EMPIRICAL EVIDENCE FOR AN OPTIMAL BODY SIZE IN SNAKES

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1 Evolution, 57(2), 2003, pp EMPIRICAL EVIDENCE FOR AN OPTIMAL BODY SIZE IN SNAKES SCOTT M. BOBACK 1 AND CRAIG GUYER 2 Department of Biological Sciences, Auburn University, Auburn, Alabama bobacsm@auburn.edu 2 cguyer@acesag.auburn.edu Abstract. The concept of optimal size has been invoked to explain patterns in body size of terrestrial mammals. However, the generality of this phenomenon has not been tested with similarly complete data from other taxonomic groups. In this study we describe three statistical patterns of body size in snakes, all of which indicate an optimal length of 1.0 m. First, a distribution of largest body lengths of 618 snake species had a single mode at 1.0 m. Second, we found a positive relationship between the size of the largest member of an island snake assemblage and island area and a negative relationship between the size of the smallest member of an island snake assemblage and island area. Best-fit lines through these data cross at a point corresponding to 1.0 m in body length, the presumed optimal size for a one-species island. Third, mainland snake species smaller than 1.0 m become larger on islands whereas those larger than 1.0 m become smaller on islands. The observation that all three analyses converge on a common body size is concordant with patterns observed in mammals and partial analyses of four other disparate animal clades. Because snakes differ so strikingly from mammals (ectotherms, gape-limited predators, elongate body shape) the concordant patterns of these two groups provide strong evidence for the evolution of an optimal body size within independent monophyletic groups. However, snakes differ from other taxonomic groups that have been studied in exhibiting a body size distribution that is not obviously skewed in either direction. We suggest that idiosyncratic features of the natural history of ectotherms allow relatively unconstrained distributions of body size whereas physiological limitations of endotherms constrain distributions of body size to a right skew. Key words. Ectotherm, island community, island-mainland, macroecology, optimal body size, snake. Because nearly every aspect of an organisms biology is correlated with its body size, this variable has been referred to as the single most fundamental character of an organism (Naganuma and Roughgarden 1990). Age at first reproduction, longevity, reproductive efficiency, susceptibility to predation, and competition ability are all intimately tied to an organism s size. Therefore, variation in body size reflects variation in innumerable correlated traits and major clades of organisms are expected to display predictable patterns of variation in body size. For example, Brown et al. (1993) and Brown (1995) used an energetic definition of fitness to define an optimal-sized organism as one that is best at taking energy left over after growth and maintenance, and converting it into reproduction (maximizing reproductive power ). Three major statistical patterns led them to develop this hypothesis for mammals. First, a logarithmic plot of the distribution of body sizes of all terrestrial mammals of North America has a mode of approximately 100 g (Brown and Maurer 1989). Second, a positive relationship exists between the body size of the largest species in a faunal assemblage and landmass area, and a negative relationship exists between the body size of the smallest species in a faunal assemblage and landmass area. Regression lines from these two relationships intersect at a point indicating that mammals occurring alone on a landmass will be 100 g (Marquet and Taper 1998). Third, mammals with body sizes larger than 100 g on the mainland tend towards dwarfism on islands, whereas those smaller than 100 g tend towards gigantism on islands (Lomolino 1985). Brown and his colleagues (Brown et al. 1993; Brown 1995) suggested that these concordant patterns are general and not specific to mammals. Indeed, similar components to these patterns have been found for fish, birds, mollusks, and insects (Morse et al. 1988; Blackburn and Gaston 1994; Marquet and 2003 The Society for the Study of Evolution. All rights reserved. Received December 12, Accepted October 14, Taper 1998; Maurer 1998; Roy et al. 2000). However, examination of all three statistical patterns has not been attempted for any major taxonomic group other than mammals. An effective test of the hypothesis of optimal size could be accomplished by attempting to replicate methods used by Brown et al. (1993), but for a taxonomic group that contrasts sharply with mammals. Herein, we explore statistical patterns indicative of an optimal body size for snakes, a monophyletic group whose elongate shape, ectothermic physiology, indeterminate growth, and restricted foraging mode (gape-limited predator) strongly contrast with groups studied previously and, therefore, have the potential to challenge the generality of macroecological patterns of body size. Nonconcordant results from snakes would suggest that the phenomenon of optimal size modeled by Brown et al. (1993) might be specific to endothermic vertebrates. Alternatively, if similar patterns were found in groups as different as snakes and mammals then a common evolutionary theory would be warranted. METHODS Data Body mass is often used as an estimate of body size in life-history studies because it is correlated with metabolism and is the common currency used in scaling models (Peters 1983; Calder 1996). Although some authors have claimed that body mass is the best indicator of body size (e.g., Hedges 1985), length may be equally appropriate for elongate organisms such as snakes. Body mass may vary more than length within an individual, depending on seasonal changes in body condition, recency of prey consumption, and reproductive status (Seigel and Ford 1987). Further, length has been shown to be correlated with body mass (Kaufman and Gibbons 1975; Guyer and Donnelly 1990), and both length

