Computer simulation of the take-all disease of winter wheat with particular reference to methodology
The theory and the practical application of the simulation of root infection of winter wheat by the take-all fungus, Gaeumannomyces graminis var. tritici, are critically evaluated with respect to field epidemics and to infection of seedlings within controlled environments. Several simple models for disease progress in field epidemics are evaluated with respect to field data, including a generalized logistic equation and systems of simple non-linear differential equations, with and without algebraic solutions. An investigation is made of disease heterogeneity in the field and transect data derived from sampling 11,000 plants are analysed for the presence of significant pattern. The effect of the observed spatial heterogeneity on the precision of field data is also empirically investigated. The use of a controlled-environment experiment to model the effect of volunteer infestation on inoculum survival in the field is demonstrated, and a simple model is used to quantitatively estimate the effect of volunteer infestation on inoculum multiplication. Data for a seedling disease epidemic are simulated by three mathematically and computationally diverse simulators derived from a single underlying theoretical model. The first is a complex simulator written in FORTRAN and run on a mainframe computer which resolves the infection process into a number of detailed submodels. The second simulator is written in BBCBASIC and 6502 machine code and makes use of a discrete root map to hold information on host growth and infection. In the third simulator the model is expressed as a series of rate equations and is run on a simulation package on the BBC microcomputer. The simulation techniques used are discussed and evaluated with respect to model development and the descriptive accuracy of the simulators. In conclusion a strategy is proposed for the development of a comprehensive model for field epidemics of take-all by means of controlled-environment experimentation.