Properties of selected mutations and genotypic landscapes under Fisher's Geometric Model

TL;DR

This study explores the properties of genotypic fitness landscapes under Fisher's geometric model, revealing how landscape ruggedness and epistasis vary with proximity to the fitness optimum and highlighting variability across different adaptive walk realizations.

Contribution

The paper provides analytical predictions and simulation results on the structure of fitness landscapes under FGMA, emphasizing the effects of distance to the optimum and stochastic variability.

Findings

Far from the optimum, landscapes are nearly additive.

Close to the optimum, landscapes exhibit ruggedness and sign epistasis.

Different adaptive walk realizations show high variability in landscape structure.

Abstract

The fitness landscape - the mapping between genotypes and fitness - determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here we generate several testable predictions for the properties of these landscapes under Fisher's geometric model of adaptation (FGMA). When far from the fitness optimum, we analytically compute the fitness effect of beneficial mutations and their epistatic interactions. We show that epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected or co-selected in an adaptive walk. Using simulations, we show that genetic landscapes built from FGMA are very close to an additive landscape when the ancestral strain is far from the optimum. However, when close to the optimum, a large diversity of landscape with substantial ruggedness and sign epistasis emerged. Strikingly, landscapes built from different realizations of stochastic adaptive walks in the same exact conditions were highly variable, suggesting that several realizations of small genetic landscapes are needed to gain information about the underlying architecture of the global adaptive landscape.