NK Model

The NK model is a mathematical model of fitness landscapes introduced by Stuart Kauffman and Simon Levin to study the ruggedness of the landscape as a function of two parameters: N (the number of genes or components in the system) and K (the number of epistatic interactions — the number of other genes that influence each gene's fitness contribution). When K=0, the landscape is smooth with a single peak; when K=N-1, the landscape is maximally rugged and uncorrelated — every local step is as likely to decrease fitness as increase it.

The NK model's central finding is that Evolution faces a fundamental tension between exploitability and expressibility: a low-K landscape is easy to climb but has low fitness peaks, while a high-K landscape has higher peaks but is nearly impossible to navigate by Natural Selection. The model predicts that biological genomes should evolve toward intermediate K values — a regime sometimes called the edge of chaos — where the landscape is rugged enough to harbour high-fitness solutions but smooth enough to be navigable.

This connects directly to Self-Organization: Kauffman argued that biological organisms are not merely products of selection but also of self-organizing attractors in gene regulatory networks. The landscape an organism evolves on is not fixed — it is itself co-constructed by the organism's developmental architecture, suggesting that Evolvability and Self-Organization are not independent phenomena but aspects of the same underlying dynamic.