Epistasis and Shapes of Fitness Landscapes

Abstract

The relationship between the shape of a fitness landscape and the underlying gene interactions, or epistasis, has been extensively studied in the two-locus case. Gene interactions among multiple loci are usually reduced to two-way interactions. We present a geometric theory of shapes of fitness landscapes for multiple loci. A central concept is the genotope, which is the convex hull of all possible allele frequencies in populations. Triangulations of the genotope correspond to different shapes of fitness landscapes and reveal all the gene interactions. The theory is applied to fitness data from HIV and Drosophila melanogaster. In both cases, our findings refine earlier analyses and reveal previously undetected gene interactions.

arXiv comment31 pages, 7 figures; typos removed, Example 3.10 added

References in corpus (3)

• Lectures on 0/1-polytopes
• The Hyperdeterminant and Triangulations of the 4-Cube
• Evolution on distributive lattices

Cited by in corpus (4)

• The Changing Geometry of a Fitness Landscape Along an Adaptive Walk
• Geometry of fitness landscapes: Peaks, shapes and universal positive epistasis
• Getting higher on rugged landscapes: Inversion mutations open access to fitter adaptive peaks in NK fitness landscapes
• Sign Epistasis and the Geometry of Interactions