Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:34:44.015Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, R. M. (1982). The population dynamics and control of hookworm and roundworm infections. In Population Dynamics of Infectious Diseases (ed. Anderson, R. M.), pp. 67–108. London: Chapman and Hall.CrossRefGoogle Scholar
Anderson, R. M. & Gordon, D. M. (1982). Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities. Parasitology 85, 373–98.CrossRefGoogle ScholarPubMed
Anderson, R. M., Gordon, D. M., Crawley, M. J. & Hassell, M. P. (1982). Variability in the abundance of animal and plant species. Nature, London 296, 245–8.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1978). Regulation and stability of host parasite population interactions I. Regulatory processes. Journal of Animal Ecology 47, 219–47.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1985). Helminth infections of humans: mathematical models, population dynamics and control. Advances in Parasitology 24, 1–101.CrossRefGoogle ScholarPubMed
Evans, N., Whitfield, P. J. & Dobson, A. P. (1981). Parasite utilization of a host community: the distribution and occurrence of metacercerial cysts of Echinoparyphium recurvatum (Digenea: Echinostomatidae) in seven species of mollusc at Harting Pond, Sussex. Parasitology 83, 1–12.CrossRefGoogle Scholar
Gordon, D. M. & Rau, M. E. (1982). Possible evidence for mortality induced by the parasite Apatenom gracilis in a population of brook sticklebacks, Culaea inconstans. Parasitology 84, 41–7.CrossRefGoogle Scholar
Guyatt, H. L., Bundy, D. A. P., Medley, G. F. & Grenfell, B. T. (1990). The relationship between the frequency distribution of Ascaris lumbricoides and the prevalence and intensity of infection in human communities. Parasitology 101, 137–43.CrossRefGoogle ScholarPubMed
Hadeler, K. P. (1982). Integral equations for infections with discrete parasites; hosts with Lotka birth law. In Mathematical Ecology, Lecture Notes in Biomathematics, Vol. 54 (ed. Levin, S. A. & Hallam, T. G.), pp. 356–365. Berlin: Springer-Verlag.Google Scholar
Hassell, M. P. & Pacala, S. W. (1990). Heterogeneity and the dynamics of host–parasitoid interactions. Philosophical Transactions of the Royal Society of London, B 330, 203–20.Google Scholar
Kostizin, V. A. (1934). Symbiosis, parasitism and evolution. In The Golden Age of Theoretical Ecology, Lecture Notes in Biomathematics, Vol. 22 (ed. Scudo, F. & Ziegler, J.), pp. 369–408. Berlin: Springer-Verlag.Google Scholar
Kretzschmar, M. (1989 a). A renewal equation with a birth death process as a model for parasitic infections. Journal of Mathematical Biology 27, 191–221.CrossRefGoogle Scholar
Kretzschmar, M. (1989 b). Persistent solutions in a model for parasitic infections. Journal of Mathematical Biology 27, 549–73.CrossRefGoogle Scholar
Lemly, A. D. & Esch, G. W. (1984). Population biology of the trematode Uvulifer ambloplitis (Hughes, 1927) in juvenile bluegill sunfish, Lepomis macrochirus, and largemouth bass, Micropterus salmoides. Journal of Parasitology 70, 466–74.CrossRefGoogle Scholar
May, R. M. (1973). Stability and Complexity in Model Ecosystems. Princeton: Princeton University Press.Google ScholarPubMed
McCallum, H. I. (1982). Infectious dynamics of Ichthyophthirus multifiliis. Parasitology 85, 475–88.CrossRefGoogle Scholar
McCallum, H. I. & Anderson, R. M. (1984). Systematic temporal changes in host susceptibility to infection: demographic mechanisms. Parasitology 89, 195–208.CrossRefGoogle ScholarPubMed
Michael, E. & Bundy, D. A. P. (1989). Density dependence in establishment, growth and worm fecundity in intestinal helminthiasis: the population biology of Trichuris muris (Nematoda) infection in CBA/Ca mice. Parasitology 98, 451–8.CrossRefGoogle ScholarPubMed
Pacala, S. W. & Dobson, A. P. (1988). The relation between the number of parasites/host and host age: population dynamic causes and maximum likelihood estimation. Parasitology 96, 197–210.CrossRefGoogle ScholarPubMed
Perry, J. N. & Taylor, L. R. (1986). Stability of real interacting populations in space and time: implications, alternatives and the negative binomial kc. Journal of Animal Ecology 55, 1053–68.CrossRefGoogle Scholar
Scott, M. E. (1987). Temporal changes in aggregation: a laboratory study. Parasitology 94, 583–95.CrossRefGoogle ScholarPubMed
Scott, M. E. & Anderson, R. M. (1984). The population dynamics of Gyrodactylus bullatarudis (Monogenea) within laboratory populations of the fish host Poecilia reticulata. Parasitology 89, 159–94.CrossRefGoogle ScholarPubMed
Taylor, L. R. (1961). Aggregation, variance, and the mean. Nature, London 189, 732–5.CrossRefGoogle Scholar