An indexed dispersion criterion for testing the sex-biased dispersal of lek mating behavior of capercaillies

Traditionally it has been assumed by ecologists that the dispersion of positions with respect to leks of female capercaillies during the mating season is superior to the dispersion of positions of male capercaillies. However some recently published articles suggest the idea that dispersion is not sex-biased, but both sexes show a similar dispersion. This article introduces a mathematical model to approach the study of the above question by means of an indexed dispersion criterion. This model is developed in detail thus deriving its main mathematical properties. On this basis, the model is applied to the analysis of the motivating problem with real data of positions of leks and female and male capercaillies. The results derived by means of the model put into doubt the traditional assumption of a superior dispersion of females supporting the new theories, that is, both sexes show a similar dispersion.