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.

Despite evidence for the existence of interspecific interactions between helminth species, there has been no theoretical exploration of their effect on the distribution of the parasite species in a host population. We use a deterministic model for the accumulation and loss of adult worms of 2 interacting helminth species to motivate an individual-based stochastic model. The mean worm burden and variance[ratio ]mean ratio (VMR) of each species, and the correlation between the two species are used to describe the distribution within different host age classes. We find that interspecific interactions can produce convex age-intensity profiles and will impact the level of aggregation (as measured by the VMR). In the absence of correlated exposure, the correlation in older age classes may be close to zero when either intra- or interspecific synergistic effects are strong. We therefore suggest examining the correlation between species in young hosts as a possible means of identifying interspecific interaction. The presence of correlation between the rates of exposure makes the interpretation of correlations between species more difficult. Finally we show that in the absence of interaction, strong positive correlations are generated by averaging across most age classes.

In this paper we address the question of detecting immunity to helminth infections from patterns of infection in endemic communities. We use stochastic simulations to investigate whether it would be possible to detect patterns predicted by theoretical models, using typical field data. Thus, our technique is to simulate a theoretical model, to generate the data that would be obtained in field surveys and then to analyse these data using methods usually employed for field data. The general behaviour of the model, and in particular the levels of variability of egg counts predicted, show that the model is capturing most of the variability present in field data. However, analysis of the data in detail suggests that detection of immunity patterns in real data may be very difficult even if the underlying patterns are present. Analysis of a real data set does show patterns consistent with acquired immunity and the implications of this are discussed.

A birth process is studied in which the birth rate at any time is a function of the difference between the current population size and a target corresponding to unit growth rate. If this controlling function is a decreasing function of its argument a stabilizing effect is to be expected. By supposing that the controlling function varies very slowly, series expansions for the properties of the process are obtained, the leading term corresponding to a diffusion approximation. The sequence of births considered as a point process of controlled variability is examined and approximations to the interval distribution and covariance density obtained.