Optimal copula duration in yellow dung flies: ejaculatory duct dimensions and size-dependent sperm displacement

We aim to interpret sperm displacement in relation to male size in the yellow dung fly, Scatophaga stercoraria, and to compare the general properties of indirect and direct size-dependent sperm displacement in insects. We examine the hypothesis that male size-dependent sperm displacement in dung flies can be explained by size-dependent increases in the ejaculatory apparatus, allowing greater sperm flow rates in larger males. We expect sperm flow rates to be proportional to the diameter of the aedeagus duct to the power x, where x lies between 2 and 3. We test this hypothesis using a simulation model of indirect sperm displacement that has been developed to accommodate recent observations on sperm transfer, in which sperm flow from the male into the female bursa and are then transferred to the spermathecae by movements of the female tract. The indirect model approximates to the pattern of size-related sperm displacement, with scaling power 3 giving a better fit than power 2. Copula duration shows a male size-dependent decrease in this species. We apply the indirect model of sperm displacement, in conjunction with parameters obtained from field and laboratory data, to predict size-dependent changes in optimal copula duration from the male perspective. This model concurs with the observations by predicting a size-dependent decline in optimal copula duration, as did an earlier model in which displacement was direct (new sperm displace previously stored sperm directly from the sperm stores). Our new approach gives a better fit than the earlier direct model. Thus, both results (displacement rates and copula duration) can be explained by size-dependent changes in the ejaculatory apparatus of the male with the female's exchange rate of sperm (from bursa to spermathecae) remaining constant with respect to male size, although we discuss the possibility that this female process may accelerate with increased male size. In general, where the sperm input rate is around the same magnitude as the exchange rate, indirect displacement will be dependent on the size of the male, as in dung flies, but this dependency is lost if the input rate is very high relative to the exchange rate across the entire range of male size. Size-dependent displacement should always apply for males with direct displacement.