Growth and sexual size dimorphism in Alberta populations of the eastern short-horned lizard, Phrynosoma douglassi brevirostre

Transcription

1 Growth and sexual size dimorphism in Alberta populations of the eastern short-horned lizard, Phrynosoma douglassi brevirostre G. LAWRENCE POWELL AND ANTHONY P. RUSSELL Department of Biology. Universitv of Cnlgcrry, 2500 University Drive N. W., Ccrlgnry, Alm., Ccrnnd~r T2N IN4 Received February 1 3, 1984 POWELL, G. L., and A. P. RUSSELL Growth and sexual size dimorphism in Alberta populations of the eastern short-horned lizard, Phpnosoma douglassi brevirostre. Can. J. Zool. 63: Alberta populations of Phrynosoma douglassi brevirostre display marked sexual size dimorphism, adult females being considerably larger than adult males. Discriminant analyses of whole mensural characters and of scaled mensural characters indicate that this dimorphism is present from birth, although it is more strongly expressed after sexual maturity. Recapture data were used to generate modified logistic by weight growth models for snout-vent length (SVL), and allometric models for each sex were generated for growth in tail length. head length, and head width. The SVL growth model for females indicates delayed maturity leading to greater adult size, an expected feature of a female viviparine. The SVL growth model for males indicates that growth ceases sooner than in females, resulting in a smaller adult size. This is possibly a result of male dispersal competition, an hypothesis further borne out by the results of a preliminary analysis of mobility in the two sexes, and may also be influenced by intersexual dietary competition. Differences in head dimensions between the sexes are a function of the differences in SVL at adulthood, but there is a significant sexual difference in the allometric relationship of tail length to SVL. No difference in the growth patterns and adult size of either sex was found to exist over the range in Alberta. POWELL, G. L.. et A. P. RUSSELL Growth and sexual size dimorphism in Alberta populations of the eastern short-homed lizard, Phrynosomn douglnssi brevirostre. Can. J. Zool. 63: Les populations de Phrynosomn douglassi brevirostre d' Alberta se caracterisent par un dimorphisme sexuel important quant a la taille et les femelles adultes sont beaucoup plus grosses que les miles. Des analyses discriminantes des mesures dans leur ensemble et des mesures considerees par classes indiquent que le dimorphisme est dcja present a la naissance et qu'il se precise surtout apres la maturation sexuelle. Des donnees sur la recapture ont servi ri construire des modeles de croissance logistiques modifies, en fonction de la masse, de la longueur du museau a I'anus (SVL) et des modeles allometriques de croissance de la longueur de la queue, de la longueur de la tete et de la largeur de la tete, pour chacun des sexes. Le modele de croissance SVL des femelles indique que la maturite est retardee, ce qui permet aux femelles adultes d'atteindre une plus grande taille, caracteristique qui n'a rien de surprenant chez une femelle vivipare. Le modele de croissance SVL des miles indique que la croissance des miles cesse avant celle des femelles, d'ou leur plus petite taille. Ces phenomenes sont peut-etre causes par la competition entre les miles au moment de la dispersion, une hypothese corroboree par les resultats d'une analyse preliminaire de la mobilite chez les deux sexes; la competition alimentaire entre les miles et les femelles peut aussi jouer un r81e. Les differences entre miles et femelles quant aux dimensions de la tete sont fonction des differences de longueurs SVL h l'fige adulte, mais il y a dimorphisme sexuel significatif dans la relation allometrique entre la longueur de la queue et la longueur SVL. II n'y a pas de differences dans les courbes de croissance ou la taille des adultes chez I'un ou I'autre des sexes chez les populations d'alberta. [Traduit par le journal] Introduction The Alberta populations of Phrynosoma douglassi brevirostre are range marginal in their distribution and are markedly sexually dimorphic (Powell and Russell 1984). In the context of this, growth parameters were examined for each sex to gain a better understanding of the maintenance of the observed dimorphism and to investigate whether both sexes grow at the same or at different rates. Thus, the primary objective of this study was to accrue mensural data from a sufficient sample of recaptures from Alberta to be able to generate quantified growth models for both sexes. These data were also used to test whether there were significant differences in adult size and growth pattern between populations over the range in Alberta. The secondary objective, employing the mensural data base outlined above, was to attempt to formulate discriminant functions that enable ihdividuals to be classified to sex, to define the observed sexual size dimorphism in an ontogenetic context. The tertiary objective was to utilize the data collected in this study to examine the hypothesis that the sexual size dimorphism displayed by these populations is produced and maintained by differing sexual selection pressures bn the two sexes associated with mating strategy and parental investment. As a biological process, growth is amenable to mathematical modelling and a number of widely applicable growth models have been outlined (Ricklefs 1967; Turner, Bradley et al. 1976; Fitzhugh 1976; Dunham 1978; Schoener and Schoener 1978; Kaufmann 1981). In the context of growth in reptiles, these have been reviewed by Andrews (1982) and it can be demonstrated that they all share a unity of mathematical form, with the major types being recognizable as special cases of one "generic growth model." The basic postulates of this have been outlined by Turner, Bradley et al. (1976). For iguanid lizards a variety of modelling methods have been applied to the study of growth. Notable among these have been the approaches of Turner, Medica et ul. ( 1976), who included increase in weight as part of a computer simulation of population energetics of Utu stansburianu; Andrews (1976), who employed Ricklef's (1967) method of applying the logistic growth model in intraspeci fic comparisons of Anolis growth rates; and Van Devender (1978), who compared growth rates between populations of Basi1isc.u~ basilisc-us by fitting his data to the Von Bertalanffy model. The most rigorous assessments of modelling as applied to lizard growth, however, have been those of Dunham (1978) and Schoener and Schoener (1978). The latter authors concluded that the logistic by weight model, as modified for length, best defined growth in Anolis; Dunham ( 1978) arrived at the same decision for Urosuurus ornatus and Sceloporus merriami. It is essentially this model that has been adopted in this study. Behind the application of any mathematical modelling technique to organismal growth lies the fundamental assumption that there is a regular, underlying pattern of growth charac-

2 CAN.I. ZOOL VO IOXS FIG. I. 'The range of Phrynosomo douglo.s.si hrevirostre in southeast Alberta (hatched area of inset map). Locations marked with stars represent study sites discussed in this paper (B. Bow Island; R, Rose Ranch; M, McKinley's Ranch: N. Nemiskam; C, Comrey). teristic of the species in question (Ricklefs 1967). However, this innate, species-specific pattern may be altered in varying ways by environmental factors (Huxley 1932; Kaufmann 1981 ; Andrews 1982). Thus, any growth model generated from field data, such as that presented in this study, will inevitably be an approximation of the intrinsic growth pattern of that population or species. If comparisons are to be made, careful attention must be given to the extrinsic environmental factors that may affect each case. In this context, appropriate use of growth models may cast light on the relative effects of such extrinsic factors (Dunham 1978). In the particular case of the genus Phrynosomtr, most considerations of growth have been descriptive and feature little or no statistical analysis. Guyer ( 1978). however, utilized a regression of snout-vent length (SVL) on time of year to differentiate between growth rates of males and females of P. d. douglassi in southern Idaho. He also considered observed individual growth rates. Sexual size dimorphism in a species implies that the two sexes have somewhat different ecological or reproductive demands (Howard 1981 ). The sexual size dimorphism and growth patterns characteristic of the Alberta populations of P. tl. hrc~viro.sfrc. can initially be attributed to one of two causes: either intraspecific dietary competition (Schoener 1969) or intrasexual selection (Ghiselin 1974). Fitch (1981) has considered sexual size dimorphism in reptiles in considerable detail and has found the emergent pattern to be extremely variable. Andrews (1982) has discussed this phenomenon in the context of growth in reptiles. For Phrynosomu Fitch noted that the female is the larger sex in the seven species that he examined. Piar~ka and Parker (1975) noted this for P. clouglclssi and P. platyrhinos and indicated a clinal trend in the latter, with dimorphism being most strongly marked in the northernmost extension of the range. Methods and materials Fielcl mc.thot1.s Lizards wcrc captured by hand and subjected to measurement in the field immcdiatcly after capture during the spring and summer of 1979 and and in thc spring of I98 1. After all of the data had been recorded. each newly captured lizard was given a unique toe clip for that study \ite. The following measurements were recorded:

