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.

DESPITE extensive theoretical effort(1,8), the evolution of lekking as a mating system remains a controversial issue(9,10). Leks are nonresource-based matins aggregations(2), but may also be regarded as patches differing in female encounter rate(2,3,5,7). We report here a new distribution model that incorporates variation in male mating skew with lek size. The model predicts that, under specified conditions, high-ranking males have smaller optimal lek sizes than low-ranking males. All males benefit from initial clustering, but only low-ranking males gain from large aggregations. This generates progressive clustering around high-ranking males at hotspots determined by female spatial distributions. The predictions of our model were validated in two ways using empirical data on lekking ruffs, Philomachus pugnax. Our model integrates the basic elements of the previously competing hotspot(2,3) and hotshot(4) models of lek evolution by a simple mechanism, and could explain the evolution of lekking.