# Universality Classes of Interaction Structures for NK Fitness Landscapes

@article{Hwang2017UniversalityCO, title={Universality Classes of Interaction Structures for NK Fitness Landscapes}, author={Sungmin Hwang and Benjamin Schmiegelt and Luca Ferretti and Joachim H A Krug}, journal={Journal of Statistical Physics}, year={2017}, volume={172}, pages={226-278} }

Kauffman’s NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $$k \le L$$k≤L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on…

## 21 Citations

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This work introduces a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance, and studies the properties of these landscapes focusing on the simplest evolutionary process: random adaptive walks.

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The distribution of the number of maxima when the limit $L \to \infty$ is taken at finite $n$ is identified and this analysis is expected to help to elucidate the fluctuation structure of metastable states in various spin glass problems.

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Epistasis occurs when the eﬀect of a mutation depends on its carrier’s genetic background. Despite increasing evidence that epistasis for ﬁtness is common, its role during evolution is contentious.…

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A distinction between easy landscapes of traditional theory where local fitness peaks can be found in a moderate number of steps, and hard landscapes where finding local optima requires an infeasible amount of time is introduced.

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This chapter reviews studies of accessibility percolation that use probabilistic fitness landscape models to explore the emergence of such paths as a function of the initial fitness, the parameters of the landscape or the structure of the genotype graph and discusses their implications for the predictability of evolutionary processes.

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A mathematical model for fitness landscapes generated by tradeoff between adaptation to environmental extremes is developed, based on experiments that determine the antibiotic dose-response curves of Escherichia coli strains, and previous observations on antibiotic resistance mutations.

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The model can be described as a system with interacting hysteretic elements, and it exhibits effects such as hysteresis loops and memory formation under antibiotic concentration cycling, which provides a general framework for studying motifs of evolutionary dynamics in biological systems in a changing environment.

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This model predicts a specific quantitative relationship between the magnitude of global epistasis and the stochastic effects of microscopic epistasis, and shows that the distribution of fitness effects takes on a universal form when epistasis is widespread, and introduces a novel fitness landscape model to show how phenotypic evolution can be repeatable despite sequence-level stochasticallyity.

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