complex transition to cooperative behavior in a structured population model复杂的过渡到合作行为在一个结构化的人口模型.pdfVIP

Complex Transition to Cooperative Behavior in a Structured Population Model 1 1 2 3 Luciano Miranda , Adauto J. F. de Souza , Fernando F. Ferreira , Paulo R. A. Campos * ´ ˆ ˜ 1 Departamento de Fısica, Universidade Federal Rural de Pernambuco, Recife-PE, Brazil, 2 GRIFE – Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo, ˜ ´ Sao Paulo, Brazil, 3 Departamento de Fısica, Universidade Federal de Pernambuco, Recife-PE, Brazil Abstract Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner’s dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the c