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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 admis...

Mean fitness is not always maximized under natural selection. In particular, in two locus models, recombination and epistasis may combine to prevent the operation of a maximizing principle for mean fitness. If inversion phenomena are considered, however, there exist fully polymorphic equilibria which maximize the mean fitness and moreover the initial progress of an inversion can proceed if and only if it gives rise to an increase in mean fitness. While not applicable to all models, the principle of mean fitness maximization is still useful heuristically.

O'DONALD1 has suggested that if the probability of an animal surviving natural selection is related to some quantitative character X, then a quadratic relationship will often be reasonable and the fitness of an individual with X = x can be assumed to be given by the fitness function. illustration where θ is the optimum value for x. He showed1–3 that if this equation does hold then it is possible to estimate α, θ and K on the basis of changes in the distribution of X as a result of selection and also measure the intensity of selection using the formula suggested by Van Valen4. Open image in new window

MANLY1 has questioned whether the quadratic fitness function can be applied in general to the measurement of selection for quantitative characters. As he points out, if individuals survive with a probability w per day, then after t days the probability of survival is wt. If then the fitness function is quadratic, we have illustrationBut after t′ days, the fitness function would then be illustration which is not quadratic. Manly argues that selection cannot therefore be generally described by a quadratic fitness function. Selection can only be quadratic if t′=t. Manly prefers the “nor-optimal” fitness function2,3 which takes the form of the normal frequency density and which does not change its form when raised to any power. Open image in new window Open image in new window