Evol Ecol Res 8: 387-398 (2006)     Full PDF if your library subscribes.

Evolutionary behaviour in ecological systems with trade-offs and non-equilibrium population dynamics

A. White,1* J.V. Greenman,2 T.G. Benton3 and M. Boots4

1Department of Mathematics, School of Mathematical and Computer Sciences, Heriot Watt University, Edinburgh EH14 4AS,  2Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA,  3Earth and Biosphere Institute, School of Biology, University of Leeds, Leeds LS2 9JT and  4Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK

Author to whom all correspondence should be addressed.
e-mail: a.r.white@hw.ac.uk


Question: Do non-equilibrium (cycles or chaos) population dynamics change evolutionary behaviour when compared with equilibrium dynamics?

Mathematical methods: The theory of adaptive dynamics is applied to a discrete ecological model with an explicit trade-off between reproduction and survival. Simulation techniques are compared with the theoretical findings.

Key assumptions: Mutations in life-history parameters are assumed to be small. A separation of the ecological and evolutionary time scales is assumed. There is a feedback loop between the environment and its inhabitants.

Conclusions: With equilibrium population dynamics the shape of the trade-off can be used to characterize the evolutionary behaviour. Trade-offs with accelerating costs produce a continuously stable strategy (CSS). Trade-offs with decelerating costs produce a non-evolutionarily stable strategy (non-ESS) repellor. The characterization holds for non-equilibrium dynamics with low amplitude population oscillations. When the magnitude of the population oscillation exceeds a threshold, the characterization fails. Trade-offs with decelerating costs can produce a CSS, multiple CSSs or evolutionary branching points. The evolution of reproduction and survival parameters may be contingent on initial conditions and sensitive to small changes in other life-history parameters. Evolutionary branching allows types with distinct reproduction and survival parameters to evolve and co-exist.

Keywords: adaptive dynamics, evolutionary branching in fecundity, population oscillations, trade-offs.

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