Changes in the selection differential exerted on a marine snail during the ontogeny of a predatory shore crab

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1 doi: /j x Changes in the selection differential exerted on a marine snail during the ontogeny of a predatory shore crab D. PAKES 1 &E.G.BOULDING Department of Integrative Biology, University of Guelph, Guelph, ON, Canada Keywords: complex traits; fitness function; Hemigrapsus; Littorina; predator growth; selection intensity; sexual dimorphism; shell thickness; size structure; viability selection. Abstract Empirical estimates of selection gradients caused by predators are common, yet no one has quantified how these estimates vary with predator ontogeny. We used logistic regression to investigate how selection on gastropod shell thickness changed with predator size. Only small and medium purple shore crabs (Hemigrapsus nudus) exerted a linear selection gradient for increased shell-thickness within a single population of the intertidal snail (Littorina subrotundata). The shape of the fitness function for shell thickness was confirmed to be linear for small and medium crabs but was humped for large male crabs, suggesting no directional selection. A second experiment using two prey species to amplify shell thickness differences established that the selection differential on adult snails decreased linearly as crab size increased. We observed differences in size distribution and sex ratios among three natural shore crab populations that may cause spatial and temporal variation in predator-mediated selection on local snail populations. Introduction Predation is an important factor affecting the species composition and size structure of communities (Paine, 1976; Sih, 1987) as well as the evolution of prey behaviour (Stachowicz & Hay, 1999), morphology (Vermeij, 1977) and life history (Reznick et al., 1996, 1997). Predation has been shown to change the phenotypic distributions of prey traits in natural populations (Kettlewell, 1973; Gunnarsson, 1998; Edgell & Rochette, 2008) and to be partially responsible for maintaining species differentiation between closely related taxa (Kruuk & Gilchrist, 1997). Many predator prey systems are ideal for manipulating the predator s presence and looking at the target and basis of selection in the prey population. However, surprisingly few studies have demonstrated so (but see Breden & Wade, 1989; Swain, 1992a,b; Reznick et al., 1996, 1997; Van Buskirk et al., 1997; Hendry et al., 2006; Stoks et al., 2007). Even fewer Correspondence: E. G. Boulding, Department of Integrative Biology, University of Guelph, Guelph, ON, Canada N1G 2W1. Tel.: , ext: 54961; fax: ; boulding@uoguelph.ca 1 Present address: 17 Bennett Lane, Stony Brook, NY 11790, USA. studies have demonstrated selection for specific morphology that allows escape from predators (McPeek, 1997; Calsbeek & Irschick, 2007; Møller et al., 2009). Predator feeding structures may show allometric changes in form and in relative size during ontogeny, and this may change the strength and form of natural selection on their prey populations. Most previous studies on the effect of predator ontogeny on prey populations have looked at how ontogenetic changes in predator feeding apparatus might affect size selection of a particular prey species (e.g. shell-breaking crabs: Behrens Yamada & Boulding, 1998; piscivorous fishes: Holmes & McCormick, 2010). No previous studies have quantified how ontogenetic changes in the feeding apparatus of a predator population affect selection gradients on a prey population, as described here. Shell-crushing predatory crabs and their intertidal gastropod prey are an excellent model system for understanding the co-evolution of prey defences and predator feeding appendages for three reasons (e.g. Kitching et al., 1966; Heller, 1976; Warner & Jones, 1976; Vermeij, 1987). First, many snail species depend solely on a single trait, shell thickness to resist shell-crushing predators (Vermeij, 1977), thus the target of selection is clear. 1613

2 1614 D. PAKES AND E. G. BOULDING Second, intertidal gastropod populations that vary in shell thickness are easily accessible. Differences in size and shell morphology between wave-exposed and wavesheltered populations occur commonly within directdeveloping Littorina species (reviewed by Boulding, 1990; Reid, 1996). The thin-shelled Littorina subrotundata (Carpenter) lives on wave-exposed shores of the northeastern Pacific, where the density of predatory crabs are low (Boulding et al., 2007), whereas the thicker-shelled L. sitkana Philippi (Boulding & Van Alstyne, 1993; Boulding et al., 1993) lives on wave-sheltered shores where the purple shore crab, Hemigrapsus nudus (Dana), the red rock crab Cancer productus Randall and other shellcrushing