SI 12
HARVARD UNIVERSITY
Library of the
Museum of
Comparative Zoology
OCCASIONAL PAPERS
of the
MUSEUM OF NATURAL HISTORY'S.
The University of Kansas
Lawrence, Kansas JiJN Z^IQfc
NUMBER 111, PAGES 1-45 13 JUNE 1984
**S
AGE VARIATION IN VOLES (MICROTUS
CALIFORNICUS, M. OCHROGASTER) AND ITS
SIGNIFICANCE FOR SYSTEMATIC STUDIES
By
J. P. Airoldi' and R. S. Hoffmann2
Age variation plays an important role in systematic studies. This is
especially true for arvicolid ( = microtine) rodents, most of which do not
have a definitive adult size. Problems arise when comparing samples from
different localities and unknown, but probably different, age structure.
Many authors assume that age variation is the same in the several
populations analyzed. There is no way to test whether the observed
differences in morphology are due to geographical, environmental or age
variation, unless some of the factors influencing variation are known or
can be estimated. The purposes of this paper are to analyze the nature of
ontological variation in morphology during the course of post-natal growth
in known-age voles of two different species in order to determine: 1)
which characters may be measured more reliably; 2) whether significant
interspecific differences in growth patterns and morphology occur; 3)
which characters best discriminate between species; and 4) which charac-
ters are least influenced by age, and which are most influenced, in order to
predict age from skull morphology.
Chitty (1952) was the first to note that season of birth influenced
subsequent growth rate in juvenile M. agrestis; young born in spring or
early summer grew rapidly, and attained puberty during the summer of
their birth, whereas young born in late summer or fall grew slowly, if at
all, until the following March. This pattern was subsequently confirmed
by Cowan and Arsenault (1954) for M. oregoni. Barbehenn (1955) also
found differential growth and size in Microtus pennsylvanicus; males born
1 Postdoctoral Fellow, Museum of Natural History, The University of Kansas, Lawrence,
Kansas 66045. (Present address: Zoological Institute, University of Bern. Baltzerstr. 3. 3012
Bern. Switzerland).
2 Curator of Mammals. Museum of Natural History, and Professor, Department of
Systematics and Ecology. The University of Kansas. Lawrence, Kansas 66045.
2 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
after mid-June did not reach puberty in the same season, while it took
females born at the same time six weeks to reach that stage. Differences
could not be related to soil factors, weather or forage composition. Bee
and Hall (1956) noted that in Microtus miurus, individuals born in the
winter grow more slowly and never become as large as individuals born in
the spring. Pinter (1968) found that body weight in Microtus montanus
was positively correlated with day-length and amount of food. Martinet
and Spitz (1971) pointed out the influence of photoperiod and quality of
food on growth in Microtus arvalis, and Pistole and Cranford (1982)
recorded reduced growth rate in M. pennsylvanicus under short pho-
toperiod. Pokrovski (1971) noted that for Lagurus lagurus and Microtus
gregalis average age of initial reproductive activity depended on date of
birth, and that there is seasonal variation in body weight, which differs in
successive generations. In Microtus oeconomus there is furthermore a
significant difference in weight of crystalline lens in specimens of the same
age born in spring or born at the end of summer.
Lidicker (1973) found that the period of reduced or suspended growth
in M. californicus was not winter in the Mediterranean climate of coastal
California, but rather was during the dry season, usually June through
October, under field conditions. Brown (1973) studied Microtus pennsyl-
vanicus in the field and reported seasonal differences in growth. Young
born in spring and early summer reached adult size in twelve weeks or
less, and then lost weight in fall. Animals born in middle to late summer
stopped growing in the fall and resumed growth in the spring; they
maintained weight throughout the Minnesota winter. In contrast, Iverson
and Turner (1974), studying the same species under the more severe
winter conditions typical of Manitoba, found that individuals lost consider-
able weight during mid-winter before beginning to gain again in February.
Winter weight reduction in juveniles was also found in M. xanthognathus
in central Alaska by Wolff and Lidicker (1980), who interpreted the
phenomenon as a means of reducing food requirements. Thomas (1976)
found that in several rodents, craniometric variation was correlated with
climatic variables such as length of growing season, precipitation,
temperature, moisture deficit and evapotranspiration. Daketse and Mar-
tinet (1977) noted for Microtus an'alis a decrease in body growth and
fertility with increasing temperature. Largest and most fertile animals
were those raised at low temperatures, under long-day conditions and fed
with alfalfa harvested in the spring. Huminski and Krajewski (1977) found
a higher body growth rate during a warm winter than in a cold one for
Microtus arvalis. Voles kept in the laboratory showed the least inhibition
of growth. Cole and Batzli (1978) noted an influence of supplemental food
on body growth of Microtus ochrogaster, and Batzli et al. (1977) found
that growth could also be suppressed by social factors. Kaneko (1978) also
observed seasonal and sexual differences in absolute and relative growth
for Microtus montebelli, and Tast (1978) reported variation from year to
year in weights of over-wintering M. oeconomus. Inhibition of juvenile
growth rate because of progeny-adult social interactions was first sug-
SIGNIFICANCE OF AGE VARIATION IN VOLES 3
gested for M. townsendii by Boonstra (1978), and similar results were
obtained by Smolen and Keller (1979) for M. montanus.
Petterborg (1978) showed that the length of photoperiod affected body
weight in Microtus montanus. Animals raised under a longer photoperiod
gained weight more rapidly than those raised under a short one. Thyroxin
levels were correlated with length of photoperiod.
Figure 1 summarizes these observations and also includes additional
factors which may play a role in growth, e.g. behavior and competition.
Some of the factors interact. Temperature and moisture are interdepend-
ent; their levels can have an influence per se, but a seasonal cycle can be
superimposed on them with effects on the vegetation, i.e. food resources.
Sampling techniques, by selecting animals of given sex, age or hierarchi-
cal position in the population, can also be a source of bias in systematic
investigations (Pizzimenti, 1979).
In systematics, phenotype is used to infer genotypic relationships
between individuals (Fig. 1). As pointed out by Frelin and Vuilleumier
(1979), a certain amount of information is lost or undergoes transforma-
tion in the ontogeny of an individual. Many factors alter the expression of
the genotype and one has to be aware that the skull of a vole, for instance,
expresses only part of the genetic information. As long as it is possible to
estimate the importance of the different components of variation, we are
able to make meaningful comparisons, systematically speaking, between
individuals or populations. Only then are we sure to compare similar
components of variation. As an example, the following questions can be
asked: are the differences observed when comparing animals from two or
GENOTYPE
DNA
Genes
EXTRINSIC FACTORS
^Location (longitude, latitude)
GEOGRAPHYC-Altitude
< Temperature
Moisture
Light
SEASONALITY
NUTRITION
^Intraspecific
BEHAVIOR^,
Interspecific
COMPETITION
-»Hphenotype|
Size
Shape
AGE
PHYSIOLOGY
BIOCHEMISTRY
SEX
INTRINSIC FACTORS
Figure 1.— Diagram of factors influencing growth and development in arvicolid rodents.
4 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
more localities only geographical and not due to age, food, or seasonality?
Anderson (1959) discussed this problem and pointed out the different
sources of variation which can overshadow or be mistaken for geographic
variation. Most authors who studied variation (age, geographic) in
arvicolids (Howell, 1924; Goin, 1943; Stombaugh, 1953; Snyder, 1954;
Martin, 1956; Anderson, 1956, 1959, 1960; Choate and Williams. 1978)
used morphological features such as degree of development of lambdoidal
crests, frontal ridges or sutures to assign animals to given age classes, thus
reducing the influence of age variation. However, the descriptions of
characters given are usually imprecise, resulting in groups lacking
homogeneity. Frank and Zimmermann (1957) considered that for Microtus
an'alis "variability of growth is so important in all age classes, that age
determination, based on morphological characters is impossible." A
recent systematic study of Pitymys (Spitz. 1978) does not even mention
age variation and includes all the specimens collected. Zejda (1971),
working with Clethrionomys glareolus, observed that in systematic stud-
ies, animals of the same developmental stage, even though of different
ages, should be used. For example, overwintered individuals captured in
June or later, while representing a mixture of different cohorts, have one
characteristic in common: their growth is almost complete. Zejda's
approach would be feasible if there were only a delay in growth; i.e. if all
specimens eventually reached a given size after a certain lapse of time.
Unfortunately this is not the case.
Thus, skulls exhibiting similar morphological features may not be the
same age, while skulls of the same age are not necessarily morphologically
identical, even when growth is completed. Since seasonal variation is
important in voles, it is advisable to select animals collected at the same
time, and of those, choose specimens of the same age (see Anderson,
1959). An obvious drawback of this procedure is that it often re-
duces sample size to a point which makes modern statistical methods
inapplicable.
One of the purposes of the present paper is to study age variation in
Microtus californicus and M. ochrogaster and predict age on the basis of
skull measurements. Similar studies have been done by Lidicker and
MacLean (1969) on Microtus californicus and by Hoffmeister and Getz
(1968) on Microtus ochrogaster, employing voles reared in captivity. The
material used here is, in part, the same used in those previous studies. The
influence of age structure in samples when comparing species and sexes
with each other was also investigated. Furthermore, some relationships of
size and shape have been examined using principal components and
canonical correlation analyses.
