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Determination of age groups in Thomomys umbrinus (Rodentia: Geomyidae).

ABSTRACT. -- A series of qualitative characters, especially the development of the zygomatics and rostrum, was used to assess four age groups of 288 specimens of Thomomys umbrinus from Sierra de Tlaxco, Mexico. Twenty-two cranial measurements were evaluated and a subset of 11 variables was subjected to both a discriminant analysis and a canonical discriminant analysis. All analyses were performed with the sexes separated. In males, the height of the maxillary crest, middle zygomatic breadth and breadth across bullae were the best discriminating characters among age groups. In females, the anterior zygomatic breadth, followed in order of importance by the middle zygomatic breadth, length of braincase and length of nasals were the best discriminators of age. To compare the efficacy of the method proposed here, to the closure of the basioccipital-basisphenoid suture, specimens were rearranged in four age groups using the condition of the suture and the set of 11 variables was subjected to discriminant techinques. Efficacy by the method of the suture was 80.4% for males and 63.1% for females. Although both methods are useful to separate male individuals in extreme age classes (I, IV), the suture-method is less accurate for age groups II and III in either sex.

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Age determination is fundamental in systematic and taxonomic studies to assess non-geographic and geographic variation of species. Because most of the morphological systematic or taxonomic studies of pocket gophers are based on randomly trapped, post mortem specimens, Thaeler (1967) and Hoffmeister (1969) proposed the degree of fusion of five and two skull sutures, respectively, as criteria for age determination in pocket gophers. Of these seven sutures, the basisphenoid (i.e., basioccipital-basisphenoid) has been the most commonly used since it was recommended by Hoffmeister (1969). However, when we examined this suture to assign specimens of Thomomys umbrinus to age groups (during a study on non-geographic variation in the species) we noticed that the criterion was highly influenced by the individual perception of relative terms such as "very" or "slightly" closed or open. Indeed, some authors have considered only three age classes in pocket gophers and have discarded specimens that did not have "closed" or "almost closed" basisphenoid suture (considered "adult" specimens) from their studies of morphological variation (Honeycutt and Schmidly, 1979; Heaney and Timm, 1983; Wilkins, 1985). However, during the examination of more than 800 specimens of Thomomys umbrinus, we noticed a number of females with "open" sutures bearing fetuses. Therefore, if the term "adult" is to reflect sexual maturity, these specimens should be included in the analyses.

Patton and his coworkers have studied a population of T. bottae in a restricted area for many years and have correlated the closure of cranial sutures, including the basisphenoid, with known-aged individuals (Smith and Patton, 1980; Daly and Patton, 1986; Patton and Brylski, 1987). Although their system allowed them to arrange skulls into six age groups, as well as to distinguish adults from juveniles, most investigators studying morphological variation in other species of pocket gophers by sampling or examining voucher specimens lack conditions in which subjectiveness can be avoided.

As a result of measuring more than 800 museum specimens from the Mexican Transvolcanic Belt, we propose a series of qualitative criteria from the general morphology of the skull of T. umbrinus which comprise the: 1) inflation of braincase; 2) proportion between braincase and rostrum; 3) development of zygomatic arches; and 4) presence and conspicuousness of parietal and, especially, maxillary crests.

Here, we present the results of discriminating multivariate techniques which we used to test the efficacy of our criteria in a sample of field-trapped T. umbrinus from Sierra de Tlaxco, State of Tlaxcala, Mexico. Among other advantages, these statistics allow the assessment of specific characters whose ranges can be described. We also show the result of comparing such efficacy with that obtained from assessment of the basisphenoid suture.

METHODS

A sample of 288 skulls from several nearby (no more than five kilometers apart) and ecologically similar localities of Sierra de Tlaxco, Tlaxcala, Mexico, which is housed at the Mammal Collection, Universidad Autonoma Metropolitana, Unidad Iztapalapa (UAMI), was selected and all individuals were separated by sex and arranged in one of four age groups as follows (Fig. 1):

Age I. Neither parietal nor maxillary crests present. Braincase highly inflated and much larger than rostrum. The rostrum is concave, fine, and short. Very slender zygomatic arches converging anteriorly.

