Inferring modularity in genotype-phenotype maps using patterns of epistasis and pleiotropy

Methods for inferring the relationship between genotype and phenotype often search for low-dimensional structure, motivated by the hypothesis that genetic loci can be organized into a small number of groups representing biological processes. These methods typically group genetic loci based on which other loci they interact with (epistasis) or based on how their effects covary across environmental conditions (patterns of pleiotropy). Here, we present two complementary methods that combine epistasis and pleiotropy to infer modular structure. The first, Sparse, Low-dimensional, Epistatic Decomposition (SLED), parametrizes the genotype-phenotype map in terms of a small number of modules: loci contribute sparse additive and epistatic effects to modules, and modules contribute sparse additive and epistatic effects to multiple phenotypes. The second method, Graph Tensor Decomposition (GTD), represents the epistatic interactions in each environment as a combination of shared basis graphs, each capturing a pattern of epistasis that recurs across environments. Since GTD does not use additive effects, learned graphs are not restricted to include only loci whose additive effects covary across environments. We validate SLED and GTD on synthetic data, then apply both methods to an experimental dataset consisting of the growth rates of yeast segregants from an F1 cross, measured across 101 environments with a hub-and-spoke structure. We evaluate the biological structure of the inferred modules and show that both models generalize well to held-out environments. Finally, we compare the modules inferred by SLED, GTD, and a previously established method that infers sparse modular structure from a locus-by-environment matrix of additive effects (SSD) and find that all three methods yield highly similar modular architectures. This suggests that the genetic architecture underlying this dataset is consistent across additive effects (SSD), epistatic effects (GTD), and both jointly (SLED). Together, our methods provide a framework for combining two sources of information, epistasis and pleiotropy, to infer interpretable low-dimensional structure in genotype-phenotype maps, expanding on previous work that has traditionally treated each independently.