female, who were convicted of having been accessory
to the rape or seduction, were burnt alive or put to death by the
ingenious torture of pouring down their throats a quantity of melted
lead.

We can understand the temper of such legislation as the work of
men filled with a temperamental fear and loathing of sexual licence,
working in a frenzy of fanatical enthusiasm ; we cannot explain it
as the work of broad-minded and tolerant men convinced by the
Gospel story of the divinity of Jesus.

(iii) That a stricter sexual morality, including a more vehement
condemnation of feticide, did in fact characterize Christian as
opposed to Pagan ethics, when these are contrasted contemporane-
ously, must be ascribed in large part to the direct appeal made by
Christianity to the sanction of the individual conscience, which made
it the more responsive to popular feeling, even when latent and un-
expressed. This effect was certainly enhanced by the solicitude of
the early Church for persons of the meanest occupational status,
since, as will be shown more fully in Chapter XI, the evolutionary
effects of variations in reproduction are greatest in the lowest social
class. In these respects the influence of the rise of Christianity upon

THE INHERITANCE OF HUMAN FERTILITY 205

the change in moral opinion was intimate and direct; it would be
beyond the scope of our subject to consider this association as a factor
in determining the triumph of Christianity in the Roman world.

Analogies of animal instinct and immunity to disease

To a remote spectator the evolution which the human instincts of
reproduction have undergone during civilized periods would seem
scarcely more remarkable in kind than the analogous modifications
which the reproductive instincts of other animals have undoubtedly
experienced in their evolutionary development. The principal con-
trast would probably seem to lie in the great intensity of the selective
process in Man, and the correspondingly rapid evolutionary progress,
in spite of the great length of the human generation. The moral
qualities are so important to ourselves, and appear to possess so
absolute a sanction, that it is not easy at once to take up this remote
view-point ; yet any sympathetic consideration of the contingencies of
reproduction among the higher animals must convince us that their
moral nature also must have been in many cases modified by a
strictly analogous form of selection. The astonishing courage shown
by many ordinarily timid species of mammals and birds in the
defence of their young, and even the abstention of carnivorous
mothers from infanticide, are cases in which we can at least be sure
that the emotional response to a situation connected with reproduc-
tion has been modified in a manner analogous to the modifications
of the moral emotions found necessary in man to overcome the temp-
tation to the specific vices to which he is exposed.

An even closer analogy might perhaps be found in the evolution of
immunity to specific diseases and to morbid cravings as for alcohol,
through the selective action of the death-rate, parallel to the evolution
of immunity to sexual vices through the selective action of the rate
of reproduction. In the case of diseases it is, I believe, accepted that
a special or specific immunity must be acquired independently against
each disease in turn ; on the other hand it is I think evident that im-
munity to such crude vices as infanticide is usually acquired through
mental modifications, which themselves aid in conferring some degree
of immunity to the more insidious temptations to feticide or to
contraception. Certain types of vital statistics are at least suggestive
of the view that, if they could be tested under equal conditions in
the same environment, the most anciently civilized peoples, or rather

206 THE INHERITANCE OF HUMAN FERTILITY

those groups in whose collective ancestry exposure to civilized condi-
tions has been greatest, are the most prolific, while those most
recently civilized are least able to maintain their numbers hi a civilized
community. For example, in the maternity statistics of the State of
Rhode Island as reported by Dr. Hoffmann we have the proportion
of women married at the time of the Census (1905) who at that time
were still childless, stated according to religious denominations,
Protestant, Catholic, or Jew, and for American born and Foreign
born women respectively. The percentages given are :

TABLE 10.

American Foreign

born. born.

Protestant . . 30-7 19-4

Catholic . . 24-2 16-9

Jewish . . . 18-9 11-4

The contrast between the American born and the Foreign born is
apparently one of social class comparable to the occupational dif-
ferences to be considered more fully in the next chapter. The religious
differences might conceivably be ascribed to the direct effect of
religious doctrine as to the practice of contraception, which is con-
demned by the religious heads of both the Catholic and of the Jewish
communities. It seems more probable that the differences are racial
in origin, and on this view it is at least interesting that the racial
stock of Protestant peoples should be relatively recently civilized,
while that of the Jews has been largely exposed to the influence of
civilization from times prior even to the classical civilization of the
Mediterranean area.

The bare fact of a people having become gradually averse to a
specific action, such as feticide, owing to its effect upon the propor-
tionate survival of different individuals in the ancestry of subsequent
generations, throws very little light upon the mental processes by
which this feeling of aversion is brought about. As a cause of such
changes Natural Selection is entirely indifferent to the means, so long
as the required end of effective reproduction is achieved. The Chinese
belief respecting infanticide, that the ghosts of the murdered babies
bring misfortune, indicates a method of modifying the reproductive
instincts by the preferential survival of the more credulous and super-
stitiously fearful. It may well be considered that the source of such
a belief is to be found in an innate tendency to experience a feeling of

THE INHERITANCE OF HUMAN FERTILITY 207

guilt on committing infanticide ; but when such a belief has grown
up, and has become widely accepted, its existence will undoubtedly
modify the incidence of selection in the particular mental qualities
which are favoured. Although the progressive strengthening of the
reproductive instincts, which may be regarded as the principal effect
of reproductive selection, will be steadily pursued, a variety of psycho-
logical modifications, together with sociological changes consequent
upon these, may all be, in different circumstances, effective means to
that end. It is convenient to regard as the primary effect of selection
directed against a conscious and voluntary action, the development
of moral aversion towards that action, while other mental attributes
which produce the same effect, through the pursuit of illusory ends,
constitute a kind of mimicry of the appropriate morality. Which type
of mental attribute will turn out in practice to be the most effective,
and in consequence be subject to the most rapid modification, must
depend in part on the extent to which knowledge of natural causation
is diffused among the people in question.

A consideration which is relevant to the conscious choice of the
parents in reproduction, equally with their moral attitude towards
the methods of family limitation available, is the motive for which
that limitation is desired. Parents in whom economic ambition is
strong, will, in like circumstances, be more inclined to limit their
families than those in whom it is weak. Consequently a progressive
weakening of the economic ambition, or at least in the average
intensity with which this motive is felt among the great body of
citizens, is to be expected as a concomitant to the strengthening of
the moral aversion towards family limitation. The attitude of men
and women towards their economic welfare cannot, however, be
ordinarily reduced by this cause to indifference, for in countries in
which the poorest class are frequently decimated by famine, it is
apparent that a stage will be reached at which what is gained in the
birth-rate is lost hi the death-rate ; and even where the extremes of
distress are ordinarily avoided, some loss of civil liberty, and of the
opportunities for reproduction, has been the common effect of indi-
gence. Moreover the rational pursuit of economic advantage must,
even in the most civilized countries, frequently place the individual
in a position favourable to normal reproduction. It would, apparently,
in most societies, be as disastrous to the biological prospects of the
individual to lack entirely the acquisitive instincts as to lack the

208 THE INHERITANCE OF HUMAN FERTILITY

primary impulses of sex, notwithstanding that the abuse of either
passion must meet with counter-selection. The moral attitude of
civilized peoples towards money, as towards sex, must be therefore
the product of much more complicated evolutionary forces than is his
attitude towards infanticide or feticide, as might perhaps be inferred
from the hypocrisy and fanaticism, the passions and the passionate
inhibitions, found among long-civilized peoples on both subjects. We
may at least gather a hint of one of the reasons for the moral disrepute
commonly associated with mercenary motives, a disrepute which
itself contrasts rather strangely with the economic theory that pay-
ments are the conventional equivalents of services freely recognized
as worth such payment ; though there is nothing in our argument so
far to show why the prevailing attitude towards wealth should differ
from that sketched at the end of the last chapter, where it was as-
sumed that the normal destiny of accumulated wealth was to provide
for a numerous posterity.

Summary

The number of children actually born to different individuals in
civilized societies is, as hi other organisms, largely influenced by chance.
Whereas in most wild organisms the contribution of other causes to
the actual variation is probably so small that it could not easily be
detected, the total variance in the number of offspring produced in
civilized man is so great that a considerable fraction must be ascribed
to causes other than chance.

Temperamental qualities exert a great influence in determining
celibacy, or age at marriage, both in men and women. They are, and
throughout human history generally have been, at least equally
important in conditioning the use or abstinence from the use of arti-
ficial methods of family limitation.

The number of children born to women is significantly correlated
with the number born to their mothers. Statistics of the upper social
classes in the ninteenth century suggest that about 40 per cent, of the
total variance observed may be ascribed to heritable causes. Of these
by far the most important must be inherited qualities of the mind, and
especially of the moral temperament. The intensity of selection by
differences of fertility, due to innate causes of the order found, is
relatively enormous in comparison to selective intensities to be
expected hi nature. In spite of the late maturity of man, it is suffi-

THE INHERITANCE OP HUMAN FERTILITY 20$

cient to produce considerable evolutionary changes in relatively short
historical periods.

The custom of infanticide in the towns of pie-Islamic Arabia was
accompanied by a change in moral outlook which finally forbade the
custom. The widespread use of exposure and feticide in the earlier
ages of the Graeco-Roman civilization was accompanied by a gradual
and persistent change of opinion in regard to these practices, until
they finally became capital crimes. The influence of Christian teach-
ing upon the abolition of these views was very great, but this influence
sprang rather from the consciences of the people than from dogmatic
doctrine.

Races may be regarded as becoming immune to race-destroying
vices in a manner analogous to the acquirement of immunity against
disease by means of selective mortality. There is some evidence in
modern statistics that those races are most immune, even to modern
methods of birth limitation, which have had the longest social
experience of civilized conditions.

The evidences examined leave little room for doubt that the most
powerful selective agency in civilized man is that acting upon the
mental and moral qualities by way of the birth-rate, and that this
agency is at work with an intensity which cannot easily be paralleled
in other species.

3653

E 6

REPRODUCTION IN RELATION TO SOCIAL CLASS

Economic and biological aspects of class distinctions. Defects of current data. Early
investigations. British data. Position in the U.S.A. Effects of differential fertility.
Summary.

The world will be thy widow and still weep

That thou no form of thee hast left behind. SHAKESPEARE.

Economic and biological aspects of class distinctions

FOR the biological study of mankind the institution of social class
has a double importance. Merely from the economic standpoint the
different occupations are graded in the rewards which they secure to
their professors, and, it is to be presumed, hi the social value of the
services performed. From this point of view, the social class which a
family occupies may be regarded as the margin of prosperity which
separates it from destitution, or at least from a level of bare sub-
sistence ; so that a comparative failure in one occupation is free, at
the expense of some loss of social class, to find some humbler mode
of living in which his talents are sufficient to win the necessary support
for himself and his family. The elasticity afforded by the range of
occupations, and by the differences in the rewards which they procure,
may thus be regarded as mitigating the severity of the consequences
which failure entails upon solitary organisms, by leaving for the
majority of the population a certain margin of safety from absolute
destitution.

An aspect of social class of more direct biological importance lies in
the profound influence which it exerts upon the intermarriage of
different families. In several instances the importance of avoiding
class intermarriage has been so strongly felt that such marriages have
been opposed by definite legal penalties, with the consequent forma-
tion of closed, more or less aristocratic, castes. This has been especially
the case where racial differences have been involved. Without any
such legal provision, however, prevailing opinion, mutual interest,
and the opportunities for social intercourse, have proved themselves
sufficient, in all civilized societies, to lay on the great majority of
marriages the restriction that the parties shall be of approximately
equal social class. In this statement social class should, of course, be

REPRODUCTION IN RELATION TO SOCIAL CLASS 211
taken to comprehend, not merely income or wealth, but also the
prestige attaching to occupation, personal talents, and family associa-
tions. Its meaning is thus somewhat different from, though closely
correlated with, the purely economic use of the term. But the factor
of intermarriage is so important in its social and biological conse-
quences that it will be best to use the term ' social class ' solely in this
sense and to lay down that the social class of an individual or his
family shall be defined by the aggregate of persons or families, inter-
marriage with whom will encounter no social obstacles.

By reason of the influence of class on mate selection, distinctions of
social class are distinctions of relatively permanent biological entities,
not indeed strictly insulated, but influencing one another by a constant
diffusion of persons who pass from class to class. This mutual diffusion
should be distinguished from the great tide of social promotion, which,
as will be seen more clearly, is now everywhere in progress, and upon
which the mutual influence by diffusion may be regarded as super-
imposed. These two social movements are, of course, confused in the
history of each several individual, but their causes and consequences
must clearly be distinguished. The relatively permanent character of
the social classes gives a special importance to the differences which
exist in their vital statistics, for, to produce an evolutionary change it
is necessary that groups contrasted, for example, in their rates of
reproduction, should also be differentiated genetically; and if this
change is to be progressive and continuous it is further necessary that
like differences in reproduction should continue generation after
generation to characterize groups showing the same genetic contrasts.

That a puzzling discrepancy existed between the birth-rate of
certain highly placed families, and those of the general population,
seems to have been suspected during a great part of the nineteenth
century ; but neither the magnitude nor the geographical extent, nor,
indeed, the sociological nature of the phenomenon seems to have
been appreciated until quite recent times. The theory, of unknown
origin, that the ' inbreeding ' supposed to be practised by exclusive
aristocracies, was a cause of sterility (and of other signs of degeneracy)
was doubtless framed under the impression that wealthy plebeian
families were as fertile as the rest of the community. Herbert
Spencer's theory of an inherent opposition of ' individuation ' and
' genesis ' would seem to suggest that he recognized some failure of
reproduction as characteristic of the brain- workers. One of the

212 REPRODUCTION IN RELATION TO SOCIAL CLASS

most important points established by the modern data is that the
deficiency in procreation is not specially characteristic of titled families,
or of the higher intellects, but is a graded quality extending by a
regular declivity from the top to the bottom of the social scale.

Defects of current data

Before considering some of the more important researches in this
field it is necessary to point out that, although the general character of
the facts may be said to be established, in most western countries
with certainty, yet the actual quantitative data available are far less
satisfactory than they might easily be made, and this for two prin-
cipal reasons. In the first place, they are much out of date, and relate,
in some of the most important instances, to the rate at which births
were occurring in different classes as much as thirty-five years ago ;
while as to what is. now occurring we can only conjecture from the past
course of events. The best data for England and Scotland as a whole,
for example, are still those which were obtained in the census of 191 1,
from the completed families of persons enumerated in that census.
Many of the children upon which these comparisons rest were, there-
fore, born quite as early as 1890 and represent the behaviour rather
of the last than of the present generation of parents. Such an interval
of time may be of great importance in bringing to pass changes in
the birth-rate ; for it is certain that, whatever changes have occurred
in the relative rates of reproduction of different classes, the birth-rate
of the country as a whole has diminished very greatly during this
period. Although the questions may be repeated in the census of 1931
it is clear that comparisons based upon statements of completed
families will, by the time they are made public, be already nearly
twenty years out of date. Direct information as to the course of
natality from year to year could, however, be obtained from the
numbers of births registered, provided the ages of the parents at such
times were recorded, and the occupation of the father, which is now
recorded, were brought into harmony with the occupational classifica-
tion employed in the census.

In the second place, a completely satisfactory comparison between
different occupational groups must involve the mortalities occurring
in those groups, and the natalities as affected, not only by the birth-
rates of married persons of a given age, but also by age at marriage
and frequency of celibacy. The basis for a complete biological com-

REPRODUCTION IN RELATION TO SOCIAL CLASS 213
parison is, in fact, to be found only in the Malthusian parameter of
population growth, of which the theory was developed in Chapter II ;
it is therefore only when the Malthusian parameters for different
occupational groups have been established, that a quantitative know-
ledge of the biological situation will have been obtained. In all the
examples to be given it will be seen that our knowledge falls very far
short of this level. It is perhaps of minor importance that mortality,
except hi early childhood, should have been generally ignored, for
this is certainly not the major factor of the comparison. Even with
respect to births, however, nearly all inquiries tend to confine them-
selves to a comparison of the births to married persons of a fixed age,
and often assemble their data in such a way as to eliminate, as far as
possible, the important factors of age at marriage and celibacy. It is,
of course, desirable in itself, that these three elements should be evalu-
ated separately, and there are reasons to think that then* separate
evaluation will be of service in disentangling the causes of the pheno-
menon. Yet, since no one item is of the same practical significance as
the total effect, more is usually lost than gained by forms of tabula-
tion in which the total effect as such is ignored.

