Skip to main content

Thank you for visiting nature.com. 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.

  • Review Article
  • Published:

Empirical fitness landscapes and the predictability of evolution

Key Points

  • A fitness landscape relates the genotype of an organism to its reproductive capacity and therefore has a central role in evolutionary biology.

  • Introduced in the 1930s, the fitness landscape concept has long been used primarily as a metaphor. This has recently changed, as new experimental tools allow the systematic construction and analysis of combinations of predefined sets of genetic mutations.

  • The topography of the fitness landscape is determined by how different mutations interact in their effect on fitness. A particular type of epistasis known as sign epistasis causes the fitness landscape to be rugged, possibly with multiple peaks.

  • A survey of experimental studies shows that most empirical fitness landscapes are rugged, but the amount of ruggedness varies systematically depending on the way the mutations that form the landscape have been chosen.

  • On rugged fitness landscapes, the accessibility of mutational pathways towards higher fitness is reduced, which makes the evolutionary process more constrained and hence predictable. In addition, predictability depends on population size in ways that can be explored using mathematical modelling.

  • A key challenge for the future is to extend current fitness landscape studies to genome-wide scales and to develop models that are informed by the interactions of biomolecules.

Abstract

The genotype–fitness map (that is, the fitness landscape) is a key determinant of evolution, yet it has mostly been used as a superficial metaphor because we know little about its structure. This is now changing, as real fitness landscapes are being analysed by constructing genotypes with all possible combinations of small sets of mutations observed in phylogenies or in evolution experiments. In turn, these first glimpses of empirical fitness landscapes inspire theoretical analyses of the predictability of evolution. Here, we review these recent empirical and theoretical developments, identify methodological issues and organizing principles, and discuss possibilities to develop more realistic fitness landscape models.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Development of the fitness landscape concept.
Figure 2: Approaches for the empirical study of fitness landscapes.
Figure 3: Trends in the ruggedness of empirical fitness landscapes.
Figure 4: Evolutionary predictability is affected by population size.

Similar content being viewed by others

References

  1. Lehner, B. Genotype to phenotype: lessons from model organisms for human genetics. Nature Rev. Genet. 14, 168–178 (2013).

    Article  CAS  PubMed  Google Scholar 

  2. Wagner, G. P. & Zhang, J. The pleiotropic structure of the genotype–phenotype map: the evolvability of complex organisms. Nature Rev. Genet. 12, 204–213 (2011).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  4. de Visser, J. A. G. M., Cooper, T. F. & Elena, S. F. The causes of epistasis. Proc. R. Soc. B 278, 3617–3624 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  5. Gavrilets, S. Fitness Landscapes and the Origin of Species (Princeton Univ. Press, 2004).

    Google Scholar 

  6. Achaz, G., Rodriguez-Verdugo, A., Gaut, B. S. & Tenaillon, O. The reproducibility of adaptation in the light of experimental evolution with whole genome sequencing. Adv. Exp. Med. Biol. 781, 211–231 (2014).

    Article  PubMed  Google Scholar 

  7. Lobkovsky, A. E. & Koonin, E. V. Replaying the tape of life: quantification of the predictability of evolution. Frontiers Genet. 3, 246 (2012).

    Article  Google Scholar 

  8. Wright, S. The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proc. 6th Int. Congress Genet. 1, 356–366 (1932). This paper introduces the concept of the fitness landscape as a key component of Wright's shifting balance theory.

    Google Scholar 

  9. Colegrave, N. & Buckling, A. Microbial experiments on adaptive landscapes. BioEssays 27, 1167–1173 (2005).

    Article  PubMed  Google Scholar 

  10. Szendro, I. G., Schenk, M. F., Franke, J., Krug, J. & de Visser, J. A. G. M. Quantitative analyses of empirical fitness landscapes. J. Stat. Mech. P01005 (2013).

  11. Wright, S. Evolution in Mendelian populations. Genetics 16, 97–159 (1931).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. Haldane, J. B. S. A mathematical theory of natural selection. Part VIII. Metastable populations. Proc. Cambridge Philos. Soc. 27, 137–142 (1931).

    Article  Google Scholar 

  13. Maynard Smith, J. Natural selection and the concept of a protein space. Nature 225, 563–564 (1970). This study presents the realization that genotypic space is discrete and that mutational pathways are only accessible when they pass through functional genotypes.

