Service de la Faune du Québec BULLETIN N° 13
A multivariate analysis of some Ontario and Quebec wolf (Canis lupus) skulls
by Charles Pichette
and Dennis R. Voigt
Ministère du Tourisme, de la Chasse et de la Pêche Québec, Canada
ABSTRACT
A multiple discriminant analysis program was used to compare 128 wolf (Canis lupus lycaon) skulls from three populations in Ontario and Quebec. Significant differences were found between the three populations when divided and undivided into sexes. The Algonquin wolves were smallest in eight of nine variables. The relative values of various measurements for de- termining significant differences between means is given.
INTRODUCTION
The last major attempt at describing the distribution of subspe- cies of North American wolves (Canis lupus) was that of Goldman (Young and Goldman, 1944). The subspecies C. lupus lycaon was described as ranging in southern Quebec, Ontario and parts of Minnesota. Within this range, how- ever, differences in skeletal and pelage characteristics exist (Standfield, 1969). This is especially the case between the Algonquin Park population and certain northern Ontario populations . This study attempted to deterrnine, using multivariate discriminant analysis, the extent of certain skeletal differ- ences between three populations of Ontario and Quebec wolves. Since some of these characters may be minor, this statistical technique may more clearly define differences between the populations .
This type of analysis has been used before on Canis species.
Jolicoeur (1959) investigated multivariate geographical variation between sev- eral Nearctic wolf populations . Lawrence and Bossert (1967) distinguished between three species of Canis They determined, using same sarnple as we did, that the Algonquin Park wolves were clearly and significantly distinguish- ed from nearby C. latrans using skeletal characteristics, but that there is considerable overlap in weight. Thus, it would be interesting to determine similarities between the Algonquin wolves and northern C. lupus lycaon
'races' with which there is also weight overlap.
The authors are indebted to Mr. G.B. Kolenasky and R.O. Stand- field, of the Ontario Department of Lands and Forests, and to Dr. B. Simard of the Quebec Wildlife Service, Department of Tourism, Fish and Game, for kindly making available much important material We also wish to sincerely thank Dr. R.C. Plowright for his assistance with the statistical analysis.
Without his help it would have been impossible to use the discriminant analysis technique.
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MATERIAL AND METHODS
A total of 128 wolf skuns from Ontario and Quebec were used in this study. The Algonquin Park sample consisted of 37 animais (17 males and 20 females) collected during a trapping program in 1963 and 1964. A Kenora district sample of 42 animais (16 males and 26 females) was collected in 1961 and 1962. The Quebec sample of 49 animais (27 males and 22 females) was obtained between 1966 and 1968 from a large portion of the province (Fig. 1).
Only adult skulls were used in this study.
Skulls were first photographed using a Polaroid Industrial MP3 Camera (Fig. 2, 3 and 4). The resulting transparencies were then enlarged 3.5 times natural size with a 3M "400" Reader-Printer and projected on a screen. The nine measurements (Fig. 5) were then read in millimetres di- rectly from the projection. The appropriate information was punched on com- puter data cards and processed by the University of Toronto IBM 1094 Computer.
Multivariate statistical techniques were used to distinguish bè- tween characters which may overlap when considered separately. A multiple discriminant analysis program described by Veldman (1967) was used to de- termine the extent and manner in which the three groups of wolves may be differentiated by a set of dependent variables operating together. The three groups were also divided into sexes providing six groups for analysis.
Each population was considered as an ellipsoid in nine dimension- al space (nine variables measured). In order to simplify calculations it is necessary to find a new set of axes such that the differences between popula- tions are maximized. The variances and covariances can be represented as 9 by 9 matrices and the sum of variance-covariance matrices for ail popula- tions is equal to the pooled variance-covariance matrix. If this within-group matrix is designated W, and the total ellipsoid variance T, then T-W is equal to the between-group variance--covariance, designated as B. The new axes must maximize the between variance-covariances relative to the within variance- covariances. For this we use BW-1 which is analogous to the F-ratio B over W in ordinary analysis of variance . With this we can calculate the new discrimi- nant axes. This becomes difficult to visualize in more than two dimensions, however. Fig. 6 depicts the principle of rotating axes to maximize population differences using only two variables. The differences of the samples can be expressed by the W1 and W2 axis or so-called discriminant functions. This is the weighted sum of characters which best separates the populations. The mean value of the discriminant function for each of the populations can be ob- tained by rnultiplying the mean value of each character over the population by the discriminant coefficient for the character and then summing.
The determinations of the discriminant analysis program can now be listed:
1. Discriminant coefficients and thus functions for all roots . 2. Percentage variance accounted for by each of the roots and
their chi-square test and probability.
