Universität zu Köln

Hwang, Sungmin, Schmiegelt, Benjamin, Ferretti, Luca ORCID: 0000-0001-7578-7301 and Krug, Joachim ORCID: 0000-0002-2143-6490 (2018). Universality Classes of Interaction Structures for NK Fitness Landscapes. J. Stat. Phys., 172 (1). S. 226 - 279. NEW YORK: SPRINGER. ISSN 1572-9613

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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 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hwang, Sungmin UNSPECIFIED UNSPECIFIED UNSPECIFIED Schmiegelt, Benjamin UNSPECIFIED UNSPECIFIED UNSPECIFIED Ferretti, Luca UNSPECIFIED orcid.org/0000-0001-7578-7301 UNSPECIFIED Krug, Joachim UNSPECIFIED orcid.org/0000-0002-2143-6490 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-180542
DOI:	10.1007/s10955-018-1979-z
Journal or Publication Title:	J. Stat. Phys.
Volume:	172
Number:	1
Page Range:	S. 226 - 279
Date:	2018
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1572-9613
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institut für Biologische Physik
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ADAPTIVE WALKS; EVOLUTIONARY ACCESSIBILITY; POPULATION-GENETICS; METASTABLE STATES; PROTEIN EVOLUTION; SIGN EPISTASIS; MODEL; ADAPTATION; NUMBER; PATHS Multiple languages Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/18054