Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Exploiting selection at linked sites to infer the rate and strength of adaptation


Genomic data encode past evolutionary events and have the potential to reveal the strength, rate and biological drivers of adaptation. However, joint estimation of adaptation rate (α) and adaptation strength remains challenging because evolutionary processes such as demography, linkage and non-neutral polymorphism can confound inference. Here, we exploit the influence of background selection to reduce the fixation rate of weakly beneficial alleles to jointly infer the strength and rate of adaptation. We develop a McDonald–Kreitman-based method to infer adaptation rate and strength, and estimate α = 0.135 in human protein-coding sequences, 72% of which is contributed by weakly adaptive variants. We show that, in this adaptation regime, α is reduced ~25% by linkage genome-wide. Moreover, we show that virus-interacting proteins undergo adaptation that is both stronger and nearly twice as frequent as the genome average (α = 0.224, 56% due to strongly beneficial alleles). Our results suggest that, while most adaptation in human proteins is weakly beneficial, adaptation to viruses is often strongly beneficial. Our method provides a robust framework for estimation of adaptation rate and strength across species.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: aMK estimates as a function of adaptation strength.
Fig. 2: The effect of BGS on α.
Fig. 3: Adaptation rate and strength estimates for human genomic data.
Fig. 4: Virally interacting genes support a high rate and strength of adaptation.

Data availability

Supplemental Data Table 1 is provided on the publisher’s website. The data that we used to parameterize our model are also available online at Columns in Supplementary Data Table 1 are as follows: 1, Ensembl coding gene identification; 2, number of non-synonymous polymorphic sites; 3, respective derived allele frequencies of these sites separated by commas; 4, number of synonymous polymorphic sites; 5, respective frequency-derived allele frequencies of these sites; 6, number of fixed non-synonymous substitutions on the human branch; and 7, number of fixed synonymous substitutions on the human branch.

Code availability

The code that we used to parameterize our model is freely available online at


  1. 1.

    Darwin, C. On the Origin of Species (Murray, 1859).

  2. 2.

    Wallace, A. R. Darwinism: an exposition of the theory of natural selection with some of its applications (MacMillan & Co., 1889).

  3. 3.

    Wright, S. On the roles of directed and random changes in gene frequency in the genetics of populations. Evolution 2, 279–294 (1948).

    CAS  Article  Google Scholar 

  4. 4.

    Kimura, M. et al. Evolutionary rate at the molecular level. Nature 217, 624–626 (1968).

    CAS  Article  Google Scholar 

  5. 5.

    Ohta, T. Slightly deleterious mutant substitutions in evolution. Nature 246, 96 (1973).

    CAS  Article  Google Scholar 

  6. 6.

    Kimura, M. Preponderance of synonymous changes as evidence for the neutral theory of molecular evolution. Nature 267, 275 (1977).

    CAS  Article  Google Scholar 

  7. 7.

    McDonald, J. H. & Kreitman, M. Adaptive protein evolution at the ADH locus in Drosophila. Nature 351, 652 (1991).

    CAS  Article  Google Scholar 

  8. 8.

    Fay, J. C., Wyckoff, G. J. & Wu, C.-I. Testing the neutral theory of molecular evolution with genomic data from Drosophila. Nature 415, 1024 (2002).

    CAS  Article  Google Scholar 

  9. 9.

    Pollard, K. S., Hubisz, M. J., Rosenbloom, K. R. & Siepel, A. Detection of nonneutral substitution rates on mammalian phylogenies. Genome Res. 20, 110–121 (2010).

    CAS  Article  Google Scholar 

  10. 10.

    Charlesworth, B. & Charlesworth, D. Neutral variation in the context of selection. Mol. Biol. Evol. 35, 1359–1361 (2018).

    CAS  Article  Google Scholar 

  11. 11.

    Corbett-Detig, R. B., Hartl, D. L. & Sackton, T. B. Natural selection constrains neutral diversity across a wide range of species. PLoS Biol. 13, e1002112 (2015).

    Article  Google Scholar 

  12. 12.

    Coop, G. Does linked selection explain the narrow range of genetic diversity across species? Preprint at bioRxiv (2016).

  13. 13.

    Kern, A. D. & Hahn, M. W. The neutral theory in light of natural selection. Mol. Biol. Evol. 35, 1366–1371 (2018).