Age II. Cranial crests starting to appear. Rostrum more developed; braincase less inflated, but still short and slightly concave. Zygomatic arches less slender, but still converging anteriorly.

Age III. Parietal and maxillary crests present. Skull completely developed. Rostrum straight and well developed. Zygomatic arches robust and parallel or tending to diverge anteriorly.

Age IV. Parietal and, especially, maxillary crests well developed and very conspicuous. Skull very ossified and bulky. Zygomatic arches very robust and diverging anteriorly.

To compare this approach with the condition of the basisphenoid suture (Hoffmeister, 1969), specimens were rearranged in four age groups according to the degree of closure. In the first age group (I), the basioccipital and the sphenoid bones are completely separated and a wide portion of cartilage is present between them. In the second age group (II), the bones are still separated and the cartilage is narrower. In the third age group (III), the bones are still separated, but their epiphyses are beginning to touch by their lateral extremes and the disappearing portion of cartilage comprises a thin layer or remains in the middle between the bones. In the fourth age group (IV), both bones are completely fused with a line of suture present or absent and the cartilage is absent.

[FIGURE 1 OMITTED]

A total of 22 measurements were taken from the skulls with a dial caliper to the nearest 0.01 millimeter; however, we only examined the 11 characters which separated every age group (Table 1). These mensural characters (Fig. 2) include: total length of skull (TLS); length of nasals (LNA); length of zygomatic arch (LZA); length of braincase (LBC); length of maxillary diastema (LDI); anterior zygomatic breadth (AZB); middle zygomatic breadth (MZB); posterior zygomatic breadth (PZB); breadth across bullae (BAB); height of maxillary crest (HMC); and middle height of braincase (HMB).

Data for each sex were entered and processed separately in a PC, using Statistical Analysis System, versions 85 and 89 (SAS Institute, Inc., 1985). Statistics for determining the accuracy of the characters proposed here were performed in two steps according to the discriminant analysis theory (Anderson, 1958; Press, 1971; Tatsuoka, 1971). The first step included a direct approach with an analysis of variance and multivariate discriminant techniques. The second step included Wilks' lambda test followed by the discriminant statistics (Norusis, 1978).

To determine which of the 22 measurements separated (P [less than or equal to] 0.05) every age group, a simple analysis of variance and Duncan's test for multiple means (PROC GLM) were run for each variable. Because SAS eliminates all specimens with one or more missing values and, therefore, results in different sample sizes for each variable, these analyses were performed on a subset of 90 females and 80 males of the specimens from Tlaxcala, which had data for all the variables. All other analyses were executed on the total sample (Table 1).

A discriminant analysis (PROC DISCRIM, SAS) was performed to ascertain the percentage of correctly-classified individuals in each of the a priori assigned age groups; the degree of overlap between age groups, and the age groups with no overlap (Table 2). The analysis also was used to examine the efficacy (or percentage success) of the characters as a function of the total number of specimens correctly classified, divided by the total number of individuals entered in the analysis.

Discriminant functions necessary (CAN) for separating age groups, and determination of their relative importance for explaining total variation, were assessed with a canonical discriminant analysis (PROC CANDISC, SAS). Canonical coefficients (Table 3) were used to determine which variables were most useful as discriminating criteria for the age groups. Centroids of each age group were calculated, and these, together with all individuals, were plotted in a bidimensional territorial map, using CAN1 and CAN 2 (Fig. 3).

Wilks' lambda analysis (PROC STEPDISC, SAS) was executed to reduce the number of variables employed in the separation of individuals into the age groups, in terms of their computed discriminating relevance. The efficacy of the resulting set of variables was estimated with PROC DISCRIM and PROC CANDISC (Tables 2 and 3).

To compare our characters for discriminating age groups with the basisphenoid suture, all procedures except Wilks' lambda were performed on the reclassified specimens. Percentage success and distributional plots (Tables 2 and 3; Fig. 3) also were obtained.

