On the evolution of epistasis II: a generalized Wright-Kimura framework.

The evolution of fitness interactions between genes at two major loci is studied where the alleles at a third locus modify the epistatic interaction between the two major loci. The epistasis is defined by a parameter epsilon and a matrix structure that specifies the nature of the interactions. When epsilon=0 the two major loci have additive fitnesses, and when these are symmetric the interaction matrices studied here produce symmetric viabilities of the Wright [1952.

A semi-symmetric two-locus model.

The two-locus symmetric viability model characterized by its invariance with respect to the exchange of alleles at each locus, is a well-studied model of classical two-locus theory. The symmetric model introduced by Lewontin and Kojima is among the few multi-locus models with epistatic interactions between loci for which a polymorphism with linkage equilibrium can be stable and this happens when recombination is sufficiently large. We show that an analogous property holds true for a different model, in which symmetry need exist at only one locus.

On the meaning of non-epistatic selection.

In population genetics, the additive and multiplicative viability models are often used for the quantitative description of models in which the genetic contributions of several different loci are independent; that is, there is no epistasis. Non-epistasis may also be quantitatively defined in terms of measures of interaction used widely in statistics. Setting these measures of epistasis to zero yields alternative definitions of non-epistasis.

Search in power-law networks.

Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph.