The accumulation of data on the genomic bases of adaptation has triggered renewed interest in theoretical models of adaptation. Among these models, Fisher's geometric model (FGM) has received a lot of attention over the past two decades. FGM is based on a continuous multidimensional phenotypic landscape, but it is mostly used for the emerging properties of individual mutation effects. Despite its apparent simplicity and limited number of parameters, FGM integrates a full model of mutation and epistatic interactions that allows the study of both beneficial and deleterious mutations and, subsequently, the fate of evolving populations. In this review, I present the different properties of FGM and the qualitative and quantitative support they have received from experimental evolution data. I then discuss how to estimate the different parameters of the model and outline some future directions to connect FGM and the molecular determinants of adaptation.


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Literature Cited

  1. Acevedo A, Brodsky L, Andino R. 2014. Mutational and fitness landscapes of an RNA virus revealed through population sequencing. Nature 505:7485686–90 [Google Scholar]
  2. Achaz G, Rodriguez-Verdugo A, Gaut BS, Tenaillon O. 2014. The reproducibility of adaptation in the light of experimental evolution with whole genome sequencing. Ecological Genomics CR Landry, N Aubin-Horth 211–31 Dordrect, Neth: Springer [Google Scholar]
  3. Atwood KC, Schneider LK, Ryan FJ. 1951. Periodic selection in Escherichia coli. Proc. Natl. Acad. Sci. USA 37:3146–55 [Google Scholar]
  4. Barrick JE, Kauth MR, Strelioff CC, Lenski RE. 2010. Escherichia coli rpoB mutants have increased evolvability in proportion to their fitness defects. Mol. Biol. Evol. 27:61338–47 [Google Scholar]
  5. Barrick JE, Lenski RE. 2013. Genome dynamics during experimental evolution. Nat. Rev. Genet. 14:12827–39 [Google Scholar]
  6. Bataillon T, Zhang T, Kassen R. 2011. Cost of adaptation and fitness effects of beneficial mutations in Pseudomonas fluorescens. Genetics 189:3939–49 [Google Scholar]
  7. Blanquart F, Achaz G, Bataillon T, Tenaillon O. 2014. Properties of selected mutations and genotypic landscapes under Fisher's geometric model. Evolution. arXiv:1405.3504 [Google Scholar]
  8. Burch CL, Chao L. 1999. Evolution by small steps and rugged landscapes in the RNA virus ϕ6. Genetics 151:3921–27 [Google Scholar]
  9. Chao L. 1990. Fitness of RNA virus decreased by Muller's ratchet. Nature 348:6300454–55 [Google Scholar]
  10. Charlesworth B. 1990. Mutation-selection balance and the evolutionary advantage of sex and recombination. Genet. Res. 55:3199–221 [Google Scholar]
  11. Chevin L-M, Decorzent G, Lenormand T. 2014. Niche dimensionality and the genetics of ecological speciation. Evolution 68:51244–56 [Google Scholar]
  12. Chevin LM, Hospital F. 2008. Selective sweep at a quantitative trait locus in the presence of background genetic variation. Genetics 180:31645–60 [Google Scholar]
  13. Chevin LM, Martin G, Lenormand T. 2010. Fisher's model and the genomics of adaptation: restricted pleiotropy, heterogenous mutation, and parallel evolution. Evolution 64:113213–31 [Google Scholar]
  14. Chou H-H, Chiu H-C, Delaney NF, Segrè D, Marx CJ. 2011. Diminishing returns epistasis among beneficial mutations decelerates adaptation. Science 332:60341190–92 [Google Scholar]
  15. Chou H-H, Delaney NF, Draghi JA, Marx CJ. 2014. Mapping the fitness landscape of gene expression uncovers the cause of antagonism and sign epistasis between adaptive mutations. PLOS Genet. 10:2e1004149 [Google Scholar]
