This paper extends the sperm displacement model of Parker et al. (Behav. Ecol. Sociobiol. 27, 55 (1990)), in which sperm displacement is viewed as a process in which one unit of sperm introduced displaces one unit of sperm from the female's sperm stores. Here this process is envisaged in terms of the change in density of sperm in the sperm stores. In matings with virgin females, only sperm store fluid is displaced at the start of sperm transfer, but if there is swift random mixing of seminal and sperm store fluid, the fluid displaced will contain sperm at the same average density as that in the sperm stores (random displacement). In mating of the same female by two or more males, the sperm density of the last male to mate is assumed to be independent of the presence of previous sperm; P2 (the proportion of eggs fertilized by the last male) thus equals the density of the last male's sperm divided by the current total density of sperm in the sperm stores. Once the sperm stores have reached the asymptotic density (equivalent to the input density, i.e. the density of sperm in the seminal fluid), the present model becomes equivalent to that of Parker et al. (1990). Predictions for this model are tested using all available data from the dung fly, Scatophaga stercoraria. They are based on the assumption that sperm are transferred at a constant rate with copulation time. The data concur with this model, and we conclude that it is better than various other simple alternatives for explaining P2 in Scatophaga.
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