Abstract
In a host-pathogen system which includes fcur genotypes for true resistance, AB, A+, +B and ++, in a host population, and four genotypes (races) for avirulence, ab, a+, +b and ++, in an airborne pathogen population, we established equations for following the race frequency changes on a given host population. Here, A and B are resistance genes, and a and b are avirulence genes which specifically correspond to the respective resistance genes. [numerical formula]where p(t) is the frequency of each race after the i-th generation, r is the multiplication rate of each race, and Q is the product of the percent of growing area (q) of a variety with a genotype for resistance and its field susceptibility (s). Subscripts 1, 2, 3 and 4, correspond to genotypes (races) fcr avirulence, ab, a+, +b and ++, in the pathogen, and to genotypes for resistance, AB. A+, +B and ++, in the host, respectively. p1+p2+p3+p4=1 and Q1+Q2+Q3+Q4=1. An equilibrium of race frequency is achieved under the following condition: [numerical formula]
