On the Virulence Analysis of Pathogen Race Frequencies

The ratio of observed value to expected value of genotype Av-i+ Av-k+ for virulence in blast fungus (abbreviated as + + genotype ratio) was studied using the available data in Japan. The + + genotype ratios were higher than one in almost all years in all ten districts. The + + genotype frequencies decreased during seven years from 1959 to 1965, with decrease of frequencies of individual virulence genes, Av-i+ and Av-k+, except Hokkaido. In Niigata, Toyama, Yamagata and Kanagawa Prefectures, significant differences are found between expected and observed values in various genotypes for virulence during the period from 1964 to 1966. The results of simulations and mathematical analysis on the change of + + genotype ratio indicate that the + + genotype ratio becomes temporarily higher than one when p2r2p3r3/p1r1p4r4 Q4/(Q2+Q4)(Q3+Q4). The + + genotype ratio asymptotically approaches to 1 under conditions where the frequency of + + genotype continues to increase and to 0 when it continues to decrease. The change of frequencies of + + genotype (race) cannot be explained by simple directional and stabilizing selections. The + + genotype ratio returns to 1 even after directional and/or stabilizing selections, and this limits the use of virulence analysis to search for the causes of the change of pathogen genotype (race) frequencies. The ratio of observed value to expected one in various genotypes (especially + + genotype) may help the studies in a sense that the use of the ratio reduces the range or kinds of factors which must be examined.