Table 12 will enable us to analyze the difference of the proportions in tables 10 and 11.

These tables yield several points of interest. First, although the proportions of normal and extra toe in table 12, a and c, are not Mendelian, yet the average increase, from F₁ to F₂ in the proportion of the recessive (4-toed) type is almost exactly what is called for by Mendel's law. That law calls for an increase of 25 per cent. The actual average increase is 23.3 per cent (20.1 and 26.5 in the two cases). It seems fair to conclude, consequently, that Mendel's law does hold here, and that the 4-toed individuals of F₁ are heterozygotes with imperfect dominance. The feet of most of the 4-toed Silkies of this generation belong, indeed, to the reduced 5-toed type (table 10, B), and the reduced condition is prima facie evidence of heterozygotism. In F₁ Silkies of the first hybrid generation, 20 per cent of the feet exhibit "reduced" types of toes, but in F₂ only 5 per cent; and this might have been anticipated, since in F₂ heterozygotes are relatively only half as numerous as in F₁. Again, in F₂ we see reappearing the high ancestral toe-numbers (practically lost in the heterozygotes of F₁, table 12, b). These I interpret as extracted dominants. 6-toed extracts are more numerous among the Silkie than the Houdan hybrids, because the Silkie ancestors were 6-toed and the Houdan ancestors only 5-toed. However, only a small proportion of the extracted Silkie dominants have as many toes as the original Silkie ancestors, and this indicates a permanent regression (through the contaminating influence of hybridization?) toward the normal condition of toes. It will be observed that, although 6 toes are not found in the Silkie hybrids of F₁, many of these heterozygotes are of the reduced triplex type. Classifying them as virtually 6-toed, we find (table 12, c) 14.5 per cent of the 6-toed type in the F₁ generation.

Among the extracted dominants of F₂ are a few showing more toes than appeared in the ancestors (table 12, a; there was also one 7-toed F₂ Silkie hybrid, not recorded in the table). It is this sort of an advance in F₂ that permits the breeder to make a forward step. Theoretically, the appearance of this more aberrant class is probably due to the greater numbers of progeny than of ancestors, since the extracted dominants of F₂ are seven times as numerous as their extra-toed grandparents. Here, as elsewhere, the absolute range of variability depends upon the number of individuals observed.

As we have seen, failure of dominance is much more complete in some of the individuals of F₂, namely, those with 4 toes, than others. There is a variation in "potency." Is the degree of potency inherited? Do the 4-toed heterozygotes produce a larger proportion of imperfect dominants in F₂ than the 5-toed heterozygotes? The answer to this question should be given by the correlation between total number of toes in the two parents and average number of toes in their offspring, as given in table 11. In the case of the Houdan crosses there is a strong positive correlation, measured by 0.683 ± 0.092; but the correlation is insignificant in the Silkie crosses (-0.085 ± 0.032). This lack of correlation in the Silkie hybrids is perhaps due to the heavy regression in toe-number characteristic of the second hybrid generation. In general, there seems to be an inheritance of potency.

It now remains to test our conclusions by reference to the mating of the heterozygote with the dominant and with the recessive types, respectively. An examination of tables 13 to 15, particularly the last, reveals several points of interest. Mendelian expectation in the DR × R cross is 50 per cent of the recessive (4-4) type. Actually, in the two crosses, A and B, 68 per cent and 67 per cent, respectively, were obtained. But recalling that of these amounts one-half of 27.3, or 13.71, and one-half of 9.4, or 4.7, are respectively due to failure to develop the extra-toe in heterozygotes, there remain 54 per cent and 62 per cent, respectively, of 4-toed offspring, which doubtless represent the extracted RR type and approach the expected proportions.

Mendelian expectation in the DR × D cross (table 15) is 50 per cent heterozygotes and 50 per cent extracted dominants. Of the heterozygotes some 14 per cent may be expected to show 4-4 toes; that the percentage is much less than that is doubtless due to the small numbers involved. What is striking is the reappearance, in the second generation, of large proportions of the extreme dominant type. These results thus confirm those of the F₂ generation.

