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Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences

Zeitschrift für angewandte Mathematik und Physik volume 67, Article number: 100 (2016) Cite this article

Abstract

Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible and illustrate that while epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.

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Author information

Authors and Affiliations

  1. School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, NSW, 2052, Australia

    Rebecca H. Chisholm

  2. School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK

    Tommaso Lorenzi

  3. Centre de mathématiques et de leurs applications, UMR 8536, CNRS, École normale supérieure de Cachan, 94235, Cachan Cedex, France

    Tommaso Lorenzi

  4. Laboratoire Jacques-Louis Lions, Équipe MAMBA, UMR 7598, CNRS INRIA, Sorbonne Universités, UPMC Univ. Paris 06, 75005, Paris, France

    Tommaso Lorenzi

  5. Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, 75013, Paris, France

    Laurent Desvillettes

  6. School of Mathematics and Statistics, University of Melbourne, Melbourne, VIC, 3010, Australia

    Barry D. Hughes

Authors
  1. Rebecca H. Chisholm
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  2. Tommaso Lorenzi
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  3. Laurent Desvillettes
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  4. Barry D. Hughes
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Corresponding author

Correspondence to Barry D. Hughes.

Additional information

This article is part of the topical collection “James Hill” guest edited by Scott McCue and Natalie Thamwattana.

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Chisholm, R.H., Lorenzi, T., Desvillettes, L. et al. Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences. Z. Angew. Math. Phys. 67, 100 (2016). https://doi.org/10.1007/s00033-016-0690-7

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  • DOI: https://doi.org/10.1007/s00033-016-0690-7

Mathematics Subject Classification

  • 35A22
  • 35K57
  • 35Q92
  • 45K05
  • 92D15

Keywords

  • Phenotypic adaption
  • Epimutations
  • Agent-based modelling
  • Integrodifferential equations