    CAS  Article  Google Scholar 

  14. 14.

    Jensen, J. D. et al. The importance of the neutral theory in 1968 and 50 years on: a response to Kern and Hahn 2018. Evolution 73, 111–114 (2018).

    Article  Google Scholar 

  15. 15.

    Leffler, E. M. et al. Revisiting an old riddle: what determines genetic diversity levels within species? PLoS Biol. 10, e1001388 (2012).

    CAS  Article  Google Scholar 

  16. 16.

    Galtier, N. Adaptive protein evolution in animals and the effective population size hypothesis. PLoS Genet. 12, e1005774 (2016).

    Article  Google Scholar 

  17. 17.

    Smith, N. G. C. & Eyre-Walker, A. Adaptive protein evolution in Drosophila. Nature 415, 1022 (2002).

    CAS  Article  Google Scholar 

  18. 18.

    Sawyer, S. A. & Hartl, D. L. Population genetics of polymorphism and divergence. Genetics 132, 1161–1176 (1992).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Tataru, P., Mollion, M., Glémin, S. & Bataillon, T. Inference of distribution of fitness effects and proportion of adaptive substitutions from polymorphism data. Genetics 207, 1103–1119 (2017).

    Article  Google Scholar 

  20. 20.

    Ratnakumar, A. et al. Detecting positive selection within genomes: the problem of biased gene conversion. Philos. Trans. R. Soc. London B 365, 2571–2580 (2010).

    CAS  Article  Google Scholar 

  21. 21.

    Fay, J. C., Wyckoff, G. J. & Wu, C.-I. Positive and negative selection on the human genome. Genetics 158, 1227–1234 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Eyre-Walker, A. & Keightley, P. D. Estimating the rate of adaptive molecular evolution in the presence of slightly deleterious mutations and population size change. Mol. Biol. Evol. 26, 2097–2108 (2009).

    CAS  Article  Google Scholar 

  23. 23.

    Messer, P. W. & Petrov, D. A. Frequent adaptation and the McDonald–Kreitman test. Proc. Natl Acad. Sci. USA 110, 8615–8620 (2013).

    CAS  Article  Google Scholar 

  24. 24.

    James, J. E., Piganeau, G. & Eyre-Walker, A. The rate of adaptive evolution in animal mitochondria. Mol. Ecol. 25, 67–78 (2016).

    CAS  Article  Google Scholar 

  25. 25.

    Enard, D., Cai, L., Gwennap, C. & Petrov, D. A. Viruses are a dominant driver of protein adaptation in mammals. eLife 5, e12469 (2016).

    Article  Google Scholar 

  26. 26.

    Pritchard, J. K., Pickrell, J. K. & Coop, G. The genetics of human adaptation: hard sweeps, soft sweeps, and polygenic adaptation. Curr. Biol. 20, R208–R215 (2010).

    CAS  Article  Google Scholar 

  27. 27.

    Messer, P. W. & Petrov, D. A. Population genomics of rapid adaptation by soft selective sweeps. Trends Ecol. Evol. 28, 659–669 (2013).

    Article  Google Scholar 

  28. 28.

    Berg, J. J. & Coop, G. A population genetic signal of polygenic adaptation. PLoS Genet. 10, e1004412 (2014).

    Article  Google Scholar 

  29. 29.

    Schrider, D. R. & Kern, A. D. Soft sweeps are the dominant mode of adaptation in the human genome. Mol. Biol. Evol. 34, 1863–1877 (2017).

    CAS  Article  Google Scholar 

  30. 30.

    Uricchio, L. H., Kitano, H. C., Gusev, A. & Zaitlen, N. A. An evolutionary compass for detecting signals of polygenic selection and mutational bias. Evol. Lett. 3, 69–79 (2019).

    Article  Google Scholar 

  31. 31.

    Elyashiv, E. et al. A genomic map of the effects of linked selection in Drosophila. PLoS Genet. 12, e1006130 (2016).

    Article  Google Scholar 

  32. 32.

    Charlesworth, B., Morgan, M. T. & Charlesworth, D. The effect of deleterious mutations on neutral molecular variation. Genetics 134, 1289–1303 (1993).

    CAS  PubMed  PubMed Central  Google Scholar 

  33. 33.

