Evolutionary Dynamics

Abstract

Evolutionary dynamics in finite populations reflects a balance between Darwinian selection and random drift. For a long time population structures were assumed to leave this balance unaffected provided that the mutants and residents have fixed fitness values. This result indeed holds for a certain (large) class of population structures or graphs. However, other structures can tilt the balance to the extend that either selection is eliminated and drift rules or drift is eliminated and only selection matters.

In nature, however, fitness is generally affected by interactions with other members of the population. This is of particular importance for the evolution of cooperation. The essence of this evolutionary conundrum is captured by social dilemmas: cooperators provide a benefit to the group at some cost to themselves, whereas defectors attempt to exploit the group by reaping the benefits without bearing the costs of cooperation. The most prominent game theoretical models to study this problem are the prisoner’s dilemma and the snowdrift game. In the prisoner’s dilemma, cooperators are doomed if interactions occur randomly. In structured populations, individuals interact only with their neighbors and cooperators may thrive by aggregating in clusters and thereby reducing exploitation by defectors. In finite populations, a surprisingly simple rule determines whether evolution favors cooperation: b > c k that is, if the benefits b exceed k-times the costs c of cooperation, where k is the (average) number of neighbors. The spatial prisoner’s dilemma has lead to the general belief that spatial structure is beneficial for cooperation. Interestingly, however, this no longer holds when relaxing the social dilemma and considering the snowdrift game. Due to the less stringent conditions, cooperators persist in populations with random interactions but spatial structure tends to be deleterious and may even eliminate cooperation altogether.

In many biological situations it seems more appropriate to assume a continuous range of cooperative investment levels instead of restricting the analysis to two a priori fixed strategic types. In the continuous prisoner’s dilemma cooperative investments gradually decrease and defection dominates just as in the traditional prisoner’s dilemma. In contrast, the continuous snowdrift game exhibits rich dynamics but most importantly provides an intriguing natural explanation for phenotypic diversification and the evolutionary origin of cooperators and defectors. Thus, selection may not always favor equal contributions but rather promote states where two distinct types co-exist — those that fully cooperate and those that exploit. In the context of human societies and cultural evolution this could be termed the Tragedy of the Commune because differences in contributions to a communal enterprise have significant potential for escalating conflicts on the basis of accepted notions of fairness.