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The Adaptive Landscape in Evolutionary Biology$
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Erik Svensson and Ryan Calsbeek

Print publication date: 2013

Print ISBN-13: 9780199595372

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199595372.001.0001

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Adaptive Dynamics: A Framework for Modeling the Long-Term Evolutionary Dynamics of Quantitative Traits

Adaptive Dynamics: A Framework for Modeling the Long-Term Evolutionary Dynamics of Quantitative Traits

Chapter:
(p.227) Chapter 14 Adaptive Dynamics: A Framework for Modeling the Long-Term Evolutionary Dynamics of Quantitative Traits
Source:
The Adaptive Landscape in Evolutionary Biology
Author(s):

Michael Doebeli

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199595372.003.0014

To describe evolution in the general case of frequency-dependent selection, one needs a mathematical framework that describes how fitness landscapes change dynamically as a consequence of evolutionary change. Adaptive dynamics provides such a framework. Adaptive dynamics can be derived from first principles governing individual-based ecological processes and is based on the notion of invasion fitness, a fitness definition that has a precise ecological meaning. Adaptive dynamics describes evolution as a dynamical system in phenotype space, with the evolving trait values as dynamic variables whose change is governed by dynamically changing fitness landscapes. This chapter reviews some fundamental definitions and properties of adaptive dynamics, including the definitions of the two central notions of stability: convergence stability and evolutionary stability. It presents examples that illustrate the definition of invasion fitness and the paradigmatic dynamic regimes that can occur when bifurcations lead to the loss of either convergence or evolutionary stability. Finally, it illustrates the importance of an ecologically based fitness definition by briefly describing the phenomenon of evolutionary suicide.

Keywords:   frequency-depdendent selction, evolutionary change, invasion fitness, adaptive dynamics, evolutionary stability, evolutionary suicide

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