FERTILISATION
The percentage of successfully fertilised eggs steeply increased with sperm concentration but dropped significantly beyond 1 × 106 (Fig. 1a). Beyond this concentration, ~60 to 80% of eggs were abnormally fertilised (Fig. 1b). Therefore, had we simply counted fertilised vs unfertilised eggs, without making a distinction between normally vs abnormally fertilised eggs, we would have seen a continuous increase in proportion of fertilised eggs (Fig. 1c) while in fact many of the fertilised eggs at the highest sperm concentration (1 × 108) were non-viable.
In the first Bayesian model, we analysed the proportion of normally fertilised eggs after excluding the highest sperm concentration (1 × 108). There was a significant effect of population of origin, sperm concentration (both linear and quadratic terms), female density, and a significant interaction between female density and sperm concentration (Table 2). Females from low density areas had lower fertilisation success across all sperm concentrations (Fig. 1a), but the significant interaction indicated that this effect becomes less important as sperm concentration increases (Table 2). We detected no effect of male density on fertilisation success (Table 2). In the second model, in which we analysed the proportion of abnormally fertilised eggs at the highest sperm concentration (1 × 108), we found no significant effect of population, body condition, gamete age, female density, male density (or their interaction) on the proportion of abnormally fertilised eggs (Table 3).
Finally, our third Bayesian model revealed some differences in the variance estimates across sperm concentrations. The variance estimates associated with intrinsic male effects (V male) were low across all sperm concentrations (range: <0.01 to 0.01; Table 4). By contrast, effects attributable to females (V female) were relatively high (range: 0.62 to 4.96; Table 4). The “male × female” interaction effects (V male × female) were relatively low at low sperm concentration (Fig. 2), but increased at higher sperm concentration (Table 4, Fig. 2).