Selection and use of a mathematical model to evaluate components of resistance to Phytophthora infestans in potato

Abstract

Five models of general epidemics, spatially homogeneous, were all shown to fit well to disease progress data forPhytophthora infestans on a susceptible potato cultivar. The models were: the logistic equation, the paralogistic or Vanderplank equation, two models from medical epidemiology with similar complexity, and a slightly more complex model with explicit treatment of lesion expansion. The use of the models for analysing the sensitivity of disease progress to changes in resistance components is discussed. Sensitivity analysis of the most complex model, by varying components within their range of genetic variation, indicates lesion expansion and infection efficiency as the components offering the best perspectives for resistance breeding. Improving two components simultaneously reduces disease progress slightly more than additively, but not enough to add other components to the list of breeding objectives. Pitfalls in using models for component sensitivity analysis, in the form of erroneous model initializations, are discussed, including implications for the role of components in the development of natural epidemics and in resistance breeding trials.