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Stability analysis of a continuous age-structured model with specific reference to North Sea cod

Andrews, J.M. and Blythe, S.P. and Gurney, W.S.C. (2004) Stability analysis of a continuous age-structured model with specific reference to North Sea cod. Journal of Biological Systems, 12 (3). pp. 249-260. ISSN 0218-3390

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Abstract

We examine the stability of a class of continuous age-structured models. Stability borders are established for the different parameters in the model, including levels required for viability. Two examples are then given, the first is a simple model for which the analysis is straightforward. An example is then shown of the cod population in the North Sea, which involves more complicated life history structures making stability analysis more difficult. The model predicts that the North Sea population will go extinct if fishing levels remain high. We show, however, that if mortality was lowered it would eventually be possible for the population to reach a point where it was stable and within safe biological limits.