Evolution of cooperation in patchy habitat under patch decay and isolation

The spatial version of Prisoner's Dilemma (PD) is studied, which incorporates habitat decay through change in the mortality parameter and habitat isolation through change in the colonization coefficient. We found four kinds of evolutionary results, which are affected profoundly by the elements of the payoff matrix and the ratio of the colonization coefficient to the mortality parameter: population extinction, a Pure cooperator Population, coexistence of cooperators and defectors., and a pure defector Population. First, the parameter region of cooperation (pure cooperator and coexistence region) shrinks with an increase in the cooperative cost. and that of defection extends. The in crease in cooperative reward makes the cooperative realon extend and the defector region become small. Second, the cooperative reward can compensate for the extinction risk due to habitat destruction and allow a population to survive even if the colonization coefficient is smaller than the mortality parameter. Third, although habitat destruction (including decay and isolation) increase the extinction risk of a population, moderate external power can push the evolution of cooperation ahead of population extinction, and even make a completely cooperative world come into being. Finally, for certain values of elements of the payoff matrix, the population suffering habitat destruction can maintain a stable Population size by regulating the frequencies of cooperators and defectors. This implies that the multibehavior strategy within a Population may be a mechanism to defend against the influences of a changing environment.