A Mathematical Approach to the Prediction of Differences in the Relative Ability of Races of Puccinia Graminis Tritici to Survive When Mixed

Abstract

A model describing the population trends for any number of races of rust in the urediospore stage during a single growing season is presented. The general case for the field is subsequently modified to describe trends in a population of rust races under constant conditions. A term which gives an estimate of the relative survival ability of each race in the population is finally obtained. This term allows the trends in the composition of the mixture to be predicted. The theoretical proportion of strain 21 Anz-2,3,7 in amixture of strains 21 Anz-2,7 and 21 Anz-2,3,7 of P. graminis trifici over a number of generations was compared with the proportion of strain 21 Anz-2,3,7 in an experimental population of the same two strains over the same period. The model was found to be a good first approximation to the results obtained with the experimental population.