Predicting genetic interactions between beneficial mutations from Fisher's geometric model

Biological evolution is modeled as a hill-climbing process fueled by genetic mutations in the fitness landscape. The complexity of this process is highly dependent on genetic interactions among different loci by shaping various valleys and peaks in the fitness landscape. The topology of fitness landscapes formed by genetic interaction is generally complicated as there can be a large number of different phenotypic traits of an organism that contribute to its fitness. \textit{Fisher's geometric model} (FGM) is a simple mathematical model that provides a geometric interpretation of the interplay between genotypic and phenotypic layers, on top of which the fitness landscape is constructed. In the framework of FGM, we discuss the statistical properties of the fitness effects when multiple mutations are combined. Experimental data for the filamentous fungus \textit{Aspergillus nidulans} are analyzed with these results to extract the biological information such as the complexities and well-adaptiveness of the organism. Finally, we discuss the geometrical interpretation of the diminishing returns pattern observed in the data in the language of FGM.\\ Reference: Proceedings of the Royal Society B 283:20161376 (2016)