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The Hitchhiker’s Guide to Adaptive Dynamics

Author

Listed:
  • Åke Brännström

    (Department of Information and Computer Sciences, Nara Women's University, Kita-Uoya Nishimachi, Nara 630-8506, Japan
    Department of Mathematics and Mathematical Statistics, Umeå University, 901 87 Umeå, Sweden
    Evolution and Ecology Program, International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg 2361, Austria)

  • Jacob Johansson

    (Department of Biology, Theoretical Population Ecology and Evolution Group, Ecology Bldg., Lund University, 223 62 Lund, Sweden)

  • Niels Von Festenberg

    (Arbeitsgruppe für nichtlineare Dynamik am Institut für Physik, University of Potsdam, Germany)

Abstract

Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

Suggested Citation

  • Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    • Handle: RePEc:gam:jgames:v:4:y:2013:i:3:p:304-328:d:26647
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    References listed on IDEAS

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    1. U. Dieckmann & M. Doebeli, 1999. "On the Origin of Species by Sympatric Speciation," Working Papers ir99013, International Institute for Applied Systems Analysis.
    2. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
    3. Champagnat, Nicolas, 2006. "A microscopic interpretation for adaptive dynamics trait substitution sequence models," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1127-1160, August.
    4. Ulf Dieckmann & Michael Doebeli, 1999. "On the origin of species by sympatric speciation," Nature, Nature, vol. 400(6742), pages 354-357, July.
    5. P. Marrow & U. Dieckmann & R. Law, 1996. "Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective," Working Papers wp96002, International Institute for Applied Systems Analysis.
    6. Michael Doebeli & Ulf Dieckmann, 2003. "Speciation along environmental gradients," Nature, Nature, vol. 421(6920), pages 259-264, January.
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    Citations

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    Cited by:

    1. Anuraag Bukkuri & Joel S. Brown, 2021. "Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach," Games, MDPI, vol. 12(4), pages 1-19, September.
    2. Lindh, Magnus & Zhang, Lai & Falster, Daniel & Franklin, Oskar & Brännström, Åke, 2014. "Plant diversity and drought: The role of deep roots," Ecological Modelling, Elsevier, vol. 290(C), pages 85-93.
    3. Matthijs van Veelen & Benjamin Allen & Moshe Hoffman & Burton Simon & Carl Veller, 2016. "Inclusive Fitness," Tinbergen Institute Discussion Papers 16-055/I, Tinbergen Institute.
    4. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    5. Zakharenko, Roman, 2016. "Nothing else matters: Evolution of preference for social prestige," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 58-64.
    6. Kira Coder Gylling & Åke Brännström, 2018. "Effects of Relatedness on the Evolution of Cooperation in Nonlinear Public Goods Games," Games, MDPI, vol. 9(4), pages 1-13, November.

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