Chromodynamics of cooperation in finite populations.
BACKGROUND
The basic idea of tag-based models for cooperation is that individuals recognize each other via arbitrary signals, so-called tags. If there are tags of different colors, then cooperators can always establish new signals of recognition. The resulting "chromodynamics" is a mechanism for the evolution of cooperation. Cooperators use a secret tag until they are discovered by defectors who then destroy cooperation based on this tag. Subsequently, a fraction of the population manages to establish cooperation based on a new tag.


RESULTS
We derive a mathematical description of stochastic evolutionary dynamics of tag-based cooperation in populations of finite size. Benefit and cost of cooperation are given by b and c. We find that cooperators are more abundant than defectors if b/c > 1+2u/v, where u is the mutation rate changing only the strategy and v is the mutation rate changing strategy and tag. We study specific assumptions for u and v in two genetic models and one cultural model.


CONCLUSIONS
In a genetic model, tag-based cooperation only evolves if a gene encodes both strategy and tag. In a cultural model with equal mutation rates between all possible phenotypes (tags and behaviors), the crucial condition is b/c > (K+1)/(K-1), where K is the number of tags. A larger number of tags requires a smaller benefit-to-cost ratio. In the limit of many different tags, the condition for cooperators to have a higher average abundance than defectors becomes b > c.
Traulsen
Arne
A
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts, United States of America. traulsen@fas.harvard.edu
Nowak
Martin A
MA
D000819:Animal Communication; D000818:Animals; D003198:Computer Simulation; D005796:Genes; D006801:Humans; D007398:Interpersonal Relations; D007858:Learning; D008957:Models, Genetic; D008962:Models, Theoretical; D009154:Mutation; D015398:Signal Transduction / Q000502:physiology; D012919:Social Behavior; D013269:Stochastic Processes