Population dynamics of Leptomeryx

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FIELDIANA • GEOLOGY

PublisJied by
FIELD MUSEUM OF NATURAL HISTORY

Volume 16 March 27, 1970 No. 16

Population Dynamics of Lejjtomeryx

John Clark

Field Musf.um of Natural Histouv

Thomas E. Guensburg

ROCKFORD NATI'RAL HISTORY Mt'SEUM

The large, carefully-documented collections of middle Oligocene
fossils made in connection with the paleogeographic studies of Clark
et al. (1967) offer unusual opportunities for interpretation of popu-
lation dynamics. Unlike several other collections which have been
used for this purpose (Shotwell, 1958; Van Valen, 1964; Voorhies,
1969), these collections have been demonstrated to constitute pertho-
taxes' accumulated over a period of time and buried essentially with-
out transportation. The enormous biases of selective transportation
have not operated upon them.

Eight lines of evidence demonsti-ate that these collections are
true perthotaxes:

1. Individuals in every stage of disintegration, from entire skele-

tons to separate chips, have been found (see Field Museum
specimens B147, B159, B163, also Hypertraguhis skeletons
at the South Dakota School of Mines).

2. Coprolites are abundant.

3. None of the bones show water abi'asion.

4. Some pai'tially disintegrated specimens have their broken

chips dispersed around them uniformly in all directions (see
FM specimens B150 and B160).

5. Complete skeletons have been found in death poses (see South

Dakota School of Mines Hypertragulns herd).

'Perthotaxis: "A death assemblajje with the animal c-orpses in various stages
of destruction l)y the set of processes normally operative under the environment
concerned." Clark el al., 1967, p. 155.

r^ ^,»T, ,,^, The Library of th«

Library of Congress Catalog Number: tO-115192

No. 1089 111 JUL 11970

University of (llinois
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412 FIELDIANA: GEOLOGY, VOLUME 16

6. The entombing sediments are heterogeneous mudstones,

which can be demonstrated to have engulfed bone with-
out transporting it appreciable distances.

7. Celtis seeds and bones of very small animals occur scattered

throughout, never accumulated as they would be along a
strand line, or washed against an obstacle.

8. Bones and skeletons of all sizes occur indiscriminately through-

out. (Field Museum B150, a shattered Metamyyiodon skull
and jaws, occurred a few feet from various scattered rodent
and small artiodactyl bones).

These lines of evidence cumulatively indicate that the fossils
represent death assemblages, essentially untransported. Specimen
B159, a group of Hypertragulus skeletons somewhat dissociated by
perthotaxy before burial, occurred as a convex layer on a front 18
inches high. This could only represent one roll of a rapidly-congealing
mudflow; the bones, although dissociated before burial, had not been
scattered by the agency of deposition and therefore could not have
been transported more than a few inches. The thickness of this
single-herd deposit indicates an incrementation of at least 18 inches
in one episode.

Leptomeryx was selected as the subject for study because it is
monospecific within the Scenic Member of South Dakota, occurs in
the collections in greater aVmndance than any other genus except
Paleolagus, and has measurable, relatively brachyodont molars with
closed roots. It has the added advantage of a close enough anatom-
ical analogy with Tragulus and the cervids to make limited develop-
mental and ecological analogy reasonable.

We chose for study the two FMNH collections from South Da-
kota having the largest numbers of Leptomeryx. The preliminary
results were so surprising that we included for comparison an excel-
lent collection of Leptomeryx from Sioux County, Nebraska. This
latter collection was made for the Walker Museum, many years ago,
with excellence of specimens rather than totality of sample as the
purpose. Correspondence of this collection with those made as part
of a statistical study is at least as amazing as any other result of this
study (Fig. 1).

Data 071 individual collections

1. Collection 26. Lower Nodular zone, Scenic Member, Brule
Formation, SW-34 of SW jj, sec. 15, T. 2S., R. 15E., Pennington

MORTALITY IN LEPTOMERYX AND
POEBROThlERIUM. DY STAGES.

Fig. 1. Mortality in Leptomeryx and Poebrotherium, by stages.

413

414 FIELDIANA: GEOLOGY, VOLUME 16

County, South Dakota. Collected by J. Clark and K. K. Kletzke,
1965. This collection comes almost entirely from the stratum in-
cluding and immediately overlying a pond limestone dz 4 feet below
the top of the Lower Nodular zone. Essentially, it represents the
perthotaxic assemblage buried by one episode of deposition. ^ The
local environment was a swamp on a grassy or savannah plain. This
collection came from an area of not over 30 acres, along the east and
south sides of a draw, roughly one quarter mile from the site of Col-
lection 32. It comprises 163 specimens of Leptomeryx, of which 73
are suitable for the present study. The remainder consist either of
upper teeth, of lower premolars, or of specimens too fragmentary for
use.

2. Collection 32. Lower Nodular zone, Scenic Member, Brule
Formation, SE-I4 of SE-34, sec. 16, T.2S., R.15E., Pennington
County, South Dakota. Collected by J. Clark, 0. L. Gilpin, and
J. Granath, 1966. This collection comes principally, but not entirely,
from a highly fossiliferous stratum rb 4 feet below the top of the
Lower Nodular zone, which is continuous with the fossiliferous level
of Collection 26. At least three-fourths of this collection, therefore,
represent one perthotaxic assemblage buried during one episode of
deposition; the remainder was buried a few years to tens of years
earlier or later (Clark et al., 1967, pp. 99-102). The local environ-
ment was a savannah plain. The collection comprises 281 specimens,
of which 114 are suitable for the present study.

3. Sioux County, Nebraska. Collection made during the decades
preceding 1940, chiefly by Paul Miller, for the Walker Museum, Uni-
versity of Chicago. Various specimens are recorded as coming from
various tributaries of Hat Creek. All are stratigraphically located
as coming from "Lower Nodular zone, Brule," but no effort was
made to establish positions within this zone. The collection includes
115 specimens suitable for this study. Many consist of complete
skulls and jaws; most include all three lower molars; in completeness
of specimens the collection far exceeds the two better-documented
ones from South Dakota.

Derivation of data

Preliminary study led to the conclusion that the lower molars
show more consistent development of wear patterns, coincident with
decreasing crown height, than do the upper molars or the premolars.

'Clark et al, 1967, p. 83.

PARACONID HEIGHT

COLLECTION 26

M,

H E

G H T 1

N

m m

1

O

1

2

3

4

o«

5

2

e

3

o

4-

•

e

•

4

•
•

• •

• 9 e

•e

4 +

•

•

5

•

•

6

• •

TOTAL

•

•• •

•

* •

•• • •

••
••

«

•

••

••

•

+ 7

G

S

■4

J

2

1

A

c i;

N Y

EARS

Fig. 2. Collection 26: paraconid height, Mi.
415

416

FIELDIANA: GEOLOGY, VOLUME 16

PARACONID HEIGHT

COLLECTION 26

HEIGHT IN

m m

3

O

1

2

3

4

•

5

4 -

• ••

4

•

• • • •

• e •

•

4 +

• • •

5

•

•

6

•
• •

TOTAL

• :• •

e e •

•
• •••••

•

Fig. 3. Collection 26: paraconid height, M2.

The lower molars also show a more consistent progression of wear,
from the third through the first, than do the uppers (see figs. 3, 4, 6,
7, 9, 10) . Presumably these differences are due either to slight differ-
ences in height of crowns relative to lakes, or to differential wear
caused by more complexity in upper-molar pattern. In any case, we
decided to use the lower molars as our basis for age determination.

CLARK AND GUENSRERG: LEPTOMERYX 417

We then set six arbitrary but objectively determinable age stages,
is follows:

Stage Terminated hy

1. Infancy Beginning of wear on Mi

2. Juvenility Beginning of wear on M2

3. Adolescence Beginning of wear on M3

4. Young Adulthood Elimination of anterior lake of M,

5. Middle Age Elimination of posterior lake of Mj

6. Senility Death

The specification "beginning of wear" was found preferable to
'complete emergence" because in some individuals M3 seems to have
jeen actively in use for some time before growth of the jaw permitted
complete emergence of the posterior lobe of the tooth.

