Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EA, UK

Background and objectives
Fungal growth, and hence the evolution of the pathozone, is a major determinant of epidemic development. Small changes at the pathozone scale can have large effects at the epidemic scale [1]. The aim of this work is to model the growth of soil-borne fungal plant pathogens to determine how the growth of the fungus depends on the microscopic properties of the fungus and the soil, and to determine how spatial and temporal variability in physical and chemical conditions in the soil affect the growth of the fungal colony.

Materials and methods
To investigate the development of a fungal colony in the absence of heterogeneity, a system of linear partial differential equations similar to those of Edelstein-Keshet et al.[2] is used. A nonlinear extension of this system enables diffusive transport of nutrients within the mycelium, uptake from the environment and depletion of the environment to be incorporated. The variability of the fungal colony is determined by selecting parameters within the PDEs from a random distribution and by using cellular automata to examine the radial variance of the colony. The effects of interactions with soil particles on the variability and distance over which the colony develops are determined by developing a stochastic model for fungal growth based on the mechanisms underlying the differential equations.

Results and conclusions
We show that for a homogeneous system, it is possible to scale-up from the hyphal to the colony behaviour: hyphal properties such as growth rate and branching probability can therefore be mapped onto colony properties. These observations have been tested against experimental data on the growth of Rhizoctonia solani The depletion of nutrients from the environment causes a change in colony shape from maintaining a maximum density in the colony centre to a maximum density on an anulus moving away from the centre. If nutrient conditions are initially heterogeneous, for example, because the fungus is deriving nutrients only from a host plant, the colony remains at its highest density at the nutrient source, although redistribution of nutrients away from the nutrient source, and suppression of growth close to the nutrient source are both required if the fungus is to maximise the region of space explored, and hence the probability of locating a susceptible host. Variability in colony growth both within and between colonies is maximised in low nutrient conditions; the selection of preferential directions of growth by the fungus enables infection to occur over large distances, but with a small associated probability. The physical make-up of the soil is shown to affect the density and rate of colony growth; the relationship between pore-size distribution within the soil and colony growth is determined.

1. Kleczkowski A, Bailey D and Gilligan CA, 1996. Proceedings Royal of the Society B 263, 777-783.
2. Edelstein-Keshet L, Hadar Y, Chet I, Henis Y, Segel LA, 1983. Journal of General Microbiology 129, 1873-1881.