  16. Costanzo M, Baryshnikova A, Bellay J, Kim Y, Spear ED. et al. 2010. The genetic landscape of a cell. Science 327:5964425–31 [Google Scholar]
  17. de Visser JAGM, Cooper TF, Elena SF. 2011. The causes of epistasis. Proc. R. Soc. B 278:17253617–24 [Google Scholar]
  18. de Visser JAGM, Hermisson J, Wagner GP, Ancel Meyers L, Bagheri-Chaichian H. et al. 2003. Perspective: evolution and detection of genetic robustness. Evolution 57:91959–72 [Google Scholar]
  19. Elena SF, Ekunwe L, Hajela N, Oden SA, Lenski RE. 1998. Distribution of fitness effects caused by random insertion mutations in Escherichia coli. Genetica 102/103:349–58 [Google Scholar]
  20. Elena SF, Lenski RE. 1997. Test of synergistic interactions among deleterious mutations in bacteria. Nature 390:6658395–98 [Google Scholar]
  21. Fares MA, Ruiz-Gonzalez MX, Moya A, Elena SF, Barrio E. 2002. Endosymbiotic bacteria: GroEL buffers against deleterious mutations. Nature 417:6887398 [Google Scholar]
  22. Fisher RA. 1930. The Genetical Theory of Natural Selection Oxford, UK: Oxford Univ. Press [Google Scholar]
  23. Frank SA. 2007. Maladaptation and the paradox of robustness in evolution. PLOS ONE 2:10e1021 [Google Scholar]
  24. Gillespie JH. 1983. A simple stochastic gene substitution model. Theor. Popul. Biol. 23:2202–15 [Google Scholar]
  25. Gillespie JH. 1991. The Causes of Molecular Evolution Oxford, UK: Oxford Univ. Press [Google Scholar]
  26. Gordo I, Campos PRA. 2013. Evolution of clonal populations approaching a fitness peak. Biol. Lett. 9:20120239 [Google Scholar]
  27. Gordo I, Charlesworth B. 2000. On the speed of Muller's ratchet. Genetics 156:42137–40 [Google Scholar]
  28. Gros PA, Le Nagard H, Tenaillon O. 2009. The evolution of epistasis and its links with genetic robustness, complexity and drift in a phenotypic model of adaptation. Genetics 182:277–93 [Google Scholar]
  29. Gros PA, Tenaillon O. 2009. Selection for chaperone-like mediated genetic robustness at low mutation rate: impact of drift, epistasis and complexity. Genetics 182:2555–64 [Google Scholar]
  30. Gu X. 2007. Evolutionary framework for protein sequence evolution and gene pleiotropy. Genetics 175:41813–22 [Google Scholar]
  31. Haigh J. 1978. The accumulation of deleterious genes in a population: Muller's ratchet. Theor. Popul. Biol. 14:2251–67 [Google Scholar]
  32. Hallatschek O. 2011. The noisy edge of traveling waves. Proc. Natl. Acad. Sci. USA 108:51783–87 [Google Scholar]
  33. Hartl DL, Taubes CH. 1996. Compensatory nearly neutral mutations: selection without adaptation. J. Theor. Biol. 182:3303–9 [Google Scholar]
  34. Hartl DL, Taubes CH. 1998. Towards a theory of evolutionary adaptation. Genetica 102/103:525–33 [Google Scholar]
  35. Hietpas RT, Bank C, Jensen JD, Bolon DNA. 2013. Shifting fitness landscapes in response to altered environments. Evolution 67:123512–22 [Google Scholar]
  36. Hietpas RT, Jensen JD, Bolon DNA. 2011. Experimental illumination of a fitness landscape. Proc. Natl. Acad. Sci. USA 108:197896–901 [Google Scholar]
  37. Jacquier H, Birgy A, Nagard HL, Mechulam Y, Schmitt E. et al. 2013. Capturing the mutational landscape of the beta-lactamase TEM-1. Proc. Natl. Acad. Sci. USA 110:3213067–72 [Google Scholar]
  38. Joyce P, Rokyta DR, Beisel CJ, Orr HA. 2008. A general extreme value theory model for the adaptation of DNA sequences under strong selection and weak mutation. Genetics 180:31627–43 [Google Scholar]
  39. Kauffman S. 1993. The Origin of Order New York: Oxford Univ. Press [Google Scholar]
