Sperm competition games: sneaks and extra-pair copulations

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Abstract
This paper examines ejaculation strategies for cases when an opportunist male `steals' a mating with the female of a paired male. This is an evolutionary game of competitive ejaculation in which two (or more) males mate with the same female. Prospective evolutionarily stable strategy (ESS) models are analysed which seek ESS sperm numbers. Sperm competition is assumed to obey the `raffle principle' (i.e. fertilization probability increases with the proportion of a given male's sperm in the female tract). The models assume a trade-off between sperm expenditure and other aspects of reproductive success. Sperm costs may be unequal for the two males (paired male; opportunist male), especially if given phenotypes tend to adopt one or other pattern. In the `sneaks and guarders' (SG) game, certain males (guarders) are paired permanently to particular females, and others (sneaks) obtain matings opportunistically. Roles are therefore constant. Guarders are assumed to have no information whether a sneak mating has occurred (their strategy is tuned to the average risk of sperm competition) and the sperm costs are assumed to be unequal for sneaks and guarders. If sneak matings are rare, guarding males should spend less effort on ejaculates than sneaks. But if sneak matings are frequent, and if the marginal cost of sperm is very low for sneaks, the guarder may expend the greater effort on sperm. If sperm are relatively very cheap for guarders, then in cases of double mating, the paternity prospects of guarders should be higher than for sneaks; otherwise sneaks should win. However, if a guarder detects a sneak mating, he should increase his sperm dose in the female tract and achieve higher fertilization prospects (paternity) than the sneak. A second model concerns cases of extra pair copulations (EPCS) where all males are paired to females, but all will mate with another male's female if the opportunity should arise. Thus roles are assigned randomly with fixed probability. In this game, sperm costs relate to reduced paternal care (or to other losses with the `primary' female) and are assumed to be equal to all males. Predictions are very similar to the sneaks--guarders game: when performing an EPC a male should expend more effort on sperm (and hence gain higher paternity) than when mating as a paired males, unless the EPC is detected, in which case a paired male should greatly increase his sperm dose in the female (and hence should predominate at fertilization).

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