Abstract
We consider a fixed size population that undergoes an evolutionary adaptation in the weak mutation rate limit, which we model as a biased Langevin process in the genotype space. We show analytically and numerically that, if the fitness landscape has a small highly epistatic (rough) and time-varying component, then the population genotype exhibits a high effective diffusion in the genotype space and is able to escape local fitness minima with a large probability. We argue that our principal finding that even very small time-dependent fluctuations of fitness can substantially speed up evolution is valid for a wide class of models.
Article PDF
Similar content being viewed by others
References
Wright, S.: The roles of mutation, inbreeding, crossbreeding, and selection in evolution. In: Proc. Sixth Int. Congress Genetics, vol. 1, pp. 355–366. Blackwell Sci., Oxford (1932)
Schrag, S., Perrot, V., Levin, B.: Adaptation to the fitness costs of antibiotic resistance in Escherichia coli. Proc. Roy. Soc. B 264(1386), 1287–1291 (1997)
Weinreich, D., Watson, R., Chao, L.: Perspective: sign epistasis and genetic constraint on evolutionary trajectories. Evolution 59(6), 1165–1174 (2005)
Poelwijk, F., Kiviet, D., Weinreich, D., Tans, S.: Empirical fitness landscapes reveal accessible evolutionary paths. Nature 445(7126), 383–386 (2007)
de Visser, J.A., Park, S.C., Krug, J.: Exploring the effect of sex on empirical fitness landscapes. Am. Nat. 174(Suppl. 1), S15–S30 (2009)
Kimura, M.: On the probability of fixation of mutant genes in a population. Genetics 47(6), 713–719 (1962)
Barrick, J., Yu, D.S., Yoon, S.H., Jeong, H., Oh, T.K., Schneider, D., Lenski, R., Kim, J.: Genome evolution and adaptation in a long-term experiment with Escherichia coli. Nature 461(7268), 1243–1247 (2009)
Gillespie, J.H.: The Causes of Molecular Evolution. Oxford University Press, London (1994)
Mustonen, V., Lässig, M.: Molecular evolution under fitness fluctuations. Phys. Rev. Lett. 100(10), 108101 (2008)
Heckel, D.G., Roughgarden, J.: A species near its equilibrium size in a fluctuating environment can evolve a lower intrinsic rate of increase. Proc. Natl. Acad. Sci. USA 77(12), 7497–7500 (1980)
MacArthur, R., Wilson, E.: The Theory of Island Biogeography. Princeton University Press, Princeton (2001)
Lande, R., Engen, S., Saether, B.-E.: An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment. Phil. Trans. R. Soc. 364(1523), 1511–1518 (2009)
Namba, T.: Competitive co-existence in a seasonally fluctuating environment. J. Theor. Biol. 111(2), 369–386 (1984)
Cushing, J.: Periodic Lotka-Volterra competition equations. J. Math. Biol. 24(4), 381–403 (1986)
Kashtan, N., Noor, E., Alon, U.: Varying environments can speed up evolution. Proc. Natl. Acad. Sci. USA 104(34), 13711–13716 (2007)
Drummond, D., Wilke, C.: The evolutionary consequences of erroneous protein synthesis. Nat. Rev. Genet. 10(10), 715–724 (2009)
Scott, M., Gunderson, C., Mateescu, E., Zhang, Z., Hwa, T.: Interdependence of cell growth and gene expression: origins and consequences. Science 330(6007), 1099–1102 (2010)
Magnasco, M.: Forced thermal ratchets. Phys. Rev. Lett. 71(10), 1477–1481 (1993)
Tarlie, M., Astumian, R.D.: Optimal modulation of a Brownian ratchet and enhanced sensitivity to a weak external force. Proc. Natl. Acad. Sci. USA 95(5), 2039–2043 (1998)
Dubkov, A., Spagnolo, B.: Acceleration of diffusion in randomly switching potential with supersymmetry. Phys. Rev. E 72(4), 041104 (2005)
Sinitsyn, N.A., Nemenman, I.: Universal geometric theory of mesoscopic stochastic pumps and reversible ratchets. Phys. Rev. Lett. 99(22), 220408 (2007)
Vergassola, M., Avellaneda, M.: Scalar transport in compressible flow. Physica D 106(1–2), 148–166 (1997)
Weiss, G., Havlin, S.: Some properties of a random walk on a comb structure. Physica A 134(2), 474–482 (1986)
Metzler, R.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1–77 (2000)
Lubelski, A., Sokolov, I., Klafter, J.: Nonergodicity mimics inhomogeneity in single particle tracking. Phys. Rev. Lett. 100(25), 250602 (2008)
Bel, G., Nemenman, I.: Ergodic and non-ergodic anomalous diffusion in coupled stochastic processes. New J. Phys. 11(8), 083009 (2009)
Redner, S.: A Guide to First-Passage Processes. Cambridge University Press, Cambridge (2001)
Gopich, I., Szabo, A.: Theory of the statistics of kinetic transitions with application to single-molecule enzyme catalysis. J. Chem. Phys. 124(15), 154712 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Otwinowski, J., Tanase-Nicola, S. & Nemenman, I. Speeding up Evolutionary Search by Small Fitness Fluctuations. J Stat Phys 144, 367–378 (2011). https://doi.org/10.1007/s10955-011-0199-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-011-0199-6