  40. Khan AI, Dinh DM, Schneider D, Lenski RE, Cooper TF. 2011. Negative epistasis between beneficial mutations in an evolving bacterial population. Science 332:60341193–96 [Google Scholar]
  41. Kibota T, Lynch M. 1996. Estimate of the genomic mutation rate deleterious to overall fitness in E. coli. Nature 381:6584694–96 [Google Scholar]
  42. Kimura M. 1983. The Neutral Theory of Molecular Evolution Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  43. Kingman JFC. 1978. A simple model for the balance between selection and mutation. J. Appl. Probab. 15:1–12 [Google Scholar]
  44. Kondrashov AS. 1988. Deleterious mutations and the evolution of sexual reproduction. Nature 336:6198435–40 [Google Scholar]
  45. Kopp M, Hermisson J. 2009. The genetic basis of phenotypic adaptation I: fixation of beneficial mutations in the moving optimum model. Genetics 182:233–49 [Google Scholar]
  46. Krakauer DC, Plotkin JB. 2002. Redundancy, antiredundancy, and the robustness of genomes. Proc. Natl. Acad. Sci. USA 99:31405–9 [Google Scholar]
  47. Lande R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry. Evolution 33:402–16 [Google Scholar]
  48. Lande R. 1980. Genetic variation and phenotypic evolution during allopatric speciation. Am. Nat. 116:4463–79 [Google Scholar]
  49. Lande R, Arnold SJ. 1983. The measurement of selection on correlated characters. Evolution 37:61210–26 [Google Scholar]
  50. Le Nagard H, Chao L, Tenaillon O. 2011. The emergence of complexity and restricted pleiotropy in adapting networks. BMC Evol. Biol. 11:326 [Google Scholar]
  51. Le Nagard H, Tenaillon O. 2013. Selection-based estimates of complexity unravel some mechanisms and selective pressures underlying the evolution of complexity in artificial networks. Advances in Network Complexity M Dehmer, A Mowshowitz, F Emmert-Streib 41–61 Hoboken, NJ: Wiley [Google Scholar]
  52. Lenski RE, Travisano M. 1994. Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial populations. Proc. Natl. Acad. Sci. USA 91:156808–14 [Google Scholar]
  53. Lewis NE, Nagarajan H, Palsson BO. 2012. Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods. Nat. Rev. Microbiol. 10:4291–305 [Google Scholar]
  54. Lourenco J, Galtier N, Glemin S. 2011. Complexity, pleiotropy, and the fitness effect of mutations. Evolution 65:61559–71 [Google Scholar]
  55. Lourenco JM, Glemin S, Galtier N. 2013. The rate of molecular adaptation in a changing environment. Mol. Biol. Evol. 30:61292–301 [Google Scholar]
  56. Maisnier-Patin S, Berg OG, Liljas L, Andersson DI. 2002. Compensatory adaptation to the deleterious effect of antibiotic resistance in Salmonella typhimurium. Mol. Microbiol. 46:2355–66 [Google Scholar]
  57. Manna F, Martin G, Lenormand T. 2011. Fitness landscapes: an alternative theory for the dominance of mutation. Genetics 189:3923–37 [Google Scholar]
  58. Martin G. 2014. Fisher's geometrical model emerges as a property of complex integrated phenotypic networks. Genetics 197:237–55 [Google Scholar]
  59. Martin G, Elena SF, Lenormand T. 2007. Distributions of epistasis in microbes fit predictions from a fitness landscape model. Nat. Genet. 39:4555–60 [Google Scholar]
  60. Martin G, Gandon S. 2010. Lethal mutagenesis and evolutionary epidemiology. Philos. Trans. R. Soc. B 365:15481953–63 [Google Scholar]
  61. Martin G, Lenormand T. 2006a. A general multivariate extension of Fisher's geometrical model and the distribution of mutation fitness effects across species. Evolution 60:5893–907 [Google Scholar]
  62. Martin G, Lenormand T. 2006b. The fitness effect of mutations across environments: a survey in light of fitness landscape models. Evolution 60:122413–27 [Google Scholar]
