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# Weinreich, D. M., Watson, R. A. & Chao, L. Perspective: sign epistasis and genetic constraint on evolutionary trajectories. Evolution 59, 1165-1174

Department of Organismic and Evolutionary Biology, Harvard University, 16 Divinity Avenue, Cambridge, Massachusetts 02138, USA.
(Impact Factor: 4.61). 07/2005; 59(6):1165-74. DOI: 10.1554/04-272
Source: PubMed

ABSTRACT

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.

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Available from: Richard A. Watson, Dec 23, 2013
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• "The RMF model has recently been found to provide a convenient parametrization of many empirical fitness data sets (Franke et al., 2011; Szendro et al., 2013b; Neidhart et al., 2013), while at the same time allowing for detailed mathematical analysis of a wide range of landscape properties (Neidhart et al., 2014; Park et al., 2015). Of particular interest for our work are the results on the existence of selectively accessible mutational pathways, defined here as pathways to the global fitness maximum along which fitness increases monotonically (Weinreich et al., 2005; Franke et al., 2011). Hegarty and Martinsson (2014) have shown that accessible pathways exist in the RMF model with a probability approaching unity for L → ∞, whereas this probability tends to zero for uncorrelated landscapes. "
##### Article: Greedy adaptive walks on a correlated fitness landscape
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ABSTRACT: We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length $L$. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached. The landscape is of the rough mount Fuji type, which means that the fitness value assigned to a sequence is the sum of a random and a deterministic component. The random components are independent and identically distributed random variables, and the deterministic component varies linearly with the distance to a reference sequence. The deterministic fitness gradient $c$ is a parameter that interpolates between the limits of an uncorrelated random landscape ($c = 0$) and an effectively additive landscape ($c \to \infty$). When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence. Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for $L \to \infty$, different from its values for $c=0$ and $c = \infty$, if $c$ is scaled with $L$ in an appropriate combination.
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• "[13] [18] [19] "
##### Article: The Valley-of-Death: Reciprocal sign epistasis constrains adaptive trajectories in a constant, nutrient limiting environment
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ABSTRACT: The fitness landscape is a powerful metaphor for describing the relationship between genotype and phenotype for a population under selection. However, empirical data as to the topography of fitness landscapes are limited, owing to difficulties in measuring fitness for large numbers of genotypes under any condition. We previously reported a case of reciprocal sign epistasis (RSE), where two mutations individually increased yeast fitness in a glucose-limited environment, but reduced fitness when combined, suggesting the existence of two peaks on the fitness landscape. We sought to determine whether a ridge connected these peaks so that populations founded by one mutant could reach the peak created by the other, avoiding the low-fitness “Valley-of-Death” between them. Sequencing clones after 250 generations of further evolution provided no evidence for such a ridge, but did reveal many presumptive beneficial mutations, adding to a growing body of evidence that clonal interference pervades evolving microbial populations.
Genomics 11/2014; 104(6). DOI:10.1016/j.ygeno.2014.10.011 · 2.28 Impact Factor
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• "ries may be more likely than others . On the other hand , strong magnitude epistasis or sign epistasis are likely to create a rugged landscape where evolutionary trajectories are restricted because some mutations are only favorable in the presence or absence of others . On such a landscape , the order and combination of mutations becomes crucial ( Weinreich et al . , 2005 ; Poelwijk et al . , 2007 ; Dawid et al . , 2010 ; de Visser et al . , 2011 ; Kvitek and Sherlock , 2011 ) . In this way , evolution becomes contingent on historical events ; depending on which mutation initially occurs , a different pathway and eventually , a different outcome , may result ( Weinreich et al . , 2005 ; Weinreich et al ."
##### Article: Dynamics and constraints of enzyme evolution
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ABSTRACT: The wealth of distinct enzymatic functions found in nature is impressive and the on-going evolutionary divergence of enzymatic functions continues to generate new and efficient catalysts, which can be seen through the recent emergence of enzymes able to degrade xenobiotics. However, recreating such processes in the laboratory has been met with only moderate success. What are the factors that lead to suboptimal research outputs? In this review, we discuss constraints on enzyme evolution, which can restrict evolutionary trajectories and lead to evolutionary dead-ends. We highlight recent studies that have used experimental evolution to mimic different aspects of enzymatic adaptation under simple, controlled settings to shed light on evolutionary dynamics and constraints. A better understanding of these constraints will lead to the development of more efficient strategies for directed evolution and enzyme engineering. J. Exp. Zool. (Mol. Dev. Evol.) 9999B: 1-20, 2014. © 2014 Wiley Periodicals, Inc.
Journal of Experimental Zoology Part B Molecular and Developmental Evolution 11/2014; 322(7). DOI:10.1002/jez.b.22562 · 2.31 Impact Factor
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