    Article  Google Scholar 

  14. Kauffman, S. A. & Levin, S. Towards a general theory of adaptive walks on rugged landscapes. J. Theor. Biol. 128, 11–45 (1987). This is the first mathematical exploration of random fitness landscapes and their consequences for adaptation.

    Article  CAS  PubMed  Google Scholar 

  15. Kauffman, S. A. & Weinberger, E. D. The NK model of rugged fitness landscapes and its application to the maturation of the immune response. J. Theor. Biol. 141, 211–245 (1989).

    Article  CAS  PubMed  Google Scholar 

  16. Harms, M. J. & Thornton, J. W. Evolutionary biochemistry: revealing the historical and physical causes of protein properties. Nature Rev. Genet. 14, 559–571 (2013).

    Article  CAS  PubMed  Google Scholar 

  17. Malcolm, B. A., Wilson, K. P., Matthews, B. W., Kirsch, J. F. & Wilson, A. C. Ancestral lysozymes reconstructed, neutrality tested, and thermostability linked to hydrocarbon packing. Nature 345, 86–89 (1990). This is the first empirical analysis of a three-locus fitness landscape of lysozymes in game birds.

    Article  CAS  PubMed  Google Scholar 

  18. Barrick, J. E. & Lenski, R. E. Genome dynamics during experimental evolution. Nature Rev. Genet. 14, 827–839 (2013).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  20. Kouyos, R. D., Silander, O. K. & Bonhoeffer, S. Epistasis between deleterious mutations and the evolution of recombination. Trends Ecol. Evol. 22, 308–315 (2007).

    Article  PubMed  Google Scholar 

  21. de Visser, J. A. G. M., Hoekstra, R. F. & van den Ende, H. Test of interaction between genetic markers that affect fitness in Aspergillus niger. Evolution 51, 1499–1505 (1997).

    Article  CAS  PubMed  Google Scholar 

  22. Hall, D. W., Agan, M. & Pope, S. C. Fitness epistasis among 6 biosynthetic loci in the budding yeast Saccharomyces cerevisiae. J. Hered. 101, S75–S84 (2010).

    Article  PubMed  Google Scholar 

  23. Kondrashov, F. A. & Kondrashov, A. S. Multidimensional epistasis and the disadvantage of sex. Proc. Natl Acad. Sci. USA 98, 12089–12092 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Weinreich, D. M., Watson, R. A. & Chao, L. Perspective: sign epistasis and genetic constraint on evolutionary trajectories. Evolution 59, 1165–1174 (2005). This paper formally introduces the concept of sign epistasis and proves its equivalence with limited pathway accessibility.

    CAS  PubMed  Google Scholar 

  25. Poelwijk, F. J., Tanase-Nicola, S., Kiviet, D. J. & Tans, S. J. Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes. J. Theor. Biol. 272, 141–144 (2011).

    Article  PubMed  Google Scholar 

  26. Weinreich, D. M., Delaney, N. F., DePristo, M. A. & Hartl, D. L. Darwinian evolution can follow only very few mutational paths to fitter proteins. Science 312, 111–114 (2006). This seminal study shows how sign epistasis limits the number of accessible trajectories on a five-locus fitness landscape of β-lactamase.

    Article  CAS  PubMed  Google Scholar 

  27. Weinreich, D. M., Lan, Y., Wylie, S. C. & Heckendorn, R. B. Should evolutionary geneticists worry about higher-order epistasis? Curr. Opin. Genet. Dev. 23, 700–707 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. O'Maille, P. E. et al. Quantitative exploration of the catalytic landscape separating divergent plant sesquiterpene synthases. Nature Chem. Biol. 4, 617–623 (2008).

    Article  CAS  Google Scholar 

  29. Lee, Y.-H., Dsouza, L. M. & Fox, G. E. Equally parsimonious pathways through an RNA sequence space are not equally likely. J. Mol. Evol. 45, 278–284 (1997).

    Article  CAS  PubMed  Google Scholar 

  30. Aita, T., Iwakura, M. & Husimi, Y. A cross-section of the fitness landscape of dihydrofolate reductase. Protein Engineer. 14, 633–638 (2001).

    Article  CAS  Google Scholar 

  31. Bridgham, J. T., Carroll, S. M. & Thornton, J. W. Evolution of hormone-receptor complexity by molecular exploitation. Science 312, 97–101 (2006).

