Theoretical studies on the methodological procedures of radiation breeding

If the expectation of the number of desirable mutants for equal size of X ₂-populations decreases with decreasing number of plants per X ₂-line, the one-plant-one-grain method (method C), the one-plant-two-grain method (method D), and the one-plant-three-grain method (method E), especially method C, would be disadvantageous in comparison with the improved ear-to-row method (method B) and the conventional ear-to-row method (method A).From theoretical considerations it can be shown that a probability of occurrence of an X ₂-line containing desirable mutant (p ₁) and a conditional probability of occurrence of such desirable mutant for each one of the plants in such an X ₂-line (p ₂) are not affected by the number of X ₂-lines (m), but by the number of plants per X ₂-line (n). Consequently, the expectation of the number of desirable mutants in an X ₂-population, E(I), can be given by E(I) = mp ₁(1– q ₂ n · n p ₂/(1 –q ₂ n) = mn p ₁ p ₂ where p ₁+q ₁=1 and p ₂+q ₂=1.Therefore, with respect to E(I), method A=B=C=D=E for equal size of X ₂-populations. However, method ABE>D>C for different sizes of X ₂-populations.Most of this work was carried out in the National Institute of Agricultural Sciences, Hiratsuka, Japan.