Stability analysis of a plant pathogen evolution model

Abstract

Stacking of multiple resistance genes in crop cultivars, pyramiding, is an effective way to control plant diseases. However, due to the evolution of the pathogen, resistance cultivar can be overcome. Breeders develop pyramids with more resistance genes to improve the durability of resistance. Since it is difficult to do field experiments on the evolution of the pathogen, mathematical models become an important tool to study the behavior of evolution of plant pathogen through stability analysis. A model for the evolution of pathogen is developed towards virulence against cultivar resistance genes. The aims of this research are to analyze the stability of the steady states of the model. The results from the analysis show that only the equilibrium point (0,0,0,1) was stable while the others were unstable. This stable equilibrium point is characterized by the strain virulent to both resistance genes. The other pathogen strains disappear from the population. Inthe future, the model can be used to determine the breeding strategic for plants which can delay the evolution of pathogen and prolong durability of pyramided plant.