    Article  CAS  PubMed  Google Scholar 

  32. Brown, K. M. et al. Compensatory mutations restore fitness during the evolution of dihydrofolate reductase. Mol. Biol. Evol. 27, 2682–2690 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. da Silva, J., Coetzer, M., Nedellec, R., Pastore, C. & Mosier, D. E. Fitness epistasis and constraints on adaptation in a human immunodeficiency virus type 1 protein region. Genetics 185, 293–303 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Goulart, C. P. et al. Designing antibiotic cycling strategies by determining and understanding local adaptive landscapes. PLoS ONE 8, e56040 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Lozovsky, E. R. et al. Stepwise acquisition of pyrimethamine resistance in the malaria parasite. Proc. Natl Acad. Sci. USA 106, 12015–12030 (2009).

    Article  Google Scholar 

  36. Lunzer, M., Miller, S. P., Felsheim, R. & Dean, A. M. The biochemical architecture of an ancient adaptive landscape. Science 310, 499–501 (2005). This study reconstructs a fitness landscape by analysing enzyme function as a phenotype that links genotype and fitness.

    Article  CAS  PubMed  Google Scholar 

  37. Novais, A. et al. Evolutionary trajectories of β-lactamase CTX-M-1 cluster enzymes: predicting antibiotic resistance. PLoS Pathog. 6, e1000735 (2010).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  38. Tan, L., Serene, S., Chao, H. X. & Gore, J. Hidden randomness between fitness landscapes limits reverse evolution. Phys. Rev. Lett. 106, 198102 (2011).

    Article  PubMed  CAS  Google Scholar 

  39. de Vos, M. G. J., Poelwijk, F. J., Battich, N., Ndika, J. D. T. & Tans, S. J. Environmental dependence of genetic constraint. PLoS Genet. 9, e1003580 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. 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).

    Article  CAS  PubMed  Google Scholar 

  42. Franke, J., Klözer, A., de Visser, J. A. G. M. & Krug, J. Evolutionary accessibility of mutational pathways. PLoS Computat. Biol. 7, e1002134 (2011).

    Article  CAS  Google Scholar 

  43. 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  PubMed  Google Scholar 

  44. Schenk, M. F., Szendro, I. G., Salverda, M. L. M., Krug, J. & de Visser, J. A. G. M. Patterns of epistasis between beneficial mutations in an antibiotic resistance gene. Mol. Biol. Evol. 30, 1779–1787 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  Google Scholar 

  46. Pumir, A. & Shraiman, B. Epistasis in a model of molecular signal transduction. PLoS Comput. Biol. 7, e1001134 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Wilke, C. O. & Adami, C. Interaction between directional epistasis and average mutational effects. Proc. R. Soc. B 268, 1469–1474 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. You, L. & Yin, J. Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage T7. Genetics 160, 1273–1281 (2002).

    PubMed  PubMed Central  Google Scholar 

  49. DePristo, M. A., Weinreich, D. M. & Hartl, D. L. Missense meanderings in sequence space: a biophysical view of protein evolution. Nature Rev. Genet. 6, 678–687 (2005).

    Article  CAS  PubMed  Google Scholar 

  50. Watson, R. A., Weinreich, D. M. & Wakeley, J. Genome structure and the benefits of sex. Evolution 65, 523–536 (2010).

    Article  PubMed  Google Scholar 

  51. Conway Morris, S. Life's Solution: Inevitable Humans in a Lonely Universe (Cambridge Univ. Press, 2003).

    Book  Google Scholar 

  52. Gould, S. J. Wonderful Life: The Burgess Shale and the Nature of History (W. W. Norton & Company, 1989).

    Google Scholar 

  53. Lang, G. I. et al. Pervasive genetic hitchhiking and clonal interference in forty evolving yeast populations. Nature 500, 571–574 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Tenaillon, O. et al. The molecular diversity of adaptive convergence. Science 335, 457–461 (2012).

