# Chromodynamics of Cooperation in Finite Populations

 Title: Chromodynamics of Cooperation in Finite Populations Author: Nowak, Martin; Traulsen, Arne Note: Order does not necessarily reflect citation order of authors. Citation: Traulsen, Arne and Martin A. Nowak. 2007. Chromodynamics of Cooperation in Finite Populations. PLoS ONE 2(3): e270. Full Text & Related Files: pone.0000270.pdf (217.3Kb; PDF) Abstract: 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. Methodology/Principal Findings: 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/Significance: 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 $$b > c$$. Published Version: http://dx.doi.org/10.1371/journal.pone.0000270 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2640567

### This item appears in the following Collection(s)

• FAS Scholarly Articles [7374]
Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University