Se você coopera, Darwin explica. Se você não coopera, Darwin explica também...

Evolution of cooperation by phenotypic similarity

Tibor Antala, Hisashi Ohtsukib,c, John Wakeleyd, Peter D. Taylore and Martin A. Nowaka,d,1

+Author Affiliations

aProgram for Evolutionary Dynamics and Department of Mathematics, Harvard University, Cambridge MA 02138;

bDepartment of Value and Decision Science, Tokyo Institute of Technology, Tokyo 152-8552, Japan;

cPrecursory Research for Embryonic Science and Technology, Japan Science and Technology Agency, Saitama 332-0012, Japan;

dDepartment of Organismic and Evolutionary Biology, Harvard University, Cambridge MA 02138; and

eDepartment of Mathematics and Statistics, Queen's University, Kingston, ON, Canada K7L 3N6

Communicated by Simon A. Levin, Princeton University, Princeton, NJ, March 10, 2009 (received for review June 15, 2008)

Abstract

The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much work in theoretical biology. Here, we study the evolution of cooperation in a model where individuals are characterized by phenotypic properties that are visible to others. The population is well-mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies can depend on distance in phenotype space. We study the interaction of cooperators and defectors. In our model, cooperators cooperate with those who are similar and defect otherwise. Defectors always defect. Individuals mutate to nearby phenotypes, which generates a random walk of the population in phenotype space. Our analysis brings together ideas from coalescence theory and evolutionary game dynamics. We obtain a precise condition for natural selection to favor cooperators over defectors. Cooperation is favored when the phenotypic mutation rate is large and the strategy mutation rate is small. In the optimal case for cooperators, in a one-dimensional phenotype space and for large population size, the critical benefit-to-cost ratio is given by b/c = 1 + 2/. We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces.

coalescent theory evolutionary dynamics evolutionary game theory mathematical biology stochastic process

Footnotes

1To whom correspondence should be addressed. E-mail: martin_nowak@harvard.edu
Author contributions: T.A., H.O., J.W., P.D.T., and M.A.N. performed research; and T.A., H.O., J.W., P.D.T., and M.A.N. wrote the paper.

The authors declare no conflict of interest.

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