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Distributions of epistasis in microbes fit predictions from a fitness landscape model


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 predictions1,2 “almost whenever multilocus genetics matters”3. Yet very few models4,5 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 model6. We show that this prediction closely matches the empirical measures of epistasis that have been obtained for Escherichia coli7 and the RNA virus vesicular stomatitis virus8. 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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Figure 1: Fitness landscape model of epistasis between mutations, based on three main assumptions (i–iii).
Figure 2: Observed and predicted distributions of fitness epistasis between random pairs of mutations.
Figure 3: Observed and predicted distributions of epistasis between VSV beneficial mutations8 (15 epistasis estimates).
Figure 4: Observed and predicted change of the distribution of log-fitness with the number of mini-Tn10 insertions in E. coli: gamma approximation.


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We thank D. Waxman and P. Jarne for comments on this work. G.M. thanks J. Goudet for hosting him during part of this work. This work was supported by an Action Concertée Incitative from the French Ministry of Research (T.L.), a PhD fellowship from the French Ministry of Research (G.M.), the Swiss National Science Foundation (grant 31-108194/1 to G.M.) and the Spanish Ministerio de Educación y Ciencia (MEC)-FEDER grant BMC2003-00066 to S.F.E.

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Authors and Affiliations



G.M. and T.L. designed the model, did the analysis and wrote the paper. S.F.E. compiled the data and wrote the paper.

Corresponding author

Correspondence to Guillaume Martin.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Fig. 1

Power curves for the tests shown in Table 1. (PDF 134 kb)

Supplementary Fig. 2

Robustness of the model to non-additivity in the phenotypic effects of mutations. (PDF 56 kb)

Supplementary Fig. 3

Agreement of the predicted approximate distributions with simulations. (PDF 384 kb)

Supplementary Table 1

Parameter estimation for the MCMC fit. (PDF 29 kb)

Supplementary Methods (PDF 140 kb)

Supplementary Note (PDF 61 kb)

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Martin, G., Elena, S. & Lenormand, T. Distributions of epistasis in microbes fit predictions from a fitness landscape model. Nat Genet 39, 555–560 (2007).

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