The coevolutionary dynamics of cryptic female choice

Abstract In contrast to sexual selection on traits that affect interactions between the sexes before mating, little theoretical research has focused on the coevolution of postmating traits via cryptic female choice (when females bias fertilization toward specific males). We used simulation models to ask (a) whether and, if so, how nondirectional cryptic female choice (female-by-male interactions in fertilization success) causes deviations from models that focus exclusively on male-mediated postmating processes, and (b) how the risk of sperm competition, the strength of cryptic female choice, and tradeoffs between sperm number and sperm traits interact to influence the coevolutionary dynamics between cryptic female choice and sperm traits. We found that incorporating cryptic female choice can result in males investing much less in their ejaculates than predicted by models with sperm competition only. We also found that cryptic female choice resulted in the evolution of genetic correlations between cryptic female choice and sperm traits, even when the strength of cryptic female choice was weak, and the risk of sperm competition was low. This suggests that cryptic female choice may be important even in systems with low multiple mating. These genetic correlations increased with the risk of sperm competition and as the strength of cryptic female choice increased. When the strength of cryptic female choice and risk of sperm competition was high, extreme codivergence of sperm traits and cryptic female choice preference occurred even when the sperm trait traded off with sperm number. We also found that male traits lagged behind the evolution of female traits; this lag decreased with increasing strength of cryptic female choice and risk of sperm competition. Overall, our results suggest that cryptic female choice deserves more attention theoretically and may be driving trait evolution in ways just beginning to be explored.


Calculation of multivariate selection estimates
To understand the realized strength of selection acting on male traits, we performed a multivariate selection analysis on males during each generation using the genotypic value of sperm trait (m), sperm number (s), and cryptic choice trait (f; Lande & Arnold, 1983;Stinchcombe et al., 2008). We included f to account for potential correlated selection; excluding f in preliminary analyses yielded similar results. We first standardized each trait to a mean of zero and a standard deviation of 1 using the mean value of all males in the population. We then calculated each male's relative fitness (Wr) by dividing the number of offspring sired by the mean number of offspring sired. We then performed a regression analysis to estimate directional selection coefficients (β) and quadratic selection coefficients ( ;Lande & Arnold, 1983;Stinchcombe et al., 2008):

Sensitivity analyses
The results presented in the main text assumed the population size was N =10,000, all traits had starting distributions of mean = 50 and SD = 5, and each trait was controlled by 20 loci. We performed several sensitivity analyses to see if these assumptions had qualitative influences on our results.
To test whether the strength of genetic drift affected our main results, we ran the simulation for smaller populations (N = 1,000), as genetic drift would be more likely to affect predicted patterns than in larger populations with N = 10,000.
Starting conditions and starting variation of traits can affect the coevolution between male and female traits in individual-based models (e.g., Millan et al., 2020), so we ran simulations at every parameter combination at both small trait variation (SD = 2.5) and large trait variation (SD = 10) compared to medium trait variation (SD = 5) for all traits. We additionally ran simulations when starting mean cryptic choice trait (f) was ~5 SDs larger than starting mean sperm trait (m), 75 vs 50. This allowed us to look at how directional selection could influence our results and/or how large initial deviations between male and female traits influenced our results.
One of our model's key assumptions is that twenty loci control each trait. We ran our model as described above when two loci determined traits to test how this assumption affected our results. To control for the scale of traits, we modified the distributions of mutational effects as well as starting allelic values to maintain approximately the same genetic variation and starting average as the 20-locus model; small: normal (mean = 12.5, SD = 1.25), medium: normal (mean = 12.5, SD = 2.5), and large: normal (mean = 12.5, SD = 5). We also scaled the distribution of mutational effects [normal (mean = 0, SD = 0.25)].        S8. Strong cryptic female choice results in less ejaculate investment than predicted by game theoretical models. Heat map of the median relative difference from predicted investment in ejaculates after 30,000 generations of evolution across different preference strengths, risks of sperm competition, population size, number of loci, starting variation, and whether a tradeoff between sperm number (s) and sperm trait (m) was present. Orange represents less investment than predicted by the analytical model, white means same as predicted, and purple means higher ejaculate investment than predicted. Ejaculate investment was calculated as s for no tradeoff scenario and ms for the tradeoff scenario. Results in the main text are from 20 Loci, medium variation, and population size of 10,000 (Fig. 2B). The median was calculated as the median genetic correlation in the last 2,000 generations across 50 populations (runs) at each parameter combination. Results in the main text are from 20 Loci, medium variation, and population size of 10,000 (Fig. 3A).  generations across different preference strengths on m, risks of sperm competition, population size, number of loci, starting variation, and whether a tradeoff between sperm number (s) and sperm trait (m) was present. Results in the main text are from 20 Loci, medium variation, and population size of 10,000 (Fig. 5A).