| Entomopathogenic nematodes (EPNs) are potent soil-dwelling parasites of insects that can have profound effects on a landscape. Causing high rates of mortality in their herbivorous host, EPNs can prevent the destruction of plants in both natural and agricultural environs. To better understand the nature of EPNs and to gain insights into general ecological phenomena, I present a series of models of these important soil microparasites and their insect hosts.; I begin with a deterministic model of the seasonal dynamics of EPNs and their hosts. The model predicts large amplitude period two population cycles of nematodes, independent of inter-annual feedback in host population numbers. The low population density at the bottom of these cycles puts forth the need for a second model that incorporates demographic stochasticity. Thus a second chapter presents a nonlinear stochastic model of host and parasite. I find approximations for the probability of extinction of the parasite. At low initial density, extinction occurs because the parasites fail to infect any host and the model reduces to a linear stochastic process. At high initial densities the parasite drives its host extinct and the model is well approximated by a non-linear deterministic one. The final chapter shows that nematode migration between spatially segregated populations reduces the risk of extinction. |