    Article  CAS  PubMed  Google Scholar 

  55. Woods, R., Schneider, D., Winkworth, C. L., Riley, M. A. & Lenski, R. E. Tests of parallel molecular evolution in a long-term experiment with Escherichia coli. Proc. Natl Acad. Sci. USA 103, 9107–9112 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. Blount, Z. D., Barrick, J. E., Davidson, C. J. & Lenski, R. E. Genomic analysis of a key innovation in an experimental Escherichia coli population. Nature 489, 513–518 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  57. Salverda, M. L. M. et al. Initial mutations direct alternative pathways of protein evolution. PLoS Genet. 7, e1001321 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Papp, B., Notebaart, R. A. & Pál, C. Systems-biology approaches for predicting genomic evolution. Nature Rev. Genet. 12, 591–602 (2011).

    Article  CAS  PubMed  Google Scholar 

  59. Gerrish, P. J. & Sniegowski, P. D. Real time forecasting of near-future evolution. J. R. Soc. Interface 9, 2268–2278 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  60. Gillespie, J. H. Some properties of finite populations experiencing strong selection and weak mutation. Am. Naturalist 121, 691–708 (1983).

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  62. Crona, K., Greene, D. & Barlow, M. The peaks and geometry of fitness landscapes. J. Theor. Biol. 317, 1–10 (2013).

    Article  PubMed  Google Scholar 

  63. Whitlock, M. C., Phillips, P. C., Moore, F. B.-G. & Tonsor, S. J. Multiple fitness peaks and epistasis. Annu. Rev. Ecol. Systemat. 26, 601–629 (1995).

    Article  Google Scholar 

  64. Hegarty, P. & Martinsson, A. On the existence of accessible paths in various models of fitness landscapes. Ann. Appl. Prob. (in the press).

  65. Schmiegelt, B. & Krug, J. Evolutionary accessibility of modular fitness landscapes. J. Statist. Phys. 154, 334–355 (2014).

    Article  Google Scholar 

  66. Roy, S. W. Probing evolutionary repeatability: neutral and double changes and the predictability of evolutionary adaptation. PLoS ONE 4, e4500 (2009).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

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

  68. Jain, K., Krug, J. & Park, S.-C. Evolutionary advantage of small populations on complex fitness landscapes. Evolution 65, 1945–1955 (2011).

    Article  PubMed  Google Scholar 

  69. Rozen, D. E., Habets, M. G. J. L., Handel, A. & de Visser, J. A. G. M. Heterogeneous adaptive trajectories of small populations on complex fitness landscapes. PLoS ONE 3, e1715 (2008).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  70. Weissman, D. B., Desai, M. M., Fisher, D. S. & Feldman, M. W. The rate at which asexual populations cross fitness valleys. Theor. Popul. Biol. 75, 286–300 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  71. Isawa, Y., Michor, F. & Nowak, M. A. Stochastic tunnels in evolutionary dynamics. Genetics 166, 1571–1579 (2004).

    Article  Google Scholar 

  72. Woods, R. J. et al. Second-order selection for evolvability in a large Escherichia coli population. Science 331, 1433–1436 (2011). This study experimentally shows the combined influence of epistasis and population dynamics on the outcome of evolution.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Szendro, I. G., Franke, J., de Visser, J. A. G. M. & Krug, J. Predictability of evolution depends non-monotonically on population size. Proc. Natl Acad. Sci. USA 110, 571–576 (2013).

    Article  CAS  PubMed  Google Scholar 

  74. Rowe, W. et al. Analysis of a complete DNA–protein affinity landscape. J. R. Soc. Interface 7, 397–408 (2010).

    Article  CAS  PubMed  Google Scholar 

  75. Pitt, J. N. & Ferré-D'Amaré, A. R. Rapid construction of empirical RNA fitness landscapes. Science 330, 376–379 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. Jiménez, J. I., Xulvi-Brunet, R., Campbell, G. W., Turk-MacLeod, R. & Chen, I. A. Comprehensive experimental fitness landscape and evolutionary network for small RNA. Proc. Natl Acad. Sci. 110, 14984–14989 (2013). This is an empirical analysis of the largest fitness landscape so far and involves >1014 RNA molecules.

    Article  PubMed  PubMed Central  Google Scholar 

  77. Hinkley, T. et al. A systems analysis of mutational effects in HIV-1 protease and reverse transcriptase. Nature Genet. 43, 487–490 (2011). This paper presents an early empirical fitness landscape of large dimensions for HIV-1 with fitness predictions for the many missing genotypes.

