An optimization problem is often represented with a set of variables, and the interaction between the variables is referred to as epistasis. In this paper, we propose two new measures of epistasis: internal epistasis and external epistasis. Then we show that they can quantify the decomposability of a problem, which has a theoretical meaning about how strongly the problem is independently optimi...

The mutation rate of a well adapted population is prone to reduction so as to have a lower mutational load. We aim to understand the role of epistatic interactions between the fitness affecting mutations in this process. Using a multitype branching process, the fixation probability of a single non-mutator emerging in a large asexual mutator population is analytically calculated here. The mutato...

Alzheimer's disease affects millions of people worldwide and incidence is expected to rise as the population ages, but no effective therapies exist despite decades of research and more than 20 known disease markers. Research has shown that Alzheimer's disease's missing heritability remains extensive with an estimated 25% of phenotypic variance unexplained by known variants. The missing heritabi...

The existence of epistasis in humans was first predicted by Bateson in 1909. Epistasis describes the non-linear, synergistic interaction of two or more genetic loci, which can substantially modify disease severity or result in entirely new phenotypes. The concept has remained controversial in human genetics because of the lack of well-characterized examples. In humans, it is only possible to de...

Consequences of directional selection on metabolic flux are explored in models for which variation in flux among individuals is generated by segregation of allelic variants at enzyme activity loci. The pattern of selection response is strongly affected by the presence of genetic dominance and epistasis, which are automatically generated in metabolic systems. The expected magnitudes of dominance...

In a comment [1] on our manuscript “Strong Selection Significantly Increases Epistatic Interactions in the Long-Term Evolution of a Protein” [2], Dr. Crona challenges our assertion that shared entropy (that is, information) between two residues implies epistasis between those residues by constructing an explicit example of three loci (say A, B, and C), in which A and B are epistatically linked ...