  A longstanding goal of biology is to identify the key genes and species that
critically impact evolution, ecology, and health. Network analysis has revealed
keystone species that regulate ecosystems and master regulators that regulate
cellular genetic networks. Yet these studies have focused on pairwise
biological interactions, which can be affected by the context of genetic
background and other species present generating higher-order interactions. The
important regulators of higher-order interactions are unstudied. To address
this, we applied a new high-dimensional geometry approach that quantifies
epistasis in a fitness landscape to ask how individual genes and species
influence the interactions in the rest of the biological network. We then
generated and also reanalyzed 5-dimensional datasets (two genetic, two
microbiome). We identified key genes (e.g. the rbs locus and pykF) and species
(e.g. Lactobacilli) that control the interactions of many other genes and
species. These higher-order master regulators can induce or suppress
evolutionary and ecological diversification by controlling the topography of
the fitness landscape. Thus, we provide mathematical intuition and
justification for exploration of biological networks in higher dimensions.
