An evolutionary explanation for the propensity to migrate

We explore the evolutionary dynamics of a population that consists of cooperators and defectors, wherein each member of the many pairs of players of a one-shot prisoner's dilemma game is drawn at random, and the number of descendents positively depends on the payoffs in the game. We demonstrate how an inclination to migrate may be mapped onto the overall evolutionary fitness of the cooperators. The threshold value of the inclination to migrate parameter is obtained. Intensities of migration higher than that value guarantee that in the long run, the population will consist entirely of cooperators. The threshold value is characterized by the payoff parameters lying at the base of the evolutionary dynamics.