Microtus californicus and M. ochrogaster have allopatric distributions
(Hall, 1981), and are placed in two different subgenera, Microtus and
Pedomys. There are differences in the bacula (Anderson, 1960). However,
the anatomy of the diastemal palate (Quay, 1954a) and the Meibomian
glands (Quay, 1954b) are not greatly different and the chromosome
numbers are the same in both species (Matthey, 1957).
SIGNIFICANCE OF AGE VARIATION IN VOLES 5
The main sources of variation (specific, age, sexual) are known. They
are also of different orders of magnitude. This should enable us to
interpret our results with fewer difficulties than when dealing with groups
in which many factors can be responsible for the observed variation.
MATERIALS AND METHODS
Specimens
Of the 373 specimens of lab-reared Microtus californicus used by
Lidicker and MacLean (1969) we used 314. Those eliminated were either
older than one year or showed malformations which made measurements
unreliable. Only 144 specimens from the original 191 studied by
Hoffmeister and Getz (1968) were used for that reason, and also because
some young individuals had skulls too fragile to measure. Twenty
specimens of Microtus ochrogaster from the field (8 males and 12 females)
of known age, collected by Martin (1956) were added to those from
Illinois, increasing the sample size to 164. Table 1 summarizes the sample
sizes according to age and sex of the two species considered.
Measurements
A total of 48 skull measurements (to the nearest 0.1 mm), plus
mandibular and cranial weights (to the nearest mg) were taken for each
Table 1. Sample sizes by species, sex, and age class (field coll.).
M.
californicus
M. «
ichrogaster
AGE (in days)
males
females
males
females
0- 19
21
13
4
3
20- 39
14
12
7
9
40- 59
28
22
8 (1)
5(2)
60- 79
17
15
10 (3)
4(2)
Age-Class 1
80
62
29 (4)
21 (4)
80- 99
20
19
5 (1)
8(1)
100-119
23
19
1 (1)
2(2)
120-139
12
15
8 (2)
5 (3)
140-159
15
4
8
2
160-179
13
9
0
0
180-199
3
6
7
5(1)
Age-Class 2
86
72
29 (4)
22(7)
200-219
0
1
4
10
220-239
1
1
0
0
240-259
1
2
4
6
260-279
1
0
8
2
280-299
2
2
0
0
300-319
0
0
3
8
320-339
0
0
7
2
340-359
1
1
0
0
360-379
1
0
4
5 (1)
Age-Class 3
7
7
30
33 (1)
Total
173
141
88 (8)
76(12)
6 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
specimen. Head and body lengths were obtained from specimen labels.
The measurements are described in Table 2, and illustrated in Figs. 2 and
3. Measurements were divided into 3 groups: lengths (L). widths or
breadths (B) and heights (H). Those marked by * were taken with needle
point calipers, those by a + with an occular micrometer (10 x ); all others
were taken with dial calipers. For H 1 , a glass blade was put underneath the
bullae tympanicae, thus defining a plane passing through the last upper
molars, from which we measured the distance to the top of the skull.
Thickness of the blade was then subtracted. The skulls were weighed on a
Mettler balance.
Table 2. Descriptions of cranial and mandibular measurements used. * measured with
needle-point calipers. + measured with ocular micrometer. All other measurements
conventional calipers.
LI
condylo-incisor length
L2
condylo-incisive length
L3
occipito-nasal length
L4
condylo-zygomatic length
L5
alveolo-incisor length
*L6
diastema length
*L7
alveolar length of upper
molar toothrow
L8
upper molar toothrow
length
L9
length of incisive foramen
*L10
incisivo-foramen length
Lll
hamular-toothrow length
L12
condylo-molar length
L13
nasal length
*L14
frontal length
*L15
parietal length
*L16
interparietal length
L17
zygomatic aperture length
+ L18
basioccipital length
L19
mandibular toothrow
length
L20
mandibular length I
posterior point of occipital condyle to most anterior
part of incisor
posterior point of occipital condyle to anterior point
of incisor at its alveolus ( 1 1
posterior point of occipital bulge to anterior point of
nasal ( I )
posterior point of occipital condyle to antero-supe-
rior edge of zygomatic process of maxilla (2)
posterior end of last molar to anterior point of
incisor at its alveolus (2)
anterior point of alveolar margin of 1st molar to
posterior point of alveolar margin of incisor (3)
posterior point of alveolar margin of last molar to
anterior point of alveolar margin of first molar ( 1 )
measured at the crowns
anterior to posterior point of foramen ( 1 )
anterior point of incisive foramen to posterior point
of alveolar margin of incisor
anterior crown of 1st upper molar to posterior part
of hamular process
posterior point of occipital condyle to anterior
crown of 1st upper molar
anterior point of nasal to suture with frontal ( 1 )
naso-frontal suture to fronto-parietal suture in the
sagittal plane
fronto-parietal suture to parieto-interparietal suture
in the sagittal plane
parieto-interparietal suture to interparieto-supraoc-
cipital suture in the sagittal plane
anterior to posterior margin of zygomatic aperture
(1)
basioccipito-basisphenoid suture to closest point on
margin of foramen magnum in the sagittal plane
measured at the crowns
most anterior part between coronoid process and
condyle to anterior ( = lowest) point of incisor at its
alveolus
SIGNIFICANCE OF AGE VARIATION IN VOLES
T\BLE 2.
(Continued)
*L21
mandibular diastema
length
L22
mandibular length II
L23
supraoccipital length
L24
supraoccipital-interparie-
tal length
L25
mandibular length III
*L26
alveolar length of man-
dibular toothrow
Bl
nasalia width
B2
rostral width
B3
zygomatic width
B4 interorbital width
B5 lambdoidal width
+ B6 incisive foramen width
+ B7 palate w idth
+ B8 pterygoid width
B9
hamular width
BIO
paroccipital width
Bll
condylar width
B12
foramen magnum width
B13
incisor width
B14
anteorbital constriction
width
HI
skull height 1
H2 skull height II
H3 skull height III
H4 zygomatic arch height
H5 foramen magnum height
H6 mandibular height I
H7 mandibular height II
H8 mandibular height III
anterior point of alveolar margin of 1st lower molar
to posterior point of alveolar margin of incisor (see
Fig. 3A)
most posterior part of condyle to most anterior part
of 1st molar at the crown
upper margin of foramen magnum to lnterparieto-
supraoccipital suture in the sagittal plane
upper margin of foramen magnum to parieto-inter-
parietal suture in the saggital plane
most posterior part of condyle to anterior ( = lowest)
point of incisor at its alveolus
as for L7
greatest width over nasalia
across bulge over foramen infraorbitale (3)
between the lateralmost points on zygomatic arch
(1)
between medial points of interorbital constriction
(1)
across lambdoidal processes (greatest width) (2)
greatest width
between medialmost points on alveolar margin of
1st molar ( 1 )
between most anterior margin of pterygoid fossae
(see Fig. 3B)
greatest width across hamular processes
greatest width across paroccipital processes
greatest width across external margin of occipital
condyle
greatest width of foramen magnum
greatest width at level of anterior alveolus of in-
cisors (see Fig. 3C) (4)
between medianmost part of fossae
perpendicular distance from a plane going through
the most inferior part of the bullae along the crown
of the most prominent molar, to highest point on
cranium (2)
from basioccipito-basisphenoid suture to inter-
parieto-parietal suture in the sagittal plane
from anterior alveolar margin of 1st molar to suture
between nasal and frontal
greatest height (usually near maxillar-jugal suture)
greatest height
from lowest point on angular process to highest
point on condyle
from lowest point between coronoid process and
condyle to closest point on anterior part of angular
process
from anterior alveolar margin of 1st molar to
posterior face of symphyseal eminence (see Fig.
3D)
HB head and body length
CRANW cranial weight
MANDW mandibular weiaht
(1) after Anderson (1969)
(2) after Howell (1924)
(3) after Pietsch (1970)
(4) after Lidicker and MacLean (1969)
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
\
^-<c-^
3
i
as
4?
\v
B*
*
:ct
~(
M^
1
ks=
ilS£3
Ej
Figure 2. — Diagram of cranial and mandibular measurements employed in this study.
SIGNIFICANCE OF AGE VARIATION IN VOLES
Figure 3.— Detail of certain measurements employed in this study; see also Table 2.
Computations and programs used
Computations were made on the Honeywell 66-60 computer of the
University of Kansas Academic Computer Center. The following BMDP
programs were used (Dixon and Brown, 1977): P-AM, description and
estimation of missing data; P-2R, stepwise regression; P-9R, all possible
(best) subsets regression; P-4M, factor analysis (principal components
option); P-6M, canonical correlation analysis; and P-7M, stepwise dis-
criminant analysis.
Estimation of missing values
Some measurements could not be taken on certain specimens, resulting
in data matrices with missing values. Because programs used in analyses
delete cases which have missing values in one or more variables, we
estimated missing values with the program which uses simple regression
on variables that showed the greatest correlation with the missing
variables. Many skulls were damaged in the rostral region, so measure-
ment B2 was eliminated from multivariate analyses. For the remaining
variables, 37 (22.6%) of the M. ochrogaster specimens had missing
values, while in M. califomicus there were 27 (8.6%). Overall, there were
314 missing values distributed over 64 specimens.
