Species density distributions as null models for ecologically significant interactions of parasite species in an assemblage

A multiple-kind lottery model is presented for use in determining whether species density distributions in parasite species assemblages reveal regularly occurring species-to-species interactions. The model utilizes a recurrence vector algorithm to rapidly calculate expected frequencies of species per host classes in such assemblages. These calculations have been a computational problem because the probability of a host individual acquiring one species of parasite is not necessarily equal to that of acquiring another species. Thus although the number of possible ways for a host to acquire x parasite species of a possible n is given by the familiar binomial expansion term n![x!(x!(n - x)!], each of these ways can have a different probability. The model is applicable to any system that mimics a multiple-kind lottery in which (1) successes are independent events and (2) it is possible to fail completely to acquire any parasites or their analogs. The algorithm is thus a null model for species density distributions in general. Application of the model is illustrated by host/parasite systems involving snails and trematodes, fish and their protozoan and platyhelminth parasites, and a relatively rich assemblage of parasites in bats.