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The Hitchhiker’s Guide to Adaptive Dynamics
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
Department of Biology, Theoretical Population Ecology and Evolution Group, Ecology Bldg., Lund University, 223 62 Lund, Sweden
Arbeitsgruppe für nichtlineare Dynamik am Institut für Physik, University of Potsdam, Germany
* Author to whom correspondence should be addressed.
Received: 7 April 2013; in revised form: 9 June 2013 / Accepted: 11 June 2013 / Published: 24 June 2013
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.
Keywords: adaptive dynamics; evolutionary game theory; pairwise invasibility plots; evolutionarily stable strategy; evolutionary branching
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Brännström, Å.; Johansson, J.; von Festenberg, N. The Hitchhiker’s Guide to Adaptive Dynamics. Games 2013, 4, 304-328.
Brännström Å, Johansson J, von Festenberg N. The Hitchhiker’s Guide to Adaptive Dynamics. Games. 2013; 4(3):304-328.
Brännström, Åke; Johansson, Jacob; von Festenberg, Niels. 2013. "The Hitchhiker’s Guide to Adaptive Dynamics." Games 4, no. 3: 304-328.