Skip to main content
SpringerLink
Log in

Idiosyncratic epistasis creates universals in mutational effects and evolutionary trajectories

  • Article
  • Published:

From Nature Ecology & Evolution

View current issue Submit your manuscript

Abstract

Patterns of epistasis and shapes of fitness landscapes are of wide interest because of their bearings on a number of evolutionary theories. The common phenomena of slowing fitness increases during adaptations and diminishing returns from beneficial mutations are believed to reflect a concave fitness landscape and a preponderance of negative epistasis. Paradoxically, fitness decreases tend to decelerate and harm from deleterious mutations shrinks during the accumulation of random mutations—patterns thought to indicate a convex fitness landscape and a predominance of positive epistasis. Current theories cannot resolve this apparent contradiction. Here, we show that the phenotypic effect of a mutation varies substantially depending on the specific genetic background and that this idiosyncrasy in epistasis creates all of the above trends without requiring a biased distribution of epistasis. The idiosyncratic epistasis theory explains the universalities in mutational effects and evolutionary trajectories as emerging from randomness due to biological complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1: Idiosyncratic index of a wide variety of phenotype landscapes.
Fig. 2: Negative correlation between mutational effect and background fitness as a result of idiosyncratic epistasis.
Fig. 3: Fitness declines decelerate during mutation accumulation as a result of idiosyncratic epistasis.
Fig. 4: Adaptation slows as a result of idiosyncratic epistasis.

Similar content being viewed by others

Data availability

Data analysis and simulations for all landscapes except the tRNA and model landscapes were performed using R version 3.5.2. Analysis and simulations for the tRNA and model landscapes were performed using Python version 3.6.9. All figures were made with the matplotlib package in Python and Keynote. New data are available at https://github.com/lyonsdm/idiosyncrasy.

Code availability

Code is available at https://github.com/lyonsdm/idiosyncrasy.

References

  1. Phillips, P. C. Epistasis—the essential role of gene interactions in the structure and evolution of genetic systems. Nat. Rev. Genet. 9, 855–867 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  2. Kondrashov, A. S. Deleterious mutations and the evolution of sexual reproduction. Nature 336, 435–440 (1988).

    CAS  PubMed  Google Scholar 

  3. Crow, J. F. & Kimura, M. Efficiency of truncation selection. Proc. Natl Acad. Sci. USA 76, 396–399 (1979).

    CAS  PubMed  PubMed Central  Google Scholar 

  4. Zhang, J. Epistasis analysis goes genome-wide. PLoS Genet. 13, e1006558 (2017).

    PubMed  PubMed Central  Google Scholar 

  5. Kemble, H., Nghe, P. & Tenaillon, O. Recent insights into the genotype–phenotype relationship from massively parallel genetic assays. Evol. Appl. 12, 1721–1742 (2019).

    PubMed  PubMed Central  Google Scholar 

  6. Couce, A. & Tenaillon, O. A. The rule of declining adaptability in microbial evolution experiments. Front. Genet. 6, 99 (2015).

    PubMed  PubMed Central  Google Scholar 

  7. Barrick, J. E. et al. Genome evolution and adaptation in a long-term experiment with Escherichia coli. Nature 461, 1243–1247 (2009).

    CAS  PubMed  Google Scholar 

  8. MacLean, R., Perron, G. G. & Gardner, A. Diminishing returns from beneficial mutations and pervasive epistasis shape the fitness landscape for rifampicin resistance in Pseudomonas aeruginosa. Genetics 186, 1345–1354 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  9. Chou, H.-H., Chiu, H.-C., Delaney, N. F., Segrè, D. & Marx, C. J. Diminishing returns epistasis among beneficial mutations decelerates adaptation. Science 332, 1190–1192 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  10. Kryazhimskiy, S., Rice, D. P., Jerison, E. R. & Desai, M. M. Global epistasis makes adaptation predictable despite sequence-level stochasticity. Science 344, 1519–1522 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. Khan, A. I., Dinh, D. M., Schneider, D., Lenski, R. E. & Cooper, T. F. Negative epistasis between beneficial mutations in an evolving bacterial population. Science 332, 1193–1196 (2011).

