The allometry of fear : interspecific relationships between body size and response to predation risk

Body size is associated with fundamental biological processes such as metabolism, movement, and the rate of reproduction and evolution. Although allometric principles should also influence the range of potential behavioral responses for a given organism, evidence for such large-scale and cross-taxon relationships is lacking. If they exist, scaling-related changes in behavior should be prominent in predatorprey interactions: body size affects the likelihood of attack and the costs of predator avoidance. We take a interspecific perspective on a traditionally intraspecific topic by using a 142-species data set containing organisms ranging over seven degrees of magnitude in body size to analyze the relationship between mean response to predation risk and both prey size and the predator : prey size ratio. We found a weak but significant relationship between two metrics of prey size (mean species-level prey mass and mean specieslevel predator : prey size ratio) and two of the five prey response variables: risk-induced changes in prey habitat use and prey fecundity were significantly correlated with prey body size and the predator : prey ratio. Risk-induced reductions in prey activity were positively correlated with prey mass. In contrast, there was no correlation between prey mass or the predator : prey size ratio and risk-induced changes in either prey growth and survival. We also document considerable variation in response to predation risk among taxa, highlighting that many additional factors contribute to the effects of predation risk on prey behavior, growth, fecundity, and survival. The weak but significant large-scale relationships we documented in our work suggest that allometric relationships may play a subtle role in structuring some of a prey organism’s response to predation risk.


INTRODUCTION
Body size is associated with many of the most fundamental processes of biology: metabolism and movement (Peters 1983, Schmidt-Nielsen 1984, Brown et al. 2004), rates of reproduction (Blueweiss et al. 1978, Peters 1983) and evolution (Allen et al. 2006), and the likelihood of extinction (Gaston andBlackburn 1995, Allen et al. 2006).Size-related properties can also affect responses to climate change (Gardner et al. 2011) as well as alter food web structure and dynamics (Brose 2010, Thierry et al. 2011).Predator-prey interactions are particularly affected by size considerations (Jackson andDial 2011, Thierry et al. 2011); size can prove a refuge for both small and large prey (Brooks andDodson 1965, Urban 2007b), and comparative studies have found broad support for a similar range of body-size ratios among consumers and their resources (Brose et al. 2006).
Anti-predator behavior often plays an integral role in predator-prey interactions (Lima and Dill 1990, Peacor and Werner 2001, Caro 2005), and the relationship between prey body size and predation risk has been extensively explored in a number of taxa (e.g., Urban 2007b and references cited therein).Within a given taxa, there are a range of potentially interactive reasons why body size might affect anti-predator behavior: body size determines energetic demands (Kleiber 1947, Schmidt-Nielsen 1984, Brown et al. 2004) that, in turn, determine the cost of anti-predator behavior.For instance, larger or better-fed organisms should experience a lower cost of foraging reductions in response to predation risk than smaller or hungry organisms (Stephens andKrebs 1986, Lima andBednekoff 1999).Larger body size also alters the likelihood of detection, attack, and capture by a predator (Brooks and Dodson 1965, Urban 2007b, Thierry et al. 2011) as well as predator-mediated competitive interactions (Peacor and Werner 2001).As one example, increased body size can increase the likelihood of prey detection but decrease the probability of capture by gape-limited predators (Urban 2007a).A key question emerging from studies that document a strong intraspecific signal of body size on predator-prey interactions is whether similar interspecific patterns also exist and, if so, the nature of the relationship(s).
A recent review (Dial et al. 2008) highlighted the fact that while broad allometric patterns have been explored in fields such as biogeography, community ecology, and evolutionary ecology (e.g., Brown et al. 2004), research into the effect of body-size scaling on behavior has lagged behind.They identify two factors as particular impediments to such efforts.First, inter-taxon comparisons are difficult because the type and range of available behavioral data often varies widely between taxa.Second, the high degree of intraspecific variability that many organisms exhibit is likely to obscure any broader interspecific relationships.Despite these challenges, it is likely that ''. ..size-related functional influences on performance profoundly influence many aspects of animal behavior, such as how animals forage, fight, flee, perceive danger, respond to risk and interact with other individuals'' (Dial et al. 2008:394).If so, research addressing such questions may provide important insights into the underlying impact of body size on behavior.
We report the results of the first comprehensive inter-taxon analysis on the role of body size in affecting predation-induced changes in behavior, growth, and fitness.Specifically, we use meta-analysis to examine species-level responses of prey to predation risk (e.g., visual, chemical, and/or tactile predator cues; Preisser and Bolnick 2008) as a function of both prey body size and the predator : prey body size ratio.A broad literature attests to the importance of examining intraspecific patterns: we complement this work with an interspecific analysis of data from 142 prey species from 11 taxonomic classes and 74 predator species from 12 classes whose body size ranges over seven orders of magnitude.Our aim in examining the relationship between prey size, predator : prey ratio, and responses to predation risk is to explore whether allometric principles provide an underlying framework for large-scale interspecific patterns of prey response to predation risk.