RESULTS
Accuracy of measurements
Ten specimens (five males and five females) were measured repeatedly
to estimate measuring error (seven of them five times, two six times and
one 10 times). The specimen measured 10 times was included twice in
10 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
each series, first as specimen 1, and then as specimen 5.
A two-way ANOVA, for which we considered only the first 5
measurements for each specimen, made it possible to determine whether
the results differed significantly from each other. Only LI 3 and H2
showed significant values for Fc (test between the columns) because they
are difficult to define accurately. L5, Bll, B12, and HI also exhibited
rather high Fc values.
Table 3a presents means, standard deviations, coefficients of variation
(CV) and standard errors for the 10 repeated measurements for all skull
variables of KU 84940. The relative error made in measuring a given
dimension is given by the CV values (Sokal and Rohlf, 1969). L15, L16,
B6, B7, B13, H4 show high values. Table 3b gives a weighted average for
the standard deviations of all specimens measured repeatedly and com-
puted according to the formula, r~ _ . „, ~~ ~ ~
v /Six, - x,)- + E(Xt-x,)2 ... E(x, -x.)
where s for each measurement is the square root of the sum of the sums of
deviation squares for each individual i divided by the corresponding
number of degrees of freedom (n = no. measurements). In cases with skull
damage, only 9 (8 or 7) specimens were used, because a given measure-
ment could not be taken. In Figure 4, a mean CV, computed using s and a
mean x for the 10 measurements, was plotted against x for each variable
and according to the measuring technique. The curve of expected CV was
computed by assuming for all of the variables, an s equal to 0.0496, the
value obtained for LI . That allowed comparisons of the different measure-
ments with each other. The CV-values of Figure 4 agree quite well with
those of Table 3a for specimen No. 84940. There are a few exceptions,
however; L17, which is more variable in No. 84940, and L18 with the
opposite tendency. By examining Figure 4, it is possible to select among
the plotted variables those which are close to the curve or even below it.
They are the ones less subject to measuring error, hence, the most reliable.
No obvious correlation with the measuring technique used is apparent.
Quite a few width measurements lie below the curve. Unfortunately, some
of the variables showing a relatively great amount of measuring error are
precisely those particularly interesting for systematic studies or age
estimation; this is discussed below.
Principal components analysis (PC-analysis)
Principal components were extracted on the correlation matrix of log, 0
transformed variables. The PC-analysis performed on the whole sample
(n = 478) revealed that approximately 65% of the total variation was
explained by the first factor (Table 4). A plot of the first two PCs showed
the species well separated (Fig. 5). Younger animals are on the left side of
the figure and older ones on the right. The greater part of the interspecific
variation was accounted for by factor 2, whereas factor 1 was mainly an
age-related size component. Specimens a (M. californicus MVZ 60182)
and b (M. ochrogaster UI 32595) of Figure 5 are outliers. The KU
specimens lie within the Illinoian population so we included them in
SIGNIFICANCE OF AGE VARIATION IN VOLES 1 1
Table 3. Statistics for repeated measurements, a) mean (x), standard deviation (s),
coefficient of variation (CV) and standard error (s^) for the 10 repeated measurements of
specimen No. 84940 (M. ochrogaster). b) mean standard deviation (s) for the repeated
measurements based on 10 specimens. Degrees of freedom in parentheses (Seven specimens
were measured 5 times, two 6 times and one 10 times).
a
b
s
X
s
CV
sx
(df)
LI
28.22
0.0422
0.1494
0.0133
0.0496
(47)
L2
28.13
0.0483
0.1717
0.0153
0.0406
(47)
L3
27.74
0.0516
0.1863
0.0163
0.0534
(42)
L4
22.02
0.0632
0.2872
0.0200
0.0460
(40)
L5
17.25
0.0527
0.3055
0.0167
0.0563
(47)
L6
8.34
0.0516
0.6192
0.0163
0.0617
(46)
L7
6.81
0.0568
0.8335
0.0180
0.0519
(47)
L8
6.27
0.0483
0.7704
0.0153
0.0503
(47)
L9
5.00
0.0000
0.0000
0.0000
0.0549
(47)
L10
2.78
0.0422
1.5167
0.0133
0.0405
(47)
Lll
10.00
0.0000
0.0000
0.0000
0.0462
(45)
L12
17.69
0.0316
0.1788
0.0100
0.0432
(47)
L13
7.55
0.0527
0.6981
0.0167
0.0600
(40)
L14
10.98
0.1033
0.9406
0.0327
0.0960
(47)
L15
5.15
0.1179
2.2884
0.0373
0.1221
(47)
L16
3.07
0.1252
4.0771
0.0396
0.0844
(47)
L17
10.63
0.1767
1.6623
0.0559
0.0977
(45)
L18
4.63
0.0483
1.0433
0.0153
0.1001
(43)
L19
5.97
0.0949
1.5891
0.0300
0.0558
(47)
L20
12.65
0.0707
0.5590
0.0224
0.0604
(40)
L21
3.67
0.0483
1.3162
0.0153
0.0756
(47)
L22
12.15
0.1080
0.8890
0.0342
0.0706
(47)
L23
3.38
0.0422
1.2474
0.0133
0.0495
(36)
L24
6.56
0.0516
0.7871
0.0163
0.0508
(36)
L25
15.99
0.0316
0.1979
0.0100
0.0812
(40)
L26
6.56
0.0516
0.7872
0.0163
0.0460
(40)
Bl
3.34
0.0516
1.5461
0.0163
0.0331
(46)
B2
5.60
0.0000
0.0000
0.0000
0.0379
(43)
B3
16.69
0.0316
0.1895
0.0100
0.0384
(47)
B4
4.30
0.0000
0.0000
0.0000
0.0422
(47)
B5
12.77
0.0483
0.3783
0.0153
0.0526
(41)
B6
1.28
0.0422
3.2940
0.0133
0.0261
(47)
B7
2.20
0.0471
2.1427
0.0149
0.0537
(36)
B8
4.26
0.0516
1 .2122
0.0163
0.0613
(43)
B9
3.09
0.0316
1.0234
0.0100
0.0835
(46)
BIO
8.79
0.0568
0.6458
0.0180
0.0678
(42)
Bll
5.81
0.0568
0.9770
0.0180
0.0477
(43)
B12
4.52
0.0422
0.9328
0.0133
0.0444
(43)
B13
3.12
0.0632
2.0271
0.0200
0.0494
(47)
B14
3.51
0.0316
0.9009
0.0100
0.0225
(40)
HI
10.74
0.0516
0.4808
0.0163
0.0363
(40)
H2
7.84
0.0699
0.8918
0.0221
0.0649
(40)
H3
8.76
0.0699
0.7982
0.0221
0.0723
(40)
H4
1.76
0.0516
2.9341
0.0163
0.0529
(47)
H5
4.32
0.0632
1.4640
0.0200
0.0170
(28)
H6
8.61
0.0316
0.3673
0.0100
0.0802
(36)
H7
5.88
0.0422
0.7171
0.0133
0.0547
(39)
H8
5.70
0.0471
0.8270
0.0149
0.0447
(47)
12
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
3.0
2.5
2.0
>
u
1.5
1.0
0.5
OL25
10
15
20
25
Figure 4.— Plot of average CV against x (mean for the 10 repeated skull measurements of
specimen No. 84940). and according to different measuring techniques. Open circle— normal
dial calipers (outside); solid circles— normal dial calipers (inside): triangles— needle-point
calipers; squares— micrometer.
further analyses. All variables with loadings greater than 0.500 on factor 2
were also selected by the stepwise discriminant analysis program
(BMDP-7M) to separate the species (see below; Table 6), with the
exception of L10, L15, and L24. Loadings for the first three factors
(analyses performed on each species treated separately) show that approx-
imately 66% of total variation in M. ochrogaster and 68% in M.
californicus can also be interpreted as an age related size factor. Factor 2
accounts for only 4.5% and 6.6% of the total variation in each species,
respectively; its interpretation is somewhat difficult. Most variables with
high loadings are those selected in the discriminant analysis to separate the
sexes (see below; Table 8), with the exception of B12 in M. ochrogaster
and L16, L24 and B14 in M. californicus. A PC-analysis by sex for each
SIGNIFICANCE OF AGE VARIATION IN VOLES
13
Table 4. Loadings of variables on first five PCs from a PC-Analysis on all specimens
(n = 478) of M. californicus and M. ochrogaster (males + females) using the correlation
matrix. I^g, ^transformation of all variables. ** loadings greater or equal to 0.750.
* loadings greater or equal to 0.500 but less than 0.750. Other values— loadings greater or
equal to 0.250 but less than 0.500. 0.— loadings less than 0.250. VP— variance proportion
explained by each component. %— cumulative percentage of variance explained by each
component.
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
LI
0.980**
-0.
-0.
-0.
-0.
L2
0.981**
-0.
-0.
-0.
-0.
L3
0.979**
-0.
-0.
-0.
-0.
L4
0.977**
-0.
-0.
-0.
-0.
L5
0.974**
-0.
-0.
-0.
-0.
L6
0.891**
-0.365
-0.
-0.
-0.
L7
0.894**
0.284
0.
0.
0.
L8
0.941**
0.
0.
-0.
