In density dependent populations, the fitness of one strategy depends upon what the rest of the population is doing. In consequence, studies of evolution in density dependent populations must use invasibility methods (typically finding evolutionary stable strategies). For populations at equilibrium, the ability of a variant type to invade a population is given by the dominant eigenvalue of the density dependent projection matrix describing the variant type evaluated at the equilibrium point of the resident population. In a stable population, offspring born at any age are of equal value, so lifetime reproductive success can be used to compare the fitness of different strategies. But when the resident population is subject to stochastic environmental variation and/or non-equilibrium population fluctuations, this simplification no longer holds and a full invasibility analysis must be carried out.
In this paper, we assess whether, for a range of fluctuating density dependent population, any of the standard measures of fitness give the same answer as the fully correct invasibility analysis. The somewhat depressing conclusion is that they do not. This has serious implications for the use of lifetime reproductive success as a fitness criterion in behavioural ecology. It will be an adequate indicator of fitness for populations that do not fluctuate in size and are neither growing nor shrinking over time. But the adequacy of lifetime reproductive success needs to be explicitly assessed using invasibility methods when populations fluctuate over time.
Work is in progress seeking to generate some guidelines on the circumstances in which lifetime reproductive success does provide a reasonable approximation to an invasibility analysis.
Centre for Ecology, Evolution and
School of Environmental Sciences
University of East Anglia
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