Early investigations

One of the earliest important investigations was that carried out
by Dr. David Heron upon the birth-rates in the different metropolitan
boroughs into which London is divided. His method consists in the
correlation of fertility with a number of indices of social status,
derived from the proportion of different occupations recorded in the
census. The districts in which the average social level is highest are
indicated by a high proportion of professional men and of domestic
servants, and by a low proportion of general labourers, pawnbrokers,
employed children, and occupants averaging more than two in a room.
The fertility was measured in 1901 by the birth-rate for a thousand
married women aged 15 to 54, and hi 1851 by the birth-rate for a
thousand married women over 20. The birth-rate was found to be
closely associated with all indications of a lower social class. Both
epochs show the same general relationships between undesirable
social conditions and a high birth-rate ; the intensity of this relation-
ship, however, has almost doubled in the interval from 1851 to 1901.
The investigation is of particular interest in showing that in 1851 a
class difference in fertility had already developed, although of only

214 REPRODUCTION IN RELATION TO SOCIAL CLASS
half the intensity of that shown at the end of the century. The com-
parison of intensity is, however, slightly obscured by the change
which Dr. Heron was obliged to make in the method of measuring
fertility, for the slightly inferior index used for 1851 would itself
probably diminish the intensity of the correlations obtained. It
should be remembered that the comparison is made only between
districts, and that what is demonstrated is no more than that, in
London, the poorest districts have the highest birth-rates. It does
not prove that the poorest classes are themselves responsible for these
birth-rates, although such a general association is a natural inference
from the results. The methods used, however, cannot be made to
distinguish whether the cause of the contrast is that the better paid
workman is less prolific than the worse paid, or merely that the
professional and salaried occupations are less prolific than the
working classes in general. The differences observed in this study do
not of course include any differences hi the incidence of celibacy, or in
the average duration of marriage before 45.

The first national statistics in which size of family can be compared
with occupational status were obtained in the French census of 1906.
For families of which the head was 60 to 65 years old at the time of
that census, and still married, the average family was 3-60. For
employers (patrons) the average was 3-59, or almost equal to that of
the general population ; for workmen (ouvriers) it was 4-04, while among
employes other than workmen it was only 3-00. The patrons are more
than half farmers, for whom the average for those married more than
25 years is 3-71, while little more than a fifth of them belong to the
liberal professions, for whom the corresponding average is 3-30, or a
trifle less than that of the employes, other than workmen, if allowance
is made for the change in the basis of classification.

The classification of the census was, however, better fitted to
compare the conditions in different industries than to compare those
in different grades of the same industry. Fresh evidence was obtained
in 1907 from schedules of families filled in by a large number of
employees and workmen, in the pay of the state, and of various
provinces and parishes. The averages for marriages which had lasted
more than fifteen years show for workmen a regular decrease in size
of family from the worst paid, with an average of 3-29, to the best
paid, earning from £160 to £240 a year, with an average of 2-34. The
employees, in the same wage-groups show a corresponding fall from

REPRODUCTION IN RELATION TO SOCIAL CLASS 215
2-77 to 2-31. Those earning from £240 to £400 a year show a further
fall to 2-29, while those earning more than £400 a year show a rise to
2-38. It is clear from these and the preceding figures, that hi the bulk
of the French population, earning less than £400 a year, reproduction,
at a period that must be referred back at least to the eighties and
nineties of the last century, was much more active among the poorer
than among the better-paid classes. For officials earning more than
£400 a year, at which point the salary subdivisions cease, there was,
apparently a slight rise in reproduction, although within the more
prosperous classes the intellectual group represented by the liberal
professions had much fewer children than the average.

For Great Britain the fullest information so far made available is
that obtained from the census of 1911, but a number of private
investigations had already made clear individually the facts of the
greatest importance. Mr. Whetham in 1909 published the results of
a study (Family and Nation, p. 140) of the fertility of the higher ranks
of the professional and official classes, in which he made use of the
information supplied by Who's Who. He finds that the average
number of children, recorded for married persons in this class, falls
from 5-19 to 3-08, hi passing from those married before to those
married after 1870. He notes that for clergymen the diminution is
much less, and for military families considerably more, than for the
remainder. A similar investigation by the same author shows that,
for families that have held a peerage for at least three generations,
the average has fallen, according to the date of marriage, from 7-10
for marriages in the thirties of the last century, to 3-13 for those con-
tracted in the eighties. Although these investigations are confined to
a small fraction of the British people they reveal significant facts,
first as to the low rate of reproduction of the English upper classes of
the last generation, and secondly that this rate of reproduction was
falling during the latter half of the nineteenth century at a rate
greatly exceeding the decline in the fertility of the general population.

It is sometimes imagined that the differences in reproduction
between different social classes, depend upon circumstances and ideas
peculiar to those who enjoy the advantages of leisure, or education,
or both combined. It seems frequently to have been deemed probable
that where poverty is severe the most healthy and efficient will
reproduce their kind the most freely, as is the case with animals in a
state of nature. Whatever may have been the case hi the past, a

216 REPRODUCTION IN.RELATION TO SOCIAL CLASS
careful and most valuable investigation has shown that data, drawn
from the poorest classes in the industrial towns of Blackburn, Preston,
Glasgow, and Birmingham, and from the Royal Albert Asylum,
Lancaster, prove that the most capable among these classes have the
fewest children. The correlations found are not large, as is to be
expected when we deal with variations within a population of nearly
uniform culture. What is established beyond doubt is that, when
proper allowance is made for the age of father and mother the larger
families subsist upon the smaller wages. In other words the poorer
wage earners have, at a given age, the greater number of surviving
children. Similar results are obtained when other tests of capacity or
status, such as health, regularity of employment, temperance of the
father, or cleanliness of the home, are substituted for wages. Of these
criteria the least satisfactory is the cleanliness of the home, since it
is probable that visitors, in grading this variate, do not make accurate
allowance for the extra work entailed by the larger families.

British data

The results of the census of 191 1 have been reported upon separately
by Dr. J. C. Dunlop for Scotland and Dr. T. H. C. Stevenson for
England. The two accounts differ considerably in the form in which
the results are reported, and since the results of the two inquiries are
closely similar, each serves in several valuable respects to supplement
the other. For Scotland Dr. Dunlop gives a comparative table of the
average numbers of children for a large number of occupations. Only
marriages which had lasted fifteen years or more were utilized, and
the age at marriage of the wife was restricted to the five year period
22 to 26. The average for all occupations is 5-82 children, and by
arranging the occupations in order of the average size of family it is
easy to compare the social status of the most fertile, with that of the
least fertile occupations. To avoid giving undue weight to the small
groups, for which the average fertility will not be very precisely
determined, we should also take account of the number of famines
represented by each average. The most fertile occupations comprise
three large groups, namely, crofters 7-04, coal, shale and ironstone
miners 7-01, agricultural labourers and farm-servants 6-42; three
groups of moderate size, namely old-age pensioners 6-95, fisherman-
crofters 6«93, and coal heavers 6-61, besides the small group of
plasterers' labourers 7-01. Turning now to the least fertile occupa-

REPRODUCTION IN RELATION TO SOCIAL CLASS 217
tions the only large group is the very composite one of clerks, scoring
4.38. Six groups of moderate size are the physicians and surgeons
3-91, advocates and solicitors 3-92, literary and scientific 4-09, school-
masters and teachers 4-25, art, music and drama 4-27, ministers and
clergymen 4-33. In addition there are three small groups of army
officers 3-76, dentists and assistants 3-86, and veterinary surgeons
4-00. The contrast between the social status of these two sets of
occupations requires no stress. Among the least fertile are the learned
professions, and, among the most fertile, the poorest of manual
labourers. The differences in the average numbers of children are the
more remarkable owing to the severe restriction to which the age
of the mother has been subjected. Together with the restriction on
the duration of marriage, this is nearly equivalent to eliminating,
between the different occupational classes, all such differences in
fertility as arise from differences in the frequency of celibacy, and in
the age of marriage. It clearly appears from the corresponding
English figures that the contrast between the real rates of reproduc-
tion in the different classes, is heightened by the inclusion of these
additional factors.

The census results are particularly valuable in showing that the
decrease of fertility with improved social class is not confined to any
one section of the social scale, as it seemed to be in the French figures
already quoted, but is equally manifest from the very poorest groups
that can be compared, to the most distinguished occupations which
provide sufficient numbers on which to base a comparison.

In several instances it is, moreover, possible to compare the fertility
of groups which are essentially grades within the same occupations.
The comparison of these is of particular importance, because we
thereby eliminate the considerable factors of differences in locality
and of industrial environment, and in the absence of these, the
averages derived, even from the smaller occupational categories,
possess considerable significance and regularity. Thus the three pah's
of categories in Dr. Dunlop's list, which seem to be strictly compar-
able, show us that bricklayers' labourers have more children than
bricklayers, that agricultural labourers have more children than farm
foremen, and that plasterers' labourers have more children than
plasterers. Since in each of these comparisons all variations in locality,
and in the conditions of employment, must be shared, in a somewhat
strict proportion, between the two grades of labour, these comparisons

3653 pf

218 REPRODUCTION IN RELATION TO SOCIAL CLASS
display the fertility differences in the clearest light. Since 1911 the
classification by occupations, used in the census, has been very greatly
improved, especially by separating the classification by industries
from the classification by grade or employment within each industry,
and if the inquiry as to number of children is repeated in the census
of 1931, many more comparisons between different grades of workers
in the same industry should become possible.

In 1920 Dr. Stevenson published an account of the results for
England and Wales in which special attention was given to over-
coming the difficulties of obtaining conclusions of direct sociological
value from data, the collection of which had been, for that purpose,
very imperfectly planned. The occupational categories, although
they include distinctions both of industry and of occupation proper,
could be roughly graded into five large sections, of which the first
represented the upper and middle classes, in a very generous inter-
pretation of this term, the third was of skilled workers and the fifth of
unskilled. Owing to the absence of grade distinctions it was necessary
to omit from this subdivision the three great groups of textile workers,
coal miners, and agricultural labourers.

For the families of continuing fertility, i. e. where the wife was
under the age of 45 years at the date of census, the average numbers
of living children for these five groups are 1-68, 2-05, 2-32, 2-37, and
2-68, the unskilled workers having on the average rather less than
twice the number of children found in class I. The greatest contrasts
are between classes I and II, with a difference 0-37, and classes IV
and V, with a difference 0-31, showing decided decreases in fertility
associated with the lower, as well as the higher, grades of ability.
Standardization with respect to age at marriage and duration of mar-
riage reduces the differences by about a third, thus showing that the
classes most fertile when married at any given age, also provide for
themselves by early marriage the greatest opportunity for fertility.
It also appears from the census report that the proportion married
is less in the professional classes than in the remainder of the popula-
tion. Consequently the disparity in reproduction receives contribu-
tions from three distinct sources. In the first place the upper classes
marry less, or remain celibate more frequently ; secondly they marry
later, and their wives during marriage are for a shorter time in the
reproductive period, and that in the later and less fertile portions of
that period ; thirdly, the number of children recorded is fewer, com-

REPRODUCTION IN RELATION TO SOCIAL CLASS 219
pared to the number of wives of any given age. The third cause is
probably of recent growth, and may principally be ascribed to the
deliberate limitation of births ; but it should be noted that this explana-
tion is not available for the important contribution of the first two
causes, which would tend to be diminished rather than increased by
the increasing use of contraception.

Dr. Stevenson attempts to trace the earlier history of the relative
fertility of different classes by comparing the average families, in the
different occupational groups, separately for marriages contracted in
successive decades, back to 1851-61, from which marriages a suffi-
cient number of husbands survived to the 1911 census. The occupa-
tional contrast in the fertilities of these early marriages is found to be
considerably reduced, and Dr. Stevenson suggests that, if the com-
parison could have been carried twenty years further back, a period
of substantial equality between all classes might have been met with.
The data from a single census, which is all that we possess, is, how-
ever, quite inadequate to supply the necessary information on this
subject ; for the marriages on which the census averages are based
are not a random sample of those which would have been recorded
at an earlier census, but a sample strictly selected on the basis of
longevity. In pedigree data of the middle class it is common to find
appreciable correlation between fertility and longevity, and the
validity of the earlier figures must be substantially affected from this
cause. The argument from convergence not only requires that the
occupational classification should be equally reliable for the oldest
groups, as for those still in employment, but that the effect, upon the
fertility of the survivors, of selection for longevity should be effec-
tively the same in all classes. From a series of comparable census
investigations some such extrapolation should be feasible, but since
the opportunity was lost in 1921, the class differences in reproduction,
before the general fall of the birth-rate set in about 1875, can now
scarcely be recovered. It is clear, however, from Heron's work, which
we have quoted above, that substantial differences existed between
the different London boroughs prior to 1851. While the period of
class equality is thus quite hypothetical, the increase in the disparity,
since the middle of the nineteenth century cannot reasonably be
doubted.

The general decline in the birth-rate since the seventies has
affected all classes, though somewhat unequally. The decline has

220 REPRODUCTION IN RELATION TO SOCIAL CLASS
been greater among the more prosperous, and less among the poorer,
classes. There seems to be no statistical justification for the assertion
that the decline has 'spread from above downwards', nor is this
inherently probable, since propaganda among the poorest classes has
been characteristic of the neo-Malthusian movement from its incep-
tion. The point is to be emphasized, since it appears to be somewhat
widely believed that the differential birth-rate, in so far as it is due
to deliberate family limitation, will automatically disappear, by the
simple process of the poorer classes adopting a practice more widely
prevalent among the more prosperous. The vital statistics of our
country give no ground whatever for this belief .

Position in the U.S.A.

The American data on the connexion between reproduction and
social class resemble that for Great Britain, in displaying the main
lines of the phenomenon with unmistakable clarity, without supply-
ing any means of entering into quantitative detail. The official
method is to ascertain the number of children of the parents at the
registration of a new birth, a method which is not at all comparable
with the size of family recorded hi a census. The average families,
however, of mothers in the age group 35-44, should supply figures
which are comparable from class to class, and, as in the case of the
Scottish census, the occupational classes may be noted which have
high or low averages. The following occupational lists are taken from
Whitney and Huntingdon's Builders of America, in which work the
averages have been reduced by one-third hi order to obtain estimates
of the average numbers of children born in completed families. This
adjustment of course does not affect the order of the occupations.
The year referred to by Whitney and Huntingdon is uncertain, but
closely parallel results, with slightly lower fertility, are shown by the
Bureau of Census report for 1925.

In the group with high fertility we have nine occupations with an
estimated average family of 4-8. These are coal-miners ; other miners ;
farm labourers; farmers; building labourers; railway labourers;
railway construction foremen ; metal moulders ; and factory labourers,
in order of decreasing fertility.

In the group with low fertility we have eleven occupations, with
an estimated average family of 2-6. These, in order of increasing
fertility, are, physicians ; technical engineers ; lawyers ; book-keepers ;

REPRODUCTION IN RELATION TO SOCIAL CLASS 221
bankers ; teachers ; agents and canvassers ; factory officials ; insurance
agents ; clerks in offices, &c. ; real-estate agents.

The group of low fertility comprises all the professional occupations
except that of clergymen, who come in the next group, while the
group with high fertility contains all classes of labourers, together
with only three other groups, among which the rural occupation of
farmers is conspicuous, in the same way as we have also seen in the
French figures. On the whole the American figures show a somewhat
wider range of variation than do those quoted from Scotland; for
example the coal, shale and ironstone miners in Scotland show 77 per
cent, more children than do the physicians and surgeons, whereas in
America the miners exceed the physicians by 119 per cent. The use
of data from birth registration would be expected rather to diminish
than to increase the ratio, but the difference may perhaps be ac-
counted for by two other circumstances, first that the age at marriage
has been partially standardized in the Scottish figures, and secondly
that the American data from birth registration refer to a much more
recent date than the nearly completed families of the 1911 census in
Scotland. It is not, therefore, certain that the differential incidence
of the birth-rate in the United States is, absolutely, greater than that
found in Great Britain, though it would be difficult to argue that it
could be appreciably less.

