Mechanisms of sperm competition: testing the fair raffle

Sperm competition is a major force of sexual selection, but its implications for mating system and life-history evolution are just beginning to be understood. Of particular importance is understanding the mechanisms of sperm competition. Models have been developed to determine if sperm competition operates in a fair raffle process, whereby each sperm from competing males has an equal chance of fertilizing a female's ova, or if it operates in a loaded raffle process, whereby one male's sperm has a fertilization advantage. These models require data on relative sperm and offspring (paternity) numbers of competing males. Here we develop a model based on maximum-likelihood methods for differentiating between the fair and loaded raffle processes. The model calculates the relative competitiveness of two males' sperm (loadings) as well as the economy of scale (nonlinear returns to sperm number). Previous models implicitly assumed that there is no economy of scale, which may not be the case when there is cooperation or interference among sperm from a given male. We demonstrate that our model has superior power-in some instances more than double-than previous models. We apply our model to an example of sperm competition in the guppy (Poecilia reticulata) and show that the system may be characterized by a loaded raffle attributable to effects of second male precedence.