0.
L9
0.871**
0.
0.263
-0.
-0.
L10
0.658*
-0.551*
-0.329
-0.
-0.
Lll
0.961**
-0.
-0.
-0.
0.
L12
0.982**
-0.
-0.
-0.
-0.
L13
0.939**
0.
-0.
-0.
-0.
L14
0.651*
-0.518*
0.
0.
-0.
L15
0.
-0.655*
0.416
-0.
0.
L16
0.318
0.836**
-0.282
0.
-0.
L17
0.908**
-0.
-0.
-0.
-0.
L18
0.938**
0.
-0.
-0.
-0.
L19
0.920**
0.
0.
-0.
0.
L20
0.785**
-0.528*
-0.
-0.
-0.
L21
0.548*
-0.347
-0.
0.285
-0.
L22
0.962**
-0.
0.
-0.
-0.
L23
0.630*
-0.318
-0.
0.377
-0.259
L24
0.613*
0.554*
-0.356
0.
-0.
L25
0.955**
-0.
0.
-0.
-0.
L26
0.893**
0.
0.
-0.
0.
Bl
0.780**
0.
0.
0.273
0.
B3
0.972**
-0.
-0.
-0.
0.
B4
-0.
-0.751**
-0.
0.
0.464
B5
0.955**
-0.
-0.
0.
0.
B6
0.327
0.750**
0.307
0.
-0.
B7
0.
0.
0.578*
0.555*
-0.
B8
0.793**
-0.
0.
0.
0.
B9
0.589*
0.
0.300
0.
0.335
B10
0.866**
0.288
-0.
-0.
0.
Bll
0.729*
0.491
0.
0.
0.
B12
0.403
0.648*
0.
-0.
0.
B13
0.707*
-0.582*
0.
-0.
0.
B14
0.335
0.354
-0.378
0.419
0.476
HI
0.892**
0.
-0.
0.
0.
H2
0.783**
0.286
-0.
0.
0.
H3
0.957**
-0.
-0.
-0.
-0.
H4
0.740*
0.365
-0.
-0.
0.
H5
0.
0.755**
0.
-0.292
0.
H6
0.948**
0.
0.
-0.
-0.
H7
0.883**
0.
0.
-0.
-0.
H8
0.854**
-0.
0.307
0.
0.
HB
0.912**
0.
-0.
-0.
-0.
CRANW
0.974**
-0.
-0.
-0.
0.
MANDW
0.949**
-0.
-0.
-0.
0.
VP
32.326
6.324
1.753
1.242
1.009
% (cumul.)
64.65
77.30
80.81
83.29
85.31
14
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
105
70
pen
35
-105
B
CD O
a
■ •
O
o
D
:
oouo
■ ■ r
-9l
• •■■■>••• fi»
2-8
70
21
PCI
Figure 5.— Plot of PC I against PC II from PC-Analysis on all specimens (n = 478) based on
the correlation matrix. Log, ^transformation of all variables. Open symbols— M. califor-
nicus; Solid symbols— M. ochrogaster; Squares— males; circles— females. For a and b. see
explanations in the text.
species revealed that the most variation was concentrated in factor 1 . The
other components are difficult to interpret, and no clear pattern is visible
from the plots.
PC-analyses using only cranial or mandibular measurements were
performed on the whole sample (n = 478). In the first case, the distinction
between the species is almost as good as when all variables were
employed. In the second case, no clear pattern appeared when the first two
factors were plotted against each other; the mandibular characters chosen
do not convey much information about the variation between the two
species in that part of the skull.
The correlation with age for the first five components of PC-analyses
performed on different groups of specimens (Table 5) showed that when
all individuals are taken together, the first two components are highly
correlated with age. Approximately 50 percent (R2 = 0.5) of the variation
accounted for by factor 1 and 25 percent by factor 2 is age variation. When
taking specimens by age-classes, about 67 percent of factor 1 and 10
SIGNIFICANCE OF AGE VARIATION IN VOLES 15
percent of factor 2 is age variation in age-class 1. In age-classes 2 and 3,
only about 3 and 13 percent, and 7 and 20 percent, respectively, of the
variation in the first two factors is due to age. Taking age-classes 2 and 3
together, 46 percent of factor 2 is age variation and the other components
only explain a very low proportion of age variation. This is somewhat
peculiar; in age-class 1, the greatest source of variation is age-related size,
while in classes 2 and 3 it is the interspecific differences. We have to keep
in mind, however, that in all analyses used to compute the correlation
Table 5. Correlations with age of the first five PCs extracted for different subsamples, using
the correlation matrix, except in the first case where the covariance matrix (COVA) was used.
Log, ^transformation of all variables. ** significant to the 0.01 level. * significant to the
0.05 level.
Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 n
Case
1. Microtus ochrogaster +
Microtus californicus .745** -.495** .019 -.004 -.103* 478
(COVA)
2. Microtus ochrogaster+ ?2Q^ _ 524** 024 095* 022 478
Microtus californicus
3. Microtus ochrogaster +
Microtus californicus .818** -.321** -111 -.179* .026 192
Age-Class 1
4. Microtus ochrogaster +
Microtus californicus .180** .363** .011 .156* .094 209
Age-Class 2
5. Microtus ochrogaster +
Microtus californicus .263* .445** .095 -.205 .013 77
Age-Class 3
6.
Microtus ochrogaster +
Microtus californicus
Age-Class 2 + 3
-.039
.679**
.027
.111
-.097
286
7.
Microtus californicus
.875**
-.033
-.109
-.118*
-.044
314
8.
Microtus californicus
males only
.970**
-.051
-.103
-.012
-.043
173
9.
Microtus californicus
females only
.860**
.009
- 215**
-.066
-.025
141
10.
Microtus ochrogaster
.880**
.075
-.090
-.120
-.043
164
11.
Microtus ochrogaster
males only
.884**
.050
-.137
-.068
.017
88
12. Microtus ochrogaster ^^ mQ _mf. ^ Mg
females only
76
16
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
coefficients of Table 5, the first factor explains about 65 percent of the
total variation, whereas the second factor accounts for only about 6%
when both species are taken together, and around 2 and 3 percent
respectively, when M. ochrogaster or M. californicus are considered
separately. That means, for instance, that in case 2 of Table 5, only 33.5
percent ( = 0.7202 x 64.65) of the total age variation is explained by factor
1. When the species are treated separately, we find the following results:
M. ochrogaster: 51 percent ( =0.882 X65.8) and M. californicus 52.1%
( = 0.8752 X68.0). Thus, factor 1 explains about half of age variation
when PC-analysis is performed on each species separately, but when the
two species are combined, it is only in the order of 30-35%.
Finally, a PC-analysis using specimens of both species from age-class
2 only was performed. Animals in that age-class are from two and one-half
to seven months old. Most specimens of arvicoline rodents used in
taxonomic studies are of that age and are sexually mature at two to three
months, though not full-grown. The correlations of factors 1 and 2 with
age are rather low, so that in this case age variation accounted for by factor
pen
■
■
Z2-
•
■
18-
• ■
• ■
•
•
4
14 -
■■••
•
•
■ ■
a
6>
1.0-
■
•
I.*"
a
60
■
■ • ■
9 o
□ no o 9)
-20
•
■
•
° ^
cP
20-
•
■
o
60
DDo
>fi w? &
B
w*$>
10
\
03 O
D D O
O
14
° DC
o °
a
o
□
o
18
□ D
D
a
22-
□
3.15
1.35
750 150
PCI
Figure 6.— Plot of PC I against PC II from PC-Analysis on specimens from age-class 2
(n = 209), based on the correlation matrix. Log ^-transformation of all variables (same
symbols as in Figure 5).
SIGNIFICANCE OF AGE VARIATION IN VOLES 17
1 and 2 is less than 3 percent. Factors 1 and 2 were plotted against each
other in Figure 6. The species separate very well; two KU specimens are
outliers, but still group with M. ochrogaster.
Discriminant function analysis (DF-analysis)
Specific differences— Each species was considered as a group; males
and females were analyzed separately as well as together for the three age
classes. Results of the DF-analysis for the first five steps (Table 6) reveal
that different variables were chosen as best discriminators for the various
age-classes in both sexes. Some of them, however, (LI 6, B4, B6, B 1 1 ,
B12, B14. and H5) were selected in several groups. H5 was a good
discriminator in females of age-classes 1 and 2 only. Microtus califomicus
was larger than M. ochrogaster in the following measurements: interparie-
tal length (L16), incisive foramen width (B6), condylar width (Bll),
foramen magnum width (B12), and anteorbital constriction width (B14).
Table 6. Discriminant analysis between M. califomicus and M. ochrogaster according to sex
and age-classes. First 5 steps. Untransformed data. Var.— variable taken at each step;
F— approximation to U-statistic; % — average percentage of correct classification.
Steps
1
2
3
4
5
Age-Class
Var.
B6
L16
B4
L21
Bll
1
F
165.8
166.3
170.2
152.3
150.1
%
89.0
96.3
97.2
98.2
100.0
Var.
Bll
B4
L16
B12
L14
2
F
364.8
313.9
331.8
302.1
264.6
MALES
%
Var.
97.4
L13
99.1
B4
100.0
L8
100.0
CRANW
100.0
L17
3
F
128.9
128.0
198.6
187.7
184.7
%
100.0
100.0
100.0
100.0
100.0
Var.
