Walsh coefficients and circuits for several alleles

Abstract

Walsh coefficients have been applied extensively to biallelic systems for quantifying pairwise and higher order epistasis, in particular for demonstrating the empirical importance of higher order interactions. Circuits, or minimal dependence relations, and related approaches that use triangulations of polytopes have also been applied to biallelic systems. Here we provide biological interpretations of Walsh coefficients for several alleles, and discuss circuits in the same general setting.