An Introduction to Adaptive Dynamics Theory
- Ulf Dieckmann (International Institute for Applied Systems Analysis, Laxenburg)
Abstract
Whenever an ecological system adapts, it affects its environment, which in turn tends to modify the selection pressures acting on it: such eco-evolutionary feedback therefore lies at the heart of understanding processes of adaptation in natural systems. The theory of adaptive dynamics is geared to analyzing evolutionary dynamics in realistically complex ecological settings. Adaptive-dynamics models are derived from considering ecological interactions and phenotypic variation at the level of individuals: extending classical birth-and-death processes, these models keep track, over time, of the phenotypic composition of a population or community in which offspring phenotypes are allowed to differ from those of their parents. Adaptive-dynamics theory formally integrates four widely used classes of evolutionary processes – individual-based models, random walks, gradient-ascent dynamics, and reaction-diffusion systems – into a single conceptual and mathematical framework, facilitating switching back and forth between alternative descriptions as research questions require. Adaptive-dynamics theory extends classical evolutionary game theory in several key dimensions: evolving traits are continuous, trait dynamics are explicitly described, mutational covariances and constraints can be examined, arbitrary forms of density dependence and frequency dependence are allowed, multi-species evolution is integrated, structured population dynamics and non-equilibrium population dynamics can be investigated, and – most importantly – fitness landscapes are derived from first principles. Novel phenomena revealed by the theory of adaptive dynamics include evolutionary slowing down, evolutionary branching, and evolutionary cycling. This presentation will provide an overview of adaptive-dynamics theory for a mathematically trained audience.
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