    CAS  PubMed  Google Scholar 

  12. Miller, C. R. The treacheries of adaptation. Science 366, 418–419 (2019).

    CAS  PubMed  Google Scholar 

  13. Maisnier-Patin, S. et al. Genomic buffering mitigates the effects of deleterious mutations in bacteria. Nat. Genet. 37, 1376–1379 (2005).

    CAS  PubMed  Google Scholar 

  14. Perfeito, L., Sousa, A., Bataillon, T. & Gordo, I. Rates of fitness decline and rebound suggest pervasive epistasis. Evolution 68, 150–162 (2014).

    CAS  PubMed  Google Scholar 

  15. De la Iglesia, F. & Elena, S. F. Fitness declines in Tobacco etch virus upon serial bottleneck transfers. J. Virol. 81, 4941–4947 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. Johnson, M. S., Martsul, A., Kryazhimskiy, S. & Desai, M. M. Higher-fitness yeast genotypes are less robust to deleterious mutations. Science 366, 490–493 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Wei, X. & Zhang, J. Patterns and mechanisms of diminishing returns from beneficial mutations. Mol. Biol. Evol. 36, 1008–1021 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Sanjuan, R. & Elena, S. F. Epistasis correlates to genomic complexity. Proc. Natl Acad. Sci. USA 103, 14402–14405 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Schoustra, S., Hwang, S., Krug, J. & de Visser, J. A. Diminishing-returns epistasis among random beneficial mutations in a multicellular fungus. Proc. Biol. Sci. 283, 20161376 (2016).

    PubMed  PubMed Central  Google Scholar 

  20. Blanquart, F., Achaz, G., Bataillon, T. & Tenaillon, O. Properties of selected mutations and genotypic landscapes under Fisher’s geometric model. Evolution 68, 3537–3554 (2014).

    PubMed  PubMed Central  Google Scholar 

  21. He, X., Qian, W., Wang, Z., Li, Y. & Zhang, J. Prevalent positive epistasis in Escherichia coli and Saccharomyces cerevisiae metabolic networks. Nat. Genet. 42, 272–276 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. Draghi, J. A. & Plotkin, J. B. Selection biases the prevalence and type of epistasis along adaptive trajectories. Evolution 67, 3120–3131 (2013).

    PubMed  Google Scholar 

  23. Greene, D. & Crona, K. The changing geometry of a fitness landscape along an adaptive walk. PLoS Comput. Biol. 10, e1003520 (2014).

    PubMed  PubMed Central  Google Scholar 

  24. Li, C., Qian, W., Maclean, M. & Zhang, J. The fitness landscape of a tRNA gene. Science 352, 837–840 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. Li, X., Lalic, J., Baeza-Centurion, P., Dhar, R. & Lehner, B. Changes in gene expression predictably shift and switch genetic interactions. Nat. Commun. 10, 3886 (2019).

    PubMed  PubMed Central  Google Scholar 

  26. Domingo, J., Diss, G. & Lehner, B. Pairwise and higher-order genetic interactions during the evolution of a tRNA. Nature 558, 117–121 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Sarkisyan, K. S. et al. Local fitness landscape of the green fluorescent protein. Nature 533, 397–401 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  28. Melamed, D., Young, D. L., Gamble, C. E., Miller, C. R. & Fields, S. Deep mutational scanning of an RRM domain of the Saccharomyces cerevisiae poly(A)-binding protein. RNA 19, 1537–1551 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Poelwijk, F. J., Socolich, M. & Ranganathan, R. Learning the pattern of epistasis linking genotype and phenotype in a protein. Nat. Commun. 10, 4213 (2019).

    PubMed  PubMed Central  Google Scholar 

  30. Diss, G. & Lehner, B. The genetic landscape of a physical interaction. eLife 7, e32472 (2018).

    PubMed  PubMed Central  Google Scholar 

  31. Olson, C. A., Wu, N. C. & Sun, R. A comprehensive biophysical description of pairwise epistasis throughout an entire protein domain. Curr. Biol. 24, 2643–2651 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  32. Costanzo, M. et al. A global genetic interaction network maps a wiring diagram of cellular function. Science 353, aaf1420 (2016).

