MODELING SOIL-BORNE PATHOGENS - REACTION-DIFFUSION MODELS

The occurrence of soil-borne disease in fields is characterised by pat chiness. Foci develop, they overlap, become diffuse, and change from s eason to season. Much of the spatial heterogeneity in disease may be a ttributed to the interaction of edaphic factors on biological variable s, especially inoculum density, rate of host growth, and susceptibilit y to disease as well as the degree of microbial antagonism. This paper examines the use of reaction-diffusion models to link the temporal an d spatial dynamics of plant disease. The models are used to generate s ome complex patterns of disease from comparatively simple yet biologic ally plausible assumptions. The reaction terms are first expanded to a llow for cyclical changes in inoculum density and disease by allowing for loss of host tissue by parasitism and gains by production of new r oots, The infected root population is further analysed to separate inf ectious from noninfectious roots. Dynamical effects of biological cont rol are introduced by expanding reaction terms to allow for interactio ns between the pathogen and populations of antagonistic microorganisms . Criteria are presented to predict whether the pathogen or antagonist will be eliminated. Spatial dynamics are added to the models by the i nclusion of a diffusion term. Simple analyses of single species models are illustrated to calculate the rate of expansion of a disease focus . Methods are presented for the estimation of the minimal patch size o f a host population necessary for the maintenance of a pathogen popula tion. The application of the concept of a critical patch size to predi ct the maintenance of a hyperparasitic biological control agent in a p opulation of a parasite is also noted. Temporal patterns in spatial he terogeneity are shown to occur when infection spreads by diffusive mov ement and roots die or are replaced during one or more seasons. Diffus ion usually leads to uniformity. The special case of diffusive instabi lity is also considered, in which the dynamics of an activator (the pa thogen) and an inhibitor (an antagonist or biological control agent) c an give rise to spatial heterogeneity even in uniform environments. Th e effects of heterogeneity in soil conditions on the rate of growth an d movement of soil-microorganisms in the soil is also shown to affect the dynamics of disease.