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The Time Scale of Evolutionary Innovation

Author

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  • Krishnendu Chatterjee
  • Andreas Pavlogiannis
  • Ben Adlam
  • Martin A Nowak

Abstract

A fundamental question in biology is the following: what is the time scale that is needed for evolutionary innovations? There are many results that characterize single steps in terms of the fixation time of new mutants arising in populations of certain size and structure. But here we ask a different question, which is concerned with the much longer time scale of evolutionary trajectories: how long does it take for a population exploring a fitness landscape to find target sequences that encode new biological functions? Our key variable is the length, of the genetic sequence that undergoes adaptation. In computer science there is a crucial distinction between problems that require algorithms which take polynomial or exponential time. The latter are considered to be intractable. Here we develop a theoretical approach that allows us to estimate the time of evolution as function of We show that adaptation on many fitness landscapes takes time that is exponential in even if there are broad selection gradients and many targets uniformly distributed in sequence space. These negative results lead us to search for specific mechanisms that allow evolution to work on polynomial time scales. We study a regeneration process and show that it enables evolution to work in polynomial time.Author Summary: Evolutionary adaptation can be described as a biased, stochastic walk of a population of sequences in a high dimensional sequence space. The population explores a fitness landscape. The mutation-selection process biases the population towards regions of higher fitness. In this paper we estimate the time scale that is needed for evolutionary innovation. Our key parameter is the length of the genetic sequence that needs to be adapted. We show that a variety of evolutionary processes take exponential time in sequence length. We propose a specific process, which we call ‘regeneration processes’, and show that it allows evolution to work on polynomial time scales. In this view, evolution can solve a problem efficiently if it has solved a similar problem already.

Suggested Citation

  • Krishnendu Chatterjee & Andreas Pavlogiannis & Ben Adlam & Martin A Nowak, 2014. "The Time Scale of Evolutionary Innovation," PLOS Computational Biology, Public Library of Science, vol. 10(9), pages 1-7, September.
    • Handle: RePEc:plo:pcbi00:1003818
    DOI: 10.1371/journal.pcbi.1003818
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    References listed on IDEAS

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    1. Walter Fontana & Peter Schuster, 1998. "Continuity in Evolution: On the Nature of Transition," Working Papers 98-04-030, Santa Fe Institute.
    2. Inna S. Povolotskaya & Fyodor A. Kondrashov, 2010. "Sequence space and the ongoing expansion of the protein universe," Nature, Nature, vol. 465(7300), pages 922-926, June.
    3. W. Fontana & P. Schuster, 1998. "Continuity in Evolution: On the Nature of Transitions," Working Papers ir98039, International Institute for Applied Systems Analysis.
    4. Frank J. Poelwijk & Daniel J. Kiviet & Daniel M. Weinreich & Sander J. Tans, 2007. "Empirical fitness landscapes reveal accessible evolutionary paths," Nature, Nature, vol. 445(7126), pages 383-386, January.
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    Cited by:

    1. Cirne, Diego & Campos, Paulo R.A., 2022. "A study about the evolutionary dynamics and repeatability in time-varying fitness landscapes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

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