Specimens examined (288 UAMI).- TLAXCALA: El Final de la Senda, 2700 m, 16; El Final de la Senda, 1750 m, 36; El Final de la Senda, limite Puebla-Tlaxcala, 15 km N Tlaxco, 2856 m, 4; Limite Puebla-Tlaxcala, 15 km N Tlaxco, 2750 m, 11; Limite Puebla-Tlaxcala, 15 km N Tlaxco, 2856 m, 12; 1 km S El Final de la Senda, 2700 m, 2; 15 km N, 3 km E Tlaxco, 2865 m, 1; Paso Ancho, 12.5 km N, 6 km E Tlaxco, 2620 m, 5; 8 km N Tlaxco, 2820 m, 1; 6 km N, 2 km E Tlaxco, 2770 m, 4; 5 km N, 3 km E Tlaxco, 2960 m, 3; 5 km N, 3 km E Tlaxco, 2920 m, 2; 5 km N, 3 km E Tlaxco, 2600 m, 2; 3 km N, 1 km E Tlaxco, 2820 m, 140; 3 km N, 1 km E Tlaxco, 2640 m, 6; 2 km N, 1 km E Tlaxco, 2880 m, 7; Acopinalco del Penon, 2730 m, 5; Acopinalco del Penon, 2800 m, 1.

[FIGURE 2 OMITTED]

RESULTS

Method Using the General Morphology of Skull

Table 1 shows the standard statistics of the 11 mensural characters examined. Of these, nine separated (p = 0.0001) all age groups in male gophers (79 df): TLS (F = 62.25); LNA (F = 39.55); AZB (F = 94.95); MZB (F = 88.16); PZB (F = 91.06); LDI (F = 74.94); BAB (F = 53.9); HMC (F = 88.46); HMB (F = 47.17). In the females (89 df), five of the seven variables, which separated (p = 0.0001) the age groups, coincided with those of the males: TLS (F = 35.05); LNA (F = 26.56); AZB (F = 17.29); LDI (F = 25.87); HMC (F = 30.18). The remaining two measurements were LZA (F = 24.89) and LBC (F = 29.22).

In the discriminant analysis with 11 variables, 79.6% of the 98 male individuals were correctly classified in the a priori assigned age categories (Table 2, Fig. 3-A). After the Wilks' lambda test, only five variables were left (LZA, AZB, PZB, BAB, and HMC), but these resulted in the correct discrimination of 74.6% of the 98 males (Table 2). In both analyses, CAN1 is highly significant (p = 0.0001), highly correlated with the variables (R = 0.92 for both), and explains most of the variation (95.01% and 96.3%, respectively). The discriminant function, CAN2, is significant (p = 0.02) in the analysis with five variables, though less correlated with the variables (R = 0.37), and together with CAN1 explains 99.1% of the total variation.

[FIGURE 3 OMITTED]

Canonical coefficients (Table 3) of the variables indicate that the height of the maxillary crest (HMC), the middle zygomatic breadth (MZB) and the breadth across the bullae (BAB) are the most important criteria among the 11 variables for discriminating the age groups. After the Wilks' test, these mensural characters are still the best, but in a different order (Table 3).

Similar results were obtained for the 136 females where the Wilks' lambda also reduced the number of variables to five (LNA, LBC, AZB, PZB, and HMB). In this case, the analysis with 11 characters discriminated 76.5% (Table 2, Fig. 3-C) of the females and the analysis with five, 74.6% (Table 2). In either analysis, only CAN1 was highly significant (p = 0.0001), highly correlated with the variables (R = 0.82 and 0.81), and explained almost all the variation by itself (93.02% and 95.85%).

Within females the most important characters for discriminating among the age groups differed from those for the males, and all but one (AZB) changed from one analysis to the other (Table 3). In fact, AZB was the best criterion in both analyses. MZB with half the value of AZB, was the second-best criterion in the analysis with 11 variables, whereas LBC and LNA were second best in the other analysis (Table 3).

Method Using the Basisphenoid Suture

In general, results with this approach are less accurate and become quite different for the sexes (Table 2). In males the percentage success or efficacy (80.4%) is almost equal to that in our method (79.6%), but in females it is 13.37% lower (63.1% vs 76.47%).

In spite of the similarity between the two methods, male specimens of ages II and III are poorly discriminated with the suture-method (Table 2, Fig. 3-A, B). Males considered in age group II overlap with those of age group I and, most noticably, with age group IV, but not with age group III. Also, specimens assigned to age class III overlap with every other group except with age group IV. The remaining specimens in age group I and IV behave much the same as in the other method.

