Sperm competition games: sperm selection by females.

We analyse a co-evolutionary sexual conflict game, in which males compete for fertilizations (sperm competition) and females operate sperm selection against unfavourable ejaculates (cryptic female choice). For simplicity, each female mates with two males per reproductive event, and the competing ejaculates are of two types, favourable (having high viability or success) or unfavourable (where progeny are less successful). Over evolutionary time, females can increase their level of sperm selection (measured as the proportion of unfavourable sperm eliminated) by paying a fecundity cost. Males can regulate sperm allocations depending on whether they will be favoured or disfavoured, but increasing sperm allocation reduces their mating rate. The resolution of this game depends on whether males are equal, or unequal. Males could be equal: each is favoured with probability, p, reflecting the proportion of females in the population that favour his ejaculate (the 'random-roles' model); different males are favoured by different sets of females. Alternatively, males could be unequal: given males are perceived consistently by all females as two distinct types, favoured and disfavoured, where p is now the frequency of the favoured male type in the population (the 'constant-types' model). In both cases, the evolutionarily stable strategy (ESS) is for females initially to increase sperm selection from zero as the viability of offspring from unfavourable ejaculates falls below that of favourable ejaculates. But in the random-roles model, sperm selection decreases again towards zero as the unfavourable ejaculates become disastrous (i.e. as their progeny viability decreases towards zero). This occurs because males avoid expenditure in unfavourable matings, to conserve sperm for matings in the favoured role where their offspring have high viability, thus allowing females to relax sperm selection. If sperm selection is costly to females, ESS sperm selection is high across a region of intermediate viabilities. If it is uncostly, there is no ESS in this region unless sperm limitation (i.e. some eggs fail to be fertilized because sperm numbers are too low) is included into the model. In the constant-types model, no relaxation of sperm selection occurs at very low viabilities of disfavoured male progeny. If sperm selection is sufficiently costly, ESS sperm selection increases as progeny viability decreases down towards zero; but if it is uncostly, there is no ESS at the lowest viabilities, and unlike the random-roles model, this cannot be stabilized by including sperm limitation. Sperm allocations in the ESS regions differ between the two models. With random roles, males always allocate more sperm in the favoured role. With constant types, the male type that is favoured allocates less sperm than the disfavoured type. These results suggests that empiricists studying cryptic female choice and sperm allocation patterns need to determine whether sperm selection is applied differently, or consistently, on given males by different females in the same population.