L16
B4
B12
B6
B13
1-3
F
559.0
618.3
600.3
530.8
463.0
%
93.9
98.9
98.9
99.2
99.6
Var.
L16
B6
H5
B4
B14
1
F
133.5
131.3
110.1
91.7
90.2
%
96.4
96.4
98.8
98.8
97.6
Var.
B4
L7
H5
L20
Bll
2
F
185.8
193.0
253.3
221.9
209.3
FEMALES
%
Var.
95.7
HB
100.0
H4
100.0
Bll
100.0
B4
100.0
B6
3
F
156.8
116.1
113.1
105.5
124.3
%
100.0
100.0
100.0
100.0
100.0
Var.
L16
B6
B4
B12
B14
1-3
F
487.8
522.5
499.9
460.7
412.1
%
96.3
98.6
99.1
99.5
99.1
MALES + . ,
FEMALES
Var.
L16
B4
B12
B6
B14
F
1050.9
1098.3
1107.0
993.7
869.9
%
96.2
99.0
99.0
99.4
99.4
18 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
Interorbital width (B4) showed the opposite trend. It is interesting that
most good discriminators are width measurements. The distinction be-
tween the species improved with age for both sexes. Results of age-class 3
have to be interpreted carefully because of the small sample size in M.
californicus. The distribution of the values for the first canonical variate
(CNVR1) for females (Fig. 7) computed with 10 variables showed the
species well separated. Table 7 reports the percentages of correct
classification in each group for the first five steps or until a 100 percent
correct classification is achieved. The jackknifed classification has been
used throughout: each case is classified into a group according to the
classification functions computed from all the data, except those from the
case being classified. In females from age-class 1, and when all age-
classes are taken together, a few specimens of M. californicus are
misclassified as M. ochrogaster, whereas no M. ochrogaster are mis-
classified. This is not true for males, except in age-class 2, where the same
proportion of misclassification occurred in both species.
Sexual differences — Each sex was considered as a group, and each
species was analyzed separately for the different age-classes. Table 8 gives
the results of the DF-analyses for the first five steps (except for M.
Table 7. Discriminant analysis between M. californicus and M. ochrogaster according to sex
and age-classes: Percentages of correct classification for each group. First 5 steps or until a
100% of correct classification is reached. Untransformed data. C/C = M. californicus
classified correctly as M. californicus, C/0 = M. californicus classified as M. ochrogaster,
etc.
MALES
FEMALES
C/C
C/O
o/c
O/O
C/C
C/O
O/C
O/O
85.00
15.00
0.00
100.00
95.16
4.84
0.00
100.00
96.25
3.75
3.45
96.55
95.16
4.84
0.00
100.00
Age-Class 1
97.50
2.50
3.45
96.55
98.39
1.61
0.00
100.00
98.75
1.25
3.45
96.55
98.39
1.61
0.00
100.00
100.00
0.00
0.00
100.00
96.77
3.23
0.00
100.00
96.51
3.49
0.00
100.00
97.22
2.78
9.09
90.91
Age-Class 2
98.84
1.16
0.00
100.00
100.00
0.00
0.00
100.00
100.00
0.00
0.00
100.00
100.00
0.00
0.00
100.00
Age-Class 3
100.00
0.00
0.00
100.00
100.00
0.00
0.00
100.00
93.06
6.94
4.55
95.45
97.16
2.84
5.26
94.74
99.42
0.58
2.27
97.73
97.87
2.13
0.00
100.00
Age-Class 1-
3 98.84
1.16
1.14
98.86
98.58
1.42
0.00
100.00
99.42
0.58
1.14
98.86
99.29
0.71
0.00
100.00
100.00
0.00
1.14
98.86
98.58
1.42
0.00
100.00
MALES + FEMALES
C/C
C/O
O/C
O/O
97.45
2.55
6.10
93.90
99.36
0.64
1.83
98.
17
Age-Class 1
-3
98.73
1.27
0.61
99.39
99.36
0.64
0.61
99.39
99.04
0.96
0.00
100.00
SIGNIFICANCE OF AGE VARIATION IN VOLES
19
Table 8. Discriminant analysis between males and females in M. californicus and M.
ochrogaster, respectively, for the different age-classes. First 10 steps. Untransformed data. A
variable with a - sign means that it has been removed in the stepwise process. For further
explanation see Table 6.
M. ochrogaster
Steps
1
2
3
4
5
Age-Class
Var.
B14
B4
B7
L24
B13
1
F
15.4
9.2
7.3
6.6
5.7
%
74.0
74.0
72.0
76.0
82.0
Var.
B3
HI
H2
B14
H7
2
F
5.9
6.1
6.3
5.5
4.9
%
64.7
70.6
78.4
72.5
72.5
Var.
B4
L19
HB
B13
MANDW
3
F
10.3
8.4
8.2
8.0
7.2
%
65.1
68.3
74.6
76.2
77.8
Var.
B14
L14
L9
MANDW
CRANW
1-3
F
11.8
7.3
8.8
8.0
9.2
%
59.1
61.6
64.0
65.2
70.1
M. californicus
Var.
Bll
L8
H2
B7
B6
1
F
7.9
9.9
9.5
8.5
8.5
%
60.6
67.6
70.4
67.6
71.1
Var.
B5
MANDW
B10
L13
H2
2
F
77.2
53.7
42.1
35.4
31.7
%
74.1
77.8
81.6
84.2
84.2
Var.
L18
HB
B8
3
F
9.6
12.8
33.3
%
78.6
92.9
100.0
Var.
H2
L8
Bll
B5
MANDW
1-3
F
24.9
26.1
29.7
27.0
24.9
%
63.1
65.6
71.3
71.0
73.6
californicus age-class 3, where a 100% of correct classification was
achieved after three steps). With five variables, the percentage classified
correctly was between 70 and 85 percent. Age-class three in M. califor-
nicus was an exception probably due to the small sample size. The sexes
do not separate well, even with ten variables (Fig. 8).
Variables which best separated the sexes are not the same in each
species, except for MANDW. In M. ochrogaster, L9, L14, B4, B13, B14
and MANDW were selected, while in M. californicus they were L8, B5,
Bll, H2 and MANDW. Sexual dimorphism is therefore expressed
somewhat differently in each species. M. ochrogaster males show larger
dimensions than females in foramen length (L9), frontal length (L14),
interorbital width (B4), incisor width (B13) and anteorbital constriction
(B14). Mandibular weight is greater in young males than females and
lower in older males than in females. Hoffmeister and Getz ( 1968) did not
report significant sexual dimorphism in measurements. Table 9 gives the
20
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
N 15
M ochrogaster
M. califormcus
CNVR 1
Figure 7.— Distribution of values for the first canonical variate (CNVR1) in DF-Analysis
between M. califormcus and M. ochrogaster females. Untransformed data. 10 variables
used.
M. califormcus
_uj*._
Da
OXL
CNVR 1
Figure 8.— Distribution of values for the first canonical variate (CNVRl) in DF-Analysis
between males (open) and females (solid) of M. califormcus from age-class 2. Un-
transformed data, 10 variables used.
percentages of correct classification (jackknifed) for the first ten steps, or
until a 100 percent correct classification was achieved.
Interspecific differences by sex— Four groups were considered in this
analysis: males and females of each species. Table 10a gives the results for
that analysis. The best discriminators were the same variables selected in
the discriminant functions between species (see above) except that H5 was
not entered and HB was more important. This result is not surprising
because the greater part of the variation was due to interspecific differ-
ences. Thus, variables that are good species discriminators also are more
important in this analysis. The classification also improves with age.
Figure 9 represents the first two canonical variates (CNVRl and CNVR2)
SIGNIFICANCE OF AGE VARIATION IN VOLES 21
plotted against each other. The species are distinct, whereas the sexes
showed considerable overlap. M. californicus specimens a (MVZ 60182)
and b (MVZ 142) are outliers. The former is the same as specimen a in
Figure 5. Table 10b gives the results of a comparison including animals of
both species, but belonging to different age-classes. M. californicus is
Table 9. Discriminant analysis between males and females in M. californicus and M.
ochrogaster, respectively for the different age-classes: Percentages of correct classification
for each group. First 10 steps or until a 100% correct classification is reached. Un-
transformed data. M/M = males classified correctly as males. M/F = males classified as
females, etc.
