Size and stability of vertebrate leks.

Lek size varies greatly among lekking species. At present there is no explicit theoretical explanation for this diversity. We extend an existing model of optimal lek size that incorporates female mating preferences and male-male contest competition. The model shows that variation in lek size is predicted by the interaction between lek size, overall copulation rate and the proportion of copulations accruing to males of different rank. In species where females prefer to mate on the largest leks and high-ranking males are able to monopolize females irrespective of the size of the lek, the maximum lek size will be large. Conversely, in species where females show weak preference for mating on large leks or increasing lek size quickly results in scramble competition, the maximum lek size will be smaller. Thus, differences between species in lek size may be due largely to differences in the extent to which high-ranking males can monopolize mating opportunities. Leks become unstable and break down when high-ranking males can no longer get their 'expected' copulation success. Therefore, the mechanism that generates male clustering, that is, sexual parasitism of high-ranking males by subordinates, also sets a limit to the largest stable lek size. Copyright 1999 The Association for the Study of Animal Behaviour.