Empirical fitness landscapes and the predictability of evolution

Journal name:
Nature Reviews Genetics
Year published:
Published online


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.

At a glance


  1. Development of the fitness landscape concept.
    Figure 1: Development of the fitness landscape concept.

    A fitness landscape can be visualized as a 'mountainous' landscape in three dimensions with genotypes arranged in the x–y plane and fitness on the z axis (part a). The landscape shown is rugged with three fitness peaks separated by fitness 'valleys', and two imaginary evolutionary trajectories are shown by white dots and arrows. Wright's two-dimensional “field of gene combinations” (Ref. 8) is shown (part b). Fitness maximum and minimum are represented as “+” and “−”, respectively; dotted lines are contours of equal fitness. A recent example of an empirical fitness landscape involves four mutations in the antibiotic resistance enzyme β-lactamase TEM1, which cause increased resistance to cefotaxime44 (part c). Nodes represent the 24 (that is, 16) genotypes; 0 and 1 indicate wild-type and mutant amino acids, respectively. Arrows connect genotypes that differ by a single mutation and point towards genotypes with higher resistance. Bold black arrows indicate the 'greedy' walk (which substitutes the existing genotype with the largest-benefit mutation among the mutations available at each step) from wild-type (0000) to the global maximum (1010).

  2. Approaches for the empirical study of fitness landscapes.
    Figure 2: Approaches for the empirical study of fitness landscapes.

    Experimental approaches for studying small-scale fitness landscapes share three essential components: a set of mutations of interest is identified (part A); mutants are constructed to carry all 2L possible combinations of the L selected mutations (in this case, L = 3, and 0 and 1 indicate the absence and presence of the mutation, respectively) (part B); and the fitness or a fitness proxy (for example, antibiotic resistance) is measured for all genotypes. Mutations of interest can come from three different sources: from phylogenetic analyses that infer the ancestor of extant genotypes (part Aa); from microbial evolution experiments in which mutations co-occur in an evolving lineage (part Ab); or from sets of mutants that each carry a single mutation (part Ac), such as alternative mutations that cause antibiotic resistance. The a posteriori approaches (parts Aa, Ab) are less likely to find much sign epistasis because these mutations have collectively 'survived' the selective pressure, whereas the a priori approach (part Ac) does not suffer from this bias.

  3. Trends in the ruggedness of empirical fitness landscapes.
    Figure 3: Trends in the ruggedness of empirical fitness landscapes.

    Three measures that quantify the ruggedness are shown for a subset of eight available fitness landscapes: the number of fitness maxima (Nmax), the fraction of mutation pairs with sign epistasis or reciprocal sign epistasis (fepi) and the roughness/slope ratio (r/s) (Box 1). For landscapes of different sizes to be comparable, all measures were calculated for subgraphs of size four10. Each plot compares two ruggedness measures for the eight landscapes, which belong to one of three classes with respect to the type of mutations involved: collectively beneficial mutations, individually beneficial mutations or individually deleterious mutations. Currently, no landscapes exist for collectively deleterious mutations. The 4–8 mutations of each landscape affect either a single gene or multiple genes in a range of microbial species, and fitness (F), growth rate (GR) or resistance (R) is measured. For comparison, expected values for a fully additive landscape (green) and a maximally rugged landscape (red; which is represented by the house-of-cards (HoC) model) are shown. Although the three measures capture different types of epistasis, they correlate reasonably well. The available empirical fitness landscapes show considerable ruggedness, especially if the combined fitness effect of mutations is unknown.

  4. Evolutionary predictability is affected by population size.
    Figure 4: Evolutionary predictability is affected by population size.

    Mutational trajectories are shown for populations of small, intermediate and large sizes on a rugged three-locus fitness landscape with global maximum 111 and local maximum 100. Nodes represent genotypes (in which 0 and 1 indicate the absence and presence of each of three mutations, respectively), and edges connect genotypes that differ in a single mutation. Arrows show mutational trajectories, which start from the wild type (000) and are realized in a limited time period that is sufficient for the fixation of a single mutation in populations of small or intermediate sizes. The width of the arrows indicates the repeatability of trajectories, which is a measure of evolutionary predictability. The small population is in the strong-selection–weak-mutation (SSWM) regime, in which different trajectories are realized owing to the chance occurrence and subsequent fixation of mutations, and predictability is therefore low. At intermediate population size, clonal interference causes the preferential fixation of the mutation with the largest benefit among the three available mutations, thereby maximizing predictability. In even larger populations, multiple mutations may sometimes fix simultaneously, which allows 'valley crossing' and decreases predictability.


