Evolution in Heterogeneous Environments

Abstract

A decision-theoretic approach is used to broaden the fitness set theory of evolution in heterogeneous environments. In previous formulations of fitness set theory, the optimum population always maximized some sort of average fitness across the environmental array with each environment being weighted solely by its actual frequency. An alternative definition of optimum is given in which minimum fitness is maximized instead of average fitness. This Maximin population is also buffered against perturbations in the environmental array (fitness homeostasis) and tends to have equal fitness in most environments (large niche breadth), particularly when the worst conditions the population faces are due to environmental uncertainty. A more generalized definition of optimum takes a mixture of these two above-mentioned populations. In such a mixture optimum, environments are weighted both by their actual frequencies and by their fitness effects. An even weaker definition of optimum is then used to create a set of admissible populations. Theorems are given which show polymorphic populations are not favored on convex fitness sets, but polymorphic optimum populations are possible on concave fitness sets in a fine-grained environment. Furthermore, a generalized adaptive function is found which identifies all possible admissible populations. This adaptive function is generalized further by incorporating a continuous grain parameter which allows not only fine- and coarse-grained environments, but also environments with grain intermediate between fine and coarse and environments with grain coarser than coarse. Many of these results are also extended to the case in which environmental heterogeneity is continuous and not discrete.