Skip to main content
SpringerLink
Log in

Environmental Stochasticity and the Speed of Evolution

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Tsimring, L.S., Levine, H., Kessler, D.A.: RNA virus evolution via a fitness-space model. Phys. Rev. Lett. 76, 4440 (1996)

    Article  ADS  Google Scholar 

  2. Rouzine, I.M., Wakeley, J., Coffin, J.M.: The solitary wave of asexual evolution. Proc. Natl. Acad. Sci. USA 100, 587 (2003)

    Article  ADS  Google Scholar 

  3. Park, S.-C., Krug, J.: Clonal interference in large populations. Proc. Natl. Acad. Sci. USA 104, 18135 (2007)

    Article  ADS  Google Scholar 

  4. Desai, M.M., Fisher, D.S., Murray, A.W.: The speed of evolution and maintenance of variation in asexual populations. Curr. Biol. 17, 385 (2007)

    Article  Google Scholar 

  5. Bell, G.: Fluctuating selection: the perpetual renewal of adaptation in variable environments. Philos. Trans. R. Soc. Lond. B Biol. Sci. 365, 87 (2010)

    Article  Google Scholar 

  6. Bergland, A.O., Behrman, E.L., O’Brien, K.R., Schmidt, P.S., Petrov, D.A.: Genomic evidence of rapid and stable adaptive oscillations over seasonal time scales in Drosophila. PLoS Genet. 10, e1004775 (2014)

    Article  Google Scholar 

  7. Gavrilets, S.: High-dimensional fitness landscapes and speciation. In: Pigliucci, M., Müller, G.B. (eds.) Evolution: The Extended Synthesis, pp. 45–79. MIT Press, Cambridge (2010)

    Chapter  Google Scholar 

  8. Messer, P.W., Ellner, S.P., Hairston, N.G.: Can population genetics adapt to rapid evolution? Trends Genet. 32, 408 (2016)

    Article  Google Scholar 

  9. Dean, A.M., Lehman, C., Yi, X.: Fluctuating selection in the Moran. Genetics 205, 1271 (2017)

    Article  Google Scholar 

  10. Steinberg, B., Ostermeier, M.: Environmental changes bridge evolutionary valleys. Sci. Adv. 2, e1500921 (2016)

    Article  ADS  Google Scholar 

  11. Taute, K.M., Gude, S., Nghe, P., Tans, S.J.: Evolutionary constraints in variable environments, from proteins to networks. Trends Genet. 30, 192 (2014)

    Article  Google Scholar 

  12. Engen, S., Sæther, B.-E.: Evolution in fluctuating environments: decomposing selection into additive components of the Robertson–Price equation. Evolution 68, 854 (2014)

    Article  Google Scholar 

  13. Sæther, B.-E., Engen, S.: The concept of fitness in fluctuating environments. Trends Ecol. Evol. 30, 273 (2015)

    Article  Google Scholar 

  14. Cvijović, I., Good, B.H., Jerison, E.R., Desai, M.M.: Fate of a mutation in a fluctuating environment. Proc. Natl. Acad. Sci. USA 112, E5021 (2015)

    Article  ADS  Google Scholar 

  15. Lande, R., Engen, S., Saether, B.-E.: Stochastic Population Dynamics in Ecology and Conservation. Oxford University Press, Oxford (2003)

    Book  MATH  Google Scholar 

  16. Chesson, P.L., Warner, R.R.: Environmental variability promotes coexistence in lottery competitive systems. Am. Nat. 117, 923–943 (1981)

    Article  MathSciNet  Google Scholar 

  17. Hatfield, J.S., Chesson, P.L.: Diffusion analysis and stationary distribution of the two-species lottery competition model. Theor. Popul. Biol. 36, 251 (1989)

    Article  MATH  Google Scholar 

  18. Chesson, P.: Multispecies competition in variable environments. Theor. Popul. Biol. 45, 227 (1994)

    Article  MATH  Google Scholar 

  19. Fisher, R.A.: The Genetical Theory of Natural Selection: A Complete Variorum Edition. Oxford University Press, Oxford (1930)

    Book  Google Scholar 

  20. Frank, S.A., Slatkin, M.: Fisher’s fundamental theorem of natural selection. Trends Ecol. Evol. 7, 92 (1992)

    Article  Google Scholar 

  21. Ewens, W.J.: An interpretation and proof of the fundamental theorem of natural selection. Theor. Popul. Biol. 36, 167 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Crowley, P.H., Davis, H.M., Ensminger, A.L., Fuselier, L.C., Kasi Jackson, J., Nicholas McLetchie, D.: A general model of local competition for space. Ecol. Lett. 8, 176 (2005)

    Article  Google Scholar 

  23. Lloyd, D.P., Allen, R.J.: Competition for space during bacterial colonization of a surface. J. R. Soc. Interface 12, 20150608 (2015)