  63. Martin G, Lenormand T. 2008. The distribution of beneficial and fixed mutation fitness effects close to an optimum. Genetics 179:2907–16 [Google Scholar]
  64. McCandlish DM, Epstein CL, Plotkin JB. 2014. The inevitability of unconditionally deleterious substitutions during adaptation. Evolution 68:51351–64 [Google Scholar]
  65. Moore FB, Rozen DE, Lenski RE. 2000. Pervasive compensatory adaptation in Escherichia coli. Proc. R. Soc. Lond. B 267:1442515–22 [Google Scholar]
  66. Nichols RJ, Sen S, Choo YJ, Beltrao P, Zietek M. et al. 2011. Phenotypic landscape of a bacterial cell. Cell 144:143–56 [Google Scholar]
  67. Ohno S. 1970. Evolution by Gene Duplication Berlin: Springer-Verlag [Google Scholar]
  68. Orr HA. 1998. The population genetics of adaptation: the distribution of factors fixed during adaptive evolution. Evolution 52:4935–49 [Google Scholar]
  69. Orr HA. 2000. Adaptation and the cost of complexity. Evolution 54:113–20 [Google Scholar]
  70. Orr HA. 2003. The distribution of fitness effects among beneficial mutations. Genetics 163:41519–26 [Google Scholar]
  71. Orr HA. 2006. The distribution of fitness effects among beneficial mutations in Fisher's geometric model of adaptation. J. Theor. Biol. 238:2279–85 [Google Scholar]
  72. Orr HA, Coyne JA. 1992. The genetics of adaptation: a reassessment. Am. Nat. 140:5725 [Google Scholar]
  73. Ostrowski EA, Rozen DE, Lenski RE. 2005. Pleiotropic effects of beneficial mutations in Escherichia coli. Evolution 59:112343–52 [Google Scholar]
  74. Paaby AB, Rockman MV. 2013. The many faces of pleiotropy. Trends Genet. 29:266–73 [Google Scholar]
  75. Peck JR, Barreau G, Heath SC. 1997. Imperfect genes, Fisherian mutation and the evolution of sex. Genetics 145:41171–99 [Google Scholar]
  76. Perfeito L, Fernandes L, Mota C, Gordo I. 2007. Adaptive mutations in bacteria: high rate and small effects. Science 317:5839813–15 [Google Scholar]
  77. Perfeito L, Sousa A, Bataillon T, Gordo I. 2014. Rates of fitness decline and rebound suggest pervasive epistasis. Evolution 68:1150–62 [Google Scholar]
  78. Poon A, Chao L. 2005. The rate of compensatory mutation in the DNA bacteriophage phiX174. Genetics 170:3989–99 [Google Scholar]
  79. Poon A, Otto SP. 2000. Compensating for our load of mutations: freezing the meltdown of small populations. Evolution 54:51467–79 [Google Scholar]
  80. Razeto-Barry P, Díaz J, Cotoras D, Vásquez RA. 2011. Molecular evolution, mutation size and gene pleiotropy: a geometric reexamination. Genetics 187:3877–85 [Google Scholar]
  81. Razeto-Barry P, Díaz J, Vásquez RA. 2012. The nearly neutral and selection theories of molecular evolution under the Fisher geometrical framework: substitution rate, population size, and complexity. Genetics 191:2523–34 [Google Scholar]
  82. Robins WP, Faruque SM, Mekalanos JJ. 2013. Coupling mutagenesis and parallel deep sequencing to probe essential residues in a genome or gene. Proc. Natl. Acad. Sci. USA 110:9E848–57 [Google Scholar]
  83. Rodríguez-Verdugo A, Gaut BS, Tenaillon O. 2013. Evolution of Escherichia coli rifampicin resistance in an antibiotic-free environment during thermal stress. BMC Evol. Biol. 13:150 [Google Scholar]
  84. Roze D, Blanckaert A. 2014. Epistasis, pleiotropy, and the mutation load in sexual and asexual populations. Evolution 68:1137–49 [Google Scholar]
  85. Sanjuan R, Moya A, Elena SF. 2004a. The contribution of epistasis to the architecture of fitness in an RNA virus. Proc. Natl. Acad. Sci. USA 101:4315376–79 [Google Scholar]
