Translating between evolutionary game theory and theoretical ecology

Both theoretical ecology and evolutionary game theory describe the dynamics of interacting populations. More than 40 years ago, Hofbauer and Sigmund established a mathematical equivalence between the Lotka-Volterra equations and the replicator dynamics from evolutionary game theory. However, this equivalence has not been exploited by empiricists so far. One of the issues is dimensionality: An ecological interaction of two species corresponds to an evolutionary game between three types. Only when we focus on a special case with identical growth rates, it is possible to translate without this trick, leading to a more direct equivalence between the frameworks. Consequently, one has to be particularly careful how to classify interactions and how to assess dynamical outcomes. For example, a ‘Prisoner's Dilemma’ interaction where the `cooperators' have a higher intrinsic growth rate than `defectors' can result in stable coexistence of the two types and may ultimately not represent a social dilemma at all.