Exact results for amplitude spectra of fitness landscapes

Neidhart, Johannes; Szendro, Ivan G.; Krug, Joachim

doi:10.1016/j.jtbi.2013.05.002

Cited by 44 publications

(87 citation statements)

References 51 publications

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“…One demonstrates several intriguing regularities among higher-order interactions in a meta-analysis of 113 combinatorially complete experiments from the engineering literature [46]. The other shares our specific interests in the statistical properties of fitness landscapes [47]. …”

Section: Conclusion: Evolutionary Biologists Should Worry About Highmentioning

confidence: 99%

Should evolutionary geneticists worry about higher-order epistasis?

Weinreich

Lan

Wylie

et al. 2013

Current Opinion in Genetics & Development

279

396

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Natural selection drives evolving populations up the fitness landscape, the projection from nucleotide sequence space to organismal reproductive success. While it has long been appreciated that topographic complexities on fitness landscapes can arise only as a consequence of epistatic interactions between mutations, evolutionary genetics has mainly focused on epistasis between pairs of mutations. Here we propose a generalization to the classical population genetic treatment of pairwise epistasis that yields expressions for epistasis among arbitrary subsets of mutations of all orders (pairwise, three-way, etc.). Our approach reveals substantial higher-order epistasis in almost every published fitness landscape. Furthermore we demonstrate that higher-order epistasis is critically important in two systems we know best. We conclude that higher-order epistasis deserves empirical and theoretical attention from evolutionary geneticists.

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Section: Conclusion: Evolutionary Biologists Should Worry About Highmentioning

confidence: 99%

Should evolutionary geneticists worry about higher-order epistasis?

Weinreich

Lan

Wylie

et al. 2013

Current Opinion in Genetics & Development

279

396

View full text Add to dashboard Cite

show abstract

“…We decomposed the fitness landscape into epistatic interactions of different orders by Fourier analysis (Stadler, 1996;Szendro et al, 2013;Weinreich et al, 2013;Neidhart et al, 2013). The Fourier coefficients given by the transform can be interpreted as epistasis of different orders (Weinreich et al, 2013;de Visser and Krug, 2014).…”

Section: Fourier Analysismentioning

confidence: 99%

Adaptation in protein fitness landscapes is facilitated by indirect paths

Dai

Olson

et al. 2016

Preprint

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The structure of fitness landscapes is critical for understanding adaptive protein evolution. Previous empirical studies on fitness landscapes were confined to either the neighborhood around the wild type sequence, involving mostly single and double mutants, or a combinatorially complete subgraph involving only two amino acids at each site. In reality, the dimensionality of protein sequence space is higher (20 L ) and there may be higher-order interactions among more than two sites. Here we experimentally characterized the fitness landscape of four sites in protein GB1, containing 20 4 = 160,000 variants. We found that while reciprocal sign epistasis blocked many direct paths of adaptation, such evolutionary traps could be circumvented by indirect paths through genotype space involving gain and subsequent loss of mutations. These indirect paths alleviate the constraint on adaptive protein evolution, suggesting that the heretofore neglected dimensions of sequence space may change our views on how proteins evolve.

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“…Franke et al (2011) applied the model to an eight-locus fitness landscape for the fungus A. niger and extracted an estimate of c from a subgraph analysis of pathway accessibility. In a study of amplitude spectra of fitness landscapes Neidhart et al (2013) showed that the correlation function of a six-locus fitness landscape obtained by Hall et al (2010) for the yeast Saccharomyces cerevisiae is well described by the RMF model. Finally, in a metaanalysis of 10 empirical fitness landscapes Szendro et al (2013b) used the RMF model to interpolate the behavior of various ruggedness measures between the limits of a completely random (HoC) and an additive landscape and found good agreement with the trends in the empirical data.…”

Section: Application To Experimentsmentioning

confidence: 99%

Adaptation in Tunably Rugged Fitness Landscapes: The Rough Mount Fuji Model

Neidhart¹,

Szendro²,

Krug

2014

Genetics

Self Cite

108

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Much of the current theory of adaptation is based on Gillespie's mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyze a simple fitness landscape model with tunable ruggedness based on the rough Mount Fuji (RMF) model originally introduced by Aita et al. in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulas for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly fit first-step background in a recent evolution experiment with a microvirid bacteriophage.T HE genetic adaptation of an asexual population to a novel environment is governed by the number and fitness effects of available beneficial mutations, their epistatic interactions, and the rate at which they are supplied (Sniegowski and Gerrish 2010). Despite the inherent complexity of this process, recent theoretical work has identified several robust statistical patterns of adaptive evolution (Orr 2005a,b). Most of these predictions were derived in the framework of Gillespie's mutational landscape model (MLM), which is based on three key assumptions (Gillespie 1983(Gillespie , 1984(Gillespie , 1991Orr 2002). First, selection is strong enough to prevent the fixation of deleterious mutations and mutation is sufficiently weak such that mutations emerge and fix one at a time [the strong selection/weak mutation (SSWM) regime]. Second, wild-type fitness is high, which allows one to describe the statistics of beneficial mutations using extreme value theory (EVT). Third, the fitness values of new mutants are uncorrelated with the fitness of the ancestor from which they arise. This last assumption implies that the fitness landscape underlying the adaptive process is maximally rugged with many local maxima and minima (Kauffman and Levin 1987;Kauffman 1993;Jain and Krug 2007), a limiting situation that is often referred to as the house of cards (HoC) landscape (Kingman 1978). Thus, the MLM is concerned with a population evolving in a HoC landscape under SSWM dynamics, starting from an initial state of high fitness.The validity of the SSWM assumption depends primarily on the population size N. Denoting the mutation rate by u and the typical selection strength by s, the criterion for the SSWM regime reads Nu ( 1 ( Ns, which can always be satisfied by a suitable choice o...

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Exact results for amplitude spectra of fitness landscapes

Cited by 44 publications

References 51 publications

Should evolutionary geneticists worry about higher-order epistasis?

Should evolutionary geneticists worry about higher-order epistasis?

Adaptation in protein fitness landscapes is facilitated by indirect paths

Adaptation in Tunably Rugged Fitness Landscapes: The Rough Mount Fuji Model

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