2 346 S. M. BOBACK AND C. GUYER and mass produce similar results in macroecological analyses (Brown 1995). Therefore, we use body length as an estimate of body size in all analyses presented below. We surveyed published field guides for data on snake body length (Donoso-Barros 1966; Pitman 1974; Arnold and Burton 1978; Vanzolini et al. 1980; Stebbins 1985; Cei 1986; Dixon and Soini 1986; Cogger 1992; O Shea 1996; Murphy and Henderson 1997; Conant and Collins 1998; Cox et al. 1998; for a list of references on insular populations, see Boback 2003). Data used for this project can be seen at edu/academic/science math/cosam/museum/machome.html. Because most sources report maximum total length (max TL in mm), we used this as an estimate of snake body size. However, for the regression of island body size on mainland body size, we used maximum snout-to-vent length (max SVL in mm) because most previous work on island populations reported this variable. For those studies that reported mean SVL, we estimated maximum SVL from an equation generated from a subset of data for which both maximum and mean SVL were reported (Boback 2003). We used the maximum value for each species regardless of sex. Snakes do exhibit sexual size dimorphism (Shine 1993). However, because we were interested in comparing snakes to macroecological patterns documented in other groups of animals, we ignored sexual size dimorphism in the same way that previous authors have done for other groups (e.g., Brown et al. 1993; Marquet and Taper 1998). Additionally, snakes have indeterminate growth. Thus, our use of measures of maximum size may overestimate the actual size distribution. However, snakes do not grow at the same rate throughout their lives because growth is severely reduced at sexual maturity (Andrews 1982). Thus, while functionally capable of continued growth, this is rarely realized in nature. Because of this, the largest individuals known for a species should be a reasonable sample of the size potential for that species. Analysis We amassed a database of the maximum total lengths of 618 snake species from around the world and generated a frequency distribution from these data. Because log-transformation is recommended for examination of frequency distributions of body size or traits related to body size across multiple species (Peters 1983; Calder 1996; Brown 1995), we used log 10 -transformation on all size measures. The distribution was tested for normality, skewness, and kurtosis. To examine patterns of body size for snakes on islands, we used a subset of the data (i.e., those species for which island body size was available, N 78) and created two separate regressions in which the dependent variables, largest or smallest snake species (log 10 [cm]), were regressed on the independent variable, island area (log 10 [km 2 ]). Individual island areas were estimated for island archipelagos from throughout the world (Gulf of California; Caribbean; Lake Erie, U.S.; Sweden; Cyclades; South Australia; and Japan; Boback 2003). Confidence limits were calculated for the point where the two regression lines, described above, bisected one another. Because species richness is correlated with island area, a relationship between body size and island area may be expected simply because larger islands tend to support more species. Therefore, we evaluated the influence of random sampling of the pool of snake body lengths (N 618) on the observed regressions of largest and smallest species on island area. For each island, a bootstrap procedure randomly created a species assemblage (drawn from the overall pool) that was equal in size to the actual assemblage. The largest and smallest species from each random assemblage (N 78) were then plotted against island area for all islands. This procedure was repeated 1000 times and the y-intercept, slope and R 2 were calculated for each iteration. The means of these parameters were used to create regression lines for the randomly drawn smallest and largest species on island area. By comparing regression statistics (slope, y-intercept, and R 2 ) from the real and randomized data, we determined how real island snake assemblages differed from those expected at random. Finally, for snake species with mainland and island populations, we regressed island body size on mainland body size and tested whether the slope from this regression differed significantly from a reference line bisecting the origin and with a slope of 1.0. A line with a slope significantly less than 1.0 was