BIOLOGICAL-CONTROL IN A DISTURBED ENVIRONMENT

Most ecological and epidemiological models describe systems with conti nuous uninterrupted?ted interactions between populations. Many systems , though, have ecological disturbances, such as those associated with planting and harvesting of a seasonal crop. In this paper, we introduc e host-parasite-hyperparasite systems as models of biological control in a disturbed environment, where the host-parasite interactions are d iscontinuous. One model is a parasite-hyperparasite system designed to capture the essence of biological control and the other is a host-par asite-hyperparasite system that incorporates many more features of the population dynamics. Two types of-discontinuity are included in the m odels. One corresponds to a pulse of new parasites at harvest and the other reflects the discontinuous presence of the host due to planting and harvesting. Such discontinuities are characteristic of many ecosys tems involving parasitism or other interactions with an annual host. T he;he models are tested against data fi om an experiment investigating the persistent biological control of the fungal plant parasite of let tuce Sclerotinia minor by the fungal hyperparasite Sporidesmium sclero tivorum, over successive crops. Using a combination of mathematical an alysis, model fitting and parameter estimation, the factors that contr ibute the observed persistence of the parasite are examined. Analytica l results show that repeated planting and harvesting of the host allow s the parasite to persist by maintaining a quantity of host tissue in the system on which the parasite can reproduce. When the host dynamics are not included explicitly in the model, ne demonstrate that homogen eous mixing fails to predict the persistence of the parasite populatio n, while incorporating spatial heterogeneity by allowing for heterogen eous mixing prevents fade-out. Including the host dynamics lessens the effect of heterogeneous mixing on persistence, though the predicted v alues for the parasite population are closer to the observed values. A n alternative hypothesis for persistence involving a stepped change in rates of infection is also tested and model fitting is used to show t hat: changes in some environmental conditions may contribute to parasi te persistence. The importance of disturbances and periodic forcing in models for interacting populations is discussed.