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Methods for exact perturbation analysis

Miller, D.; Morgan, B.J.T.; Ridout, M.S.; Carey, P.D.; Rothery, P.. 2011 Methods for exact perturbation analysis. Methods in Ecology and Evolution, 2 (3). 283-288. 10.1111/j.2041-210X.2010.00074.x

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Abstract/Summary

1. The dominant eigenvalue of the population projection matrix provides the asymptotic growth rate of a population. Perturbation analysis examines how changes in vital rates affect this rate. The standard approach to evaluating the effect of a perturbation uses sensitivities and elasticities to provide a linear approximation, which is often inappropriate. 2. A transfer function approach provides the exact relationship between growth rate and perturbation. An alternative approach derives the exact solution using symbolic algebra by calculating the matrix characteristic equation in terms of the perturbation parameters and the symptotic growth rate. 3. This provides integrated sensitivities and plots of the exact relationship. The same method may be used for any perturbation structure, however complicated. 4. The simplicity of the new method is illustrated through two examples - the killer whale and the lizard orchid.

Item Type: Publication - Article
Digital Object Identifier (DOI): 10.1111/j.2041-210X.2010.00074.x
Programmes: CEH Topics & Objectives 2009 onwards > Biodiversity > BD Topic 1 - Observations, Patterns, and Predictions for Biodiversity > BD - 1.4 - Quantify and model interactions to determine impacts ...
CEH Sections: Pywell
ISSN: 2041-210X
Additional Keywords: asymptotic growth rate, characteristic equation, elasticity, Maple, numerical method, population, projection matrix, sensitivity, symbolic algebra, transfer function
NORA Subject Terms: Ecology and Environment
Date made live: 08 Jun 2011 11:40
URI: http://nora.nerc.ac.uk/id/eprint/11745

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