    PubMed  PubMed Central  Google Scholar 

  33. De Visser, J. A. & Krug, J. Empirical fitness landscapes and the predictability of evolution. Nat. Rev. Genet. 15, 480–490 (2014).

    CAS  PubMed  Google Scholar 

  34. Seetharaman, S. & Jain, K. Adaptive walks and distribution of beneficial fitness effects. Evolution 68, 965–975 (2014).

    PubMed  Google Scholar 

  35. Masel, J. & Trotter, M. V. Robustness and evolvability. Trends Genet. 26, 406–414 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  36. Wagner, A. Robustness and evolvability: a paradox resolved. Proc. Biol. Sci. 275, 91–100 (2008).

    PubMed  Google Scholar 

  37. Wei, X. & Zhang, J. Why phenotype robustness promotes phenotype evolvability. Genome Biol. Evol. 9, 3509–3515 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  38. Bershtein, S., Segal, M., Bekerman, R., Tokuriki, N. & Tawfik, D. S. Robustness–epistasis link shapes the fitness landscape of a randomly drifting protein. Nature 444, 929–932 (2006).

    CAS  PubMed  Google Scholar 

  39. Gerrish, P. J. & Lenski, R. E. The fate of competing beneficial mutations in an asexual population. Genetica 102–103, 127–144 (1998).

    PubMed  Google Scholar 

  40. Silander, O. K., Tenaillon, O. & Chao, L. Understanding the evolutionary fate of finite populations: the dynamics of mutational effects. PLoS Biol. 5, e94 (2007).

    PubMed  PubMed Central  Google Scholar 

  41. Wunsche, A. et al. Diminishing-returns epistasis decreases adaptability along an evolutionary trajectory. Nat. Ecol. Evol. 1, 0061 (2017).

    Google Scholar 

  42. Wagner, G. P., Pavlicev, M. & Cheverud, J. M. The road to modularity. Nat. Rev. Genet. 8, 921–931 (2007).

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

We thank A. Kondrashov, A. Lauring and members of the Zhang laboratory for valuable comments. This work was supported by US National Institutes of Health (NIH) research grant R01GM103232 to J.Z. D.M.L. was supported by NIH F31AI140618.

Author information

Author notes

  1. These authors contributed equally: Daniel M. Lyons, Zhengting Zou.

Authors and Affiliations

  1. Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI, USA

    Daniel M. Lyons, Zhengting Zou, Haiqing Xu & Jianzhi Zhang

Authors
  1. Daniel M. Lyons
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengting Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haiqing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jianzhi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

D.M.L., Z.Z. and J.Z. conceived of and designed the study. D.M.L. and Z.Z. performed the research and analysed the data. H.X. provided the mathematical proofs. All authors contributed to writing the paper.

Corresponding author

Correspondence to Jianzhi Zhang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 The high idiosyncrasy indices (Iid) observed are not due to phenotype measurement errors or the use of standard deviation (SD) instead of range of mutational effects.

a, SD-based Iid of the yeast tRNA fitness landscape is insensitive to the number of experimental replicates used in the fitness estimation. Boxplots show the distribution of Iid values of 828 single mutations in the tRNA landscape, calculated based on different numbers of replicates. The lower and upper edges of a box represent the first (qu1) and third (qu3) quartiles, respectively, the horizontal line inside the box indicates the median (md), the whiskers extend to the most extreme values inside inner fences, md ± 1.5(qu3 − qu1), and the grey dots represent values outside the inner fences (outliers). Violet dots show mean Iid of all mutations calculated based on respective numbers of replicates. b, Range-based Iid for various phenotype landscapes. Error bars show standard errors. Detailed information of each landscape is provided in Supplementary Table 1. Shown in red is the fraction of mutations exhibiting sign epistasis in each phenotype landscape.