3 POWELL AND RUSSEL-I, 14 1 (i) snout-vent length (SVL), distance from the tip of the snout to the anterior lip of the vent, measured ventrally. to the nearest 0.5 mm; (ii) weight, mass of the lizard to the nearest 0.5 g; (iii) tail length (TL), distance from the posterior lip of the vent to the tip of the tail. measured ventrally. to the nearest 0.5 mm (phrynosonies are not autotomic, and so tail length can be used as a consistent and repeatable statistic); (i~j) head width (HW), linear width of the jaws at the corners of the mouth, to the nearest 0.5 mm; (L)) head length (HL). linear distance from the tip of the snout (rostra1 scale) to the occipital notch. to the nearest 0.5 mm. HW and HL were taken with a pair of vernier callipers. Weight was measured with a 5 or 30 g Pesola spring balance. depending on size. SVL and TL measurements were recorded employing a stainless steel ruler, the lizard being stretched firmly against it to minimize measurement error owing to muscular contraction. To minimize the masking effect of measurement error on growth increment, no measurements were taken on lizards recaptured less than 14 days after a previous set of measurements. The data used in this study were collected at five separate localities in southeastern Alberta (Fig. I): Comrey ( I 10'41 ' W. 49'05' N). Nemiskam Community Pastures ( 1 10'3 1 ' W. 49' 17' N). McKinley's Ranch (1 10'25' W, 49' 17' N), Rose Ranch ( 1 10'06' W, 50' 17' N), and Bow Island (I 11'30' W, 49'55' N). Detailed accounts of the five sites and the distribution of the lizards at each are available elsewhere (Powell 1982). Se.ruol dimorphi.sm Male lizards of all ages are immediately distinguishable from females by the presence of enlarged postanal scales. Sexual dimorphism in SVL. weight. and 'TL are obvious after sexual maturity. but not in sexually immature individuals. The morphological data set for all captures was subjected to discriminant analysis to derive a discriminant function which would describe some aspects of this sexual dimorphism (McRae et ( ). Weight, SVL. TL. HW, and HL were the variables used. No attempt was made to adjust the variables for the effect of size in the initial analysis, since weight and SVL were two of the variables being tested. A two-group stepwise discriminant analysis (Cooley and Lohnes ) was performed by means of the SPSS (statistical package for the social sciences) subprogramme DISCRIMINANT (Nie et ( ). This yielded a discriminant function which can be used to classify any individual lizard by sex on the basis of the five measurements used in the analysis. In addition, for each case, proportional values for several of the morphological variables were derived ("case" here refers to a complete set of measurements taken from one lizard at onc capture). TL. HW, and HL were expressed as percentages of SVL (equivalent to the "percra" of Werner ( )) and for each case, the ratio of HL to HW was calculated. A two-group stepwise discriminant analysis. similar to that described above, was performed on the scaled values of the entire morphological data set to produce another classificatory discriminant function. Groulth The results of the analysis of sexual size dimorphism indicated that the growth patterns of each sex should be considered separately. Longitudinal data (successive measurements of an individual animal over a period of time (Fitzhugh 1976)) were used to fit the model to the growth patterns of each sex. Recapture data for each sex were organized into cases. each case consisting of a measurement taken at the first capture of an individual ( LI ). the number of days between capture and recapture (D), and the equivalent measurement taken at the recapture of the individual (L2 ). LI and LI are linear measurements such as SVL or HW. A number of individuals were recaptured more than once; in these cases, LI was given the value.obtained at the immediately preceding recapture. Each case was considered separately in the analyses, regardless of whether other cases of the same lizard were included in the data set. This may have biased the results. but was unavoidable in view of the relatively small sample sizes. If winter intervened between capture and recapture. a value for D was approximated by subtracting the estimated time spent in brumation from the actual number of days between capture and recapture. The estimated brumation period was determined from the dates of the last capture in the fall and the first capture in the following spring. as precise dates fix onset of brumation and spring emergence could not be obtained. especially for any particular individual. Cases in which there was an apparent decrease in size over time were assumed to be the result of measuremcnt error and not used in the analysis; i.e., the data set was "fixed" (Dunharn ; Schocner and Schoener 1978). Dunham ( 1978) and Schoener and Schoener ( 1978) fhund that the most suitable model for describing lizard growth was the logistic by weight model. modified for SVL. 'This model assumes a determinate asymptotic size, reached by an inflected. S-shaped growth pattern (Schoener and Schoener J 978). It is derived by substituting the cubed linear dimension for weight into the simple logistic by weight growth model (Schoener and Schoener 1978). Andrews ( 1982). in a review of the various models applied to reptile growth. recommended the logistic by weight model for small iguanids. such as Phryt~osomcr. However, weight in free-living lizards can vary with condition, food availability, and. particularly in females. with reproductive condition. all of which will obscure growth ratc (Dunham ; Schocner and Schoener 1978). Change in weight is thus not as satisfactory an index of growth as is a change in a linear measuremcnt such as SVL for use in a static model such as that employed here. The differential form of the logistic by weight equation. as modified by Schoener and Schoener ( 1978) for length. is [I] dl/dt = (rl/3)(1 - ( ~'/(r:)) where L is length (a linear dimension of the lizard). r is time. r is the characteristic growth ratc. and tr, is the asymptotic or maximum length attained by the lizard. Thc instantaneous solution to Eq. I is where e is the base of the natural logarithm and where L,, is the length at birth. Schoener and Schoener (1978) also derived an interval equation for this model: where LI is the length of the lizard at the beginning of the interval. L1 is the length at the end of the interval. and D is thc length of the interval. Equation 4 can be used to predict the size of a lizard of length L, after the passage of D units of time. The parameters rrl and r can be estimated by the use of nonlinear least squares regression techniques. In this study, the IMSL (International Mathematical and Statistical Libraries. Inc. ) computer routine RSMITZ (Anonymous 1979). as modified by the University of Calgary Academic Computer Serviccs (NONLIN). was used to estimate these parameters from the recapture cases. NON Ll N converges on those values of the parameter nearest the hypothesized starting values which give a minimum sum of squares for a user-supplied model. The model in this case was Eq. 4. A data matrix of a series of recapture cases with one dependent variable (L2) and two independent variables ( LI and D) was used to arrive at the parameter estimates. NONLIN used this data matrix in con.junction with Eq. 4 to estimate values for crl and r that fit cases which resemble those in the original data matrix. In addition. it yielded asymptotic standard deviations of each estimate, which permit the calculation of two kinds of confidence intervals. "conventional" confidence intervals and support-plane confidence intervals. The support-plane confidence interval is the mcwe conservative of the two estimates (Dunham 1978; Schoener and Schoener 1978). Maximum size (crl) and characteristic growth rate (r) were estimated for the pooled SVL cases for each sex from all study sites. These parameters were also estimated fix pooled 'TL. HW. and HL cases for each sex from all study sites. Growth curves for SVL. TL,

