On the Spatial Spread of Insect Pathogens: Theory and Experiment

Abstract

The mathematical theory of animal diseases has seen explosive growth in the past decade, yet most of the existing theory examines only temporal disease spread, ignoring the effects of patchy host or pathogen spatial distributions. Here I present a model for the within—season spatial spread of insect pathogens that incorporates host movement in an otherwise conventional insect host—pathogen model. Mathematical analysis of the model reveals that the pathogen will spread through the host population in a moving wave front of disease, known as a "travelling wave." This analysis shows how the spatial rate of spread of the pathogen depends upon the transmission rate of the disease, the rate of production of the pathogen by infected hosts, the initial population of the host, the decay rate of the pathogen, and the death rate of infected hosts. To test the predictions of the model, I performed a series of field experiments with the nuclear polyhedrosis virus (NPV) of Douglas—fir tussock moth, Orgyia pseudotsugata. First, I estimated each of the parameters of the model in the field with a series of small—scale experiments, and used the parameter estimates to predict the spatial rate of spread of the NPV through a population of tussock moth larvae (NPV diseases, like many insect pathogens, do not infect adults). To test this prediction, I then performed an experiment in which I measured the rate of spread of the NPV in an experimental population of tussock moth larvae on linear arrays of Douglas—fir seedlings. The model predicts the rate of spread of tussock moth NPV fairly accurately, suggesting that one can use this type of model to extrapolate individual behavior and localized transmission patterns to broader—scale spatial dynamics.