There is only one discriminating canonical function (CAN1, p = 0.0001) for males with this method. However, it is less correlated with the variables (R = 0.84) and explains only 88.6% of the variation in the analysis. As in our method, the best discriminating characters among age groups (Table 3) are HMC, BAB, and, instead of MZB, AZB. In this analysis, LZA also is important.

The lower efficacy obtained by this method for females results in an impoverished discrimination in all age categories (Table 2, Fig. 3-C, D). In contrast to the results of our method, a specimen previously assigned to age group I is classified in category II; specimens assigned to age groups II and IV overlap with every other category; and a third of the specimens assigned to age group III are placed in the next age class. Also, the only resulting discriminant function (CAN1, p = 0.0001) is less correlated (R = 0.72) and explains 10.63% less of the total variation (82.39% vs 93.02%). Except for MZB, none of the mensural characters most important for discriminating among age groups coincide in both methods (Table 3).

DISCUSSION

In general, all statistical analyses support the validity of the qualitative characters employed here to classify specimens of T. umbrinus into age groups. The 11 variables obtained in the analysis of variance and Duncan's test (Table 1) are closely related to such characters, especially with regard to the development of the zygomatic arches, the rostrum, and the maxillary crests (Figs. 1 and 3).

Indeed, in the Wilks' test and all canonical discriminant analyses (Tables 2 and 3), the most important variables have to do with the expansion (AZB, MZB, PZB) and enlargement (LZA) of the zygomatic arches, the appearance and development of the maxillary crest (HMC), and the enlargement of the face (LDI, LNA). And, discriminant analyses show that more than three-fourths of the total specimens of T. umbrinus of either sex are correctly classified using this set of characters (Table 2).

Results of Wilks' method emphasize that even though the classifying efficacy in both sexes remains almost the same with 11 as with five variables (Table 2), the accuracy in the discrimination is better with more than with fewer variables because there is more overlap between age categories with five variables.

Conversely, while the qualitative characters are useful for both females and males, the mensural characters are distinctively important both in number and nature between the sexes (Table 3). In males, the main discriminating measurements are related to the maxillary crest, the middle zygomatic breadth and the breadth across the bullae in all discriminating analyses, but in females the anterior zygomatic breadth is the only consistent measurement. Other measurements seemingly important in females are the length of the nasals and the length of the braincase.

The fact that mensural characters for females and males of T. umbrinus are divergent, reflects characteristic differential allometric rates of development, which in turn, result in sexual dimorphism in the species. Whereas the widening of the skull with the development of the maxillary crest is characteristic for males, the enlargement of the skull is peculiar to the females. Thus, the data in this study have implications for understanding differential patterns in the development of the sexes. The means and ranges (Table 1) of the variables investigated imply a starting point for an a priori assignment of specimens to age groups in each sex.

The comparison between this and the basisphenoid suture approach shows that either method is useful when dealing with very young and old male specimens (Table 2, Fig. 3A, B) of T. umbrinus. This results from the ease with which a wide open suture is distinguished, and from the readiness with which one notices the poor development of the rostrum and the convergence of the zygomatics (Fig. 1). However, the method proposed here is more accurate with regard to intermediate age categories in males of T. umbrinus because the overlap of specimens is less extensive in either number or categories (Table 2, Fig. 3A, B).

The situation is even more critical in females of T. umbrinus, where the use of the basisphenoid suture is much more subjective and results in an extensive overlap in all age categories (Table 1, Fig. 3C, D). Here, the evidence that a set of characters is more useful than a single criterion is supported. Moreover, the fusion of the basisphenoid suture appears to be independent of sexual maturity. This possibly indicates that the energy necessary for the deposition of calcium in the female skull is secondary to the maternal role which, in turn, implies more energy input into gestation and nursing activities, especially in intermediate age classes, as in other rodent species (Eisenberg, 1981). This may also be the reason why female skulls are not as readily separated into age groups as male skulls of T. umbrinus. Unlike males, females divert substantial energy in maternity roles, hence, calcium deposition in their skull is perhaps of less adaptive value, thus, the skull morphology remains almost the same during their most actively reproductive ages (i.e., intermediate age groups). The presence of very old females whose skulls resemble those of males in their highly developed maxillary crests, as well as expanded and bulky zygomatics, reinforces this idea because those females may be no longer reproductively active and, consequently, experience deposition of calcium in their skulls. Ossification of the skull in males by the deposition of calcium, on the other hand, might be sexually adaptive for their role in territorial and mating behaviour.