These stages are definite and objective. As a further refinement,
ninus and plus signs were recorded for those individuals respectively
ust entered into their age gi'oup or almost passing from it. This re-
quired subjective decisions, which we minimized but could not elimi-
late completely by ranking the specimens independently and confer-
ing on the few borderline cases in which our ranking differed.

Observations on wear of teeth in Oligocene Poebrotherium and
"^rotoceras, plus observations on the large cervid collection in Field
Vluseum, demonstrate that these wear stages approximately repre-
sent their corresponding age stages. If anything, "senility" includes
ome middle-aged animals. This is further discussed on page 426.

Comparison with the wear patterns of those specimens possessing
omplete molar batteries made it possible to assign individual molars
o stages. We experimented by assigning to a stage individual teeth
)f a series without observing the whole series, then checking against
he other teeth of the series. Since the error demonstrated by the
experiments is insignificant, we have included evaluations of single
eeth. Tables 1, 2, and 3 list the teeth present in each specimen, mak-
ng the data susceptible to critical re-examination in detail.

In the hope of arriving at actual measurements rather than ranks,
eeth in various stages of wear were studied closely. It was at once
-pparent that measurements of the external crescents would give un-
eliable results, due to the interaction of variations in the slope of the
rescent at different elevations from its base and to considerable
'ariations in occlusal pattern. Of the internal crescents the para-

418

FIELDIANA: GEOLOGY, VOLUME 16

PARACONin MCtGMT

COLLECTION 26

HEIGHT IN mm

ID

<

I-

0)

r
1-

o

4 +

TOTAL

o

1

2

3

4

•

5

«

•
•

• •

•

• • •

• •

•

•

• •

••• • e

•
• • •

•

Fig. 4. Collection 26: paraconid height, M3.

conid seemed the more satisfactory since it received wear earliest and
gave a uniform basis for measurement of all three molars. Measure-
ments were made from the enamel border upward along the outer-
most ridge of the cusp, which is usually inclined at a slight angle
forward of normal to the antero-posterior axis of the tooth. In un-
worn teeth, this measurement invariably gives a maximum dimen-
sion, running to the apex of the cusp.

PARACONID HEIGHT

COLLECTION 32

M ,

HEIGHT 1 ^

m m

1

O

1

2

3

4

5
• •

2

•
•

3

•

•

4-

• •

4

O
•«

e •

4 +

e
• ••

e

5

• •

•

6

•
•

•

TOTAL

•
•

• • •

•

••
• •••

•
•• •
••• • • •

•

•

••• ••

• •

+ 7 1 6

5

A

^ 3

2 1 A

G E 1 N Y

EARS

Fig. 5. Collection 32: paraconid height, Mi.
419

420 FIELDIANA: GEOLOGY, VOLUME 16

However, three unavoidable sources of variation enter into these
measurements. First, the enamel border is not at all uniform in out-
line. Figure 11 illustrates the three commonest configurations. A
fourth consists of a gradual downward thinning of enamel, effecting
a gradation rather than a sharp border. These variations can pro-
duce more than 0.1 mm. difference in measurement of teeth in equi-
valent stages of wear.

The second source of variation is difference in occlusal wear. All
conceivable permutations of the three patterns illustrated in Figure
11 have been observed. They can produce variations of at least
0.2 mm. in teeth of equivalent wear stages.

Finally, differences in overall size of teeth can certainly influence
measurements of paraconid height. Attempts to arrive at a meaning-
ful ratio of paraconid height to tooth length were defeated by inter-
dental wear, which changes the tooth length considerably with
increasing age. Measurements of tooth width proved to be not com-
parable from specimen to specimen, due to variations in curvature
and position of the cusp perimeters.

Visual inspection of the specimens revealed no such relation be-
tween size and hypsodonty as occurs in Mesohippus. A large individ-
ual is not proportionally more hypsodont than a small one. There-
fore, the wear stages are equally valid in large and small specimens,
and are probably more valid than measurements of paraconid height.

Measurements of total size of teeth failed to reveal a significant
dichotomy which could be referred to sexual dimorphism. This
might be due to the considerable size range within the species, to an
absence of dimorphism in tooth size, or to the blurring effect of other
sources of variance. We are, therefore, compelled to make estimates
of sex ratios based upon comparisons with tragulids, cervids, and
antelopes of roughly similar size and habits.

Analysis of Data

The graph by stages reveals a highly anomalous situation: 60 per
cent of the individuals in Collection 32, and 76 per cent of those from
Sioux County and from the better documented collection 26, died in
early maturity. The small number of infants and juveniles usual to
fossil collections is balanced by an equally small number of individ-
uals dying in middle age to old age. The mortality graph is almost
perfectly inverse to what a mortality graph in a stable, natural pop-
ulation should be. Since these specimens were not subject to trans-
portation before burial, they represent perthotaxic assemblages

PARACONID HEIGHT

COLLECTION 32

M.

HEIGHT IN mm

TOT A L

o

1

2

3

4

5
•• •

•

• ••

• • •

• ••

• • • ••••

•

•
• • • •

• •

• »••••

••

••

•
• ••«

9 •»• 9*

•

• •

• •••

Fig. 6. Collection 32: paraconid height M2.

421

422

FIELDIANA: GEOLOGY, VOLUME 16

PARACONID HEIGHT

COLLECTION 32
Mo

HEIGHT IN mm

O

< ^-

t-

0)

4

r

0 4-

tr.

ID

o

1

2

3

A

5
•

6

«

••

•• •

• f

•

• •

# •

•

•

•

•

• • •

• • •

•
•• •

•

: « «

•

Fig. 7. Collection 32: paraconid height, Ma.

(Clark et aL, 1967, pp. 117-118). The factors influencing these pop-
ulations, therefore, must be biotic, thanatic, or perthotaxic, or some
interaction of the three.

Figures 8 and 13 demonstrate that even simple measurements of
tooth height support the conclusion of high young-adult mortality.
Since the height of unworn Mi paraconids is ± 5.0 mm. and wear to
0.0 is demonstrable, 2.5 mm. constitutes the purely arithmetic mid-

CLARK AND GUENSBERG: LEPTOMERYX 423

point of wear, or approximately of the animal's life. Fifty-five speci-
mens of the Nebraska collection have paraconids more than 2.5 mm.
long, and 23 have shorter, for a 71.8 per cent young-adult mortality.
In the two South Dakota collections combined the figures are 43 of
58, for a 74.1 per cent young-adult mortality.

Whether one uses as a standard wear stage, or overall height of
tooth, or interpretation of age in years, the results are the same;
between two-thirds and three-quarters of these animals died before
middle age.

These specimens comprise perthotaxic assemblages at three places,
one more than 100 miles from the other two. The two neighboring
ones therefore represent all individuals who died within a two to three
month period scattered over a 30-acre swampy area and a 20-acre
grassy savannah, respectively. The Nebraska collection represents
individuals who died on a grassy to forested savannah over an area
of several square miles. It is, therefore, reasonable to presume that
these are fair samples of the death assemblages of their respective
districts for the times of year represented, not merely a single mass
mortality at a particular place. The close correspondence of the
three collections increases the probability that they represent a gen-
eral situation rather than a local one.

Let us consider what inferences may be drawn regarding the life
history of Leptomeryx relative to thanatic and perthotaxic factors.
First, Leptomeryx probably attained full adult size, represented by
stage 4 in the graph, within six to eight months of birth. Davis
(1965) recorded that in Tragulus javanicus breeding maturity is at-
tained at 41 2 months and adult size at five months. In the much
larger Moschus, "This deer attains puberty before it is 1 year old.
Rut takes place in January and the young are born in June after a
gestation of 160 days" (Asdell, 1964, p. 558). In Rhynchotragus
"The females reach puberty at about six months" (Asdell, 1964,
p. 616). The general gi-owth pattern of small tragulines, cervids,
and antelope seems to be attainment of adult size and of breeding
maturity in about six to eight months.

Second, the period of gestation in Leptomeryx was probably
120-160 days. Davis (1965) gives 152-155 days as normal for Trag-
ulus; Rhynchotragus is recorded at 170-174 days, and Moschus at 160
(Asdell, 1964, p. 558).

