Evol Ecol Res 12: 23-33 (2010)     Full PDF if your library subscribes.

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

Feng Zhang^1,2, Yi Tao¹, Zizhen Li³ and Cang Hui²

¹Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Science, Beijing, China, ²Centre for Invasion Biology, Department of Botany and Zoology, Stellenbosch University, Matieland, South Africa and ³Department of Mathematics and Statistics, Lanzhou University, Lanzhou, China

Correspondence: C. Hui, Centre for Invasion Biology, Department of Botany and Zoology, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa.
e-mail: chui@sun.ac.za

ABSTRACT

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.

Keywords: evolutionary game, habitat loss, invasion analysis, pair approximation, Prisoner’s Dilemma.

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