Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T04:57:56.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode–ruminant interactions as a case study

Published online by Cambridge University Press:  06 April 2009

B. T. Grenfell ,
K. Wilson ,
V. S. Isham ,
H. E. G. Boyd  and
K. Dietz
B. T. Grenfell
Affiliation:
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
K. Wilson
Affiliation:
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
V. S. Isham
Affiliation:
Department of Statistical Science, University College London, Cower Street, London WCIE 6BT, UK
H. E. G. Boyd
Affiliation:
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
K. Dietz
Affiliation:
Department of Medical Biometry, University of Tübingen, 72070 Tübingen, Westbahnhofstr. 55, Germany
Get access Rights & Permissions [Opens in a new window]

Summary

The characteristically aggregated frequency distribution of macroparasites in their hosts is a key feature of host–parasite population biology. We begin with a brief review of the theoretical literature concerning parasite aggregation. Though this work has illustrated much about both the sources and impact of parasite aggregation, there is still no definitive analysis of both these aspects. We then go on to illustrate the use of one approach to this problem – the construction of Moment Closure Equations (MCEs), which can be used to represent both the mean and second moments (variances and covariances) of the distribution of different parasite stages and phenomenological measures of host immunity. We apply these models to one of the best documented interactions involving free-living animal hosts – the interaction between trichostrongylid nematodes and ruminants. The analysis compares patterns of variability in experimental infections of Teladorsagia circumcincta in sheep with the equivalent wildlife situation – the epidemiology of T. circumcincta in a feral population of Soay sheep on St Kilda, Outer Hebrides. We focus on the relationship between mean parasite load and aggregation (inversely measured by the negative binomial parameter, k) for cohorts of hosts. The analysis and empirical data indicate that k tracks the increase and subsequent decline in the mean burden with host age. We discuss this result in terms of the degree of heterogeneity in the impact of host immunity or parasite-induced mortality required to shorten the tail of the parasite distribution (and therefore increase k) in older animals. The model is also used to analyse the relationship between estimated worm and egg counts (since only the latter are often available for wildlife hosts). Finally, we use these results to review directions for future work on the nature and impact of parasite aggregation.

Keywords

Wildlife diseasesparasiteaggregationTeladorsagia circumcinctasheepSt Kildamodelnegative binomial distributionmoment closure equationsegg countsimmunity
Type
Research Article
Information
Parasitology , Volume 111 , Supplement S1: Ecology of wildlife host-parasite interactions , January 1995 , pp. S135 - S151
Copyright
Copyright © Cambridge University Press 1995