used to indicate that, on average, small mainland species evolved large island races and large mainland species evolved small island races (Lomolino 1985). Based on the regression analysis, confidence intervals were calculated for the regression line and 95% confidence limits were determined for the point at which the regression line crossed the reference line. We did not consider phylogeny in our study and acknowledge that within snakes numerous ecologically or phylogenetic groups exist which may show different properties relative to the overall patterns revealed (Pough 1983). Analyses considering such groups would be fruitful, but current phylogenetic hypotheses for snakes are far from complete. However, we note that a previous analysis suggests that phylogenetic effects are likely to be minimal for analyses of snake body sizes (Boback 2003). All tests were performed using SPSS 10.0 statistical software (SPSS 1999) and included tests of normality, skewness and kurtosis, linear regression, analyses of covariance (AN- COVA), and overlap of 95% confidence intervals. The skewness coefficient was considered significant if the absolute value of skewness divided by its standard error was greater than 2 (Reed and Boback 2002). For all tests, was set at P 0.05 (Zar 1984). RESULTS A frequency distribution of the base 10 logarithms of snake body sizes (N 618 species, 24% of the world s 2700 total species; Greene 1997) was unimodal and significantly nonnormal (mode 2.0, Kolmogorov-Smirnov Statistic 0.062, df 618, P 0.001, SD 0.283; Fig. 1). The modal size category included snakes of 0.88 to 1.08 m in total length. Additionally, the distribution was leptokurtotic (kurtosis 0.435, SE 0.196) and positively skewed (skewness 0.029, SE 0.098), but the latter was not significant ( skewness /SE of skewness 0.296). Significant regressions were obtained for both the largestsized (N 78, R , F 30.57, slope 0.073, P

3 OPTIMAL BODY SIZE IN SNAKES 347 FIG. 1. Frequency distribution of body sizes of 618 snake species from across the world. This sample represents approximately onefourth of the world s 2700 species ) and smallest-sized (N 78, R 2.30, F 33.28, slope 0.119, P 0.001) snake species in island assemblages plotted against island area (Fig. 2). Body sizes of the largest species decreased with decreasing area whereas the body sizes of the smallest species increased with decreasing area. The regression lines for the body sizes of the largest and smallest species in an assemblage intersected at a point implying that landmasses of 0.1 km 2 would support a single species with a body size of 1.22 m (95% CI m). Direct examination of one-species islands from our data revealed a mean body size of 1.06 m (95% CI m; N 20 populations of six species). These results encompass the modal category from the previous analysis. Because larger islands tend to support a greater number of species and thus have a greater probability of supporting species of extreme body sizes, we tested the effect of random sampling on the regressions of the largest and smallest species plotted against island area. We found that the y-intercept from the regression of the largest species on island area was significantly greater than the y-intercept of the regression using randomized data (P 0.037; Fig. 3D). However the slope and R 2 of these regressions were not statistically different (P 0.301, 0.076, respectively; Fig. 3E, F). These results suggest that, in general, the largest snake species in island assemblages are consistently larger than expected at random regardless of area. The y-intercept, slope and R 2 from the regression of the smallest species on island area were significantly different from those generated from a randomization procedure (P 0.001, 0.002, and 0.023, respectively; Fig. 3A, B, C). Specifically, the y-intercept was greater and the slope steeper than the regression based on randomized assemblages (Fig. 2). This indicates that on small islands the smallest species was larger than expected at random and on large islands the smallest species was smaller than expected at random. The intersection of the regressions of the largest and smallest species on island area was at a slightly greater body size but at a much greater island area for real data than for randomized data (1.22 m compared to 0.92 m for body length; 0.12 km 2 compared to 0.03 km 2 for island area).this indicates that single-species islands are larger in area than expected at random, and both random and real data predicted a similar body size for these islands. The relationship between size of the smallest species and island area was stronger for real data than for random data, suggesting a constraint on the sizes of the smallest snakes present in island assemblages. To explore body size change within a species, we compared populations on islands to the mainland source population by regressing island body size on mainland body size and testing whether the slope of this line differed from a reference line FIG. 2. Linear regression of the largest ( ) and smallest ( ) snake species in an assemblage plotted against island area (N 78). Regression lines based on real data are shown as solid lines. Regressions based on 1000 iterations of randomly created species assemblages are shown as dotted lines.

