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

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Abstract
Evolutionary game theory has been used to predict the effect on sperm expenditure of a trade–off between the value of a mating and the cost of its acquisition. In particular, G. A. Parker has predicted that if two males ‘know’ whether they are first or second to mate, but these roles are assigned randomly, 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 always contain enough sperm to ensure complete fertilization after mating. The slightest risk of incomplete fertilization, however, is enough to ensure that favoured males expend more than disfavoured males in the presence of sperm competition, unless the competition is perfectly fair. Divergence of expenditures increases with unfairness until unfairness reaches a critical value, beyond which a disfavoured male should no longer compete. The higher the fertilization risk, the lower the critical unfairness. All predictions are independent of the probability of mating first or second. Implications are discussed for the mechanisms that underlie sperm competition.

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