Deterministic evolutionary dynamics: A unifying approach

• DOI: 10.1007/bf01193636
• Publication Date: 2005-02-18T10:54:09Z
• Authors: Reinoud Joosten
• Keywords: Evolutionarily stable strategy; Evolutionary Dynamics; Evolutionary game theory; Inclusive fitness; Replicator equation; Fitness landscape

We tackle three components of evolutionary modelling: payoffs, dynamical systems and equilibrium concepts. Firstly, we merely require that fitness functions are continuous. Secondly, we examine very general classes of dynamics. Thirdly, we give useful parallels to the Nash equilibrium and the evolutionarily stable strategy. Under (weakly) sign-compatible dynamics the change in population share of every (at least one) subgroup present in the population corresponds in sign with its relative fitness. At a saturated equilibrium, each subgroup with positive population share has highest fitness. We examine two evolutionary stability concepts: the evolutionarily stable equilibrium and the generalized evolutionarily stable state.