Male rank and optimal lek size

Abstract

Widemo and Owens presented a model that calculates the expected copulation rates of males on leks of a range of sizes. They claim that a negative relationship between lek size and male mating skew will result in low-ranking males having greater optimal lek sizes than higher ranking rivals. Widemo and Owens offered no proof of their claim, and their model assumes that the rank of a male does not change as lek size increases, whereas in reality, rank may change as more males arrive. We present a general model that allows rank to change as lek size increases. We show that the crucial determinant of whether optimal lek size increases with male rank is whether relative competitive differences increase with lek size. Contrary to the claim of Widemo and Owens, the relationship between skew and lek size has no direct bearing on the optimal levels of aggregation of males of different rank. We show that a negative relationship between skew and lek size can exist even when high-ranking males have the greatest optimal lek sizes.