Size and stability of vertebrate leks

Lek size varies greatly among lekking species. At present there is no expli cit theoretical explanation for this diversity. We extend an existing model of optimal lek size that incorporates female mating preferences and male-m ale contest competition. The model shows that variation in lek size is pred icted by the interaction between lek size, overall copulation rate and the proportion of copulations accruing to males of different rank. In species w here 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 pre ference for mating on large leks or increasing lek size quickly results in scramble competition, the maximum lek size will be Smaller. Thus, differenc es between species in lek size may be due largely to differences in the ext ent to which high-ranking males can monopolize mating opportunities. Leks b ecome unstable and break down when high-ranking males can no longer get the ir 'expected' copulation success. Therefore, the mechanism that generates m ale clustering, that is, sexual parasitism of high-ranking males by subordi nates, also sets a limit to the largest stable lek size. (C) 1999 The Assoc iation for the Study of Animal Behaviour.