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The Fitness of Fitness Concepts and the Description of Natural Selection

"Fitness" has been used to indicate a measure of general adaptedness, and to indicate a short-term measure of reproductive success. The former concept seems unproductive in evoutionary biology, but consensus on the exact form of the latter might be possible. Fitness as a short-term measure of reproductive success can be defined from the demographic recurrence equations for genotypic number; it refers to a genotype or to a genotypic combination, if genotypes interact. Fitness summarizes a model for genotypic demography for a given set of assumptions about the population and the genotypic and individual interactions within it. For a population growing at a constant rate, demographic genotypic fitness has the same shape as reproductive value at birth; but reproductive value refers to a cohort of a genotype, while demographic genotypic fitness refers to organisms of one genotype at one moment in time. This is a major conceptual difference, although the numerical identity between demographic genotypic fitness and reporductive value for a population growing at a constant rate explains why models of life history evolution based upon reproductive value are successful. The Secondary Theorem of Natural Selection (Robertson, 1968) Predicts the selection response in mean trait value by the genetic covairance between trait and fitness. Selection on a quantitative trait is often formulated as involving the heritability and the phenotypic covariance between trait and fitness or the phenotypic selection grandien β, the (partial) regression of fitness on the trait. The change in the covariance between the genotypic and the phenotypic level introduces an assumption on the additivity of fitness. The selection gradient, as a regression, focuses on differences in fitness as derived from differences in the trait. In the Secondary Theorem, trait and fitness play equivalent roles. The Secondary Theorem implies a different understanding of the process of selection from a phenotypic selection gradient and a heritability, on those two counts. Fitness might arise from the phenotype in interaction with the environment, but phenotype and fitness might both arise as consequences of development. The study of selection thus becomes the study of the biological mechanisms underlying and generating the genetic covariance between phenotype and fitness.