    Article  CAS  PubMed  Google Scholar 

  78. Kouyos, R. D. et al. Exploring the complexity of the HIV-1 fitness landscape. PLoS Genet. 8, e1002551 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Otwinowski, J. & Nemenman, I. Genotype to phenotype mapping and the fitness landscape of the E. coli lac promoter. PLoS ONE 8, e61570 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Kinney, J. B., Murugan, A., Callan, C. G. & Cox, E. C. Using deep sequencing to characterize the biophysical mechanism of a transcriptional regulatory sequence. Proc. Natl Acad. Sci. 107, 9158–9163 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  81. Provine, W. B. Sewall Wright and Evolutionary Biology (Chicago Univ. Press, 1986).

    Google Scholar 

  82. de Visser, J. A. G. M., Park, S.-C. & Krug, J. Exploring the effect of sex on empirical fitness landscapes. Am. Naturalist 174, S15–S30 (2009).

    Article  Google Scholar 

  83. Wagner, A. Neutralism and selectionism: a network-based reconciliation. Nature Rev. Genet. 9, 965–974 (2008).

    Article  CAS  PubMed  Google Scholar 

  84. Hietpas, R. T., Jensen, J. D. & Bolona, D. N. Experimental illumination of a fitness landscape. Proc. Natl Acad. Sci. USA 108, 7896–7901 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  85. Heckmann, D. et al. Predicting C4 photosynthesis evolution: modular, individually adaptive steps on a Mount Fuji fitness landscape. Cell 153, 1579–1588 (2013).

    Article  CAS  PubMed  Google Scholar 

  86. Perfeito, L., Ghozzi, S., Berg, J., Schnetz, K. & Lässig, M. Nonlinear fitness landscape of a molecular pathway. PLoS Genet. 7, e1002160 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Chan, H. S. & Bornberg-Bauer, E. Perspectives on protein evolution from simple exact models. Appl. Bioinformat. 1, 121–144 (2002).

    CAS  Google Scholar 

  88. Schuster, P. Prediction of RNA secondary structures: from theory to models and real molecules. Rep. Progress Phys. 69, 1419–1477 (2006).

    Article  CAS  Google Scholar 

  89. Mustonen, V., Kinney, J., Callan, C. G. & Lässig, M. Energy-dependent fitness: a quantitative model for the evolution of yeast transcription factor binding sites. Proc. Natl Acad. Sci. 105, 12376–12381 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  90. Heo, M., Kang, L. & Shakhnovich, E. I. Emergence of species in evolutionary “simulated annealing”. Proc. Natl Acad. Sci. USA 106, 1869–1874 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  91. Wylie, S. C. & Shakhnovich, E. I. A biophysical protein folding model accounts for most mutational fitness effects in viruses. Proc. Natl Acad. Sci. USA 108, 9916–9921 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  92. Russell, C. A. et al. The potential for respiratory droplet-transmissible A/H5N1 influenza virus to evolve in a mammalian host. Science 336, 1541–1547 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Gong, L. I., Suchard, M. A. & Bloom, J. D. Stability-mediated epistasis constrains the evolution of an influenza protein. eLife 2, e00631 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  94. Hall, B. G. Predicting evolution by in vitro evolution requires determining evolutionary pathways. Antimicrob. Agents Chemother. 46, 3035–3038 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Palmer, A. C. & Kishony, R. Understanding, predicting and manipulating the genotypic evolution of antibiotic resistance. Nature Rev. Genet. 14, 243–248 (2013).

    Article  CAS  PubMed  Google Scholar 

  96. Ferguson, Andrew, L. et al. Translating HIV sequences into quantitative fitness landscapes predicts viral vulnerabilities for rational immunogen design. Immunity 38, 606–617 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Hansen, T. F. & Wagner, G. P. Modeling genetic architecture: a multilinear theory of gene interaction. Theor. Popul. Biol. 59, 61–86 (2001).

    Article  CAS  PubMed  Google Scholar 

  98. Neher, R. A. & Shraiman, B. I. Statistical genetics and evolution of quantitative traits. Rev. Modern Phys. 83, 1283–1300 (2011).

    Article  Google Scholar 

  99. Stadler, P. F. & Happel, R. Random field models of fitness landscapes. J. Math. Biol. 38, 435–478 (1999).

    Article  Google Scholar 

  100. Neidhart, J., Szendro, I. G. & Krug, J. Exact results for amplitude spectra of fitness landscapes. J. Theor. Biol. 332, 218–227 (2013).

