Frank, S. A. and Slatkin, M. 1990. Evolution in a variable environment. American Naturalist 136:244-260.

Over the past four decades several authors have stressed that it is not just good performance, on average, that matters in evolution, but that variation in performance also plays an important role in determining long-term evolutionary trends. Several independent lines of research have arisen from considering different kinds of variation. Dempster (1955) introduced a model in which temporal fluctuations in reproductive success for competing genotypes favor the genotype with the highest geometric mean reproductive success. Levene (1953) studied a case in which the relative success of alleles varies spatially within a generation. These two papers established the dichotomy between temporal and spatial variation that most authors continue to use. Gillespie (1974a) considered still another kind of variation—variation in the reproductive success of each individual, where the amount of variation depends on factors such as developmental homeostasis. Gillespie's (1974a) model has led to extensive discussion of the idea of evolutionary ‘bet hedging’ (Slatkin 1974; Seger and Brockmann 1988).

In still another lineage of models, several authors have considered the problem of how variability in resource acquisition by different individuals affects reproductive success (Caraco 1980; Real 1980; Rubenstein 1982). These models suggest that individuals will tend to avoid behavioral strategies that lead to variation in resource acquisition and have led to discussions of ‘risk aversion’ (e.g., Stephens and Krebs 1986).

In this paper we develop a framework for analyzing these different types of variation. The key to our approach is the partitioning of variance in reproductive success of genotypes into parts attributable to variation in individual reproductive success and to correlations in reproductive success among individuals. We will use our approach to show the simple relationships among the models mentioned above, which have previously been treated in different ways. We generalize these models to include any correlation structure in the reproductive success among individuals of the same and different genotypes. We also apply our method to two examples: a model of developmental homeostasis and a model of competition between semelparity and iteroparity when there is variable resource acquisition. Finally, we discuss some generalizations that emerge from considering these models together, in particular the the geometric mean principle and ideas of bet-hedging and risk aversion.