Effects of differential fertility

The facts revealed by the vital statistics of the present century, with
respect to the distribution of fertility, are in such startling opposition
to the rational anticipations of the earlier sociologists, that it will not
be out of place to conclude this chapter with a few reflections upon
the sociological consequences, which the observed distribution of the
birth-rate, whatever may be its causes, inevitably carries with it.

(i) In the first place the language of evolutionary writers has
endowed the word ' success ' with a biological meaning, by bestowing
it upon those individuals or societies, who, by their superior capacity
for survival and reproduction, are progressively replacing their com-
petitors as living inhabitants of the earth. It is this meaning that is
conveyed by the expression 'success in the struggle for existence ' and
this, it will probably be conceded, is the true nature of biological
success. To social man, however, success in human endeavour is
inseparable from the maintenance or attainment of social status;

222 REPRODUCTION IN RELATION TO SOCIAL CLASS
wherever, then, the socially lower occupations are the more fertile,
we must face the paradox that the biologically successful members
of our society are to be found principally among its social failures,
and equally that classes of persons who are prosperous and socially
successful are, on the whole, the biological failures, the unfit of the
struggle for existence, doomed more or less speedily, according to
their social distinction, to be eradicated from the human stock. The
struggle for existence is, within such societies, the inverse of the
struggle for property and power. The evolutionary task to which the
forces of selection are harnessed is to produce a type of man so
equipped in his instincts and faculties, that he will run the least risk
of attaining distinction, through qualities which are admired, or are
of service to society, or even of attaining such modest prosperity
and stability of useful employment as would place him in the middle
ranks of self-supporting citizens. In societies so constituted, we have
evidence of the absolute failure of the economic system to reconcile
the practice of individual reproduction with the permanent existence
of a population fit, by their mutual services, for existence in society,
(ii) The existing evidence indicates that this curious inversion
exists throughout the civilized nations of the modern world. Of the
eastern civilizations of India and China we are, unfortunately, not in
a position to produce satisfactory statistical evidence. In the absence
of European administration, the tremendous mortality among the
poorest class in these countries occasioned by war, pestilence, and
famine, must constitute a factor of great importance, and one that
might arrest the progress of racial deterioration, though at a some-
what low level, if the conditions were otherwise similar to those
observed in the West. The prolonged phase of stagnation and lack of
enterprise, from which both these peoples suffered before the impact
of European ideas, is at least suggestive of an equilibrium produced
by these means. Among ancient civilizations the testimony of Greek
and Latin writers is, moreover, unanimous and convincing, in declar-
ing that a similar inversion was vividly evident during the period
when the arts and social organization were most highly developed.
We may remember that the Latin word Proletarii for the class of citizens
without capital property meant in effect 'The beggars who have
children', and that numerous, though perhaps ineffective laws, of the
early Empire, were designed to encourage parentage among the
higher classes.

REPRODUCTION IN RELATION TO SOCIAL CLASS 223
(iii) The causes which tend to induce the inversion of the birth-
rate must be deferred to the next chapter, but we may now note that
these causes must have encountered and overcome great natural
obstacles. Owing to the burden of parentage, and to the inheritance
of wealth, its constant tendency is to make the rich richer and the
poor poorer. Such a tendency is not only to be deplored in the public
interest, as interfering with the distribution of wealth according to
the value of the services exchanged, and will therefore be resisted hi
some measure by legislation, but, what is far more important, it
will be resisted in the economic interests of private individuals, as
would be a tendency to tax the poor more heavily than the rich.
The total burden of rearing the next generation of citizens would be
more easily borne, if distributed more in accordance with the ability
to support it. Those who can afford most of comforts and luxuries
can assuredly afford to have the most children, and upon purely
economic grounds, removed from all biological considerations, the
large households of the rich might be reasonably expected to produce
and support more children than the small households of the poor. We
have moreover no a priori reason to assume that mankind is an
exception to the rule, which holds for other organisms, whether of
plants or animals, that an increased abundance of the necessities of
life is favourable to reproduction.

The indirect effect of the favourable conditions of the more pros-
perous classes should also be borne in mind. If the optimal level of
fertility of species in general is determined by the requirements of
parental care, it is a relevant fact that the superior classes have, and
have had in all ages, the power to delegate a large proportion of their
parental cares to others. The pressure of parental care is thereby
relieved, and the optimum level of fertility raised, as in the case of
the cuckoo. An obvious example is the provision of wet nurses for
the care of infants, a custom which must greatly increase the prospect
of an early conception by the mother. The physiological mechanism
by which this is brought about may be regarded as the means by
which the fertility is increased as soon as the natural burden of
parental care is removed, as it would be by the death of the infant.
The same principle applies to the cares required of parents in reducing
the incidence of all infant and child mortality, and it is obvious
that, in so far as these cares can be delegated to skilled professionals,
the biological optimum of fertility, in the privileged class, will be

224 REPRODUCTION IN RELATION TO SOCIAL CLASS
progressively raised. If such a privileged class were biologically iso-
lated, its innate fertility would therefore increase to a higher level than
that found in classes who had to care for their own children, and this
apart from the fact that, for the same level of innate fertility, the
more prosperous class should, in fact, be the more prolific.

In comparatively recent times efforts have been made on a national
scale to relieve the poverty of the poor, and make a reasonable pro-
vision for the education of their children, by direct taxation of the
higher incomes and the larger estates. An important factor, if not
the whole cause, of the need for this continual redistribution of
national wealth, evidently lies in the disparity with which the burden
of parenthood is distributed and hi its peculiarly heavy incidence
upon the poorest class. Enormous as is the expenditure incurred, and
important as may perhaps be its biological consequences, in relieving
the poorest class of much of the burden of parental care, and conse-
quently, though indirectly, increasing their fertility, it would be a
mistake to suppose that the burden of parental expenditure, in any
class of self-supporting citizens, is appreciably relieved. The support
of a normal family of three or four children entails in the greater part
of our industrial population, a period of the harshest poverty, con-
trasting violently in comfort, security, and the possibility of saving,
with the standard of living which a childless man can enjoy on the
same wage. The economic pressure of low wages, while unable to
control the actual incidence of parenthood, with which it is in con-
flict, is yet able to inflict extreme hardship upon the mothers of the
next generation ; and it is a feature of our social system which should
not be overlooked, that an unduly large proportion of each generation
is derived from homes which have experienced the severity of this
conflict. The inversion of the birth-rate is a fruitful mother of social
discontent.

(iv) Intimately bound up with the concentration of reproductive
activity in the poorer classes of citizens, is a consequence, which, at
first sight, has its beneficial aspect, namely that very extensive social
promotion must take place hi every generation, in order that the
numbers of the better paid classes may maintain a constant proportion
to those of the worse paid. Social promotion due to this cause must,
however, be distinguished from such normal promotion, due to in-
creasing age and experience, as will leave the children to start with
no greater social advantages than their parents, and also from that

REPRODUCTION IN RELATION TO SOCIAL CLASS 225
relative promotion of special merit or talent, which allows the more
gifted, whether greatly, or in only a slight degree, a proper opportun-
ity for the exercise of their special abilities. Promotion of these two
kinds should, of course, characterize any society wisely and generously
organized, whatever may be the distribution of reproduction within
it ; and in wishing prosperity to deserving merit we do not necessarily
desire the continuous replacement of whole classes by those of
humbler origin, unless such replacement can be shown to conduce to
general prosperity. The sympathy which we feel, too, for the efforts
of dutiful parents, to aid their children to good fortune, would be
misplaced if it led us to desire the existence of increased numbers of
children who require good fortune to attain a useful and prosperous
way of life, and a decrease of those children who might claim such
a life as their birthright.

If we take account of the natural consequences which flow from
promotion throughout the whole social scale, involving the transfer
of many millions in every generation, we shall find some which may
be desirable, and others which are certainly harmful. In any body
of people whose parents and grandparents occupied, on the average,
a distinctly humbler position than themselves, it is obvious that we
should not expect to find that pride of birth and ancestry, which is
characteristic of many uncivilized peoples. The conservative virtue,
which strives to live up to an honourable name, will be replaced by
the more progressive virtue, which strives to justify new claims. At
the worst pride of birth is replaced by pride of wealth, and popular
sentiment tends to grant the privileges of an aristocracy, rather to
the wealthy than to the well-born.

A second and less equivocal effect of wholesale social promotion
is the retardation of the cultural progress of every class of the com-
munity, by reason of the need to educate up to a higher level those
suffering from early disadvantages. The strain put by this factor
upon our educational system seems to be severe, and it doubtless
accounts, in large measure, for the slow progress of genuine culture,
and for the set-backs which it seems, here and there, to be receiving.
This consequence of social promotion would, of course, show itself,
whatever the hereditary aptitudes of the different classes might be.

The third and most serious disadvantage is that, whereas the
efficiency of the better paid classes may, in some measure, be main-
tained, by progressively perfecting the machinery for social promo-

226 REPRODUCTION IN RELATION TO SOCIAL CLASS
tion, in such a way as to make the best use of every grade of talent,
wherever it may be found, yet the worst-paid occupations have no
source from which they can recruit ability, and consequently suffer
a continual degradation in the average level of the talents they
possess. Without underestimating the value of the services, which
those promoted perform in their new spheres, it would be fatal to
ignore the extent to which the prosperity of any co-operative com-
munity rests upon the average efficiency of the great masses of citi-
zens, and, I should add, the extent to which its well-being rests on
the level 'at which their self-respect, enterprise and spirit can be
maintained.

Summary

The different occupations of man in society are distinguished eco-
nomically by the differences in the rewards which they procure.
Biologically they are of importance in insensibly controlling mate
selection, through the influences of prevailing opinion, mutual
interest, and the opportunities for social intercourse, which they
afford. Social classes thus become genetically differentiated, like
local varieties of a species, though the differentiation is determined,
not primarily by differences from class to class in selection, but by
the agencies controlling social promotion or demotion.

Comparisons between the vital statistics, and especially between
the birth-rates, of different classes, are generally defective and much
out of date. The principal need in our own country is to bring the
occupational classification, used in the registration of births and
deaths, into harmony with that used in the census, and to record the
ages of the parents in birth registration.

Numerous of investigations, hi which the matter is approached from
different points of view, have shown, in all civilized countries for
which the data are available, that the birth-rate is much higher in
the poorer than in the more prosperous classes, and that this dif-
ference has been increasing in recent generations. As more complete
data have become available, it has appeared that this difference is
not confined to aristocratic or highly educated families, but extends
to the bottom of the social scale, in the contrast between the semi-
skilled and the unskilled labourers. There is no direct evidence of a
period at which the birth-rate in all classes was equal, and the decline
in the birth-rate hi all classes in recent decades has been apparently
simultaneous, though greater hi the more prosperous classes.

REPRODUCTION IN RELATION TO SOCIAL CLASS 227

Since the birth-rate is the predominant factor in human survival in
society, success in the struggle for existence is, in societies with an
inverted birth-rate, the inverse of success hi human endeavour. The
type of man selected, as the ancestor of future generations, is he
whose probability is least of winning admiration, or rewards, for
useful services to the society to which he belongs.

If, as is still uncertain, a similar inversion has prevailed in the
Asiatic centres of civilization, the mortality suffered by the poorest
class must have tended to arrest the progress of racial deterioration,
and had perhaps produced an equilibrium before the impact of
European ideas. The condition of the Roman empire was certainly
similar to that observed in modern countries.

The causes, which have produced the inversion of the birth-rate,
must have been sufficiently powerful to counteract both direct and
indirect economic agencies, favouring a higher birth-rate among the
more prosperous. By its tendency to make the rich richer and the
poor poorer, and, especially, to inflict hardship upon the parents of
the next generation, the inversion of the birth-rate is an important
cause of social discontent.

A consequence which, at first sight, appears beneficial, is the very
large amount of social promotion which is required to maintain the
proportion of the classes. Upon examination it appears that this kind
of promotion should not be confused with increasing prosperity, and
that it carries with it the serious disabilities of the retardation of the
cultural progress of every class, and the uncompensated depletion of
the poorest class in the ability to maintain then- self-respect and
economic independence.

XI
THE SOCIAL SELECTION OF FERTILITY

History of the theory. Infertility in all classes, irrespective of its cause, gains social
promotion. Selection the predominant cause of the inverted birth-rate. The decay of
ruling classes. Contrast with barbarian societies. Heroism and the higher human
faculties. The place of social class in human evolution. Analogy of parasitism among
ants. Summary.

May it befall that an only begotten son maintain the ancestral home, for thus
tuealth is increased in a house. HESIOD, eighth century B.C.

History of the theory

WE have seen in the last chapter that among civilized peoples, both
in modern and ancient times, an anomalous condition has come into
existence, in which the more prosperous social classes, whom we
would naturally compare to the successful and well-adapted of an
animal species, reproduce their kind considerably more slowly than
the socially lower classes. In the ninth chapter we had seen reason
to conclude that the innate and heritable disposition has in civilized
man a powerful influence upon the rate of reproduction. It is now
proposed to show that a logical connexion exists between these two
conclusions. It is not denied that what may be called the accidents
of history have from time to time determined the social position of
various types of men, and have influenced the fertility of various
classes. The widespread nature of the phenomenon of the differential
birth-rate, existing in great bodies of people, in different nations, and
reappearing after long intervals of time in entirely different civiliza-
tions, is not, however, to be explained by historical accidents. No
explanation of it can be accepted, which does not flow from agencies
in almost universal operation, among civilized societies of the most
various types.

The theory to be here developed may be found in germ in an
interesting observation noted by Francis Galton in the course of his
genealogical researches; it has since been extended by several
writers, step by step with the advance of our knowledge of the
sociological phenomena, but neither its logical cogency, nor its im-
portance to sociological theory, seem to have been ever widely
grasped, and apart from a few ephemeral papers of my own, and a

THE SOCIAL SELECTION OF FERTILITY 229

brief discussion in Major Darwin's recent book The Need for Eugenic
Reform, it might be said to have been totally neglected.

In his book on Hereditary Genius, published in 1 869, Galton considers
the problem presented by the generally acknowledged fact that the
families of great men tend, with unusual frequency, to die out. Of
thirty-one peerages received by the judges of England, twelve were
already extinct. Galton examined the family history of these thirty-
one peerages, and lit upon an explanation which he rightly describes
as 'Simple, adequate and novel'. A considerable proportion of the
new peers and of their sons had married heiresses.

But my statistical lists showed, with unmistakable emphasis, that
these marriages are peculiarly unprolific. We might have expected that
an heiress, who is the sole issue of a marriage, would not be so fertile as
a woman who has many brothers and sisters. Comparative infertility
must be hereditary in the same way as other physical attributes and I
am assured that it is so in the case of domestic animals. Consequently
the issue of a peer's marriage with an heiress frequently fails and his
title is brought to an end.

After giving the individual histories of these families he arrived at
the following results.

(i) That out of 31 peerages there were no less than 17 in which the
hereditary influence of an heiress or coheiress affected the first or second
generation. That this influence was sensibly an agent producing sterility
in 16 out of these 17 peerages, and the influence was sometimes shown
in two, three or more cases in one peerage.

(ii) That the direct male lines in no less than 8 peerages (Galton gives
the names in full) were actually extinguished through the influence of
the heiresses, and that 6 others had very narrow escapes from extinction,
owing to the same cause. I literally have only one case, where the race
destroying influence of heiress blood was not felt.

(iii) That out of the 12 peerages that have failed in the direct male
line, no less than 8 failures are accounted for by heiress marriages.

Now what of the four that remain. Lords Somers and Thurlow both
died unmarried. Lord Alvanley had only two sons of whom one died
unmarried. There is only his case and that of the Earl of Mansfield, out
of the ten who married and whose titles have since become extinct,
where the extinction may not be accounted for by heiress marriages.
No one can therefore maintain, with any show of reason, that there are
grounds for imputing exceptional sterility to the race of judges. The
facts when carefully analysed, point very strongly in the opposite
direction.

