Bak, Per, Henrik Flyvbjerg, and Benny Lautrup. “Coevolution in a rugged fitness landscape.” Physical Review A 46, no. 10 (1992): 6724.
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A variant of Kauffman’s NKC -model for the coevolution of haploid organisms is shown to have two phases: a frozen phase in which all species eventually reach local fitness maxima and stop evolving, and a chaotic phase in which a fraction of all species is at local maxima, while another fraction evolves towards maxima. In doing so, they set other species back in evolution, thereby maintaining a steady fraction of evolving species. The evolutionary activity of the steady state is a natural order parameter for the ecosystem. Closed expressions are given for this order parameter and for the system’s relaxation time. The latter quantity diverges at the phase boundary, showing the system is critical there. All results were obtained analytically for the maximally rugged case of K +1=N , and to leading order in N , the number of genes in a species.