Sperm competition games: a prospective analysis of risk assessment

Abstract

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 expand 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.

Nocturnal mating behaviour and dynamic male investment of copulation time in the southern blue-ringed octopus, Hapalochlaena maculosa (Cephalopoda: Octopodidae)

“…Additionally, amongst maleterminated copulations, copulation times significantly increased with the numbers of other males that the female had mated with. These patterns are consistent with predicted behaviours based on models of sperm competition (Parker, 1970;Parker et al, 1997), and with behaviours recorded in both S. lycidas (Wada et al, 2010) and an unidentified pygmy octopus (Cigliano, 1995) where males of these species were reported to adjust copulation times, presumably spent performing sperm removal and transferring multiple spermatophores, with females based on whether they were the last male to mate with her.…”

“…Relevant models of sperm competition, where sperm supply is limited, imply that male cephalopods could potentially achieve optimal fertilisation success by investing less time copulating with females that they have already mated with (Parker, 1970), with females that are holding less sperm from competing males and therefore pose less risk of sperm competition (Ball & Parker, 2007), and/or when additional factors such as male mating order might give males an inherent advantage towards successful fertilisation (Parker, 1990). Likewise, male cephalopods should be expected to invest more time and/or spermatophores with novel females and females posing a high-risk of sperm competition (Parker, 1970;1990;Parker et al, 1997;Ball & Parker, 2007).…”

Sexual selection and genital allometry in the Hottentot golden mole (Amblysomus hottentotus)

“…Under cryptic female choice the prediction is that variation in male genital traits will be related to male fertilisation success; therefore, non-random fertilisation success would be expected among males (Arnqvist, 1997). Sperm competition occurs when the ejaculates of multiple males compete for the fertilisation of an ovum (Hosken & Stockley, 2004;Parker, Ball, Stockley & Gage, 1997;Møller & Birkhead, 1989). Arnqvist (1997) suggested that irrespective of whether males compete directly (via genital morphology) or indirectly (via their ability to stimulate/coerce female sperm use), an element of sperm competition will always be present.…”

Sperm competition games played by dimorphic male beetles: fertilization gains with equal mating access

“…When a male mates with a female, there is a probability between zero and one that his ejaculate will have to compete for fertilizations with that of another male; this probability is termed the risk of sperm competition (Parker 1970;Parker et al 1997). Game theoretical models have revealed the potential for sperm competition in in£uencing ejaculation strategies; species in which males face a high risk of sperm competition are predicted to have a higher ejaculate expenditure than species in which males face a low risk of sperm competition (Parker 1982;Parker et al 1997). This theoretical expectation has been met by comparative analyses of testis mass from a number of taxa (Harcourt et al 1981;Stockley & Purvis 1993;Gage 1994;Hosken 1997) although in insects the diversity of sperm competition mechanisms can make the interpretation of such analyses problematic (see Simmons & Siva-Jothy 1998).…”