Although the continuous growth of cheekteeth in geomyids prevents use of degree of wear of the occlusal surface (Hoffmeister, 1951), several methods have been proposed for determining age classes. Some authors sought a relationship between age and size or weight, but Hansen (1960 and references therein) has thoroughly discussed and discarded such an approach. More recently, Patton and Brylski (1987) have shown that, besides development, several intrinsic and extrinsic factors affect both size and weight. Therefore, the most suitable methods for determining age categories in field-trapped geomyids have been those based on the closure of the cranial sutures (Thaeler, 1967; Hoffmeister, 1969), especially of the basisphenoid suture. Nevertheless, in the light of our results, we think that the method proposed here represents a better option because of reduced subjectiveness due to the consideration of more than one character to determine age class, and what we think are more reliable characters than closure of cranial sutures.

This approach, as any method based on the aspect of one or more characters, results in a discontinuous view of the growth and development of a species and has to be used with appropriate caution. Construction of growth curves by means of regression analysis or determination of age groups using principal components analysis are among the strategies recently implemented in Geomys by systematic researchers with the intent of avoiding this fragmented panorama (M. Smolen, pers. comm.). These methods will certainly allow a better understanding of age development and growth patterns in pocket gophers, but they imply access to a known population and are not necessarily related to analyses of intra- and interpopulation variation.

Patton and his colleagues (Daly and Patton, 1986; Patton and Brylski, 1987) used the basioccipital-basisphenoid and the exoccipital-supraoccipital sutures to distinguish three age classes in T. bottae. These authors considered midpoints between classes, thus reducing the discontinuous appreciation of growth and development, and ended with a total of six age categories or scores. Also, they had the advantage of being able to establish the relationship between cranial scores and chronological age from known-age individuals. This highly recommendable approach involves (as with growth curves) a long-term study in a known population.

Until studies sensu Daly and Patton (1986) of growth curves are made for T. umbrinus and other species of pocket gophers, the method presented here offers a valid option for randomly-trapped or museum specimens. We believe that the authors' experience and knowledge of the species let them understand their results of age variation, in spite of the discontinous pattern inherent to the method. Furthermore, the statistical techniques used here provide a robust option to test any qualitative characters used in the determination of age groups in geomyids.

DEDICATION

This paper is dedicated to the memory of Dr. J. Knox Jones, Jr., a man who became a legend by his way of being but, especially, by his labor among mammalogists. Dr. Jones knew how to incite our minds and our smiles at the same time with a roguish flash in his eyes. While his behavior harmonized with his free spirit, his advice, comments, and works let us know how he cherished any genuine intent to contribute to mammalogy, both among his colleagues and his students.
TABLE 1. Mean value ([bar.x]), interval (Min-Max) and sample size (N) of
11 mensural characters of the skull which separate age groups (I-IV)
within sexes (males, M; females, F) using 288 specimens of Thomomys
umbrinus from Sierra de Tlaxco, Tlaxcala, Mexico. Measurements are given
in millimeters.

 Males Females
Age
Groups [bar.x] Min-Max N [bar.x] Min-Max N

Total length of skull (TLS)
I 30.67 28.3-32.3 11 30.91 29.4-32.1 19
II 33.98 31.6-36.5 30 33.27 30.9-35.1 84
III 36.44 34.6-38.2 47 34.67 33.1-37.3 57
IV 37.64 35.5-40.0 22 36.12 34.2-37.6 6

Length of nasals (LNA)
I 9.65 8.5-10.6 10 9.66 8.8-10.5 16
II 11.32 9.5-13.1 30 10.84 9.2-12.0 82
III 12.41 11.0-14.2 47 11.65 10.6-13.2 60
IV 13.01 11.6-14.0 22 12.47 11.2-13.7 6

Length of zygomatic arch (LZA)
I 14.21 13.4-15.1 11 14.13 13.4-15.2 20
II 15.64 14.4-17.1 31 15.53 14.2-16.9 86
III 16.96 16.0-18.5 49 16.20 15.1-17.2 63
IV 17.38 16.0-18.5 22 17.13 16.1-19.0 6

