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 active and inactive alleles of multiple genes (multi-gene systems) is becoming common, a standard analysis method for such data has not been established. The currently common approaches have three major drawbacks. First, although it is a long tradition in genetics, modeling the effect of an inactive allele (a null mutant allele) contrasted against that of the active allele (the wild-type allele) is not suitable for mechanistic understanding of multi-gene systems. Second, a commonly-used additive model (ANOVA with interaction) mathematically 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 derived an averaging model based on algebraic principles to solve all these problems within the framework of a general linear model. In the averaging model: the effect of the active allele is contrasted against the effect of the inactive allele for easier mechanistic interpretations; there is mathematical stability in estimation of higher-order interactions even when the phenotypic response is not linear; and interpretations of higher-order interactions are intuitive and consistent-interactions are defined as the mean effects of the last active genes added to the system. Thus, the key outcomes of this study are development of the averaging model, which is suitable for analysis of multi-gene systems, and a new, intuitive, and mathematically and interpretationally consistent definition of a genetic interaction, which is central to the averaging model.