Multilevel selection in a resource-based model

In the present work we investigate the emergence of cooperation in a multilevel selection model that assumes limiting resources. Following the work by R. J. Requejo and J. Camacho [Phys. Rev. Lett. 108, 038701 (2012)], the interaction among individuals is initially ruled by a prisoner's dilemma (PD) game. The payoff matrix may change, influenced by the resource availability, and hence may also evolve to a non-PD game. Furthermore, one assumes that the population is divided into groups, whose local dynamics is driven by the payoff matrix, whereas an intergroup competition results from the nonuniformity of the growth rate of groups. We study the probability that a single cooperator can invade and establish in a population initially dominated by defectors. Cooperation is strongly favored when group sizes are small. We observe the existence of a critical group size beyond which cooperation becomes counterselected. Although the critical size depends on the parameters of the model, it is seen that a saturation value for the critical group size is achieved. The results conform to the thought that the evolutionary history of life repeatedly involved transitions from smaller selective units to larger selective units.