Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

TL;DR

This study investigates how different gene interaction schemes in NK fitness landscapes affect the landscape's shape, local maxima distribution, and adaptive walk dynamics, revealing correlations with the interaction pattern's rank.

Contribution

It introduces a detailed analysis of how interaction schemes influence NK landscape topology and adaptive walk properties, emphasizing the role of Walsh function coefficients.

Findings

Local maxima distribution varies with interaction scheme

Adaptive walk length and height depend on landscape structure

Most measures correlate with the scheme's Walsh coefficient rank

Abstract

Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined. The focus is on how this scheme influences the overall shape of the landscape. Our main tool for the analysis are adaptive walks, an idealized dynamics by which the population moves uphill in fitness and terminates at a local fitness maximum. We use three different types of walks and investigate how their length (the number of steps required to reach a local peak) and height (the fitness at the endpoint of the walk) depend on the dimensionality and structure of the landscape. We find that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern. Most quantities that we measure are simply correlated to the rank of the scheme, which is equal to the number of nonzero coefficients in the expansion of the fitness landscape in terms of Walsh functions.