期刊
JOURNAL OF THEORETICAL BIOLOGY
卷 246, 期 4, 页码 681-694出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2007.01.024
关键词
evolutionary dynamics; evolutionary game theory; population structure; evolutionary graph theory; replicator equation; cooperation
资金
- NIGMS NIH HHS [R01 GM078986-01, R01 GM078986, 1 R01 GM078986-01] Funding Source: Medline
We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree I. We show that cooperation is favored by natural selection if b/c > hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak-selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g = h = l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix. (C)) 2007 Elsevier Ltd. All rights reserved.
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