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Analysis of aggregation, a worked example: numbers of ticks on red grouse chicks

Published online by Cambridge University Press:  07 August 2001

D. A. ELSTON ,
R. MOSS ,
T. BOULINIER ,
C. ARROWSMITH  and
X. LAMBIN
D. A. ELSTON
Affiliation:
Biomathematics and Statistics Scotland, Environmental Modelling Unit, Macaulay Land Use Research Institute, Craigiebuckler, Aberdeen AB15 8QH, UK
R. MOSS
Affiliation:
Centre for Ecology and Hydrology, Banchory, Aberdeenshire AB31 4BW, Scotland
T. BOULINIER
Affiliation:
Laboratoire d'Ecologie, C.N.R.S–U.M.R. 7625, Université Pierre et Marie Curie, 7 Quai St Bernard, 75252 Paris, France
C. ARROWSMITH
Affiliation:
Department of Zoology, University of Aberdeen, Tillydrone Avenue, Aberdeen AB24 2TZ, Scotland Present address: 10 Strathmore Court, Thurso, KW14 7PS, Scotland.
X. LAMBIN
Affiliation:
Department of Zoology, University of Aberdeen, Tillydrone Avenue, Aberdeen AB24 2TZ, Scotland
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Abstract

The statistical aggregation of parasites among hosts is often described empirically by the negative binomial (Poisson-gamma) distribution. Alternatively, the Poisson-lognormal model can be used. This has the advantage that it can be fitted as a generalized linear mixed model, thereby quantifying the sources of aggregation in terms of both fixed and random effects. We give a worked example, assigning aggregation in the distribution of sheep ticks Ixodes ricinus on red grouse Lagopus lagopus scoticus chicks to temporal (year), spatial (altitude and location), brood and individual effects. Apparent aggregation among random individuals in random broods fell 8-fold when spatial and temporal effects had been accounted for.

Keywords

analysing aggregationgeneralized linear mixed modelIxodes ricinusLagopus lagopus scoticusPoisson-lognormal distributionvariance components
Type
Research Article
Information
Parasitology , Volume 122 , Issue 5 , May 2001 , pp. 563 - 569
Copyright
2001 Cambridge University Press

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References

BOAG, D. A., WATSON, A. & PARR, R. (1975). Patagial streamers as markers for red grouse chicks. Bird-Banding 46, 248.CrossRefGoogle Scholar
BOULINIER, T., IVES, A .R. & DANCHIN, E. (1996). Measuring aggregation of parasites at different host population levels. Parasitology 112, 581–587.CrossRefGoogle Scholar
CLAYTON, D. & KALDOR, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43, 671–681.CrossRefGoogle Scholar
DUNCAN, J. S., REID, H. W., MOSS, R., PHILLIPS, J. D. P. & WATSON, A. (1978). Ticks, louping ill and red grouse on moors in Speyside, Scotland. Journal of Wildlife Management 42, 500–505.CrossRefGoogle Scholar
GENSTAT 5 COMMITTEE (1997). Genstat 5, Release 4.1 Reference Summary. Numerical Algorithms Group, Oxford.Google Scholar
GRENFELL, B. T., WILSON, K., ISHAM, V. S., BOYD, H. E. G. & DIETZ, K. (1995). Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study. Parasitology 111 (Suppl.), S135–S151.CrossRefGoogle Scholar
LAWSON, A., BIGGERI, A., BÖHNING, D., LESAFFRE, E., VIEL, J.-F. & BERTOLLINI, R. (Eds) (1999). Disease Mapping and Risk Assessment for Public Health. Wiley, New York.Google Scholar
LAWSON, A., BIGGERI, A., BÖHNING, D., LESAFFRE, E., VIEL, J.-F. & BERTOLLINI, R. (1999). Disease Mapping and Risk Assessment for Public Health. Wiley, New York.Google Scholar
LEE, Y. & NELDER, J. A. (1996). Hierarchical generalised linear models (with discussion). Journal of the Royal Statistical Society, B 58, 619–678.Google Scholar
LEE, Y. & NELDER, J. A. (2000). Two ways of modelling overdispersion. Applied Statistics 49, 591–598.Google Scholar
LITTELL, R. C., MILLIKEN, G. A., STROUP, W. W. & WOLFINGER, R. D. (1996). SAS System for Mixed Models. SAS Institute Inc., Cary, N.C.
MACCOLL, A. D. C., PIERTNEY, S. B., MOSS, R. & LAMBIN, X. (2000). Spatial arrangement of kin affects recruitment success in young male red grouse. Oikos 90, 261–270.CrossRefGoogle Scholar
MCCULLAGH, P. & NELDER, J. A. (1989). Generalized Linear Models, 2nd Edn. Chapman and Hall, London.
MILNE, A. (1950a). The ecology of the sheep tick, Ixodes ricinus L. Microhabitat economy of the adult tick. Parasitology 40, 14–34.Google Scholar
MILNE, A. (1950b). The ecology of the sheep tick, Ixodes ricinus L. Spatial distribution. Parasitology 40, 35–45.Google Scholar
PARR, R. (1975). Aging red grouse chicks by primary molt and development. Journal of Wildlife Management 39, 188–190.CrossRefGoogle Scholar
PATERSON, S., WILSON, K. & PEMBERTON, J. (1998). Major histocompatibility complex variation associated with juvenile survival and parasite resistance in a large unmanaged ungulate population (Ovis aries). Proceedings of the National Academy of Sciences, USA 95, 3714–3719.CrossRefGoogle Scholar
PAYNE, R. W. & ARNOLD, G. M. (eds) (1998). Genstat 5 Release 4.1 Procedure Library Manual PL11. Numerical Algorithms Group, Oxford.Google Scholar
PIELOU, E. C. (1977). Mathematical Ecology. John Wiley & Sons, New York.
SCHALL, R. (1991). Estimation in generalized linear models with random effects. Biometrika 78, 719–727.CrossRefGoogle Scholar
SHAW, D. J. & DOBSON, A. P. (1995). Patterns of macroparasite abundance and aggregation in wildlife populations: a quantitative review. Parasitology 111 (Suppl.), S111–S133.CrossRefGoogle Scholar
WILK, M. B. & GNANADESIKAN, R. (1968). Probability plotting methods for the analysis of data. Biometrika 55, 1–17.CrossRefGoogle Scholar