    Barton, N. H. Linkage and the limits to natural selection. Genetics 140, 821–841 (1995).

    CAS  PubMed  PubMed Central  Google Scholar 

  34. 34.

    McVicker, G., Gordon, D., Davis, C. & Green, P. Widespread genomic signatures of natural selection in hominid evolution. PLoS Genet. 5, e1000471 (2009).

    Article  Google Scholar 

  35. 35.

    Haller, B. C. & Messer, P. W. asymptoticMK: a web-based tool for the asymptotic McDonald–Kreitman test. G3 (Bethesda) 7, 1569–1575 (2017).

    Article  Google Scholar 

  36. 36.

    Evans, S. N., Shvets, Y. & Slatkin, M. Non-equilibrium theory of the allele frequency spectrum. Theor. Popul. Biol. 71, 109–119 (2007).

    Article  Google Scholar 

  37. 37.

    Kimura, M. Diffusion models in population genetics. J. Appl. Probab. 1, 177–232 (1964).

    Article  Google Scholar 

  38. 38.

    Phung, T. N., Huber, C. D. & Lohmueller, K. E. Determining the effect of natural selection on linked neutral divergence across species. PLoS Genet. 12, e1006199 (2016).

    Article  Google Scholar 

  39. 39.

    Consortium TGP et al. A global reference for human genetic variation. Nature 526, 68 (2015).

    Article  Google Scholar 

  40. 40.

    Boyko, A. R. et al. Assessing the evolutionary impact of amino acid mutations in the human genome. PLoS Genet. 4, e1000083 (2008).

    Article  Google Scholar 

  41. 41.

    Kim, B. Y., Huber, C. D. & Lohmueller, K. E. Inference of the distribution of selection coefficients for new nonsynonymous mutations using large samples. Genetics 206, 345–361 (2017).

    Article  Google Scholar 

  42. 42.

    Eyre-Walker, A., Woolfit, M. & Phelps, T. The distribution of fitness effects of new deleterious amino acid mutations in humans. Genetics 173, 891–900 (2006).

    CAS  Article  Google Scholar 

  43. 43.

    Hill, W. G. & Robertson, A. The effect of linkage on limits to artificial selection. Genet. Res. 8, 269–294 (1966).

    CAS  Article  Google Scholar 

  44. 44.

    Smith, J. M. & Haigh, J. The hitch-hiking effect of a favourable gene. Genet. Res. 23, 23–35 (1974).

    CAS  Article  Google Scholar 

  45. 45.

    Macpherson, J. M., Sella, G., Davis, J. C. & Petrov, D. A. Genomewide spatial correspondence between nonsynonymous divergence and neutral polymorphism reveals extensive adaptation in Drosophila. Genetics 177, 2083–2099 (2007).

    CAS  Article  Google Scholar 

  46. 46.

    Castellano, D., Coronado-Zamora, M., Campos, J. L., Barbadilla, A. & Eyre-Walker, A. Adaptive evolution is substantially impeded by Hill–Robertson interference in Drosophila. Mol. Biol. Evol. 33, 442–455 (2015).

    Article  Google Scholar 

  47. 47.

    Marsden, C. D. et al. Bottlenecks and selective sweeps during domestication have increased deleterious genetic variation in dogs. Proc. Natl Acad. Sci. USA 113, 152–157 (2016).

    CAS  Article  Google Scholar 

  48. 48.

    Bullaughey, K. L., Przeworski, M. & Coop, G. No effect of recombination on the efficacy of natural selection in primates. Genome Res. 18, 544–554 (2008).

    CAS  Article  Google Scholar 

  49. 49.

    Hussin, J. G. et al. Recombination affects accumulation of damaging and disease-associated mutations in human populations. Nature Genet. 47, 400 (2015).

    CAS  Article  Google Scholar 

  50. 50.

    Jensen, J. D., Thornton, K. R. & Andolfatto, P. An approximate Bayesian estimator suggests strong, recurrent selective sweeps in Drosophila. PLoS Genet. 4, e1000198 (2008).

    Article  Google Scholar 

  51. 51.

    Hernandez, R. D. et al. Classic selective sweeps were rare in recent human evolution. Science 331, 920–924 (2011).

    CAS  Article  Google Scholar 

  52. 52.

    Enard, D., Messer, P. W. & Petrov, D. A. Genome-wide signals of positive selection in human evolution. Genome Res. 24, 885–895 (2014).

    CAS  Article  Google Scholar 

  53. 53.

    Comeron, J. M. & Kreitman, M. Population, evolutionary and genomic consequences of interference selection. Genetics 161, 389–410 (2002).

    CAS  PubMed  PubMed Central  Google Scholar 

  54. 54.

    Uricchio, L. H. & Hernandez, R. D. Robust forward simulations of recurrent hitchhiking. Genetics 197, 221–236 (2014).

    Article  Google Scholar 

  55. 55.

    Hernandez, R. D., Williamson, S. H. & Bustamante, C. D. Context dependence, ancestral misidentification, and spurious signatures of natural selection. Mol. Biol. Evol. 24, 1792–1800 (2007).

    CAS  Article  Google Scholar 

  56. 56.

    Ewing, G. B. & Jensen, J. D. The consequences of not accounting for background selection in demographic inference. Mol. Ecol. 25, 135–141 (2016).

    Article  Google Scholar 

  57. 57.

    Torres, R., Szpiech, Z. A. & Hernandez, R. D. Human demographic history has amplified the effects of background selection across the genome. PLoS Genet. 14, e1007387 (2018).

    Article  Google Scholar 

  58. 58.

    Huang, Y.-F. & Siepel, A. Estimation of allele-specific fitness effects across human protein-coding sequences and implications for disease. Preprint at bioRxiv (2018).

  59. 59.

    Huber, C. D., Kim, B. Y., Marsden, C. D. & Lohmueller, K. E. Determining the factors driving selective effects of new nonsynonymous mutations. Proc. Natl Acad. Sci. USA 114, 4465–4470 (2017).

    CAS  Article  Google Scholar 

  60. 60.

    Yates, A. et al. Ensembl 2016. Nucleic Acids Res. 44, D710–D716 (2015).

    Article  Google Scholar 

  61. 61.

    Kent, W. J. BLAT—the BLAST-like alignment tool. Genome Res. 12, 656–664 (2002).

    CAS  Article  Google Scholar 

  62. 62.

    Löytynoja, A. & Goldman, N. webPRANK: a phylogeny-aware multiple sequence aligner with interactive alignment browser. BMC Bioinformatics 11, 579 (2010).

    Article  Google Scholar 

  63. 63.

    Hernandez, R. D. & Uricchio, L. H. SFS_CODE: more efficient and flexible forward simulations. Preprint at bioRxiv (2015).

  64. 64.

    Uricchio, L. H., Torres, R., Witte, J. S. & Hernandez, R. D. Population genetic simulations of complex phenotypes with implications for rare variant association tests. Genet. Epidemiol. 39, 35–44 (2015).

    Article  Google Scholar 

  65. 65.

    Beaumont, M. A., Zhang, W. & Balding, D. J. Approximate Bayesian computation in population genetics. Genetics 162, 2025–2035 (2002).

    PubMed  PubMed Central  Google Scholar 

  66. 66.

    Tennessen, J. A. et al. Evolution and functional impact of rare coding variation from deep sequencing of human exomes. Science 337, 64–69 (2012).

    CAS  Article  Google Scholar 

Download references


We thank A. Aw, N. Rosenberg and members of the Rosenberg and Petrov laboratories for helpful discussions. L.H.U. was partially supported by an IRACDA fellowship through NIGMS grant No. K12GM088033. L.H.U was supported by National Institutes of Health grant R01 HG005855 and National Science Foundation grant DBI-1458059 (to N. Rosenberg). We also thank the Stanford/SJSU IRACDA Program for support.

Author information




Designed the research: L.H.U., D.A.P., D.E. Performed the modeling and simulations: L.H.U. Analyzed the data: L.H.U., D.A.P.. Designed inference procedure: L.H.U. Wrote the paper: L.H.U. Edited and approved paper: L.H.U., D.A.P., D.E.

Corresponding authors

Correspondence to Lawrence H. Uricchio or David Enard.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Figs. 1–20

Reporting Summary

Supplementary Data 1

Data we used to parameterize the model.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Uricchio, L.H., Petrov, D.A. & Enard, D. Exploiting selection at linked sites to infer the rate and strength of adaptation. Nat Ecol Evol 3, 977–984 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing