FAST GAME DYNAMICS COUPLED TO SLOW POPULATION-DYNAMICS - A SINGLE POPULATION WITH HAWK-DOVE STRATEGIES

We study a model of a population subdivided into two subpopulations co rresponding to hawk and dove tactics. It is assumed that the hawk and dove individuals compete for a resource every day, i.e., at a fast tim e scale. This fast part of the model is coupled to a slow part which d escribes the growth of the subpopulations and the long term effects of the encounters between the individuals which must fight to have an ac cess to the resource. We aggregate the model into a single equation fo r the total population. It is shown that in the case of a constant gam e matrix, the total population grows according to a logistic curve who se r and K parameters are related to the coefficients of the hawk-dove game matrix. Our result shows that high equilibrium density populatio ns are mainly doves, whereas low equilibrium density populations are m ainly hawks. We also study the case of a density dependent game matrix for which the gain is linearly decreasing with the total density.