The evolution of cooperation on fragmented landscapes: the spatial Hamilton rule

Question: How does habitat destruction affect the evolution of cooperation? Methods: Differential equations of the probabilities for different states in pairwise sites based on the Prisoner’s Dilemma game in a regular network. Key assumptions: Individuals play the Prisoner’s Dilemma game with other individuals on directly connected (adjacent) sites. Individuals’ average payoff affects the birth rate. The population undergoes a birth–death process. Habitat loss and fragmentation in the network affect the population dynamics and the invasion and persistence of cooperation. Predictions: (1) The evolution of cooperation is made possible through non-random encounters in a spatially local process. (2) Derive a spatial Hamilton rule whereby the proportion of cooperators among the neighbouring individuals of a cooperator serves the same role of relatedness as in kin selection, which is consistent with other forms of Hamilton rules. (3) The evolution of cooperation becomes easier in harsh environments. (4) The co-existence of multiple strategies in a species can maintain population size at a constant level.We are grateful to Yoh Iwasa, Jeffrey Fletcher, Tadeusz Platkowski, Weini Huang, and Marius-Ionut Ochea for helpful discussion of this work during the 2009 IIASA Conference on the ‘Evolution of Cooperation: Models and Theories’. This work was supported by the National Basic Research Program (973 Program) (#2007CB109107), the NRF Blue Skies Research Programme, and the DST-NRF Centre of Excellence for Invasion Biology at Stellenbosch University