4 142 CAN. J. ZOOL. VOL x5 TABLE I. Statistics pertaining to Eq. 5, discriminant analysis using whole morphological values. and classification success of Eq. 5. Canonical correlation Wilks' A x Box's M F, = * % of all cases classified correctly Actual group membership Males Females "Significant at /I = Predicted group membership Males Females HW, and HL, extrapolated to their respective asymptotes, were modelled by inserting the estimated parameters for each measurement into Eq. 2; Lo was determined by averaging the appropriate measurement of lizards born in captivity and used to calculate h. 'The 95%' confidence intervals for each extrapolated curve were calculated by inserting the upper and lower 95% support-plane confidence interval values for the two parameters into the appropriate form of Eq. 2. In addition, SVL recaptures for each sex were grouped into northern (Bow Island, Rose Ranch) and southern (Comrey. Nemiskam, McKinley Ranch) location groups (Fig. I). The trl and r values for SVL were estimated for each location group by sex and used to construct a growth curve and limits as described above. In all pairwise comparisons of parameter estimates, they were considered to be different if their 95% support-plane confidence intervals did not overlap (Dunham ). The difference in goodness of fit of the male and female SVL growth models was tested by means of an F test (Sokal and Rohlf 1969). Error variance for each model was derived by generating predicted L, values for each recapture case by means of the appropriate interval equation (Eq. 4) and summing the differences between observed and predicted values. A two-tailed F statistic of 0.05 probability was used as the critical value. Change in growth rate with change in SVL was approximated by inserting the appropriate values of (11 and r into Eq. I and calculating dl/dr over the SVL range to al for each of the sexes. The same was done with 95% support-plane confidence limits of dl and r for each sex to establish upper and lower 95% confidence limits for dl/dr. Observed growth rates were calculated for each recapture series by (L, - LI )ID. The corresponding SVL was approximated by (L, - L1)/2. As a basis for comparison for the logistic growth models of TL, HW, and HL, allometric models of growth in each of these measurements were generated for each sex. Each allometric model was derived from the linear regression of the logarithm of the measurement on the logarithm of SVL, using the entire morphological data base. Because the least squares regression method assumes no error in the independent variable, Bartlett's "best-fit" method or reduced major axis are normally advocated for deriving the parameters of an allometric equation (Grine er NI. 1978; Kermack and Haldane 1950). It was felt, however, that the large sample size involved here would adequately offset the potential measurement error factor and would permit a least squares regression method to be employed for this data set. In addition, the aptness of a particular method depends upon the degree of correlation between the two variables; when the correlation is high, the results given by the different methods are very similar (Gould 1966; Seim and Saether 1983). The correlations between each pair of variables in this study were sufficiently high that we felt justified in using least squares regression for our parameter estimates. The strength of the relationships between variables was examined by means of their correlation coefficient (Smith 1980, ; Aiello 1981 ) and by an inspection of residual plots (Smith ). Comparisons between the regression slopes of the two sexes for each measurement were performed by means of an analysis of covariance (ANCOVA). If there was a significant difference between slopes, the mensural character was held to be sexually dimorphic in allometry. All statistics for the allometric analysis were obtained by means of SPSS (Nie sr trl. 1975). The allometric models were compared with the logistic models for each sex by fitting the appropriate extrapolated lines with confidence limits to scatterplots of the observed distributions of the mensural character against SVL. Mohilitj. Sexual size dinlorphism can possibly be promoted by male dispersal competition. in which males are in a race to find and inseminate as many females as possible (Ghiselin 1974). This sort of intrasexual selection will be associated with greater mobility in males than in females (Ghiselin 1974). It was hypothesized that there might be a difference in home range size between males and females if male dispersal competition is active in maintaining the sexual size dimorphism characteristic of these lizards. Consequently. an effort was made to examine home range size in the Alberta populations. A strip of plastic surveyor's tape with the date and clip code was tied in place to thc closest piece of vegetation to the point of capture or recapture of each lizard. The distance between the tags of successive recaptures was measured at the end of each field season. In cases where an intervening tag was missing, the distance between the tags for the immediately preceding and immediately succeeding captures was used. There were not enough sequential recapture series of individuals, particularly of males, to permit the computation of a sufficiently large sample of minimum polygon home range estimates for statistical purposes. This lack precluded the use of Schoener's (1981) test for independence of successive recaptures. The distance in metres between capture and recapture, the number of days between these events. and the estimated rate of movement in metres per day were pooled by sex without regard to the individual lizards which yielded the data. Each pair of recaptures was considered as a "case," in much the same manner as the morphological recapture data were treated in the estimation of the growth parameters. The three variables were found to be normal in distribution by a Kolmogorov-Smirnov goodness of fit test. Differences in rate of movement. distance covered, and number of days between recaptures between the sexes were tested by a Student's t-test. Lndependence of successive recaptures was evaluated by the mean number of days between them. Schoener (1981 ) allowed at least 112 day between observations in an attempt to maintain independence, and this amount of time was used as a minimum acceptable interval. All statistical computations were performed by the SPSS package (Nie er dl. 1975; Hull and Nie 1979). Results Ccipturc. und rucbupturu.sucbc-ess A total of 446 sets of measurements were taken from 316 individuals in the course of the entire study. Sample size varied between locations, with Comrey, Nemiskam, and Bow Island supplying most of the captures. Elimination of cases with missing values resulted in a sample size of 429 cases which were used in the analyses. There was a high overall recapture rate of cases yielding data useable in growth studies (29.2% of total captures). There were far more recaptures of females (102) than of males (30), although the degree of disparity varied from study site to study site. Recapture success itself varied between study sites, partly as a function of the size of the study site itself and partly as a function of the amount of time spent investigating each. Thus, Comrey, which is a small site and was intensively studied, is

