Ecological symmetry breaking can favour the evolution of altruism in an action-response game

The evolution of altruistic behaviour is studied in a simple action-respons e game with a tuneable degree of conflict of interest, It is shown that for the continuous, mixed-medium approach no stable polymorphism favours altru ism. Ecological dynamics are explored with the addition of a spatial dimens ion and a local energy variable. A continuous spatial model with finite loc al range does not introduce any substantial difference in the results with respect to the level of altruism. However, the model illustrates how ecolog ical coupling may lead to the formation of stable spatial patterns in the f orm of discrete and isolated clusters of players as a consequence of invers e density dependence. A discrete, individual-based model is built in which local interactions are also modelled as occurring within a finite neighbour hood of each individual and spatial positions are not restricted as in latt ice models. This model shows substantially different results. A high level of altruism is observed for low (but positive) degrees of conflict and this level decreases linearly for higher degrees of conflict. The evolution of altruism is explained by studying the broken symmetries introduced by the s patial clusters themselves, mainly between their central and peripheral reg ions which, in combination with the discrete and the stochastic nature of t he model, result in the stabilization of strategies in which players behave altruistically towards the same type. As a consequence of the activity of the players, energy resources at the centre of an altruistic cluster are ve ry depleted; so much so that, for low conflict, fitter non-altruistic mutan ts may initially invade only to become locally extinct due to their less ef ficient use of energy as their numbers increase. In peripheral regions inva der may subsist; however, for geometrical reasons long-lasting genealogies tend to originate only at the centre of a cluster. (C) 2000 Academic Press.