Evolutionary fitness in ecology: Comparing measures of fitness in stochastic, density-dependent environments

Several different measures of ‘fitness’ are commonly used in evolutionary studies. Each measure makes different assumptions, so is appropriate only in some circumstances. Many recent studies have recommended using invasibility arguments to identify the evolutionarily unbeatable strategy (EUS), rather than choosing a measure of fitness to maximize, thereby avoiding the potential pitfalls in choosing. Here we use the ‘invasion exponent’ to determine the EUS of reproductive allocation in environments that vary in density dependence and environmental stochasticity. We then compare the EUS effort with that predicted by a range of other measures of fitness: r (the deterministic per capita rate of increase), a (the stochastic per capita rate of increase), R0 (lifetime reproductive success) and population size (arithmetic and geometric means). When the population is at an equilibrium in a constant environment, different measures of fitness predict the same optima. However, when population size is not constant (either due to environmental variation or non-equilibrium dynamics), no single fitness measure universally predicts the EUS. In most circumstances, measures of population size perform best followed by measures of reproductive performance. Measures of population growth perform least well.