5 POWELL AND RUSSELL 143 TABLE 2. Statistics pertaining to Eq. 6, discriminant analysis using percras* and HL/HW, and classification succcss of Eq. 6. Canonical correlation Wilks' A x Box's M F, = t Actual group membership Predicted group membership Males :':See Materials and methods and Werner ( ) tsignifican~ at 1) = Females represented by a higher recapture rate than Bow Island, which has a much larger area. Sexuul dimorphism The two-group discriminant analysis using whole morphological values yielded the following function: where SI is the determinant value of the sex. Lizards with a value of Sl > are classed as male, those with an Sl < are classed as female. The pertinent statistics for this analysis are presented in Table I. There is some overlap in the distributions of the two sexes in the plot of case values along the discriminant function, but the two groups are distinct, as is evidenced by the high cannonical correlation and the large Box's M with its associated significant F. The Wilks' h is not great, but has a significant X' value and can be considered adequate in view of the high percentage of cases classified correctly by the discriminant function. The majority of incorrectly classified male cases are in the mm SVL range. The total SVL range within which misclassified male cases were found extends from 28.0 to 45.5 mni. Misclassified cases constituted 22.12% of all male cases with an SVL of less than 46.0 mm. Most incorrectly classified female cases range from 22.5 to 39.0 mm SVL, with a total SVL range of mm. Within this SVL range, 32.38% of all female cases were incorrectly classified. The absolute values of the standardized discriminant scores indicate that TL is the most important variable, followed in order by SVL, HW, and HL. Weight was removed from the discriminant function as part of the stepwise process. HL and HW contribute little to the diminution of Wilks' h. The size of the TL and SVL coefficients indicate that these two variables account for most of the sexual dimorphism in the data set. 'The two-group discriminant analysis using scaled morphological values yielded the following function: where S, is the discriminant value for the sex. Lizards with a value of Sz < are classed as male, those with a value of Sz > are classed as female. The statistics for this analysis are summarized in Table 2. The Wilks' h for Eq. 6 is slightly larger than that for Eq. 5 (Table I), indicating slightly less acuity in distinguishing between the sexes by Eq. 6. The Box's M is large and its associated approximate F is significant, indicating that there is a significant difference in the group dispersions. Overlap along the discriminant function is greater than in the whole value analysis and the spread of the male cases is greater than that of the female cases. The absolute value of the standardized discriminant coefficient for HL/SVL is the greatest, followed in order by those for HL/HW, HW/SVL, and TL/SVL. Thus, in this analysis scaled head dimensions are the most useful variables in discriminating between the sexes, in contrast to the preceding analysis in which SVL and TL were the most useful. A slightly higher percentage of the total cases were classified correctly by Eq. 6 than by Eq. 5 (Table 1 ), but there is a marked discrepancy between the percentages of each sex classified incorrectly. Very few females (6.8%) were classified as males, whereas almost one-quarter of the males (24.8%) were classified as females by Eq. 6. All of the females classified incorrectly are neonates or yearlings (total range, mm SVL) and these cases constitute 15.38% of all female cases falling within this SVL range. Most of the misclassified males are neonates or early yearlings ( mm SVL). The total SVL range of incorrectly identified males is mm and these constitute % of all male cases below 46.0 mm SVL. The discriminant analysis using whole morphological values shows that the greater part of the obvious sexual dimorphism is in terms of SVL and TL, the two most conspicuously dimorphic features. The discriminant analysis using scaled values shows that head measurements proportional to SVL also differ between the sexes. The SVL distributions of misclassified cases of both sexes in both analyses are below the adult size ranges. By the time that a lizard is large enough to breed for the first time, it will be classified correctly to sex by both discriminant functions. Growth Estimates of the values of ul and r, together with their 95% conventional and support-plane limits, for SVL of the two sexes are given in Table 3. There is considerable difference between the estimates of asymptotic SVL of the two sexes and the 95% support-plane confidence intervals of these estimates do not overlap. The extrapolated relationships between TL, HL, and HW and SVL as modelled by the logistic equation for each of these measurements did not fit the observed distributions for each sex as well as the extrapolated allometric lines (Figs. 7, 8, and 9). For this reason the logistic models of TL, HW, and HL are not discussed further, and subsequent discussions of sexual dimorphism in these measurements will be based on the allometric models. The estimates of ul and r for male and female SVL were inserted into Eq. 2 to produce models of SVL growth for each sex. These models were used to generate a series of growth curves typifying the expected SVL distributions and growth patterns of each sex over the entire study period. The 95% confidence intervals of these curves were included to further define the expected population SVL distributions against the observed distributions. SVL distributions of all males captured over the study period generally correspond with the extrapolated SVL distributions (Fig. 2). Data points for neonates and very small males tend to fall outside the 95% confidence intervals of the extrapolated curves, probably because the initial value of the model is the mean of observed neonate SVLs. It is possible that instances of larger individuals also fall outside of the 95% confidence limits of the line that they are associated

6 CAN. J. ZOOL. VOL Time (days since Jan. 1) FIG. 2. All observed male SVLs over entire study period (estimated brumation period excluded), with extrapolated male growth patterns (solid lines) and their upper and lower 95% support-plane confidence limits (dashed lines). Origins of extrapolated growth patterns were estimated from approximate time of parturition and average SVL of neonate males. Lines with no origin on figure were extrapolated from preceding years. TABLE 3. Parameter estimates with 95% conventional and support-plane confidence limits for SVL of females and males (A) Estimates and confidence limits of asymptotic length (ti ) (I I (asymptotic 95% conventional 95% support-plane length, mm) interval (mm) interval (mm) Female SVL a Inl Male SVL t1~ t (B) Estimates and confidence limits of characteristic growth rates (r) r (characteristic 95% conventional 95% support-plane growth rate) interval interval Female SVL r r Male SVL r r with, but the overlap of confidence limits near the asymptote makes this impossible to ascertain. No observations lie above the asymptote of the upper 95% confidence limit. Since the asymptotic SVL is approached rapidly (Fig. 6) no clear differentiation can be made between age-size classes above 45 mm SVL or after a cohort of recruits has finished the summer after their first brumation (Fig. 2). However, the observed SVLs in Fig. 2 can be divided into three age-size groups: (i) young of the year (YoY), individuals of approximately mm SVL, present between the end of July and the onset of brumation in September; (ii) yearlings, individuals of approximately mm SVL, born in the previous summer and preient throughout the active season; (iii) adults, individuals of 246 mm SVL, present throughout the active season. Recapture series of males do not extend over long periods of time, and so it is not possible to say how long the life-span is after asymptotic SVL is reached. No histological examinations of yearling males were made to determine the age of onset of sexual maturity, but enlargement of the hemipenial sacs behind the vent and production of femoral pore wax were taken as evidence of the onset of sexual maturity in males. These features became evident in yearlings between the end of May and the middle of June ( active days after birth), when the yearlings are mm SVL. On this basis, no sexually immature males were present in any population after the middle of June in 1979 and 1980, excluding each season's YoY. Asymptotic SVL in males is reached in approximately active days after birth, according to the model (Fig. 6), or (on average) towards the end of the individual's second full summer (Fig. 2). From the SVL distributions about the asymptote in Fig. 2, a life-span of 3 years, at the least, is implied. 'The extrapolated growth rate of males, when plotted against SVL (Fig. 3), increases from birth to a peak within the yearling SVL range, then declines sharply as asymptotic SVL is

7 POWELL AND RUSSEL.L. 145 \ \,,, = \,, \,,,,, Snout- vent length (mm) FIG. 3. Observed male growth rates ((L? - Ll )ID) plotted against average SVL over growing period ((LI + L2)/2). The extrapolated curve of growth rate against SVL (solid line) with upper and lower 95% support-plane confidence limits (dashed lines) was plotted from a differential form of the male growth model. approached. The extrapolated 95% confidence interval for the growth rate includes most of the observed growth rates, although the model tends to underestimate growth rates within the yearling SVL range. Observed growth rates within the large yearling-adult SVL range are almost all within the 95% confidence interval. The relationship of all observed female SVLs, over the entire study period, to the extrapolated SVL growth patterns with 95% confidence intervals (Fig. 4) is generally one of conformity, although there are a number of observations lying above the upper 95% confidence limit of the asymptote and a few observations in the mm SVL range which are not clearly associated with any growth curve covering that size range. Again, observed SVLs of very young individuals and neonates tend to lie outside of the 95% confidence limits of their associated curves because the model uses the average SVL of female neonates at parturition. Asymptotic SVL is approached at a slower rate in females than in males and female growth is more prolonged, although the growth patterns of the two sexes are similar until approximately active days after birth (Fig. 6). As with males, three age-size groups are evident: (i) Young of the year (YoY), individuals of approximately mm SVL, present between the end of July and the onset of brumation in September; (ii) yearlings, individuals of approximately mm SVL, born the previous summer and present throughout the active season; ( iii) adults, individuals of approximately 260 mm SVL, present throughout the active season. Variable growth rates (Fig. 5) and the overlap of 95% confidence intervals near the asymptote (Fig. 4) make further attempts to subdivide the female age-size groups inadvisable. Longitudinal recapture series of some individuals, interpreted in the light of the female SVL growth model, indicate that the female life-span may extend at least into the fifth summer after birth. Since growth in SVL may continue after the model's asymptote is reached, statements about when asymptotic SVL is reached are perforce rather vague. ~xtrapojation from the model (Fig. 6) indicates that asymptotic SVL is reached between 350 and 600 active days after birth, in the summer after the second brumation, at the earliest (Fig. 4). There are no obvious external signs of sexual maturity in female lizards, and no dissections were performed to determine at what SVL the gonads mature. Sexual maturity most likely occurs in the yearling age-size stage, since individuals that were marked at that stage in 1979 were observed to breed in The extrapolated female growth rate curve plotted against SVL (Fig. 5) is smoother than that for males (Fig. 3), with a lower maximum amplitude and without a well-marked peak. The extrapolated growth rate curve tends to underestimate the growth rates of YoY and yearlings and to over- and underestimate the growth rates of adults. A similar phenomenon was noted by Dunham ( 1978) and Schoener and Schoener ( 1978). The variability of observed female growth rates is higher than that of observed male growth rates (Fig. 3). Nonetheless, the pattern of observed female growth rates broadly follows the pattern set in the extrapolated growth rate curve. As in the male growth rate curve (Fig. 3). there is an increase in the extrapolated female growth rate between the YoY and yearling SVL ranges and a decrease to the SVL asymptote from the yearling SVL range. The model SVL growth curves for the two sexes are similar in shape (Fig. 6). A mixed cohort of males and females would display similar growth rates until they reached an age of roughly 270 active days, by which time the slowest growing female with the lowest asymptotic SVL would have a greater SVL than that attained by any male and growth would have virtually ceased in all but the slowest growing males. The females of the cohort would continue growing until they reached an asymptotic SVL at least 14 mm greater than the greatest asymptotic SVL reached by any male. Growth in females continues as the lizards enter the adult SVL range and slows down gradually within this range, unlike growth in males, which levels off at the upper end of the yearling SVL range and continues, if at all, at a very slow rate within the adult SVL range. There is no significant difference in goodness of fit between the male and female SVL growth models (F test, p > 0.05). Table 4 contains the statistics relevant to the least squares regressions used to arrive at the parameters of the allometric equations. In all cases, the correlation coefficient between the variables is large. The distribution of the residuals from the regression of TL on SVL in males indicates that there is some nonlinearity in the relationship between TL and SVL in the lower reaches of the SVL range. This is also true of the residual plot of the HW regression in males, to a lesser extent, and of the residual plot of HW in females. However, the variations are not great and the strength of the correlations (Table 4) indicates that the allometric equations generated from these regressions are a good approximation of the scaling of the mensural characters with regard to SVL. There is considerable difference in the allometric relationship of TL to SVL between the sexes (Fig. 7, Table 4), with a significant difference in the slopes of the regressions (Table 4), indicating sexual dimorphism in both size and allometry. Males have a longer tail relative to SVL. However, there are no significant differences between the slopes of the allometric equations of HW (Fig. 8, Table 4), nor between the slopes of the allometric equations of HL (Fig. 9, Table 4) between the sexes. These two features must be considered to be sexually dimorphic only as a function of SVL, since their growth in males can be expected to cease with the cessation of SVL growth and so their maximum sizes will be smaller than in females, which prolong SVL growth (Fig. 6), and thus growth in HL and HW. No great difference in head dimensions is to be expected between a male and a similarly sized female.

