The population dynamics of pathogens that control insect outbreaks

The population dynamics of an insect pathogen with a free-living infectious stage are considered. Most of the time, the insect host is regulated at an equilibrium density below that at which the pathogen can maintain itself. At regular or irregular intervals, the host escapes its normal regulatory agencies resulting in an outbreak that is eventually brought under control by the pathogen. Models are developed to explore the factors that influence the persistence of the pathogen in such an interaction. If all outbreaks are assumed to be of identical form, and if the occurrence of outbreaks is controlled by a Poisson process, analytical estimates of the mean and variance of the persistence time can be obtained. Such estimates provide good approximations to the numerical predictions of more realistic models in which the dynamics during an outbreak are represented explicitly so that outbreaks vary in size. In the latter models, outbreak size is predicted to be linearly related to the time since the last outbreak. It is argued that the type of model developed here may describe many naturally occurring insect-pathogen interactions, and that it can assist in the choice of pathogens for use in biological control and in the design of genetically manipulated pathogens.