Microtus ochrogasater
M
icrotus californicus
M/M
M/F
F/M
F/F
M/M
M/F
F/M
F/F
68.97
31.03
19.05
80.95
66.25
33.75
46.77
53.23
72.41
27.59
23.81
76.19
67.50
32.50
32.26
67.74
68.97
31.03
23.81
76.19
70.00
30.00
29.03
70.97
75.86
24.14
23.81
76.19
67.50
32.50
32.26
67.74
82.76
17.24
19.05
80.95
71.25
28.75
29.03
70.97
Age-Class 1
79.31
20.69
9.52
90.48
68.75
31.25
29.03
70.97
86.21
13.79
14.29
85.71
72.50
27.50
25.81
74.19
79.31
20.69
14.29
85.71
72.50
27.50
17.74
82.26
79.31
20.69
14.29
85.71
75.00
25.00
19.35
80.65
86.21
13.79
9.52
90.48
58.62
41.38
37.27
72.73
73.26
26.74
25.00
75.00
65.52
34.48
22.73
77.27
75.58
24.42
19.44
80.56
75.86
24.14
18.18
81.82
81.40
18.60
18.06
81.94
68.97
31.03
22.73
77.27
83.72
16.28
15.28
84.72
72.41
27.59
27.27
72.73
83.72
16.28
15.28
84.72
Age-Class 2
75.86
24.14
13.64
86.36
84.88
15.12
15.28
84.72
82.76
17.24
22.73
77.27
89.53
10.47
15.28
84.72
82.76
17.24
18.18
81.82
90.70
9.30
8.33
91.67
79.31
20.69
13.64
86.36
88.37
11.63
12.50
87.50
79.31
20.69
9.09
90.91
87.21
12.79
11.11
88.89
56.67
43.33
27.27
72.73
85.71
14.29
28.57
71.43
70.00
30.00
33.33
66.67
100.00
0.00
14.29
85.71
73.33
26.67
24.24
75.76
100.00
0.00
0.00
100.00
73.33
26.67
21.21
78.79
100.00
0.00
0.00
100.00
Age-Class 3
73.33
80.00
80.00
83.33
83.33
86.67
26.67
20.00
20.00
16.67
16.67
13.33
18.18
15.15
15.15
18.18
18.18
15.15
81.82
84.85
84.85
81.82
81.82
84.85
67.05
32.95
50.00
50.00
67.05
32.95
41.84
58.16
60.23
39.77
36.84
63.16
61.27
38.73
29.08
70.92
61.36
38.64
32.89
67.11
71.10
28.90
28.37
71.63
63.64
36.36
32.89
67.11
71.68
28.32
29.79
70.21
Age-Class 1-3
68.18
32.82
27.63
72.37
73.99
26.01
26.95
73.05
70.45
29.55
27.63
72.37
76.88
23.12
26.24
73.76
73.86
26.14
23.68
76.32
76.30
23.70
23.40
76.60
72.73
27.27
27.37
77.63
76.88
23.12
21.28
78.72
77.27
22.73
21.05
78.95
78.61
21.39
24.11
75.89
77.27
22.73
23.68
76.32
78.03
21.97
20.57
79.43
22
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SIGNIFICANCE OF AGE VARIATION IN VOLES
23
zs
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60
Figure 9.— Distribution of values for canonical variates 1 (CNVR1) and 2 (CNVR2) in DF-
Analysis between M. californicus and M. ochrogaster, and the sexes. Untransformed data, 10
variables used. Numbered triangles are group centroids (1,3 male; 2. 4 female). For a and b.
see explanations in the text. Same symbols as in Figure 5.
larger than M. ochrogaster in most measurements, so by combining M.
californicus of age-class 2 and M. ochrogaster of age-class 1 , the size
difference is exaggerated, while by combining M. californicus of age-class
1 and M. ochrogaster of age-class 2, the size difference is minimized. We
know this because in the first case only three variables are needed, among
them HB. a good size indicator, to classify correctly all specimens
according to species, whereas in the second case four are needed. These
variables (B4. L16, B13 and Bl 1) are less age-dependent. Table 1 1 gives
the percentages of correct classification (jackknifed) with ten variables for
the different age classes, except in part B, where only nine variables were
used because the F-to enter was less than 1.0 after step 9. In general, the
correct classification of specimens according to sex is not as good as when
sex alone is considered (see above). This result was expected because
sexual and species variation are of different orders of magnitude, so that
the former is overshadowed by the latter.
Canonical Correlation Analysis
The following comparisons were made for cranial measurements only:
24
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26
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
width vs. length, height vs. width, height vs. length, and cranial vs.
mandibular measurements. The first few canonical variates of both sets
show significant correlations with each other, indicating that they convey
similar information about the skull. Untransformed and transformed
(log10) data were used in a preliminary test, but the differences in the
results were only minor, and untransformed data were thereafter em-
ployed.
Similar results to those obtained when taking only one species were
observed. One interesting comparison, however, was that involving length
and width measurements. The first canonical variate of the first set
(CNVRF1) is highly correlated (r = 0.979) with the first one of the second
set (CNVRS1). Table 12 gives the loadings on the first five canonical
Table 12. Canonical correlation analysis for M. californicus and M. ochrogaster (Males +
females). Comparison of width (B) and length (L) measurements. First 5 canonical variates.
Untransformed data. For further explanation see Table 4.
CNVRF 1
CNVRF 2
CNVRF 3
CNVRF 4
CNVRF 5
Bl
0.762**
-0.
-0.
-0.367
0.
B3
0.983**
0.
-0.
0.
0.
B4
-0.
0.801**
0.
-0.
0.
B5
0.960**
0.
-0.
-0.
0.
B6
0.284
-0.761**
-0.437
0.
-0
B7
0.
-0.
-0.544*
-0.500*
0.
B8
0.777**
0.
-0.
-0.
0.
B9
0.546*
-0.
-0.353
-0.
0.
BIO
0.869**
-0.337
0.
0.
-0.262
Bll
0.701*
-0.449
-0.
0.
-0.
B12
0.354
-0.609*
-0.271
0.348
0.
B13
0.717*
0.625*
-0.
0.
-0.
B14
0.304
-0.415
0.438
-0.281
0.
CNVRS 1
CNVRS 2
CNVRS 3
CNVRS 4
CNVRS 5
LI
0.990**
0.
0.
0.
-0.
L2
0.990**
0.
-0.
0.
-0.
L3
0.978**
-0.
-0.
-0.
-0.
L4
0.985**
0.
0.
-0.
-0.
L5
0.979**
0.
-0.
0.
0.
L6
0.901**
0.334
-0.
-0.
-0.
L7
0.861**
-0.348
-0.
-0.
0.
L8
0.927**
-0.
-0.
0.
0.
L9
0.840**
-0.
-0.458
0.
-0.
L10
0.668*
0.532*
0.376
-0.
0.
Lll
0.959**
-0.
-0.
-0.
0.
L12
0.986**
-0.
0.
0.
0.
L13
0.936**
-0.
-0.
-0.
-0.
L14
0.647*
0.580*
-0.
-0.
0.
L15
0.
0.659*
-0.275
-0.
0.
L16
0.317
-0.859**
0.
-0.
0.
L17
0.921 **
0.
0.
0.
0.
L18
0.950**
-0.
0.
0.
-0.
L23
0.620*
0.250
-0.
-0.307
-0.
L24
0.595*
-0.604*
0.
-0.
0.
SIGNIFICANCE OF AGE VARIATION IN VOLES
27
variates for each variable in each set. Animals with large dimensions in the
following variables: LI, L2, L3. L4, L5, L6, L7, L8, L9, Lll, L12, L13,
L17. L18 (and to some extent L10, L14, L23 and L24) also have large
dimensions in Bl, B3, B5, B8, BIO (and to some extent B9, Bll andB13).
In Figure 10, the second canonical variates (CNVRF2 and CNVRS2) are
plotted against each other; two groups corresponding to the species are
clearly apparent. The relationship between CNVRF2 and CNVRS2, which
show a correlation of 0.888, can be summarized as follows, according to
the loadings of Table 12: M. ochrogaster possesses relatively larger
dimensions in B4, B13, L10, L14, L15 and smaller ones in B6, Bl 1, B12,
LI 6, L24 than does M. californicus. The specimens indicated by an arrow
in Figure 10 are young individuals (less than 1 month old) of M.
ochrogaster. They lie closer to the M. californicus than to the M.
ochrogaster group. However, not all young specimens of M. ochrogaster
are to be found within the M. californicus population, indicating that age is
not the only factor determining their position.
24
20-
80-
40-
CNVRS2
00-
-40
-80-|
I
■ :
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•« •■• ■■ .
■ » ■ • • • i m.-it J
• "j •: ■
o
: \
. )9° <8n O O
DOr
-13
CNVRF 2
Figure 10.— Canonical correlation analysis on M. californicus and M. ochrogaster. Plot of
canonical variate 2 of first set (CNVRF2) against canonical variate 2 of the second set
(CNVRS2). Untransformed data. For individuals designated by arrow, see explanations in
the text. Same symbols as in Figure 5.
28 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
Multiple regression analysis; predicting individual age
The age criteria provided by Hoffmeister and Getz (1968) for M.
ochrogaster do not extend beyond an age of 6 weeks; older animals could
not be distinguished unless eye lens weights were used. Most age criteria
proposed were qualitative, such as sutures, and subject to considerable
error. Lidicker and Mac Lean (1969) presented two complex procedures
for estimating age in M. californicus, based on growth curves and
regression analysis respectively. Their data were divided into two subsam-
ples: animals less than and more than 100 days old. A regression analysis
was then performed on each subsample, because they felt that a formula
derived from the whole data set would have given poor estimators of age.
Thus, to estimate the age of an animal one has to go through a series of
steps leading to the formula to be used.
Our objective was to seek a simpler, more general model to predict
age. First we transformed our variables (including age) into logarithms
(log10) to linearize our data (Chatterjee and Price. 1977). With only a few
exceptions, all variables showed stronger correlations with age than when
they were untransformed.