Literature search
We analyzed a large data set containing information on the strength of nonconsumptive effects (NCEs) of predation risk on prey.The data set includes information from 196 papers published prior to 2006.Our search methods are presented in detail elsewhere (Preisser et al. 2007); briefly, we began by carrying out key word searches in three online databases (BIOSIS, JSTOR, and Web of Knowledge Science Citation Index) for papers that reported the results of manipulative experiments reporting the response(s) of prey organisms to non-lethal predation risk (e.g., visual and/or olfactory cues, a caged or nonlethal predator, etc.).In each paper identified using this method, we searched both the cited literature and subsequent literature that cited it.Because we were primarily interested in population-level consequences of NCEs, we only used papers that include measurements of one or more of the following prey variables that have been shown to respond strongly to the risk of predation (Preisser and Bolnick 2008): somatic growth (i.e., mass gain per time), fecundity (i.e., offspring per individual, brood size), density, and survival.Because so little data were available on prey density, we chose not to analyze this response variable.We recorded data from any papers containing information on one or more of these variables.In addition, we recorded data from these papers regarding prey activity (distance moved, moves/hr, or other metrics assessing prey mobility) or open (i.e., non-refuge) habitat use (proportion of time spent in open versus refuge habitats, percentage of individuals in predator-accessible areas, or other metrics assessing prey presence in potentially risky habitats).In summary, our database contained information about five prey response variables: activity, habitat use, somatic growth, fecundity, and survival.To evaluate whether systematic differences in experimental duration and venue size might affect our results, we also recorded data on experimental length (in days) and size of the experimental arena (in m 3 ).

Body size information
For each study, we recorded any information regarding prey size at the beginning of the experiment.One hundred out of 196 papers (accounting for 483 of 1042 records in the database) used in our analysis reported data on prey mass; of the remainder, 82 papers (424/1042 records) reported data on prey developmental stage sufficient to estimate prey mass and 26 papers (135/1042 records) reported some measurement of prey length sufficient to estimate prey mass (the total number of papers exceeds 196 because some papers that reported data on multiple prey species used different metrics for each species).Because research assessing bodysize relationships traditionally uses wet mass measurements (e.g., Kleiber 1947) and most papers provided data on prey mass, we chose this metric for our analyses.When data on prey size were reported using other metrics (e.g., Gosner stage, snout-vent length), we searched published journals, printed reference materials (e.g., Altman and Dittmer 1964), and online databases (e.g., Froese and Pauly 2011) for regressions or other information necessary to convert these measurements into wet mass.We only employed regressions or searched for mass information when organisms were identified to species.
Although we gathered similar data on preda-tors, we found that information regarding predator mass was often lacking or ambiguous (e.g., reporting only the sex of the predator;  Werner 2001).Although most of these papers reported some measurement of predator developmental stage and/or length, the lack of specieslevel information precluded us from confidently estimating wet mass.The relative paucity of predator data, and the consideration that inaccuracy in either species' measurement can induce significant error in calculating size ratios, are important to keep in mind when interpreting results obtained using an analysis of predator : prey ratios.Because of this, our database may be less suited to an analysis of the predator : prey ratio than to prey body size per se.

