Table 54.—Distribution of frequency of grades of "openness" in offspring when both parents are extracted recessives (extracted RR × RR).

[A] Cf. Serial No. 12a.
Serial
No.		Pen
No.		Mother.Father.Total
gr.		Offspring.
No.Gen.Races.Grade.No.Gen.Races.Grade.Grade 1Grade 2
128728[A]912F2Houd. × Legh.21298F2Houd. × Legh.1333
129827298F2Pol. × Min.23852F3Do.2455

At the outset, then, we find (table 55) that even pure races with high nostril (Polish, Houdans), when bred together, vary much in the height of nostril (in perfection of dominance) and, in 2 per cent of the offspring, even show the typical narrow nostril (fig. B, a). On the other hand, in the narrow-nostriled races I have never obtained any such variation. The most deviation that I have seen from grade 1 is found in my strain of Dark Brahma bantams that frequently give grade 2. The variability of the high nostril, the stability of the low nostril, is prima facie evidence that the former is due to the presence of a particular factor and the latter to its absence.

Fig. B.—Polygons of frequency of grades of "openness" of nostril in offspring of various parents.
a, Both parents pure bred dominants; b, both parents extracted dominants; c, one parent heterozygous, the other a dominant; d, both parents heterozygous; e, dominant by recessive; f, heterozygous by recessive; g, heterozygous by extracted recessive; h, extracted recessives; i, heterozygous by dominant; k, both parents second generation hybrids.

Next, the heterozygotes of F1 (table 46), may be appealed to; but they will give no critical answer. For expectation, dominance being imperfect, is that the hybrids will be intermediate, and the result will be the same whichever extreme grade is taken as dominant. The empirical mode in the distribution of the offspring is at grade 2. This implies much greater imperfection of dominance on the hypothesis that grade 10 is dominant than on the hypothesis that grade 1 is dominant; but this very fact supports the former hypothesis, since imperfection of dominance is obviously a feature of the character with which we are dealing.

The critical test is afforded by the F2 generation (tables 48 and 49). By hypothesis, 25 per cent of the offspring are expected to be pure ("extracted") recessives, and the same number pure dominants; and also, by hypothesis, the recessives are massed at or near one grade while the dominants are variable. Now, as a matter of fact, the upper 25 per cent range over 5 to 7 grades, while the lower 25 per cent are nearly massed in grade 1 (21 per cent are so massed in one table, 17 per cent in the other). Therefore, in accordance with hypothesis we must regard the lower grade—narrow slit—as recessive. Similarly, heterozygous × low nostril (table 47) should give, on our hypothesis, 50 per cent low nostril. If that is recessive we should expect a massing of this 50 in the first two grades; if dominant a greater scattering. The former alternative is realized. Again, in the heterozygous × high nostril hybrid (table 50) the upper 50 per cent will be massed or scattered according as high nostril is recessive or dominant. Allowing for the 50 per cent heterozygotes in the progeny, the 50 per cent of high nostrils are scattered through at least 8 grades of the possible 10. High nostril is dominant. Finally, extracted high nostrils bred together produce offspring (table 52) with a great range of variability (through all grades), while extracted low nostrils (unfortunately all too few) give progeny with grades 1 and 2 (table 53; fig. B, h). Accepting, then, the general principle of the greater variability of the dominant character, we have demonstrated conclusively that high nostril, or rather the factor that determines high nostril, is dominant.

Comparing tables 45 to 54, we see that recessive parents are characterized by a low grade of nostril and they, of course, tend to produce offspring with a low grade. Similarly, dominants have a high grade and tend to produce offspring of the same sort, while heterozygous parents are of intermediate grade and their children have nostril grades that are, on the average, intermediate. Without regarding the gametic constitution, we might conclude, with Castle, that offspring inherit the grade of their parents, and consequently it would be possible to increase the grade, perhaps indefinitely, by breeding from parents with the highest grade. Considering the gametic constitution of the parents, it is obvious that such a conclusion is premature. To get an answer to the question it is necessary to find if there is, inside of any one table, among parents of the same gametic constitution, any such relation between parental and filial grades. This can be determined by calculating the correlation between the grades of parents and progeny. Such calculation I have made for table 48 with the result: index of correlation, r = 0.018 ± 0.032, which is to be interpreted as indicating that no correlation exists; and in so far the hypothesis of Castle proves not to apply in the cases of booting and doubt is thrown on the significance of his conclusion.

Finally, if we throw together the frequency distributions of all tables into one table (table 55; compare fig. B) we shall find the totals instructive. Table 55 shows that, when all results are thrown together, including hybrids of all sorts, grade 2 and grade 9 are the most frequent and grade 6 is the least frequent, the frequency gradually rising towards the extremes of the series. The same result appears in the individual series that range from grade 1 to grade 10. What is the meaning of this result? It seems to me to bear but one interpretation, namely, that there are only two centers of stability—about grades 1 and 9—and true blending of these grades, giving an intermediate condition, does not occur. Otherwise, in consequence of the repeated hybridization, the intermediate grades must be the commonest instead of the rarest. There is alternative inheritance of the nostril height.

Table 55.—Summary of tables 45 to 54.