Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully connected networks and on spatial lattices. The time t(*) for a favorable mutation to dominate scales with the population size N as N(D+1)/D in D-dimensional hypercubic lattices and as NlnN in fully-connected graphs. It is shown that the surface of the interface between mutants and nonmutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction.