Journal of Mathematical Biology

, Volume 67, Issue 4, pp 935-962

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games

  • K. ArgasinskiAffiliated withDepartment of Mathematics, University of Sussex Email author 
  • , M. BroomAffiliated withCentre for Mathematical Science, City University London


In the standard approach to evolutionary games and replicator dynamics, differences in fitness can be interpreted as an excess from the mean Malthusian growth rate in the population. In the underlying reasoning, related to an analysis of “costs” and “benefits”, there is a silent assumption that fitness can be described in some type of units. However, in most cases these units of measure are not explicitly specified. Then the question arises: are these theories testable? How can we measure “benefit” or “cost”? A natural language, useful for describing and justifying comparisons of strategic “cost” versus “benefits”, is the terminology of demography, because the basic events that shape the outcome of natural selection are births and deaths. In this paper, we present the consequences of an explicit analysis of births and deaths in an evolutionary game theoretic framework. We will investigate different types of mortality pressures, their combinations and the possibility of trade-offs between mortality and fertility. We will show that within this new approach it is possible to model how strictly ecological factors such as density dependence and additive background fitness, which seem neutral in classical theory, can affect the outcomes of the game. We consider the example of the Hawk–Dove game, and show that when reformulated in terms of our new approach new details and new biological predictions are produced.


Replicator dynamics Mortality Fertility Eco-evolutionary feedback Trade-off Density dependence

Mathematics Subject Classification