A mathematical investigation of the induced mutation rate which is optimum for genetic improvement : Part I. Mutagenic treatment of the haploid: the three-locus case.

Even if there is a high ratio of unfavorable to favorable mutations, there is still a finite probability that a favorable genotype will arise by mutation, if only favorable mutants happen to occur or if the effects of the favorable ones outweigh the effects of the unfavorable ones. The object of this investigation was to determine the mutation rate (termed the optimum mutation rate) that maximizes the probability of a favorable genotype. This was investigated for a diploid plant with pollen treatment followed by self-fertilization to essential homozygosity.The parameters considered are block (chromosome) number, number of loci per chromosome, ratio of favorable to unfavorable mutants, and amount of recombination (c). The exact ranges in the interval 0 ≤ c ≤ 0.5 have been obtained for the optimum mutation rate and the corresponding probability of obtaining an improved genotype.In later publications the effects of seed treatment and of random mating before self-fertilization are considered. It is found, and will be discussed in a later publication, that (1) seed treatment is better than pollen treatment, and (2) if the number of loci is sufficiently large the optimum dosage of the mutagen may be so small as to make artificial mutagenic treatment undesirable.