Effects of habitat fragmentation on biodiversity patterns

The understanding of how species diversity is related to habitat conditions is a major issue in ecology. In this sense, spatial heterogeneity can have great influence on the number of species. The diversity of species in natural communities is also related to the rate at which energy flows through the ecosystem.
There is an increasing interest in understanding the effects of habitat fragmentation on biodiversity patterns. In this work we investigate the effects of habitat destruction on species diversity patterns by using a spatial computer simulation model in which species compete for limiting resources on habitats with spatial heterogeneity. In our model each site of the lattice holds n resources and the amount of each available resource is obtained from a uniform distribution. Each species $k$ is characterized by a set of $n$ half-saturation constants $K_{kj}$, where j denotes the resource label. The efficiencies of each species in the management of resources are taken into account by using the fitness function of species $k$ on site $i$, which is given by $f_{ki} = \min(R_{i1}/(K_{k1} + R_{i1}), R_{i2}/(K_{k2} + R_{i2}), \ldots, R_{in}/(K_{kn} + R_{in}))$. In order to study the effects of habitat fragmentation on biodiversity patterns we assume that a proportion $p$ of the sites can not be colonized. The distribution of unsuitable sites is controlled by a fractional Brownian motion, which produces spatially correlated landscapes. We investigate the behavior of the species-area relationship and the distribution of species abundance for some values of $p$ and also by varying the degree of spatial autocorrelation of the landscape. Our results indicate that both the level of spatial correlation and the degree of fragmentation have a strong influence on the shape of the species-area relationship and also on the distribution of species abundance.