Data analysis
We used data on the mean and variance in the control and experimental groups in each published study to calculate the log response ratio effect size (predator risk treatment in the numerator, control treatment in the denominator) for each study in the dataset.By standardizing risk-induced changes relative to control values, the approach facilitates the comparison of multiple studies and is recommended for ecological meta-analysis (Gurevitch and Hedges 1999).Because many prey species were the subject of multiple experiments assessing their response to predation risk, we used the effect size and variance from each study to calculate a single cumulative mean effect size per species per response variable.A detailed explanation of the effect size calculation is contained in Appendix A. Data from individual studies was also used to calculate a single value for mean prey mass at the time of the experiment per species per response variable; we accounted for differences in sample size by weighting mass measurements from each study by the total number of individual prey measured.
We used meta-analysis to assess the specieslevel relationship between prey wet mass in grams and predator : prey wet mass ratio, coded as continuous random variables, and response to predation risk for two behavioral variables (prey activity and open habitat use), somatic growth, and two fitness-related variables (prey fecundity and survival).Our treatment of prey wet mass and predator : prey wet mass ratio as random variables reflects our assumption that there is a truly random component to between-study differences in effect sizes and is consistent with our goal of broad-sense inference.To determine whether taxon-specific patterns were driving our results, we also analyzed the species-level relationship between mass and effect size separately for the two most common classes in each response variable for both prey wet mass and predator : prey mass ratio.All meta-analyses were performed used Metawin 2.14 (Rosenberg et al. 2000).
To determine whether our findings might be the result of confounding factors such as experimental duration or size of experimental venue, we used linear regression to assess the experiment-level relationship between each variable and prey body size.If multiple predator-prey species pairs were tested within the same experiment, data from each predator-prey pair was added as a separate data point.If there was a significant relationship, we used meta-analysis to assess the relationship between the factor, coded as a continuous variable in a fixed effects model, and effect size for the five prey variables.

Meta-analysis of prey body size
Experimental duration and venue size.-There was no experiment-level relationship between experimental duration and prey size (linear regression, F 1, 150 ¼ 0.53, p ¼ 0.47) or between the size of the experimental venue and prey size (F 1, 182 ¼ 0.54, p ¼ 0.46).Because there was no significant relationship between prey size and either variable, we did not conduct individual meta-analyses of the relationship between these factors and the response variables.
Taxonomic width and breadth.-Our196-paper dataset contained data on 142 prey species from 12 classes: Actinopterygii, Amphibia, Arachnida, Aves, Bivalvia, Branchiopoda, Gastropoda, Insecta, Isopoda, Malacostraca, Mammalia, and Reptilia.The classes Amphibia and Insecta dominated the data set, with 42 and 41 species respectively.Conversely, the classes Aves and Arachnida were represented by four and two species, respectively, and the class Reptilia contributed a single species.A list of all species and studies is contained in Appendix B.
Behavioral metrics (Fig. 1).-For both prey activity and open habitat use, the species-level response to predation risk increased (shown by a greater departure from zero) as a function of body mass.In terms of prey activity, every 10fold increase in body mass increased the magnitude of the response to predation risk by 6.7 6 4.9% SE (n ¼ 47 species; y ¼ À0.0671x À 0.575, p[rand] ¼ 0.018).The use of open (i.e., nonrefuge) habitats showed a similar trend, decreasing 5.5 6 6.0% for every 10-fold increase in species-level body mass (n ¼ 33 species; When the most abundant classes were analyzed individually, there were no consistent within-group relationships between body size and response to predation risk (Table 1).Reductions in activity were not correlated with body mass in either the Amphibia and Insecta, the two most represented classes (20 and 19 species, respectively; p[rand] .0.18 in both cases).Body mass was correlated with increased use of open habitats for the class Insecta (y ¼À0.535xÀ 1.177, p ¼ 0.001) but not for Amphibia.
Growth and fitness-related metrics (Fig. 2).-Larger-bodiedspecies experienced a slight but significantly higher cost of predation risk for two of three metrics (Fig. 2).Risk-related reductions in fecundity increased by 2.4 6 2.1% for every 10fold increase in body mass (n ¼ 32 species: y ¼ À0.0239x À 0.302, p[rand] ¼ 0.001).There was a marginally significant negative relationship between body size and survival (n ¼ 37: y ¼ À0.0007x À 0.0373, p[rand] ¼ 0.083).There was no relationship between risk and size in growth, the dataset for which the most species-level information is available (n ¼ 108: As with the behavioral metrics, there was no consistent intra-class relationship between body mass and response to predation risk for the two most abundant classes in each response variable (Table 1).Survival was positively correlated with size in the Insecta (7 species), fecundity was negatively correlated with size in the Mammalia (6 species), and there was no correlation between body size and predation risk within the other five most abundant families.

