Ruggedness and neutrality—the NKp family of fitness landscapes

It has come to be almost an article of faith amongst population biologists and GA researchers alike that the principal feature of a fitness landscape as regards evolutionary dynamics is “ruggedness”, particularly as measured by the auto-correlation function. In this paper we demonstrate that auto-correlation alone may be inadequate as a mediator of evolutionary dynamics, specifically in the presence of large scale neutrality. We introduce the NKp family of landscapes (a variant on NK landscapes) which possess the remarkable property that varying the degree of neutrality has minimal effect on the correlation structure. It is demonstrated that NKp landscapes feature neutral networks which have a "constant innovation" property comparable with the neutral networks observed in models of RNA secondary structure folding landscapes. We show that evolutionary dynamics on NKp landscapes vary dramatically with the degree of neutrality at high neutrality the dynamics are characterised by population drift along neutral networks punctuated by transitions between networks. The relevance of these models to natural and artificial evolution is discussed.