An estimator of the Opportunity for Selection that is independent of mean fitness

Abstract

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crows Opportunity for Selection (I), which is the variance in relative fitness [Formula]. Crows I has been widely used but remains controversial because it depends on mean offspring number in a sample [Formula]. Here I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crows I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance [Formula] to its expected value at a fixed [Formula] removes dependence of I on mean offspring number, but the result still depends on choice of [Formula]. A new index is introduced, [Formula], which makes I independent of sample [Formula] without the need for variance rescaling. {Delta}I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. {Delta}I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.