Rugged Fitness Landscapes of Kauffman Model with a Scale-Free Network

Kazumoto Iguchi, Shuichi Kinoshita, Hiroaki Yamada

Published 2005-07-03, updated 2005-11-24Version 4

We study the nature of fitness landscapes of 'quenched' Kauffman's Boolean model with a scale-free network. We have numerically calculated the rugged fitness landscapes, the distributions, its tails, and the correlation between the fitness of local optima and their Hamming distance from the highest optimum found, respectively. We have found that (a) there is an interesting difference between the random and the scale-free networks such that the statistics of the rugged fitness landscapes is Gaussian for the random network while it is non-Gaussian with a tail for the scale-free network; (b) as the average degree $<k>$ increases, there is a phase transition at the critical value of $<k > = < k >_{c} = 2$, below which there is a global order and above which the order goes away.