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Aggregation and stability in parasite—host models

Published online by Cambridge University Press:  06 April 2009

F. R. Adler  and
M. Kretzschmar
F. R. Adler
Affiliation:
Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA Section of Ecology and Systematics, Cornell University, Ithaca, NY 14853, USA
M. Kretzschmar
Affiliation:
Department of Statistics and Modelling Science, Livingstone Tower, University of Strathclyde, Glasgow G1 1XH, Scotland
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Summary

This paper generalizes the two-dimensional approximation of models of macroparasites on homogeneous populations developed by Anderson & May (1978), focusing on how the dispersion (the variance to mean ratio) of the equilibrium distribution of parasites on hosts is related to the stability of the equilibrium. We show in the approximate system that the equilibrium is stabilized not by aggregation, but by dispersion which increases as a function of the mean. Computer simulations indicate, however, that this analysis fails to capture properly the dynamics of the full system, raising the question of whether any two-dimensional system could produce an adequate approximation. We discuss the relevance of our results to several empirical studies which have examined the relation of dispersion to the mean.

Keywords

aggregationstabilityhost–parasite models
Type
Research Article
Information
Parasitology , Volume 104 , Issue 2 , April 1992 , pp. 199 - 205
Copyright
Copyright © Cambridge University Press 1992

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References

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