The dominant features of an epidemic, such as its overall severity, its distribution over areas of land, and its evolution through time are the result of the dynamic interactions of the host and pathogen systems, both of which are influenced by numerous complex biological processes. If successful disease control strategies are to be designed, it is important that the pathologist has an understanding of what are the most important processes, and how they combine to define the dynamics of an epidemic. Mathematical models can be used to develop understanding of quantitative, or qualitative behaviour, or to make predictions of the dynamics of biological systems. At SCRI, pathologists and mathematicians are working together in order to bring mathematical modelling to bear on problems in plant epidemiology.

In this approach, the main biological interactions between host and host, host and pathogen, or pathogen and pathogen are represented in the form of mathematical functions specified by parameters which quantify the relative strengths of interactions or the rates at which processes evolve.

Examples of processes and interactions which are typically represented in models of plant epidemics include gene-for-gene interactions between host and pathogen whereby a host only suffers attack by pathogens with a specific genotype, the development of pathogen populations on hosts, for example, sporulation and lesion growth, and the spatial movement of pathogens from one host to another.

While deterministic models have been extremely successful in some applications, there is now a growing appreciation that in other cases random, or stochastic, processes must be modelled in order to reproduce the behaviour encountered in the real world. These are incorporated into spatial models, an approach which is particularly relevant in plant epidemiology.

In contrast to animal populations, plant populations are unable to mix freely, and whether an individual plant is healthy or diseased is often closely related to the state of other plants in its immediate neighbourhood. These approaches are all being used at SCRI [1, 3, 5].

New statistical methods are also being developed to improve the precision of field trialing [2, 4, 6] and thereby the quality of the resultant data, especially data used in genetic mapping of quantitative traits.

References

[1] Goleniewski G, Newton AC, 1994. Modelling the spread of fungal diseases using a nearest neighbour approach: the effect of geometrical arrangement. Plant Pathology 43, 631-643.

[2] Hackett CA, Reglinski T, Newton AC, 1995. Use of additive models to represent trends in barley field trials. Annals of Applied Biology 127, 391-403.

[3] Goleniewski G, Newton AC, 1993. Modelling aerial and root-borne disease using nearest neighbour spatial simulators. Sixth International Congress of Plant Pathology, Montreal, Abstract number 6.1.2

[4] Hackett CA, Newton AC, 1985. Modelling spatial trends in barley field trials using generalised additive models. Aspects of Applied Biology 43, 59-66.

[5] Newton AC, Gibson G, Cox D, 1995. Understanding plant disease epidemics through mathematical modelling. Scottish Crop Research Institute Annual Report for 1994, 124-127.

[6] Hackett CA, Newton AC, 1996. Improving the accuracy of field trials by modelling spatial trends with generalised additive models. Scottish Crop Research Institute Annual Report for 1995.