Tradeoffs and Benefits Explain Scaling, Sex Differences, and Seasonal Oscillations in the Remarkable Weapons of Snapping Shrimp (Alpheus spp.)

Evolutionary theory suggests that individuals should express costly traits at a magnitude that optimizes the cost-benefit ratio for the trait-bearer. Trait expression varies across a species because costs and benefits vary among individuals. For example, if large individuals pay lower costs than small individuals, then larger individuals should reach optimal cost-benefit ratios at a greater magnitude of trait expression. Using the remarkable cavitation-shooting weapons found in the big claws of male and female alpheid snapping shrimp, we test whether size- and sex-dependent expenditures explain the scaling of weapon size relative to body size and why males have larger proportional weapon size than females. We found that males and females from three snapping shrimp species (Alpheus heterochaelis, Alpheus angulosus, and Alpheus estuariensis) exhibit resource allocation tradeoffs between weapon and abdomen mass. For male A. heterochaelis, the species for which we had the greatest sample size and statistical power, the smallest individuals showed the steepest tradeoff. Our extensive dataset in A. heterochaelis also included data about pairing, breeding season, and egg clutch size. Therefore, we could test for reproductive tradeoffs and benefits in this species. Female A. heterochaelis exhibited additional tradeoffs between weapon size and egg count, average egg volume, and total egg mass volume. For average egg volume, the smallest females exhibited the steepest tradeoff relative to weapon size. Furthermore, in males but not females, large weapons were positively correlated with the probability of being paired and the relative size of their pair mate. In conclusion, we establish that size-dependent tradeoffs underlie reliable scaling relationships of costly traits. Furthermore, we show that males and females differ in weapon investment, suggesting that weapons are especially beneficial to males and especially burdensome to females.


Introduction 32
Weapons, ornaments, and other secondary sexual traits often scale with the trait-bearer's 33 quality. Larger weapons can better deter or damage competitors, and more intense ornaments can 34 better attract mates. By first approximation, one might expect that all individuals should express 35 these traits to arbitrarily high magnitudes because greater expression yields fitness benefits. 36 However, fitness costs and physical limitations ensure that traits are expressed honestly instead 37 of arbitrarily (reviewed in Searcy & Nowicki, 2005). Despite decades of research, the costs that 38 maintain reliable scaling relationships remain hotly debated. 39 One hypothesis called the handicap principle suggests that sexual traits are costly, and 40 these costs ensure that trait expression is not arbitrary. Individuals should therefore express traits at a level that maximizes their benefits relative to their 44 unit of cost (Grafen, 1990a(Grafen, , 1990bNur & Hasson, 1984;Zahavi, 1977). For example, the 45 handicap principle posits that sexually selected traits scale with quality because low-quality 46 individuals pay more for, or benefit less from, costly traits compared to high-quality individuals. 47 These differential costs set the optimal trait expression at a lower value for lower-quality 48 individuals compared to higher-quality ones (Grafen, 1990a(Grafen, , 1990bNur & Hasson, 1984;49 Zahavi, 1977). Even though this is a widely accepted explanation for honest scaling of sexual 50 traits, empirical evidence is scarce (Kotiaho, 2001;Penn & Számadó, 2020) . 51 In addition to scaling relationships, costly traits can also differ depending on sex and 52 season. For example, some secondary sexual traits are expressed in both sexes but at greater 53 magnitudes in males than females ( For each species, we hypothesized that growing a larger snapping claw would coincide 164 with reduced abdomen size. We tested this relationship by calculating the residuals from the log-165 log abdomen and snapping claw scaling relationships defined above, where positive residuals 166 indicate a larger abdomen or snapping claw than predicted by the scaling relationship. To test for 167 a morphological tradeoff, we built regressions using abdomen residuals as the response variable 168 and snapping claw residuals, sex, and their interaction as the explanatory variables. We repeated 169 this analysis for A. heterochaelis, A. angulosus, and A. estuariensis. 170 Then, we tested whether slopes of the tradeoff depended on quality. Here and throughout 171 the rest of the paper, we used carapace length as a measure of quality because it's the best known 172 proxy for resource holding potential, the best-known predictor for female fecundity, and a 173 reliable predictor of dominance and subordinance in dyadic contests (Dinh et al., 2020). We 174 hypothesized that the slope of the tradeoff would increase as carapace length decreased. To test 175 this, we standardized carapace length so that the mean was zero and each increment of one 176 represents an increase of one standard deviation. We built a regression with abdomen residual as 177 the response variable and snapping claw residual, standardized carapace length, and their 178 interaction as the explanatory variable. We performed this analysis only for Alpheus 179 heterochaelis, the species for which we had the greatest sample size and statistical power. We 180 predicted a negative coefficient for the interaction, meaning that the tradeoff slope would 181 approach zero as carapace length increased. 182 We reanalyzed data from Dinh & Patek (2022) Patek, 2022). Here, we tested if these relationships also depended on weapon 197 residuals. We built three linear models that used either log 10 (average angular velocity), 198 log 10 (bubble duration), or sound pressure level (a logarithmic measure of pressure) as the 199 response variable. In each model, we used log 10 (claw mass) and weapon residual as explanatory 200 variables. We built separate models for males and females. For each performance metric, we 201 hypothesized that performance would decrease with high-residual snapping claws, and we 202 therefore predicted a negative coefficient for snapping claw residuals. 203 204

