Fisher's Fundamental Theorem of Natural Selection Revisited

Abstract

W. J. Ewens, following G. R. Price, has stressed that Fisher's fundamental theorem of natural selection about the increase in mean fitness is of general validity without any restrictive assumptions on the mating system, the fitness parameters, or the numbers of loci and alleles involved, but that it concerns only a partial change in mean fitness. This partial change is obtained by replacing the actual genotypic fitnesses by the corresponding additive genetic values and by keeping these values fixed in the change of the mean with respect to changes in genotype frequencies. We propose an alternate interpretation for this partial change which uses partial changes in genotype frequencies directly consequent on changes in gene frequencies, the fitness parameters being kept constant. We argue that this interpretation agrees more closely with Fisher's own explanations. Moreover, this approach leads to a decomposition for the total change in mean fitness which explains, unifies, and extends previous decompositions. We consider a wide range of models, from discrete-time selection models with nonoverlapping generations to continuous-time models with overlapping generations and age effects on viability and fecundity, which is the original framework for Fisher's fundamental theorem.] 1997 Academic Press

A First Formal Link between the Price Equation and an Optimization Program

“…Ewens (1989) expanded Price's argument, and the subject is reviewed by Edwards (1994). Lessard (1997) claims a more authentic interpretation of Fisher's argument, while Frank (1997 presents his own exposition and development of the fundamental theorem.…”

“…This extended sense of ''environmental change'', including changes in genotype frequencies, as the effect of an allele on phenotype can be altered by its genic environment. Lessard (1997) proposes a revision of the exact nature of this distinction.…”

“…Ewens (1992), Frank (1997Frank ( , 1998 and Lessard (1997) have extended Fisher's result to incorporate all of gene frequency change. The approach in the current paper focusses solely on the partial fitness with which Fisher's original version dealt.…”

Individual histories and selection in heterogeneous populations

“…In experimental evolution, where one hopes to directly observe selection in action, selection measurements have been based on changes in bulk population growth rate and on the variance of reproductive rates (1). The insight of Fisher (6) was to partition the change in the population growth rate into two terms, the first due to changes in allele frequencies, and the second due to changes in environmental conditions (7)(8)(9)(10). The first term was defined as the measure of selection and was proven to be equal to the population's variance of fitness.…”

Evolution of what? A network approach for the detection of evolutionary forces

“…, refers to natural selection ( ), in line with Fisher's fundamental theorem of natural selection (Fisher, 1930;Lessard, 1997;Edwards, 2002). The theorem states that the change in average fitness caused by natural selection is proportional to the variance in fitness.…”