Exact Results for Amplitude Spectra of Fitness Landscapes

TL;DR

This paper derives exact analytical expressions for the amplitude spectra of various fitness landscape models, aiding interpretation of empirical data and development of better models.

Contribution

It provides the first exact formulas for the amplitude spectra of common fitness landscape models, including NK and Mount Fuji landscapes.

Findings

Correlations decaying exponentially lead to exponentially decaying spectra.

Analytical spectra match well with experimentally measured landscapes.

Results facilitate interpretation of empirical fitness landscape data.

Abstract

Starting from fitness correlation functions, we calculate exact expressions for the amplitude spectra of fitness landscapes as defined by P.F. Stadler [J. Math. Chem. 20, 1 (1996)] for common landscape models, including Kauffman's NK-model, rough Mount Fuji landscapes and general linear superpositions of such landscapes. We further show that correlations decaying exponentially with the Hamming distance yield exponentially decaying spectra similar to those reported recently for a model of molecular signal transduction. Finally, we compare our results for the model systems to the spectra of various experimentally measured fitness landscapes. We claim that our analytical results should be helpful when trying to interpret empirical data and guide the search for improved fitness landscape models.