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.
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.
DOWNLOAD A FREE, FULL PDF COPY
IF you are connected using the IP of a subscribing institution (library, laboratory, etc.)
or through its VPN.
© 2008 J.A.J. Metz. All EER articles are copyrighted by their authors. All authors endorse, permit and license Evolutionary Ecology Ltd. to grant its subscribing institutions/libraries the copying privileges specified below without additional consideration or payment to them or to Evolutionary Ecology, Ltd. These endorsements, in writing, are on file in the office of Evolutionary Ecology, Ltd. Consult authors for permission to use any portion of their work in derivative works, compilations or to distribute their work in any commercial manner.
Subscribing institutions/libraries may grant individuals the privilege of making a single copy of an EER article for non-commercial educational or non-commercial research purposes. Subscribing institutions/libraries may also use articles for non-commercial educational purposes by making any number of copies for course packs or course reserve collections. Subscribing institutions/libraries may also loan single copies of articles to non-commercial libraries for educational purposes.
All copies of abstracts and articles must preserve their copyright notice without modification.