Abstract
The condition for superior index selection using I=X
1-bX
2 to direct selection was theoretically confirmed. When 1) h
12/h
22>r
2G and 2) phenotypic regression of X
2 on X
1> genotypic regression of X
2 on X
1 are satisfied, a constant b lies between limits 0<b<A where A = 2[rp δ
1/(δ
2)-rGδ
1ˆ2/(δ
2ˆ2)δG
2/(δG
1)]/[1-r
2G δ
1ˆ2(δ
2ˆ2)δˆ2G
2(δˆ2G
1]as given by PURSER (1960). Further, in those conditions above, the conditions for the superior index Selection using; I=b
1X
M+b
2X
L to direct Selection were examined. The author is greatly indebted to Professor Dr. M. NAITO for reading and criticis of the manuscript. '
