Exact results for amplitude spectra of fitness landscapes

Author-Highlights
• Amplitude spectra quantify the epistatic interactions between genetic loci.
• We compute spectra analytically from the corresponding fitness correlations.
• For several commonly used models, the spectra have a surprisingly simple form.
• We fit the analytic formulae to different data sets and extract epistasis parameters.
• We show that Fourier decomposition is useful for analyzing empirical fitness data.

Starting from fitness correlation functions, we calculate exact expressions for the amplitude spectra of fitness landscapes as defined by Stadler [1996. Landscapes and their correlation functions. J. Math. Chem. 20, 1] 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.