Abstract1. Certain statistical methods that have been used for studies of quantitative inheritance are presented together with illustrations of their application. 2. The effect of the substitution of the first dominant, second dominant and the effect of both were calculated as the following differences between genotypes: Aa-aa, AA-Aa and AA-aa respectively, the latter being the algebraic sum of the other two. 3. Significant associations between certain qualitative and quantitative characters were found. Of the significant effects, there were several in which the first dominant produced the full effect, several in which the second produced the full effect, while in a few each produced an effect. 4. The vv (6-row) genotype was higher in yield than VV (2-row) while kk (awned) was higher in yield than either Kk or KK (hooded). Higher number of seeds per head and lower weight per seed were found in vv than in either Vv or VV. The kk genotype had a higher weight per seed than KK and a higher number of seeds per head than either Kk or KK. 5. For the most part, the above associations are explainable as expected from the known morphological or physiological effects caused by the factor pairs. 6. The Br and Fe factors were associated with higher yields and were higher in all components than the homozygous recessives. 7. The N vs. n gene pair showed no differential effects, indicating that a high-yielding naked barley is a definite possibility. 8. When the effects of a given gene pair are considered in the different non-allelic genotypes it was found that the V vs. v and K vs. k as a general rule were very consistent in their effects in all genotypes. 9. For the other gene pairs, certain genotypes showed specific interactions with certain non-allelic genotypes. For example, the addition of the second N decreased the weight per seed in the VV while it increased it in the Vv genotype. Also the effect of N on yield was an increase in KK plants and a decrease in kk plants. 10. The nature of these interactions was such as to permit no general conclusions. While several of them may have been due to chance, it seems clear from the number obtained that such specific interactions are a part of the general picture as to the action of quantitative factors. 11. An unexpected linkage was found between K and N of 46.1 ± 1.71. A cytological study was not made to determine the cause of this unexpected result although a translocation is suspected.
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