predators are abundant (Behrens Yamada & Boulding, 1996). Finally, the differences in shell thickness between populations that live in both high-predation and those that live in low-predation habitats are heritable. The larger size and thicker shells of snails from wave-sheltered shores have been shown to be partially because of genetic adaptation to predatory shore crabs (which have been shown to prefer smaller and thinner-shelled individuals Seeley, 1986; Johannesson & Johannesson, 1996; Rolán- Alvarez et al., 1997; Rochette et al., 2007) and partially because of crab-effluent-induced plasticity (Johannesson & Johannesson, 1996; Trussell, 1996; Dalziel & Boulding, 2005). However, no one has estimated how variation in shell thickness within a single population of a marine snail species translates into variation in resistance to a population of predatory shore crabs with a particular sex ratio and size distribution. Positive selection differentials could result in evolution of thicker shells, because shell shape and shell thickness have been shown to be significantly heritable (h 2 = ) in a wave-exposed L. subrotundata population (Boulding & Hay, 1993). The object of this study was to test whether the purple shore crab shows a preference for thinner-shelled adults from within a single population of L. subrotundata, whether the strength of the preference decreases with increasing crab size, and whether the selection differentials on shell thickness exerted by different sizes of these crabs vary as a result. We then demonstrate that there exists significant variation in the size distribution and sex ratios of natural crab populations that we hypothesize would be great enough to cause spatial variation in the selection differentials for shell thickness among their local L. subrotundata populations. Materials and methods Study system Experiments testing effect of predator ontogeny on selection on prey morphology were carried out near Bamfield Marine Sciences Centre (BMSC) on the west coast of Canada between 1999 and The predator species used was the purple shore crab, H. nudus, a generalist omnivore (Kozloff, 1987). Its unspecialized claws make it an inefficient predator on large, thickshelled snails which it must attack by slowly chipping away at the shell aperture (Behrens Yamada & Boulding, 1998). The focal prey species used was the herbivorous intertidal snail Littorina subrotundata that lays attached egg masses that develop directly into crawl-away juveniles resulting in low dispersal (see Boulding et al., 1993). When tethered in areas of high shell-crushing predation, individuals of the thin-shelled species (L. subrotundata) have substantially higher mortality than similarly sized individuals of the thick-shelled species (L. sitkana) (Boulding et al., 1999, 2007). This difference in mortality has been confirmed by laboratory experiments (Boulding et al., 2007) to be a result of shell thickness alone, because crabs showed no preference for live snail tissue between the two species (E.G. Boulding, pers. obs.). Expt 1: Preference for thinner-shelled snails within a prey population Feeding trials were conducted using snails collected from Seppings Island, BC in July 1999 to test whether predatory purple shore crabs (H. nudus) prefer the thinner-shelled individuals from within a single population of snails (L. subrotundata). The shell thickness of L. subrotundata was estimated from the blotted wet weight of the live snail. We chose to measure blotted wet weight: x (± 0.1 mg) because it is highly repeatable (r = 0.995, N = 48, P < 0.001) and is highly correlated with dry shell weight: y (y = x)0.7197, r = 0.896, N = 41, P < 0.001) because it gives a more precise estimate of shell thickness for this small and very thin-shelled species than measuring shell lip thickness directly with callipers (Pakes, 2002). We also measured maximum snail length (from the tip of the apex to the base of the collumella) and shell width (at the widest point perpendicular to the shell length). The snails were first sorted into a medium adult size-class by sieving (shell lengths mm) and were then further separated into narrow 0.1-mm-shell length size-classes using electronic callipers. The ten snails from a particular narrow size class that were offered to a particular crab were individually marked with coloured paint. Previous work has shown that crab preference was not affected by paint colour (Pakes, 2002). Containers were monitored twice daily, and the trials were terminated once the crab had eaten half of the snails. In total, 22 different male purple shore crabs of three size classes ( mm, mm and mm carapace width) ate at least half the snails in each trial. These consisted of ten replicates of the 10-mm size class, three replicates of the 14-mm size class and nine replicates of the 18-mm size class, with each replicate trial consisting of 10 individually marked snails. Note that we can calculate standardized selection differentials within a particular trial for a particular crab using the usual formula (eqn 2). Before analysing the dataset, we standardized the snail morphometric data, so that we