Third, Leptomeryx almost certainly had a definite annual life
cycle, including a rutting season and a fawning or birth season. Davis
records a most amazing life cycle for Tragulus javanicus, with copu-

PARACONID HEIGHT

SIOUX COUNTY, NEBRASKA COLLECTION

UJ

<

0)

r

o

o

HEIGHT 1

N

m m

1

O

1

2

3

4

•

5

2

• ••

3

•

4-

•

• ••••

• •••••

•

4

• O •

• • •

•

• •

•• •

•• •• •

•

4 +

• • «•

• •• 9*

• •••« ••

•

• •

• • •

5

•
• •

•

• •

• •• • • •

6

•
•

TOTAL

•
•

•
• •

• •

• ••• ••

• ••• ••

•• •••• ••

••••••• ••

• •

: :

•• • •

•• • •••

s:u:n::d

•
•
•

•
• ••

+ 7

6

5

4

i

3

2

1 A G

E

1 N Y

EARS

Fig. 8. Sioux County: paraconid height, Mi.
424

PARACONID HEIGHT

SIOUX COUNTY, NEBRASKA COLLECTION

Mo

H E 1 S H T 1

■^ mm

O

1

2

3

4

5

1

2

3

•

• •

• • •

4-

•• •

• •••••••

•

•

•

• •

•

e •

•

• ••• •

••• •

4

• • •••••

•••• •

•

e ••

»••

• •••••• •

4-1-

•••

• •••••o**

•

••

5

• ••

•
••

6

•

•

•

•

•

• •••

• •

• • ••• •

• •

• • ••• •

• •

TOTAL

•

•

• ••

••••

•• ••••

• • •
•••• • •

•

Fig. 9. Sioux County: paraconid height, M-..

425

426 FIELDIANA: GEOLOGY, VOLUME 16

lation taking place within 48 liours of parturition. With a gestation
period of 153 days and a growth period of 4'2~6 months, births
of successive generations would be out of phase and might occur at
any season. However, Tragulus is a tropical animal inhabiting re-
gions of very low seasonal pressures upon its life. Cervids and ante-
lopes in general have life cycles highly attuned to seasonal fluctu-
ations in temperature or rainfall (Asdell, 1964, pp. 557-581; 607-619).
The range of species without definite breeding seasons extends very
little beyond the tropics.

Fourth, the probability is high that one young was produced at
a birth, with only occasional twins. Davis found this true of Tragulus
javanicus. Blanfoi'd (1891, p. 556) mentions that Tickell (p. 420)
I'eported that the young of T. meminna are two in number. However,
Phillips (1935, p. 346) says, "It has been stated that the female has
two young at a birth, but I have never found more than one." All
other references available to us make general statements, none of
them suggesting definite experience on the author's part. Phillips'
statement of actual observation seems the most valid; until further
evidence is adduced, we regard T. meminna as also producing but
one young at a birth. One young is also characteristic of Moschus,
Muntiacus, Blastocerus, Cephalophus, Sylvicapra, and Rhynchotragus,
plus many of the larger cervids and antelopes. It must be admitted
that Capreolus, Hydropotes, and Mazama, among the smaller deer,
customarily have twins or multiple births, but the heavier weight of
evidence favors single births. The three last-named genera all con-
sist of considerably larger animals than Leptomeryx and Tragulus.

Fifth, the life span in Leptomeryx was probably not over eight
years. It is difficult to find estimates of the average life span of
cervids not subject to hunting or other human modification, but
Child and Wilson (1964) suggest that wear on Mi of duikers with
milk teeth not yet replaced indicates that the teeth are worn down
rapidly in an area of sandy soils. Taber and Dasmann's (1957)
survivorship curves show life spans of about 10 years for the much
larger black-tailed deer, and 7 to 9 for the roe deer, but both of these
are influenced by hunting and migration.

Internal evidence of the life span of Leptomeryx is not lacking, but
depends upon interpretation of the rate of growth. Figures 3, 7, and
11 show that unworn Mj paraconids (Stage 1) have a height of 4.8-
5.1 mm. By the time M3 has erupted and begun to wear, in stage
4-, the Ml paraconid height averages about 3.7 mm. If, as postu-

CLARK AND GUENSRERG: LEPTOMERYX 427

lated above, growth to adult size required not over six to eight
months, then the difference in time represented by first use of Mj and
M3 could not have been over six months. Projection of a wear of
1.1-1.2 mm. per six months would give a life span of about 2.5-
three years until Mi was worn absolutely to the roots. However,
this is improbable: first, Tragnlits is known to have a breeding life
of more than three years (total span not recorded), and second, M2
and M3 would share the dental burden and thereby lessen the rate
of adult attrition. Figure 13 bears this out: the average tooth heights
seem to shift about 0.5 mm. in successive stages; the graph of total
numbers also shows successive lows and highs on approximately 0.5
mm. modes. If we accept 0.5 mm. as an average annual rate of wear
for Ml during adult life, and 3.5-3.7 mm. as the average height of
Ml at the end of the first j^ear of life, the two aged individuals with
all enamel worn off must be seven to eight year-olds. These assign-
ments to years reduce the probability that the abnormal young-adult
death rate is an artifact produced by improperly-interpreted age
stages.

Much of the spread in stage 4 is due to difference in overall size
of individuals. Although we could not work out a quantitative ratio,
we were unable to detect by inspection any proportional difference
in stage due to size; a large individual would achieve successive stages
about at the same rate as a smaller one. This is reflected on the Mi
graphs by the general parallelism of the upper and lower envelopes
to the central trend lines, throughout stages 4 and 5.

Summarizing, Leptomeryx is postulated as an animal with seasonal
breeding and fawning times, producing one young per birth with
occasional twins. The period of gestation was probably 120-160
days. Full size was attained in six to eight months; the total life
span was about eight years. As a corollary to these propositions, the
young were produced, almost certainly, one per year per doe; taking
into account decline of fertility with senility, the average doe certain-
ly could not have produced over six live fawns during her lifetime.

Collating these assumptions regarding the life history of Lep-
tomeryx with the paleoclimates of Middle Oligocene time (Clai-k et al.,
1967, pp. 72 and 97), explains the apparently minuscule infant-juve-
nile mortality.

The climate is described as temperate, with winters slightly too
cool to permit habitation by alligators. The present wind system
of prevailing westerlies was establishing itself. Presumably the sum-
mers were warm and dry, with showers somewhat more frequent than

428

FIELDIANA: GEOLOGY, VOLUME 16

PARACGNID HEIGHT

SIOUX COUNTY. NEBRASKA COLLECTION

HEIGHT IN mm

4-

O

1

2

3

• •

4

•
•• •
• • •• •

5

• •

J

' 4

•

• •

• ••

• •••

•

• •

•• •

•••••

•••••••• •

•

)

4 +

•

•

• • •

• • •

•
•• •
•• • •

5

•
• ••

••*•• • •

)

6

• •••

TOT A L

• • ••••

•

H. d

••••• ••••

•

• • •

• • •

••• o«

»••• •• •

•••••••• •

•••

Fig. 10. Sioux County Collection: paraconid height, Ms.

at present; winters were frosty, with little or no snow; and the major
rains occurred in November, February, or March; the year's crop
of fawns reached full size by October, and bred in late October or
early November. This is, of course, the approximate breeding cycle
of most temperate-latitude cervids of small-to-medium size.

However, streams under a depositional regimen would, neces-
sarily, flood during the major rainy season. Sedimentation, and
hence burial, would occur when all of the year's normal crop of fawns
were full grown, and before the next year's fawning season occurred.
The only infants and juveniles available for death and burial would
be the very few abnormally late or extremely early births. Voorhies
(1969) suggested such a mechanism.

CLARK AXD GUEXSRERG: LEPTOMERYX 429

The junior author has experimented with bodies of adult musk-
rats, skunks, rabbits (Sylvilagus), and domestic cats in the area
around Rockford. IlHnois. He finds that in average dry woodland
and forest border, summer perthotaxic processes completely remove
the flesh of animals within three weeks, and destroy the bones in
about three more weeks. The climate of Rockford is considerably
drier than that of Virginia, where Payne (1965) studied perthotaxy
in baby pigs, and the adult animals naturally have more resistant
bones, but perthotaxy still progresses to destruction within six to
seven weeks.