Extended Data Fig. 2 Negative correlation between mutational effect and background phenotype in GFP and RNA stability landscapes.

a, Distribution of Pearson’s correlation coefficient (r) between mutational effect and background phenotype for individual mutations in the GFP landscape. b, Distribution of r for individual mutations in the RNA stability landscape. c, Relationship between background phenotype and mutational effect for all mutations in the GFP landscape. d, Relationship between background phenotype and mutational effect for all mutations in the RNA stability landscape. MFE, minimum free energy. The red line depicts the running mean in non-overlapping X-axis bins of width = 0.02 and 2 in (c, d), respectively, in all bins with more than 10 data points. There is no measurement error in the RNA stability landscape. Shared measurement error between mutational effect and background fitness cannot be controlled for in GFP as replicate fitness measurements are not available. For each mutation and its reverse, we considered a random one of them in (c, d).

Extended Data Fig. 3 Patterns of correlation between mutational effect and background fitness/phenotype for individual beneficial or deleterious mutations in various landscapes.

a, Boxplots showing distributions of correlations in a series of n-order landscapes of 16 sites (where the highest order of nonzero interaction is indicated on the X-axis) for beneficial (blue) and deleterious (red) mutations, respectively. The lower and upper edges of a box represent the first (qu1) and third (qu3) quartiles, respectively, the horizontal line inside the box indicates the median (md), the whiskers extend to the most extreme values inside inner fences, md ± 1.5(qu3 − qu1), and the dots represent values outside the inner fences (outliers). b-d, Frequency distributions of correlations for individual beneficial mutations (blue) and deleterious mutations (red) in the tRNA (b), GFP (c), and RNA stability (d) landscapes. Whether a mutation is beneficial or deleterious is determined in reference to the wild-type (tRNA and GFP) or an arbitrary reference genotype (n-order and RNA stability). The wider distribution for deleterious than beneficial mutations is at least in part due to the larger number of deleterious than beneficial mutations.

Extended Data Fig. 4 Average fitness trajectories of mutation accumulation simulated in various n-order additive landscapes (k = 1) with different numbers of sites (n).

The mean trajectories are scaled so that the minimum fitness appearing in the trajectory is 0 and the maximum is 1 to allow direct comparison.

Extended Data Fig. 5 Fitness declines decelerate during mutation accumulation as a result of idiosyncratic epistasis.

a, A total of 5000 fitness trajectories of mutation accumulation simulated in the GFP landscape, with the average trajectory shown in black, at each step when the trajectory number exceeds 10. b, A total of 350 fitness trajectories of mutation accumulation simulated in the RNA stability landscape, with the average trajectory shown in black. The dotted lines indicate the mean phenotypic value of all genotypes in the landscape, excluding non-active genotypes in the GFP landscape. For comparison, the dashed line in (a) or (b) represents the predicted linear decline given the slope in the first mutational step.

Extended Data Fig. 6 Idiosyncratic epistasis is necessary but not sufficient to cause decelerating adaptations.

a, Gamma distributions of genotype fitness for house-of-cards landscapes, with different values of the gamma shape parameter α. b, Theoretically computed mean fitness trajectories of adaptation on landscapes in (a) with corresponding colors. c, Average adaptive trajectories starting from the genotype with the lowest fitness (0), simulated in a series of n-order landscapes of 16 sites where each nonzero interaction term of each genotype is drawn from a gamma distribution of α = 1. d, Average adaptive trajectories starting from the genotype with the lowest fitness (0), simulated in a series of n-order landscapes of 16 sites where each nonzero interaction term of each genotype is drawn from a beta distribution with a=b=0.25. For each landscape in (c) and (d), the distribution of epistasis between mutations is symmetrical with mean equal to 0.

Extended Data Fig. 7 Adaptation slows in empirical phenotype landscapes.

a, A total of 5000 adaptive trajectories simulated in the GFP landscape, with the average trajectory shown in black, at each step when the trajectory number exceeds 10. b, A total of 350 adaptive trajectories simulated in the RNA stability landscape, with the average trajectory shown in black, at each step when the trajectory number exceeds 10. For comparison, the dashed line in (a) or (b) represents the predicted linear increase given the slope in the first mutational step.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lyons, D.M., Zou, Z., Xu, H. et al. Idiosyncratic epistasis creates universals in mutational effects and evolutionary trajectories. Nat Ecol Evol 4, 1685–1693 (2020). https://doi.org/10.1038/s41559-020-01286-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41559-020-01286-y

  • Springer Nature Limited

This article is cited by

Search

Navigation