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

Abstract

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 (s) 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 s is directly proportional to the mean E for a species; across species s 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 sfE/M; both E and M increase with sperm competition, but E increases differently with sperm competition in its two ranges.

Sperm competition games: the risk model can generate higher sperm allocation to virgin females

“…There is an obvious relation between n * , the expected matings per male during the time it takes a female to complete one batch of eggs, and (1 + q), those expected per female (Ball & Parker, 1998;Parker & Ball, 2005). In a population of N f adult females and N m adult males, the total male copulations, N m n * , must equal the total female copulations, N f (1 + q).…”

“…Parker & Ball, 2005), where the quantity in square brackets is the average total cost of a mating (finding a female and ejaculating), and n is the average number of the matings involved.…”

“…The proportion of effort spent on the ejaculate (and hence relative testis size, r; Parker & Ball, 2005), is:…”

“…Predictions about sperm allocation depend critically on the measure of allocation used (Parker & Ball, 2005): relative ejaculate expenditure (E) is the expenditure on the ejaculate as a proportion of the total cost of each mating, and is likely to be analogous to relative testis size (r). In contrast, allocation can be expressed in terms of s, the absolute number of sperm (or mass of ejaculate).…”

“…In contrast, allocation can be expressed in terms of s, the absolute number of sperm (or mass of ejaculate). In models that allowed average sperm competition level to covary with sperm expenditure, Parker & Ball (2005) predicted that across species, E and r should increase with average risk or intensity, but that s should decrease with average intensity where the mean number of competing ejaculates exceeds two (as predicted for perceived intensity where males can assess perfectly the number of competing ejaculates; Parker et al, 1996;. Williams et al (2005) also investigated a model in which sperm competition level and sperm-allocation strategies are dependent coevolving traits, and found that, under certain conditions, s could decrease across high average risk levels.…”