It is safe to presume, therefore, that any Leptomeryx who died
Ijefore October would be completely destroj^ed before perthotaxy was
halted by cold late in November. The collections represent a pertho-
taxic assemblage of animals who died after the onset of autumn, not
a representation of an annual or longer incrementation of corpses.
The proportion of infants and juveniles is low because the corpses
resulting from juvenile mortality on the regular annual cohort were
destroyed by perthotaxy before annual sedimentation occurred.

Even a cursory examination of Figure 1 reveals that the death
rate among post-juveniles cannot possibly represent a normal mor-
tality rate in a stable population. In a stable population, the life
table of any one cohort yields the same statistics as a vertical sample
of the whole population. A mortality rate of 76 per cent among
young adults, who could not have produced an average of more than
one young before death, added even to the minimal juvenile mor-
tality of our biased sample, would result in extirpation of the pop-
ulation within about eight years. With the addition of a probable
infant-juvenile mortality at least three times as gi'eat as the recorded
one, the population would be extirpated much more quickly.

The collection of Poebrotherium recorded in Figure 1 probably
does represent, by contrast, a normal moitality in a relatively stable
population (except for the usual absence of juveniles). The young-
adult and middle-age stages are low, with a large number of aged
individuals. This graph, it may be noted, is almost the inverse of
that of Leptomeryx. It further tends to validate the wear stages as
accurately repi'esenting the age stages assigned to them.

Deevey (1947, p. 288) pointed out that vertical population sam-
ples such as this one have no statistical validity unless they represent
samples of populations stable in time. In that case, the actual age
distribution and the life table age distribution would be identical.
Since these collections obviously do not represent mortality in a pop-

430 FIELDIANA: GEOLOGY, VOLUME 16

Illation stable in time, we must forego the usual statistical analyses
and approach them from a basis of observation and cautious induc-
tion.

The possibility that this might be a natural, stable population,
misinterpreted due to a misinterpretation of age stages, has been men-
tioned above but must be more carefully considered. Certainly there
is justification for assuming that all animals up to and including stage
4- died in the first year of their lives. The amount of wear on M,
during the time, less than six months, between stages 2 and 3 is much
greater than the amount between stages 3 and 4- (see figs. 2, 5, 8),
therefore, the interval between stages 3 and 4- cannot have been
longer than six months. Using the Sioux County collection, and
counting all individuals with wear equal to the maximum of stage 4
as yearlings, one arrives at 31 yearlings and under, from a total of 78
individuals. Accepting the natural breaks in the graph to demarcate
years thereafter (fig. 8) gives 20 two-year olds, 15 three-year olds, 10
four-year olds, and two much older. Wear from the first through the
fourth year apparently averages 0.5 mm. per year. By projection of
this rate to the aged individuals with enamel completely worn off,
seven or eight years is seen to be the life span of the most aged in-
dividuals represented.

Figure 13 shows that the South Dakota assemblage consisted of
30 yearlings, 11 two-year olds, six three-year olds, three four-year
olds, six five-year olds, and two six-year olds.

Therefore, stages 4, 4 + , and 5 very apparently do not include
senile individuals. The stages have not been misinterpreted; we are
forced to seek explanation for an abnormally high death rate in young
adults. Conversely, since the South Dakota collections represent
animals who died, and presumably lived, on the actual acres where
their bones were collected, we are forced to explain a population with
a minuscule proportion of middle-aged to senile individuals. This
collection does not represent normal mortality in a stable population.
It also does not represent catastrophic death, i.e., a life sample, in a
stable population.

Figure 12 contrasts the survivorship curve of a relatively stable
population of Ovis dalli (Deevey, 1947, p. 289) with those of the
Nebraska and Dakota populations of Leptomeryx. Significantly, the
average age in Ovis dalli is 7.06 years, almost exactly half of the 14-
year life span. In Leptomeryx (Table 4), with a seven- to eight-year
life span, the average age is 2.14-2.18 years. This is not merely a

CLARK AND GUENSBERG: LEPTOMERYX 431

population with a high mortality of young adults; it is definitely
a life population with a high number of young adults.

The similarity of the Leptomeryx growth-stage data to those re-
ported by Child and Wilson (1964, p. 866) for duikers is striking and,
we believe, significant. The duiker population had been heavily
hunted for several years with a respite of 28 months preceding sam-
pling. Child and Wilson collected a grab sample of 61 individuals,
by shooting every one they saw within a restricted area during one
week. Despite a very low number of infants, which they attribute
to hunting problems in high gTass, they found 45 individuals, or 74
per cent of their sample, under 22 months old. This would be the
equivalent of our stages 1 through 4 (duiker first calve at 12 to 14
months) but probably not 4 + .

Child and Wilson's data represent a catastrophe (hunting) pro-
ducing a I'ough life sample of a population undergoing rapid growth
following an earlier similar catastrophe (hunting for tse-tse fly con-
trol). The general pattern of the sample certainly corresponds with
that of our samples of Leptoyneryx. We suggest, therefore, that our
collections represent a catastrophically slaughtered sample of a life
population which was undergoing rapid expansion following a sim-
ilar catastrophe a few years earlier. The Nebraska population pre-
sumably suffered its previous catastrophe five yeai's earlier. With
the Dakota collections the evidence is not so sharp, but any time from
four to seven years previously is possible.

Biostratonomic evidence makes determination of the nature of
these catastrophes possible by elimination.

First, the animals were not killed by flood. The bones are gen-
erally dissociated and partially destroyed by perthotaxy, showing
clearly that the individuals died wrecks or a few months before they
were buried.

Kurt^n's (1953, pp. 69-75) discussion of various factors leading to
mass accumulations of fossils is of great interest here, but does not
directly apply because our collections represent fossiliferous areas
I'ather than mass accumulations. Kurt^n does not always clearly
separate mechanically-transported assemblages from herd assem-
blages, nor perthotaxic pi'ocesses from taphic' ones. Tt is also pos-
sible that the rarity of fossilization in an environment subject to

^Taphic Factors — "Factors determining whether ur nut an animal's bones will
he buried." Clark ct al, 1967, p. 155.

Fig. 11. Variations in
wear pattern and in enamel
border of Mi paraconids in
Leptomeryx.

432

CLARK AND GUENSBERG: LEPTOMERYX 433

successive depositional episodes may have been over-stressed, both
by Kurt^n and by his predecessors. In such environments, fossih-
zation of bone which has survived perthotaxy may indeed be more
nearly the rule than the exception.

Second, ash falls and dust storms were not the cause of death.
Tliere are no ash beds, loessic sediments, or indications of wind action
within the sediments of the Lowei- Nodular zone. The specimens
were buried by thin mudflows (Clark et al., 1967, pp. 82, 113) passintj
over a surface presumably grass-covered. Wind-transported mate-
rial in any quantity would certainly have accumulated on such a
surface and been buried by the next mudflow.

Third, lightning-induced fire is so improbable an agent of death
as to be almost impossible. The climate is believed to have resem-
bled that of present eastern Nebraska, Kansas, and Oklahoma (save
for warmer, rainier winters), where lightning-induced grass fires are
unheard of. The sediments include no trace of the carbonized wood
which should have been abundantly present on the surface, if a
swampy savannah were burned over.

Fourth, drought is also extremely improbable as a cause of death.
Both the Nebraska and the South Dakota populations lived within
two miles of pei-manent, through-going streams. The Dakota
streams had their sources in the Black Hills; the Nebraska stream
originated in the Medicine Bow and other high ranges which presently
nourish the North Platte. Periodic drying of two such stream sys-
tems is highly improbable. In the event of a severe drought, the
vigoi'ous, young-adult population of Le/ptomeryx would certainly have
made its way to these streams.

Collection 26, from a swamp environment, gives added evidence
that drought was not the cause of death. Ostracods, pond snails,
fishes, and five individuals of the aquatic rhinoceros Metamynodon
have been found associated. It is extremely unlikely that such a
fauna would inhabit an ephemeral swamp. The sediments are both
calcareous and stained with ferrous iron, showing clearly that no
prolonged drying (and thus oxidation) occurred. Therefore, di'ought
becomes improbable.

