Abstract
Using equations developed in a previous paper, the race frequency change of a race with the genotype Av-a Av-k+ (Av=a the avlrulence allele and Av-k+= the virulence allele) from 0 to 0.8 was traced. Shift in the frequency of occurrence of genotypes Av-a+ Av-k and Av-a+ Av-k+ from O.5 to O.1 were also traced. These shifts occurred over a several year period in Kanagawa Prefecture, Japan. These results indicate that an average multiplication rate more than 1.32 by the avirulence gene compared to the virulence gene is necessary to explain the change in race frequency. Under the same conditions, races Av-aAv-k+ and Av-a+ Av-k+ reduce when a variety with the Pi-k resistance gene is eliminated. Through these simulations, we thought that races Av-aAv-k+ and Av-a+ Av-k origin ated from race Av-a Av-k which decreased with release of a variety with Pi-k according to the rule that avirulent races decrease under the existence of resistant plants in a large proportion.
