Sperm competition games: sperm size and sperm number under adult control

Abstract

Evolutionary games of sperm competition in which two males mate with the same female have previously considered sperm size to be fixed at some (small) constant level. Although male gametes in multicellular organisms are typically small compared with ova, they vary greatly both between and within groups, and sperm size sometimes correlates with the probability of sperm competition. This paper examines `raffle principle' sperm competition games in which both size and number of gametes can be varied strategically under control of the diploid parent. If ejaculate investment trades off against the number of matings that a male can achieve, the evolutionarily stable strategy (ESS) ejaculate expenditure (as a fraction of reproductive effort per mating) approximates to p/4 when the probability, p, of sperm competition is low. Sperm size may either: (i) increase a sperm's competitive weight (a measure of its advantage in the fertilization raffle), or (ii) influence its mortality rate in the female tract. On the simplest model, size is optimized after the marginal value theorem, and may be large or small depending on how size influences competitive weight or survivorship. Further, sperm size is independent of the risk of sperm competition, and only sperm numbers increase with this risk. However, some recent studies show sperm size to increase with sperm competition. The present analysis offers the following possibilities: (i) there are unidentified constraints on sperm number, so that ejaculate mass can increase only by increase in sperm size; (ii) competitive benefits of size become more important as sperm numbers increase; (iii) size mainly increases survivorship, and sperm competition risk increases with the mean duration between mating and fertilization; and (iv) size increases competitive ability at the expense of survivorship, and sperm competition risk decreases with time between mating and fertilization. These conclusion relate to advantages conferred by size on sperm before fertilization; they do not affect the prediction of previous models that no component of sperm size should evolve for provisioning the zygote.