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

Abstract

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.

References

  1. Phillips, P., Otto, S.P. & Whitlock, M.C. in Epistasis and the Evolutionary Process (eds. Wolf, J.B., Brodie, E.D. & Wade, M.J.) 20–38 (Oxford University Press, Oxford, 2000).

    Google Scholar 

  2. Otto, S.P. & Lenormand, T. Resolving the paradox of sex and recombination. Nat. Rev. Genet. 3, 252–261 (2002).

    Article  CAS  Google Scholar 

  3. Michalakis, Y. & Roze, D. Epistasis in RNA viruses. Science 306, 1492–1493 (2004).

    Article  CAS  Google Scholar 

  4. Szàthmary, E. Do deleterious mutations act synergistically - metabolic control-theory provides a partial answer. Genetics 133, 127–132 (1993).

    PubMed  PubMed Central  Google Scholar 

  5. Segré, D., DeLuna, A., Church, G.M. & Kishony, R. Modular epistasis in yeast metabolism. Nat. Genet. 37, 77–83 (2005).

    Article  Google Scholar 

  6. Martin, G. & Lenormand, T. A multivariate extension of Fisher's geometrical model and the distribution of mutation fitness effects across species. Evolution 60, 893–907 (2006).

    Article  Google Scholar 

  7. Elena, S.F. & Lenski, R.E. Test of synergistic interactions among deleterious mutations in bacteria. Nature 390, 395–398 (1997).

    Article  CAS  Google Scholar 

  8. Sanjuàn, R., Moya, A. & Elena, S.F. The contribution of epistasis to the architecture of fitness in an RNA virus. Proc. Natl. Acad. Sci. USA 101, 15376–15379 (2004).

    Article  Google Scholar 

  9. Malmberg, R.L. & Mauricio, R. QTL-based evidence for the role of epistasis in evolution. Genet. Res. 86, 89–95 (2005).

    Article  CAS  Google Scholar 

  10. Burch, C.L., Turner, P.E. & Hanley, K.A. Patterns of epistasis in RNA viruses: a review of the evidence from vaccine design. J. Evol. Biol. 16, 1223–1235 (2003).

    Article  CAS  Google Scholar 

  11. Bonhoeffer, S., Chappey, C., Parkin, N.T., Whitcomb, J.M. & Petropoulos, C.J. Evidence for positive epistasis in HIV-1. Science 306, 1547–1550 (2004).

    Article  CAS  Google Scholar 

  12. Wloch, D.M., Borts, R.H. & Korona, R. Epistatic interactions of spontaneous mutations in haploid strains of the yeast Saccharomyces cerevisiae. J. Evol. Biol. 14, 310–316 (2001).

    Article  CAS  Google Scholar 

  13. Fong, S.S. & Palsson, B.O. Metabolic gene-deletion strains of Escherichia coli evolve to computationally predicted growth phenotypes. Nat. Genet. 36, 1056–1058 (2004).

    Article  CAS  Google Scholar 

  14. Fisher, R.A. The Genetical Theory of Natural Selection, (Oxford University Press, Oxford, 1930).

    Book  Google Scholar 

  15. Orr, H.A. The genetic theory of adaptation: a brief history. Nat. Rev. Genet. 6, 119–127 (2005).

    Article  CAS  Google Scholar 

  16. Barton, N.H. & Keightley, P.D. Understanding quantitative genetic variation. Nat. Rev. Genet. 3, 11–21 (2002).

    Article  CAS  Google Scholar 

  17. Orr, H.A. The “sizes” of mutations fixed in phenotypic evolution: a response to Clarke and Arthur. Evol. Dev. 3, 121–123 (2001).

    Article  CAS  Google Scholar 

  18. Waxman, D. & Welch, J.J. Fisher's microscope and Haldane's ellipse. Am. Nat. 166, 447–457 (2005).

    Article  CAS  Google Scholar 

  19. Martin, G. & Lenormand, T. The fitness effect of mutations in stressful environments: a survey in the light of fitness landscape models. Evolution 60, 2413–2427 (2006).

    Article  Google Scholar 

  20. Akaike, H. A new look at the statistical model identification. IEEE Trans. Automatic Control 19, 716–723 (1974).

    Article  Google Scholar 

  21. Otto, S.P. & Feldman, M.W. Deleterious mutations, variable epistatic interactions and the evolution of recombination. Theor. Popul. Biol. 51, 134–147 (1997).

    Article  CAS  Google Scholar 

  22. Kouyos, R.D., Otto, S.P. & Bonhoeffer, S. Effect of varying epistasis on the evolution of recombination. Genetics 173, 589–597 (2006).

    Article  CAS  Google Scholar 

  23. Lande, R. The genetic covariance between characters maintained by pleiotropic mutations. Genetics 94, 203–215 (1980).

    CAS  PubMed  PubMed Central  Google Scholar 

  24. Burger, R. in The Mathematical Theory of Selection, Recombination, Mutation Ch. V, 158–160 (John Wiley & Sons, Chichester, UK, 2000).

    Google Scholar 

  25. Mathai, A.M. & Provost, S.B. Quadratic Forms in Random Variables (Marcel Dekker, New York, 1992).

    Google Scholar 

  26. Whitlock, M.C. & Bourguet, D. Factors affecting the genetic load in Drosophila: synergistic epistasis and correlations among fitness components. Evolution 54, 1654–1660 (2000).

    Article  CAS  Google Scholar 

  27. Lenski, R.E. & Travisano, M. Dynamics of adaptation and diversification - a 10,000-generation experiment with bacterial-populations. Proc. Natl. Acad. Sci. USA 91, 6808–6814 (1994).

    Article  CAS  Google Scholar 

  28. Elena, S.F., Ekunwe, L., Hajela, N., Oden, S.A. & Lenski, R.E. Distribution of fitness effects caused by random insertion mutations in Escherichia coli. Genetica 103, 349–358 (1998).

    Article  Google Scholar 

  29. Sanjuàn, R., Moya, A. & Elena, S.F. The distribution of fitness effects caused by single-nucleotide substitutions in an RNA virus. Proc. Natl. Acad. Sci. USA 101, 8396–8401 (2004).

    Article  Google Scholar 

  30. Kidwell, M.G. & Lisch, D. Transposable elements as sources of variation in animals and plants. Proc. Natl. Acad. Sci. USA 94, 7704–7711 (1997).

    Article  CAS  Google Scholar 

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Acknowledgements

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

Contributions

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.

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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). https://doi.org/10.1038/ng1998

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