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

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Abstract
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.