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

TL;DR

This study explores the ruggedness and statistical properties of fitness landscapes in Kauffman's Boolean model with scale-free networks, revealing phase transitions and differences from random networks.

Contribution

It provides the first detailed analysis of fitness landscapes in Kauffman's model with scale-free networks, highlighting non-Gaussian distributions and phase transitions at critical connectivity.

Findings

Fitness landscape statistics are Gaussian in random networks but non-Gaussian with tails in scale-free networks.

A phase transition occurs at average degree <k> = 2, separating ordered and disordered regimes.

The correlation between local optima fitness and Hamming distance varies with network type.

Abstract

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.