Games 2013, 4, 304-328; doi:10.3390/g4030304 OPEN ACCESS games ISSN 2073-4336 www.mdpi.com/journal/games Article The Hitchhiker’s Guide to Adaptive Dynamics Ake˚ Brannstr¨ om¨ 1,2,3,*, Jacob Johansson4 and Niels von Festenberg5 1 Department of Information and Computer Sciences, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630-8506, Japan 2 Department of Mathematics and Mathematical Statistics, Umea˚ University, 901 87 Umea,˚ Sweden 3 Evolution and Ecology Program, International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg 2361, Austria 4 Department of Biology, Theoretical Population Ecology and Evolution Group, Ecology Bldg., Lund University, 223 62 Lund, Sweden 5 Arbeitsgruppe fur¨ nichtlineare Dynamik am Institut fur¨ Physik, University of Potsdam, Germany * Author to whom correspondence should be addressed; E-Mail:
[email protected]. 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.