Predicting variation in sperm precedence

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Abstract
Sperm competition theory predicts that males are adapted for success in sperm competition by the production of large numbers of sperm. This is supported by both inter– and intraspecific studies showing that males mating under high sperm competition risk increase investment in sperm production. Such an increase in sperm production is an advantage if sperm mix randomly or if sperm displacement occurs. When two males mate with the same female, the measurement of the proportion of eggs fertilized by the second male to mate (termed P 2 ) has been used to help elucidate sperm competition mechanisms. P 2 is usually quoted as a mean value, with little attention being paid to its variance, although P 2 estimates are notoriously variable. By predicting an expected variance for P 2 , additional information on sperm competition mechanisms may be obtained. Here we present a technique for analysing the variance in P 2 when a given mechanism of P 2 is assumed. We apply this technique to P 2 data collected from Plodia interpunctella (Lepidoptera, Pyralidae), assuming a ‘fair raffle’ mechanism of sperm competition. We compare observed distributions of P 2 with theoretical distributions generated assuming random mixing of two ejaculates drawn randomly from a population of known mean and variance in sperm numbers. Ejaculates of known size were obtained by counting the number of sperm ejaculated by males mating for the first (large ejaculate) or second (small ejaculate) time. Females either received two small or one small and one large ejaculate, and the distribution of P 2 (estimated using the sterile male technique) was compared with our theoretical predictions. The observed variance in P 2 was greater than our model prediction, thus we conclude that sperm from P. interpunctella do not mix randomly before fertilization.