The well-known herd assemblage of over 20 skeletons of Lep-
lomeryx, FM P12320, offei's additional indirect evidence against
drought as a cause of death. Field data give the locality as "lower
Brule, Cain Creek, South Dakota," which of itself would not ])e
helpful because Cain Creek is 20 miles long. However. Llie specimen
is listed in series with a group of many, all coming IVoin Chambei'lain

434 FIELDIANA: GEOLOGY, VOLUME 16

Pass (SE-1^ sec. 25, T3S, R 13E, Pennington Co., S. Dak.), between
Bear Creek and Cain Creek, about Sy? miles ESE of Scenic. This
spot was a famous collecting locality during the early 20th century;
it is one of very few fossiliferous localities within the Lower Nodular
Zone of Cain Creek drainage. Brule stream No. 8 (Clark et al., 1967,
fig. 33) lies within 500 yards of the outermost limits of the fossiliferous
area.

It is, therefore, reasonable to presume that this herd of Leptomeryx
died within 500 yards of a major, through-going stream which almost
certainly did not undergo periods of complete cessation of flow. The
skeletons are in an early stage of perthotaxy, with only a few limbs
disarticulated. Although they have not been prepared sufficiently
to allow accurate determination, the height of the teeth suggests that
most individuals are in stages 4- or 4, with a few 4+ and one 5.
We have here a herd essentially of yearlings and two-year olds which
died, quickly and peacefully, within easy reach of a major stream,
and lay exposed for a short time before burial.

Animals dying of drought usually jam themselves into a desperate
heap actually within the drying mudholes. Representatives of all of
the local species occupying the area congregate at such places (per-
sonal observation). Monospecific herds such as the one described,
or the three known herd assemblages of Hyperfragulus, actually con-
stitute strong evidence against rather than for drought as a cause of
death. Kurten (1953, p. 72) has clearly expounded this.

Neither predation nor intraspecific strife could possibly be re-
sponsible for the deaths of such herd assemblages. Either could
have caused some of the deaths at Sage Creek and Sioux County.
However, predation selection of young adults at a catastrophic level
is practically impossible: this age group would be best equipped to
escape predators. Genocidal intraspecific strife, especially among
hornless cervids with inadequate canine teeth, is almost equally
impossible.

The one remaining cause of death, epidemic disease, perfectly fits
the evidence, and becomes almost the inevitable explanation by de-
fault of all others. Repetition of the epidemics every few years would
be a normal phenomenon, and would explain both the catastrophic
death recorded and the general youth of the population. It would
also make any such computations as life expectancy, deviation from
average age, or any more complex figures, completely meaningless;
for this reason we have in Table 4 constructed only those portions of

CLARK AND GUENSBERG: LEPTOMERYX

435

SURVIVORSHIP IN OVIS DALLI

(FROM DEEVEY) AND IN LEPTOMERYX

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436 FIELDIANA: GEOLOGY, VOLUME IG

the life tables which the data justify. It is of interest in this connec-
tion to note that the average age, 2.16 years, probably is not repre-
sented by any individual in the collection. If fawning time was in
March, and time of death in late autumn, practically all of these in-
dividuals would be ± 0.6, or 1.6, or 2.6 years old, and so forth.

We therefore conclude that the collections of Leptomeryx studied
represent populations killed by an epidemic disease, and that epi-
demics recurred at intervals considerably shorter than the life span
of Leptomeryx. The cause of the disease and its mode of transmission
are unknown. Presuming that the cause of death in the herd assem-
blage is the same as that in the collections, the herd assemblage
testifies that it must have been highly contagious and run a very
rapid, debilitating, fatal course, and that death was not attended by
delirium or convulsions. A slower course would have allowed the less
weakened individuals to wander away from those already incapaci-
tated. Convulsive death would have thrown the animals out of the
comfortable, resting positions in which most of them lie.

Clark et al. (1967, p. 128j have already indicated that the same
general situation of a high percentage of young adults occurs in
Hypertragulus calcaratus, from the same horizon and localities. Two
herd assemblages of Hypertragulus also exhibit the phenomenon of
20 to 30 young adults lying in moderately close proximity to each
other and in comfortable poses. One might presume that the same
disease which affected Leptomeryx also struck its smaller relative.
The much more distantly related Poebrotkerimn, on the other hand,
apparentl}'^ was not affected.

Presence of the same death rate in herds and non-herd collections
of two genera which, though not closely related, are closer to each
other than to other members of the community, increases the prob-
ability of disease as the cause of death. It also decreases somewhat
the probability of such disturbing factors as age-specific disease or
herds of selected age, which are much le.ss likely to occur in two
genera than in one.

Speculation regarding the nature of the disease is almost pure
guesswork. One might suppose that transmission was probably not
by insects or ectoparasites, since such diseases are more usually
pandemic than epidemic. By consideration of usual modes of trans-
mission, rate of development, and high mortality, one might also
suppose that the disease was more probably viral or bacterial than
epizootic or fungal. Further pursuit of this line of supposition seems
utterly futile.

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438 FIELDIANA: GEOLOGY, VOLUME 16

In summary, direct evidence indicates that Lepfomeryx popula-
tions pulsated violently in response to highly lethal epidemics which
struck every four to six years. The disease, whatever its nature, was
debilitating, rapidly fatal, and not attended by terminal convulsions.
The total life span of Leptomeryx was seven to eight years, but due
to the epidemics very few individuals lived out their lives.

Wear on lower molars was approximately 0.5 mm. per year after
the first year during which Mi lost 1.0 mm. of its height.

Indirect evidence suggests that Leptomeryx had an annual cycle of
spring fawning, six months' gi'owth to maturity, a late autumn breed-
ing and a 120-160-day gestation period. Probably only one young
was produced per birth, and the average doe could not have produced
more than five or six young during her lifetime.

The graphs of paraconid height in M2 and M3 (figs. 3, 4, 6, 7, 9, 10)
reveal the same general rate of molar atti'ition relative to growth
stage as that shown by Mi. The slope of the median line through
each closely parallels the slope of the median line in the graphs of Mi.

Detailed analysis of these graphs must await final curating of the
extensive collections from the Sage Creek locality. It is hoped that
this will make available enough specimens including all three molars
on one jaw to yield statistically significant samples without inclusion
of isolated teeth. Variations in the relationship of tooth height to
enamel pattern can then be studied in detail. At present, such
studies would be premature.

General Conclusions

This study presents an hypothesis which offers an internally con-
sistent explanation for a surprising age distribution in three collec-
tions. It does not by any means achieve proof, or even demonstration
to a high degree of probability. To quote Kurt^n (1953, p. 85) "the
calculations leading to this datum are riddled with subjective assump-
tions."

We do not actually know, for example, the life span, period of
gestation, number of young per birth, duration of juvenility, pro-
portion of males to females in the adult population, actual seasonality
of either the life cycle or the weather, or the relationship of these two
cycles to each other. The graphs of mortality and tooth wear relative
to growth stage are highly suggestive, but the samples are too small to
give a reasonable degree of confidence in the age determinations.

However, paleoecologic literature reveals a growing number of
studies based upon data less satisfactory and assumptions fully as

CLARK AND GUENSRERG: LEPTOMERYX 439

sul)jective. This paper demonstrates the necessity for differentiation
between :

1. Mass death caused by a catastrophic agent of deposition, as
at Pompeii. This yields a virtual life census.

2. Mass death caused by catastrophe not related to deposition,
producing a dilated perthotaxy, such as the herd assemblage of Lep-
tomeryx. The life census killed will have been modified by perthotaxy.

3. Perthotaxic assemblages developed from normal mortality in
continuing populations. Accuracy of representation of mortality
depends upon timing and frequency of depositional episodes inter-
acting with differential perthotaxy.

4. Mechanically transported assemblages.

The last of these is absolutely unsuited for census studies or
studies of population dynamics, unless it can be demonstrated that
the transporting medium has taken a single, contemporaneous death
or perthotaxic assemblage and has carried it without selective abra-
sion or selective transport. Both of these requirements constitute
almost impossible situations. Mechanically transported samples,
therefore, are strongly but unpredictably biased samples of unknown
universes or combinations of universes. Each quarry assemblage
constitutes a unique sample of a separate universe of unknown size.
The combination of bias, uniqueness of sample, and unknown size of
universe makes statistical analysis indefensible. Since many anal-
yses of fossil mammal collections have been made upon just such
samples, let us consider certain of the weakness inherent in even the
more carefully reasoned ones.