Meta-analysis of predator : prey body size ratio
Taxonomic width and breadth.-Ourdataset contained data on 162 predator-prey species pairs (74 predator species, 106 prey species).There were fewer prey species represented in the analysis of predator : prey ratios (106 species) than in the prey species analysis (142 species) because cases where the prey was identified to species but the predator was identified only to genus were included in the prey species analysis v www.esajournals.orgbut not the predator-prey species analysis.
Predators from 12 classes were represented in the dataset: Actinopterygii, Amphibia, Arachnida, Asteriodea, Aves, Gastropoda, Hirudinea, Insecta, Isopoda, Malacostraca, Mammalia, and Reptilia.The classes Actinopterygii (29 species, 114 entries in the dataset) and Insecta (21 species, 109 entries) made up 68% of the predator species and 82% of the entries in the dataset.The other predator classes were represented by six or fewer species and, with the exception of Malacostraca (13 entries), six or fewer entries in the dataset.
Prey species from 11 classes were represented in the dataset: Actinopterygii, Amphibia, Arachnida, Aves, Bivalvia, Branchiopoda, Gastropoda, Insecta, Malacostraca, Mammalia, and Reptilia.The most represented classes were the Amphibia (36 species, 125 entries in the dataset) and Insecta (33 species, 54 entries in the dataset), which made up 63% of species and 66% of entries in the dataset.Aves and Reptilia were the least represented prey classes in the dataset, with one species each and one and two dataset entries, respectively.
Behavioral metrics.-There was no consistent relationship between predator : prey body size ratio and behavioral responses to predation risk (Fig. 3).In terms of open habitat use, every 10fold increase in the predator : prey body size ratio decreased the magnitude of the response to predation risk by 8.1 6 4.0% SE (23 predatorprey species pairs; y ¼ 0.0813x À 0.3375, p[rand] ¼ 0.001).Thus, prey response decreased as the size of their predators increased.There were more data available for prey activity (46 predator-prey species pairs); for this metric, there was no significant relationship between body size ratio and response to predation risk (y ¼ À0.169x À 0.251, p[rand] ¼ 0.62).
Growth and fitness-related metrics.-There was no consistent relationship between the predator : prey body size ratio and fitness-related responses to predation risk (Fig. 4).The effect of predation risk on prey fecundity (33 predatorprey species pairs) decreased significantly by 8.1 6 2.5% SE for every 10-fold increase in the predator : prey body size ratio (y ¼ 0.081x À 0.386, p[rand] ¼ 0.001).In contrast, the two metrics for which more data was available (growth ¼ 108 species pairs; survival ¼ 41 species pairs) showed no relationship between body size ratio and the response to predation risk (both p .

