کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4498939 1319006 2007 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Evolutionary graph theory: Breaking the symmetry between interaction and replacement
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
Evolutionary graph theory: Breaking the symmetry between interaction and replacement
چکیده انگلیسی

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 l  . We show that cooperation is favored by natural selection if b/c>hg/lb/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=lg=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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Theoretical Biology - Volume 246, Issue 4, 21 June 2007, Pages 681–694
نویسندگان
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