230 THE SOCIAL SELECTION OF FERTILITY

After drawing similar conclusions from other groups of peers Galton

continues :

I tried the question from another side, by taking the marriages of
the last peers, and comparing the numbers of the children when the
mother was an heiress with those when she was not. I took precautions
to exclude from the latter all cases where the mother was a coheiress,
or the father an only son. Also since heiresses are not so very common,
I sometimes went back two or three generations for an instance of an
heiress marriage. In this way I took fifty cases of each. I give them
below, having first doubled the actual results, in order to turn them into
percentages.

TABLE 11.

Number of sons
to each marriage.

Number of cases
in which the mother
was an heiress.

Number of cases
in which the mother
was not an heiress.

0

22

2

1

16

10

2

22

14

3

22

34

4

10

20

5

6

8

6

2

8

7

0

4

I find that among the wives of peers 100 who are heiresses have 208
sons and 206 daughters, 100 who are not hen-esses have 336 sons and
284 daughters.

The following important paragraphs may also be quoted as showing
the weight which Galton attached to this principle.

Every advancement in dignity is a fresh inducement to the intro-
duction of another heiress into the family. Consequently, Dukes have
a greater impregnation of heiress blood than Earls, and Dukedoms might
be expected to be more frequently extinguished than Earldoms, and
Earldoms to be more apt to go than Baronies. Experience shows this
to be most decidedly the case. Sir Bernard Burke in his preface to the
Extinct Peerages states that all the English Dukedoms created from the
commencement of the reign of Charles II are gone, excepting 3 that are
merged in Royalty, and that only 11 Earldoms remain out of the many
created by the Normans, Plantagenets and Tudors.

It is with much satisfaction that I have traced and, I hope finally
disposed of, the cause why families are apt to become extinct in propor-
tion to their dignity — chiefly so, on account of my desire to show that
able races are not necessarily sterile, and secondly because it may put
an end to the wild and ludicrous hypotheses that are frequently started
to account for their extinction.

THE SOCIAL SELECTION OF FERTILITY 231

Alphonse de Candolle after noting these remarkable researches, and

properly distinguishing between the extinction of the family and that

of the male line, reasonably observes that similar conclusions must

apply to the rich and affluent classes hi general.

La difference de fecondite des heritieres et non heritieres anglaises
est si grande qu'elle avertit d'une cause, jusqu'a present inconnue, du
petit nombre des naissances dans les families aisees ou riches, de la
noblesse et de la bourgeoisie. En general, les filles riches se marient
aisement et selon toutes les probabilites physiologiques, confirmees par
les faits que Monsieur Galton a decouverts, ce sont elles qui ont la plus
petite chance de laisser des descendants. Leur proportion doit done
diminuer 1'augmentation de population des classes qui vivent dans
1'aisance.

Unfortunately M. de Candolle associates this rational explanation
of the relative infertility of the upper classes with others such as that
of Herbert Spencer, which evidently belong to the category to which
Galton had hoped to put an end. Nor is it quite clear that he grasped
the pouit of Galton's argument, which is not so much that heiresses can
marry more easily than other girls, but that they may more reason-
ably aim at a marriage which is socially advantageous, and so are
liable to mingle their tendencies to sterility with the natural abilities
of exceptionally able men.

In a brief but important note contributed in 1913 to the Eugenics
Review, J. A. Cobb has given reasons for believing that the case of
heiresses, observed by Galton, is but a particular instance of a far
more general tendency. Restricting himself to the unconscious causes
of relative infertility, Mr. Cobb points out that, just as the fortune of
an heiress enables her to make a socially advantageous marriage, so
among the children of parents of any class, members of the smaller
families will on the average commence life at a social advantage com-
pared to members of larger families. Alongside the many excellent
qualities which enable a family to improve its social position, relative
inf ertility also plays its part. In this way the less fertile stocks, having
the social advantage, will gradually permeate the upper classes of
society, and there cause the peculiar situation in which the more
fortunate and successful of mankind have the smallest birth-rate.

A quotation from Mr. Cobb's paper will enable the reader to
appreciate the point of view from which this important conclusion
was reached.

232 THE SOCIAL SELECTION OF FERTILITY

Eugenists agree that the rising generation is largely recruited from
the less fit. This is attributed partly to the fact that the upper classes
marry later and partly to the fact that apart from the question of post-
ponement of marriage the upper classes are less prolific than the lower.

There can be no doubt that at the present time the smaller fertility
of the upper classes is almost entirely due to artificial limitation, but
there is another cause of their smaller fertility, and it is to this that I
wish to direct attention. It is important for the Eugenist to know to
what cause he is to attribute this smaller fertility of the upper classes ;
if it is entirely due to artificial limitation, which is merely a temporary
fashion, the consequences are not likely to be very serious, since the
fashion for limiting the family is likely to take the usual course and
spread downwards in the community, eventually equalizing the fertility
in all ranks of society ; or the fashion may die out altogether when its
disastrous effect on the future of the race is perceived. It seems also
possible that the advantage of limiting the family will appeal more to
the poor than to the rich, for an additional child is a greater burden to
the poor, and perhaps eventually the artificial limitation of families will
have a beneficial effect on the race by reducing the size of the families
of the less efficient.

If, however, as I shall try to show, there is a natural tendency under
modern conditions for the more intelligent to become less fertile, the
problem is a more serious one.

If variations in fertility are inherited and the wealthier classes have
for generations been put through a process of selection by which mem-
bers of small families have been given an advantage over members of
large families, we should expect that the wealthier classes would, as a
whole, be less fertile than the poorer classes.

There must be some general cause which prevents the average in-
telligence in a civilized community from advancing beyond a certain
point. That cause seems to me to be the grading of society according
to a standard of wealth. This puts in the same class the children of
comparatively infertile parents and the men of ability, and their inter-
marriage has the result of uniting sterility and ability.

Infertility in all classes, irrespective of its cause, gains
social promotion

In the development of the theory by the three writers quoted, it is
evident that the progress made has consisted almost entirely in the
extension of the application of the principle to a wider and wider
range of social classes. This evidently followed merely from the
extension of OUT knowledge of the classes in which an inverted birth-
rate manifested itself. Galton was thinking principally of titled

THE SOCIAL SELECTION OF FERTILITY 233

families, because he was aware that among these the extinction of the
title took place with surprising frequency; De Candolle was aware
that a low birth-rate also characterized the rich bourgeois class, and
perceived immediately that the principle which Galton had dis-
covered, in the genealogies of titled families, must apply with equal
force wherever social position was greatly influenced by inherited
capital. It is probable that Cobb was not aware, in 1913, that the
results of the census in 1911, in Great Britain, showed that the inver-
sion was strongly developed, even in the poorest class ; but he evidently
has no hesitation in believing that it characterized the great mass of
the population, and his note has the great merit of applying the prin-
ciple to classes in which inherited wealth is relatively unimportant.
That the economic situation in all grades of modern societies is
such as favours the social promotion of the less fertile is clear, from
a number of familiar considerations. In the wealthiest class, the
inherited property is for the most part divided among the natural
heirs, and the wealth of the child is inversely proportioned to the
number of the family to which he belongs. In the middle class the
effect of the direct inheritance of wealth is also important ; but the
anxiety of the parent of a large family is increased by the expense of
a first-class education, besides that of professional training, and by
the need for capital in entering the professions to the best advantage.
At a lower economic level social status depends less upon actually
inherited capital than upon expenditure on housing, education,
amusements, and dress ; while the savings of the poor are depleted or
exhausted, and their prospects of economic progress often crippled,
by the necessity of sufficient food and clothing for their children.
These obvious facts are corroborated by the arguments upon which
the limitation of families is advocated ; of these by far the most weighty
is the parent's duty of giving to his children the best possible start in
life, and the consequent necessity both of savings, and of expendi-
ture— an argument at least as forcible for the poor as for the rich.

Selection the predominant cause of the inverted birth-rate

It has been shown in Chapter IX that not merely physiological
infertility, but also the causes of low reproduction dependent upon
voluntary choice, such as celibacy, postponement of marriage, and
birth limitation by married couples, are also strongly influenced by
hereditary factors. The inclusion of the hereditary elements respon-

3653 H h

234 THE SOCIAL SELECTION OF FERTILITY

sible for these, to which are certainly due the greater part of the
variance in reproduction among civilized men, multiplies many -fold
the efficacy of the selective principle at work. We have seen in
particular that hereditary differences in the mental and moral quali-
ties affecting reproduction, must be of such a magnitude as to produce
considerable evolutionary changes, in the course of relatively short
historical periods, and that such changes have in fact taken place in
the moral temperament of peoples known to have been exposed to
the selective action of voluntary family limitation. Consequently it
is impossible to avoid the conclusion that, in a society in which
members of small families are on the average at a social advantage
compared to members of large families, the parents being in other
respects equivalent, society will become graded, not only in respect
of physiological infertility, but much more rapidly and more steeply
graded in respect of those temperamental differences which conduce
to celibacy, postponement of marriage and birth limitation.

This inclusive character of the theory when fully developed serves
to explain a characteristic of differential reproduction, which would
otherwise be quite unintelligible, namely that all the sociological
factors into which differential reproduction can be analysed, alike
exert their influence in the same direction. If any single sociological
cause favoured contraceptive practices in the upper classes, as, for
example, freer access to medical knowledge might be supposed to do,
the effect to be expected would be a lower birth-rate to parents of
a given age, partially compensated in the statistical aggregate by
greater readiness to marry. Equally, if something inherent in the
occupational conditions of the better-paid classes were supposed to
induce more frequent postponement of marriage, this cause, acting
alone, would be naturally accompanied by an increased birth-rate of
those married in the higher age groups. What is actually observed,
however, is the concurrence in the more prosperous classes, of in-
creased celibacy, of higher age at marriage, and of a lower birth-rate
of married persons of a given age ; and this we should expect if the
effective cause of the phenomenon were the selective promotion into
higher social strata of net infertility as such, irrespective of the
psychological causes which have induced it.

It is possible to test in another way whether hereditary influences
supply a major and controlling cause of the differential birth-rate, or
a minor and subsidiary one. Even in Galton's time many causes had

THE SOCIAL SELECTION OF FERTILITY 235

been suggested for the portion of the phenomenon then known,
ascribing the differences in fertility to differences in social environ-
ment, or to some assumed physiological connexion between infertility
and the powers of the mind. Since then the list of suggestions has
increased: they may be exemplified by, excess of food, which the
upper social classes are presumably supposed to consume ; excess of
leisure ; the stress of brainwork ; the enervating influence of comfort.
However baseless the supposed causes may appear to be when each
is examined in detail, it is certainly possible a priori, that there might
be some subtle influence, of the social environment of the more
prosperous classes, really unfavourable to reproduction. The sharpest
possible test between the two views would be to ascertain the relative
fertilities, among men of a given social class, of those who had risen
rapidly in the social scale as opposed to those who were born in that
class. For, on the theory that we have to do principally with heritable
factors affecting fertility, the fertility of the upper social classes must
be prevented from rising by the lower fertility of those whom social
promotion brings into their ranks ; the stream of demotion of the
more fertile members of the upper classes being relatively a very feeble
one. Consequently, the groups enjoying rapid social promotion should,
on this theory be even less fertile than the classes to which they rise.
If, on the contrary, the important causes were any of those to be
included under 'social environment', we should confidently expect
the families who rise in the social scale to carry with them some
measure of the fertility of the classes from which they originated.
We have seen that the differential birth-rate is strongly developed
in the United States, and a test is therefore afforded by a table given
by Huntington and Whitney of the average number of children per
person in the American Who 's Who, when the persons are subdivided
according to the education they received. They are given in descend-
ing order.

TABLE 12.

Estimated children per

Kind of education. person.

College and Professional 2-4

College and Ph.D. 2-3

CoUege 2-3

Normal, Business, Trade, Secretarial 2-3

Highschool 2-1

Elementary schools and home 2-1

Professional school only 1-9

236 THE SOCIAL SELECTION OF FERTILITY

As the total number of persons dealt with is about 25,000 the trend
of these averages cannot possibly be ascribed to chance ; the table
appears to show unmistakably, that among Americans who attain
a sufficient level of eminence to be included in Who's Who, those
whose social promotion has been most striking have, on the average,
fewer children than those whose social promotion has been less. Such
a result would appear inexplicable on any of the views that connect
the differential fertility of different classes with elements in their
social environment, and is a striking confirmation of one of the most
unexpected consequences of the theory that the dominating cause lies
in the social promotion of the relatively infertile.

Whitney and Huntington give also the results of another inquiry
which bear upon the same problem. They have studied the average
abilities shown by Yale students coming from families of 1, 2, 3 and
up to 6 or more. They find, in general, that the average ability rises
as we pass from families of one, to families of two, and so on up to
the largest families. This, of course, is not at all what we should
expect to find, either in England or America, if we were to test
the sons of the population at large. In the population generally, the
classes which furnish the largest families would certainly show the
lowest average scores, whether we took a scholastic, an athletic or an
intelligence test. The Yale students, however, are the sons of a
selected group of the population, of persons who can afford to give
their children an expensive education. This basis of selection favours
the more prosperous parents, who, in so far as their prosperity is due
to innate causes, will be innately abler than the general population ;
but this selection of parental prosperity will be much more stringent
for the parents of six or more children than for the parents of one
only. Remembering that the only child may be expected to have a
better start in life ceteris paribus than the member of a family of six,
we may perhaps expect to find at Yale the only children of less suc-
cessful parents educated at equal expense and side by side with the
children of the more stringently selected parents, who are able, with
families of six or more, still to send them to Yale.

It is in fact a necessary consequence of our theory of the social
selection of fertility, that, whereas in the population at large fertility
must become negatively correlated with such characters as intelli-
gence, which conduce to social promotion, yet, if we could select a
group of children about to enter the world with absolutely equal

THE SOCIAL SELECTION OF FERTILITY 237

social opportunities we should find, within this group, fertility
positively correlated with these characters. For parents who can give
to a large family a certain level of educational advantage, could
certainly have launched a smaller family with greater advantages,
and must therefore possess a higher average level of qualities, apart
from fertility, favourable to social promotion, than do the parents
of smaller families whose children are actually receiving the same
advantages.

I believe no investigation has aimed at obtaining a group in which
the educational advantages provided by the parents are completely
equalized, but the effect of a partial equalization, in raising the cor-
relation between fertility and intelligence, is shown by some interest-
ing data published by H. E. G. Sutherland and Godfrey H. Thomson
in 1926. In an unselected group of 1924 elementary school children
of the Isle of Wight, between the ages of 10| and 11^ years a correla-
tion coefficient,- 0-154, with a probable error 0-023, was obtained.
Since the correlation is negative and clearly significant, it appears
that, with this unselected group the least intelligent children belong
to the largest families. On the other hand 386 boys of the Royal
Grammar School, Newcastle-on-Tyne, the intelligence quotients of
which are stated to be very reliable, and 395 boys and girls of Moray
House School, Edinburgh, show correlations - 0-058 + 0-04, and - 0-075
+ 0-034 both of which, though still negative, are insignificant in
magnitude. Since within the same school, even if of very definite
class, much variation must exist in the social advantages with which
different pupils enter life, these data leave little doubt that in a
group in which these advantages were strictly equalized the correla-
tion between fertility and intelligence would have been raised to a
positive value. It is obvious that such results are opposed to any
theory which implies a physiological opposition between fertility and
intelligence, and are unintelligible upon the view that class differences
of fertility are derived wholly or indeed largely from class environ- V/^

ment. c<%

•3?

The decay of ruling classes

The fact of the decline of past civilizations is the most patent in
history, and since brilliant periods have frequently been inaugurated,
in the great centres of civilization, by the invasion of alien rulers, it is
recognized that the immediate cause of decay must be the degenera-

238 THE SOCIAL SELECTION OF FERTILITY

tion or depletion of the ruling class. Many speculative theories have
been put forward in explanation of the remarkable impermanence of
such classes. Before proceeding further it may be as well to consider
what elements of truth these suggestions may contain.