8 CAN. 1. ZOOL. VOL x5 Time (days since Jan. 1) FIG. 4. All observed female SVLs over entire study period (estimated brumation period excluded), with extrapolated female growth patterns (solid lines) and their upper and lower 95% support-plane confidence limits (dashed lines). Origins of extrapolated growth patterns were estimated frorn approximate time of parturition and average SVL of neonate females. Lines with no origin on figure were extrapolated frorn preceding years. Snout- vent length (mm 1 FIG. 5. Observed female growth rates ((Lz - L, )ID) plotted against average SVL over growing period ((L, + Lz)/2). The extrapolated curve of growth rate against SVL (solid line) with upper and lower 95% support-plane confidence limits (dashed lines) was plotted frorn a differential form of the female growth model. The estimates of a, and r, with their 95% confidence limits, for the grouped populations from the northern and southern parts of the range in Alberta are given in Table 6. Insufficient sample size prevented estimation of a, and r for northern males. There was no significant difference between the parameter estimates for the SVLs of the grouped southerri males and those of all males. That the elimination of the northern male sample did not significantly alter the male parameter estimates implies that male growth patterns and asymptotic SVL do not vary significantly over the geographic range examined. There is some overlap of the 95% support-plane confidence intervals of asymptotic SVL between the northern and southern females and considerable overlap between the intervals of r for these two groups. Growth patterns and asymptotic SVL of females must, therefore, also be considered as nonvarying over the species' range in Alberta. Mobility The statistics resulting from the analysis of the mobility data are summarized in Table 5. The mean distance between capture and recapture of males is considerably greater than the mean distance between capture and recapture of females, but the difference between the means of the two sexes is only marginally significant (p = 0.05). This should be taken as indicating that a difference does exist, but, due to the low level of probability, it does not seem wise to predicate a great deal upon it. Nonetheless, that there were no significant differences in the number of days between capture and recapture or in the rate of movement between the sexes, indicates that the difference in the average distance between capture and recapture between the sexes is a real one. Independence of successive recaptures is suggested by the large mean number of days between them (Table 5). Discussion Possible sources of error Despite efforts to reduce measuring error, such error is inevitable in the taking of mensural data from a living animal, as is evidenced by the necessity of fixing the recapture data. The morphological data base is sufficiently large, however, that measurement error of any particular individual should be offset. Similarly, sample size should compensate for measurement error in individual recapture cases. The recapture sample for females is roughly thrice that of the males. Few males were recaptured more than once, whereas

9 POWELL AND RUSSELL b Time (days since birth) FIG. 6. Extrapolated male (solid line) and female (dashed and dotted line) SVL growth over time, from birth, with upper and lower 95% support-plane confidence limits (male, dotted lines; female, dashed lines). Origins of curves were estimated by average SVLs of male and female neonates Snout- vent length (mm ) Snout - vent length m m FIG. 7. (A) Distribution of tail length against SVL for all male captures, with allometric line (solid) and? 1 SD of its exponent (dashed lines). TL = ISVL' "", n = 165. (B) Distribution of tail length against SVL for all female captures, with allometric line (solid) and + I SD of its exponent (dashed lines). TL = SVL' OM4, n = 264. sequential recaptures of individual females, extending over several months, were not uncommon. It is possible that male mortality is much higher, but this cannot be substantiated from the data available. The larger number of female recapture cases available for analysis of growth patterns means that the confidence intervals (conventional or support plane) calculated for parameter estimates used in the model of female growth are narrower than those for equivalent parameter estimates used in the model of male growth. The degrees of freedom of these statistics, and thus the absolute size of the resulting confidence limit, are partly determined by the sample size (Sokal and Rohlf 1969; Schoener and Schoener 1978). The smaller number of male recapture cases results in a larger t or F statistic, as well as a larger standard deviation for the parameter estimate, and thus wider confidence intervals will be calculated for estimates of male parameters than for estimates of female parameters. It is possible that the degree of sexual size dimorphism displayed by P. d. brevirostre in the study area is greater than that indicated by the model presented here, although there is no significant

10 CAN. J. ZOOL. VOL Snout - vent length (mm) Snout -vent length (mm) FIG. 8. (A) Distribution of head width against SVL for all male captures, with allometric line (solid) and -+ I SD of its exponent (dashed I HW = sVL0 ""', n = 165. (B) Distribution of head width against SVL for all female captures, with allometric line (solid) and + of its exponent (dashed lines). HW = IsvL"~~~, n = 264. Snout - vent length (mm) Snout - vent length (mm) FIG. 9. (A) Distribution of head length against SVL for all male captures, with allometric line (solid) and + I SD of its exponent (dashed lines). HL = SVL" 7"X', n = 165. (B) Distribution of head length against SVL for all female captures, with allometric line (solid) and 5 I SD of its exponent (dashed lines). HL = SVL"~'"'" tn = 264. difference in goodness of fit between the two models. A larger male recapture sample should result in narrower 95% confidence intervals for the male parameter estimates and thus a reduced possibility of overlap between the support-plane confidence limits of the two sexes' parameter estimates. This is not likely true, however, of the u, estimates for SVL of the northern and southern females. Both recapture samples in this case were sufficiently large that further diminution of the t and F statistics with increased sample size would have been negligible. One assumption made in using the modified logistic by weight growth model is that growth is determinate in P. d. brevirostre. This may not be the case. Growth is determinate in Anolis (Schoener and Schoener 1978), to which this model was first fitted, but there is some evidence for nondeterminate growth in many other reptiles (Bellairs 1969). Cessation of linear growth in lizards is signified by fusion of the epiphyses ines). I SD and diaphysis of each long bone of the limbs (Haines 1969); this phenomenon does not seem to have been examined in Phrynosornu. Effectively, however, growth in P. d. brevirostre appears to be determinate in that it slows down markedly and in many individuals stops completely within a definite SVL range, depending upon the sex. Sexual dimorphism urzd growth The degree to which males were correctly distinguished from females by Eqs. 5 and 6 (Tables 1,2) indicates that there is significant sexual dimorphism in head, body, and tail dimensions and in body proportions. The SVL range, which includes all of the incorrectly classified cases for both analyses ("zone of uncertainty"), differs between the sexes, but includes only YoY- to yearling-sized individuals of either sex. No adults were misclassified as to sex by either of these discriminant