3 Ontogenetic changes in selection differentials 1615 could compare different trials. We calculated the relative wet weight by dividing each snail s weight by the average weight and calculated the relative width by dividing each snail s shell width by the average width of the snails in that particular trial. The data for all three size-classes of crabs combined were then initially analysed using multivariate logistic regression in SPSS with binary fitness (eaten or not) as the dependent variable, and relative wet weight and relative shell width as the independent variables (Janzen & Stern, 1998). Analyses were carried out separately for the large and small size-classes of crabs and also for all size-classes with carapace length as a categorical covariate. This analysis showed that relative shell width could be removed from the model, so subsequent logistic regression analyses used only relative weight. Selection of the best univariate logistic regression model was then performed using Akaike Information Criterion (AIC): AIC ¼ 2k 2lnðLÞ ð1þ where k is the number of parameters in the statistical model, and L is the maximized value of the likelihood function for the estimated model, which estimates how well the model fits the data (Akaike, 1974). The models compared were linear and quadratic univariate logistic regression models with binary fitness (probability of survival) as the dependent variable (Janzen & Stern, 1998) and relative wet body weight (@ relative shell weight) as the primary independent variable and shell width as a second independent variable. Akaike (1974) recommends using the model with an AIC value that is smaller by at least 2.0 than those of competing models. Burnham and Anderson (2002) recommend selecting the model with an Akaike weight that is large relative to those of competing models. AIC model selection calculations were carried out by modifying unpublished R Scripts for R (D. Schluter accessed February : Rtips.models.html#gam). A cubic spline analysis was used to determine whether the shape of the fitness function for shell thickness in this population of L. subrotundata was better approximated by a linear, by a quadratic or by some higher order polynomial. This method estimates a fitness function using a non-parametric method, which is useful because no assumptions are made regarding the form of the function (Schluter, 1988; Schluter & Nychka, 1994). The computer program GLMS 4.0 (Schluter, 2000) was used to estimate the best spline fit and its standard error. The program searches over a range of values of the smoothing parameter lambda minimizing the generalized crossvalidation function (GCV score). The program also estimates the number of effective parameters needed to fit the data; an example of a fit with two effective parameters will be a straight line logistic regression with a positive slope whereas an inverse parabola (or hump) would be an example of a fit with three effective parameters (Schluter, 2000). We estimated the shape of the fitness functions for each of the following size classes: (i) 10-mm carapace width size-class (small) crabs, (ii) 18-mm size-class (large) crabs, (iii) all three size classes combined with carapace width as a categorical covariate (with three levels: 10, 14, and 18 mm), and (iv) 10-mm and 14-mm size-classes combined. Expt 2: Selection differentials on shell thickness as a function of predator size To quantify how the standardized selection differential exerted by the purple shore crab on the shell thickness of its prey changed with predator size, we did an additional experiment using a wide and continuous range of crab sizes. To increase statistical power in this second experiment, we used two different species of Littorina as prey that had a large difference in mean shell thickness. The shell of an adult L. subrotundata is very similar in shape to that of L. sitkana, but its shell is only about half as thick (Boulding et al., 2007). Snails were collected from wave-exposed shores (L. subrotundata) and from tide pools (L. sitkana) on Seppings Island and were then sorted into size-classes by sieving. The medium size-class used for this experiment was defined as snails that passed through 4.00-mm mesh sieve but were retained on a 3.35-mm mesh sieve. Laboratory conditions for keeping crabs and snails were as described for previous trials. Equal numbers the two prey species (25 of each Littorina species for crabs 17 mm carapace width and 50 