Reproductive Tradeoffs 205
We collected 37 ovigerous A. heterochaelis females. We removed each egg clutch and 206 photographed them. We only included eggs in the early stage of development when the egg yolk 207 was barely consumed and oblong deformation by the embryo was minimal. We counted the total 208 number of eggs in each egg clutch and measured the estimated average egg volume using the Fiji 209 distribution of ImageJ (version 2.0.0) (Schindelin et al., 2012). For each egg clutch, we measured 210 the egg volume for 20 randomly selected eggs and calculated their mean as the average egg 211 volume = , where V egg represents egg volume, d min represents the minimum 212 egg diameter, and d max represents the maximum egg diameter (Kuris, 1990). Finally, we 213 calculated total egg mass volume (EMV) as the egg count multiplied by the average egg volume. 214 Egg count and EMV increased as carapace length increased. Therefore, we regressed egg 215 count and EMV against carapace length and calculated egg count residuals and EMV residuals 216 from the scaling relationship. These residuals reflect investment into eggs, where more positive 217 residuals indicate greater investment and more negative residuals indicate less investment. We 218 did not use residual analysis for average egg volume because it did not scale with carapace 219 length. To test for reproductive tradeoffs between eggs and weapons, we built three linear 220 regressions that used either egg count residual, average egg volume, or EMV residual as the 221 response variable. All models included snapping claw residual as the sole explanatory variable. 222 We predicted a negative relationship that reflected a reproductive tradeoff. We performed separate t-tests for each sex in Alpheus heterochaelis. We predicted that snapping 257 claw residuals would be elevated during the breeding season for males but not females, and that 258 shift would coincide with a reduction in abdomen residuals. Then, to test if the scaling slope of 259 the snapping claw changed between seasons, we built a linear model for each sex with 260 log 10 (snapping claw length) as the response variable and log 10 (rostrum-to-telson-length), 261 breeding season, and their interaction as the predictor variables. A significant interaction term 262 would indicate a seasonal allometric shift. If the interaction term was nonsignificant, we 263 removed it from the model to test if there was an overall shift in weapon investment without a 264 change in slope across breeding and non-breeding seasons. 265 266

Results 267
Morphology 268 The allometric slope of snapping claw scaling differed significantly between sexes for 269 Alpheus heterochaelis and Alpheus angulosus but not for Alpheus estuariensis (Figure 1). 270 Scaling slopes and 95% confidence intervals are presented in Supplemental Table 1.  Table 5). By contrast, we found no evidence of size-dependent 278 slopes for female weapons (interaction p-value = 0.93; Supplemental Table 6). 279 280 281   Table 15). 323   boost fitness by pairing with larger females, and females sacrifice fitness by reducing investment 417 into eggs. These sex-specific tradeoffs and benefits can therefore explain why females have 418 smaller proportional weapon sizes compared to males, why this sex difference amplifies during 419 the breeding season, and why female weapon scaling slopes become more shallow during the 420 breeding season when egg production and pairing is at a premium. 421

Figure 1: Snapping claw length and abdomen length increased with rostrum-to-telson length
We tested for size-dependent weapon expenditures using morphological tradeoffs. For 422 both males and females, individuals with larger weapons had smaller abdomens (Figure 2). This 423 was true in all three species of snapping shrimp that we tested. Additionally, in male Alpheus 424 heterochaelis, smaller males exhibited a steeper tradeoff than larger males, indicating a size-425 dependent expenditure of weaponry (Figure 3). 426 The proportion of the claw made of muscle decreases as weapon residual increases (Dinh, 427 2022). Therefore, we tested whether weapon residuals were negatively correlated with average 428 angular velocity in the snapping claw, cavitation bubble duration, and snap pressure. 429 Surprisingly, weapon residuals were not correlated with any of these metrics. 430 The expenditures and benefits of growing a large weapon also differed by sex. For 431 ovigerous A. heterochaelis females, greater weapon size led to lower egg counts, smaller average 432 egg volume, and lower egg clutch volume (Figure 4). Reproductive expenditures were also size-433 dependent: the tradeoff between weapons and average egg volume was steepest for females with 434 the smallest carapace lengths. Sex-specific costs could explain why females have smaller 435 proportional weapon sizes than males. 436 In addition, we showed that male A. heterochaelis benefited by investing in weaponry 437 through pairing, whereas females did not. In males, weapon residuals were positively correlated 438 with the probability of being paired and the relative body length of their pair mates (Figure 6 -439 7). Females did not exhibit either of these benefits. Male-specific benefits could therefore 440 contribute to sex differences in weapon investment. 441 Egg production is particularly salient to female snapping shrimp because they bear the 442 entire energetic burden of egg production (Knowlton, 1980). Likewise, there is incentive for 443 males to pair with large and fecund females. Therefore, growing a large weapon is particularly 444 burdensome to females and particularly beneficial for males. These reproductive expenditures and benefits could therefore explain why males have larger proportional weapon sizes than 446 females. 447 The sex-specific expenditures and benefits are also consistent with seasonal oscillations 448 in weaponry. A. heterochaelis males had greater weapon residuals during the breeding season 449 compared to the non-breeding season, whereas female weapon residuals remained consistent 450 throughout the year (Figure 8). Furthermore, the scaling slope of the snapping claw became more 451 shallow during the breeding season for females. By contrast, males did not show a significant 452 seasonal change in scaling slope, but across the range of body sizes, snapping claw lengths 453 increased during the breeding season ( Figure 9) Ideally, we would be able to link each of the expenditures and benefits we identified here 477 to a fitness cost (Kotiaho, 2001). However, this bar is infeasibly high in snapping shrimp. They 478 are prolific breeders, cryptic, and difficult to mark and recapture because they molt each month. 479 The egg production tradeoffs are as close to a direct fitness cost as we could identify. 480 Morphological tradeoffs, on the other hand, are more distant to fitness costs. However, it is a 481 reasonable possibility that abdomen tradeoffs impact survival. For example, the primary mode of 482 predator escape in many decapod crustaceans is the tailflip, during which individuals contract 483 their abdomen to propel themselves backwards (Wiersma, 1947). Tailflip velocity and 484 acceleration in crayfish increases with abdomen length (Hunyadi et al., 2020). If the same holds 485 in snapping shrimp, then the abdomen tradeoff that we found here could influence survival. 486 However, future work is required to reach a definitive answer. The handicap principle suggests that individuals are plastic in their ability to signal at 513 different levels, and they signal at the level that optimizes their cost-benefit ratio (Grafen, 1990a, 514 1990b; Nur & Hasson, 1984;Zahavi, 1977). This hypothesis requires costs or benefits that differ 515 between individuals. However, the debate and acceptance of this principle has relied more on 516 theory and less on empirical evidence (Penn & Számadó, 2020). We showed through field 517 observations that size-dependent expenditures can ensure signal reliability through 518 morphological and reproductive tradeoffs. Furthermore, we co-opted the same logic of 519 differential costs and benefits to show that large weapons are particularly beneficial to males and 520 particularly burdensome to females. These sex-specific implications of weaponry on 521 reproduction could underlie sex and seasonal differences in costly trait expression.  Note: * p<0.05; ** p<0.01; *** p<0.005

Supplemental Figure 1: Morphological measurements used in this study. Example shown is an
Alpheus angulosus female.

Supplemental Figure 1: Scaling relationships for snapping claw length and abdomen length
shown in linear scaling.