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Beyond sensitivity: nonlinear perturbation analysis of transient dynamics
Article first published online: 11 JUN 2012
DOI: 10.1111/j.2041-210X.2012.00199.x
© 2012 The Authors. Methods in Ecology and Evolution © 2012 British Ecological Society
Additional Information
How to Cite
Stott, I., Hodgson, D. J. and Townley, S. (2012), Beyond sensitivity: nonlinear perturbation analysis of transient dynamics. Methods in Ecology and Evolution, 3: 673–684. doi: 10.1111/j.2041-210X.2012.00199.x
Publication History
- Issue published online: 30 JUL 2012
- Article first published online: 11 JUN 2012
- Received 6 January 2012; accepted 26 February 2012 Handling Editor: Robert Freckleton
Keywords:
- inertia;
- perturbation analysis;
- population management;
- population projection matrix;
- sensitivity;
- transfer function;
- transient dynamics
Summary
1. Perturbation analyses of population models are integral to population management: such analyses evaluate how changes in vital rates of members of the population translate to changes in population dynamics. Sensitivity and elasticity analyses of long-term (asymptotic) growth are popular, but limited: they ignore short-term (transient) dynamics and provide a linear approximation to nonlinear perturbation curves.
2. Population inertia measures how much larger or smaller a non-stable population becomes compared with an equivalent stable population, as a result of transient dynamics. We present formulae for the transfer function of population inertia, which describes nonlinear perturbation curves of transient population dynamics. The method comfortably fits into wider frameworks for analytical study of transient dynamics, and for perturbation analyses that use the transfer function approach.
3. We use case studies to illustrate how the transfer function of population inertia may be used in population management. These show that strategies based solely on asymptotic perturbation analyses can cause undesirable transient dynamics and/or fail to exploit desirable transient dynamics. This highlights the importance of considering both transient and asymptotic population dynamics in population management.
4. Our case studies also show a tendency towards marked nonlinearity in transient perturbation curves. We extend our method to measure sensitivity of population inertia and show that it often fails to capture dynamics resulting from perturbations typical of management scenarios.