The Comte de Gobineau, to whose active mind the decline of
civilizations presented itself as the greatest of human problems,
believed that the disappearance of the original aristocracies was
universally due to race mixture. Others have not hesitated to ascribe
the infertility of the upper classes to inbreeding ; but since this view
is now, on the biological side, universally discredited, it need not
be further considered. There was, on the other hand, nothing in
Gobineau's theory of the effects of race mixture which could have
been disproved by the science of his time ; if the progress of genetical
knowledge has rendered his views unlikely they would still have
claims to acceptance on an historical basis, were they the only avail-
able explanation of the historical facts.

The general consequences of race mixture can be predicted with
confidence, without particular knowledge of the factors in which the
contrasted races differ. If the races and their descendants intermarry
freely, the factors which are inherited independently will be recom-
bined at random ; each person of mixed race will resemble the one
parental stock in respect of some factors, and the other stock in
respect of others. Their general character will therefore be interme-
diate, but their variability will be greater than that of the original
races. Moreover, new combinations of virtue and ability, and of their
opposites, will appear in the mixed race, combinations which are not
necessarily heterozygous, but may be fixed as permanent racial
characters. There are thus in the mixed race great possibilities for the
action of selection. If selection is beneficent, and the better types
leave the greater number of descendants, the ultimate effect of mix-
ture will be the production of a race, not inferior to either of those
from which it sprang, but rather superior to both, in so far as the
advantages of both can be combined. Unfavourable selection, on the
other hand, will be more rapidly disastrous to a mixed race than to
its progenitors. It should of course be remembered that all existing
races show very great variability in respect of hereditary factors, so
that selections of the intensity to which mankind is exposed would
be capable of producing rapid changes, even in the purest existing
race.

THE SOCIAL SELECTION OF FERTILITY 239

It does not seem unreasonable to conjecture that within each of
the great divisions of mankind, internal adaptations or adjustments,
between the different faculties of the mind and body, have been
established during the long ages of selection under which these races
were originally formed. If this were true, the crossing of widely
different races would disturb this internal harmony and put the
mixed race at an initial disadvantage, from which, even under favour-
able selection, it might take several generations to recover. The
theory of Gobineau depends upon the effect of intermixture of a
ruling aristocracy, which Gobineau invariably traces to the European
stock, to whose merits he ascribes the progress and stability of all
civilizations, with a mixed and coloured people inhabiting one of the
great and ancient centres of population, such as China proper, or the
valleys of the Ganges, the Euphrates or the Nile. Apart from his
assumption of the racial origin of the rulers, the historical importance
of such cases cannot be doubted ; and it is in all respects probable
that, as intermixture progressed, the ruling class, in the absence of
selection, would entirely change its character ; the qualities by which
it had been distinguished would be diffused among those of the more
numerous race, and in the absence of native ability, could no longer
achieve the great results, for which, concentrated in a ruling class,
they were originally responsible. Nevertheless, granting that the
process of racial diffusion sets a certain term to any civilization which
depends upon the virtues of an alien minority, it remains to be
explained why great civilizations should be assumed always to rest
upon so precarious a foundation. If the peoples of the world's great
centres of ancient population are inherently incapable of producing
of themselves a great and vigorous civilization, an explanation of so
remarkable a fact is certainly required. We cannot reasonably be
satisfied by accepting it as an accident, that the great civilizing races
should have originally occupied only those regions of the earth,
where civilization was for so long unknown.

It has been suggested that the disappearance of ruling races of
foreign origin in ancient civilizations was due to the selective influence
of the climate. This theory stands in the same position as that of
race mixture, in respect of the main criticism to which the latter is
exposed. It does not explain why the foreign element should be
necessary. Apart from this it certainly appears to be a real factor
in the situation. Races exposed to a new climate, and to unfamiliar

240 THE SOCIAL SELECTION OF FERTILITY

diseases, are certainly in some cases at a disadvantage as regards their
death-rate, and probably also as regards their birth-rate. As are the
negroes in centres of population infected with tuberculosis, or Euro-
peans in regions suffering from uncontrolled malaria.

In one respect the theory of selection by climate and disease ap-
pears to possess an advantage over that of race mixture. If the latter
were the only agency at work, the disappearance of the ruling class
would be accompanied by a permanent improvement of the natives.
The effect of successive conquests should accumulate; so that we
should expect that a people, such as the Egyptians, should be
reasonably far advanced towards the type of a ruling race. The
reverse appears to be the case. The effect of the selective influence
of climate and disease, on the other hand, would appear to undo
completely the racial benefits of an invasion. Further consideration
shows that both agencies acting together would lead to an inter-
mediate result, for in the distribution of the hereditary factors,
immunity to local diseases would often be combined with the qualities
of the immigrants. This consideration suggests that unless selection
is directed against the qualities of the ruling race as such, some
permanent improvement of the native population is a necessary
consequence. On the other hand beneficial selection combined with
race mixture would lead to the formation of a race combining the
condition of acclimatization with the valuable qualities of the in-
vaders. It would seem then, from the history of ancient civilizations
in the East, that the rate of reproduction has never permanently
favoured the ruling classes. If we consider further that, in any
ordered society, the burden of maintaining the population is likely
to fall upon the parents, and that the possession of wealth is likely
sooner or later to be of social advantage, it is possible to offer a
rational explanation, not only of the disappearance of ruling classes
of foreign origin, but of the paucity of the necessary types of ability
from the indigenous population. It would seem not improbable on
this view that in its origin civilization was indigenous, favoured by
the natural causes which admit of a dense population ; that the most
capable elements of this primitive civilization formed themselves
sooner or later into the upper classes, that they were slowly imbued
with those factors of heritable disposition which make for a reduced
prolificacy ; and that with the consequent development of wholesale
social promotion, they were, by a rapidly increasing process, elimi-

THE SOCIAL SELECTION OF FERTILITY 241

nated from the race. Their territory, dowered with immense natural
resources, and destitute of a vigorous and united government,
became the natural prey of a succession of invaders. Once it is
apparent that natural causes sufficiently explain the attenuation of
the original rulers, the disappearance of aristocracies of foreign origin
raises no new problem. The same agencies which destroyed the
founders of a civilization are capable of destroying their successors ;
the more easily if the unfavourable action of selection were furthered
by race mixture and the influence of climate.

The belief that the mere existence of civilized conditions causes
degeneracy among the races which experience them, has been held
by many writers, and is strongly supported by the instances of bar-
barous territories which have received the civilization, and shared
the decay, of some more advanced state. The people of Roman Gaul
and Britain, originally hardy and warlike, were, during the decay of
Roman power, scarcely more capable of supporting and safeguarding
their civilization, than were the Romans; they fell a natural prey
to inferior numbers of warlike barbarians, without suffering from a
foreign climate, or from intermixture with an inferior race.

No explanation of the manner in which civilization produces this
deleterious effect, by reference to the inheritance of acquired charac-
ters, can now be regarded as satisfactory ; and in any case it must be
doubted if the characters acquired in a state of civilization, which
include habits of industry and discipline, in addition to the training
of the intellectual faculties, can be regarded as unfitting a people to
hold its own. It is said that luxury saps the vigour, and dependence
the initiative of civilized peoples, and even if this were the unquali-
fied truth as to the effect upon the individual of civilized life, the
first generation of misfortune should restore the vigour, and give
unexampled opportunities to the initiative, of a threatened people.

We know that the tide of social promotion throughout the Roman
dominion must have flowed rapidly. The demand for men for the
Imperial services extended freely to provincials, and in the commer-
cial and industrial development of the provinces a large scope was
given to the initiative of all, even in then* home towns. The upper
classes, and especially the wealthier of these, were certainly drawn
into the vortex of a cosmopolitan society, recruiting itself extensively
from the lower orders. Gauls were admitted to the Senate as early as
the reign of Claudius, who first occupied Britain. With these facts

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II

242 THE SOCIAL SELECTION OF FERTILITY

in mind it is not surprising that after several hundred years absorp-
tion in the Roman civilization, Britain and Gaul showed scarcely
greater capacity for resistance than the older provinces. For even
if the conquest of Britain was a matter of difficulty to the barbarians,
the very possibility of the overthrow of an organized Romano-
British society shows that very inadequate use must have been made
of the resources of the island.

Contrast with barbarian societies

It appears, then, that the social selection of infertility will charac-
terize all states of society in which (1) distinctions of social class
exist ; (2) wealth is influential in determining the social position of an
individual or his descendants; and (3) the economic charge of produc-
ing the next generation is borne exclusively or principally by the
parents who produce them, at least in the sense that they would have
been better off had they produced fewer. These conditions are of such
wide application that we can have no hesitation in postulating them
in all societies, ancient or modern, consisting of individuals co-operat-
ing for mutual advantage in a state of law and order. The essentially
dysgenic features of the situation may, however, be expressed more
aptly by saying that they are implied by the existence of a dif-
ferentiation of social class in which social promotion, or demotion, is
determined by the combination of two different attributes (1) socially
valuable qualities, and (2) infertility. It is thus not quite exact to
say that the selective agency considered must be dysgenic in any
society graded according to wealth; this would imply too wide an
application of the principle, for gradations of wealth in the form of
the control of material property, and authority over the services of
others, would seem to be inseparable from any organization of society
whatever.

There have certainly existed societies, though not properly speak-
ing civilized societies, in which the institution of social class was
highly developed, in which the power and prestige of the individual
rested largely upon his pedigree and kinship, in which these class
distinctions were doubtless correlated with personal wealth, and in
which, nevertheless, the social advantage lay with the larger families.
Since in such societies we should infer from the principle of the
inheritance of fertility, and the absence of any countervailing causes,
that the fertility of the socially superior should be the higher, and

THE SOCIAL SELECTION OF FERTILITY 243

consequently that the powerful evolutionary force, which such dif-
ference of fertility has been shown to exert, will be directed towards
the increase of the qualities favourable to success hi these societies,
and to the qualities admired in them, their importance for the study
of our theory, and for the evolutionary history of mankind, is very
great.

The state of society with which we are here concerned, which may
be exemplified by the primitive peoples of Northern Europe, as
represented in the Icelandic Sagas, in Tacitus' description of the
Germans, and probably in the Homeric poems, by the pre-Islamic
Bedouin of the Arabian desert, by many, if not all, of the Turkish and
Tartar peoples of the Central Asiatic steppes, and by the Polynesians
of New Zealand and Samoa, is characterized by a tribal organization,
influenced, or indeed dominated, by the blood feud. All these show
a strong feeling for aristocratic or class distinction, and this character,
as well as the blood feud, seems to be rather rare among uncivilized
peoples generally. For this reason it is convenient to designate this
particular type of society by a special term, which shall contrast
them with civilized, and distinguish them from the other uncivilized
peoples. We may conveniently call them barbarians. This term
is the more appropriate in that the examples given, few as they are,
include the most important groups of peoples, who have, in the
course of history, overrun the great centres of relatively permanent
civilization, and to whom the existing organization of society can be
traced back in historical continuity.

Different civilized nations, although potentially at war with one
another, may yet show essentially the same ideas, and an equivalent
development of material civilization. The cultural unity of different
barbarian tribes is usually much closer, for they are bound together
by common language, and a common oral literature, intermarry much
more frequently than can the large aggregates which constitute
civilized nations, and frequent the same fairs and festivals for trade,
religion or recreation. It is necessary to emphasize this unity of
culture because, unlike civilized societies having comparable unity,
barbarian peoples recognize private, or more properly tribal war as
a normal means for avenging and checking crime. The obligation to
avenge a kinsman was felt extremely keenly as a moral duty, to
shirk which would be incompatible with self-respect or an easy con-
science, or, in Wilfred Blunt 's forcible phrase as 'almost a physical

244 THE SOCIAL SELECTION OF FERTILITY

necessity'. The existence of this obligation requires that the
tribes of kinsmen to which it applies shall be somewhat sharply
defined, and with this obligation follows, of course, the obligation to
pay, and the right to share, blood money, or to share in booty. A
certain degree of economic communism thus characterizes these
kindred groups, so that there is little exaggeration in saying that the
economic and the military units in such societies are made to coincide.
This is at least a convenient form in which to express the contrast
with all civilized societies, in which the interests of the economic unit,
consisting of a single individual and his dependents, may differ
widely from those of the military unit, consisting of the entire nation
to which he belongs. The interests of the kindred group as a whole,
whose rights to life and property can only be safeguarded by military
preparedness, are of course, in the first degree, founded upon military
strength, and consequently, among other qualities, upon the fertility
of its members.

Social position in barbarian societies consists partly in differences
in kind, partly in differences in degree. A powerful group comprises
not only the body of free tribesmen of authentic, or noble, pedigree,
but also dependent freemen harboured by the tribe, who may have
been outlawed from their own tribes, or be the remnants of tribes too
weak to stand by themselves ; further there may be unfree depen-
dents, whose position only differs from that of the slaves of civilized
societies, in lacking the protection of civil law, and, on the other
hand, in differing but little from their masters in education or standard
of living. It is important here that differences in social standing are
at least as strongly felt among barbarian peoples, as in civilization,
and that it is there based not so much on occupation, as on personal
and family prestige. Such differences in prestige are not, however,
confined to social distinctions within the tribe, but extend to great
differences in the repute and distinction of different kindred groups,
according to their exploits and power.

It will be admitted, therefore, that in such barbaric societies as we
have described, well-defined class distinctions are combined with a
distinct social advantage of the more prolific stocks. Nor can we
doubt on independent evidence that the families of the highest repute
were in fact the most prolific. The high importance given to pedigree,
and the care taken to preserve the names, even of a remote ancestry,
is evidence of this; for such care would not generally be taken to

THE SOCIAL SELECTION OF FERTILITY 245

preserve the memory of ancestors, if these were on the average less
distinguished than their descendants. We can thus understand one
of the factors which enables such peoples to base their social system
upon blood relationship. This evidence indicates, moreover, not only
a higher birth-rate but a greater natural increase, when the death-
rate also is taken into account. It may well be suspected that the
most eminent families suffered in war the highest death-rate, but in
the severe losses which barbarian peoples suffer in times of dearth or
enforced migration, the more powerful groups would certainly be at
a substantial advantage ; and if, as we have seen, selection would tend
to increase their innate fertility above that of the less distinguished
groups, it is not surprising that we should be led to conclude that
society was derived generation after generation, predominantly from
its more successful members.

The most important consequence of this conclusion is that human
evolution, at least in certain very ancient states of society, has
proceeded by an agency much more powerful than the direct selec-
tion of individuals, namely the social promotion of fertility into the
superior social strata. In particular, it is important that the quali-
ties recognized by man as socially valuable, should have been the
objective of such a selective agency, for it has hitherto only been
possible to ascribe their evolutionary development to the selection of
whole organized groups, comparable to the hives of the social insects.
The selection of whole groups is, however, a much slower process
than the selection of individuals, and in view of the length of the
generation in man the evolution of his higher mental faculties, and
especially of the self-sacrificing element in his moral nature, would
seem to require the action of group selection over an immense
period. Among the higher human faculties must moreover be counted
the power of aesthetic appreciation of, or emotional response to,
those qualities which we regard as the highest in human nature. It
will aid the reader to weigh the efficacy of the social advantage of
fertility in barbarous societies, if we analyse in more detail its re-
actions upon a single group of qualities typical of barbarian culture.

Heroism and the higher human faculties

The social ideas of all peoples known to us in the stage of emergence
from the barbaric condition are dominated by the conception of
heroism, and civilized peoples normally look back to so-called ' heroic

246 THE SOCIAL SELECTION OF FERTILITY

ages' in which this conception moulded to an important degree the
structure of society. The emotional influence of this idea has been
so great, especially through the poetic tradition, that it is difficult to
give a technically accurate characterization of the phenomenon
without using terms charged with rhetorical associations. The reader
must remember that we are not concerned to evaluate heroism either
through praise or disparagement, but merely to consider its nature
and implications as a sociological phenomenon.

