Indirect effects of habitat destruction in model ecosystems

Habitat destruction is one of the primary causes of species extinction in recent history. Even if the destruction is restricted to a local area, its accumulation increases the risk of extinction. To investigate the effect of local habitat destruction, we studied two- and three-species model systems. The former contains prey (X) and predator (Y), while the latter is composed of X, Y and a top predator (Z). If the species Z goes extinct, then the latter becomes the former. Species dynamics are modeled within the lattice applying local and global interactions. Local interaction occurs between neighboring lattice points. In contrast, global interaction is allowed between any pair of lattice points, and its dynamics can be represented by the mean-field theory that is equivalent to Lotka-Volterra equation. Barriers, representing habitat loss, are randomly located between adjacent lattice points with the probability p. The barrier interrupts the reproduction of the prey X, but the predators Y and Z suffer no direct damage from the barriers. It is found that the effects of barriers on both species X and Y in the two-species model are usually opposite to those in the three-species model. Namely, if extinction occurs, the influence of habitat destruction on surviving species changes dramatically. We also find that when the density p of barriers increases the two models exhibit different extinction patterns: sometimes species X goes extinct, but sometimes the predator or top predator become extinct depending on the level of barrier density. The mean-field theory adequately predicts such species extinction, but it cannot explain some of the results. We interpret the results as an indirect relation between habitat destruction and species extinction.