ELSEVIER The Population Dynamics of Communities of Parasitic Helminths M. G. ROBERTS AgResearch, Wallaceville Animal Research Centre, P.O. Box 40063, Upper Hutt, New Zealand AND A. P. DOBSON Ecology and Evolutionary Biology, Eno Hall, Princeton University, Washington Road, Princeton, New Jersey 08544-1003 Received 12 October 1993; revised 14 June 1994 ABSTRACT This paper considers the dynamics of a host (animal) species that would grow exponentially in the absence of parasitism, and a community of parasite species that may regulate this growth. The model consists of a single differential equation for the host and one for each of the parasite species. This level of simplicity is achieved by assuming that each parasite species has a negative binomial distribution within the host population, with either zero covariance between the species (exploitation competition), or a specified covariance structure (interference competition). Condi- tions on the model parameters that determine the abundance of the different species are formulated, as are conditions that determine when a parasite species can invade a community and when a species is likely to be squeezed out. The results show that highly aggregated parasite species are more likely to coexist, but are less able to regulate their host population. A negative correlation between the distributions of the parasite species enhances both their ability to coexist and their ability to regu- late the host population. The results of this analysis apply more generally to other systems where communities of exploiter species coexist on discretely distributed hosts, for example, insects on plants. 1. INTRODUCTION Anderson and May [2] demonstrated with the aid of a simple differ- ential equation model that a parasite species could regulate the size of a host population that would otherwise grow exponentially. In construct- ing the model they assumed that the distribution of the parasites with- in the host population was negative binomial and invariant with time. MATHEMATICAL BIOSCIENCES 126:191-214 (1995) © Elsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010 0025-5564/95/$9.50 SSDI 0025-5564(94)00036-Y