The hero is one fitted constitutionally to encounter danger; he
therefore exercises a certain inevitable authority in hazardous enter-
prises, for men will only readily follow one who gives them some hope
of success. Hazardous enterprises, however, are not a necessity save
for the men who, as enemies or leaders, make them so, and the high
esteem in which tradition surrounds certain forms of definite im-
prudence cannot be ascribed to any just appreciation of the chances
of success. In modern times it is obvious that a man with any
immoderate heritage of this quality has an increased probability of
perishing young in some possibly useful border expedition, besides
an increased probability of entering an occupation not easily to be
reconciled with family life. It is undeniable that current social
selection is unfavourable to heroism, at least in that degree which
finds it sweet as well as proper to give one's life for his country. Any
great war will reveal, I believe, a great fund of latent heroism in the
body of almost any people, though any great war must sensibly
diminish this fund. No one will, however, doubt that in respect of
prudence, long civilized peoples do differ materially from those races
in which the highest personal ambition of almost every man was to
win renown through heroic achievement.

An examination of the action of selection in barbarous societies in
the tribal condition, reveals the possibility of the selection of the
heroic qualities beyond the limits set by prudence, by a method
analogous to that used in Chapter VII to explain the evolution of
distasteful qualities hi insect larvae. The mere fact that the prosperity
of the group is at stake makes the sacrifice of individual lives occa-
sionally advantageous, though this, I believe, is a minor considera-
tion compared with the enormous advantage conferred by the prestige
of the hero upon all his kinsmen. The material advantage of such
prestige in barbarous society will, I think, scarcely be questioned ; it
is evident in all the heroic literature ; it is directly evidenced by the

THE SOCIAL SELECTION OF FERTILITY 247

deliberate vaunting of tribal achievements by professional poets;
equally convincing is the great importance attached to genealogy in
all such societies, by which the living boast their descent from the
mighty dead. The positive aim before the hero is undying fame, he is
therefore bound to all that is of good repute ; to the heroic spirit all
material achievements are of lesser importance. Equally important
with the phenomenon of heroism itself is the esteem in which it is held.

It is inevitable in a tribal state of society that certain stocks should
distinguish themselves above others in the heroic qualities. If we may
assume that such qualities do in fact benefit their tribesmen, which
benefit can be most readily understood through the effects of prestige,
then in a tribal society heroism may become a predominant quality.
In this matter sexual selection seems in man to have played a most
important role. I do not here specially stress the evidence of the
poetic tradition, which, in spite of the reputation of poets for effemi-
nacy, insists on associating heroism with true love. I should rather
rely on the actual marriage customs of barbarous peoples. It should
be emphasized that in such marriages the political element is more
in evidence than the romantic, without their being the less dominated
by the emotional reactions. A marriage is likely to involve blood feud
obligations ; union with a powerful kindred is an essential asset. The
corporate tribe is interested in the match, and sexual selection is
most powerfully exerted by tribal opinion. The prestige of the con-
tracting parties is all-important, and while this is partly personal, it
also is largely tribal. The wooer relies upon his reputation even for
the decision of the lady herself. Both in the Icelandic sagas and in
the pre-Islamic poems, marriages are nearly always prompted by the
political aspirations of the parties.

Such sexual selection by public opinion must influence many other
qualities besides valour. Beauty, highmindedness and every other
highly esteemed quality must be thereby enhanced. Its importance
for us is that it influences the esteem in which the group of qualities
most closely associated with heroism are held. Just as the power of
discrimination of the female bird has been shown to be influenced by
sexual selection paripassu with the ornaments which she appreciates,
so in a barbarous society, in which the heroic qualities do possess an
intrinsic tribal advantage, the power to appreciate and the proneness
to admire such qualities will be enhanced, so long at least as reproduc-
tion is actually greatest in the predominant families. The reader who

248 THE SOCIAL SELECTION OF FERTILITY

will candidly compare the current attitude towards rash actions in
any long civilized society with that among the peoples under dis-
cussion, will scarcely doubt that the hero-worship of barbarous
peoples was in fact a mental attitude which, however useless to

x^x

modern man, played in their lives a very essential part. Changed
conditions which have reversed the advantage of the heroic qualities,
have also reversed the advantage of being able to recognize and
appreciate them. It is obvious that the barbarous element in the
tradition of our culture is that which emphasizes and indeed exag-
gerates, the natural inequality of man, whereas the religious and legal
elements emphasize his civil equality. From the fact that the bar-
barians valued more highly certain qualities of human character, it is
a fair inference that they perceived such differences more clearly than
do civilized men. Direct evidence on this point is necessarily elusive.
On questions on which we are better informed than our ancestors it
is easy for us to perceive the evidences of our advantage. If the
reverse were the case, it would be easier for our ancestors than for
ourselves to point out the difference. The only objective fact known
to me relevant to the present issue is that moderns with highly
trained powers of appreciation do find in the earliest examples of
extant poetry a certain elusive quality in the delineation of character,
which gives to such verse a recognizable supremacy in the particular
literature to which it belongs.

It is, of course, difficult to distinguish between non-percipience and
indifference to the distinctions perceived. The antipodes to the
spontaneous choice of emotional passion is exhibited in the account
given by Risley of the importance of a University degree in the
Bengalese marriage market. The successful candidate who emerges
with an M.A. becomes instantly, and hi virtue of this alien qualifica-
tion, a highly eligible match, and may collect in a few months a series
of endowered brides. It would be difficult to decide whether this
throwing upon the board of examiners the onus of grading the
candidates in sexual selection is due to those personal differences,
which still to some extent influence European lovers, being but
faintly perceived, or, although perceived, to their being esteemed of
much less real importance than the University degree.

Among peoples with a considerable contribution of the barbarous
element in their social tradition the predominant non-personal factor
in mate selection is social class. Social class may, as we have seen, be

THE SOCIAL SELECTION OF FERTILITY 249

best defined as a synthesis of such distinctions as wealth, occupation,
and family as influence eligibility in marriage, taking account of
these distinctions only in so far as they do in fact influence such
eligibility. Historically this distinction of social class is continuous
with the political and romantic prestige of the predominant clans.
It is thus not an accident that the social ostentation of earlier days
should survive most conspicuously in weddings. The attenuation and
decay of the sentiment of class distinction is the necessary con-
comitant of the progressive elimination of those elements of the
population which enjoy the higher rank. It will be readily understood,
if the supposition is correct that among barbarian peoples the pre-
dominant class did in fact enjoy a selective advantage, that aristo-
cratic institutions should appear to peoples recently civilized to be
based on natural justice.

To summarize the points of sociological importance: (i) A bar-
barian people organized in kindred groups and recognizing the blood
feud as the principle of social cohesion, can scarcely fail to experience
a selection in favour of two qualities on which the success of the
kindred group principally depends (a) the public spirited, patriotic,
or heroic disposition (6) fertility, (ii) The stratification of society in
these two qualities implies a selective advantage of the heroic tem-
perament beyond the optimum advantage ascribable to prudent
boldness, by reason of the social advantage of fame or heroic reputa-
tion, (iii) The power of recognizing the heroic qualities, and of con-
scious choice in intermarriage, introduces the dual effect of sexual
selection in intensifying both the qualities selected and the communal
recognition and appreciation of such qualities, (iv) This selection of
the popular emotional response to the heroic qualities has the im-
portant effects of (a) stabilizing the foundations of the system by
strengthening the existing basis of social cohesion, (6) intensifying the
selective advantage ascribable to fame or prestige, (c) increasing the
selective advantage of all qualities consciously envisaged in sexual
selection, (d) exaggerating the realities of natural inequality by the
development of an extreme aristocratic doctrine of hereditary nobil-
ity. It is important to notice that such practices as polygamy or
servile concubinage are not in any sense primary principles of the
system of causes described, but may be grafted into the system in so
far as they harmonize with the prestige of the hero, or the fertility
of his class. Such practices necessarily decay or are transformed to

3653 K k

250 THE SOCIAL SELECTION OF FERTILITY

fulfil a secondary social purpose, such as domestic service, as soon as
the mahi conditions of the system are undermined.

The place of social class in human evolution

The combination of conditions which allows of the utilization of
differential fertility for the acceleration of evolutionary changes,
either progressive or destructive, seems to be peculiar to man. It
requires a social organism, and one which is individualistic in repro-
duction. Accessory factors of great importance are the elasticity of
effective fertility, introduced by infanticide and other methods of
family limitation, and the peculiarly heavy burden of parental care
occasioned by the extraordinary long childhood of the human race.
Up to a certain stage, which was almost certainly prehuman, the
ancestors of man were doubtless solitary animals, and until social life
began to be developed then* fertility must have been stabilized at or
near the optimum appropriate to the requirements of parental care.
It is to be presumed that infanticide came to be practised, in conse-
quence of an increasing foresight of impending hardships, at an
exceedingly remote period, perhaps early in man's history as a social
animal. During the immense period of early social life he appears to
have learnt to co-operate with his fellows, probably by sympathy
with their expressed emotions, instinctively to shun social oppro-
brium, and perhaps to improve his chances of posterity by mate
selection. The sentiment of preference, seems at least so essential to
the sexual instincts of man that it is difficult to doubt that sexual
selection was early established in mankind, though it may be that the
special conditions experienced by their barbarian ancestors prejudices
the opinion of civilized man in this matter. Apart from this factor,
the evolution of man hi the early social stages must have been directed
principally towards the establishment of the characteristics favouring
individual survival in the social environment.

At some stage, the period of which it would be useless to conjecture,
societies must have come into existence, in which some degree of
continuity of social class was ensured by the inheritance of property,
privilege, prestige or social function, and in which individual dif-
ferences hi the socially valuable qualities were strongly appreciated,
and allowed to contribute towards the assessment of social rank. If
these characteristics, perhaps in quite a rudimentary form, were
combined with a tribal organization of society, in which the rights of

THE SOCIAL SELECTION OF FERTILITY 251

each kindred group were established ultimately upon its military
power, so that the most fertile were mingled with the most admired
or eminent strains in the predominant clans, a profound change must
have come over the speed and direction of evolutionary progress in
such societies. The new force acted through, and by means of, man's
appreciation of human excellence in his fellow men. This appreciation,
both in the social selection, and in the sexual selection which formed
a part of it, was doubtless guided, from the first, by the interests of
the tribal group, or of society as a whole. Such a process provides the
means of relatively rapid evolutionary progress in qualities which
subordinate the individual interest to that of others, the evolution
of which, merely by the selective elimination of entire societies,
would seem to be extraordinarily slow. It has, however, all the
dangers noted in the case of sexual selection, of running into extrava-
gance ; for the standards of taste will necessarily be modified, step by
step, with the qualities to which preference is given, and it may,
indeed, be that some of the virtues which appeal most to our imagina-
tion are more of the nature of ornaments than of serviceable moral
ideals. Among the qualities which seem to have been extravagantly
developed among all barbarian peoples are personal and family
pride, and, but for the sharp lessons which must always be learnt in
a harsh environment, made harsher by mutual warfare, extravagances
of this kind might, it would seem, have become much more common
than they are in man's moral nature.

It would be of great interest, if it were possible, to compare the
rapidity of progress among barbarian peoples, with that of the decline
among the civilized. The variations available for evolutionary
changes of a destructive nature must be so much more abundant
than those available for progressive changes, that we might expect
selective intensities of the same order to take some hundreds, or
perhaps a thousand generations, to build up in their perfection
attributes of the mind, which ten generations of adverse selection
might demolish. It does not appear that there should be any great
difference in the selective intensities developed in the two cases, if
each were in a steady state. The effect of differences of fertility would
be increased in the barbarian condition, and diminished among
civilized man, by the direct action of prosperity in favouring repro-
duction, and this might seem to make the favourable selection among
barbarian peoples more intense than the unfavourable selection

252 THE SOCIAL SELECTION OF FERTILITY

among the civilized. Against this should, I believe, be set the fact
that, although uncivilized peoples, by practising infanticide, can
produce as great a variation in net fertility as can birth limitation in
civilized man, yet the selective effect of these differences in fertility
must, in a harsh environment, be much diminished by heavier mortal-
ity in infancy and childhood, so that the net differences of fertility
available may be less. With respect to the action of sexual selection
it might be thought that this factor, while accelerating progress
among barbarians, must be retarding decay among the civilized.
But this is certainly not the case in a society in which the prospects
of fertility diminish with social advancement, for in such a society
it will, on the average, be biologically advantageous, to make, of two
possible marriages, that which is socially the less eligible. Moreover
those who are most particular in the choice of a mate will most
frequently diminish their fertility by postponement of marriage or
celibacy. Consequently sexual selection must be judged to intensify
the speed of whichever process, constructive or degenerative, is in
action. The intensity of this influence must, however, be much
diminished in the later stages of civilized societies, with the decay of
the appreciation of personal differences.

Analogy of parasitism among ants

The reaction of economic causes upon the distribution of fertility hi
human civilization is so disastrous that we could scarcely expect to
find it adequately paralleled in insect societies, for among these an
active intercommunal selection appears always to be possible. Never-
theless the interpretation put by Forel upon the reaction of the ant
Tetramorium cespitum to a rather rare parasitic ant Strongylognathus
testaceus is sufficiently apposite to be compared to the human situa-
tion. The structure of the parasitic ant suggests that it was formerly
a slavemaker, but it is now too feeble to be an effective combatant,
and the mixed colonies rely for defence upon the host workers. The
parasite neuters, though able to excavate and to feed independently,
contribute little or nothing to the structure of the nest, and probably
obtain most of their food from the tongues of the hosts. They take
no part in the care of the young, even of then* own queen, and, being
thus apparently a survival useless to their own species, it is not
surprising that they are produced in relatively scanty numbers
compared to the males and queens, which are very small and produced

THE SOCIAL SELECTION OF FERTILITY 253

in abundance. The sexual forms of the host, on the other hand, are
relatively enormous, since the queens have to supply the biological
capital for founding new and independent colonies. In most cases of
ant parasitism the mother of the parasitized community is in some
manner or other eliminated, and the parasitism consists in the ex-
ploitation of the social instincts of the surviving workers for rearing
an alien brood. The case under consideration is peculiar in that it
appears to be well established that the host queen continues to h've
and, in addition to the parasite queen, to lay, in the parasitized
colony ; but that in this condition she never produces fertile females,
the parasites thus gaining a continual supply of host workers to
house, feed, educate and defend them, while the fertile queens
issuing from the nest are of the parasite species only. Forel ascribes
this remarkable condition to the regulatory or economic instincts of
the host workers, for the females and males of the parasite are smaller
and less troublesome to nourish. This, he says, is evidently sufficient
to induce the host workers to rear them in place of their own enormous
queens and males, the larvae of which they therefore undoubtedly
devour or neglect, as they do in the case of all that seems to be
superfluous.

Whether or not Forel is right in this interpretation, his suggestion
illustrates well the effect of economic law, if allowed blindly to act in
the regulation of fertility. Since the parasites are found in only a
small proportion of the Tetramorium nests, these insects have pre-
sumably some defensive instincts, which usually succeed in resisting
infestation. In human societies man is his own parasite, a circum-
stance which seems to ensure that all civilized societies shall be fully
infested.

Summary

In accordance with the theory, developed with successive extensions
by Galton, De Candolle, and J. A. Cobb, it is shown that the inversion
of the birth-rate is a consequence of two causes which have now been
fully demonstrated: (i) The inheritance of the characters, whether
physical or psychological, determining reproduction ; (ii) The social
promotion of the less fertile. The various theories which have sought
to discover in wealth a cause of infertility, have missed the point that
infertility is an important cause of wealth.

In the light of this theory we can understand how it is that the

254 THE SOCIAL SELECTION OF FERTILITY

more prosperous classes, not only have fewer children when married
and at a given age, but that they also tend to marry later in life, and
to remain more frequently celibate, than do less prosperous classes.
We can understand how it is, although the poorer classes generally
have more children than the rich, yet that persons of distinction, who
have enjoyed great social promotion, are found to have fewer children
than persons of equal distinction who have been less promoted. Again,
although among the general population the larger families of the less
successful classes produce a negative correlation between the ability
of a child, measured in various ways, and the size of the family to
which he belongs, yet in selected groups of children, chosen as receiv-
ing more equal social opportunities, we should expect to find, as
indeed is found, with the Yale students, and to a less degree with some
middle-class English schools, that the correlations tend to be raised
to a positive value. All these facts would be highly paradoxical upon
the view that the differences in fertility were the direct result of
differences in social environment.

