The beta-binomial model for host specificity among organisms in trophic interactions

In this paper, we present a new stochastic model where the host specificity among organisms in trophic interactions in a community, say parasite-host interactions, is estimated by a beta-binomial model. The expected proportion of the host species in a community that a given parasite species is utilizing is modeled as a realization from an inhomogeneous Poisson process, where the rate of this process is assumed to be proportional to a beta probability distribution. The observed number of host species utilized by the parasites is then binomially distributed with the number of trials equaling the number of different host species in the sample. When the degree of polyphagy is estimated by the parameters of the beta-binomial model, quantities like community host specificity and the expected total number of parasite species that will utilize the host species in the community can be predicted as functions of the number of host species available. The predictions can then be applied in analysis of, e.g., symbiotic interactions among organisms, local species richness, and community structure.