of each snail species for crabs > 17 mm) were offered to each of 19 different crabs that were held individually in plastic containers. The containers were checked every two to three hours for larger crabs and twice daily for the smaller crabs. A trial for a particular crab was ended when approximately half of the snails were eaten. To estimate the selection differential on shell thickness for each crab, the standardized selection differential, i, for each trial was calculated using the usual form of eqn 2 (Endler, 1986). The variables substituted into eqn (2) were slightly modified because in this feeding experiment shell thickness is a discrete variable with only two possible values for this particular size-class: the mean thickness of the thin-shelled species, L. subrotundata, or the mean thickness of the thick-shelled species, L. sitkana, rather than having a continuous distribution as when a single species is used; these are shown in eqns 3 to 5 below which are the usual equations for calculating means and variances from frequency distributions of counts (Snedecor and Cochran, 1980) when there are only two classes of prey: The standardized selection differential for each trial (each crab), which measures the selection intensity on a trait, was then calculated using the following formula (from Endler, 1986, pg. 171):

4 1616 D. PAKES AND E. G. BOULDING r 2 b ¼ i ¼ ðl a l b Þ r b l b ¼ l a ¼ P 2 j¼1 P 2 j¼1 N b f j X j P 2 k¼1 N a g k X k f j ðx j l b Þ 2 N b 1 ð2þ ð3þ ð4þ ð5þ (a) (b) where l b is the mean shell weight of the prey offered before selection, l a is the mean shell weight after selection, f j is the frequency of each of the two snail species before selection, whereas g k is the frequency of each of the two snail species after selection, X j are the mean shell weights of mm mesh size-class of each species j, which are equivalent to X k when j = k, N b is the total number of both species before selection, whereas N a is the total number of both species after selection, and r 2 b is the sample variance of the mean weight of both species of snails before selection. Note that the selection differential will be positive when more of the thin-shelled species are eaten relative to the thickshelled species. Linear regression was then used to test for a relationship between the selection differential on shell thickness and crab size. Only male crabs were used in this calculation, because as shown below purple shore crabs have sexually dimorphic claws. Spatial variation in size distribution of crabs Three field sites were surveyed to examine whether there was significant variation in the size distribution of natural purple shore crab (H. nudus) populations. All sites chosen were semi-exposed areas where the purple shore crab is known to be abundant near BMSC. Two sites were on Dixon Island, the first on the west side and the second on the east side (see Fig. 1 in Boulding et al., 1999). The third site was on the east side of the mouth of Grappler Inlet. Because crabs move up and down the shore depending on the tidal level, a search was first performed to find the tidal level that had the highest densities of crabs. The tidal level sampled ranged from 0.0 to 2.0 m above 0.0 m datum of Canadian Hydrographic Services. Measuring tape was laid out to form a horizontal transect parallel to the shoreline at a particular site. Five 1.0 m 2 quadrats were then placed at random immediately above or below the measuring tape. These surveys were carried out at the time of the lowest daily tide, during the first week of January All crabs within a quadrat were captured, sexed and measured before being released. The measurements included sex, carapace width and claw Fig. 1 Cubic spline generated fitness function (Schluter, 2000) showing probability of survival as a function of relative blotted wet weight of Littorina subrotundata collected from Seppings Island. Surviving snails were assigned a fitness of 1, and those eaten by Hemigrapsus nudus were assigned a fitness of 0. Dashed curves indicate ± 1 SE of predicted values from 200 bootstrap replicates of the fitness function. (a) Crabs of carapace width of 10 mm. N snails = 94, ln(k) = 10, parameters = 2.0, shape = linear, GCV = (b) Crabs of carapace width of 18 mm. N snails = 88, ln(k) =)5, #parameters = 2.84, shape = inverse parabola, GCV = size (maximum length of fixed finger). The data from all transects at a particular site were combined for subsequent analysis. To test whether sites differed significantly in their size distribution of crabs, Kolmogorov-Smirnov two-sample tests were performed between all pairs of sites for the trait carapace width. This was performed both within sites between sexes and among sites within sexes. The sexual dimorphism in claw size between males and females was tested using the ANCOVA model: Y ¼ B X þ S i þ S i X ð6þ where Y is claw size, X is carapace width, B is the slope, and S i is sex. The frequency distribution for the selection differentials exerted by male crabs of different sizes was predicted separately for each site. The data for each site were obtained by multiplying the number of male crabs of each size class by the selection differential predicted for that particular size class using the regression equation

