Simulating natural selection as a culling mechanism on finite populations with the hawk–dove game

The behaviors of individuals and species are often explained in terms of evolutionary stable strategies (ESSs). The analysis of ESSs determines which, if any, combinations of behaviors cannot be invaded by alternative strategies. Two assumptions required to generate an ESS (i.e., an infinite population and payoffs described only on the average) do not hold under natural conditions. Previous experiments indicated that under more realistic conditions of finite populations and stochastic payoffs, populations may evolve in trajectories that are unrelated to an ESS, even in very simple games. The simulations offered here extend earlier research by employing truncation selection with random parental selection in a hawk–dove game. Payoffs are determined in pairwise contests using either the expected outcome, or the result of a random variable. In each case, however, the mean fraction of hawks over many generations and across many independent trials does not conform to the expected ESS. Implications of these results and philosophical underpinnings of ESS theory are offered.