Universality Classes of Interaction Structures for NK Fitness Landscapes

Universality Classes of Interaction Structures for NK Fitness Landscapes 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 the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

Universality Classes of Interaction Structures for NK Fitness Landscapes

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
DOI
10.1007/s10955-018-1979-z
Publisher site
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Abstract

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 the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

Journal

Journal of Statistical Physics – Springer Journals

Published: Feb 13, 2018

References

  • Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: application to prolyl endopeptidase and thermolysin
    Aita, T; Uchiyama, H; Inaoka, T; Nakajima, M; Kokubo, T; Husimi, Y
  • Handbook of Evolutionary Computation
    Altenberg, L
  • On the (un)predictability of a large intragenic fitness landscape
    Bank, C; Matuszewski, S; Hietpas, RT; Jensen, JD
  • The number of accessible paths in the hypercube
    Berestycki, J; Brunet, É; Shi, Z
  • Accessibility percolation with backsteps. ALEA, Lat
    Berestycki, J; Brunet, É; Shi, Z
  • An analysis of NK landscapes: interaction structure, statistical properties and expected number of local optima
    Buzas, J; Dinitz, J
  • Optimal adaptive performance and delocalization in NK fitness landscapes
    Campos, PRA; Adami, C; Wilke, CO
  • Optimal adaptive performance and delocalization in NK fitness landscapes (Erratum)
    Campos, PRA; Adami, C; Wilke, CO
  • Adaptive landscapes and protein evolution
    Carneiro, M; Hartl, DL
  • The peaks and geometry of fitness landscapes
    Crona, K; Greene, D; Barlow, M
  • Inferring genetic interactions from comparative fitness data
    Crona, K; Gavryushkin, A; Greene, D; Beerenwinkel, N
  • Metastable states in short-ranged $$p$$ p -spin glasses
    Oliviera, VM; Fontanari, JF; Stadler, PF
  • Empirical fitness landscapes and the predictability of evolution
    Visser, JAGM; Krug, J
  • Exploring the effect of sex on empirical fitness landscapes
    Visser, JAGM; Park, SC; Krug, J
  • The causes of epistasis
    Visser, JAGM; Cooper, TF; Elena, SF
  • Extreme Value Theory: An Introduction
    de Haan, L; Ferreira, A
  • Metastable states of spin glasses on random thin graphs
    Dean, DS
  • Mutational reversions during adaptive protein evolution
    DePristo, MA; Hartl, DL; Weinreich, DM
  • Rigorous results for the NK model
    Durrett, R; Limic, V
  • Estimating some features of NK fitness landscapes
    Evans, SN; Steinsaltz, D
  • Measuring epistasis in fitness landscapes: the correlation of fitness effects of mutations
    Ferretti, L; Schmiegelt, B; Weinreich, D; Yamauchi, A; Kobayashi, Y; Tajima, F; Achaz, G
  • Encoding of memory in sheared amorphous solids
    Fiocco, D; Foffi, G; Sastry, S
  • Evolution in a rugged fitness landscape
    Flyvbjerg, H; Lautrup, B
  • Evolutionary accessibility in tunably rugged fitness landscapes
    Franke, J; Krug, J
  • Evolutionary accessibility of mutational pathways
    Franke, J; Klözer, A; de Visser, JAGM; Krug, J
  • Fitness Landscapes and the Origin of Species
    Gavrilets, S
  • Numerical computation of multivariate normal probabilities
    Genz, A
  • A simple stochastic gene substitution model
    Gillespie, JH
  • Molecular evolution over the mutational landscape
    Gillespie, JH
  • A mathematical theory of natural selection, Part VIII: metastable populations
    Haldane, JBS
  • What can we learn from fitness landscapes?
    Hartl, DL
  • On the existence of accessible paths in various models of fitness landscapes
    Hegarty, P; Martinsson, A
  • Genotypic complexity of Fisher’s geometric model
    Hwang, S; Park, SC; Krug, J
  • Generic rugged landscapes under strain and the possibility of rejuvenation in glasses
    Isner, BA; Lacks, DJ
  • Number of adaptive steps to a local fitness peak
    Jain, K
  • Multiple adaptive substitutions during evolution in novel environments
    Jain, K; Seetharaman, S
  • Linear Integral Equations: Theory & Technique
    Kanwal, RP
  • The Origins of Order
    Kauffman, SA
  • Towards a general theory of adaptive walks on rugged landscapes
    Kauffman, S; Levin, S
  • The NK model of rugged fitness landscapes and its application to maturation of the immune response
    Kauffman, SA; Weinberger, ED
  • On the probability of fixation of mutant genes in a population
    Kimura, M
  • A simple model for the balance between selection and mutation
    Kingman, JFC
  • Topological features of rugged fitness landscapes in sequence space
    Kondrashov, DA; Kondrashov, FA
  • Exploring the complexity of the HIV-1 fitness landscape
    Kouyos, RD; Leventhal, GE; Hinkley, T; Haddad, M; Whitcomb, JM; Petropoulos, CJ; Bonhoeffer, S
  • Adaptation on rugged landscapes
    Levinthal, DA
  • More rigorous results on the Kauffman-Levin model of evolution
    Limic, V; Pemantle, R
  • Protein evolution on rugged landscapes
    Macken, CA; Perelson, AS
  • Evolutionary walks on rugged landscapes
    Macken, CA; Hagan, PS; Perelson, AS
  • Tunably rugged landscapes with known maximum and minimum
    Manukyan, N; Eppstein, MJ; Buzas, JS
  • From fitness landscapes to seascapes: non-equilbrium dynamics of selection and adaptation
    Mustonen, V; Lässig, M
  • Adaptive walks and extreme value theory
    Neidhart, J; Krug, J
  • Exact results for amplitude spectra of fitness landscapes
    Neidhart, J; Szendro, IG; Krug, J
  • Adaptation in tunably rugged fitness landscapes: the rough Mount Fuji Model
    Neidhart, J; Szendro, IG; Krug, J
  • Accessibility percolation on $$n$$ n -trees
    Nowak, S; Krug, J
  • Multidimensional epistasis and the transitory advantage of sex
    Nowak, S; Neidhart, J; Szendro, IG; Krug, J
  • The meaning of near-neutrality at coding and non-coding regions
    Ohta, T
  • The population genetics of adaptation: the adaptation of DNA sequences
    Orr, HA
  • A minimum on the mean number of steps taken in adaptive walks
    Orr, HA
  • The population genetics of adaptation on correlated fitness landscapes: the block model
    Orr, HA
  • Impact of epistasis and pleiotropy on evolutionary adaptation
    Østman, B; Hintze, A; Adami, C
  • $$\delta $$ δ -exceedance records and random adaptive walks
    Park, SC; Krug, J
  • The speed of evolution in large asexual populations
    Park, SC; Simon, D; Krug, J
  • Phase transition in random adaptive walks on correlated fitness landscapes
    Park, SC; Szendro, IG; Neidhart, J; Krug, J
  • Greedy adaptive walks on a correlated fitness landscape
    Park, SC; Neidhart, J; Krug, J
  • Protein evolution on partially correlated landscapes
    Perelson, AS; Macken, CA
  • Epistasis—the essential role of gene interactions in the structure and evolution of genetic systems
    Phillips, PC
  • Empirical fitness landscapes reveal accessible evolutionary paths
    Poelwijk, FJ; Kiviet, DJ; Weinreich, DM; Tans, SJ
  • Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes
    Poelwijk, FJ; Tănase-Nicola, S; Kiviet, DJ; Tans, SJ
  • The context-dependence of mutations: a linkage of formalisms
    Poelwijk, FJ; Krishna, V; Ranganathan, R
  • Sewall Wright and Evolutionary Biology
    Provine, WB
  • Combinatorial landscapes
    Reidys, CM; Stadler, PF
  • Analysis of a complete DNA-protein affinity landscape
    Rowe, W; Platt, M; Wedge, DC; Day, PJ; Kell, DB; Knowles, J
  • High-order epistasis shapes evolutionary trajectories
    Sailer, ZR; Harms, MJ
  • Evolutionary accessibility of modular fitness landscapes
    Schmiegelt, B; Krug, J
  • Length of adaptive walk on uncorrelated and correlated fitness landscapes
    Seetharaman, S; Jain, K
  • Landscapes and their correlation functions
    Stadler, PF
  • Random field models for fitness landscapes
    Stadler, PF; Happel, R
  • Complex-network analysis of combinatorial spaces: the NK landscape case
    Tomassini, M; Vérel, S; Ochoa, G
  • The large deviation approach to statistical mechanics
    Touchette, H
  • An NK-like model for complexity
    Valente, M
  • Fourier and Taylor series on fitness landscapes
    Weinberger, ED
  • Local properties of Kauffman’s N-k model: a tunably rugged energy landscape
    Weinberger, ED
  • Sign epistasis and genetic constraint on evolutionary trajectories
    Weinreich, DM; Watson, RA; Chao, L
  • Darwinian evolution can follow only very few mutational paths to fitter proteins
    Weinreich, DM; Delaney, NF; DePristo, MA; Hartl, DL
  • Should evolutionary geneticists worry about higher-order epistasis?
    Weinreich, DM; Lan, Y; Wylie, CS; Heckendorn, RB
  • The nk model and population genetics
    Welch, JJ; Waxman, D
  • Multiple fitness peaks and epistasis
    Whitlock, MC; Phillips, PC; Moore, FBG; Tonsor, SJ
  • Adaptive walks on time-dependent fitness landscapes
    Wilke, CO; Martinetz, T
  • The computational complexity of N-K fitness functions
    Wright, AH; Thompson, RK; Zhang, J
  • Adaptation in protein fitness landscapes is facilitated by indirect paths
    Wu, NC; Dai, L; Olson, CA; Lloyd-Smith, JO; Sun, R
  • Beyond the hypercube: evolutionary accessibility of fitness landscapes with realistic mutational networks
    Zagorski, M; Burda, Z; Waclaw, B

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