5 Ontogenetic changes in selection differentials 1617 Selection differential (i) Crab carapace width (mm) Fig. 2 The selection differential on shell thickness for a range of male crab sizes offered two species of Littorina that differ on shell thickness. The regression equation is y = )0.0175x r 2 = 0.184, P = See Fig. S2 for an alternate presentation of these data in terms of crab preference. from Fig. 2. A Kruskal-Wallis test on the mean ranks was then used to see whether there were significant differences among the selection intensities predicted for each of the three sites. was substantially higher when the covariate, carapace width was omitted from the analysis and was higher for the quadratic model than for the linear model (Table S2). However, the Akaike weight for the combined data for the 10-mm and 14-mm size-classes was higher for the linear model than that for the quadratic model (Table S2). The cubic spline analysis indicated that the shape of the fitness function relating snail shell weight to survival differed for the smallest and largest size-classes of crabs. A parameter value of 2.0 was obtained for the small crabs (10 mm size-class: N = 96) and suggests that the fitness function fits a linear spline with a positive slope (Fig. 1a). In contrast, a parameter value of 2.83 was obtained for the large crabs (18 mm size-class; N = 89) and suggests that the fitness function has a more humped shape (Fig. 1b). The logistic regression for the pooled data for all 22 crabs of different sizes also had a parameter value of 2.83 suggesting linear directional selection perhaps with some stabilizing selection (Fig. S1a). This interpretation was supported by the parameter value of 2.03 suggesting linear directional selection that was obtained when a spline was fit to the small and medium size-classes combined (Fig. S1b). Results Expt 1: Preference for thinner-shell snails within a prey population Individual purple shore crabs often exerted positive selection differentials on the shell thickness of their prey within a particular feeding trial. Standardized selection differentials obtained for shell weight for 10-mm sizeclass of crabs averaged (SD = 0.147, N = 6) and ranged from to For 18-mm size-class of crabs, the selection differentials averaged (SD = 0.198, N = 8) and ranged from to Most of the values were positive, indicating that the crabs were selectively eating lighter (= thinner-shelled) individuals and rejecting the heavier (= thicker-shelled) snails. Multivariate logistic regression analysis indicated that smaller purple shore crabs selected snails within a single population of L. subrotundata from Seppings Island based on variation in shell weight (Table S1). As relative shell width was not significantly related to fitness, it was removed from the multivariate logistic regression model. When the data were reanalysed with the univariate logistic model, relative wet weight (@ shell weight) had a significant effect on the probability of survival (Table S1). Model selection using AIC values and Akaike weights suggested that the 10-mm size-class was best modelled using a linear logistic regression model but that the 18-mm size-class was best modelled using quadratic logistic regression model (Table S2). Interestingly, the Akaike weight for the combined data for all size-classes Expt 2: Selection differentials on shell thickness as a function of predator size Figure 2 highlights that the standardized selection differential on shell thickness of a single size-class of snails decreased approximately linearly as crab size increased. The selection differential on shell thickness was high for the smaller crabs (i = 0.4), because they ate relatively more of the thin-shelled species (Fig. S2). In contrast, the selection differential on shell thickness was low for larger crabs, because they ate approximately equal amounts of the two snail species (Fig. S2). A regression with the selection differential as the dependent variable and the crab size as the independent variable explained 69% of the variance and had a negative slope that was significantly different from zero (y = )0.0175x , P < 0.001, F = 19.58, df = 1, 16, r 2 = 0.69, n = 17, Fig. 2). Spatial variation in the size distribution of crabs The size distributions of the purple shore crab differed among the three field sites (Fig. S3a c). There were significant differences in the size distribution of females between all pairwise comparisons of the sites (P < 0.001). There were also significant differences in the size distribution of males in 2 3 pairwise comparisons (sites 1 2 P < 0.001; sites 2 3 P = 0.074; sites 1 3 P < 0.001). In addition, there was a significant difference in the size distribution of the sexes in site one, but not in sites 2 and 3 (Kolmogorov-Smirnov two sample test between pairs of groups: site 1 maximum difference (md) = 0.44

