1 Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EA, UK; lSilsoe Research Institute, Wrest Park, Silsoe, Bedford, MK45 4HS, UK

Background and objectives
A major objective of soil-borne botanical epidemiology is to scale up from the infection of single plants or roots to disease progress among a population of hosts. This paper describes how, using a combination of experimentation and mathematical modelling, we examined the pathozone behaviour of Rhizoctonia solani on single radish (Raphanus sativus) seedlings in order to predict disease progress among a population of seedlings. The damping-off of radish seedlings is characterized by growth of the pathogen over the soil surface and infection of the radish hypocotyl. We examine the growth of R. solani through the soil and use the results to discuss the influence of the soil physical environment on pathozone dynamics for the infection of roots.

Results and conclusions
Pathozone dynamics. The pathozone is defined as the region of soil surrounding a subterranean host organ within which a propagule must occur if it is to have any chance of causing infection. The pathozone can be characterized by a curve or profile describing changes in the probability of infection when inoculum occurs within the pathozone but at different distances from the host. The shape of the profile was determined experimentally by placing several replicates of inoculum at different distances from the host and scoring for the proportion of plants which became infected. We selected a three-parameter form of the critical exponential model to provide a simple, nonlinear description of the pathozone profile. Two parameters were found to vary with time. By making these parameters time-dependent we characterized the evolution of the pathozone profile over time.
From pathozone dynamics to disease progress. The proportions of inoculum and the associated probabilities of infection that occur at different distances from the surface of the host were summed over time to estimate the progress of disease from inoculum distributed at random among a population of host plants. In this way, we successfully predicted the progress of disease in experimental microcosms. We conclude that, in a controlled environment, it is possible to predict the progress of disease among a population of hosts from the pathozone behaviour of single plants [1,2].
Fungal growth through soil. The shape of the pathozone for R. ;solani on radish is particularly sensitive to changes in growth of the mycelial colony [3]. While changes in soil physical conditions have little effect on the spread of R. ;solani over the soil surface, they have substantial effect on the variability, extent and rate of mycelial spread through soil. Rhizoctonia solani spreads faster and further over surfaces, even though the same amount of biomass is produced in each case. Within soil, the spread is mediated by the geometry and connectivity of the air-filled pore space. Preferential spread along surfaces not only accelerates the progress of damping-off disease, but may affect subterranean spread where cracks, biopores and aggregates constitute a framework of surfaces. It follows that soil physical conditions have a profound effect on the probability of contact and that manipulation of physical conditions may provide a plausible mechanism for disease control.

1. Bailey DJ, Gilligan CA, 1997. New Phytologist 136, 359-367.
2. Kleczkowski A, Gilligan CA, Bailey DJ, 1997. Proceedings of the Royal Society of London Series B 264, 979-984.
3. Gilligan CA, Bailey DJ, 1997. New Phytologist 136, 343-358.