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 X~ 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-threegrain 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 X~-line with one or more desirable mutants among X~-lines is equal to the probability of detecting at least one desirable mutant among plants in that Xz-line. In methods C, D and E, one, two or three grains respectively, taken from each of the Xl-plants of the number required to detect at least one desirable X~-plant, are sown to obtain corresponding X2-plants.
The number of Xl-plants, total X2-plants, and X 1-and X2-plants in the aggregate required to obtain at least one desirable mutant (m, mn and mรทmn respectively) shows the following relations: method C>D>A>E>B for m, A>~B>~E>D>C for mn and A>~B>~C>D>E (the last two being very close to each other) for mรทmn.
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. rNTRODUCTION Recently, it has been made clear that beneficial or desired mutants could be induced in plants by radiation. A desirable mutant is defined in this report as one having an additional desirable morphological or physiological character which is not found in