Shotwell's (1958) method of arriving at a distinction between
"animals living together in a community from those also appearing
in the site but representing other communities" makes four basic
assumptions which are stated.

"1. Reasonably large collections from quarry assemblages are a
random sample of what is present in the quaiTy providing all speci-
mens are retained from the volume of sediment worked." This as-
sumption contains the subjective element of what constitutes a "rea-
sonably large" collection, plus a very much more serious error in
understanding of sedimentation. A quarry assemblage such as Shot-
well envisages is usually a lens-shaped accumulation of assorted sizes
and shapes of disarticulated bone in a sandstone matrix. Depending
upon local situations and sizes of bone, there may be placering out of
smaller bones in the lee of larger ones, concentrations of larger bones

440 FIELDIANA: GEOLOGY, VOLUME 16

at the upcurrent side of the deposit, size separation near the edges of
the lens, separation of partially flesh-covered bone from bone dry
before transportation, and many other sedimentary situations pre-
cluding a random distribution of elements from animals of different
sizes throughout the lens. No one portion of this non-randomly
assembled mass can give a random or a representative sample of the
whole; collection of the whole is necessary.

"2. An indication of the relative density of mammals of the
proximal community may be obtained from the use of the minimum
number of individuals." This depends, naturally, upon three non-
random variables, (a) The depth and velocity of the transporting
currents may be such that all elements above a certain size and shape
are left relict in the area from which bones are being washed, and all
elements below a certain size are transported on through the partic-
ular site later quarried, (b) Differences in shape between the same
element in different taxa strongly influence distance of transport.
Among Oligocene bones, for example, the astragulus of a Mesohippus
would roll much farther than the more angulated astragulus of a
Dinictis of the same size, (c) Sullegic' and trephic- factors militate
in favor of identification of bones belonging to monospecific genera or
monogeneric families, in any collection.

"3. If a community other than the proximal one is represented
in a quarry sample, that community must be present in the region of
the quarry." This, accepting the subjective decision of what consti-
tutes a region, depends upon the well-established fact that water
transport destroys bone in distances never over a few miles. It is
generally true, with only the unusual exception of flotation of gas-
inflated corpses.

"4. Mammals whose community in life was close to the site of
deposition will be more completely represented than will those whose
community was farther away." This depends upon the assumption
that all areas of a stream or beach system are equally subject to
erosion of equal power. Consider, for instance, a river-bank flood-
plain community immediately upstream of a large tributary whose
current is bringing in numerous bones from an erosional area five
miles away. A bar at the confluence would receive most of its bones

'Sullegic — Those factors influencing the collecting of fossils which determine
whether or not any particular fossil at the surface will find its way into a collection.

^Trephic — Factors incident to curating and identifying a specimen which de-
termine whether or not a fossil in a collection becomes available for use — Both
footnotes i and ^ in Clark et al., 1967, pp. 118-120.

CLARK AND GUENSBERG: LEPTOMERYX 441

from the tributary; only those single bones which adventitiously fell
into the main stream would represent individuals of the proximal
community. Since every site of erosion and of deposition is a con-
figurational rather than an imminent phenomenon (Simpson, 1963,
p. 24). and since every quarry site must be inteipreted in terms of its
individuality, this fourth assumption becomes untenable.

Shotwell's method also necessitates two other basic assumptions,
implicit but unexpressed: (a) that a quarry assemblage is always a
transported assemblage. This is usually but not universally true;
(b) that all elements of skeleton and dentition will respond equally
to abrasion and will be transported equal distances in the same cur-
rent. Thus one sees in his table (p. 273) rabbit molars equated with
proboscidean skulls, and an equid astragulus equated with its pelvis.
Voorhies (1969. appendix) presents careful experimental evidence of
extreme differences in rate and mode of transport. To anyone pos-
sessed of knowledge of stream transportation, Voorhies' evidence
belabors the obvious: Shotwell's basic assumption is mechanically
unsound. Since his population analyses are based upon purely
mechanical assemblages of clastic objects which happen to be fossil
bones, the analyses are equally unsound.

Van Valen (1964) carries this one step further by stating that
"the species present in the matrix may not have been in the same
proportions when alive. This could be due to differential destruction
or transportation prior to burial, which will be ignored because it
cannot be corrected for and because the faunas are balanced ..."
His statement: (1) overlooks the fact that Shotwell's purpose, no
matter how much in error, was specifically to deteiTnine the difference
between the proportionate abundance of species in the matrix and
the proportions in life; (2) states that a major known bias shall be
ignored because it cannot be evaluated. Surely this is peculiar
mathematics- — data know^n to be seriously inaccurate may be re-
garded as accurate, provided that the error cannot be evaluated; (3)
states that the faunas are balanced — an impossible conclusion, since
no census of any recent mammalian population has ever been taken
for comparison.

The majority of paleoecologic anabases of recent years have been
performed upon mechanically-transported assemblages no more reli-
able than the two cases cited above. It is to be hoped that realization
of the considerable biases and subjective opinions necessarily in-
volved in a studv of even so definite a perthotaxic assemblage as ours

442 FIELDIANA: GEOLOGY, VOLUME 16

will in the future engender distrust of transported assemblages before,
rather than after, the fact of publication.

A second major conclusion of this paper is the necessity for de-
tailed field observation by persons trained at sedimentation. Voor-
hies' (1969) excellent analysis bears witness to this. The contribu-
tions from study of the sediments to the present interpretation of
population dynamics in Leptomeryx are obvious. Differentiation be-
tween the types of fossil assemblage suggested above depends upon
study of field evidence. The seasonality of incrementation helps to
determine the age distribution which will be preserved. Environ-
ment of deposition, e.g., the swamp represented by Collection 26 of
this report, inevitably influences any paleoecologic interpretation
and can be determined only by field study. Use of the Nebraska
collection in this report is justified solely, in our opinion, by its close
correspondence with the Dakota collections. Otherwise, its inade-
quate field data fail to establish contemporaneity, and the purpose
of collection militates against completeness of the sample.

A third major conclusion relates to infant-juvenile mortality.
Kurt^n's careful analysis (1953, pp. 83-87) seems to indicate a gen-
eral rate of 55-81 per cent, with a suggested usual rate around 70
per cent. We believe that this is too high for mammals bearing
generally single young, one per annum, with life spans under eight or
nine years.

Over a period of years long enough to include both population
explosions and minima, an average female must produce somewhat
more than two individuals who survive to maturity, if the popula-
tion is to continue. Assuming, as in the case of most cervid popula-
tions not subject to human predation, that the proportion of males
and females is approximately 1:1. the amount above two young
must equal the number who survive to maturity but do not them-
selves live enough longer to produce two young who live to maturity.
Admittedly, the assumption of a 1 : 1 sex ratio is highly debatable.

Leptomeryx, if our presumptions are correct, had a life span of
seven to eight years and a birth rate of one per year. A doe during
a full life span could not have produced more than six fawns; due to
still-births and occasional missed pregnancies, the actual maximum
was probably between five and six. Seventy per cent of six is 4.2;
that is, a doe producing the absolute maximum number of fawns
would under this mortality rate have seen only 1.8 live to breeding
maturity. This would not have maintained the population, even if

CLARK AND GUENSBERG: LEPTOMERYX 443

the resulting fawns had all lived full life spans and themselves had
produced the maximum possible number of young. Either one of
our assumptions is wrong, oi- juvenile mortality was highly selective
against males, or the juvenile mortality rate was much less than 70
per cent. On entii-ely subjective grounds, it seems most probable
that Leptomeryx underwent a smaller juvenile mortality.

The very fact of numerous, large litters is usually equated with
a high infant-juvenile mortality. Conversely, single births and short
life span must equate with lower juvenile mortality. Were it not foi-
this, Leptomeryx producing at most six young per doe could not pos-
sibly have maintained populations stable relative to such animals as
Eumys and Paleolagus, in which a female of full but shorter life span
probably produced 30 to 50 j^oung.

As a fourth major conclusion, probably very few fossil assem-
blages represent pure life-samples, pure samples of catastrophic death,
or pure samples of normal mortality in relatively stable populations.

