Generalized conditions for coexistence of competing parasitoids on a shared host

Abstract

Motivated by the univoltine life histories of insects residing in the temperate-regions of the world, there is a rich tradition of modeling arthropod host-parasitoid interactions using a discrete-time formalism. We introduce a general class of discrete-time models for capturing the population dynamics of two competing parasitoid species that attack the same vulnerable stage of the host species. These models are characterized by two density-dependent functions: an escape response defined by the fraction of hosts escaping parasitism; and a competition response defined by the fraction of parasitized hosts that develop into adult parasitoids of either species. Model analysis reveals remarkably simple stability conditions for the coexistence of competing parasitoids. More specifically, coexistence occurs, if and only if, the adult host density increases with host reproduction rate, and the log sensitivity of the competition response is less than half. The latter condition implies that any increase in the adult parasitoid density will result in a sufficiently slow increase in the fraction of parasitized hosts that develop into parasitoids of that type. We next consider a model motivated by differences in parasitism risk among individual hosts with risk from the two parasitoid species assumed to be independently distributed as per a Gamma distribution. In such models, the heterogeneity in host risk to each parasitoid is quantified by the corresponding Coefficient of Variation (CV). Our results show that parasitoid coexistence occurs for sufficiently large reproduction rate, if and only if, the sum of the inverse of the two CV squares is less than one. This result generalizes the "CV greater than one" rule that defined the stability for a single parasitoid-host system to a multi parasitoid-host community.