  86. Sanjuan R, Moya A, Elena SF. 2004b. The distribution of fitness effects caused by single-nucleotide substitutions in an RNA virus. Proc. Natl. Acad. Sci. USA 101:228396–401 [Google Scholar]
  87. Sella G, Hirsh AE. 2005. The application of statistical physics to evolutionary biology. Proc. Natl. Acad. Sci. USA 102:279541–46 [Google Scholar]
  88. Sellis D, Callahan BJ, Petrov DA, Messer PW. 2011. Heterozygote advantage as a natural consequence of adaptation in diploids. Proc. Natl. Acad. Sci. USA 108:5120666–71 [Google Scholar]
  89. Silander OK, Tenaillon O, Chao L. 2007. Understanding the evolutionary fate of finite populations: the dynamics of mutational effects. PLOS Biol. 5:4e94 [Google Scholar]
  90. Sousa A, Magalhães S, Gordo I. 2012. Cost of antibiotic resistance and the geometry of adaptation. Mol. Biol. Evol. 29:51417–28 [Google Scholar]
  91. Stearns FW. 2010. One hundred years of pleiotropy: a retrospective. Genetics 186:3767–73 [Google Scholar]
  92. Tenaillon O, Rodríguez-Verdugo A, Gaut RL, McDonald P, Bennett AF. et al. 2012. The molecular diversity of adaptive convergence. Science 335:6067457–61 [Google Scholar]
  93. Tenaillon O, Silander OK, Uzan JP, Chao L. 2007. Quantifying organismal complexity using a population genetic approach. PLOS ONE 2:e217 [Google Scholar]
  94. Trindade S, Sousa A, Gordo I. 2012. Antibiotic resistance and stress in the light of Fisher's model. Evolution 66:123815–24 [Google Scholar]
  95. Turelli M, Barton NH. 1994. Genetic and statistical analyses of strong selection on polygenic traits: What, me normal?. Genetics 138:3913–41 [Google Scholar]
  96. Wagner GP, Gabriel W. 1990. Quantitative variation in finite parthenogenetic populations: What stops Muller's ratchet in the absence of recombination?. Evolution 44:715–31 [Google Scholar]
  97. Wagner GP, Kenney-Hunt JP, Pavlicev M, Peck JR, Waxman D, Cheverud JM. 2008. Pleiotropic scaling of gene effects and the “cost of complexity.”. Nature 452:7186470–72 [Google Scholar]
  98. Wagner GP, Zhang J. 2011. The pleiotropic structure of the genotype-phenotype map: the evolvability of complex organisms. Nat. Rev. Genet. 12:3204–13 [Google Scholar]
  99. Walsh B, Blows MW. 2009. Abundant genetic variation + strong selection = multivariate genetic constraints: a geometric view of adaptation. Annu. Rev. Ecol. Evol. Syst. 40:41–59 [Google Scholar]
  100. Wang Z, Liao BY, Zhang J. 2010. Genomic patterns of pleiotropy and the evolution of complexity. Proc. Natl. Acad. Sci. USA 107:4218034–39 [Google Scholar]
  101. Waxman D, Peck JR. 1998. Pleiotropy and the preservation of perfection. Science 279:53541210–13 [Google Scholar]
  102. Waxman D, Welch JJ. 2005. Fisher's microscope and Haldane's ellipse. Am. Nat. 166:4447–57 [Google Scholar]
  103. Weinreich DM, Delaney NF, Depristo MA, Hartl DL. 2006. Darwinian evolution can follow only very few mutational paths to fitter proteins. Science 312:5770111–14 [Google Scholar]
  104. Weinreich DM, Knies JL. 2013. Fisher's geometric model of adaptation meets the functional synthesis: Data on pairwise epistasis for fitness yields insights into the shape and size of phenotype space. Evolution 67:102957–72 [Google Scholar]
  105. Welch JJ, Waxman D. 2003. Modularity and the cost of complexity. Evolution 57:81723–34 [Google Scholar]
  106. Wilke CO, Adami C. 2001. Interaction between directional epistasis and average mutational effects. Proc. R. Soc. Lond. B 268:14751469–74 [Google Scholar]
  107. Wiser MJ, Ribeck N, Lenski RE. 2013. Long-term dynamics of adaptation in asexual populations. Science 342:61641364–67 [Google Scholar]

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