Predicting Development of an Epidemics on Cultivar Mixtures

A mathematical model for the development of an epidemic on a plant cultivar mixture illustrates the influence of the infection efficiency, spore production rate, proportion of deposited spores, frequency of autodeposition, and composition of the mixture on the genetic composition of the pathogen population and on the long-term rate of disease increase.

In the model, the long-term composition of the pathogen population is determined from the long-term rates of disease increase of each pathotype. Alteration of any one of the model parameters may change the long-term composition of the pathogen population qualitatively. Detailed analysis of mixtures with two components showed that a pathotype reproducing on both components will predominate if the frequency of autodeposition is low and both components are present at intermediate frequencies.

Predictions for different mixing strategies are given for host-pathogen systems where the host-pathogen interaction is described by a gene-for-gene relationship with “stabilizing selection.” These mixing strategies include changing the composition of the mixture, the number of components in the mixture, the frequency of autodeposition (related to crop density), and finally mixing fields instead of plants.

A relation was found between the long-term rate of disease increase of a pathotype and its number of virulence genes, and this relation was used for evaluating the different strategies.