On the meaning of non-epistatic selection

In population genetics, the additive and multiplicative viability models are often used for the quantitative description of models in which the genetic contributions of several different loci are independent; that is, there is no epistasis. Non-epistasis may also be quantitatively defined in terms of measures of interaction used widely in statistics. Setting these measures of epistasis to zero yields alternative definitions of non-epistasis. We show here that these two definitions of non-epistasis are equivalent; that is, in the most general case of a multilocus, multiallele system, the additive and multiplicative viability models are unique solutions of the additive and multiplicative conditions, respectively, for non-epistasis.