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

Adler, F. R. & Kretzschmar, M. (1992). Aggregation and stability in parasite–host models. Parasitology 104, 199–205.Google Scholar
Anderson, R. M. & Gordon, D. (1982). Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities. Parsitology 85, 373–8.Google Scholar
Anderson, R. M. & May, R. M. (1978 a). 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. (1978 b). Regulation and stability of host–parasite population interactions. II. Destabilising processes. Journal of Animal Ecology 47, 248–67.Google Scholar
Anderson, R. M. & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford: O. U. P.Google Scholar
Anderson, R. M. & Medley, G. F. (1985 a). Community control of helminth infections of man by mass and selective chemotherapy. Parasitology 90, 629–60.CrossRefGoogle Scholar
Anderson, R. M. & Medley, G. F. (1985 b). Community control of helminth infections of mass and selective chemotherapy. Parasitology 90, 629–60.Google Scholar
Anderson, R. M. & Michel, J. (1977). Density-dependent survival in populations of Ostertagia ostertagi. International Journal for Parasitology 7, 321–9.Google Scholar
Coyne, M. & Smith, G. (1994). Trichostrongylid parasites of domestic ruminants. In Parasitic and Infectious Diseases: Epidemiology and Ecology (ed. Scott, M. & Smith, G.). San Diego: Academic Press.Google Scholar
Crofton, H. (1971). A quantative approach to parasitism. Parasitology 62, 179–93.Google Scholar
Dietz, K. (1982). Overall population patterns in the transmission cycle of infectious agents. In Population Biology of Infectious Diseases (ed. Anderson, R. & May, R.). Berlin: Springer.Google Scholar
Grenfell, B. T. (1988). Gastrointestinal nematode parasites and the stability and productivity of intensive ruminant grazing systems. Philosophical Transactions of the Royal Society of London Series B – Biological Sciences 321, 541–63.Google ScholarPubMed
Grenfell, B. T. (1992). Parasitism and the dynamics of ungulate grazing systems. American Naturalist 139, 907–29.Google Scholar
Grenfell, B. T., Das, P., Rajagopalan, P. & Bundy, D. (1990). Frequency distribution of lymphatic filariasis microfilariae in human populations: population processes and statistical estimation. Parasitology 101, 417–27.CrossRefGoogle ScholarPubMed
Grenfell, B. T., Dietz, K. & Roberts, M. (1995). Modelling the immuno-epidemiology of macroparasites in wildlife host populations. In Ecology of Infectious Diseases in Natural Populations (ed. Grenfell, B. T. & Dobson, A.). Cambridge. C. U. P.Google Scholar
Grenfell, B. T., Price, O., Albon, S. & Clutton-Brock, T. (1992). Overcompensation and population cycles in an ungulate. Nature 355, 245–8.CrossRefGoogle Scholar
Grenfell, B. T., Smith, G. & Anderson, R. (1987 a). A mathematical model of the population biology of Ostertagia ostertagi in calves and yearlings. Parasitology 95, 389–406.CrossRefGoogle ScholarPubMed
Grenfell, B. T., Smith, G. & Anderson, R. (1987 b). The regulation of Ostertagia ostertagi populations in calves: the effect of past and current experience of infection on proportional establishment and parasite survival. Parasitology 95, 363–72.Google Scholar
Gulland, F. (1992). The role of nematode parasites in Soay sheep (Ovis aries L.) mortality during a population crash. Parasitology 105, 493–503.Google Scholar
Gulland, F. & Fox, M. (1992). Epidemiology of nematode infections in Soay sheep (Ovis aries L.) on St Kilda. Parasitology 105, 485–92.Google Scholar
Hadeler, K. & Dietz, K. (1983). Nonlinear hyperbolic partial differential equations for the dynamics of parasite populations. Computing and Mathematics with Applications 3, 415–30.Google Scholar
Hong, C., Michel, J. & Lancaster, M. (1987). Observations on the dynamics of worm burdens in lambs infected daily with Ostertagia circumcincta. International Journal for Parasitology 17, 951–6.Google Scholar
Hudon, P. & Dobson, A. (1995). Macroparasites: observed patterns. In Ecology of Infectious Diseases in Natural Populations (ed. Grenfell, B. & Dobson, A.). Cambridge: C. U. P.Google Scholar
Isham, V. (1991). Assessing the variability of stochastic epidemics. Mathematical Biosciences 107, 209–24.Google Scholar
Isham, V. (1993). Stochastic models for epidemics with special reference to AIDS. Annals of Applied Probability 3, 1–27.Google Scholar
Isham, V. (1995). Stochastic models of host–macroparsite interaction. Annals of Applied Probability 5, (In Press).Google Scholar
Kretzchmar, M. (1989). Persistent solutions in a model for parasitic infections. Journal of Mathematical Biology 27, 549–73.Google Scholar
Kretzschmar, M. & Adler, F. (1993). Aggregated distributions in models for patchy populations. Theoretical Population Biology 43, 1–30.Google Scholar
Kurtz, T. (1971). Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability 8, 344–56.CrossRefGoogle Scholar
Michel, J. (1970). The regulation of populations of Ostertagia ostertagi in calves. Parasitology 61, 435–47.Google Scholar
Pacala, S. & Dobson, A. (1988). The relation between the number of parasites/host and host age: population dynamic causes and maximum likelihood estimation. Parasitology 96, 197–210.Google Scholar
Quinnell, R. & Keymer, A. (1990). Acquired immunity and epidemiology. In Parasites: Immunity and Pathology: the Consequences of Parasitic Infections in Mammals (ed. Behnke, J.). London: Taylor & Francis.Google Scholar
Roberts, M., Smith, G. & Grenfell, B. (1995). Mathematical models for macroparasites of wildlife. In Ecology of Infectious Diseases in Natural Populations (ed. Grenfell, B. & Dobson, A.). Cambridge: C. U. P.Google Scholar
Shaw, D. (1994). Distributions of Macroparasites in Naturally-fluctuating Host Populations. PhD thesis, University of Cambridge.Google Scholar
Smith, G. (1989). Population biology of the parasitic phase of Ostertagia circumcincta. International Journal for Parasitology 19, 385–93.Google Scholar
Smith, G. (1995). Macroparasite group report. In Ecology of Infectious Diseases in Natural Populations (ed. Grenfell, B. & Dobson, A.). Cambridge: C. U. P.Google Scholar
Smith, G. & Galligan, D. (1988). Mathematical models of the population biology of Ostertagia ostertagi and Teladorsagia circumcincta and the economic evaluation of control strategies. Veterinary Parasitology 27, 73–83.Google Scholar
Stear, M., Bairden, K., Duncan, J., Gettinby, G., McKellar, Q., Murray, M. & Wallace, D. (1995). The distribution of fecal nematode egg counts in Scottish blackface lambs following natural, predominantly Ostertagia circumcincta infection. Parasitology 110, 573–81.Google Scholar
Whittle, P. (1957). On the use of the normal approximation in the treatment of stochastic processes. Journal of the Royal Statistical Society B19, 268–81.Google Scholar
Wilson, K. (1994). Analysis of worm and egg counts from the 1992 crash. Technical report, Department of Zoology, University of Cambridge.Google Scholar
Woolhouse, M. (1992). A theoretical framework for the immunoepidemiology of helminth infection. Parasite Immunology 14, 563–78.Google Scholar