6 1618 D. PAKES AND E. G. BOULDING (P < 0.001), site 2 md = 0.26 (P = 0.17), site 3 md = 0.13 (P = 0.82). ANOVA followed by a Tukey test confirmed that the male crabs at site 1 had a smaller mean carapace width than crabs at sites 2 and 3 (Table S3). The morphometric analysis showed that the purple shore crabs surveyed at the study sites had sexually dimorphic claws. The length of the fixed finger of the claws of males was significantly larger than those of females of the same carapace width (ANCOVA, P < 0.001). The linear regression equation for claw length as a function of carapace width for males was y = x) (N = 124, P < 0.001) and for females was y = x) (N = 125, P < 0.001). Because of this difference, we only consider the selection differentials from male crabs below. We used the regression of size vs. selection differential and the size distribution of the male crabs at the three sites to test whether there was likely to be differences in the median selection differential for shell thickness among the three field sites. The standardized selection differential for increased shell thickness predicted for the male crab population based on the distribution of carapace widths was much greater at site 1 than at sites 2 or 3 (Fig. 3). A Kruskal-Wallis test comparing the ranked intensities of selection for the different crab sizeclass distributions among the three sites was highly significant (P < ). The mean ranks of the selection intensities for site 1 (median = 0.406) was significantly greater (P < ) than those for site 2 (median = 0.310) or for site 3 (median = 0.270). Discussion Intrapopulation selection on shell thickness The first laboratory preference experiment described here is unique in that it found directional selection for shell thickness within a single L. subrotundata population in which the phenotypic variation was comparatively small. Previous studies testing whether crabs prefer thin- over thick-shelled prey have compared snails from different populations known to differ on thickness (e.g. Kitching et al., 1966; Palmer, 1985; Johannesson, 1986; Rochette et al., 2007). Similarly, purple shore crabs show a significant preference for snails from thinner-shelled population of L. subrotundata over snails from a thickershelled population (Pakes, 2002). This suggests that natural phenotypic variation within a single population is sufficient to result in the evolution of thicker shells in response to selection by crabs given that live wet weight has a heritability of 0.3 (Boulding & Hay, 1993). The present study provides direct evidence that shore crabs prefer to consume thinner-shelled individuals within a single population and therefore supports the hypothesis that predation pressure may have been a key factor in the initial divergence of the thicker wavesheltered ecotypes typical of many direct-developing Frequency Site 1 Site 2 Site Littorina species from the thinner wave-exposed ecotypes (Boulding, 1990). Two major agents of selection that favour thicker gastropod shells on wave-sheltered shores are (i) crab predation (Kitching et al., 1966; Heller, 1976; Johannesson, 1986) and (ii) the risk of shell damage from moving boulders or stones (Shanks & Wright, 1986). Differences in predation intensity among habitats with and without crabs have repeatedly resulted in the evolution of wave-exposed and wave-protected ecotypes of L. saxatilis in Sweden (Janson, 1983), in Britain (Wilding et al., 2001) and in Spain (Rolán-Alvarez et al., 1997, 2004). Ontogenetic selection The cubic spline analysis suggests that the shape of the fitness function for shell thickness within a single L. subrotundata population was different when the snails were preyed upon by small or medium-sized crabs than when they were preyed upon by large crabs; however, it is important to consider uncertainties in the fit of the spline to the data. The shape of the fitness function for shell thickness exerted by the small (10 mm) size class of crabs was linear with a positive slope suggesting that directional selection is operating. However, the fitness function exerted by the large (18 mm) crabs was humpshaped suggesting stabilizing selection. Given the size of the estimated standard errors, it is also plausible that the function for the large