Abstract
Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration.
Original language | English (US) |
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Pages (from-to) | 97-105 |
Number of pages | 9 |
Journal | Journal of Theoretical Biology |
Volume | 299 |
DOIs | |
State | Published - Apr 21 2012 |
All Science Journal Classification (ASJC) codes
- General Immunology and Microbiology
- Applied Mathematics
- General Biochemistry, Genetics and Molecular Biology
- General Agricultural and Biological Sciences
- Statistics and Probability
- Modeling and Simulation
Keywords
- Cooperation
- Evolutionary game theory
- Evolutionary graph theory
- Mutation
- Population structure