DISCUSSION
Strong interspecific relationships have been documented between body size and a variety of physiological and life-history parameters (Peters 1983, Schmidt-Nielsen 1984, Brown et al. 2004), but the potential for similar large-scale relationships exist between body size and behavior has been largely unexplored.As predicted (Dial et al. 2008),we found that (1) the cross-taxon relationships between body size and response to predation risk, although often significant, were uniformly weak; (2) they depended strongly on the prey characteristic being measured (i.e., behavioral metrics or growth-and fitness-related metrics) and (3) they varied as a function of the size metric (i.e., prey mass or the predator : prey ratio).Taken together, these findings suggest that body size, in addition to its impacts on individual organisms, may also influence some prey v www.esajournals.orgresponses at the inter-taxon level.Importantly, our analyses of both prey size and predator : prey ratio also documented substantial interspecific variation in the effect of risk on prey, a finding that accords with our understanding of behavior as sensitive to changes in biotic and abiotic conditions (Dial et al. 2008).Despite this variation and the often-weak nature of the relationship, our results regarding prey body size and the predator : prey size ratio imply that allometric principles already known to affect metabolism, life-history characteristics, and evolution (Peters 1983, Brown et al. 2004, Allen et al. 2006) may also provide insights into behavior.
The observed trends in the size-behavior relationship may reflect size-related differences v www.esajournals.org in metabolic rates.While larger organisms have greater overall metabolic costs, per-gram metabolic costs decrease as a function of body size (e.g., the 'mouse to elephant' curve; Schmidt-Nielsen 1984).Metabolic scaling in mammals (reviewed in Capellini et al. 2010), for instance, means that shrews and other small-bodied predators must spend far more time actively foraging than do larger predators.Predator cues force prey to balance the risk of attack with the rewards of activity (foraging, mating, territorial defense, etc.; Brown and Kotler 2004), and the costs of predator-induced reductions in activity should be higher for smaller organisms.More generally, there is increasing interest in how prey alter anti-predator behavior in response to temporal variation in both the duration and predictability of risk (i.e., the risk allocation hypothesis; Lima and Bednekoff 1999).Although our analyses of species-level data precludes an Fig. 4. Relationship between predator : prey body mass ratio and prey growth and fitness-related metrics due to predation risk, measured as the response ratio effect size.Dotted line indicates zero effect; solid line indicates best-fit linear regression (given only when p , 0.10).Symbols indicate cumulative effect size and mean log 10 (predator body mass/prey body mass) for each species pair included in analysis.Symbol legend and weighting as in Fig. 3. v www.esajournals.orgexamination of temporal dynamics, our finding that larger species (organisms that generally possess greater energetic reserves and face a lower risk of predator-induced starvation) are more likely to reduce activity is consistent with the predictions of the risk allocation hypothesis.
Another potential explanation for our results involves scaling-related changes in organisms' power : mass ratios.Across a range of taxa, there is generally a negative relationship between body size and an organism's ability to rapidly accelerate (i.e., burst locomotor performance; Jackson and Dial 2011), change speeds, and maneuver.Such mass-specific differences in burst performance and maneuverability underlie the avian phenomena of 'predator mobbing', where individual or small groups of small-bodied prey surround and attack larger predators (Dial et al. 2008).This apparently risky strategy succeeds because, at close range, smaller birds are quicker and more maneuverable than their predators.These interactions may play out differently in aquatic systems, especially for small-bodied organisms that are expected to experience large differences in drag forces due to their relatively large amount of surface area relative to their volume and the viscosity and density of the surrounding aqueous fluid.Generally, however, size-related differences in propulsion imply that larger prey should require more warning to escape and thus respond more strongly to predation risk.
Body size can also affect response to predation risk by altering the likelihood that prey will detect predators and the likelihood of predator encounter.For some sensory modalities (e.g., vision; Mech and Zollner 2002) size may increase perceptual range and enable larger prey to more reliably detect and respond to cues (Stankowich and Blumstein 2005).Both empirical (Sinclair et al. 2003) and theoretical (Otto et al. 2007) research suggest that larger-bodied prey are fed upon by a less diverse predator assemblage than are smaller-bodied species, which would likely reduce relative predator encounter rates for larger prey.Although large prey may benefit from a size refuge from predation, larger prey are also eaten by larger predators (Brose et al. 2006) that are generally perceived as more threatening than smaller-bodied predators (Stankowich and Blumstein 2005).Because predation risk experi-ments almost always test prey responses to 'harmful' predators, larger-bodied prey may generally be exposed to cues from rarer but relatively more dangerous predators.In contrast, smaller species may be more likely to come from environments containing cues from a wider range of predator species, such that cues from one particular predator type may not be particularly informative relative to other indicators of risk (e.g., Orrock et al. 2004).Larger organisms also have larger home ranges (Kelt and Van Vuren 2001) and lower per-gram costs of movement (Peters 1983, Schmidt-Nielsen 1984); in addition, large-bodied predators may further reduce the per-unit-time likelihood of predator encounters for larger-bodied prey species.If predator cues are more indicative of an immediate threat to large-bodied prey, they might well react more strongly than do smaller species.
Following an encounter, the likelihood of predator attack (or prey escape) is strongly influenced by the body size of both predator and prey (Domenici 2001, Cooper and Stankowich 2010, Jackson and Dial 2011, Thierry et al. 2011).Although the relationship between body size and predator attack is undoubtedly influential in specific predator-prey interactions, it seems unlikely that this factor could produce a consistent cross-taxa relationship between prey size and predation risk.Predators seeking to maximize the energetic benefits of prey consumption may preferentially target large-bodied prey, providing smaller species with a refuge from attack (Brooks and Dodson 1965).Conversely, large body size reduces the risk posed by gape-limited predators (Urban 2007b).A unimodal size-risk relationship may also occur if predator handling time is lowest with optimally-sized prey: in such cases, prey smaller or larger than optimally-sized individuals are less likely to be attacked (Molles and Pietruszka 1987).Size-dependent anti-predator behavior may also be mediated by ontogenic changes in predator dietary preferences (e.g., Carbone et al. 1999).Another plausible post-encounter explanation for our findings is that large prey typically occur in lower densities than small-bodied organisms (Marquet 2002).As a result, largebodied organisms that detect a predator cue may be more likely to be attacked since predators have fewer conspecifics from which to choose (i.e., the 'dilution' of predation risk; Lima andDill 1990, Caro 2005).Because these explanations are likely to be functions of the interplay between predator, prey, and their environment, our crosstaxon study cannot robustly test their contribution to size-dependent anti-predator behavior.
