Uninterpretable interactions: epistasis as uncertainty

Epistasis is a common feature of genotype-phenotype maps. Understanding the patterns of epistasis is critical for predicting unmeasured phenotypes, explaining evolutionary trajectories, and for inferring the biological mechanisms that determine a map. One common approach is to use a linear model to decompose epistasis into specific pairwise and high-order interactions between mutations. Such interactions are then used to identify important biology or to explain how the genotype-phenotype map shapes evolution. Here we show that the coefficients extracted from such analyses are likely uninterpretable. They cannot be extracted reliably from experimental genotype-phenotype maps due to regression bias. Further, we can generate epistatic \"interactions\" indistinguishable from those in experimental maps using a completely random process. From this, we conclude that epistasis should be treated as a random, but quantifiable, variation in these maps. This perspective allows us to build predictive models with known error from a small number of measured phenotypes. It also suggests that we need mechanistic, nonlinear models to account for epistasis and decompose genotype-phenotype maps.