Predicting transient amplification in perturbed ecological systems

Authors

  • STUART TOWNLEY,

    1. Mathematics Research Institute, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter EX4 4QF, UK; and
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  • DAVID CARSLAKE,

    1. Centre for Ecology and Conservation, School of Biosciences, University of Exeter, Cornwall Campus, Tremough, Penryn TR10 9EZ, UK
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  • OWEN KELLIE-SMITH,

    1. Mathematics Research Institute, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter EX4 4QF, UK; and
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  • DOMINIC MCCARTHY,

    1. Mathematics Research Institute, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter EX4 4QF, UK; and
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  • DAVID HODGSON

    1. Centre for Ecology and Conservation, School of Biosciences, University of Exeter, Cornwall Campus, Tremough, Penryn TR10 9EZ, UK
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Stuart Townley, Mathematics Research Institute, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter EX4 4QF, UK (fax + 44 1392 26-4067; e-mail s.b.townley@exeter.ac.uk).

Summary

  • 1Ecological systems are prone to disturbances and perturbations. For stage-structured populations, communities and ecosystems, measurements of system magnitude in the short term will depend on how biased the stage structure is following a disturbance.
  • 2We promote the use of the Kreiss bound, a lower bound predictor of transient system magnitude that links transient amplification to system perturbations. The Kreiss bound is a simple and powerful alternative to other indices of transient dynamics, in particular reactivity and the amplification envelope.
  • 3We apply the Kreiss bound to a discrete-time model of an endangered species and a continuous-time rainforest model.
  • 4We promote the analysis of transient amplification relative to both initial conditions and asymptotic dynamics.
  • 5Transient amplification of ecological systems, following exogenous disturbances, has been implicated in the success of invasive species, persistence of extinction debts and species coexistence.
  • 6Synthesis and applications. The Kreiss bound allows simple assessment of transient amplification in ecological systems and the response of potential amplification to changes in system parameters. Hence it is an important tool for comparative analyses of ecological systems and should provide powerful predictions of optimal population management strategies.

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