In addition to highlighting significant crosstaxa relationships between body size and antipredator behavior, another interesting outcome of our work is that, whereas behavioral responses to predation risk, especially refuge habitat use, scale with prey body size (Figs.1-2), the slope of the relationship is weaker for fecundity, marginally significant for survival, and absent for growth (Fig. 2).The attenuation of the size-risk relationship when moving from behavior-to fitness-related metrics suggests that larger organisms are capable of compensating for their increased response to predation risk.This might arise via allocation towards growth at the expense of fecundity, a hypothesis supported by the non-significant relationship for growth and significant relationship for fecundity.While prey that forego growth are likely to substantially increase their mortality risk, iteroparous species that reduce their fecundity in response to predator cues may be able to compensate by increasing their subsequent reproductive efforts.The interpretation that larger organisms are capable of tolerating greater predator-mediated reductions in activity (Fig. 1) without incurring equivalent fitness-related costs in terms of survival and growth (Fig. 2) is also consistent with the lower relative energetic costs of reduced activity for larger-bodied prey (and thus in agreement with the risk allocation hypothesis; Lima and Bednekoff 1999).It is also possible that prey may be able to compensate physiologically for predator-induced behavioral changes (McPeek 2004).In agricultural systems, for instance, the presence of predators induces Manduca sexta caterpillars to reduce their feeding rates.This does not affect growth, however, because the caterpillars compensate via increased digestive efficiency (Kaplan and Thaler 2009).
We found that two different measures of body size, i.e., prey mass and the predator : prey mass ratio, were both correlated with interspecific trends in prey habitat use, fecundity, survival, and growth.However, changes in activity were significant for prey mass but not for the predator : prey ratio.As the number of studies used was similar for both prey mass and predator : prey ratio analyses (47 and 46 studies, respectively), the lack of agreement between these analyses may reflect differences in the quality of data used for each analysis.Perhaps because researchers working in this area use predator cues rather than the predators themselves, data on predator size is rarely reported and/or takes the form of species-specific measurements (e.g., larval instar).In contrast, prey size is virtually always reported, and often in terms of mass or length.The lower quality and quantity of information on predator size may have increased the amount of variation in our data on predator : prey size ratios and thus affected our analyses.
Biological realities may also contribute to the difference between prey mass and predator : prey size ratio we observed for prey activity.For example, experiments exploring predation risk often use chemical cue of predator presence rather than the predators themselves.Such cues may provide little information to the prey regarding predator size, especially for predators that exhibit substantial intraspecific variation in size (e.g., fish predators with indeterminate growth).The decision to reduce activity in such cases may be more reliably linked to prey body size in such experiments because (A) this quantity is known by the prey with much more accuracy than predator body size; and (B) prey size is a primary determinant of the costs of reduced activity, since larger prey are more likely to be able to afford a bout of reduced activity.As such, the prey size, not the ratio of predator : prey size, would be important in determining whether or not to reduce activity in these experiments.This contrasts with experiments on prey behavior when visual information about predators, and thus accurate information regarding predator size, is presented (Stankowich and Blumstein 2005).
While we believe that our work documents a hitherto unrecognized trend in prey behavior, our approach has a number of limitations.Our interest in the relationship between prey behavior and fitness meant that we only analyzed behavioral data from studies that also measured some metric of prey fitness.Relaxing this requirement would have increased the studies from which to draw, but would have precluded our comparisons of behavioral and fitness-level responses.Our reliance on published studies also means that systematic bias could have been introduced if relatively harmful predators were used in research on large-bodied prey species and relatively harmless predators were used in research on small-bodied prey species.While we cannot reject this possibility, we believe that the number of species tested and range of variables assessed makes such bias unlikely.The relatively low number of predator-prey species pairs in our dataset meant that we were also unable to examine predator-specific factors like hunting mode and habitat domain (Preisser et al. 2007).The hunting strategies employed by predators in our analysis varied widely, from actively-hunting species in both terrestrial and aquatic systems to sit-and-wait predators and others that are akin to browsers (e.g., predatory snails 'grazing' on sessile mussels).While such differences clearly affect predator-prey interactions, the data were insufficient to rigorously explore the impact of hunting mode or other subfactors at the crosstaxon level.
More generally, any meta-analytic approach to understanding broad-scale, cross-taxon patterns may be affected by the presence of systemic biases.In this work, we have evaluated our data for the presence of size-related biases where possible.However, although methodological factors like experimental duration or venue size did not correlate with body size and thus appear unlikely to explain our results, we did not account for factors like size-related differences in food resources, cue concentrations, or predator hunting mode.Even if we could address these issues, we cannot reject the hypothesis that another explanation (e.g., size-based variation in predator and/or prey developmental stage) exists for our findings.Such challenges might be better addressed via experiments testing a wide array of differently-sized organisms under standardized conditions.Such an experimental approach would be feasible but logistically challenging and still vulnerable to critique.As one example, experimental duration could be held constant or scaled to prey lifespan; both approaches are justifiable but explore different research questions.Ultimately, a challenge inherent in addressing cross-taxon questions at a broad scale is that many confounding factors may exist; we hope our synthetic work will catalyze the experimentation and methodological advances required to build upon the patterns we present here.
Although the influence of allometry is wellrecognized in a number of other fields, our work suggests that cross-taxa constraints may also subtly structure behavioral patterns.Our work supports the prediction of Dial et al. (2008) that similar patterns may not be manifest at the within-class level (Table 1; also see Fig. 3 in Dial et al. 2008); this suggests that the predation riskbody size relationship for a given group of organisms is primarily a function of their ecological and evolutionary context.Our study illustrates that body size is weakly but consistently indicative of broad-scale taxonomic variation in anti-predator behavior.The considerable unexplained variation that we document implies that body size is likely only one of many factors that mediate the effect of predation risk on prey behavior and fitness.Ultimately, discriminating between the mechanisms capable of producing such a large-scale relationship between body size and anti-predator behavior will require research examining behavioral trends at both the withinand between-taxa level and as a function of factors such as prey resources (Preisser et al. 2009).Such questions are especially important given large-bodied organisms' relative vulnerability to anthropogenic disturbance and global warming (Gardner et al. 2011).Future studies that elucidate these mechanisms and traits will be critical for understanding the processes that mediate this and perhaps other equally subtle broad-scale trends in behavior.response variable: where E i and w i are the effect size and weight, respectively, for study i, and the study weight is the reciprocal of the study's sampling variance: w i ¼ 1/v i (Rosenberg et al. 2000).The cumulative variance for each mean effect size was calculated for each species-response variable effect size as: We used data from individual experiments to calculate a mean prey wet mass for each speciesresponse variable combination.Since different experiments varied in both the number of individuals tested and their mean weights, we calculated a single cumulative mean body mass across all experiments for each species-response variable combination: where m i and x i are the prey wet mass and number of individual organisms tested in the experiment, respectively.