    Article  Google Scholar 

  24. Haeno, H., Maruvka, Y.E., Iwasa, Y., Michor, F.: Stochastic tunneling of two mutations in a population of cancer cells. PLoS ONE 8, e65724 (2013)

    Article  ADS  Google Scholar 

  25. Danino, M., Kessler, D.A., Shnerb, N.M.: Stability of two-species communities: drift, environmental stochasticity, storage effect and selection. Theor. Popul. Biol. 119, 57 (2018)

    Article  MATH  Google Scholar 

  26. Danino, M., Shnerb, N.M., Azaele, S., Kunin, W.E., Kessler, D.A.: The effect of environmental stochasticity on species richness in neutral communities. J. Theor. Biol. 409, 155 (2016)

    Article  Google Scholar 

  27. Hidalgo, J., Suweis, S., Maritan, A.: Species coexistence in a neutral dynamics with environmental noise. J. Theor. Biol. 413, 1 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  28. Crow, J.F., Kimura, M., et al.: An Introduction to Population Genetics Theory. The MIT Press, Cambridge (1970)

    MATH  Google Scholar 

  29. Gerrish, P.J., Lenski, R.E.: The fate of competing beneficial mutations in an asexual population. Genetica 102, 127 (1998)

    Article  Google Scholar 

  30. Danino, M., Shnerb, N.M.: Fixation and absorption in a fluctuating environment. J. Theor. Biol. 441, 84 (2018)

  31. Meyer, I., Shnerb, N.M.: Noise-induced stabilization and fixation in fluctuating environment. arXiv preprint arXiv:1801.05970 (2018)

  32. Fisher, R.A.: The wave of advance of advantageous genes. Ann. Hum. Genet. 7, 355 (1937)

    MATH  Google Scholar 

  33. Van Saarloos, W.: Front propagation into unstable states. Phys. Rep. 386, 29 (2003)

    Article  ADS  MATH  Google Scholar 

  34. Maruvka, Y.E., Shnerb, N.M.: Nonlocal competition and logistic growth: patterns, defects, and fronts. Phys. Rev. E 73, 011903 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  35. Fuentes, M., Kuperman, M., Kenkre, V.: Nonlocal interaction effects on pattern formation in population dynamics. Phys. Rev. Lett. 91, 158104 (2003)

    Article  ADS  Google Scholar 

  36. Hekstra, D.R., Leibler, S.: Contingency and statistical laws in replicate microbial closed ecosystems. Cell 149, 1164 (2012)

    Article  Google Scholar 

  37. Chisholm, R.A., Condit, R., Rahman, K.A., Baker, P.J., Bunyavejchewin, S., Chen, Y.-Y., Chuyong, G., Dattaraja, H., Davies, S., Ewango, C.E., et al.: Temporal variability of forest communities: empirical estimates of population change in 4000 tree species. Ecol. Lett. 17, 855 (2014)

    Article  Google Scholar 

  38. Kalyuzhny, M., Seri, E., Chocron, R., Flather, C.H., Kadmon, R., Shnerb, N.M.: Niche versus neutrality: a dynamical analysis. Am. Nat. 184, 439 (2014a)

    Article  Google Scholar 

  39. Kalyuzhny, M., Schreiber, Y., Chocron, R., Flather, C.H., Kadmon, R., Kessler, D.A., Shnerb, N.M.: Temporal fluctuation scaling in populations and communities. Ecology 95, 1701 (2014b)

    Article  Google Scholar 

  40. Fung, T., O’Dwyer, J.P., Rahman, K.A., Fletcher, C.D., Chisholm, R.A.: Reproducing static and dynamic biodiversity patterns in tropical forests: the critical role of environmental variance. Ecology 97, 1207 (2016)

    Article  Google Scholar 

  41. Wienand, K., Frey, E., Mobilia, M.: Evolution of a fluctuating population in a randomly switching environment. Phys. Rev. Lett. 119, 158301 (2017)

    Article  ADS  Google Scholar 

  42. Shtilerman, E., Kessler, D.A., Shnerb, N.M.: Emergence of structured communities through evolutionary dynamics. J. Theor. Biol. 383, 138 (2015)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

N.M.S. acknowledge the support of the ISF-NRF Singapore joint research program (Grant No. 2669/17).

Author information

Authors and Affiliations

  1. Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Matan Danino, David A. Kessler & Nadav M. Shnerb

Authors
  1. Matan Danino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David A. Kessler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nadav M. Shnerb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nadav M. Shnerb.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Danino, M., Kessler, D.A. & Shnerb, N.M. Environmental Stochasticity and the Speed of Evolution. J Stat Phys 172, 126–142 (2018). https://doi.org/10.1007/s10955-018-1990-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-018-1990-4

Keywords

Search

Navigation