In the problem of the decay of ruling classes it is shown that neither
race-mixture, nor the selective action of climate and disease, would
suffice to explain their failure under favourable selection. The causes
to which we have traced the inversion of fertility must have been
operative in the most ancient civilizations, as in our own, and serve
to explain the historical importance of ruling races, through the
absence of the proper attributes in the native populations. The same
causes ensure an adverse selection acting upon each conquering
people in turn.

The decline of barbarian peoples, which have received the civiliza-
tion, and shared the decay, of some more advanced state, without
suffering from a foreign climate or from intermixture with an inf erior
race, is intelligible by the social promotion and extinction of their
more capable members.

Certain uncivilized peoples characterized by a tribal organization,
the blood feud, and the importance attached to kinship and pedigree,
exhibit a state of society in which the more eminent are certainly the
more fertile, and in which the effects of Natural Selection are greatly
enhanced by social and sexual selection. The action of these factors
is of particular importance in respect of the qualities recognized by
man as socially valuable, which have, in this way, received a selective
advantage very much greater than any which could be ascribed to the

THE SOCIAL SELECTION OF FERTILITY 255

differential elimination of entire tribes. The group of qualities under-
stood by these barbarian peoples as associated with heroism has
thus been developed considerably beyond the optimum of individual
advantage. The higher mental qualities of man, and especially his
appreciation of them, seem to be ascribable to the social selection of
this type of society.

The selection in favour of the qualities admired among barbarian
peoples was probably almost as intense as that hi the opposite direc-
tion among the civilized. The destructive effect of the adverse
selection on these qualities, must, however, be much more rapid than
the process by which they were built up.

If the opinion of Forel be accepted as to the reaction of the host ant
Tetramorium Cespitum to its parasite Strongylognathus testaceus the
situation established in parasitized colonies bears some analogy to the
economic reactions of civilized man towards reproduction. Whereas,
however, the majority of Tetramorium nests keep themselves free
from parasites, human societies inevitably show the necessary varia-
tions to ensure their own infestation.

XII
CONDITIONS OF PERMANENT CIVILIZATION

Apology. A permanent civilization not necessarily unprogressive. Redistribution of
births. Social promotion of fertility. Inadequacy of French system. Problem of exist-
ing populations. Summary.

And nothing 'gainst time's scythe can make defence

Save breed to brave him when he takes thee hence. SHAKESPEARE.

But a good ivitt is as a mighty god. SOPHOCLES.
Apology

IT is to be supposed that all scientific men accept, at least in theory,
the view that the advancement of biological knowledge will ulti-
mately be of service in the practical affairs of mankind ; but there
can be little doubt that most would feel some embarrassment if their
views had to be made the basis of practical, and therefore contro-
versial, policy. There is good reason for this ; for scientific men, no
less than others, imbibe, before their profession is chosen, and perhaps
later, the same passions and prejudices respecting human affairs as do
the rest of mankind ; and while the standard of critical impartiality
necessary to science may, perhaps, be easily maintained, so long as
we are discussing the embryology of a sea-urchin, or the structure of
a stellar atmosphere, it cannot be relied on with confidence in subjects
in which these prejudices are aroused. Any failure in this respect is,
moreover, harmful to Science. The enthusiast whose sole interest in
science is to find support for a preconceived social policy, not only
deceives himself, and perhaps others, who are not aware of his bias,
but inevitably brings some discredit upon all other workers in the
same field. The investigator undoubtedly best preserves both his
scientific reputation and his peace of mind, who refrains from any
opinion respecting human affairs, and declines the responsibility for
any practical action which might be based upon the facts he has
brought to light. If such a one were to admit that mankind might,
with advantage, make more use of scientific knowledge of all kinds,
his practical policy would, apparently, go no further than to advocate
a more general diffusion of this scientific knowledge, its application to
mundane affairs being relegated to others (unspecified) who might
make it their particular business.

CONDITIONS OF PERMANENT CIVILIZATION 257

The reader will have realized that our conclusions as to the selective
agencies at work in civilized societies come perilously near to being
capable of practical application. Conscious as I am of the incon-
veniences of such a course, it would appear to me merely cynical if,
having established, as I believe, the main cause of the instability of
human civilizations, I were not to attempt at least to specify the
conditions of permanence for a civilization similar to our own. If
these conditions should seem to involve far-reaching changes, difficult
to be brought about, I trust this will not be imputed to the very
academic irresponsibility which I am anxious to deprecate, but to the
deep-seated nature of the cause to which the instability has been
traced.

A permanent civilization not necessarily unprogressive
By a permanent civilization it is evident that we should not mean
a rigid or a stagnant one. Our current civilization does already, no
doubt, embrace the entire earth, although it has not yet experienced
the final reactions to it of several important bodies of people. We
may, however, grant that it has no competition to fear, without
admitting that, to be permanent, it need not be progressive. For, so
long as it exists, progress in the sciences and arts will certainly change
the environment hi which men live, and thereby change the social
value of different kinds of men. It is, in fact, a necessary condition
of the permanence of a civilization resembling our own, that the
human race should be capable of making biological progress in what-
ever direction may be required by the current state of society. Even
if it were argued, therefore, that a rigid system of occupational castes,
each compelled to bear the burden of its own necessary reproduction,
would ensure biological permanence, much as the permanence of a
society of genes is ensured in cell-division, yet this could not be
admitted as solving the problem of a permanent civilization. On the
other hand, this phrase need not be taken to imply an absolute im-
munity against destruction from all causes, but only such mundane
immortality as is enjoyed by one-celled animals and plants, which
may perish, and indeed do hi great numbers, but which have, in their
inner constitution, no inevitable causes of senility and decay.

Redistribution of births

The most obvious requirement for a society capable of making
evolutionary progress, in accordance with its current needs, is that

3653

258 CONDITIONS OF PERMANENT CIVILIZATION

reproduction should be somewhat more active among its more
successful, than among its less successful members. In comparison
with the actual distribution of reproduction found in civilized
societies, such a condition, apart from the reason for which it is
propounded, or the means by which it may be brought about, would
seem to be attended by considerable advantages. Extreme poverty
would certainly be mitigated, and a more even distribution of wealth
insensibly brought about. There would be less need for the process
of transferring wealth from the rich to the poor by direct taxation,
and this should be welcomed by those who believe that this process is
in practice extremely inefficient, in that the real wealth transferred
to the poor is much less than the loss incurred, directly and indirectly,
by the rich. There is, I believe, only one undesirable consequence
which would seem, at first sight, to follow from a redistribution of the
incidence of reproduction, namely that the accumulation of capital,
now possible in the wealthier classes, might be diminished. Without
denying that this might be an effect of a more adequate birth-rate
among the wealthier classes, it is possible at least to see a counter-
vailing advantage ; for if there were less free money for investment, or,
at least if a rise in interest rates, were necessary to induce the same
rate of the accumulation of savings, the capital withdrawn from
the investment as money, would in fact, have been invested in the
production of men of average ability somewhat above that of the
general population, and adequately educated for their work in life.
This is a form of capital which also earns dividends, and is, indeed,
necessary for the profitable investment of all other capital. It may be
suspected that wealth would accumulate just as rapidly as at present,
only more in the form of capable men, and perhaps, less in bricks and
mortar designed for hospitals and reformatories.

Social promotion of fertility

A moderate superiority of upper class fertility would, if we accept
the argument of Chapter XI, be established, without interference with
personal liberty, by a moderate tendency towards the social promo-
tion of the more fertile strains in the population, using this phrase
to designate those who, whether physically or psychologically, are
more inclined to bring children into the world. Different as such
a condition seems from the incidence of the system of wages and
salaries current in this country, it certainly appears on examination

CONDITIONS OF PERMANENT CIVILIZATION 259

that our wage system could with some advantage be modified in this
direction, both from the point of view of the purely economic function
of the wage system, and from that of current canons of natural
justice. If, postponing the consideration of the machinery by which
equitable arrangements are made between different employers, we
contrast, with the utmost simplicity, the two systems by which the
amounts received by the employed may be determined, (A) equal pay
for equal work, implying considerable differences in the standards
of living, of industrially equivalent persons, supporting families of
different sizes, or, measured in the realities of consumption and
savings, a bonus for childlessness of about 12 per cent, of the basic
wage, for each child avoided, against (B) an equal standard of living
for equal work, by the inclusion in the wage of a family allowance
equivalent to the actual average cost of the children, it will be seen
that the second system (B) while abolishing the social promotion of
effective sterility, possesses the economic advantage of increasing the
inducement to increased efficiency. The wage system is simplified for
the recipient, whose standard of living now depends solely upon the
value of the services which he can perform ; regarding the system of
differential wages or salaries as a means by which the community,
either directly or through the private employer, induces the individual
to perform socially valuable services, its capacity is now wholly
exerted towards this end, instead of being, as in the first system (A)
partially dissipated in inducing him also to refrain from parenthood.
A principal motive for the adoption of the systems of family
allowances, now almost universal in France, was the need of making
provision for the children of the poorer wage-earners in the post-war
period, when it was felt that French industry could not bear the
burden of maintaining a satisfactory standard of living among the
workers, if it were also saddled with the necessity of supporting a
higher standard of living for those among them who were childless.
In this respect the French system may be regarded as aimed at
relieving poverty without increasing the burden of wages borne by
the industry; though it is probable that, in the outcome, the saving
effected by the redistribution of wages has been divided between the
work-people, as wage earners, and the industries which they serve,
the advantage to these being in part handed on to the general body
of consumers in the form of lower prices. As soon as it became
realized that these advantages could be gained, by the simple

260 CONDITIONS OF PERMANENT CIVILIZATION

expedient of establishing equalization pools among the different em-
ployers, it is easily understood that the system should have spread
rapidly. The actual amounts paid into or out of these pools on account
of individual employers are of course small, for any large employer
will support out of wages a number of children nearly proportional
to his total wage bill ; they play, nevertheless an essential part in the
working of the system, by removing from the individual employer
the economic inducement, which he would otherwise have, to give
employment preferentially to childless persons. Any employer who
happens to be supporting, through the family allowances included in
his wage bill, more than the average number of children supported
by his association, will, therefore, recoup himself, by means of the
equalization pool, from other employers who happen to be supporting
less than the average number of children.

A second motive, which was important in establishing a family
allowance system in France, was the national desire to check the
tendency towards a diminution of population through the insuffi-
ciency of the number of births to replace the existing adults. The
decline of the birth-rate had begun somewhat earlier in France than
elsewhere, and its onset had been more gradual, so that it was more
widely realized among the French people than it is now in other
European countries, and especially in Great Britain, which, after
a more sudden fall, are now failing much more considerably than is
France to maintain the numbers of their existing populations . Where-
as, however, the economic objects of the French system, in combating
unmerited poverty, in inducing industrial contentment, and in giving
full employment to the industrial population, seem to have been
very satisfactorily realized, the biological object of increasing the
number of births has met, so far, with no appreciable success, even
in those associations in which the allowances for the later children
are sufficient to give a positive economic inducement to further
parentage. When account is taken of the age distribution of the adult
population, the supply of children fell short, in 1927, by about 9 per
cent, of the number needed to maintain a stationary population, and
this shortage has been increasing in recent years, although much
more slowly than in England, Germany or Scandinavia. A recent
estimate for Western and Northern Europe as a whole, in 1926, shows
a deficiency of 7 per cent., and in view of the rapidly falling birth-
rate among the larger populations in this area, it is certain that this

CONDITIONS OF PERMANENT CIVILIZATION 261

deficiency is increasing rapidly. In 1927 it appears to have been
about 18 per cent, for England and Wales.

It is arguable, therefore, but by no means certain, that the in-
corporation of family allowances into the French wage-system has
exerted some influence towards checking the tendency to a decrease
in population ; though, if it is ultimately to prove itself effective in
this respect, it must be admitted that its action is remarkably slow.
Whether it will prove more effective to a generation that has grown
up under its influence, and whether it is largely inoperative owing
to the example of better paid classes, to whom the system has so far
been very inadequately applied, further experience can alone deter-
mine. Its importance for us is that it provides the only known
means, which has a rational expectation of proving effective, of
controlling a tendency to population decrease, which has already
gone alarmingly far in Northern and Western Europe, and may be
foreseen with some confidence for English-speaking peoples hi other
parts of the world.

We need not, of course, here consider the problem of the regulation of
population density in general, but need only notice that the objection
that the wage system must be used to encourage childlessness, because
no other means are sufficiently powerful to restrain over-population,
is not one that can weigh with those familiar with modern tendencies.

Inadequacy of French system

For the purpose of counteracting the social advantage of the less
fertile, a purpose which was, of course, far from the minds of its
founders, the system of family allowances now established in France,
must be judged to be very inadequate. This is particularly true of
its failure to establish family allowances proportionate to the basic
wage throughout the salaried occupations, for, in the absence of such
a provision, the tendency to eliminate the higher levels of intellectual
ability, which show themselves particularly in these occupations,
must be almost unchecked. For a permanent and progressive
civilization we must postulate that this defect should be remedied,
a requirement which is the more moderate since the system presents
the same economic advantages to whatever income levels it be
applied. A more serious difficulty seems to be presented in counter-
acting the social promotion of the less fertile in occupations not in
receipt of fixed wages or salaries, but rewarded by fees or payments

262 CONDITIONS OF PERMANENT CIVILIZATION

from many different individuals. Save in a population anxious to do
the best for itself, both biologically and economically, the economic
situation of these occupations must present a difficulty ; though with
goodwill, and in pursuit of an intentional policy, the difficulty
would seem to lie rather with the establishment, than with the work-
ing, of a system of mutual insurance, which would provide a redistri-
bution of income equivalent to that experienced by the earners of
wages and salaries. If the bulk of the population were convinced by
experience of the advantages of the system to those involved, it
would be surprising if the remainder should prove themselves unable
to devise and adopt co-operative schemes suitable to their own needs.
The foregoing paragraphs will have served their purpose if they
have put before the reader, in a sufficiently definite and concrete
form, the proposition that it is not inherently impossible for a
civilization essentially similar to our own to be so organized as to
obviate the disastrous biological consequences to which our own
seems to be exposed. It is to be presumed that much more advantage-
ous proposals could be elaborated. My point is merely that the bio-
logical difficulty, though intimately related to economic organization,
is not imposed upon mankind by economic necessity.

Problem of existing populations

If we turn from the relatively easy problem of specifying the condi-
tions, on which a human society might avoid the unfortunate bio-
logical consequences of the selective agencies, by which human
societies are threatened, to the problem of establishing an equally
advantageous condition, among the populations of our existing
civilization, it is obvious that we shall be faced with the necessity for
far more drastic methods than those which would suffice for the easier
problem. For existing populations are already stratified hi respect
of the various innate characters which have, hi recent centuries,
favoured social promotion. This has been demonstrated, hi the case
of intelligence, by the comparison of the average scores attained, by
the children of different occupational groups, in the tests judged by
psychologists to be most suitable for gauging intelligence. What is,
perhaps, more important, is that a number of qualities of the moral
character, such as the desire to do well, fortitude and persistence in
overcoming difficulties, the just manliness of a good leader, enterprise
and imagination, qualities which seem essential for the progress, and

CONDITIONS OF PERMANENT CIVILIZATION 263

even for the stable organization of society, must, at least equally with
intelligence, have led to social promotion, and have suffered, in
consequence, a relative concentration in the more prosperous strata
of existing populations. These classes have, however, also been
selected for relative infertility. We have seen reason to believe that
they must be, to some extent, congenitally averse to the consequences
of normal reproduction in existing economic conditions, and to
some extent, also, to actions such as early and relatively imprudent
marriage, which are favourable to reproduction. They are now
producing, in countries such as England, probably less than half the
children needed to maintain their numbers, and there can be no
doubt that this fraction is still decreasing somewhat rapidly. The
reformer must expect to encounter deep-seated opposition in the
classes on which he would naturally rely for an intelligent anxiety for
the future of their country, owing to the fact that many in these
classes owe the social promotion of their forbears, and their present
prosperity, less to the value of their services to society than to a
congenital deficiency in their reproductive instincts. While it is
certain, however, that opposition will be experienced from this source,
it cannot be affirmed with certainty that members of the more
prosperous classes in receipt of salaries would not respond to a
generous system of family allowances, sufficiently to maintain their
numbers, after an initial loss of a considerable fraction of the valuable
qualities now concentrated in these classes. The decline in fertility
has been more rapid among the more prosperous classes than in the
general population and, in so far as this is due to these classes being
more sensitive to economic and prudential considerations, we might
reasonably anticipate that their response to family allowances on a
scale adequate to meet the actual expenditure incurred in respect of
children, might be more rapid and ultimately greater than that of the
other classes. If this were so, and if, at the same time, preferential
promotion of infertile strains from the less prosperous classes were
entirely to cease, it seems not impossible that the fertility of the upper
classes might be restored, by the differential elimination of the less
fertile strains, within no very lengthy historical period.