Since extra-toe frequently fails to dominate, there should be certain 4-toed heterozygotes which throw extra-toe offspring, and such are found. In table 16 are given six matings of 4-toed DR's. One sees that they produce some 5-toed offspring. On the other hand, extracted 4-toed recessives are obtained, as table 17 shows.

Finally, we must consider whether, among the polydactyl birds of one class, e. g., Houdans or Silkies, there is any difference in the "centgener power" of parents corresponding to the degree of development of their extra toes. This inquiry is suggested by Castle's study (1906, p. 20) of polydactyl guinea-pigs. He finds that when the extra toes of the mothers are graded into the 5 classes, good (G), fair (F), poor (P), normal though of abnormal ancestry (N), and normal of normal ancestry (N'), it follows: "first, that the proportion of polydactylous young produced by a male decreases in the successive classes from G to N'; and, secondly, that the degree of development of the toes produced on those polydactylous young diminishes in the same order." It is possible to test this conclusion in poultry because, inside of any one type of extra-toe, e. g., the triplex type, variation appears in the absolute size of the toes and in the degree of their separateness. Our questions, then, are: (1) does the proportion of polydactyl young produced by a pair of birds of any type diminish with the degree of development of toes inside of that type, and (2) does the degree of development of the toes produced on the polydactylous offspring diminish in the same order?

Two sets of data are available for answering these questions. The most direct set includes the data derived from crossing "pure-bred" polydactyl birds and the other includes the data derived from using hybrids between normal-toed and polydactyl ancestors. The latter data have the advantage that the parents offer a greater variability; but they have the disadvantage that the germinal condition of those parents is incompletely known.

The pure races may be considered first. Eight matings of Houdans, each parent with 5 toes, gave 122 offspring, of which 116 had 5-5 toes, 3 had 4-5 toes, and 3 had 4-4 toes. The variability of the toes is not great in the parent Houdans. But, arranging them in the order of development of the toes, the most developed first, the series of table 18 results.

No direct relation here appears between development of the extra toe in the parents and the average number of toes in the offspring.

Of the Silkies, 3 hens were used in 5 matings. The same 6-toed cock (No. 774) was employed throughout (table 19).

In table 19 the series a of observed average numbers of filial toes (10.3, 10.9, 10.0) and the series b obtained by assigning the typical full number to all reduced types (11.4, 11.4, 10.5) are decidedly irregular. There is, however, between the parental and the filial series a correlation of +0.250 ± 0.070. This indicates a slight tendency for the number of toes in the progeny to vary with those of the parentage.

The second set of data is derived from special matings made with hybrids between Houdans and 4-toed races. On the one hand, in pens 728 and 813, cocks with well-developed toes of the duplex type were mated with hens as nearly as possible of the same sort; while in pens 765, 769, and 820 cocks with small, imperfectly separated toes (probably of the duplex type[4]) were mated with hens as far as possible of the same sort.

Tables 20, 21, and 22 give in detail and in summary the distribution of types of polydactylism in the families from well-developed and in those from poorly developed parents. They show a great difference between the offspring of parents with good extra-toe (table 20) and those with poor extra-toe (table 21). The former yield over 80 per cent offspring with 5 toes or more on one or both feet, while the latter yield about 57 per cent of such.

On the other hand, in the former families there are less than half as many offspring with only 4 toes as in the latter. Classifying "reduced" forms with their proper advanced type, we find highly polydactyl parents yielding only 16 per cent non-polydactyl offspring, while slightly polydactyl parents yield 43 per cent non-polydactyl offspring. The percentage of polydactylous young diminishes with the size and distinctness of the extra toes and the grades of the polydactyl offspring are lower (absence in table 22, b, of 6 toes). Both of Castle's conclusions seem to be confirmed.