A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Yet biological interactions between genes ( 1, 2 ), species ( 3–6 ), and different environmental contexts ( 7–9 ) change the individual effects due to non-additive interactions, known as epistasis. In the fitness landscape concept, each gene/organism/environment is modeled as a separate biological dimension ( 10 ), yielding a high dimensional landscape, with epistasis adding local peaks and valleys to the landscape. Massive efforts have defined dense epistasis networks on a genome-wide scale ( 2 ), but these have mostly been limited to pairwise, or two-dimensional, interactions ( 11 ). Here we develop a new mathematical formalism that allows us to quantify interactions at high dimensionality in genetics and the microbiome. We then generate and also reanalyze combinatorically complete datasets (two genetic, two microbiome). In higher dimensions, we find that key genes (e.g. pykF ) and species (e.g. Lactobacillus plantarum ) distort the fitness landscape, changing the interactions for many other genes/species. These distortions can fracture a “smooth” landscape with one optimal fitness peak into a landscape with many local optima, regulating evolutionary or ecological diversification ( 12 ), which may explain how a probiotic bacterium can stabilize the gut microbiome.

High dimensional geometry of fitness landscapes identifies master regulators of evolution and the microbiome