11 POWELL AND RUSSELL TABLE 4. Components of allometric equations for I'L, H W, and HL of the two sexes Exponent n Constant (.f+sd) R ' F TL Males ,df=2,423 Females ? (p<0.005) HW Males ? I.X3, 423 Females (NS) HL Males ,df=2,423 Females I (NS) NOTE F statistics with significances were produced by ANCOVA perl'ormed with logarithms ol'mensural characters and testing differences between slopes ol'regrcssions. which produced allornetric parariioters. R' was derived from regressions of logarithms of mensural characters on the logarithm of SVL. TABLE 5. Mean distance travelled between captures of males and of females. mean number of days between captures, and mean estimated rate of travel. Statistics for the difference in the variance and in the mean are included Distance between consecutive capture points (m) Males Females No. of days between consecutive captures Males Females Rate of travel between consecutive captures (m/day) Males Females (NS) , df= 146 (NS) 3' '01 Oe802 I. IO(NS) -0.69, df= 146 (NS) NOTE: NS, not significant: 11, no. of cases (see text for explanation). functions. This indicates that sexual dimorphism in dimensions and proportions is definite in adults but less well defined in subadults. Also, less than a third of the subadults were incorrectly classified by either discriminant function. Equation 5 indicates that there are definite differences in absolute dimensions between the two sexes and that most of the differences are defined by SVL and TL (Table I). Roughly the same percentage of subadult males and subadult females (27.19% of the total) were mistakenly classified by Eq. 5. This is not a large percentage of the total number of subadult lizards and is not composed solely of very young individuals, but of individuals ranging in SVL from neonate to the largest yearling of each sex. The existence of a zone of uncertainty over this SVL range is evidence that sexual dimorphism in absolute dimension is not so definite a phenomenon below the SVL at which breeding first takes place, as it is above this SVL. That over 70% of the cases within the zone of Lncertainty were classified correctly by sex does indicate, though, that the sexual dimorphism defined by Eq. 5 is at least covertly manifested in most subadults. This is not evident from a cursory examination of subadults in the hand, particularly YoY. Equation 6 misclassified more subadult males than subadult females (Table 2). 'This suggests that subadult males tend to be proportioned more like subadult females than the reverse, despite the differences in absolute dimension defined by Eq. 5. Equation 6 differentiates between the sexes largely on the basis of head dimensions (Table 2), which have less effect in Eq. 5 (Table I). However, the allometric equations for both sexes indicate that scaled head dimensions should not serve as a basis for differentiating between the sexes, since there are no significant sexual differences between the slopes of the equations for HW or HL (Table 4). The effect of TL in Eq. 6 undoubtedly accounts for the discrepancy between the discriminant analysis and the allometric analyses in the matter of head dimensions. Subadults should be expected to have similar scaled head dimensions regardless of sex at any SVL less than the one at which male growth ceases. TL should be the most important variable in Eq. 6, since its allometric relationship with SVL is significantly different between the sexes (Table 4). The subtle difference in SVL between the sexes at all stages of growth discerned by Eq. 5 are important in classification; possibly this difference, rather than

12 150 CAN. J, ZOOL. VOL TABLE 6. Parameter estimates with 95% conventional and support-plane confidence intervals for SVL growth of males and females, grouped geographically a (asymptotic 95% conventional 95% support-plane r (characteristic 95% conventional 95% support-plane length, mm) interval (mm) interval (mm) growth rate) interval interval Northern female ~ ~ tr r r Southern female ~~ a r r Standard male* a ~ r r Southern male lnl ~~ r r :''Standard rriale statistics are derived frorri all rriale recaptures regardless ol'geographic location. They are provided lor comparison with the southern rriale statistics, since an inadequate sample si~e prevented estimation of northern male parameters. a difference in HL, accounts for the importance of HL/SVL in Eq. 6. The zone of uncertainty of each sex for Eq. 6, as for Eq. 5, is limited approximately by the SVL characteristic of lizards which are thought to be of an age capable of breeding for the first time. The logistic growth models for both sexes predict a close similarity in SVL between subadult males and subadult females, at least until male growth slows down. The SVL distributions of cases misclassified by both discriminant functions reflects this predicted similarity. However, the number of subadult lizards correctly classified to gender by the two functions shows that sexual dimorphism in the dimensions examined is evident throughout the lizard's life, though more strongly expressed after sexual maturity is reached. This is not unequivocally clear from the logistic growth curves (Fig. 6) or the allometric equations (Table 4) for the two sexes, but could reflect a difference in acuity between the two analyses. For the purposes of this discussion, sexual size dimorphism can be categorized in a tripartite manner: male+, in which the males of a species are the larger sex at adulthood (male SVL/female SVL > 1.0); female+, in which the females of a species are the larger sex at adulthood (male SVL/female SVL < 1.0); and monomorphic, in which there is no significant size difference between the sexes at adulthood (male SVL/female SVL = 1.0). Fitch (1976) found a correlation between climatic seasonality and male+ dimorphism in Anolis, but noted that of the 50 species that he examined, a greater proportion were nearly monomorphic than were dimorphic. In a survey of the genus Sceloporus, Fitch ( 1978) found that more than one-third of the species examined were female+ dimorphic. This could be related to selection pressure imposed by large clutch size and (or) being single clutched. Species from higher latitudes also tend to display female+ dimorphism owing to the concentration of reproductive effort associated with a seasonal climate, which produces a similar result to that of being single clutched. Schoener ( 1977) tabulated the available information on sexual size dimorphism in lizard species for which data on social structuring are also available. Of the 59 species examined, 57.75% are male+ dimorphic, 28.88% are female+ dimorphic, and 13.37% are monomorphic. If attention is restricted to the iguanid species, the breakdown is as follows: male+ dimorphic, 73.53%; female+ dimorphic, 5.88%; monomorphic, 20.59%. These percentages indicate that, in general, lizard species which are monomorphic are in the minority. Of the majority of species which are dimorphic, a greater percentage of the species tallied are male+ dimorphic and this is particularly true of the Iguanidae, to which Phrynosoma belongs. Fitch ( ) performed a comprehensive census of sexual size dimorphism in the Reptilia and noted that male+ dimorphism is more common in lizards and that monomorphic reptile species are very uncommon. He likewise pointed out the predominance of male+ dimorphism in the Iguanidae. Dietary niche partitioning in association with sexual size dimorphism has been documented in some lizard species. Anolis lizards, which generally display male+ dimorphism or monomorphism, have been discussed in this regard by Roughgarden ( 1974) and Schoener ( 1967, 1969, 197 1, 1977). Female size can be strongly affected by requirements of clutch size, which may establish a minimum adult size necessary for reproductive success. Selection for a particular size in one sex may result in the other sex being forced away from this size by intraspecific competition (Schoener 1970, 1977). Phrynosomes can all be classed as model I predators, defined simply as predators which sit and wait for their prey to come by, selecting it on the basis of its size and distance (Schoener 1969). Model I predators, from considerations of foraging theory, are expected to display sexual size dimorphism, particularly when few competitors are present (Schoener 1969), assuming that food availability is a limiting factor. Since the two sexes are of different sizes, they would be expected to have different prey-handling capabilities, and thus to exploit differing prey size ranges. 'This would enable the species as a whole to widen its dietary niche and to reduce intraspecific competition for food (Roughgarden 1974; Sc hoener 1 969, 1 977). Prey-handling capabilities will depend upon jaw size in phrynosomes, and jaw size is determined by head dimensions. If jaw size is different between the sexes, some difference in prey-handling capability might be expected as well. The allometric models of HL and HW growth (Figs. 8, 9, Table 4) indicate that there will be a considerable difference in jaw size between the sexes at adulthood. This lends some weight to the dietary niche partitioning hypothesis. Sexual size dimorphism would not be so important in subadult lizards, since its main importance in dietary niche partitioning would be to reduce dietary competition between breeding females and adult males. Females must deal with the metabolic costs of vitellogenesis (Packard et al. 1977) and, in viviparines, gravidity (Guillette 1982), while the males have no such energetic costs to meet. Dietary niche partitioning associated with sexual size dimorphism has been noted in Natrix natrix, another female+ dimorphic viviparine (Madsen 1983). In this case, size-associated female fecundity was implicated as the selective force directly producing the dimorphism, dietary niche partitioning being regarded as a corollary reinforcing the dimorphism (Madsen 1983). A proper evaluation of this hypothesis with regard to the Alberta populations of P. d. brevirostre requires information on the diet, on whether these populations are food limited, and also on whether female+ dimorphism is less marked in this species in areas where there are saurian competitors. Dietary analysis indicates that the dietary niche is partitioned between

