An averaging model for analysis and interpretation of high-order genetic interactions

While combinatorial genetic data collection from biological systems in which quantitative phenotypes are controlled by functional and non-functional alleles of multiple genes (multi-gene systems) is becoming common, a standard analysis method for such data has not been established. A common additive model of the non-functional allele effects contrasted against the functional alleles, based on ANOVA with interaction, has three issues. First, although it is a long tradition in genetics, modeling the effect of the non-functional allele (a null mutant allele) contrasted against that of the functional allele (the wild-type allele) is not suitable for mechanistic understanding of multi-gene systems. Second, an additive model fails in estimation of interactions among more than two genes when the phenotypic response is not linear. Third, interpretation of higher-order interactions defined by an additive model is not intuitive. I propose an averaging model, which is suitable for mechanistic understanding of multi-gene systems: the effect of the functional allele is contrasted against the effect of the non-functional allele for easier mechanistic interpretations; it is stable in estimation of higher-order interactions even when the phenotypic response is not linear; and the higher-order interactions it defines are highly intuitive. Yet, the averaging model is still a general linear model, so model fitting is easy and accurate using common statistical tools.