Measurement of Natural Selection in Natural Populations

Abstract

VAN VALEN¹ has proposed a measure of natural selection intensity as an extension of Haldane's² measure of intensity I and applied this to data on fossil horses. Van Valen's measure, at least in the example given, is actually a special case of Haldane's I. Van Valen wrote: “The intensity I_p of natural (or artificial) selection by means of differential viability, relative to statistical parameter or set of parameters p, may be defined as the minimum reduction of the original population that would yield a population with specified values of the parameter or set of parameters”. For a single normally distributed character this corresponds to the truncation area of a normal curve necessary to shift the mean and standard deviation to the new observed values under directional selection. Haldane's measure of intensity is defined as: where s₀ is the survival percentage at the optimum phenotype or genotype and S is the overall survival percentage. Haldane has shown that (1) can be written: where ƒ₁(x₀) and ƒ₂(x₀) are the probability densities of the characters at the optimum value x₀ before and after selection, respectively. Furthermore, if ƒ₁(x) and ƒ₂(x) are normal densities (the notation of Rao³ is used throughout)