  1. Lehner, B. Genotype to phenotype: lessons from model organisms for human genetics. Nature Rev. Genet. 14, 168178 (2013).
  2. Wagner, G. P. & Zhang, J. The pleiotropic structure of the genotype–phenotype map: the evolvability of complex organisms. Nature Rev. Genet. 12, 204213 (2011).
  3. Phillips, P. C. Epistasis — the essential role of gene interactions in the structure and evolution of genetic systems. Nature Rev. Genet. 9, 855867 (2008).
  4. de Visser, J. A. G. M., Cooper, T. F. & Elena, S. F. The causes of epistasis. Proc. R. Soc. B 278, 36173624 (2011).
  5. Gavrilets, S. Fitness Landscapes and the Origin of Species (Princeton Univ. Press, 2004).
  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, 211231 (2014).
  7. Lobkovsky, A. E. & Koonin, E. V. Replaying the tape of life: quantification of the predictability of evolution. Frontiers Genet. 3, 246 (2012).
  8. Wright, S. The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proc. 6th Int. Congress Genet. 1, 356366 (1932).
    This paper introduces the concept of the fitness landscape as a key component of Wright's shifting balance theory.
  9. Colegrave, N. & Buckling, A. Microbial experiments on adaptive landscapes. BioEssays 27, 11671173 (2005).
  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, 97159 (1931).
  12. Haldane, J. B. S. A mathematical theory of natural selection. Part VIII. Metastable populations. Proc. Cambridge Philos. Soc. 27, 137142 (1931).
  13. Maynard Smith, J. Natural selection and the concept of a protein space. Nature 225, 563564 (1970).
    This study presents the realization that genotypic space is discrete and that mutational pathways are only accessible when they pass through functional genotypes.
  14. Kauffman, S. A. & Levin, S. Towards a general theory of adaptive walks on rugged landscapes. J. Theor. Biol. 128, 1145 (1987).
    This is the first mathematical exploration of random fitness landscapes and their consequences for adaptation.
  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, 211245 (1989).
  16. Harms, M. J. & Thornton, J. W. Evolutionary biochemistry: revealing the historical and physical causes of protein properties. Nature Rev. Genet. 14, 559571 (2013).
  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, 8689 (1990).
    This is the first empirical analysis of a three-locus fitness landscape of lysozymes in game birds.
  18. Barrick, J. E. & Lenski, R. E. Genome dynamics during experimental evolution. Nature Rev. Genet. 14, 827839 (2013).
  19. Kondrashov, A. S. Deleterious mutations and the evolution of sexual reproduction. Nature 336, 435440 (1988).
  20. Kouyos, R. D., Silander, O. K. & Bonhoeffer, S. Epistasis between deleterious mutations and the evolution of recombination. Trends Ecol. Evol. 22, 308315 (2007).
  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, 14991505 (1997).
  22. Hall, D. W., Agan, M. & Pope, S. C. Fitness epistasis among 6 biosynthetic loci in the budding yeast Saccharomyces cerevisiae. J. Hered. 101, S75S84 (2010).
  23. Kondrashov, F. A. & Kondrashov, A. S. Multidimensional epistasis and the disadvantage of sex. Proc. Natl Acad. Sci. USA 98, 1208912092 (2001).
  24. Weinreich, D. M., Watson, R. A. & Chao, L. Perspective: sign epistasis and genetic constraint on evolutionary trajectories. Evolution 59, 11651174 (2005).
    This paper formally introduces the concept of sign epistasis and proves its equivalence with limited pathway accessibility.
  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, 141144 (2011).
  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, 111114 (2006).
    This seminal study shows how sign epistasis limits the number of accessible trajectories on a five-locus fitness landscape of β-lactamase.
  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, 700707 (2013).
  28. O'Maille, P. E. et al. Quantitative exploration of the catalytic landscape separating divergent plant sesquiterpene synthases. Nature Chem. Biol. 4, 617623 (2008).
  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, 278284 (1997).
  30. Aita, T., Iwakura, M. & Husimi, Y. A cross-section of the fitness landscape of dihydrofolate reductase. Protein Engineer. 14, 633638 (2001).
  31. Bridgham, J. T., Carroll, S. M. & Thornton, J. W. Evolution of hormone-receptor complexity by molecular exploitation. Science 312, 97101 (2006).
  32. Brown, K. M. et al. Compensatory mutations restore fitness during the evolution of dihydrofolate reductase. Mol. Biol. Evol. 27, 26822690 (2010).
  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, 293303 (2010).
  34. Goulart, C. P. et al. Designing antibiotic cycling strategies by determining and understanding local adaptive landscapes. PLoS ONE 8, e56040 (2013).
