The Epistasis Boundary: Linear vs. Nonlinear Genotype-Phenotype Relationships

Abstract

Nonlinearity in the genotype-phenotype relationship can take the form of dominance, epistasis, or gene-environment interaction. The importance of nonlinearity, especially epistasis, in real complex traits is controversial. Network models in systems biology are typically highly nonlinear, yet the predictive power of linear quantitative genetic models is rarely improved by addition of nonlinear terms, and association studies detect few strong gene-gene interactions. We find that complex traits satisfying certain conditions can be well represented by a linear genetic model on an appropriate scale despite underlying biological complexity. Recent mathematical results in separability theory determine these conditions, which correspond to three biological criteria (Directional Consistency, Environmental Compensability, and Pathway Redundancy) together making up an Epistatic Boundary between systems suitable and unsuitable for linear modeling. For nonlinear traits, we introduce a classification of types of nonlinearity from a systems perspective, and use this to illustrate how upstream controlling genes, potentially more important to explaining biological function, can be intrinsically harder to detect by GWAS than their downstream controlled counterparts.