Biological fitness arises from interactions between molecules, genes, and
organisms. To discover the causative mechanisms of this complexity, we must
differentiate the significant interactions from a large number of
possibilities. Epistasis is the standard way to identify interactions in
fitness landscapes. However, this intuitive approach breaks down in higher
dimensions for example because the sign of epistasis takes on an arbitrary
meaning, and the false discovery rate becomes high. These limitations make it
difficult to evaluate the role of epistasis in higher dimensions. Here we
develop epistatic filtrations, a dimensionally-normalized approach to define
fitness landscape topography for higher dimensional spaces. We apply the method
to higher-dimensional datasets from genetics and the gut microbiome. This
reveals a sparse higher-order structure that often arises from lower-order.
Despite sparsity, these higher-order effects carry significant effects on
biological fitness and are consequential for ecology and evolution.Comment: 71 pages, various figure