Stepwise regression was first computed for our different subsamples
grouped according to species and sexes (Table 13. row A). The RSQ
values (multiple correlation coefficients) indicate what proportion of the
variation is explained by the regression model. About 85 percent was
accounted for with three variables. 88-92 percent with 10 variables and
91-96 percent with 20 variables (Table 13. row A). These values are
somewhat reduced when species are combined. The increase in RSQ can
be used to judge whether the inclusion of a new variable adds much to the
predictive power of the regression equation and makes it possible to select
the number of variables to be employed. Selection of variables in the
stepwise procedure can be influenced by variables already in the equation;
i.e. we do not know what the outcome would have been had another
variable been taken first. This was pointed out by Lidicker and MacLean
(1969). Daniel and Wood (1971). and Chatterjee and Price (1977). The all
possible subsets regression, which computes the best subset of variables,
was also available; "best" is defined as the subset with the smallest CP.
This statistic compares the residual sum of squares for the equation with all
variables to that of smaller subset; the number of specimens and variables
in the equation are also taken into account (Daniel and Wood. 1971;
Chatterjee and Price, 1977). Results from the best subsets regression are
presented in Table 13, row B. Variable names are only given as long as
they correspond to those selected by stepwise regression program.
Usually, the first five to six variables chosen by both programs are the
same, after which some divergences occur. Some variables had to be
excluded from the best subsets regression analyses because they produced
a singular matrix.
Figures 11 and 12 compare the RSQ values of stepwise and best
subsets regression programs for M. californicus and M. ochrogaster,
respectively. If the results were identical we should observe a straight line;
SIGNIFICANCE OF AGE VARIATION IN VOLES
29
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30
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
the results are very similar for both species. However, there are a few
differences worth pointing out. In M. californicus males, the first variable
chosen (LI) by best subsets regression is not as good as that chosen (B3)
by stepwise regression; the first variable selected by stepwise regression
(B3) was not included in the best subsets regression analysis because it
showed a high correlation with LI, which in turn was not as highly
correlated with age as B3. Thus excluding LI instead of B3 would have
been a better strategy. However, after a few steps the results became very
similar again. When 10 or more variables were in the equation, stepwise
regression performed slightly better than best subsets regression, due
probably to excluded variables. In M. ochrogaster males, and to some
extent in males + females, best subsets regresssion performed better than
stepwise regression from the seventh variable onwards, but the differences
in RSQ are less than 0.005 ( = 0.5%).
In regression analysis, two main approaches are possible. The first
consists of finding an equation describing a relationship between a
dependent variable and one or more independent ones. The fewer
cc
d
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.80
M.californicus
O Females
• Males
A Females + Males
.80
r
.84 .86 .88 .90
STEPWISE REGRESSION (BMDP-2R)
9^
.96
Figure 1 1 .—Comparison between Best subset (program BMDP-9R) and stepwise regression
(program BMDP-2R). Plot of RSQ values from both programs against each other for M.
californicus.
SIGNIFICANCE OF AGE VARIATION IN VOLES
31
variables needed for a good fit (reflected in RSQ or RMS) the more easily
the relationship can be explained. The second approach concerns the
predictive power of a model. It is important to minimize RMS with, if
possible, a minimum number of variables; this is the approach we have
used. By comparing RSQ and RMS values (Table 14), we can see that the
lowest RSQ are observed for the untransformed data, and the highest ones
are those in which all 50 variables have been used. RMS is usually lowest
in equations with fewer variables. When the number of variables gets close
to the number of specimens, as is the case for M. ochrogaster especially,
RSQ tends toward 1 and is misleading. The adjusted RSQ (ADJRSQ)
(Chatterjee and Price, 1977) which depends on the number of variables in
the equation and is always lower than RSQ, gives a better idea of the
goodness of fit of a model. With the exception of M. ochrogaster females,
ADJRSQ is highest and RMS lowest for analyses using program
BMDP-9R with untransformed independent variables and log10-age (sec-
ond row of each group in Table 14, except for M. calif omicus males,
.96
M_ ocjuog aster
O Females
• Males
A Females + Males
.80
.8 2
r
.84 .86 .88 .90 .92
STEPWISE REGRESSION (BMDP2R)
i
94
.96
Figure 12.— Comparison between Best subset (program BMDP-9R) and stepwise regression
(program BMDP-2R). Plot of RSQ values from both programs against each other for M.
ochrogaster.
32
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
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SIGNIFICANCE OF AGE VARIATION IN VOLES 33
where it is in fourth row). However, analyses using only the first ten
variables selected by the stepwise regression program (the last line of each
group in Table 14) show only minor differences in ADJRSQ (^0.02 in
most cases) or in RMS (5; 0.002) compared to the best cases. Micro-
tus ochrogaster males and males + females show somewhat higher dis-
crepancies.
Cp-values from different groups should not be compared with each
other unless the number of variables is the same; they represent a
minimum for a given analysis. According to Chatterjee and Price (1977) it
should be close to p (the number of terms in the regression equation).
When this is not the case, it is mainly due to the fact that the variance used
to estimate CP is taken from the model with all the variables. If the RMS of
the model with all variables is greater than that for a subset with fewer
variables, as is the case in our analyses, the Cp-values will be distorted and
not be very useful in variable selection.
Cook's distance (Cook, 1977; Dixon and Brown, 1977) is a measure of
the change in the coefficients of the regression that would occur if the case
were omitted from the computation of the coefficients. In Table 14, only
maximal values are given. Cook's distance values are plotted against
log10-age for M. califomicus females (Fig. 13). No correlation with age is
evident; only a few cases present high values and can be considered as
outliers. For Mahalanobis distances, again only maximum values are
given in Table 14. Mahalanobis distances are also plotted against log10-age
for M. califomicus females (Fig. 14). A few points can be considered as
outliers, but they are not the same individuals as in Fig. 13.
Because our goal was to predict age using cranial measurements, it was
desirable to investigate how far the model fitted the real data and see how
the residuals were distributed. Figure 15 represents the predicted age
(log10) plotted against log10-age for M. califomicus females. For ages
around 1 month ( = 30 days, log10=1.48) there were only two serious
outliers, but as age increased, the prediction tended to diminish in
accuracy. The residuals (predicted-observed values, in log10-units) are
plotted against log10-age in Figure 16 for M. califomicus females. They
are normally distributed, but show a significant positive correlation with
log10-age (a < 0.01). This is also the case for the other subsamples.
A deleted residual is defined as the residual that would be obtained had
the case been omitted from the computations of the regression line. If the
removal of a case does not change the value of the residual, then by
plotting residuals against deleted residuals, as in Figure 17, for M.
califomicus females, we should get a straight line. That is what we
observe; there are no serious outliers.
In Figure 18, the studentized residuals are plotted against their
expected values for M. califomicus females. A straight line should be
obtained, which is the case, except for the extreme values, both positive
and negative. Similar results were obtained for the other subsamples.
It is possible to use the standard error of the estimation (SE), which is
the square root of the residual mean square (RMS), to define a confidence
34
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
interval for the estimation of age by the regression model. By taking an
average standard error of 0.12 (in logl0-units) we have the following
CO
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Figure 13.— Plot of Cook's distances against logl(l age for M. californicus females. Results
from the multiple regression analysis using program BMDP-9R with the first 10 variables
selected by program 2R. Log, ^transformation of all variables. Solid circle =1, open
circle = 2, open square = 3, open triangle = 4. solid triangle = 5. dotted circle = 6. solid
square = 7. half-solid square = 9.
SIGNIFICANCE OF AGE VARIATION IN VOLES
35
confidence intervals: 1 month (17-52 days), 2 months (35-104 days), 3
months (52-156 days), 6 months (104-313 days), 12 months (107-626
days). By transforming the logarithmic values into real numbers, two
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Figure 14.— Plot of Mahalanobis distances against log10-age for M. californicus females
(n= 141). Results from the same analysis, and same symbols, as in Figure 13.
36
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
things happen: the confidence intervals become asymmetrical and they
increase with age. This is one of the drawbacks of transforming data into
logarithms. However, as mentioned above, without a logarithmic transfer-
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Figure 15.— Plot of logl() = predicted age against logm-age for M. californicus females
(n= 141). Results from the same analysis, and same symbols, as in Figure 13.
SIGNIFICANCE OF AGE VARIATION IN VOLES
37
mation, we could not have applied a linear model to our data. The
logarithmic transformation and the positive correlation of residuals with
age are both responsible for the wider confidence intervals as age
increases.
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Figure 16.— Plot of residuals against logl0-age for M. californicus females (n = 141).
Results from the same analysis, and same symbols, as in Figure 13.
38
OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
A comparison of our results with those given by Lidicker and
Mac Lean (1969) is difficult because of their division of the sample into
two groups: individuals less than and more than 100 days old. We can,
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Figure 17. — Plot of residuals against deleted residuals for M. californicus females (n =
Results from the same analysis, and same symbols, as in Figure 13.
141).