crabs could be flat indicating that they are exerting neither directional nor stabilizing selection. Indeed, the uncertainty of the shape of the curve generated by the cubic spline program is known to be greatest at the ends of the phenotypic distribution where the density of data points is least (Schluter, 1988). Interestingly, the fitness function for all size-classes of crabs combined shows a significant fit to linear logistic Selection intensity Fig. 3 Frequency distribution for the selection intensities exerted by male crabs of different sizes found during our surveys of three sites (1: Dixon Island West, 2: Dixon Island East, 3: Grappler Inlet). The frequency distribution was obtained by multiplying the number of male crabs in each size-class (Fig. S3a c) by the selection differential predicted for that size-class by the regression equation from our second laboratory experiment (Fig. 2). 0.55

7 Ontogenetic changes in selection differentials 1619 model but a slightly higher Akaike weight for the quadratic logistic model as might be expected if the smallest size-class of crabs were exerting directional selection but the largest size-class was not. This is supported by our finding that the small and the medium size-classes combined fit the linear model best whereas the large size-class fit the quadratic model best. We present the first example from a predator-prey system where both the mechanism of selection and the change in the selection differential with predator size distribution are quantified. In the second laboratory feeding experiment that used two snail species to amplify the variation in shell thickness, the smaller crabs exerted a significantly larger selection differential for shell thickness than did larger crabs. This resulted in a linear decrease in selection intensity on this particular size-class of adult snails with increasing crab size. Size-dependent predation has been shown to strongly influence the structure and dynamics of natural populations (Sprules, 1972; Paine, 1976; Wootton, 1992; Sousa, 1993). In some cases, large size alone affords prey species a refuge from predation (Paine, 1976). However, our field tethering experiments demonstrate that even below an absolute size refuge, both size and shell thickness affect preference for L. subrotundata over L. sitkana by the purple shore crab (Boulding et al., 1999, 2007). Even when a predator may be capable of consuming a large prey individual, it may elect not to do so because of the longer handling time (Elner & Hughes, 1978; Boulding, 1984). What might this mean in terms of the evolution of prey in the presence of this type of predator? We speculate that where the predator population is dominated by small crabs, directional selection will act to shift the prey population to thicker-shelled snails. However, if large crabs dominate the predatory population, then the average shell thickness of the prey population is unlikely to shift. Of course, constraints on the evolution of thicker shells like reduced growth rate and higher allocation of energy to shell material (Palmer, 1981) could prevent a response to selection unless it is very strong. Variation in selection differentials and fitness functions The results presented here suggest the possibility that the shape of the fitness function for prey defensive traits may be different in different areas at different times because of the variation in the size distributions and in sex ratios of predator populations. Mathematical models of the evolution of quantitative traits lead to different conclusions depending on whether fitness functions are assumed to be Gaussian or quadratic (Gimelfarb, 1984). Previous studies in this predator prey system have assumed that the width of the fitness functions in different habitats were the same (Boulding, 1990; Boulding and Hay, 2001 but see Boulding et al., 2007). To predict the evolution of a phenotypic character in response to an agent of selection, the shape of the fitness function for all phenotypically correlated characters must be estimated. Further, study systems with more than one predatory agent of selection on the same trait make it more difficult to estimate the fitness function for that trait. For example, Weis et al. (1992) was able to distinguish the effects of multiple predators on the gallinducing insect Eurosta solidaginis and characterized the nature of selection on gall size and thickness. They found that size-dependent predation was caused by two primary sources, parasitoids that cause positive directional selection on gall size and predatory birds that cause negative directional selection. In our study with shore crabs (H. nudus) and snails (L. subrotundata), the agent and precise mechanism of selection is known, and the spatial variability in the selection