  35. Lozovsky, E. R. et al. Stepwise acquisition of pyrimethamine resistance in the malaria parasite. Proc. Natl Acad. Sci. USA 106, 1201512030 (2009).
  36. Lunzer, M., Miller, S. P., Felsheim, R. & Dean, A. M. The biochemical architecture of an ancient adaptive landscape. Science 310, 499501 (2005).
    This study reconstructs a fitness landscape by analysing enzyme function as a phenotype that links genotype and fitness.
  37. Novais, A. et al. Evolutionary trajectories of β-lactamase CTX-M-1 cluster enzymes: predicting antibiotic resistance. PLoS Pathog. 6, e1000735 (2010).
  38. Tan, L., Serene, S., Chao, H. X. & Gore, J. Hidden randomness between fitness landscapes limits reverse evolution. Phys. Rev. Lett. 106, 198102 (2011).
  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).
  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, 11901192 (2011).
  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, 11931196 (2011).
  42. Franke, J., Klözer, A., de Visser, J. A. G. M. & Krug, J. Evolutionary accessibility of mutational pathways. PLoS Computat. Biol. 7, e1002134 (2011).
  43. Whitlock, M. C. & Bourguet, D. Factors affecting the genetic load in Drosophila: synergistic epistasis and correlations among fitness components. Evolution 54, 16541660 (2000).
  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, 17791787 (2013).
  45. Draghi, J. A. & Plotkin, J. B. Selection biases the prevalence and type of epistasis along adaptive trajectories. Evolution 67, 31203131 (2013).
  46. Pumir, A. & Shraiman, B. Epistasis in a model of molecular signal transduction. PLoS Comput. Biol. 7, e1001134 (2011).
  47. Wilke, C. O. & Adami, C. Interaction between directional epistasis and average mutational effects. Proc. R. Soc. B 268, 14691474 (2001).
  48. You, L. & Yin, J. Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage T7. Genetics 160, 12731281 (2002).
  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, 678687 (2005).
  50. Watson, R. A., Weinreich, D. M. & Wakeley, J. Genome structure and the benefits of sex. Evolution 65, 523536 (2010).
  51. Conway Morris, S. Life's Solution: Inevitable Humans in a Lonely Universe (Cambridge Univ. Press, 2003).
  52. Gould, S. J. Wonderful Life: The Burgess Shale and the Nature of History (W. W. Norton & Company, 1989).
  53. Lang, G. I. et al. Pervasive genetic hitchhiking and clonal interference in forty evolving yeast populations. Nature 500, 571574 (2013).
  54. Tenaillon, O. et al. The molecular diversity of adaptive convergence. Science 335, 457461 (2012).
  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, 91079112 (2006).
  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, 513518 (2012).
  57. Salverda, M. L. M. et al. Initial mutations direct alternative pathways of protein evolution. PLoS Genet. 7, e1001321 (2011).
  58. Papp, B., Notebaart, R. A. & Pál, C. Systems-biology approaches for predicting genomic evolution. Nature Rev. Genet. 12, 591602 (2011).
  59. Gerrish, P. J. & Sniegowski, P. D. Real time forecasting of near-future evolution. J. R. Soc. Interface 9, 22682278 (2012).
  60. Gillespie, J. H. Some properties of finite populations experiencing strong selection and weak mutation. Am. Naturalist 121, 691708 (1983).
  61. Orr, H. A. The genetic theory of adaptation: a brief history. Nature Rev. Genet. 6, 119127 (2005).
  62. Crona, K., Greene, D. & Barlow, M. The peaks and geometry of fitness landscapes. J. Theor. Biol. 317, 110 (2013).
  63. Whitlock, M. C., Phillips, P. C., Moore, F. B.-G. & Tonsor, S. J. Multiple fitness peaks and epistasis. Annu. Rev. Ecol. Systemat. 26, 601629 (1995).
  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, 334355 (2014).
  66. Roy, S. W. Probing evolutionary repeatability: neutral and double changes and the predictability of evolutionary adaptation. PLoS ONE 4, e4500 (2009).
  67. Gerrish, P. J. & Lenski, R. E. The fate of competing beneficial mutations in an asexual population. Genetica 102103, 127144 (1998).
  68. Jain, K., Krug, J. & Park, S.-C. Evolutionary advantage of small populations on complex fitness landscapes. Evolution 65, 19451955 (2011).
  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).
  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, 286300 (2009).
  71. Isawa, Y., Michor, F. & Nowak, M. A. Stochastic tunnels in evolutionary dynamics. Genetics 166, 15711579 (2004).
  72. Woods, R. J. et al. Second-order selection for evolvability in a large Escherichia coli population. Science 331, 14331436 (2011).
    This study experimentally shows the combined influence of epistasis and population dynamics on the outcome of evolution.
  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, 571576 (2013).