    Article  PubMed  Google Scholar 

  101. Kingman, J. F. C. A simple model for the balance between selection and mutation. J. Appl. Probabil. 15, 1–12 (1978).

    Article  Google Scholar 

  102. Lobkovsky, A. E., Wolf, Y. I. & Koonin, E. V. Predictability of evolutionary trajectories in fitness landscapes. PLoS Comput. Biol. 7, e1002302 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Palmer, M. E., Moudgil, A. & Feldman, M. W. Long-term evolution is surprisingly predictable in lattice proteins. J. R. Soc. Interface 10, 20130026 (2013).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  104. Ferrada, E. & Wagner, A. A comparison of genotype-phenotype maps for RNA and proteins. Biophys. J. 102, 1916–1925 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Martin, G., Elena, S. F. & Lenormand, T. Distributions of epistasis in microbes fit predictions from a fitness landscape model. Nature Genet. 33, 555–560 (2007).

    Article  CAS  Google Scholar 

  106. Rokyta, D. R. et al. Epistasis between beneficial mutations and the phenotype-to-fitness map for a ssDNA virus. PLoS Genet. 7, e1002075 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Pearson, V. M., Miller, C. R. & Rokyta, D. R. The consistency of beneficial fitness effects of mutations across diverse genetic backgrounds. PLoS ONE 7, e43864 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  108. Chou, H.-H., Delaney, N. F., Draghi, J. A. & Marx, C. J. Mapping the fitness landscape of gene expression uncovers the cause of antagonism and sign epistasis between adaptive mutations. PLoS Genet. 10, e1004149 (2014).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  109. Orr, H. A. The probability of parallel evolution. Evolution 59, 216–220 (2005).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

The authors thank I. Szendro for assistance with figure 3. They thank D. Weinreich and G. Achaz for sharing subsequently published manuscripts during the preparation phase of this Review, and four anonymous reviewers for constructive comments. This work was supported by Deutsche Forschungsgemeinschaft within SFB 680 “Molecular Basis of Evolutionary Innovation” and SPP 1590 “Probabilistic Structures in Evolution”.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to J. Arjan G.M. de Visser or Joachim Krug.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Related links

PowerPoint slides

Glossary

Fitness

A measure of reproductive success of an organism that determines the change of the corresponding genotypic frequency in the population by natural selection.

Epistasis

Any kind of genetic interaction that leads to a dependence of mutational effects on the genetic background.

Ruggedness

A measure of the complexity of fitness landscapes due to multidimensional epistasis. However, it is often used in a more restricted way to reflect the presence of multiple peaks.

Magnitude epistasis

Epistatic interactions that affect the magnitude but not the sign of mutational effects on fitness.

Hamming distance

The distance between two genotypes measured by the number of mutations in which they differ.

Unidimensional epistasis

A description of epistasis based on the curvature of the relationship between average fitness and the number of mutations.

Multidimensional epistasis

Epistatic interaction that reflects the high-dimensional nature of genotypic space.

Sign epistasis

Epistatic interaction that affects the sign of mutational effects on fitness, such that a given mutation can be deleterious or beneficial depending on genetic background.

Strong-selection–weak-mutation

(SSWM). A regime of population dynamics in which beneficial mutations are sufficiently rare to arise and fix independently, while selection is strong enough to prevent the fixation of deleterious mutations.

Direct paths

Shortest mutational pathways between genotypes, along which the distance to the target genotype decreases by one in each step. There are d! direct paths between two genotypes at Hamming distance d.

Adaptive walks

Trajectories of monomorphic populations moving through genotypic space in single mutational steps, each of which increases fitness.

'Greedy' adaptation

An adaptive walk in which the available mutation of largest effect is fixed in each step.

Stochastic tunnelling

A mechanism for the crossing of fitness 'valleys', in which the escape genotype arises by mutation from a small valley population. This mechanism is different from that proposed by Wright for crossing valleys through the fixation of deleterious mutations, which happens only under weak selection.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Visser, J., Krug, J. Empirical fitness landscapes and the predictability of evolution. Nat Rev Genet 15, 480–490 (2014). https://doi.org/10.1038/nrg3744

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nrg3744

This article is cited by

Search

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