A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as
cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs, using tools such as random walk theory and harmonic analysis.
Here is a list of the scholars participating in this program.