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The rate at which asexual populations cross fitness valleys

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  • Weissman, Daniel B.
  • Desai, Michael M.
  • Fisher, Daniel S.
  • Feldman, Marcus W.

Abstract

Complex traits often involve interactions between different genetic loci. This can lead to sign epistasis, whereby mutations that are individually deleterious or neutral combine to confer a fitness benefit. In order to acquire the beneficial genotype, an asexual population must cross a fitness valley or plateau by first acquiring the deleterious or neutral intermediates. Here, we present a complete, intuitive theoretical description of the valley-crossing process across the full spectrum of possible parameter regimes. We calculate the rate at which a population crosses a fitness valley or plateau of arbitrary width, as a function of the mutation rates, the population size, and the fitnesses of the intermediates. We find that when intermediates are close to neutral, a large population can cross even wide fitness valleys remarkably quickly, so that valley-crossing dynamics may be common even when mutations that directly increase fitness are also possible. Thus the evolutionary dynamics of large populations can be sensitive to the structure of an extended region of the fitness landscape — the population may not take directly uphill paths in favor of paths across valleys and plateaus that lead eventually to fitter genotypes. In smaller populations, we find that below a threshold size, which depends on the width of the fitness valley and the strength of selection against intermediate genotypes, valley-crossing is much less likely and hence the evolutionary dynamics are less influenced by distant regions of the fitness landscape.

Suggested Citation

  • Weissman, Daniel B. & Desai, Michael M. & Fisher, Daniel S. & Feldman, Marcus W., 2009. "The rate at which asexual populations cross fitness valleys," Theoretical Population Biology, Elsevier, vol. 75(4), pages 286-300.
  • Handle: RePEc:eee:thpobi:v:75:y:2009:i:4:p:286-300
    DOI: 10.1016/j.tpb.2009.02.006
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    References listed on IDEAS

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    1. Christoph Lengauer & Kenneth W. Kinzler & Bert Vogelstein, 1998. "Genetic instabilities in human cancers," Nature, Nature, vol. 396(6712), pages 643-649, December.
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    Cited by:

    1. Anne-Florence Bitbol & David J Schwab, 2014. "Quantifying the Role of Population Subdivision in Evolution on Rugged Fitness Landscapes," PLOS Computational Biology, Public Library of Science, vol. 10(8), pages 1-15, August.
    2. Serhii Aif & Nico Appold & Lucas Kampman & Oskar Hallatschek & Jona Kayser, 2022. "Evolutionary rescue of resistant mutants is governed by a balance between radial expansion and selection in compact populations," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    3. Osmond, Matthew M. & Otto, Sarah P., 2015. "Fitness-valley crossing with generalized parent–offspring transmission," Theoretical Population Biology, Elsevier, vol. 105(C), pages 1-16.
    4. Rendel, Mark D., 2011. "Adaptive evolutionary walks require neutral intermediates in RNA fitness landscapes," Theoretical Population Biology, Elsevier, vol. 79(1), pages 12-18.
    5. Michael D Nicholson & Tibor Antal, 2019. "Competing evolutionary paths in growing populations with applications to multidrug resistance," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-25, April.
    6. Santiago, Enrique, 2015. "Probability and time to fixation of an evolving sequence," Theoretical Population Biology, Elsevier, vol. 104(C), pages 78-85.
    7. Proulx, Stephen R., 2011. "The rate of multi-step evolution in Moran and Wright–Fisher populations," Theoretical Population Biology, Elsevier, vol. 80(3), pages 197-207.
    8. Agarwala, Atish & Fisher, Daniel S., 2019. "Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics," Theoretical Population Biology, Elsevier, vol. 130(C), pages 13-49.
    9. Van Cleve, Jeremy & Lehmann, Laurent, 2013. "Stochastic stability and the evolution of coordination in spatially structured populations," Theoretical Population Biology, Elsevier, vol. 89(C), pages 75-87.
    10. Daniel Nichol & Peter Jeavons & Alexander G Fletcher & Robert A Bonomo & Philip K Maini & Jerome L Paul & Robert A Gatenby & Alexander RA Anderson & Jacob G Scott, 2015. "Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-19, September.

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