Measuring the Mating Skew

Abstract

Charles Darwin (1871) defined sexual selection as a difference inreproductive success due to competition over mates, a definition that is still valid today. Being able to quantify such differences is thus essential for explaining the consequences of sexual selection, say, the ornamentation rdisplay behavior of males. In the specific ase of lekking (aggregated, non-resource-based display of males), attempts to do so have proven difficult. Any measure that does not take into account the possibility of random mating to produce the observed pattern of mating success is unsatisfactory as a measure of the intensity of sexual selection (Sutherland 1987; Mackenzie et al. 1995b). That variation in male mating success on leks is systematically higher than expected from pure random mating has been verified by Bradbury et al. (1985) and Mackenzie et al. (1995a). However, these studies do not yet provide means to estimate the expected mating success of individuals displaying together. Since a lek is not itself a trait but an assemblage of several males, each trying to optimize their own fitness (Hoglund and Alatalo 1995), fitness considerations of single individuals are required in explaining the evolution of lekking. The skew index, defined as the ratio of observed to maximum skew (Keller and Vargo 1993; Reeve and Ratnieks 1993), has been gaining popularity as a measure of skewed reproductive success (e.g., Bourke and Heinze 1994; Keller and Reeve 1994; Reeve and Keller 1995), and it has also been used to estimate the expected fitness of lekking individuals (Widemo and Owens 1995). However, this measure has been shown to have undesirable discontinuities (Pamilo and Crozier 1996). Moreover, it interprets random variation as real differences in mating success. This is most clearly seen in models of pure random mating, which nevertheless lead to positive values of the skew measure (Mackenzie et al. 1995b). Recently, Keller and Krieger (1996) proposed a method for correcting the skew index for random variation. We shall show, however, that the corrected measure still is not satisfactory, and we suggest a novel, statistically rigorous method. We give two criteria for a proper measure of skewed mating success. First, it should allow determining the most probable underlying distribution of mating