Evol Ecol Res 10: 629-654 (2008)     Full PDF if your library subscribes.

When does evolution optimize?

J.A.J. Metz,1,2,3* S.D. Mylius4 and O. Diekmann5

1Institute of Biology and Mathematical Institute, Section of Theoretical Biology, Leiden University, Leiden, Netherlands,  2International Institute for Applied Systems Analysis, Evolution and Ecology Program, Laxenburg, Austria,  3Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland,  4RIVM, National Institute for Public Health and the Environment, Expertise Centre for Methodology and Information Services, Bilthoven, Netherlands and  5Department of Mathematics, University of Utrecht, Utrecht, Netherlands

Address all correspondence to J.A.J. Metz, Institute of Biology, Leiden University, PO Box 9561, 2300 RA Leiden, Netherlands.
e-mail: j.a.j.metz@biology.leidenuniv.nl


Aim: To elucidate the role of the eco-evolutionary feedback loop in determining evolutionarily stable life histories, with particular reference to the methodological status of the optimization procedures of classical evolutionary ecology.

Key assumption: The fitness ρ of a type depends both on its strategy X and on the environment E, ρ = ρ(X, E), where E comprises everything, biotic and abiotic, outside an individual that may influence its population dynamically relevant behaviour. Through the community dynamics, this environment is determined (up to non-evolving external drivers) by the resident strategy Xr: E = Eattr(Xr).

Procedures: Use the indicated notation to derive necessary and sufficient conditions for the existence of an evolutionary optimization principle, and for the reduction of such a principle to straightforward r- or R0-maximization. Develop quick tests to diagnose whether an eco-evolutionary model supports an optimization principle.

Results: It is necessary and sufficient for the existence of an optimization principle that the strategy affects fitness in an effectively monotone one-dimensional manner, or equivalently, that the environment affects fitness in an effectively monotone one-dimensional manner. In particular, there should exist functions ψ of the strategies and ϕ of the environments such that sign[ρ(X, E)] = sign[ψ (X) + ϕ(E)]. Pairwise invasibility plots of an eco-evolutionary model that supports an optimization principle have a special, easily recognizable shape. Natural selection just maximizes r, or R0, if and only if r(X, E) can be written as α(r(X, E0), E), or R0(X, E) can be written as exp[α(ln[R0(X, E0)], E)], with α increasing in its first argument, and E0 fixed, but otherwise arbitrary.

Conclusion: A pure optimization approach holds water only when the eco-evolutionary feedbacks are of a particularly simple kind.

Keywords: eco-evolutionary feedback, environmental dimension, evolutionary optimization, invasion fitness, life-history theory, r-optimization, R0-optimization.

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