This paper uses simple mathematical models and statistical estimation techniques to analyse the frequency distribution of microfilariae (mf) in blood samples from human populations which are endemic for lymphatic filariasis. The theoretical analysis examines the relationship between microfilarial burdens and the prevalence of adult (macrofilarial) worms in the human host population. The main finding is that a large proportion of observed mf-negatives may be ‘true’ zeros, arising from the absence of macrofilarial infections or unmated adult worms, rather than being attributable to the blood sampling process. The corresponding mf distribution should then follow a Poisson mixture, arising from the sampling of mf positives, with an additional proportion of ‘true’ mf-zeros. This hypothesis is supported by analysis of observed Wuchereria bancrofti mf distributions from Southern India, Japan and Fiji, in which zero-truncated Poisson mixtures fit mf-positive counts more effectively than distributions including the observed zeros. The fits of two Poisson mixtures, the negative binomial and the Sichel distribution, are compared. The Sichel provides a slightly better empirical description of the mf density distribution; reasons for this improvement, and a discussion of the relative merits of the two distributions, are presented. The impact on observed mf distributions of increasing blood sampling volume and extraction efficiency are illustrated via a simple model, and directions for future work are identified.

Twelve populations of bats were examined to determine the extent of interspecific associations in determining the species richness of intestinal helminth infracommunities. The pool of helminth species which was available to individual bats ranged from 2 to 21. The ‘summed binomial’ distribution was determined to underlie the host frequency distribution of the number of helminth species per host. Overall covariation in occurrences of species in replicated communities can be detected by testing for the equality of the observed variance of the host frequency distribution to the variance expected when species are allocated to hosts at random. Where statistically significant the covariance was indicative of a majority of positive rather than negative interspecific associations. As the mean number of species per host in a host population increases not only does the number of positive associations increase but so does the proportion of species pairs which exhibit positive associations. Although there is an increase in the proportion of species pairs which exhibit positive associations as the number of species increases, the magnitude of the associations (as indicated by the mean positive or the mean negative pairwise covariances) does not. Therefore, we concluded that positive interactions are more common than negative interactions in determining the species richness of helminth infracommunities of bats. Further, positive associations become even more important as the community becomes more complex. However, the increased importance is derived from the number rather than the strength of the associations.