GENETIC MEASUREMENT THEORY OF EPISTATIC EFFECTS

Epistasis is defined as the influence of the genotype at one locus on the effect of a mutation at another locus. As such it plays a crucial role in a variety of evolutionary phenomena such as speciation, popula tion bottle necks, and the evolution of genetic architecture (i.e., th e evolution of dominance, canalization, and genetic correlations). In mathematical population genetics, however, epistasis is often represen ted as a mere noise term in an additive model of gene effects. In this paper it is argued that epistasis needs to be scaled in a way that is more directly related to the mechanisms of evolutionary change. A rev iew of general measurement theory shows that the scaling of a quantita tive concept has to reflect the empirical relationships among the obje cts. To apply these ideas to epistatic mutation effects, it is propose d to scale A x A epistatic effects as the change in the magnitude of t he additive effect of a mutation at one locus due to a mutation at a s econd locus. It is shown that the absolute change in the additive effe ct at locus A due to a substitution at locus B is always identical to the absolute change in B due to the substitution at A. The absolute A x A epistatic effects of A on B and of B on A are identical, even if t he relative effects can be different. The proposed scaling of A x A ep istasis leads to particularly simple equations for the decomposition o f genotypic variance. The Kacser Burns model of metabolic flux is anal yzed for the presence of epistatic effects on flux. It is shown that t he non-linearity of the Kacser Burns model is not sufficient to cause A x A epistasis among the genes coding for enzymes. It is concluded th at non-linearity of the genotype-phenotype map is not sufficient to ca use epistasis. Finally, it is shown that there exist correlations amon g the additive and epistatic effects among pairs of loci, caused by th e inherent symmetries of Mendelian genetic systems. For instance, it i s shown that a mutation that has a larger than average additive effect will tend to decrease the additive effect of a second mutation, i.e., it will tend to have a negative (canalizing) interaction with a subse quent gene substitution. This is confirmed in a preliminary analysis o f QTL-data for adult body weight in mice.