  74. Rowe, W. et al. Analysis of a complete DNA–protein affinity landscape. J. R. Soc. Interface 7, 397408 (2010).
  75. Pitt, J. N. & Ferré-D'Amaré, A. R. Rapid construction of empirical RNA fitness landscapes. Science 330, 376379 (2010).
  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, 1498414989 (2013).
    This is an empirical analysis of the largest fitness landscape so far and involves >1014 RNA molecules.
  77. Hinkley, T. et al. A systems analysis of mutational effects in HIV-1 protease and reverse transcriptase. Nature Genet. 43, 487490 (2011).
    This paper presents an early empirical fitness landscape of large dimensions for HIV-1 with fitness predictions for the many missing genotypes.
  78. Kouyos, R. D. et al. Exploring the complexity of the HIV-1 fitness landscape. PLoS Genet. 8, e1002551 (2012).
  79. Otwinowski, J. & Nemenman, I. Genotype to phenotype mapping and the fitness landscape of the E. coli lac promoter. PLoS ONE 8, e61570 (2013).
  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, 91589163 (2010).
  81. Provine, W. B. Sewall Wright and Evolutionary Biology (Chicago Univ. Press, 1986).
  82. de Visser, J. A. G. M., Park, S.-C. & Krug, J. Exploring the effect of sex on empirical fitness landscapes. Am. Naturalist 174, S15S30 (2009).
  83. Wagner, A. Neutralism and selectionism: a network-based reconciliation. Nature Rev. Genet. 9, 965974 (2008).
  84. Hietpas, R. T., Jensen, J. D. & Bolona, D. N. Experimental illumination of a fitness landscape. Proc. Natl Acad. Sci. USA 108, 78967901 (2011).
  85. Heckmann, D. et al. Predicting C4 photosynthesis evolution: modular, individually adaptive steps on a Mount Fuji fitness landscape. Cell 153, 15791588 (2013).
  86. Perfeito, L., Ghozzi, S., Berg, J., Schnetz, K. & Lässig, M. Nonlinear fitness landscape of a molecular pathway. PLoS Genet. 7, e1002160 (2011).
  87. Chan, H. S. & Bornberg-Bauer, E. Perspectives on protein evolution from simple exact models. Appl. Bioinformat. 1, 121144 (2002).
  88. Schuster, P. Prediction of RNA secondary structures: from theory to models and real molecules. Rep. Progress Phys. 69, 14191477 (2006).
  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, 1237612381 (2008).
  90. Heo, M., Kang, L. & Shakhnovich, E. I. Emergence of species in evolutionary “simulated annealing”. Proc. Natl Acad. Sci. USA 106, 18691874 (2009).
  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, 99169921 (2011).
  92. Russell, C. A. et al. The potential for respiratory droplet-transmissible A/H5N1 influenza virus to evolve in a mammalian host. Science 336, 15411547 (2012).
  93. Gong, L. I., Suchard, M. A. & Bloom, J. D. Stability-mediated epistasis constrains the evolution of an influenza protein. eLife 2, e00631 (2013).
  94. Hall, B. G. Predicting evolution by in vitro evolution requires determining evolutionary pathways. Antimicrob. Agents Chemother. 46, 30353038 (2002).
  95. Palmer, A. C. & Kishony, R. Understanding, predicting and manipulating the genotypic evolution of antibiotic resistance. Nature Rev. Genet. 14, 243248 (2013).
  96. Ferguson, Andrew, L. et al. Translating HIV sequences into quantitative fitness landscapes predicts viral vulnerabilities for rational immunogen design. Immunity 38, 606617 (2013).
  97. Hansen, T. F. & Wagner, G. P. Modeling genetic architecture: a multilinear theory of gene interaction. Theor. Popul. Biol. 59, 6186 (2001).
  98. Neher, R. A. & Shraiman, B. I. Statistical genetics and evolution of quantitative traits. Rev. Modern Phys. 83, 12831300 (2011).
  99. Stadler, P. F. & Happel, R. Random field models of fitness landscapes. J. Math. Biol. 38, 435478 (1999).
  100. Neidhart, J., Szendro, I. G. & Krug, J. Exact results for amplitude spectra of fitness landscapes. J. Theor. Biol. 332, 218227 (2013).
  101. Kingman, J. F. C. A simple model for the balance between selection and mutation. J. Appl. Probabil. 15, 112 (1978).
  102. Lobkovsky, A. E., Wolf, Y. I. & Koonin, E. V. Predictability of evolutionary trajectories in fitness landscapes. PLoS Comput. Biol. 7, e1002302 (2011).
  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).
  104. Ferrada, E. & Wagner, A. A comparison of genotype-phenotype maps for RNA and proteins. Biophys. J. 102, 19161925 (2012).
  105. Martin, G., Elena, S. F. & Lenormand, T. Distributions of epistasis in microbes fit predictions from a fitness landscape model. Nature Genet. 33, 555560 (2007).
  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).
  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).
  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).
  109. Orr, H. A. The probability of parallel evolution. Evolution 59, 216220 (2005).