3. F-ratio to determine significance of differences between groups.
4. Means of die groups in discriminant space.
5. Correlation coefficients between old variables and new dis- criminant variables.
6. Analysis of variance (F-ratio) on each of the original varia- bles .
7. Means of the groups over old variables.
8. Co-ordinates of each individual in the discriminant space.
RESULTS
The analysis of wolf skulls was based on two methods of com- parison. One involves using the complexes of characters to calculate dis- criminant fonctions and determine multivariate skull variations, while the other was a simple comparison of means of the original variables (Murdoch, 1957). Of these methods, the latter is not as useful because of the overlap of characters among the groups. However, histograms ofmeans do indicate some interesting generalizations (Fig. 7).
For instance, females were smaller than males especially in total length and zygomatic width. Algonquin wolves were the smallest and tended to have relatively long narrow rostrums. Such relative differences will be discussed further in the Discussion. Table 1 gives means of the three populations when not grouped by sexes.
For this study an analysis of the new (discriminant) variables is most important. Table 2 gives the discriminant coefficients resulting when the three groups are considered. It will be noted that significant differences exist between all three populations (F-ratio = 4.772, p = 0.0000) and that 100
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per cent of the variance can be accounted for by two discriminant functions, W1 and W2 (Table 4). When the three groups are divided into sexes, signifi- cant differences exist between some or all of the six groups but 90.86 per cent of the variance can be accounted for by three discriminant functions of the five (Table 4). Table 3 gives discriminant coefficients for the six groups. Fig. 8 depicts the group dispersion for the three groups. Also included are ellipsoids based on two standard deviations from the population means . This was calcu- lated from the co-ordinates of each individual in the discriminant space.
Evaluating the relative merit of the nine measurements is one of the most important considerations. The variable F-ratio of the new and origi- nal variances indicates that measurements 4, 5, 6, 7 and 8 are most useful to determine significant differences in the means of the three groups. How- ever, when the three groups are divided into sexes all nine measurements become useful and any one may be used for significant determinations among the six groups (Table•5).
DISCUSSION
Geographical isolation of two populations may cause speciation or development of new races (Simpson, 1964). In spite of the mobility of wolves, the three groups studied here must be considered relatively isolated from each other. This is especially the case with the Kenora group. To what extent environmental influences or geographical separation (which may cause genetic differentiation, Li, 1955) affect skeletal structure is only speculation.
Jolicoeur (1959) found northeastern specimens to be shorter but relatively broader-skulled than southwestern ones in northwest Canada. In this study, similar geographical trends were noted. The Algonquin wolves were smallest in all respects especially the width of rostrum and zygomatic arch. The Que- bec wolves, although shorter than the Kenora wolves, had the greatest zygo- matic width, but tapered to a narrow rostrum. The Kenora wolves were long and relatively slender. When these differences are compared with Young and Goldman's (1944) subspecies interesting similarities are noted. The Quebec wolves have broader frontals, more massive skull and broader postorbital region as does the C. I. labradorius subspecies. Similarly, the Kenora wolves have broader rostrums and are much larger as is C. 1. hudsonicus. This suggests that differences may be related to integration of adjacent populations of subspecies. The overlap illustrated in Fig. 7 also suggests reasons for the differences among our populations. The Algonquin sample was collected in a small area in the southern portion of the Park. In contrast, the Quebec sample was taken from a large heterogeneous area in southern Quebec. The Kenora sample was obtained mainly in the northern portion of the district. It is logical to assume that the greater variation of the Quebec wolves is due to the larger sample area. Algonquin wolves feed mainly on deer whereas Kenora wolves
mainly on moose . However, the Quebec wolves feed both on moose and deer.
This may account for the large overlap of skeletal features of Quebec wolves on the other two populations .
The authors would like to comment briefly on certain aspects of this project. The authors feel the use of multivariate analysis for evolution- ary comparisons with respect to complexes of characters is a very efficient method. If time had permitted it would have been advantageous to take more measurements (approximately 20) and to standardize the size of sampling area. We also do not know to what estent age composition affects variance analysis . With more populations it would be interesting to correlate variables with longitudinal-latitudinal co-ordinates to more accurately determine geo- graphical variation.
This type of analysis also assumes a normal distribution of population variables . This may in fact not be the case. The accuracy of the method used is questionable in certain individuals even though precision was increased by enlarging the projections . Although the method used to measure skulls retains a permanent record of the skull for later measurements it is probably more time-consuming and requires more equipment.
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Quebec Algonquin iii Keriora
Fig. 1. Origin of samples
Fig. 2. Camera and skull in position.
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Fig. 3. Close-up of stand with skull in position.
Fig. 4. Print of transparency from which skull me asurements were taken.
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Fig. 5. Skull dimensions measured and numbered designations. (Ventral view).
