Protein fitness landscapes are simpler under evolutionary distributions

Abstract

Understanding how mutations combine to shape protein fitness remains a central challenge in biology, driven in part by the prevalence of highorder epistasis. Existing analyses of epistasis, however, implicitly define epistatic interactions under a uniform probability measure over sequence space, even though evolution constrains natural proteins to a highly structured, non-uniform distribution of sequences. Here, we show that the apparent complexity of protein epistasis depends fundamentally on the underlying evolutionary distribution of sequences. We develop an evolution-aware spectral framework that incorporates the evolutionary distribution of amino acids at each sequence position, inducing an orthogonal decomposition under the evolutionary measure while preserving efficient spectral algorithms for scalable analysis. Across diverse protein fitness landscapes, this framework consistently produces more compact spectral representations, explaining more phenotypic variation with fewer epistatic interactions while substantially reducing apparent high-order epistasis. It also enables more accurate recovery of fitness landscapes from limited experimental measurements and concentrates the remaining higher-order interactions into localized, structurally interpretable motifs. These results suggest that a substantial fraction of apparent high-order epistasis arises from defining epistatic interactions under a uniform measure over sequence space and can be resolved by aligning spectral analysis with evolutionary constraints.