Alternative definitions of epistasis: dependence and interaction

Although epistasis is at the center of the Fisher-Wright debate, biologists not involved in the controversy are often unaware that there are actually two different formal definitions of epistasis. We compare concepts of genetic independence in the two theoretical traditions of evolutionary genetics, population genetics and quantitative genetics, and show how independence of gene action (represented by the multiplicative model of population genetics) can be different from the absence of gene interaction (represented by the linear additive model of quantitative genetics). The two formulations converge with weak selection but not with strong selection or, for multiple loci, when the aggregated interaction terms are not negligible. As a result of the different formulations of gene interaction,the presence or absence of linkage disequilibrium, D, does not necessarily indicate the presence or absence of fitness epistasis. Indeed, linkage disequilibrium is generated in 'additive' models in quantitative genetics whenever two (or more) loci experience simultaneous selection. As a research strategy, it is often practical, for theoretical or experimental reasons,to minimize gene interaction by assuming independence of gene action in regard to fitness, or by assuming linear additive effects of multiple loci on a phenotype. However, minimizing the role of epistasis in theoretical investigations hinders our understanding of the origins of diversity and the evolution of complex phenotypes.