Density Dependence and Spatial Structure in the Dynamics of Insect Pathogens

Abstract

Many forest-defoliating Lepidoptera exhibit long-term cyclic fluctuations in density that span several orders of magnitude. One hypothesis to explain these fluctuations is that they are driven by pathogens with long-lived infectious stages capable of surviving outside the host. The basis of the argument is that, for realistic parameter values, a mathematical disease model incorporating such an infectious stage is likely to show cycles with the same period as is observed in nature. The mathematical model used to make this argument, however, is so simple that it may not be biologically meaningful. In this article, I extend the original model by including two realistic complications: density-dependent host reproduction and host movement behavior. Including density-dependent host reproduction greatly increases the likelihood of cycles; additional realism thus strengthens the original conclusion. Including host movement behavior makes the model more versatile, as it allows comparison of the model output with literature data on the spatial spread of insect viruses. This comparison suggests that the spatial spread of the viruses of Gilpinia hercyniae and Oryctes rhinoceros can be explained with a very simple model of host movement, without recourse to complicated mechanisms of dispersal. The introduction of host movement behavior also introduces the possibility of cycles of outbreaks in space and time simultaneously-that is, waves of disease that will reappear at regular intervals.