May random processes explain mating success in leks?

The object of this paper is to verify whether in specific cases the variance of mating success among lekking males may be due exclusively to a random mechanism, as opposed to the adaptive mechanisms of mate choice which are usually postulated in the literature in the framework of sexual selection theory. In fact, some studies attempted to compare observed distributions of male mating success with a Poisson 'null' distribution based on the conjecture of random mating; the conjecture is usually rejected. In this paper we construct a plausible model (the 'null' hypothesis) for a strictly random non-adaptive pattern of social behaviour of lekking males and females and we perform several simulations for reasonable choices of parameter values. It should be observed that some of the simulations based on our random model lead to a distribution of male mating success which is Poisson-like. However, contrary to predictions, in several simulations a random process of mate choice lead to non-Poissonian distributions. Accordingly, the fact that, when performing a statistical test on several sets of field data, we find both cases which are in agreement with Poisson distribution, or a normal one, and cases which are not, does not allow us to reject the assumption of random male reproductive success. Thus it is legitimate to conjecture that in many cases the inter-individual variability of male mating success might indeed be determined by random processes. If this conjecture were to be confirmed by further studies, the actual significance of sexual selection in the evolution of lekking species should be reassessed, and a novel approach in the analysis of field data would be called for.