On sperm competition games: incomplete fertilization risk and the equity paradox

Evolutionary game theory has been used to predict the effect on sperm expen diture of a trade-off between the value of a mating and the cost of its acq uisition. In particular, G. A. Parker has predicted that, if two males 'kno w' whether they are first or second to mate, but these roles are assigned r andomly, then sperm numbers should be the same for both males whether the ' raffle' for fertilization is fair or unfair. This prediction relies on the assumption that, in the absence of sperm competition, ejaculates would alwa ys contain enough sperm to ensure complete fertilization after mating. The slightest risk of incomplete fertilization, however, is enough to ensure th at favoured males expend more than disfavoured males in the presence of spe rm competition, unless the competition is perfectly fair. Divergence of exp enditures increases with unfairness until unfairness reaches a critical val ue, beyond which a disfavoured male should no longer compete. The higher th e fertilization risk, the lower the critical unfairness. All predictions ar e independent of the probability of mating first or second. Implications ar e discussed for the mechanisms that underlie sperm competition.