The length of the time necessarily required before the present
agencies causing racial deterioration could be completely annulled,
presents, perhaps, the most formidable obstacle to such an attempt.
It would be contrary to all experience to suppose that the history of

264 CONDITIONS OF PERMANENT CIVILIZATION

the next two centuries will not be broken by violent political vicissi-
tudes. The policy of every nation will doubtless, from time to time,
fall under the sway of irrational influences, and the steadfastness
of intention necessary to maintain a policy in pursuit of a remote,
though great, advantage, however clearly the reasons for that policy
were perceived, is not to be expected of every people. Peoples
naturally factious and riven by mutual distrust cannot well exert, or
even attempt, any great effort. This, however, is no reason for men
of goodwill to abandon in despair such influence for good as is placed
within their reach.

A people among whom no rational motive for reproduction is
widely recognized, but who are principally urged thereto by impru-
dence and superstition, will, inevitably and rapidly, become irrational
and fanatical. The experience of previous civilizations should warn us
of the probability of the increase of these elements among modern
peoples. We should not ignore the possibility that even a rightly
directed policy, adopted with enthusiasm, might be frustrated by
this cause before it had time to work its effects. This danger would
perhaps be minimized if the knowledge that parenthood, by worthy
citizens, constituted an important public service, were widely in-
stilled in the education of all, and if this service were adequately
recognized as such in the economic system.

A danger of a more intellectual kind lies in the growing tendency
towards a divorce between theory and practice. Specialization in the
sphere of intellectual endeavour is necessary, and justified by the
limitations imposed by nature upon our individual abilities. There
is less justification for the thinker to detach himself from the
natural outcome, in the real world, of his theoretical researches.
Such detachment sterilizes theory as much as it blinds practice. It
carries with it the natural, but unfortunate consequence, that the men
of will and energy whose business is practical achievement, having
learnt a natural contempt for irresponsible theorists, should also
ignore the practical guidance afforded by theoretical considera-
tions.

It would be idle to speculate upon the probability that our civiliza-
tion should attain that permanence which has been denied to all its
predecessors. The thought that the odds may be heavily against us
should not influence our actions. The crew of a threatened ship are
not interested in insurance rates, but in the practical dangers of

CONDITIONS OF PERMANENT CIVILIZATION 265

navigation. Without ignoring these dangers we may perhaps gain
some hope in that they are not wholly uncharted.

Summary

A redistribution of births, apart from the reason for which it is
propounded, or the means by which it may be brought about, would
be attended by economic advantages.

A moderate social promotion of fertility, such as should maintain
a favourable birth-rate, is not incompatible with the economic
organization of our own civilization, and would provide a means of
combating the current tendency to a decrease of population.

The system of family allowances adopted in France is, however,
definitely inadequate to preserve the higher levels of intellectual
ability. There is, at present, no reason to doubt that a permanent
civilization might be established on a more complete system.

The composition of existing populations, graded both in social
ability and in effective infertility, presents special, and much graver
difficulties, which only a people capable of deliberate and intentional
policy could hope to overcome.

3653

M

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INDEX

Abispa (Monerebia) ephippium, Fab.,

Plate I.

Abraxas grossulariata, 161.
Abundance, 97.

Acraea zeies acara, Hew., Plate II.
Adaptation, 38.
Age at death, 23.
Age at marriage, 190, 191.
Age distribution, 25, 26.
Agouti, 123.
Agriculture, 177.
Albinism, 19, 51, 52, 56.
Ancestry, 125.
Anosia plexippus, 161.
Ants, 16, 156, 252.
Aquatic organisms, 128.
Arabs, 192, 201, 243, 247.
Argyll, Duke of, 133.
Aristotle, 202.
Australia, Commonwealth of, 28, 190,

191.

Bacon.

Barbarians, 242, 243.

Bates, 147, 148, 149, 157, 168.

Bateson, ix, 1, 54, 111, 124.

Bean, 18.

Bengalese marriages, 248.

Biometrical methods, 104.

Biometry, 17, 18.

Birds, 135, 141, 151, 159.

Blending theory of inheritance, 1, 5, 6, 9,

11, 17, 18, 20.
Blood feud, 243.
Blunt, Wilfrid, 243.
Bridges, 53.
Buddhism, 192.
Budgerigars, 60.
Buff-tip moth, 160.
Bull, 114, 115.
Butterflies, 54, 147, 159, 162, 182.

Cameron, 161.

Canaries, Cinnamon, 60.

Castle, 165.

Castnia linus, Cramer, Plate I.

Catholic, 206.

Caverns, 128.

Cavy, 53.

Chance of improvement, 39.

China, 192, 222.

Chinese, 206.

Christianity, 203.

Chromosomes, 9, 51, 103.

Chrysomelid beetles, 161.

Claudius, 241.

Climate* changes of, 41.

Cobb, J. A., 231, 233, 253.

Colitis, 167, 168, 169.

Comb, 60.

Conscience, 173, 199.

Constantino, 204.

Contraception, 192.

' Contributions to the study of Variation ',

124.

Correlation, 4, 17, 33, 198.
Correns, vi.
Cotton, 59.
Crest, 60.

Crinkled Dwarf, 59.
Cross-fertilization, 101, 102, 118, 119.
Crossing over, 103.
Crows, 133.
Cuckoos, 186, 223.
Cynthia cardui, 161.

Danaida tytia, Gray, Plate II.

Danaine butterflies, 161.

Darwin, vii and ix, 1, 4, 5, 6, 10, 12, 20,
22, 44, 66, 67, 97, 98, 131, 138, 139,
141, 170, 178.

Darwin, Major L., 185, 229.

'Darwinism', 134.

Deaf-mutism, 19.

Death-rate, 23, 25.

De CandoUe, 7, 231, 233, 253.

'Descent of Man', 141.

Destructive selection, 40, 251.

De Vries, viii.

Diffusion, 127, 211.

Dimensional representation of adapta-
tion, 39, 40.

Discontinuity, 111, 124.

Dispersal, 127.

Distastefulness, 158, 246.

Dixey, 153.

Dogs, 116.

Dominance, x, 8, 9, 18, Chap. Ill, 48, 105,
108.

Dominant white, 60, 167.

Drosophila, 18, 19, 51, 53, 55, 56, 64, 65,
164, 174.

Dunlop, Dr. J. C., 216, 217.

Dutch pattern, 165.

Economic system, 182.
Eddington, viii, 36.

270

INDEX

Education of birds, 149.
Eel, 114.

Effect of gene substitution, 31.
England, 212, 216, 260.
England and Wales, 261.
Environment, deterioration of, 41.
Epistatic, 54.

Ethesis ferrugineus, Macleay, Plate I.
Excess associated with gene substitu-
tion, 30.
Eye, 19, 39.
Eyes, loss of, 128.

Family allowances, 259, 260, 261.

Fecundity, 43.

Feebleness of mind, 19.

Fertility, 185, 188, 189, 194.

Fertility of women in N.S.W., 189.

Feticide, 192, 202.

Fiji, 154.

Fishes, 113, 142.

Fission of species, 99, 125, 131.

Fixation, 127.

Flatfish, 115.

Ford, E., 114, 115.

Ford, E. B., 55, 97.

Forel, 252, 253, 255.

Forked, 65.

' Foundations of the Origin of Species ',
3,6.

France, 214, 259, 260, 261.

Fryer, 166, 167.

Fundamental Theorem of Natural Selec-
tion, Chap. H, 22, 35.

Fusion, Theory of Inheritance, 1.

GaJlus bankiva, 60.
Galton, 170, 228, 229, 232, 234, 253.
Oammarus chevreuxi, 55.
Gaul, 241.

Gene-ratio, stability of, 99, 105, 118, 166.
Genotypic and Genetic values, 33, 112.
Geographical range, 98, 126.
Geometrical representation of adapta-
tion, 39, 40.
Germans, 243.
Germany, 260.
Germinal selection, 16.
Gerould, 167.
Gibbon, 204.

Gobineau, Gomte de, 238, 239.
Gothic moth, 160.
Great Britain, 215, 216, 260.
Greece, 193, 202.
Greeks, 178.
Gregarious larvae, 159.
Guinea-pig, 53.

Harland, C. S., 59.

Hawks, 133.

Hebrew scriptures, 193.

Heiresses, 229.

Hduxmius erato erato, Linn., Plate I.

Helvia, 203.

' Hereditary genius', 229.

Heroism, 162, 245.

Heron, D., 190, 213, 214, 219.

Herring, 114.

Hesiod, 228.

Heterozygote, superiority of, 100.

Heterozygotes, 103.

Hoffman, 206.

Homeric poems, 243.

Homogamy, 99, 129.

Hooded pattern, 165.

Hooker, 97.

Hormones, 131, 140.

Howard, 135.

Huntington, 220, 235, 236.

Hutchinson, J. B., 59.

Huxley, 1, 6, 22, 170.

Icelandic sagas, 243, 247.
Imms, A. D., 160.
Immunity, 205.
Improvement, chance of, 39.
India, 222.
Infanticide, 192, 199.
Intra-communal selection, 182, 183.

Jesus, 204.
Jews, 193, 206.
Johannsen, 18.
Jones, D. F., 129.
Judges, 229.
Julius Paulus, 203.

Koraish, 201.
Koran, 193, 201.

Lancefield, 65.

Lankester, Ray, 128.

Lamarck, 12.

Lebistes, 164.

Lethal mutations, 18.

Life Table, 22.

Linkage, x, 8, 9, 103, 110, 119.

London, 213, 214, 219.

Magpie moth, 161.

Maize, 129.

Malthus, 26, 44.

Malthusian parameter, 25, 41, 213.

Mammals, 56, 113.

INDEX

271

Mania typica, 160.

Man, x, 19, 129, 162, Chaps. VHI-XII,

170, 186, 188.
Manu, laws of, 193.
Marshall, G. A. K., 150, 152, 153, 162,

163, 169.
Mecca, 201.
Mendel, viii, ix, 8, 9.
Mental and moral qualities, 190.
Meristic characters, 111, 116.
Methona confusa, Butler, Plate I.
Metrical characters, 104, 114, 116.
Migration, 127.

Mimicry, Chap. VII, 146, 207.
Mites, 156.
Morgan, 53.
Moths, 97, 160.
Motile animals, 119.
Mouse, 123.
Muhammad, 201.
Mulattoes, 17.
Miiller, 147, 149, 168.
Mutation, 12, 16, 18, 19, 49, 104.
Mutation rates, 13, 19, 20, 21, 52, 78,

107, 108, 122.

Nasturtium, 55.

Neck, 113, 115.

' Need for Eugenic Reform', 229.

Negroes, 17.

Neptis imitans, Oberth., Plate II.

Nest, 133.

New South Wales, 189.

New Zealand, 243.

Normal distribution, 17.

Oenothera, 129.

Onethocampa processioned, 161.

'Origin of species', 2, 97.

Painted lady, 161.

Papilio agestor, Gray, Plate II.

PapUio aristolochiae, 166.

Papilio hector, 166.

Papilio polytes, 163, 165, 166, 167, 168,

169.

Parasitism, 252.
Parental expenditure, burden of, 142,

185.
Particulate theory of Inheritance, ix,

1, 2, 7, 9, 10, 11, 12, 13, 17, 20.
Peacock butterfly, 161.
Pearson, 195.
Peerage, 195, 229.
Pericopis phyleis, Druce, Plate I.
Peruvian cotton, 59.

Pigmentation, 17, 52, 53, 165.

Plato, 202.

Platypoecttus, 164.

Pliny, 193, 203.

Poisson series, 75, 117.

Pollen, 129.

Polybius, 202.

Polygamy, 249.

Polymorphism, 163, 166, 181, 182.

Polynesians, 243.

Population, 42, 240.

Poulton, 146, 149, 154, 155, 157, 159, 160.

Poultry, 60, 61.

Powys, A. 0., 189.

Prostitution, 192.

Protestants, 206.

Pseudacraea boisduvali trimenii, Butler,

Plate H.

Psychophysical experiments, 15.
Punnett, 162, 163, 164, 169.
Pure lines, 18, 20, 112.
Pyrameis atalanta, 161.

Rajputs, 193.

Range, 98, 126, 131.

Rats, 165.

Receptaculum seminis, 16.

Recessive pied, 165.

Recombination, 103, 238, 240.

Red Admiral, 161.

Regan, Tate, 113.

Regression, 116.

Reproduction (Man), Chaps. IX, X.

Reproduction, table of, 24.

Reproductive value, 27, 28, 73.

Reversion, 6, 9.

Rhode Island, 206.

Risley, 248.

Robertson Smith, 48.

Robson, 54, 146.

Rodent, 52.

Roman Britain, 241.

Roman Empire, 177.

Rome, 193, 202.

Romulus (form of Papilio polytes), 166.

Salinity, 128.
Saltations, 162.
Samoa, 243.
Saw-fly larvae, 161.
Scandinavia, 260.
Scotland, 212, 216.
Schmidt, 112.
Sea Island cotton, 59.
Selection value, 15.
Selective advantage, 19.

272

INDEX

'Selective Fertilization', 129.

Self-fertilization, 101, 102, 112, 118, 119.

Semi-forked, 65.

Seneca, 203.

Sex, 164.

Sex-ratio, 141.

Sexual preference, 99, 129.

Sexual reproduction, ix, 119, Chap. VT,

121.

Sexual selection, 66, 121, 131, 247.
Shakespeare, 188, 210, 256.
Shrimp, 55.
Sloths, 113, 115.
Social insects, 180.
Sophocles, 70, 256.
Specific modifier, 64.
Spedan Lewis, 62.
Spencer, Herbert, 180, 211, 231.
Stability of gene ratio, 99, 105, 118, 166.
Stature, 17, 99, 105, 107.
Stevenson, Dr. T. H. C., 216, 218, 219.
Strongylognathus testaceus, 252, 255.
Struggle for existence, 43.
Sturtevant, 53.
Style, 129.

Sutherland, H. E. G., 237.
Swynnerton, C. F. M., 149.

Tacitus, 243.

Taoism, 192.

Tartars, 243.

Termites, 180.

Territory, 135, 159.

Tertullian, 203.

Tetramorium cespitum, 252, 253, 255.

Thebes, 193.

Thermo-dynamics, second law of, 36.

Thomson, Godfrey H., 237.

Time of relaxation, 87.

Tortoise-shell butterfly, 161.

Toy breeds, 116

Tragoc&rus formosus, Pascoe, Plate I.

Tschermak, viii.

Turks, 243.

Turner, H. H., 154.

Upland cotton, 59.
Urban, 15.
U.S.A., 220, 235.

Valentinian, 203.

Vanessa, 161.

Variability, 97, 98.

Variance, 4, 9, 10, 11, 18, 30, 97, 98.

Variance, genetic, 30.

' Variation of Animals and Plants under

Domestication', 2, 3, 7.
Varieties, 127.
Vertebrae, 111, 112, 113, 114, 115.

Wallace, vii, 44, 132, 133, 134, 141, 172,

178.

Weismann, 13, 16, 66.
Weiss, 55.
Westennarck, 192.
Wheeler, 156, 181.
Whetham, W. C. Dampier, 215.
Whitney and Huntingdon, 220, 235, 236.
'Who's Who', 215, 235, 236.
Wing-colour, 97.
Wright, S., 53, 87.
Wrinkled leaf, 59.

Yale, 236.

Zygaera bucefihala, 160.

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