1USDA Agricultural Research Service, PO Box 370, Pendleton, OR 97801, USA; 2 INRA, Station de Pathologie Vegetale, BP 29, 35650 Le Rheu Cedex, France

Background and objectives
The simulation of pathogen effects on a host plant requires an understanding of the growth and development of both organisms. Winter wheat (Triticum aestivum L.) and the take-all pathogen (Gaeumannomyces graminis var. tritici) have been studied sufficiently to attempt such a simulation. Take-all provides an opportunity to examine an apparently simple host-pathogen interaction. The pathogen infects wheat roots as they extend past an inoculum source located in the soil. The probability of a root becoming infected depends upon the concentration and distribution of inoculum in the soil. Once infected, a root becomes nonfunctional for supplying nutrients and water to the plant as the pathogen occupies the cortex, endodermis, and phloem . The successful pathogen, however, does not appear to be a continuing sink for the plant's photosynthetic resources. Take-all simply prunes the root system. It is the objective of this paper to use the wheat model MODWht [1] and a root infection model to simulate the effect of timing and extent of root infection on wheat development and growth.

Materials and methods
The MODWht model computes the time of appearance and size of each plant part on a daily time step from germination through grain ripened. To simulate the effect of take-all, once a root is infected and fully occupied it will be considered nonfunctional and the plant will continue to grow with a restricted root system. The time of appearance of each root axis on a wheat plant can be computed as a linear function of cumulative degree days using the Celsius temperature scale and zero base temperature. The time of appearance of branches along each root can be also be approximated with linear functions using degree days, constant branch spacing and constant extension rates [2]. The axes and branches need not extend at the same constant rate. A more complex estimation of extension rates is possible using partitioned photosynthate supplies. Only after the consequences of possible infection patterns have been examined will it be worthwhile to estimate root extension using a daily photosynthate-dependent growth increment. Even when using the constant extension rate approximation for root extension, roots are determined to be infected or not during the daily computation cycle of the wheat model. Each root or branch is assigned a random number between 0 and 1. If the random value exceeds the probability of infection, that root or branch is considered uninfected and it continues to grow unrestricted. The probability of infection may change with time as it is dependent upon the amount of inoculum in the soil. The ratio of number of infected roots to number of roots on an undiseased plant at the same stage of development is used as a stress function to limit nutrient and water uptake. The effect of the disease on a plant is measured by comparing it to an unrestricted plant.

Results and conclusions
The computed effect of take-all on a plant is dependent upon the set of random values that determine which roots are infected and therefore nonfunctional. Since each run produces a new set of random numbers, each run produces a different result. It is only after creating a population of diseased plants that the effect of the disease on a crop can be examined. A population of diseased plants can be produced for each probability of infection. These populations also will differ depending on the nature of the statistical distribution from which random variables are chosen. The relationship between observed inoculum concentration and infection will determine whether a normal distribution or perhaps a log-normal distribution best represents this pathogen. Comparisons of simulation results with field observations will help to select the most appropriate distributions and host pathogen interactions.

1. Rickman, RW, Waldman SE, Klepper B, 1996. Agronomy Journal 88, 176-185.
2. Rickman RW, Klepper B, Belford RK, 1985. Proc. NATO Advanced Research Workshop on Wheat Growth and Modelling. April 9-12, 1984. Bristol UK, pp. 83-98.