FAST GAME-THEORY COUPLED TO SLOW POPULATION-DYNAMICS - THE CASE OF DOMESTIC CAT POPULATIONS

We study a deterministic model of a population where individuals alter natively adopt hawk and dove tactics. It is assumed that the hawk and dove individuals compete for some resources at a fast time scale. This fast part of the model is coupled to a slow part that describes the g rowth of the population. It is shown that, in a constant game matrix, the population grows according to a logistic curve whose r and K param eters are related to the payoff of the tactics. Results show that the highest population density is obtained when all individuals are dove. We also study a density-dependent game matrix for which the gain is a function of the population density. In this case, we show that two sta ble equilibria can occur, a first one at low density with a high propo rtion of hawk individuals and a second one at large density with a low proportion of hawk individuals. Our model is applied to domestic cat populations for which the behavior of individuals in competition with one another can be modeled by two tactics: hawk and dove. Such tactics change with density of population. The results of the model agree wel l with observed data: high-density populations of domestic cats are ma inly doves, whereas low-density populations are mainly hawks. (C) 1998 Elsevier Science Inc. All rights reserved.