Indirect effect of habitat destruction on ecosystems

Habitat destruction is one of the primary causes of species extinction in recent history. Even if the destruction is restricted to a local and small area, its accumulation increases the risk of extinction. To study local destruction of habitat, we present a lattice ecosystem composed of prey (X) and predator (Y). This system corresponds to a lattice version of the Lotka-Volterra model, where interaction is allowed between neighboring lattice points. The lattice is partly destroyed, and destructed sites or barriers are randomly located between adjacent lattice points with the probability p. The barrier interrupts the reproduction of X, but the species Y suffers no direct damage by barriers. This system exhibits an extinction due to an indirect effect: when the density p of barriers increases, the species Y goes extinct. On the other hand, an initial suppression of X may later lead to the increase of X. The predator Y decreases in spite of the increase of X. These results cannot be explained by a mean-field theory such as the Lotka-Volterra equation. We discuss that endangered species may become extinct by a slight perturbation to their habitat.