Optimal copula duration in dungflies: effects of frequency dependence and female mating status

Summary

The addition of frequency dependence to the marginal value theorem (MVT) model of the dung fly (Scatophaga stercoraria) male's optimal copula duration makes virtually no difference to the predicted competitive optimum (ESS). However, this evolutionarily stable strategy (ESS) version allows an explicit solution for the optimum. In a general sense, MVT optima will be close to their ESS equivalent when the cycle duration (expected time between the starts of two successive patch exploitations) is long relative to the plausible patch exploitation times. The optimal copula duration for male dung flies will depend on the ratio of virgin to mated females arriving at the droppings and on whether a male can discriminate between the two sorts of female. In nature, we found only an average of 3% of the total females arriving at the droppings to be virgins, rather less than had been estimated. This means that matings away from droppings (“extra-dung matings”) must be much commoner than previously suspected. Cumulative gains through copulation time rise much more steeply with virgins than with mated females, and so if males are able to discriminate, on the present model, we calculate that the ESS copula durations (at 20° C) would be around 42 min for non-virgins and 11 min for virgins. If they do not discriminate, the ESS is to copulate for a fixed duration of 41.5 min, i.e. very close to the optimum for mated females. The data indicate that copula duration does not differ for the two types of mating (mated females; virgins), suggesting that males cannot discriminate (or that the copula duration with virgins is not optimised to male interests). ESS copula durations with discrimination are almost entirely independent of the frequency of virgins in the population of females arriving at the droppings; without discrimination the optimal copula duration shifts between the ESS for mated females and that for virgins as the virgin frequency increases from 0 to 1. But at their naturally occurring frequency of only 3%, virgins can be ignored from calculations of optimal copula duration without significant loss of precision.