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Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest

D. Ludwig, D. D. Jones and C. S. Holling
Journal of Animal Ecology
Vol. 47, No. 1 (Feb., 1978), pp. 315-332
DOI: 10.2307/3939
Stable URL: http://www.jstor.org/stable/3939
Page Count: 18
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Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest
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Abstract

(1) A procedure has been described for the qualitative analysis of insect outbreak systems using spruce budworm and balsam fir as an example. This consists of separating the state variables into fast and slow categories. (2) The dynamics of the fast variables are analysed first, holding the slow variables fixed. Then the dynamics of the slow variables are analysed, with the fast variables held at corresponding equilibrium values. If there are several such equilibria, there are several possibilities for the slow dynamics. (3) In the case of the budworm, this analysis exhibits the possibility of `relaxation oscillations' which are familiar from theory of the Van der Pol oscillator. In more modern terminology, the jumps of the system are governed by a cusp catastrophe. (4) Such an analysis can be made on the basis of qualitative information only, but additional insight emerges when parameter ranges are defined by the kind of information typically available from an experienced biologist. (5) At the least this can be a guide to assess subsequent priorities for both research and policy.

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