Citation:
Antal T, Ohtsuki H, Wakeley J, Taylor PD, Nowak M. Evolution of cooperation by phenotypic similarity. Proc. Natl. Acad. Sci., USA. 2009;106 :8597-8600.
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Abstract:
The emergence of cooperation in populations of selfish individu-
als 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 popu-
lation 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.