Mathematical models for the population biology of Ostertagia ostertagi and the significance of aggregated parasite distributions.

Parasite frequency distributions are frequently aggregated. Such distributions are conveniently described using the negative binomial frequency distribution. This distribution is completely characterized by two parameters: the mean of the distribution and an exponent, k. The degree of aggregation is inversely proportional to the value of k. Aggregated parasite distributions enhance the ability of regulatory processes to maintain parasite populations at or near their equilibrium level but incorporating parasite frequency distributions in realistic models of parasite population biology is fraught with difficulty (several simplified examples are given). Indeed, it is not always possible to incorporate parasite frequency distributions and the question arises whether this compromises model performance. Trichostronglyid nematodes, including Ostertagia ostertagi, are aggregated but the estimated value of k for such populations is usually greater than 1. This is typical of populations with high population means (tens of thousands). It is shown that when the degree of aggregation is such that k > 1, the results of a model which recognizes parasite frequency distribution is not much different from the results of a model which assumes all hosts contain exactly the same number of parasites.