Adaptive Dynamics: A Framework for Modeling the Long-Term Evolutionary Dynamics of Quantitative Traits
Michael Doebeli · Oxford University Press eBooks · 2013
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.