Martin G, Elena SF, Lenormand T. Distributions of epistasis in microbes fit predictions from a fitness landscape model. Nature Genet 39: 555-560

University of Lausanne, Lausanne, Vaud, Switzerland
Nature Genetics (Impact Factor: 29.35). 05/2007; 39(4):555-60. DOI: 10.1038/ng1998
Source: PubMed


How do the fitness effects of several mutations combine? Despite its simplicity, this question is central to the understanding of multilocus evolution. Epistasis (the interaction between alleles at different loci), especially epistasis for fitness traits such as reproduction and survival, influences evolutionary predictions "almost whenever multilocus genetics matters". Yet very few models have sought to predict epistasis, and none has been empirically tested. Here we show that the distribution of epistasis can be predicted from the distribution of single mutation effects, based on a simple fitness landscape model. We show that this prediction closely matches the empirical measures of epistasis that have been obtained for Escherichia coli and the RNA virus vesicular stomatitis virus. Our results suggest that a simple fitness landscape model may be sufficient to quantitatively capture the complex nature of gene interactions. This model may offer a simple and widely applicable alternative to complex metabolic network models, in particular for making evolutionary predictions.

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    • "From this initial use in theories of adaptation , the FGM can also serve as a null model to fit and interpret empirical DFEs. Indeed, this model was shown to capture the DFE of single mutants (Martin and Lenormand 2006b), of epistasis (Martin et al. 2007) or of dominance (Manna et al 2011). With respect to environmental effects, which is our focus here, (Martin and Lenormand 2006a) showed that mutation accumulation data was consistent with a concave, nearly Gaussian phenotype-fitness function with constant shape and varying optima across environments . "
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    ABSTRACT: When are mutations beneficial in one environment and deleterious in another? More generally, what is the relationship between mutation effects across environments? These questions are crucial to predict adaptation in heterogeneous conditions in a broad sense. Empirical evidence documents various patterns of fitness effects across environments but we still lack a framework to analyse these multivariate data. In this paper, we extend Fisher's geometrical model to multiple environments determining distinct peaks. We derive the fitness distribution, in one environment, among mutants with a given fitness in another and the bivariate distribution of random mutants' fitnesses across two or more environments. The geometry of the phenotype-fitness landscape is naturally interpreted in terms of fitness trade-offs between environments. These results may be used to fit/predict empirical distributions or to predict the pattern of adaptation across heterogeneous conditions. As an example, we derive the genomic rate of substitution and of adaptation in a metapopulation divided into two distinct habitats in a high migration regime and show that they depend critically on the geometry of the phenotype-fitness landscape. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.
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    • "anjuan and Elena , 2006 ; Martin et al . , 2007 ; Aylor and Zeng , 2008 ; Perfeito et al . , 2011 ; Walkiewicz et al . , 2012 ) . Indeed , studies of whole viruses , bacteria etc . have revealed more epistasis among mutations than studies looking at the protein level ( Bonhoeffer et al . , 2004 ; Michalakis and Roze , 2004 ; Segre et al . , 2005 ; Martin et al . , 2007 ; Kryazhimskiy et al . , 2011 ; Breen et al . , 2012 ; Kachanovsky et al . , 2012 ; Kouyos et al . , 2012 ; Flynn et al . , 2013 ) . However even in a simplified model of enzyme evolution , in which enzymatic activity in the cell is directly related to fitness ( as is the case for essential metabolic enzymes or antibiotic resistance mar"
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    • "This is a pure effect of dimensionality on hybrid fitness, which occurs even when controlling for the effect on the overall selection strength, as measured by s 0 (Fig. 2). Note that e i j is also a measure of the pairwise fitness epistasis between mutations in FGM (Martin et al. 2007). Hence in this model, the hybrid load can be expressed in terms of the mean epistasis between mutations fixed within each population, rather than different populations as for classic DMI. "
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    ABSTRACT: Niche dimensionality is suggested to be a key determinant of ecological speciation ('multifarious selection' hypothesis), but genetic aspects of this process have not been investigated theoretically. We use Fisher's geometrical model to study how niche dimensionality influences the mean fitness of hybrids formed upon secondary contact between populations adapting in allopatry. Gaussian selection for an optimum generates two forms of reproductive isolation: an extrinsic component due to maladaptation of the mean phenotype, and an intrinsic variance load resulting from what we term transgressive incompatibilities between mutations fixed in different populations. We show that after adaptation to a new environment, RI increases with (i) the mean initial maladaptation of diverging population, and (ii) niche dimensionality, which increases the phenotypic variability of fixed mutations. Under mutation-selection-drift equilibrium in a constant environment, RI accumulates steadily with time, at a rate that also increases with niche dimensionality. A similar pattern can be produced by successive shifts in the optimum phenotype. Niche dimensionality thus has an effect per se on post-zygotic isolation, beyond putative indirect effects (stronger selection, more genes). Our mechanism is consistent with empirical evidence about transgressive segregation in crosses between divergent populations, and with patterns of accumulation of reproductive isolation with time in many taxa. This article is protected by copyright. All rights reserved.
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