Sperm competition, mating rate and the evolution of testis and ejaculate sizes: a population model

There are various ways to estimate ejaculate expenditure. Ejaculate size or sperm number (s) is an absolute number of units of ejaculate. Relative ejaculate expenditure (E) is the expenditure on the ejaculate as the proportion of the total expenditure on all aspects of the mating, including finding and acquiring a female, and so on. Relative testis size or gonadosomatic index (sigma) is testes mass divided by body mass; it is assumed to reflect the product of mating rate (M) and ejaculate mass (s). In a new model, where mating rate, sperm competition and sperm allocation interact, and where the female's inter-clutch interval is assumed to be independent of s or M, we show that sigma is directly proportional to the mean E for a species; across species sigma and E increase monotonically with sperm competition. However, the relation between s and sperm competition across species depends on the range of sperm competition (low risk or high intensity): s increases with sperm competition at low risk levels, but decreases with sperm competition at high intensity levels. This situation arises because s proportional to E/M; both E and M increase with sperm competition, but E increases differently with sperm competition in its two ranges.