# 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

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics.

- BiologyTheoretical population biology
- 2019

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

- BiologybioRxiv
- 2018

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.

Evolutionary constraints in fitness landscapes

- Computer ScienceHeredity
- 2018

This paper presents some measures of evolutionary constraints based on the similarity between accessible paths and the abundance and characteristics of “chains” of obligatory mutations, that are paths going through genotypes with a single fitter neighbor, and shows how they shed light on evolutionary constraints and predictability in experimentally resolved landscapes.

Distribution of the number of fitness maxima in Fisher’s geometric model

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

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.

Epistasis and Adaptation on Fitness Landscapes

- Environmental Science
- 2022

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.…

Computational Complexity as an Ultimate Constraint on Evolution

- BiologyGenetics
- 2019

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.

Accessibility percolation in random fitness landscapes 3

- Biology
- 2019

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.

Global epistasis emerges from a generic model of a complex trait

- BiologybioRxiv
- 2020

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.

Accessibility percolation in random fitness landscapes

- Biology
- 2019

This chapter reviews studies of accessibility percolation that use probabilistic fitness landscape models to explore the emergence of 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.

Evolving generalists in switching rugged landscapes

- BiologyPLoS Comput. Biol.
- 2019

A generative model is presented to estimate the propensity of evolving generalists in rugged landscapes that are tunably related and alternating relatively slowly, and environmental cycling can substantially facilitate the search for fit generalists by dynamically enlarging their effective basins of attraction.

## References

SHOWING 1-10 OF 111 REFERENCES

ESTIMATING SOME FEATURES OF NK FITNESS LANDSCAPES

- Mathematics
- 2002

Kauffman and Levin introduced a class of models for the evolution of hereditary systems which they called NK fitness landscapes. Inspired by spinglasses, these models have the attractive feature of…

Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

- Mathematics
- 2015

This paper studies the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined and finds that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern.

Evolutionary Accessibility of Modular Fitness Landscapes

- Computer Science
- 2014

The block model can be viewed as a special case of Kauffman’s NK-model, and it is shown that the number of accessible paths can be written as a product of the path numbers within the blocks, which provides a detailed analytic description of the paths statistics.

Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations.

- Environmental ScienceJournal of theoretical biology
- 2016

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

- Biology
- 2012

Some measures of accessibility behave non-monotonically as a function of K, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2, and the relation between models for fitness landscapes and spin glasses is addressed.

Genotypic Complexity of Fisher’s Geometric Model

- BiologyGenetics
- 2017

The analysis shows that thephenotypic dimension, which is often referred to as phenotypic complexity, does not generally correlate with the complexity of fitness landscapes and that even organisms with a single Phenotypic trait can have complex landscapes.

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

- BiologyGenetics
- 2014

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 is proposed and compared to the known behavior in the MLM model.

On the existence of accessible paths in various models of fitness landscapes

- Mathematics
- 2014

The main results resolve open questions about three well-known mathematical models for genetic mutations, which in the biophysics literature are known as house of cards (HoC), constrained house of card (CHoC) and rough Mount Fuji (RMF).

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

- BiologybioRxiv
- 2016

Accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences, suggesting that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.

An Analysis of $N\!K$ Landscapes: Interaction Structure, Statistical Properties, and Expected Number of Local Optima

- Computer ScienceIEEE Transactions on Evolutionary Computation
- 2014

It is proved that NK landscapes can be represented by parametric linear interaction models where model coefficients have meaningful interpretations and the statistical properties of the model coefficients are derived, providing insight into how the NK algorithm parses importance to main effects and interactions.