Evolutionary Game Theory and the Adaptive Dynamics Approach: Adaptation where Individuals Interact

Evolutionary game theory and the adaptive dynamics approach have made invaluable contributions to understand how gradual evolution leads to adaptation when individuals interact. Here, we review some of the basic tools that have come out of these contributions to model the evolution of quantitative traits in complex populations. We collect together mathematical expressions that describe directional and disruptive selection in class- and group-structured populations in terms of individual fitness, with the aims of bridging different models and interpreting selection. In particular, our review of disruptive selection suggests there are two main paths that can lead to diversity: (i) when individual fitness increases more than linearly with trait expression; (ii) when trait expression simultaneously increases the probability that an individual is in a certain context (e.g. a given age, sex, habitat, size or social environment) and fitness in that context. We provide various examples of these and more broadly argue that population structure lays the ground for the emergence of polymorphism with unique characteristics. Beyond this, we hope that the descriptions of selection we present here help see the tight links among fundamental branches of evolutionary biology, from life-history to social evolution through evolutionary ecology, and thus favour further their integration

A multitype Hawk and Dove game

International audienceWe consider in this paper the Hawk-Dove game in which each of infinitely many individuals, involved with pairwise encounters with other individuals, can decide whether to act aggressively (Hawk) or peacefully (Dove). Each individual is characterized by its strength. The strength distribution among the population is assumed to be fixed and not to vary in time. If both individuals involved in an interaction are Hawks, there will be a fight, the result of which will be determined by the strength of each of the individuals involved. The larger the difference between the strength of the individuals is, the larger is the cost for the weaker player involved in the fight. Our goal is to study the influence of the parameters (such as the strength level distribution) on the equilibrium of the game. We show that for some parameters there exists a threshold equilibrium policy while for other parameters there is no equilibrium policy at all