Estimating some features of \(NK\) fitness landscapes.
type: Item
instance of: scholarly article
title: Estimating some features of \(NK\) fitness landscapes.
zbMATH Open document ID: 1040.60043
author: Steven Neil Evans
author: David Steinsaltz
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: The authors reduce some asymptotic features of \(NK\) fitness landscapes to questions about eigenvalues and Lyapunov exponents. When \(K\) is fixed, the expected number of local maxima grows exponentially with \(N\) at a rate depending on the top eigenvalue of a kernel derived from the distribution of the fitness, and the average height of a local maximum converges to a value determined by the corresponding eigenfunction. The global maximum converges in probability as \(N\rightarrow\infty\) to a constant given by the top Lyapunov exponent for a system of i.i.d. max-plus random matrices, and this constant is nondecreasing with \(K\). Various such quantities are computed for certain special cases when \(K\) is small, and these calculations can, in principle, be extended to larger \(K\).
reviewed by: Andreas Martin
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 92D15
zbMATH DE Number: 1906151
zbMATH Keywords: genetics
zbMATH Keywords: evolution
zbMATH Keywords: eigenvalue
zbMATH Keywords: Perron-Frobenius
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: max-plus algebra
zbMATH Keywords: random field
zbMATH Keywords: spin glass
zbMATH Keywords: extreme value
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1037125864
OpenAlex ID: W2004146996
cites work: Ergodic theory of stochastic Petri networks
cites work: Rigorous results for the NK model.
cites work: Q4866647
cites work: Q4321474
cites work: Q3687398
DOI: 10.1214/AOAP/1037125864
description: scientific article; zbMATH DE number 1906151