Fig. 1 .
Fig. 1.Relationship between prey body mass and risk-induced behavioral changes, measured as the response ratio effect size.Dotted line indicates zero effect; solid line indicates best-fit linear regression.Symbols indicate cumulative effect size and mean body mass for each prey species included in analysis.Symbol size is weighted by log 10 (1/cumulative variance).

Fig. 2 .
Fig. 2. Relationship between prey body mass and fitness-related metrics due to predation risk, measured as the response ratio effect size.Dotted line indicates zero effect; solid line indicates best-fit linear regression.Symbols indicate cumulative effect size and mean body mass for each prey species included in analysis.Symbol legend and weighting as in Fig. 1.

Fig. 3 .
Fig. 3. Relationship between predator : prey body mass ratio and prey behavioral changes due to predation risk, measured as the response ratio effect size.Dotted line indicates zero effect; solid line indicates best-fit linear regression (given only when p , 0.10).Symbols indicate cumulative effect size and mean log 10 (predator body mass/prey body mass) for each predator-prey species pair included in analysis.Symbol legends give class of predator species before hyphen, and class of prey species after hyphen.Symbol size is weighted by log 10 (1/ cumulative variance).

Table 1 .
Within-class relationships between prey body mass (top) and predator : prey ratio (bottom) and response to predation risk for species in the two most abundant prey classes for each of the five tested variables.P[rand] tests the null hypothesis that the slope of the relationship equals zero.
Note: For analyses of prey mass, N ¼ number of prey species; for predator : prey mass ratio, N ¼ number of predator-prey pairs.v www.esajournals.org0.15).

Table B1 .
A list of all species and 196 studies.