Black hole models of ungulate lek size and distribution

Models of lek breeding based on female preferences for mating with high quality males have predicted that leks should be evenly distributed at distances approximating the diameter of female home ranges, and empirical studies have cited lek distribution in support of these models. In the ‘black hole’ model of lek evolution, leks arise because clusters of male territories retain mobile females; female mating preferences are not assumed. Here this model is extended to include sufficient space and animals for multiple leks to form, and it is used to generate predictions about the size and spacing of leks in different populations. Like models based on female choice, black hole models predict that leks will be evenly spaced at distances of approximately one female home range diameter, that lek size will increase with increasing male density, and that females will be concentrated near the centre of leks where male territories will be smallest. The addition of female copying to the model decreases the tendency for leks to form, but this influence is mitigated by an upper limit on harem size. Since similar lek distributions are predicted by contrasting models, the even distribution of leks may imply some mechanism causing females to aggregate at the largest accessible cluster of territories, but does not clarify the nature of this mechanism.