Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 106, Issue 21, Pages 8597-8600Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0902528106
Keywords
coalescent theory; evolutionary dynamics; evolutionary game theory; mathematical biology; stochastic process
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Funding
- John Templeton Foundation
- National Science Foundation/National Institutes of Health [R01GM078986]
- Bill and Melinda Gates Foundation [37874]
- Japan Society for the Promotion of Science
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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/root 3. We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces.
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