Multiple Adaptive Substitutions During Evolution in Novel Environments

Jain, Kavita; Seetharaman, Sarada

doi:10.1534/genetics.111.134163

Cited by 19 publications

(79 citation statements)

References 35 publications

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“…We also recover the previous results for uniformly and exponentially distributed fitnesses [10]. Equations (25) and (26) also match the results of [11] in which a fixed set of mutants during the entire walk is assumed.…”

Section: Equation (3) and Changing The Variable To Z = (1+κf )/Lsupporting

confidence: 79%

“…Recently the walk length distribution was calculated within an approximation for the model described above [10] and the mean walk length was computed exactly in a simplified version of the adaptive walk [11]. However these studies assume that the fitness distribution has a finite mean.…”

mentioning

confidence: 99%

“…When κ → ∞, the adaptive walk model reduces to a greedy walk [12] for which the walk length distribution is finite for infinitely long sequences [17] while for κ → −∞, a random adaptive walk is obtained [12] for which the walk length distribution is a Poisson distribution with mean ln L [18]. Recently the adaptive walk model described above was studied in detail for κ = −1 and κ → 0 and the walk length distribution was computed [10]. Here we are interested in the properties of adaptive walk when κ is arbitrary but finite.…”

mentioning

confidence: 99%

“…The walk length distribution Q J that exactly J steps are taken is related to P J (f ) according to the following relation [10]:…”

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confidence: 99%

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Number of adaptive steps to a local fitness peak

Jain¹

2011

EPL

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Abstract. -We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean. If the mean is finite, all the walk length cumulants grow with the sequence length but approach a constant otherwise. Experimental implications of our analytical results are also discussed.

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Section: Equation (3) and Changing The Variable To Z = (1+κf )/Lsupporting

confidence: 79%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…The walk length distribution Q J that exactly J steps are taken is related to P J (f ) according to the following relation [10]:…”

mentioning

confidence: 99%

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Number of adaptive steps to a local fitness peak

Jain¹

2011

EPL

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“…The mean walk length in the HoC landscape has been analyzed using various approaches (Gillespie 1983;Flyvbjerg and Lautrup 1992;Orr 2002;Jain and Seetharaman 2011;Jain 2011;Neidhart and Krug 2011;Seetharaman and Jain 2014). Because of the lack of isotropy in the RMF landscapes, analytical results for the walk length are much harder to derive for this model, and the results described in the following paragraphs were therefore obtained from simulations.…”

Section: Adaptive Walksmentioning

confidence: 99%

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

Neidhart¹,

Szendro²,

Krug

2014

Genetics

106

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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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Universality Classes of Interaction Structures for NK Fitness Landscapes

Hwang¹,

Schmiegelt²,

Ferretti³

et al. 2018

J Stat Phys

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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 ≤ 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

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Multiple Adaptive Substitutions During Evolution in Novel Environments

Cited by 19 publications

References 35 publications

Number of adaptive steps to a local fitness peak

Number of adaptive steps to a local fitness peak

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

Universality Classes of Interaction Structures for NK Fitness Landscapes

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