SIGNIFICANCE OF AGE VARIATION IN VOLES
39
however, compare our two month-values with the less-than-100-days old
and the 6 month-values with the over- 100 days old. We see then that our
values for the confidence intervals are higher than those reported by
Lidicker and Mac Lean ( 1969) for both of the methods they described and
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STANDARDIZED ( = STUDENTIZED ) RESIDUAL
Figure 18.— Plot of expected normal values against standardized (studentized) residuals for
M. californicus females (n= 141). Results from the same analysis as in Figure 13.
40 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
in both age-classes, although those for the growth curve method are nearly
as high as ours for the older specimens. The usefulness or appropriateness
of either model is debatable. Ours encompasses all specimens up to one
year, but needs more variables and a logarithmic transformation of the
data, whereas the approach by Lidicker and MacLean (1969) has the
advantage of using fewer variables, without a logarithmic transformation,
and gives somewhat more accurate results, but is more cumbersome to
use.
DISCUSSION
Analysis of repeated measurements (2-way ANOVA) indicated that for
most variables, observed discrepancies were not statistically significant;
only in two cases was there a significant difference. This should give
morphometrists confidence in cranial measurements. It is, however, worth
stressing that care should be taken in defining and describing measure-
ments.
The coefficient of variation (CV) measures the relative error compared
to the mean. Thus a large measurement will have a lower CV than a
smaller one with the same standard deviation. By defining an expected CV
over the whole measuring range based on a given standard deviation which
is assumed to be the same for all the measurements, it was possible to
compare the different variables with each other through their CV-values
(see Figure 4). Most good discriminators between the two species, such as
B4, B6, B12, B14, H5 show a lower CV than expected, L16 being an
exception. The best discriminators between sexes (L9. L14, B4, B13, B14
for M. ochrogaster and L8, B5, Bll, H2 for M. californicus) are rather
close to the expected values, although L14 and H2 have higher CVs and
B4 and B14 lower ones. Good age indicators are to be found both above
(L13, L16, H3) and below (B3) the curve of expected values. It is difficult
by inspection of Figure 4 to select variables for further analyses. Variables
which would have been discarded because of high CV are the most useful
in species or sex discrimination or age estimation, L16 being a good
example. In cases where two or more variables are highly correlated with
each other, as for instance, LI, L2, L3, L4, L5, or B3, it would be
advisable to take those with the lowest CV. For these variables, however,
the differences are only minor, and any of them could be chosen.
Moreover, some measurements are easier to take or do not need special
calipers, so that eventually several factors have to be considered when
selecting a set of variables to be measured.
In PC-analysis performed on both species taken together, the first PC
accounts for approximately 65 percent and the second about 13 percent of
the total variation. Their interpretation is somewhat difficult because each
of them includes different components of variation. It is not possible in this
case to conclude, as many authors have done in other species, that factor 1
is a size factor only and the other components are shape vectors. Oxnard
(1978) warns against a too simplistic interpretation of principal compo-
nents in terms of size and shape. Furthermore, both age and species
SIGNIFICANCE OF AGE VARIATION IN VOLES 41
components in size variation are being studied here. Unless both groups
overlap in the multivariate space, it will not be possible to fit axes
accounting for size, age or species variation only. Each component will be
of a mixed nature. Possibly, by rotation of axes, as in factor analysis, it
would be possible to maximize (or minimize) variation on the different
components considered. A PC-analysis performed on each species sepa-
rately showed that the first factors of each had different directions, the
angle between them being about 22° (cos0 = 0.928).
An initial step in many multivariate data analyses is PC-analysis in
order to detect groups. We have shown, in a situation where two groups
were already well defined, that interpreting PC axes as simple size and
shape vectors was hazardous. The goal of PC-analysis is to extract
components of variation, reducing the whole set of variables to a few
components accounting for as much variation as possible, and usually
easier to interpret. In our study, factor 1 accounts mainly for age-related
size variation and factor 2 for the interspecific differences (Figure 5). By
taking each species separately, the results are somewhat clearer, factor 1
being the only component highly correlated with age, but the other
components, especially factor 2, while more difficult to interpret, carry
information about sexual variation.
In DF-analysis, age variation can mask other sources of variation,
mainly that variation due to taxonomic differences. Naturally this is
considered a major problem by systematists and explains why animals are
usually assigned to different age classes which are then analyzed sepa-
rately. In our case, age variation does not play too important a role when
discriminating between species, perhaps because interspecific variation is
of a different character than age variation, the former being mainly due to
shape differences and the latter to size differences. In other cases in which
interspecific and age variation are similar, it might be useful to remove the
effect of age. Burnaby (1966) has proposed growth invariant discriminant
functions. Vectors correcting for the factors whose effects we wish to
eliminate must first be estimated; one way to make such a correction might
consist of taking factor 1 from a PC-analysis and consider it as a growth
factor (Jolicoeur, 1963). However, as we have pointed out, factor 1 from
an analysis performed on each species taken separately should be used,
rather than from a PC-analysis computed from both species together. In
each species, factor 1 is highly correlated with age (r = 0.9) and accounts
for approximately 50% of the total age variation.
Canonical correlation analysis is a parsimonious way to express
relationships between variables. In our case, we have three sets of
variables— lengths, widths and heights— which are perpendicular to each
other, but not uncorrelated. Canonical variates are orthogonal (uncorre-
cted) within the same set, and the loadings on them for the several
variables considered allow us to find out which variables are mainly size
or age related. Paired comparison between the different sets showed a high
correlation between the canonical variates; i.e., the different sets of
variables carry similar information. In the comparison of width versus
42 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY
length, variables which determine different shapes such as B4, B6. Bll.
VB12. B13, L10, L14, L15, L16, L24 become apparent in the second pair
of canonical variates. For example, in M. ochrogaster wide interorbitals
(B4) is correlated with wide incisors (B13), while in M. californicus the
interorbital is narrow, and the incisors also narrow. Different shapes are
determined by the relative size of these measurements. By plotting the
second canonical variates of each set against each other two groups which
correspond to the species appeared (Figure 10). A canonical correlation
analysis using more than two sets of variables (Horst. 1961; Kettenring,
1971) could be used to perform a simultaneous comparison of height,
width and length measurements.
Canonical correlation has been used to relate morphological to climatic
data (Boyce, 1978) or morphological variables from different parts of the
body (Johnston, 1976). but not, to our knowledge, to compare different
skull variables. We think that an approach along that line would reveal
interesting relationships between variables, leading to a better understand-
ing of differences in shape between taxa.
Both programs used in multiple regresssion analysis (best subset
(BMDP-9R) and stepwise regression (BMDP-2R)) gave similar results
(Figures 1 1 and 12). With the former, one is sure that no variable has been
overlooked, because all relevant combinations are tried. In the stepwise
procedure it may happen that a variable entered at the beginning of the
analysis is not the best one when other variables are also included in the
equation. However, in such cases, it is often removed in a later step and
replaced by a more suitable one. One decisive advantage of program
BMDP-9R resides in the availability of Cook's and Mahalanobis distances,
studentized residuals, and deleted residuals, which allow a thorough
analysis of residuals and outliers. In most cases, the first variable entered
in the analysis accounts for approximately 80 percent of age variation. To
get another 10 percent it is necessary to include up to 10 variables. Thus,
most variables used in our study were redundant, and once a variable
which is highly correlated with age is selected, any other variable makes
only a meager contribution to explain age variation. It is probably
impossible to find skull variables whose combination gives a better fit. Our
results can be considered as a limit and there will always remain around 10
to 15% of total age variation which cannot be explained with cranial
measurements.
ACKNOWLEDGMENTS
We are grateful to J. W. Koeppl and N. A. Slade for criticizing early
drafts of this paper, and to D. F. Hoffmeister and W. Z. Lidicker for the
loan of specimens. The senior author was supported by a grant from the
Swiss Science Foundation, and by National Science Foundation Grant No.
GB40131X to the junior author. Computations at the University of Kansas
Academic Computer Center were funded by allocation to the Museum of
Natural History; Judith Franklin of the Center staff provided helpful
SIGNIFICANCE OF AGE VARIATION IN VOLES 43
advice. Deb Bennett drafted the figures, and Jan Elder typed the final
drafts.
SUMMARY
A morphometric analysis of 314 specimens of Microtus californicus
and 164 of M. ochrogaster reared in the laboratory was conducted using
47 skull measurements, cranial and mandibular weights and head + body
length.
Repeated measurements performed on a separate sample of M.
ochrogaster (n= 10) were used to estimate the measuring error through a
2-way analysis of variance. Nearly all variables can be considered as
reliable when defined correctly.
Factor 1 from a principal components analysis performed on both
species combined is highly age correlated and accounts for approximately
30 percent of total age variation. Factor 2, though also age correlated,
accounts mainly for interspecific difference. The first factors from
analyses on each species separately account for about 50 percent of total
age variation whereas second factors are age independent and account for
much of the differences between sexes.
Discrimination between the species improved with increasing age of
specimens. Sexual dimorphism is not very pronounced in either species.
Mandibular measurements separate the species and the sexes less well than
the cranial variables.
Canonical correlation analysis showed that length, width, height,
cranial and mandibular measurements convey similar information about
the skull. Second canonical variates derived from the comparison between
length and width measurements separate the species well and allow a
characterization of shape for each group through the interpretation of the
loadings on the canonical variates.
Multiple regression analysis was used to predict age from skull
measurements. A log ^-transformation was performed to linearize the
data. About 85% of age variation can be accounted for by a model with 3
variables and 90% with one comprising 10 variables. Many variables used
here are highly correlated and therefore not needed for age prediction.
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