Time, space and scale in plant disease epidemics

C.A. Gilligan,
Epidemiology and Modelling Laboratory, University of Cambridge, Downing Street, Cambridge, CB2 3EA., U.K. email cag1@cam.ac.uk

The concepts of invasion and persistence are central to our understanding of epidemiology, risk assessment and the deployment of genetically and other methods of control. Typical questions are: will control persist? Will a new isolate of the parasite invade? If so, how long will it take to invade? Will it persist and if not, what is the time to extinction? Epidemics of plant disease are non-linear, spatial and stochastic processes. This poses considerable challenge in constructing and, still more, in testing models. It requires us to understand how disease dynamics change over time and space and how scale impacts on the dynamics of disease. Nonlinearity means that small differences can become magnified leading to rapid invasion of a new pathotype, while sometimes large changes in density may be quickly buffered. Transmission between infected and susceptible hosts is often locally restricted for many diseases with occasional long-distance dispersal leading to two or more scales of spread, typified by within-field or within-farm and regional spread. Although experimenters frequently try to minimise, if not eliminate variability, stochasticity within and between epidemics is the norm rather than the exception. Temporal heterogeneity also occurs at a range of scales including diurnal and seasonal variations together with alternating phases of parasitic amplification of inoculum and saprotrophic activity or survival. One of the challenges in understanding and modelling invasion and persistence is to select only those levels of complexity that are essential for our understanding. Drawing on our recent work from a range of scales from the invasion of Rhizomania and Dutch elm disease in the U.K. through fungicide resistance and down to much more local spread typified by biocontrol of Sclerotinia minor on lettuce and Rhizoctonia solani on a range of hosts, I propose to illustrate some of the processes listed above in the construction and use of models to devise and test criteria for invasion and persistence. In particular, I shall summarise some results from the following topics: scaling from individual to population level and the variability amongst replicate epidemics; allowing for seasonality and disturbance in the persistence of disease; invasion in a single field or patch of hosts; invasion a larger scales