Abstract
Using the data on race frequencies of blast fungus through Japan obtained by Yamada et al.33), multiple regression analyses were carried out to get an equation for predicting frequencies for virulence genes in each prefecture in Japan. Resistance gene frequencies in each prefecture was calculated from growing areas of each variety in each prefecture in 16 years from 1961 to 1976. After arcsin transformation of frequencies of resistance genes and the corresponding virulence genes, 1) resistance gene frequencies, 2) the first and second component scores in principal component analysis computed from the resistance gene frequencies in the 16 years, and 3) means and slopes of resistance gene frequencies in each five or six year period when the 16 years were divided into three sections were used as three series of independent variables for a regression equation. The choice of a multiple regression equation from many equations obtained was performed to minimize the prediction sum of squares and to gain a better understanding. The virulence gene frequencies (F) in 1976 were expressed by F=0.14-1.89S2+1.44M1+0.53Da-0.62M12+0.63M1Dk+2.42S2Da, where S2 was the slope showing change of resistance gene frequencies from 1966 to 1971, M1 was the mean of resistance gene frequencies from 1972 to 1976, and Da and Dk were dummy variables for Pi-a and Pi-k resistance gene, respectively.