13 POWELL AND RUSSEI-L 151 adult females on one hand and all males and subadult females on the other (Powell and Russell I984), but it was not determined if food was limiting for these populations, or if intersexual dietary competition did occur. Information on the geographical variation in sexual size dimorphism in this species, and its relationship to diet, are still lacking, and so intraspecific dietary competition cannot be accepted as the sole force producing and maintaining the sexual size dimorphism characteristic of the Alberta populations. Possibly. dietary niche partitioning is a corollary of a sexual size dimorphism produced by some other selective force, rather than the selective force itself. It is also possible that it works in conjunction with other selective forces to produce sexual size dimorphism (for a more extensive consideration see Powell and Russell 1984). Ghiselin (1974) discussed the phenomenon of sexual size dimorphism in the context of sexual selection and set out four possible types of male- male competition which could promote it. Three of these would most likely lead to male+ dimorphism or to monomorphism. The fourth, male dispersal competition, puts a premium on mobility and early maturation in males, since they are in a race to find and inseminate as many females as possible. This last category of male-male competition is likely to lead to female+ dimorphism. If niales are selected for mobility and early maturation, they are likely to devote niore resources to these functions than to growth in body size, and thus are likely to be smaller at maturity than females, which are under no such constraints. Dwarf males are more likely to occur under certain circumstances: (i) when greater body size reduces mobility; (ii) when there is a premium on long life in females, but not in males; (iii) when population densities are low, intraspecific encounters are rare, and there is little selection for features associated with male-male agonistic encounters but much selection for features facilitating male mobility and mate-searching abilities. Ghiselin ( 1974) considers this last condition to be the most important. Berry and Shine ( 1980) employed sexual selection theory to explain sexual size dimorphisni in chelonians, and found that the mating system and the type of sexual size dimorphism found in a particular species conformed to the predictions of Ghiselin's ( 1974) theory. They also suggested that the relationship of size to fecundity is important in establishing female size. A minimum female size could be set by selection pressures on clutch size. In addition, viviparity, particularly in lizards, tends to be correlated with delayed niaturity and greater body size at sexual niaturity (Tinkle c>t ( ). These factors could serve to hold minimum female size relatively invariable, while not constraining minimum male size. Delayed reproduction and female+ dimorphism are found in the viviparous red-sided garter snake (Th~imrzophis.sirrc~li.s purieru1i.s) near the northern extreme of its range in Manitoba (Gregory 1977) and viviparity has been suggested as a selective force contributing to female+ dimorphism in T. sirrulis in the north-central United States (Benton 1980). Madsen (1983) found that females of the viviparine Nurrix nurrix in southern Sweden exhibited delayed maturity compared with males and also grow at a faster rate, resulting in female+ dimorphism at maturity. There is a positive correlation betw-een female size and fecundity, but no apparent relationship between greater male size and reproductive success, which probably accounts for this dimorphism (Madsen 1983). Delayed maturity in female P. d. br~virosrre in Alberta is evident from Fig. 6, and the viviparity of the species is well documented. This suggests that female size is under the constraints outlined above. The predicted SVL growth curves of both sexes (Fig. 6) show that. while growth patterns are similar for the first active days of growth, male growth ceases rapidly after this, with niales reaching a consequently smaller SVL at niaturity. Female SVL growth continues longer and tapers off more slowly. A similar pattern was observed in P. el. do~~glci,s,si in ldaho by Guyer ( 1978). The similarity of growth rate until the smaller sex reaches asymptotic size is characteristic of freshwater turtles, but generally in reptiles the sex which is larger at adulthood grows faster in the juvenile stage (Andrews 1982). These observations suggest that maturation occurs earlier in male P. dougl~i~~i than in females. Possibly more resources are devoted to early maturation than to growth, with a consequent sniall size at maturity in males. If this, indeed, is the case, then male P. d. hrcwirosrre, when compared with females, exhibit relative paedomorphosis by means of truncation of somatic growth and acceleration of the developnient of reproductive organs (Gould 1977). Densities in Phrynosom~i populations are usually low (Pianka and Parker 1975), considerably less than the geometric mean of 51 individuals/ha estimated for lizards by Turner ( 1977). The densities of the populations examined in this study were not determined with any degree of accuracy, but were certainly lower than Turner's ( 1977) mean. Social behaviours and structuring are generally held to be weakly developed in phrynosomes (Carpenter and Ferguson 1977; Stanips 1977) and associated display organs are not evident. However, Tollestrup ( ) found that P. coronurum and P. plcirvrhirzos have welldeveloped display repertoires, implying that social structuring is niore complex in these two species than is generally imagined. These findings cannot yet be extended to other species, although Montanucci and Bauer (1982) described a moderately complex courtship repertoire for P. douglassi. In the course of this study, only one male-male interaction, of short duration and intensity, was observed, in late May of 1979, and lizards were seldom found in close proximity to one another. The low number of sequential male recaptures suggests that males may be relatively mobile. The sedentary habits of females seem well established by the number of individuals for which long sequential recapture records exist. If the females are sedentary, males, by implication, will be mobile, as they will have to seek the females out to mate with them. This hypothesis cannot be adopted with a great deal of certainty because there is some question as to the underlying reason for the paucity of sequential male recaptures. Guyer (1978) found a preponderance of female P. ~iouglussi at his study site in ldaho and posited heavy winter mortality of yearling niales to explain this. There was no significant difference in distribution of home range size between adults of the two sexes (males, n = 3; females, n = 5; Mann-Whitney U-test, p > 0.05) at this ldaho site (Guyer 1978), which casts some doubt on the hypothesized greater mobility of males. The results of the analysis of male and female mobility presented here (Table 5) are suggestive, however, but cannot be taken as strong evidence for the male dispersal competition hypothesis. A sample of male and female home range sizes to which statistics could be applied is necessary to be able to establish whether or not there is a difference in size between them. An investigation of sex-specific survivorship in the Alberta populations is also required to test the possibility that the difference in recapture rate between the sexes is due to differential mortality rates rather than greater mobility in one sex.

