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.\ud \ud 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.\ud \ud 3. This provides integrated sensitivities and plots of the exact relationship. The same method may be used for any perturbation structure, however complicated.\ud \ud 4. The simplicity of the new method is illustrated through two examples - the killer whale and the lizard orchid
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