Let us accept, for the moment, our hypothesis of catastrophic
death due to epidemic in the case of Leptomeryx. Assuredly the
sample includes also those individuals dying under conditions of
normal mortality. The sample is therefore a life census population
taken by catastrophe, plus a normal death population, and no one
system of statistics is directly applicable. Any one collection will be
weighted toward a mortality sample or a life census by the interaction
of the size of the total life population, the virulence of the epidemics
or other catastrophes, the rate of natural mortality, the nature and
rate of perthotaxy, and the timing and nature of incrementation of
sediment.

Finally, this study seems to demonstrate the necessity for de-
veloping and maintaining multiple hypotheses. Clark et al. (1967,
p. 128) proposed as a reason for the high number of young-adult
deaths in Hypertragulus the action of an age-specific epidemic. A
second alternative explanation might be either a seasonal immigration
to the areas of sedimentation by young adults, or an emigration by
all others.

The combination of perthotaxy removing infant and juvenile
corpses, plus repeated general epidemics producing a young-adult
population and catastrophically sampling it, seems more probable
than an age-specific epidemic striking two genera. However, this
does not at all I'emove the possibility of age-specific epidemics.

The herd deaths seem to us conclusive evidence of death by epi-
demic. Once again, however, this does not remove the possibility

444

FIELDIANA: GEOLOGY, VOLUME Ifi

that large herds of older individuals were either dying of the same
disease or surviving without it in areas other than the sites of de-
position.

Finally, the possibility that x, the factor one has overlooked or
misinterpreted, leads inevitably to y, the hypothesis one has not even
considered, should never be forgotten.

We have thus at least three possibilities in addition to the one
preferred. Because choice between the four is based upon a subjec-
tive weighing of probabilities, we feel that none of the four can safely
be entirely discarded. We believe that a factor which cannot be
evaluated must never be ignored.

We wish to thank Professor J. R. Beerbower of McMaster Uni-
versity for critically reviewing the manuscript of this paper.

Table L — Paraconid Height
Collection: 26

Number Teeth Class M, M. M.,

14068
14074
14130
14132
14133
14134
14135
14136
14146
14147
14148
14149
14150
14151
14152
14153
14154
14155
14156
14157
14158
14159
14160
14161
14162
14163
14164
14165
14166
14167
14168
14169

P4-M,

LP4,M:,

P4 - M,

LP4-M,

LM,.,

LM,...

LM,-2

RM2-,

RM,

KM,

RM,

RM.

RM,

RM,

RM,

RM,

RM,

RM,

RM,

RM,

RM,

RM,

LM,

RM,

RM.2

RM,

RM,

RM3

RM3

RM3

RM,

RM.,

1
5 —

4 +

4

6

4

4-

4

4

4

5

4

4

1 +

4

4

4

4

4-

5-

4-

4-

4 +

4

5

6

4 +

4 +

4 +

4 +

4

5-

4.8

3.1
2.9
1.3
2.9

4.8
3.0

4.7
3.9
3.8
4.7

2.0
5.0
3.5

3.7 4.2

3.2
3.0
2.5
3.9

2.5

4.6 5.4

3.9
3.3
4.0
3.3
2.9

CLARK AND GUENSBERG: LEPTOMERYX 445

Table 1. — Paraconid Height
Collection: 26

Number Teeth Class M, M. M,

14170 RM. 4 +

14171 RM, 4 +

14176 P4-M, 5 1.2 2.6

14180 LP4-M, 4 3.8

14181 LM1.2 3+ 4.3

14182 LM,-o 4- 4.1 4.8

14183 LMi... 4 3.9 4.0

14184 LMi... 4+ 3.4

14185 LM.>-:i 4 2.9 3.4

14186 LM.-, 4 4.9

14187 LM.-., 3 4.7 4.9

14193 LM, 4 4.0

14194 LM, 4+ 4.2

14195 LM,-, 6 1.5 2.2

14196 LM, 4

14197 LM, 4 4.2

14198 LM, 4 4.4

14199 LM, 4

14200 LM, 4-

14201 LM, 2- 4.7

14202 LM, 4 3.3

14203 LM, 3 4.3

14204 LM. 4 3.9

14205 LM, 4 +

14206 LM. 4 5.2

14207 LM. 4 3.4

14208 LM. 4-

14209 LM. 4

14210 LM. 4 4.9

14211 LM. 4 4.5

14212 LM, 4

14213 LM:. 4 +

14214 LM, 4 +

14215 LMs 4+ 3.2

14216 LM:: 4-

14217 LM, 4- 5.4

14218 LM., 3.7

14219 LM.

14220 LM:, 6-

14221 LMs 5

14222 LM, 4 +
14224 LMiors 4

446

FIELDIANA: GEOLOGY, VOLUME 16

Table 2. — Paraconid Height

Collection:

32

Number Teeth

Class

M,

M2 Ms

14557

RMi.3

4

4.6 5.0

14558

RMi-,

5 +

2.5

14559

RP4-M3

4

3.2

3.9 4.1

14560

RP4-M,

5 +

1.9

2.1 2.5

20287

RMi

3 +

4.6

20288

RM,

1

5.1

20289

RMi

4 +

2.5

20290

RM,

4

3.1

20291

RMi

4 +

2.6

20292

RMi

4 +

2.5

20293

RM,

4

20294

RM,

1-

20295

RM,

4

20296

RM,

2-

20297

RM,

4 +

20298

LM,

5 +

20299

LM,

4-

20300

LM.>

4

3.3

20301

LM,

4

3.9

20302

LM,

4

20303

LM,

4

20304

LM,

4

3.2

20305

LM,

4

4.5

20306

LM,

4

3.1

20307

LM,

3-

3.7

20308

LM,

1-

5.2

20309

LM,

4

4.2

20310

LM,

6

20311

LM,

4

20312

LM,

4-

2.4

20313

LM.,

2-

5.2

20314

LM.,

2

5.1

20315

LM.,

2

20316

LM..

4

4.4

20317

LM.,

3-

20318

LM2

3-

5.4

20320

LM2

5 —

2.9

20321

LM.

4

20322

LMo

4-

3.2

20323

RMo

4-

4.0

20324

RM.

