NKalpha: Non-uniform epistatic interactions in an extended NK model

Kauffman’s seminal NK model was introduced to relate the properties of fitness landscapes to the extent and nature of epistasis between genes. The original model considered genomes in which the fitness contribution of each of N genes was influenced by the value of K other genes located either at random or from the immediately neighbouring loci on the genome. Both schemes ensure that (on average) every gene is as influential as any other. More recently, the epistatic connectivity between genes in natural genomes has begun to be mapped. The topologies of these genetic networks are neither random nor regular, but exhibit interesting structural properties. The model presented here extends the NK model to consider epistatic network topologies derived from a preferential attachment scheme which tends to ensure that some genes are more influential than others. We explore the consequences of this topology for the properties of the associated fitness landscapes.