4 348 S. M. BOBACK AND C. GUYER FIG. 3. Frequency distributions of regression statistics (y-intercept, slope, and R 2 ) created from 1000 iterations of randomly drawn species assemblages. The top three graphs (A, B, and C) are the y-intercept, slope, and R 2 values, respectively, from the smallest species in an assemblage plotted against island area. The bottom three graphs (D, E, and F) are the y-intercept, slope, and R 2 values, respectively, from the largest species in an assemblage plotted against island area. The relative positions of real values are indicated with stars (significant) and arrows (not significant). of no change (Fig. 4). ANCOVA revealed a significant linear relationship, the slope of which was significantly less than 1.0 (Y 0.893X 0.523, F 22.56, P 0.001, N 30). The body size at which mainland and island races were expected to be of equal size (i.e., the intersection between the FIG. 4. Linear regression of island body size [log 10 (max SVL)] plotted against mainland body size [log 10 (max SVL)] for 30 species of snakes from four snake families: Colubridae, Viperidae, Boidae, and Elapidae. The dotted line indicates a line through the origin with a slope of 1. regression line and the reference line) was 0.74 m (95% CI m). These results encompass values derived from the previous two analyses. DISCUSSION We found three patterns that suggest an optimal length of 1.0 m for snakes, a length that converts to a mass of 384 g ( g, based on M TL 3.02 from Pough 1980). These patterns replicate those published for mammals, a group with an optimal size of 100 g (Brown 1995). The concordant patterns from these two disparate animal clades strongly argues for a common explanation for the evolution of optimal sizes for all large taxonomic groups. However, our results do differ from previous studies in suggesting that the shape of body size distributions of major clades are not constant and that it may be easier for some groups to become small than it is for them to become large. In evaluating these results, we discuss the implications of each pattern separately and explore possible explanations for each. The frequency distribution of snake body sizes indicates a single mode and dispersion around the mode that is not heavily skewed. Such a unimodal distribution is consistent with the expectation of an optimality hypothesis, a hypothesis that would have been inconsistent with uniform or multimodal distributions of body size. However, this evidence alone is weak because other hypotheses make the same prediction of a unimodal distribution. For example, random evolutionary walks beginning at a particular size (i.e., a 1.0-m ancestor) could theoretically produce the distribution that we observed for snakes.

5 OPTIMAL BODY SIZE IN SNAKES 349 Our observation of a log-normal size distribution for snakes differs from nearly all other groups for which body size distributions have been evaluated, the majority of which have a strong right skew (Brown 1995). We see three plausible explanations for this finding. One explanation is that body size distributions may appear approximately log normal when sampling is inadequate and will become more right skewed as remaining taxa are added (Blackburn and Gaston 1998). Reed and Boback (2002) found that recently described species from North American and Australian snake faunas were smaller than expected from random draws from the overall size distribution of snakes. Thus, it is likely that undiscovered snake species are of a small size and when the sizes of all species are known, the snake distribution will become more right skewed. However, the body size distribution for the North American snake fauna, a group for which relatively complete data are available, is not significantly right skewed (Reed and Boback 2002). From this, we suggest that the final distribution for the world s snake fauna will not be altered strongly by missing species (for a similar argument, see Roy et al. 2000). For this reason we expect the distribution of snake body sizes to remain different from those of other animals (Brown 1995). A second plausible explanation for the disparity in the shape of size distributions between snakes and other animals is differences between energy demands of endotherms and ectotherms (Pough 1980). Birds and mammals appear to have limited scope to become significantly smaller than the modal size because energetic demands to maintain body temperature through physiological means become too high due to unfavorable surface-to-volume ratios. This and related ecological features (e.g., a need for small endotherms to consume diet items of high energetic content) are thought to create the right skew to the distribution of body size in birds and mammals (Brown and Maurer 1989). Ectotherms, like snakes, lack such a constraint and, therefore, may have greater scope to become smaller than the modal size (Pough 1980). If this is true, then other features may constrain distributions of body size in ectotherms. Four such ectothermic groups have been studied to date and all possible patterns of skewness have been observed: mollusks are left skewed (Roy et al. 2000), fish are right skewed (Brown et al. 1993), and snakes and insects show no skew (this study; Morse et al. 1988; Schoener and Janzen 1968). Therefore, idiosyncratic features of the natural history of ectotherms may create patterns of body size that require independent explanations rather than the consistent physiological constraint of endotherms. Nevertheless, common constraints should characterize the smallest species within clades. For example, the smallest mammals appear to be constrained to eat rich foods that are patchily distributed because only these foods provide enough energy to overcome problems associated with high surfaceto-volume ratios of small endotherms (Brown and Maurer 1989). Small snakes should face similar challenges and thus the lower size limit for snakes may be similarly bound, although such physiological constraints should occur at smaller body sizes in snakes than in mammals. Such constraints are inferred because the mass-specific metabolic rates of mammals and snakes increase exponentially as body sizes approach minimum values for the two groups (Bennett and Dawson 1976; Vaughan 1986). Interestingly, the smallest species of snakes (families Leptotyphlopidae and Typhlopidae) specialize on soft-bodied invertebrate prey, such as ant and termite larvae, that are distributed in discrete patches across the landscape. Limited data on foraging ecology of these small snakes indicate that they encounter nests of insects infrequently, but when they do they engorge themselves on larvae (Webb et al. 2000). If colonies of these social insects become inactive or move because of the presence of a predator (e.g., Munger 1984), then small snakes may be required to move relatively widely to find the next rich patch of prey. If this is true, then small snakes should mirror small mammals in having larger home ranges and larger geographic ranges than expected based on positive correlations of home range or geographic range sizes and body size (Marquet and Taper 1998). A third explanation for differences in the shape of the size distribution among animal groups is mechanical constraints on locomotion. For example, minimum and maximum wing beat frequencies associated with flapping flight may set distinct limits on the body masses available to flying animals (Pennycuick 1986). Similar locomotive constraints may be operating in snakes, most of which propel themselves forward by using sinusoid lateral waves of their elongate bodies to push off of irregularities of the substrate (Cundall 1987). Locomotor efficiency of such limbless crawling depends on the distance between substrate irregularities and body size (Gray 1968). If sizes of, and distances between, such irregularities are log-normally distributed like most objects in the universe (e.g., sand grains; Brown 1995), then the body size distribution of snakes might be constrained to a similar shape because of their need to make use of the substrate irregularities. Although no data are available to test this hypothesis, we view it to be worthy of consideration and encourage examination of similar constraints in altering size distributions of other organisms. In examining the assemblages of snakes on islands, we found that, as island area decreases, the extremes of body size of the snake fauna decrease and the body size predicted for snakes on single-species islands approaches that of the modal body size of all species (1.0 m). However, this pattern alone is weak evidence for a convergence towards an optimal size because the null expectation makes a very similar prediction. Thus, this analysis appears to have little chance of documenting an optimal body size that differs greatly from the mode of the overall size distribution. Nevertheless, the converging regression lines still are interesting for what they imply about single-species islands. Additionally, observed data for snakes differ from the null expectation in three interesting ways. First, the largest snakes are consistently but only slightly larger than expected regardless of island size (or faunal diversity). This corroborates previous analyses that show that snakes are unlikely to get very large when they do become giants (Boback 2003). Second, the smallest snakes have greater scope to change in body size as area decreases or faunal diversity decreases. Current data indicate that the smallest snakes are smaller than expected on large (speciesrich) islands and larger than expected on small (species-poor) islands. This may indicate a strong role for competition in setting the size of the smallest species and that there is stron-

6 350 S. M. BOBACK AND C. GUYER ger pressure for species that are smaller than the mode to reach the optimal size than for species that are larger than the mode. Overall, the data indicate that on two-species islands there will be one species larger than the mode and one species smaller than the mode, but that the smaller species will be closer to the mode than the larger one. This may indicate that the mechanism creating the pattern of body sizes observed in Anolis lizards on one- and two-species islands in the Caribbean (i.e., character displacement or taxon-loop cycle; Schoener 1970; Losos 1990) may be broadly applicable to squamates. For snake species that have island and mainland populations, we found that small species become larger on islands, whereas large species become smaller on islands. Estimates of the size at which island populations will be unchanged relative to mainland populations were nearly identical to the mode from the size distribution (1.0 m). This pattern is the strongest evidence that body sizes within groups are evolving toward an optimum. Lomolino (1985) documented a similar pattern in mammals (viz., the island rule; Foster 1964) and reasoned that reduced competition in depauparate insular communities enables small species to increase in size and take advantage of resources normally consumed by larger members of the communities while resource limitation causes large species to become dwarfed. If this is true of snakes, then competition is a relatively unimportant force and resource limitation a relatively important force in shaping changes of body size within species because relatively few small snakes become giants on islands and relatively many large snakes become dwarfs. In this respect, snakes appear to differ from mammals. However, this disparity in the level of response of small versus large snakes corroborates previous analyses that found dwarfism to be more prevalent in snakes (Case 1978; Boback 2003). The patterns emerging from studies of body size of monophyletic groups across broad landscapes suggest a common explanation for optimal body sizes in such groups. One such explanation is the reproductive power hypothesis of Brown et al. (1993). This model has successfully predicted the observed distributions of body size in mammals (Brown et al. 1993), birds (Maurer 1998), and mollusks (Roy et al. 2000). To test this model in snakes, either data on biomass density and biomass turnover within populations or data on individual growth and reproductive output are needed from a representative sample of snake species. Unfortunately, such data are not available. However, such data can be generated and, if the reproductive power model successfully recreates the observed distribution of snake body sizes, then this would provide powerful new support for a universal model for the evolution of body size within disparate lineages of animals. ACKNOWLEDGMENTS Discussions with R. N. Reed and W. D. 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