Length of braincase (LBC)
I 20.84 19.7-22.0 11 21.00 20.1-22.3 19
II 22.79 20.9-24.4 30 22.46 20.8-23.7 84
III 24.15 23.2-25.3 47 23.16 22.2-24.8 57
IV 24.63 23.3-25.6 22 24.05 23.5-22.2 6

Length of the diastema (LDI)
I 10.36 9.2-11.3 11 10.52 9.1-11.3 20
II 12.48 11.0-14.3 31 12.17 10.6-14.4 86
III 13.98 13.0-15.2 49 12.94 12.2-14.5 63
IV 14.70 13.6-15.8 22 13.80 12.6-15.2 6

Anterior zygomatic breadth (AZB)
I 18.75 17.2-20.2 10 19.07 17.5-20.1 19
II 21.93 20.3-23.9 30 20.96 11.8-22.8 78
III 23.87 21.9-25.6 46 22.15 20.6-24.0 61
IV 24.94 23.7-25.8 21 23.75 22.4-25.3 6

Middle zygomatic breadth (MZB)
I 18.80 17.9-19.8 8 19.25 18.0-20.0 11
II 22.11 20.5-24.2 28 21.17 22.2-22.9 74
III 24.02 22.3-25.6 44 22.36 21.1-24.2 59
IV 25.24 23.8-26.4 21 23.82 22.7-25.5 6

Posterior zygomatic breadth (PZB)
I 20.24 19.2-21.2 8 20.41 18.6-21.6 13
II 23.20 21.4-24.8 28 22.40 21.3-24.0 77
III 25.19 23.6-26.5 45 23.66 22.0-25.5 58
IV 26.44 24.9-27.8 21 24.70 23.1-26.8 6

Breadth across the bullae (BAB)
I 17.13 16.1-18.0 11 17.38 16.0-18.9 19
II 18.92 17.3-19.9 30 18.39 16.6-20.0 84
III 19.84 18.9-21.1 47 18.93 17.5-20.4 57
IV 20.40 19.7-21.5 22 19.83 19.0-21.0 6

Height of maxillary crest (HMC)
I 9.98 9.1-10.7 11 10.21 9.3-11.0 20
II 11.71 10.6-12.8 31 11.48 10.2-12.3 86
III 12.94 12.2-14.0 49 12.18 11.1-14.2 63
IV 13.50 12.7-14.1 22 12.83 12.0-13.9 6

Maximum height of skull (MHS)
I 11.85 10.9-12.7 11 11.92 10.8-13.0 20
II 12.77 11.8-13.4 30 12.57 11.4-13.5 85
III 13.52 12.8-14.7 48 13.05 12.1-14.2 62
IV 13.98 13.2-14.8 22 13.57 12.9-14.4 6

TABLE 2. Numbers and percentages of individuals of Thomomys umbrinus
correctly classified in four age groups (I-IV) as corroborated by
discriminant analysis and Wilks' lambda test. Specimens were assigned a
priori into the age categories according to a series of qualitative
characters from the general morphology of skull (A) and by the
basisphenoid suture (B).

A. General Morphology of Skull

 11 Variables
 Males = 79.6% Females = 76.5%
 n I II III IV n I II III IV

I 8 8 0 0 0 9 9 0 0 0
 100.00 0 0 0 100.00 0 0 0
II 27 1 23 3 0 70 8 48 14 0
 3.70 85.19 11.11 0 11.43 68.57 20.00 0
III 42 0 11 30 1 51 0 6 42 3
 0 26.19 71.43 2.38 0 11.76 82.35 5.88
IV 21 0 0 4 17 6 0 0 1 5
 0 0 19.05 80.95 0 0 16.67 83.33

 5 Variables
 Males = 75.5% Females = 74.6%
 I II III IV I II III IV

I 8 0 0 0 9 0 0 0
 100.00 0 0 0 100.00 0 0 0
II 2 21 4 0 9 43 17 1
 7.41 77.78 14.81 0 12.86 61.43 24.29 1.43
III 0 2 29 11 0 6 41 4
 0 4.76 69.05 26.19 0 11.76 80.39 7.84
IV 0 0 5 16 0 0 2 4
 0 0 23.81 76.19 0 0 33.33 66.67

