Sperm competition games: a prospective analysis of risk assessment

We develop the logic of assessment of sperm competition risk by individual males where the mechanism of sperm competition follows a 'loaded raffle' (first and second inseminates of a female have unequal prospects). Male roles (first or second to mate) are determined randomly. In model 1, males have no information about the risk associated with individual females and ejaculation strategy depends only on the probability, q, that females mate twice. Evolutionarily stable strategy (ESS) ejaculate expenditure increases linearly from zero with q, and reduces with increasing inequality between ejaculates, though the direction of the loading (which role is favoured) is unimportant. In model 2, males have perfect information and can identify each of three risk states: females that will (1) mate just once ('no risk'), (2) mate twice but have not yet mated ('future risk'), and (3) mate twice and have already mated ('past risk'). The ESS is to ejaculate minimally with 'no risk' females, and to expend equally with 'past' and 'future' risk females; the direction of the competitive loading is again unimportant. Expenditure again increases with risk, but is now non-zero at extremely low risk. Model 3 examines three cases of partial information where males can identify only one of the three risk states and cannot distinguish between the other two: they therefore have just two information sets or 'contexts'. Expenditure in both contexts typically rises non-linearly from zero with q, but (whatever the loading direction) expenditure is higher in the context with higher risk (e.g. if contexts are 'mated' and 'virgin', males spend more with mated females). However, in highly loaded raffles, sperm expenditure can decrease over part of the range of risk. Also, the direction of the loading now affects expenditure. Biological evidence for the predictions of the models is summarized and discussed.