Parasites are often aggregated on a minority of the individuals in their host populations. Although host characteristics are commonly presumed to explain parasite aggregation on hosts, spatio-temporal aggregation of parasites during their host-seeking stages may have a dominant effect on the aggregation on hosts. We aimed to quantify, using mixed models, repeatability and autocorrelation analyses, the degree to which the aggregation of blacklegged ticks (Ixodes scapularis) on white-footed mice (Peromyscus leucopus) is influenced by spatio-temporal distributions of the host-seeking ticks and by heterogeneity among mice. Host-seeking ticks were spatially aggregated at both the larval and nymphal life-stages. However, this spatial aggregation accounted for little of the variation in larval and nymphal burdens observed on mice (3% and 0%, respectively). Conversely, mouse identity accounted for a substantial proportion of the variance in tick burdens. Mouse identity was a significant explanatory factor as the majority of ticks parasitized a consistent set of mice throughout the activity seasons. Of the characteristics associated with mouse identity investigated, only gender affected larval burdens, and body mass and home range sizes in males were correlated with nymphal burdens. These analyses suggest that aggregation of ticks on a minority of mice does not result from the distribution of host-seeking ticks but from characteristics of the hosts.

A class of point processes is considered, in which the locations of the points are independent random variables. In particular some properties of the process in which the distribution function of the position of the nth event is the n-fold convolution of some distribution function F, are investigated. It is shown that, under fairly general conditions, the process remote from the origin will be asymptotically Poisson. It is also shown that the variance of the number of events in the interval (0, t] is . Some generalisations are discussed.