14 152 CAN. J. ZOOL. VOL x5 If a smaller size at maturity in males is a result of the rechannelling of resources into early maturation and vagility, then the benefits of smallness are evident. There are no grounds for believing that smaller adult size of itself confers any advantage in mobility to males. However, male dispersal competition as an explanation for female+ dimorphism in the Alberta populations of P. d. brcwirostre has considerable plausibility. Female phrynosomes will be under different selectional constraints from males with regard to growth. It is evident from Fig. 4, and particularly from Fig. 6, that females exhibit relatively delayed maturity compared with males. Tinkle et ell. (1970) observed that the females of viviparous lizard species display delayed maturity and a greater body size at maturity. Delayed reproduction confers a reproductive advantage to the individual, because the larger a female is at the time of her first clutch, the larger the clutch mass that she can produce (Tinkle and Hadley 1975). Tinkle and Ballinger ( 1972). in their study of intraspecific demographic variability in the oviparous Scbeloporus undulcitus, suggested that growth is faster in southern populations owing to selection for rapid maturation, but that life-spans were longer in the northern populations owing to the selection for delayed reproduction. The viviparity of P. ciouglussi is established (Pianka and Parker 1975). SVL growth in females continues until active days after birth, according to extrapolation from the model (Fig. 6), a considerable period after the cessation of male growth as extrapolated from the male model. Placed in a seasonal context, curves extrapolated from the female SVL growth model show growth slowing in the summer after the second brumation and effectively ceasing in the summer after the third brumation (Fig. 4). No yearling females were found to be gravid, although this cannot be stated with certainty owing to problems with the ascertaining of gravidity (see above). The youngest females that can be said with assurance to have bred are estimated, from longitudal records, to have been in the summer after their second brumation, and by the time of parturition (late July - early August) they would have achieved near-asymptotic SVL (Fig. 4). Ballinger ( 1973) found that females of the viviparous Sc~eloporus poinsetti likewise did not breed until the summer after their second brumation, although they attained sexual maturity a year earlier. However, females of the lowland populations of the viviparine S. jcrrrovi may breed for the first time in the summer after their first brumation (Ballinger 1973; Tinkle and Hadley 1975). Pilorge ( 198 lu, 19816) noted similar early maturity in females of the viviparine Lcrc-erta virtipuru in central France, and stated that viviparity should not be considered as an adaptive strategy per se, but as a component of each individual species' reproductive strategy (Pilorge 1981 b). Thus, delayed maturity is not necessarily a correlate of viviparity in lizards. Nonetheless, in high-latitude or montane viviparines, the association between delayed maturity in females and viviparity seems to be valid (Tinkle et ul. 1970; Ballinger 1973). Phynosomu d. douglussi in southern.ldaho displays similar female SVL growth patterns ta P. d. brvvirostre in Alberta, growth continuing through the summer after the second brumation (Guyer 1978), although no data are available on breeding age. Unfortunately, there are no comparative data on growth patterns and breeding age for P. douglussi elsewhere in its range. However, the Alberta populations seem to conform to other predictions of Tinkle et ul. ( 1970) with regard to viviparous lizards. They are long-lived according to the longitudinal records, although, as discussed above, this can be said with more assurance about the females than about the males. They are single clutched in Alberta, a strategy which is apparently characteristic of the species over its range (Pianka and Parker 1975) and one to be expected in a viviparous lizard (Tinkle c)t ell. 1970). Slow growth and delayed maturity in females would also be selected for in lizard populations dwelling in ecologically marginal situations (Tinkle 1967), such as montane areas or the northern margins of the species' range (Ballinger 1979; Ferguson and Brockman 1980). Fitch ( 1978) found there to be a correlation between female+ dimorphism and a large clutch mass and (or) a single clutch in the genus Sc.~lo~porus, and a greater tendency towards female+ dimorphism in temperate zone species of this genus. Selection for delayed maturity and greater size at maturity would naturally affect females but not males, since the selection pressure is related to viviparity and (or) clutch size. Male dispersal competition would put a premium on rapid, invariate growth in males, as a certain size must be reached to make mating physically possible; after this point is reached, resources would be diverted into gonadal maturation and vagility. Males are engaged in a race to reach a minimum breeding size and mature sexually as quickly as possible. By this hypothesis, selection will constrain growth. Females, on the other hand, are not competing to attain a particular size and mate as frequenlly as possible. Selection pressures require them to delay maturity and maximize size at first breeding, but after that point is reached there is no reason to believe that these selection pressures will operate with such force, and so subsequent growth may be more variable. Attainment of great size in a female entails great clutch size and thus reproductive success, but maximum size attainable will be controlled by growing season length (Stewart 1979) and the various environmental factors enumerated above which affect growth. The above data and discussion thus indicate that males attain their asymptotic size more rapidly than females do theirs, by early cessation of growth, and that females attain a greater asymptotic SVL by relative prolongation and a more gradual tapering off of growth. The male growth pattern corresponds to that expected if selection is for early maturation. This conforms, at least in part, to the explanation of female+ dimorphism in these populations as being related to male dispersal competition. The female SVL model also reveals positive factors related to survival in a range-marginal area and can be interpreted as the result of selection for delayed maturity. Selection pressure on growth rate and asymptotic size would not be so extreme in females. Thus, the degree to which maturity is delayed, and the associated growth rate and asymptotic size, would be expected to be more variable than is the case with males. The major criteria being selected for in females, if this line of reasoning is followed, would be associated with the minimum body size at which a reasonably sized clutch could be carried. Associated with this may be the delaying of reproduction until the size of the female's cloaca is sufficient to allow the unhindered passage of neonates of a certain minimum size, this threshold size being associated with a reasonable chance of surviving the first brumation. The size of neonates tends to increase towards the northern limits of the geographical range in viviparines (Stewart 1979). Such factors would set a premium on female cloaca (and hence body) size at the time she first breeds. Together with the selection for adequate clutch size, this factor will also likely promote delayed maturity. While dietary competition cannot be ruled out as the selec-

15 POWELL AND RUSSELL 153 tive force producing and maintaining the sexual size dimorphism found in these populations (Powell and Russell 1984), the evidence presented here argues strongly for sexual selection more closely associated with reproductive strategy and viviparity. At present, neither alternative can be ruled out as the main selective force, and it is quite possible that the two work in conjunction to produce and maintain this sexual size dimorphism. Acknowledgements We would like to thank Leonard and Mary Jane Piotrowski, Phil Flaig, Dick and Janet Rose, Will and Rose McKinley, and the Laidlaw family for permission to work on their lands. Dr. E. Swierstra of the Dominion Agricultural Research Station in Lethbridge is to be thanked for pern~ission to use the Onefour schoolhouse as field headquarters. We are obliged to Jan Vrbik, David Schrothe, and Judy Szikora, all of the University of Calgary Academic Computer Services, for help with various parts of the computer analysis, and Dr. Gordon Fick for a discussion of regression methods. We are grateful to Mr. Larry Linton for assistance in regard to these matters also. Thanks are also owed to Dr. Thomas Schoener. for his helpful comments; Dr. Michael Ryan, for his methodological critique; Craig Guyer, for sharing some unpublished material; and to Drs. Ronald Davies, Gordon Pritchard, and Robert Weyant for reading and constructively criticizing an earlier draft of this manuscript. 'The comments of two anonymous reviewers greatly improved the final product. Financial support for this project was provided partially by the Department of Biology, University of Calgary, and partially by a Natural Sciences and Engineering Research Council of Canada grant (A-9745) to A. P. Russell. The manuscript was typed by Marg Hunik. AIELLO. L. C. I98 1. 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