5 —

2.6

20325

RM.2

4

4.2

20326

RMo

4-

4.0

20328

RM,

3-

5.1

20329

RM2

4

4.8

20330

RM,

4-

4.7

20331

RMo

3-

5.3

20332

RM2

4-

3.4

20333

RM2

3-

4.7

20334

RM2

4

4.9

20335

RM2

4

20336

RM2

4

20337

RM2

4

20338

RM3

4

20339

RM3

4 +

20340

RM3

4 +

3.2

20341

RM3

4-

CLARK AND GUENSBERG: LEPTOMERYX 447

Table 2. — Paraconid Height
Collection: 32

Number Teeth Class Mi M, Mj

20342 RMs 5-

20343 KM:, 3 +

20344 KM, 2 +

20345 RM.-i 4+ 4.1

20347 RM, 4 4.0

20348 LMs 4 5.4

20350 LM, 4 4.4

20351 LMr, 3+ 6.1

20352 LMs 4 +

20353 LMs 4+ 5.8

20354 LMs 5 +

20355 LMs 4+ 2.7

20356 LMs 4+ 3.7

20357 LMs 5- 3.9

20358 LM3 4+ 3.5

20359 LMs 5

20360 LM3 4 +

20361 LM3 4-

20362 LM3 4- 5.1

20363 LMs 4

20364 LM3 5-

20374 RMi-o 6 1.7

20458 LMi-. 4+ 3.9

20459 RP4-M.2 5- 1.6 2.7

20460 P4-M2 4+ 3.3 4.1

20470 LDP4-

Mi 2- 4.6

20471 RDP4-

Mi 2- 4.6

20472 RMi 4

20473 RP4-M1 4 3.2

20474 RP4-M1 3

20475 RP4-M1 6 0.7

20476 LP4-M1 5-

20477 LP4-M, 5 +

20478 LP4-M1 4+ 2.6

20479 LM2-3 6 1.7

20480 LP4-Mi 4+ 2.5

20481 LMi-3 6

20482 LMi-2 4 3.7 4.7

20483 LMi-3 4- 4.1 4.9 5.0

20484 LM.-3 6 1.3 1.8

20485 LMi-2 4+ 2.7

20486 LMi-2 4- 4.0

20487 LP4-Mi 4

20488 LMi-2 4

20489 RP4-M1 4

20490 LMi-2 2- 5.4

20491 LM0.3 3

20492 LM2-3 6

20493 RM1.2 5 2.0

20494 LM,.2 2 +

20495 RM, 4 3.5 4.1

20496 RMi 2+ 5.0

20497 LM2-3 6 2.0

20498 RM2-3 5

20499 RM2-3 4+ 4.5

448 FIELDIANA: GEOLOGY, VOLUME Ifi

Table 2. — Paraconid Height
Collection: 32

Number Teeth Class Mi M2 Ms

20500

LM,.,

4 +

20501

LM.,.,

4 +

20502

LM,-3

4

3.8

20503

LM,-:,

5.5

20504

LM,-3

5

2.8

Table 3. — Paraconid Height

Collection: Sioux Co., Nebraska

Number Teeth Class Mi M2 Ma

450

LMi-3

5 +

2.4

2.7

2.7

480

LP:,-M3

5 —

3.0

3.6

497

RP3-M3

4

3.0

3.6

3.9

498

LM0.3

4

3.6

3.8

902

RP3-M,

4

903

P3-M:,

5

2.8

3.1

3.0

913

P3&

M,..;

4-

3.5

4.4

4.6

914

P .-3 &

M.>-:,

4 +

3.3

4.3

915

P3-M,

4-

3.6

916

P3-M3

4

3.3

3.4

4.7

917

P3-M3

4 +

2.5

3.5

4.3

918

P3-M3

4 +

3.4

3.7

924

M,.3

4

2.5

925

P4-M.,

4-

4.0

4.8

926

DP4-M,

1 +

4.8

928

M2-3

4

4.5

4.1

929

DP4-M,

2-

4.8

930

P4-M3

5

2.0

2.8

3.2

931

P4-M2

4 +

2.8

3.5

935

P.,-M,

4 +

2.4

2.7

936

P3-M,

4

3.8

938

P3-M3

4 +

2.9

3.6

3.8

939

P.2-M,

4 +

2.5

2.7

3.1

940

P2-M,

5 +

1.7

942

RM,.3

4-

3.7

4.1

943

LP2-M3

4 +

3.1

3.8

4.0

944

LP4-M.

4

3.0

3.5

4.3

945

LM0.3

4-

4.0

4.6

946

LDP4

M,

4 +

2.3

3.2

947

LP3-M3

2 —

4.6

987

LP2-M.,

4 +

3.2

988

LP.-M,

4 +

2.1

2.8

3.0

989

RP2-M3

4

2.6

3.7

CLARK AND GUENSBERG: LEPTOMERYX
Table 3.— Paraconid Height

Collection: Sioux Co., Nebraska

Number Teeth Class Mi M,

M,

449

990

RP-Ms

4-

3.9

3.9

4.5

991

RP.-M.

4

3.3

4.1

4.6

992

RPs-M,

4 +

2.8

3.7

3.7

993

RP=-M3

4

2.9

3.5

3.0

994

RPa-M,

5 —

2.6

995

LP3-M3

5 +

1.7

2.3

2.8

996

LP,-M3

6

2.2

997

LP3-M3

4

3.1

3.3

3.9

998

LP3-M3

4

3.0

3.0

3.8

999

LP..3 &

M..3

4-

3.8

4.4

4.7

1000

LPs-M-

4

3.3

3.9

4.5

1001

LP3-M1

4 +

2.3

1002

LP3-M1

4 +

3.3

1004

RDPs-

Mo

9

4.7

1031

RP1-M3

4-

3.6

4.3

4.3

1032

RP4-M3

4 +

3.0

3.6

3.9

1033

RP4-M3

4 +

2.4

3.0

3.5

1034

RP4-M3

4 +

3.3

3.9

4.2

1035

RP4-M3

4

3.1

4.0

4.4

1036

RP4-M3

4

4.0

4.3

1037

RP4-M3

4

4.0

4.3

4.5

1038

RP4-M3

4

3.1

3.7

4.1

1039

RDP4-

M3

3-

4.0

4.9

1040

RP4-M3

5 —

2.1

3.3

1041

RP4-M3

4

3.7

3.8

4.3

1042

RM,.3

4-

3.2

3.6

3.9

1043

RM,.3

4-

3.2

5.0

5.3

1044

RM..3

4

3.6

3.7

1045

RM,-3

4

3.4

4.1

4.2

1046

RM,-3

4 +

2.8

3.3

3.4

1047

RM1.3

5 +

2.0

2.4

2.4

1048

RMi-,

4

3.0

3.5

3.9

1049

RMi-3

4

3.4

3.7

3.8

1050

RM,.3

4 +

3.0

3.7

3.9

1051

RM,-3

4

3.6

3.5

3.9

1052

RM,.3

6

2.6

1053

RM,.3

4-

4.5

4.9

1054

RM,.3

4-

3.5

4.5

4.9

1055

RM1.3

4

3.0

4.0

4.2

1056

RMi-3

5 +

1.9

2.8

3.2

1057

RM1.3

5

2.2

2.7

3.1

1058

RP4-M.2

4 +

3.3

3.9

1059

RP4-M3

4-

3.7

4.2

4.6

1060

RP4-M,

4-

3.8

4.8

1061

RP4-M3

4-

3.7

4.0

4.5

1063

RM2-3

4-

4.7

5.0

1064

RM2-3

4

3.3

4.0

1065

RM2-3

5-

3.1

3.2

1066

RM,-,

4-

3.7

1067

RM,.3

4 +

2.9

2.9

1068

RM,.3

5

2.9

3.0

1069

RM3

4 +

4.2

1070

RM.,

4 +

4.0

1071

RM,

6

2.7

450 FIELDIANA: GEOLOGY, VOLUME Ifi

Table 3. — Paraconid Height

Collection: Sioux Co., Nebraska
Number Teeth Class Mi M2 M,

1072

RM,

4 +

3.9

1073

RM,

4 +

4.2

1074

LPs-M,

4-

6.1

4.2

1075

LP4-M:,

4

3.3

3.9

4.5

1076

LP,-M3

4 +

2.9

3.0

3.1

1077

LP4-M.

4 +

2.5

3.3

3.7

1078

LP4-M,

4 +

2.9

3.1

1079

LP4-M,;

5 +

2.1

2.8

3.4

1080

LM,.:;

6

1.9

2.8

1081

LM,.,

4 +

2.5

2.8

3.1

1082

LM.-3

4 +

2.4

2.8

3.4

1083

LM,.3

4

4.2

4.2

1084

LM,-,

4

4.1

4.5

1085

LM,..

4 +

2.9

3.2

3.6

1086

LM,.,,

4

2.6

3.3

3.8

1087

LM,.3

5 —

2.7

3.8

1088

LP4-M2

4

2.9

3.3

1089

LP,-M,

4 +

2.6

3.0

1090

LP4 M.

4 +

3.4

1091

LM,.,

5

2.6

2.8

1092

LM,.,

4 +

No measure-
ments possible

1093

LM,.,

4

4.0

4.7

1094

LMo.;,

4

4.0

4.2

1095

LM3

4

4.4

1406

P.,-M,;

M3

4

3.8

5.1

1409

RP2-M.,

5-

2.1

2.6

3.0

1425

RP,-M.,

4-

3.8

4.6

4.9

Table 4.— Partial Life Table

Leptomeryx. Sioux County, Nebraska
Age dx Ix lOOOqx

0-

-1

397

1000

397

1-

-2

256

603

425

2-

-3

192

347

553

3-

-4

128

155

826

4-

-5

27

0

0-

-6

27

0

6-

-7

2.6

27

1000

Average age

2.18 years.

Leptomeryx. Sage Creek — Coll. 32-26
Age dx Ix lOOOqx

0-1

517

1000

517

1-2

189

483

392

2-3

103

294

350

3-4

51

191

267

4-5

103

140

736

5-6

37

37

1000

Average age 2.14 years.

CLARK AND GUENSBERG: LEPTOMERYX 451

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