B. Basisphenoid Suture

 11 Variables
 Males = 80.6% Females = 63.1%
 n I II III IV n I II III IV

I 6 6 0 0 0 4 3 1 0 0
 100.00 0 0 0 75.00 25.00 0 0
II 7 2 4 0 1 13 1 9 2 1
 28.57 57.14 0 14.29 7.69 69.23 15.38 7.69
III 32 1 2 25 4 64 0 8 35 21
 3.12 6.25 78.12 12.50 0 12.50 54.69 32.81
IV 52 0 0 9 43 56 0 3 13 40
 0 0 17.31 82.69 0 5.36 23.21 71.43

TABLE 3. Classifying criteria (VAR) used in the separation of 234 skulls
of Thomomys umbrinus from Sierra de Tlaxco, Tlaxcala, Mexico, in four
age groups based on the general morphology of skull (A) and the closure
of the basioccipital-basisphenoid suture (B). The five variables in A
were selected by Wilks' lambda test. Only the coefficients of the
canonical functions which were significant (p = 0.0001), correlated (R
[greater than or equal to] 0.70) and most important for explaining the
variation are shown (11 variables=a; 5 variables=b).

VAR MALES FEMALES

A. General Morphology of Skull

 CAN1a CAN1b CAN2b CAN1a CAN1b

LTC 0.1405 0.3628
LNA -0.2989 0.2868 0.5389
LAC -0.0829 0.0416 -1.5514 0.1765
LBC -0.0022 0.2421 0.5651
ACA 0.4793 1.2380 0.8581
ACM 0.6978 1.1250 3.9863 -0.6082
ACP 0.0564 0.0710 -3.0903 -0.2297 -0.3712
LDI 0.4651 0.0512
AAB 0.6035 0.5162 1.1450 0.0457
HBR 0.8269 0.8307 -0.5614 0.2810
HMC -0.2832 0.1503 0.3926

B. Basioccipital-Basisphenoid Suture

 CAN1a CAN1a

LTC -0.2708 -0.4813
LNA 0.3237 0.1750
LAC -0.5416 0.3775
LBC 0.2366 0.3536
ACA 0.9945 -0.1924
ACM -0.2340 0.4394
ACP 0.2272 0.1002
LDI -0.1574 0.7740
AAB 0.5486 -0.0391
HBR 1.1153 0.2296
HMC -0.3927 -0.1868


ACKNOWLEDGMENTS

We are grateful to R. Wilson, M. E. Holden, and R. D. Owen for their critical reviews and comments to this manuscript and to M. Smolen for his helpful suggestions when the work was being developed. Several people participated in different parts of this study: field work and preparation of specimens was carried out by J. Patino, B. Vieyra, and B. Vargas; R. Bernal took the photographs and redrew Figure 3. This investigation was supported by CONACyT Grant no. 1253-N9203 to JRP.

LITERATURE CITED

Anderson, T. W. 1958. An introduction to multivariate statistic analysis. Wiley, New York, USA.

Daly, J. C. and J. L. Patton. 1986. Growth, reproduction, and sexual dimorphism in Thomomys bottae pocket gophers. J. Mamm., 67:256-265.

Eisenberg, J. E. 1981. The Mammalian Radiations. An analysis of trends in evolution, adaptation, and behavior. Univ. Chicago Press, USA. 610 pp.

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ALONDRA CASTRO-CAMPILLO, OBDULIA GONZALEZ-ROBLES, AND JOSE RAMIREZ PULIDO

Universidad Autonoma Metropolitana, Iztapalapa/CBS, Depto. Biologia, Apartado Postal 55-535, 09340 Mexico, D. F. (ACC, JRP), and Universidad Autonoma Metropolitana/CBI, Depto. Matematicas, Apartado Postal 55-534, 09340 Mexico, D. F. (OGR)
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Author:Castro-Campillo, Alondra; Gonzalez-Robles, Obdulia; Pulido, Jose Ramirez
Publication:The Texas Journal of Science
Geographic Code:1MEX
Date:Aug 1, 1993
Words:5469
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