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  1. Laboratory of Genetics, Wageningen University, Droevendaalsesteeg 1, 6708PB Wageningen, The Netherlands.

    • J. Arjan G.M. de Visser
  2. Institute for Theoretical Physics, University of Cologne, Zülpicher Str. 77, 50937 Köln, Germany.

    • Joachim Krug

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  • J. Arjan G.M. de Visser

    J. Arjan G. M. de Visser is an evolutionary geneticist who uses experiments with microorganisms to address the causes and constraints of evolution. He graduated in 1996 from Wageningen University, the Netherlands, where he carried out research on experimental tests of epistasis among deleterious mutations. During postdoctoral work at Michigan State University, East Lansing, USA, he studied evolutionary consequences of high mutation rates. Since 2001, he is on the faculty at Wageningen University, where he studies, among others, the evolutionary causes and consequences of empirical fitness landscapes. Arjan G. M. de Visser's homepage.

  • Joachim Krug

    Joachim Krug is a theoretical physicist with a background in statistical physics. After graduating from Ludwig Maximilians Universität in Munich, Germany, in 1989, he held appointments at the International Business Machines (IBM) T. J. Watson Research Center, New York, USA; Forschungszentrum Jülich, Germany; and the University of Duisburg-Essen, Germany. He entered the field of evolutionary biology when he moved to the University of Cologne, Germany, in 2004, and is primarily interested in developing models of adaptation in the context of microbial evolution. Joachim Krug's homepage.

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