Invasion and persistence of plant parasites in a spatially structured hostpopulation

Spatial structure is of central importance in the dynamics of plant-parasit e interactions and is imposed by the growth habit and distribution of host plants and by parasite dispersal which is frequently restricted. To investi gate the effects of spatial heterogeneity on the dynamics of plant parasite s we introduce a simple model for epidemic development within a spatially s tructured host population. Here the host population is subdivided into a nu mber of patches which are linked to allow for transmission from one patch t o another with the connections defining the spatial structure of the host p opulation. Three key parameters are identified that play a critical role in the ability of the parasite to invade and persist within the host populati on: the within-patch parasite basic reproductive number which characterises the infection dynamics at the local spatial scale: and the neighbourhood o f interaction which describes which patches interact with which and the str ength of coupling between patches within the neighbourhood which together c haracterise the spread of the parasite over larger spatial scales. Using bo th deterministic and stochastic formulations of the model, we investigate h ow the thresholds and probabilities of invasion and persistence are affecte d by these parameters, by demographic stochasticity and by differences in t he initial level of infection.