Effects of the spatial heterogeneity on the diversity of ecosystems with resource competition

The understanding of the mechanisms that promote biodiversity has implications for conservation and extinction of species and has raised the interest of the scientific community in the last decades. It is well established that spatial heterogeneity is an important factor influencing species richness. In this work we use a discrete computer simulation model to survey the impact of spatial heterogeneity on biodiversity patterns of an ecosystem in which species compete for limiting resources. The main feature of the model relies on the assumption that species have different requirements for a given resource. Individuals are arranged over a square lattice, where the sites are occupied by at most one individual. Individuals die at a fixed rate. Empty sites may be recolonized by newborn individuals according to a growth rate which depends on the ability of the individuals in the use of resources. We investigate the species-area relationship (SAR), the species abundance distribution and the dependence of species richness on the number of limiting resources and the degree of spatial heterogeneity. Commonly, the changes in the number of species with area is well approximated by a power law. Here, we show that the SAR displays two power law regimes. By assuming that the species' abilities to consume resources are uneven, we found that the relationship between species richness and the degree of habitat heterogeneity is described by a unimodal function, being in agreement with experimental data. The dependence of the number of species with the number of resources was also investigated. Remarkably, it is the observation of an optimum value for the number of resources that maximizes the biodiversity.