Fitness is often defined as the average payoff an animal obtains when it is engaged in several activities, each taking some time. We point out that the average can be calculated with respect to either the time distribution, or to the event distribution of these activities. We show that these two averages lead to the same fitness function. We illustrate this result through two examples from foraging theory, Holling II functional response and the diet choice model, and one game-theoretic example of Hamilton's rule applied to the time-constrained Prisoner's dilemma (PD). In particular, we show that in these models, fitness defined as expected gain per unit time equals fitness defined as expected gain divided by expected time. We also show how these fitnesses predict the optimal outcome for diet choice and the prevalence of cooperation in the repeated PD game.

Department of Mathematics City University of London London UK

Department of Mathematics Faculty of Science University of South Bohemia Branišovská 1760 České Budějovice 370 05 Czech Republic; Czech Academy of Sciences Biology Centre Institute of Entomology Branišovská 31 České Budějovice 370 05 Czech Republic

Department of Mathematics Wilfrid Laurier University Waterloo Ontario Canada

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