Analytical discussions on species extinction in competitive communities due to habitat destruction

An improvement of a metapopulation model is developed and used to analyze the behaviors of abundant and extinct species in the system analytically. By approximating the direct effect rate of habitat destructions on individual species using differentiable functions, the model enables us to discuss the equilibrium and stability of the system. Special cases of the habitat destruction functions, constant, piecewise linear, exponential and periodic functions, are discussed analytically and numerically. The conditions for system stability are also given.