differential can be quantified. In future studies, the selection differential could be manipulated in the field (e.g. Boulding et al., 2007) by building shelters for different sizes of crabs. Consequences of ontogenetic variation in selection Variation in the selection differential because of spatial and temporal variation in size distribution and sex ratios among predator populations is a possible mechanism for the maintenance of genetic polymorphism for shell thickness in snail populations. This generalization can be applied to most crab species feeding on gastropod prey as they all experience episodic growth in their claws as they grow and moult; as their claws become larger they will become stronger particularly if relative claw height increases allometrically resulting in a higher mechanical advantage (Warner & Jones, 1976). In this study, we found that male purple shore crabs showed higher rates of increase in claw length with ontogeny relative to females. Therefore, the sex ratio and growth rate of the predator population will likely affect the selection differentials on the prey population. Increases in claw length of purple shore crabs are correlated with increases in claw gape which allows larger snails to be placed inside the claw, so they can be crushed outright rather than slowly peeled open which greatly reduces handling time (Behrens Yamada & Boulding, 1998). In our experiment, only the small and medium purple shore crabs showed a preference for thinner-shelled L. subrotundata. However, in another laboratory study using the comparatively thick-shelled L. sitkana, even large purple shore crabs show a significant preference for the smallest and thinnest-shelled size-class that they were offered (Behrens Yamada & Boulding, 1998). Further, the size-adjusted shell weight of another thick-shelled snail, L. obtusata and the size-adjusted crusher claw-size of its predator, the European green crab were found to be highly correlated among sites along the northwestern Atlantic shores, suggesting local adaptation by this poorly dispersing snail (Edgell & Rochette, 2008).

8 1620 D. PAKES AND E. G. BOULDING We hypothesize that in this and other systems some of the genetic variation in a predator-selected trait may be maintained by spatial and temporal variation in the size structure of either the predator or the prey. Hairston & Dillon (1990) found year-to-year fluctuation in the selection differential by a fish predator which they attributed solely to variation in population density. The effect of prey size on the selection differential exerted by predators of a particular size has been investigated. Swain (1992a) found that the optimal ratio of abdominal to caudal vertebrae number in stickleback juveniles that were preyed upon by sunfish decreased as they grew larger because of its relationship to burst swimming speed. The maintenance of variation in vertebrate numbers in stickleback populations occurs because of both direct selection on vertebrae number and indirect selection on a correlated character; the ratio of caudal to precaudal length which change over the preys ontogeny (Swain, 1992b). Previous studies that do examine the target and basis of selection (Breden & Wade, 1989; Swain, 1992a,b; McPeek, 1997; Van Buskirk et al., 1997; Hendry et al., 2006) use only the presence and the absence of predators as their treatment and control respectively. Our experiments are novel, because they identify the direct mechanism of selection and provide the possibility of changing the selection differential by manipulating the size structure of crab populations. This study highlights the importance of predation as an agent of selection and suggests a mechanism that could maintain genetic variation in prey defences. We provide the first direct evidence for selection by predatory shore crabs of thicker-shelled snails within a population and suggest that the selection differentials from this agent of selection can vary during the ontogeny of the predator and therefore may also vary with the size structure of the predator population. Estimates of how predator-mediated selection changes with predator size are rare in the literature. If changes in predator-mediated selection with ontogeny are common, but are rarely estimated, then this could skew meta-analyses of the strength of phenotypic selection, especially as predator-mediated selection on morphology, here i = 0.4 for small crabs, is often stronger than selection mediated by other agents (Fig. 6 in Kingsolver et al., 2001). Acknowledgments We thank C. Caruso, T. Crease, T. Hay, B. Robinson and members of the Bogart Boulding Fu lab group for their suggestions for improving the manuscript and Ian Smith for redrawing our figures. We also thank D. 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