Abundance patterns in multi-species communities exposed to habitat destruction.

Habitat destruction resulting from human activity is a serious threat to biodiversity. The model developed by Tilman et al. [Tilman, D., May, R.M., Lehman, C.L., Nowak, M.A., 1994. Habitat destruction and the extinction debt. Nature 371, 65-66] has become an important tool for analyzing persistence of species in habitats under destruction. However, most analysis and applications of this model have been limited to the studies of species richness and the order of extinction. In this paper, we address other important issues related to succession of species abundances. We are interested in how the abundance ranking (i.e., the ranking of species according to their relative abundances), the rank-abundance curve and the community diversity alter in habitats under destruction. We treat analytically the model of Tilman et al. and investigate three different scenarios. We consider that before destruction: (i) best competitors are most abundant; (ii) all species are equally abundant; (iii) poor competitors are most abundant. In each case, we have derived explicit expressions for equilibrium species abundances depending on proportion of destroyed sites. Then we follow analytically alteration in the initial abundance ranking, show complex patterns of succession of species abundances and consider transformations in the rank-abundance curve. We demonstrate patterns of self-organization in abundance distributions emerging as a response to habitat destruction. We show non-monotonic dependence of community diversity and community evenness on proportion of destroyed sites.