1. Condylobasal length 2. Palatal length 3. Postpalatal length 4. Zygomatic width
5. Palatal width outside the first upper rnolars 6. Palatal width inside the second upper premolars 7. Width between the postglenoid foramina
8. Least width of braincase
9. Width between the auditory bullae 12
° \ vvi m a1 X+ a 2Y
/
►
1
1
\vv2 x c2Y
This maximizes differences between populations. The new axis, W1 and W
2 are discriminant functions and a, 2 c,and c 2 are discriminant coefficients. Ellipsoids represent populations within a subspecies.
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Va r. 2 X
Va r. 1 Y
Fig. 6. Hypothetical example of rotating axes.
Varia bles
Fig. 7. Actual means of three populations for nine variables (sexes seperated, males - total height; female - stippled height).
501
30 w2
2 0
10-
70 80 90 160 110 120 130
NA/1
Fig. 8. "Group mean" dispersion in discriminant fonctions W1 and W2. (Ellipsoids based on 2-SD: 95% prob.).
Table 1. Means of three populations for vine measurements (mm).
Variable
Means
Quebec Algonquin Kenora
1
219.68 219.08 221.35
2
102.40 104.50 104.48
3
95.37 92.72 94.96
4
126.14 122.11 125.77
5 74.10 72.20 72.86
6 28.50 27.92 29.51
7 46.40 44.60 45.43
8
35.56 35.82 38.46
9
16.43 17.18 16.91
Table 2. Discriminant coefficients for 3-Group analysis.
Variable
Coefficient
1 2
1 0.143 0.0223
2 -0.2759 -0.0161
3 0.0831 0.0589
4 -0.0363 0.1077
5 0.5135 -0.5484
6 0.0956 0.6957
7 0.3477 -0.1848
8 0.1196 0.3818
9 -0.7123 -0.1394
Table 3. Discriminant coefficients for 6-Group analysis.
Coefficient
Variable 1 2 3 4* 5
1 0.0618 0.0426 -0.0065 0.0561 -0.0261
2 0.0084 0.4238 0.1154 -0.0152 -0.2207
3 0.0760 -0.1323 -0.0768 -0.1095 0.0935
0.1416 0.0203 -0.0789 -0.2582 0.1284
5 0.6238 -0.4974 0.5108 0.1347 0.1938
6 -0.2823 0.0529 -0.7441 0.5207 0.5690
7 0.0551 -0.1437 0.1405 0.7779 -0.4389
0.4771 0.0978 -0.2921 -0.1221 -0.4210
-0.5204 0.7213 0.2341 -0.0930 0.4406
Not significant
Table 4. Discriminatory analysis for 3-Group and 6-Group analysis.
3 Groups 6 Groups
Roots W1 W2 W1 W2 W3 W 4 W5
Pct. Variance 59.21 40.79 43.81 29.65 17.40 7.15 1.99
Chi-square 44.210 32.086 64.359 47.062 29.778 13.140 3.794
Pr obability 0.0000 0.0002 0.0000 0.0000 0.0008 0.0694 0.5818
F-ratio = 4.772 F-ratio = 3.887
p = 0.0000 p = 0.0000
Table 5e F-ratio of variable correlation for 3-Group and 6-Group analysis.
Variable
3-Group 6-Group
F-ratio p F-ratio
1 0.5611 0.5774 7.6919 0.0000*
1.7264 0.1802 10.9024 0.0000*
2.8107 0.0622 5.2322 0.0004*
4.6614 0.0111* 10.3431 0.0000*
4.3029 0.0153* 11.1142 0.0000*
6.0557 0.0035* 5.4335 0.0003*
7 7.2178 0.0014* 4.3003 0.0015*
10.4840 0.0002* 7.1532 0.0000*
2.1463 0.1191 2.5557 0.0305*
* Significant probabilities
O
LITERATURE CITED
Jolicoeur, P. 1959. Multivariate geographical variation in the wolf,Canis lupus L. Evolution, 13 (3): 283-299.
Lawrence, B., and W.H. Bossert 1967. Multiple Character Analysis of Canis lupus latrans, and familiaris, With a Discussion of the Relationships of Canis piger. Amer. Zool., 7: 223-232.
Li, C.C. 1955. Population genetics. The University of Chicago Press, Chicago, XI + 366 pp.
Murdoch, D.C. 1957. Linear algebra for undergraduates. John Wiley and Sons; Inc. , New York, XI + 239 PP •
Simpson, G.G. 1964. This View of Life: The World of an Evolutionist.
Harcourt, Brace, World Inc., New York, XVII + 368 pp.
Standfield, R .0 . 1969. Personal communication.
Veldman, D.J. 1967. Fortran Programming for the Behavioural Sciences.
Holt, Rinehart and Winston, Inc., New York, 406 pp.
Young, S.P., and E.A. Goldman 1944. The Wolves of North America. The American Wildlife Institute, Washington, D.C., XX + 636 pp., illustr.
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