Theoretical studies on the methodological procedures of radiation breeding

Radiation breeding for the introduction of additional desirable characters into improved varieties in autogamous plants, especially in cereals, would be much more feasible if more efficient screening methods could be found. Such methods are proposed in this report. From the standpoint of the theory of probability, it is intended to establish effective screening methods by which a desirable X₂ mutant can be detected in a minimum total of X₂-plants, and/or X₁- and X₂-plants in the aggregate.The relative efficiencies of four new methods and the standard method are compared, the improved ear-to-row method (method B), the one-plant-one-grain method (method C), the one-plant-two-grain method (method D) and one-plant-three-grain method (method E) all of which are more effective than the conventional ear-to-row method (method A). In method B, the total number of X₂-plants required to recover at least one desirable X₂-plant is obtained when the probability of detecting at least one X₂-line with one or more desirable mutants among X₂-lines is equal to the probability of detecting at least one desirable mutant among plants in that X₂-line. In methods C, D and E, one, two or three grains respectively, taken from each of the X₁-plants of the number required to detect at least one desirable X₂-plant, are sown to obtain corresponding X₂-plants.The number of X₁-plants, total X₂-plants, and X₁- and X₂-plants in the aggregate required to obtain at least one desirable mutant (m, mn and m+mn respectively) shows the following relations: method C>D>A>E>B for m, ABED>D>C for mn and ABC>D>E (the last two being very close to each other) for m+mn.Each of the new methods B, C, D and E will be applicable in radiation breeding. When the discrimination of a mutant is difficult method B will be useful. On the contrary, when a mutant is easily distinguishable, method C, with dense planting in X₁, will frequently be much better. In some cases methods D and E, especially D, will be more useful in the practice of radiation breeding than method C. Method A should not be used in any case.