PT - JOURNAL ARTICLE
AU - Antal, Tibor
AU - Ohtsuki, Hisashi
AU - Wakeley, John
AU - Taylor, Peter D.
AU - Nowak, Martin A.
TI - Evolution of cooperation by phenotypic similarity
AID - 10.1073/pnas.0902528106
DP - 2009 May 26
TA - Proceedings of the National Academy of Sciences
PG - 8597--8600
VI - 106
IP - 21
4099 - http://www.pnas.org/content/106/21/8597.short
4100 - http://www.pnas.org/content/106/21/8597.full
SO - Proc Natl Acad Sci USA2009 May 26; 106
AB - 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+2/3. We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces.