The single comb recorded in the case of 7 birds is doubtless merely the limiting condition of a Y comb in which the median element is developed to its fullest extent. All but 2 of the 7 were recorded from early embryos when an incipient bifurcation would be more difficult to detect. This explanation applies generally, and accounts for the usual excess of I comb when compared with Y comb, as for instance in table 3, page 7. Returning to table 7, it is, consequently, probable that only the Y-combed and non-median-combed offspring are produced and that they are in the proportion of 99 to 115 or of 46 per cent to 54 per cent. If we add together all records of a oo×Y cross, disregarding the generation of the parents, we get a total I comb 5,[1] Y comb 177, oo comb 172, and absent 3, or 182 (51 per cent) with the median element and 175 (49 per cent) without. Thus the oo×Y cross gives the 1:1 proportion called for on the first and third hypotheses and not at all the variety required by the second hypothesis.

Finally, we must consider the result of mating a bird without papillæ (No. 1420, pen 704) with a median-combed hen (480). When this typical single-combed hen was used the 49 progeny were all of the Y type.[2] This proves that the combless type behaves only as an extreme of the non-median type.

When Y-combed hens were used with the combless cock the offspring had Y comb and non-median-comb in nearly equal numbers, 23:27 (table 8), but the latter included an unusually large proportion of combless fowl (15 in 27). When a combless hen (No. 4257) was used, 9 of the offspring had oo comb and 2 no comb; not a greater proportion of combless birds than in the no-comb×Y-combed cross. All of these facts indicate that "comblessness" is not entire absence of the comb factors, but a minimum case of the oo or paired comb. This result is opposed to the second hypothesis.

The statistics of all matings between I, Y, and no comb on the one side and no comb on the other thus speak unanimously for the conclusion that in these matings we are not dealing with 2 pairs of allelomorphs, but with a single comb and its absence (third hypothesis) or with a case of particulate inheritance (first hypothesis). Moreover, it must be said that the split comb is obtained also when the Polish-Houdan comb is crossed with a pea comb or a rose comb; and the pea and rose combs can not be said to have "lateral comb absent," as required by the second hypothesis. Consequently the second hypothesis is definitely excluded.

It now remains to decide between the two remaining hypotheses. First of all, it may be said that the perfection with which I and oo combs can be extracted from Y-combed birds indicates that we are here dealing with a case of Mendelian inheritance and, in so far, favors the third hypothesis. To accord with the theory of particulate inheritance, of which the first hypothesis is a special case, the two united characters should transmit the mosaic purely; but this they do not do. Hence the third hypothesis is to be preferred to the first.

Comblessness is a necessary consequence of the second hypothesis and is inexplicable on the first hypothesis. On the third hypothesis it may be accounted for as follows: Absence of single comb is allelomorphic to its presence. The lateral comb is a character common to fowl either with or without the median comb, but it is ordinarily repressed in the birds with single comb and gains a large size when the median element is absent. It is a very variable element. At one extreme it forms the cup comb; at the other there is an absence of any trace of comb. My own records show all grades between these extremes, including minute papillæ on both sides of the head or on one side only, low paired ridges, the butterfly comb, and cup comb shorter than normal. This variability of the lateral element is comparable to the fluctuation in size of the single comb itself, as illustrated by the Single-comb Minorca on the one hand and the Cochin on the other. It is comparable, also, to the fluctuation in the paired part of the Y comb, which we shall consider in the next section, and to the variability of the oo comb as met with in the pens of fanciers.

The foregoing considerations do not, at first sight, account for the Y comb as seen in F₁. Yet they provide us with all the data for an explanation. Median comb of the Minorca dominates over no median of the Polish, and so in F₁ we have the median element represented. But, on the well-known principle of imperfection of dominance in F₁, the median comb is usually incomplete and, probably for some ontogenetic reason, incomplete only behind. The incompleteness behind permits the development there of the elsewhere repressed lateral comb, and we therefore have the Y comb—evidence at the same time of a repressed lateral-comb Anlage in the single-combed birds and of imperfection of dominance of the single comb in the first hybrid generation.

B. VARIABILITY OF THE Y COMB AND INHERITANCE OF THE VARIATIONS.

As already stated, the proportions of the median and the lateral elements in the Y comb are very variable; the median element may, indeed, constitute anywhere from 100 per cent to 0 per cent of the entire comb. Even full brothers and sisters show this variability. Thus the offspring of No. 13 ♀ Single-comb Minorca and No. 3 ♂ Polish have the median element of the Y comb ranging from 0 per cent to 70 per cent of the whole comb. Notwithstanding this variability of the median element in any family there is a difference in the average and the range of variability in families where different races are employed. Thus the offspring of two Polish × Minorca crosses show an average of 46 per cent of the median element in the comb; the Houdan × Minorca cross gives combs with 60 per cent of the median element; and in the combs of the offspring of two Houdan × White Leghorn crosses there is, on the average, 71 per cent of the median element. The Houdan × Dark Brahma (pea comb) gives combs with an average of 87 per cent median element and the Polish × Rose-comb Minorca cross gives 89 per cent median. The rose-combed hens used in this last cross were heterozygous, having single comb recessive; consequently they produced also chicks with typical Y combs. Such had, on the average, only 59 per cent of the median element and were thus in striking contrast with the slightly split rose combs. In the case of the partially split rose combs the median element ranged from 60 per cent to 100 per cent of the whole length of the comb; but in the split single combs the range is from 0 to 100 per cent. Thus, in the two cases, the proportion of the median element and the range of its variability differ greatly.

Also, in generations subsequent to the first, the Y comb exhibits this same variability. We have already seen that the progeny of the Y-combed offspring of any generation may be compared with those of any other, and so we may mass together the progeny of all hybrid generations so long as they are derived from the same ancestral pure races.

In inquiring into the meaning of this variability we must first construct the polygon of frequency of the various grades of median element. This is plotted in fig. A, which is a composite whose elements are, however, quite like the total curve. There is one empirical mode at 70 per cent and another at 0 per cent. The smaller mode at 50 per cent is, I suspect, due to the tendency to estimate in round numbers, and may be, in this discussion, neglected. From this polygon we draw the conclusions, first, that the median element in the Y comb tends to dominate strongly over the absence of this element, as 7:3, and, second, that dominance is rarely complete. Yet there is an important number of cases, even in F₁, where the median element is almost or completely repressed (down to 10 to 0 per cent of the whole) and the comb consists of two high and long lateral elements—the "cup comb" of Darwin. There are, then, in the offspring of a median-combed and a non-median-combed parent, two types with few intergrades—the type of slightly incomplete dominance of the median element and the type of very incomplete dominance.

We have now to consider how these two types of comb and their fluctuations behave in heredity. When two parents having each combs of the 70 per cent or 80 per cent median type are mated, their offspring belong to the three categories of I, Y, and "no-median" comb, but the relative frequency of these three categories is not close to the ideal of 25 per cent, 50 per cent, and 25 per cent, respectively. For there is actually in 336 offspring a marked excess of the I comb, 36 per cent, 44 per cent, and 20 per cent, respectively, resulting. When, on the other hand, two parents having each combs of the 10 per cent and 0 per cent types are mated their offspring are of the same three categories and the proportions actually found in 241 offspring (28 per cent, 47 per cent, 25 per cent) closely approximate the ideal. It is clear, then, that even the cup comb, without visible median element, has such an element in its germ-cells and is totally different in its hereditary behavior from the Polish comb, in which the median element is absent, not only from the soma, but also from the germ-cells.

We have seen in the last paragraph that the Y comb with only 10 per cent to 0 per cent median element has germ-cells bearing median comb as truly as the Y comb containing 70 per cent to 80 per cent median element, but we have also seen that in the latter case there is an excess of single-combed progeny. We have now to inquire whether, in general, there is a close relation between the proportion of median element in the comb of the parents and the percentage of single-combed offspring. These relations are brought out in the lower half of table 9.

The proportion of single-combed offspring in the total filial population is 30.0 per cent, a departure of such magnitude from the expected 25 per cent as to arrest our attention. Further inspection of table 9 shows that the excess of single-combed offspring is found only in the lower half of the series. When the percentage of median element in the parents is under 50 the proportions of I, Y, and no-median combs are as 25.5 per cent, 49.8 per cent, 24.7 per cent, or close to expectation; but when the percentage is 50 or over the proportions are, on the average, 33.6 per cent, 45.2 per cent, and 21.2 per cent, a wide departure from expectation, 1108 individuals being involved. An examination of table 9 shows, moreover, that the proportion of offspring with single comb rises steadily as the proportion of the median element in the parentage increases from 50 per cent. The meaning of this fact is at present obscure, but the suspicion is awakened that, while the "cup comb" and the more deeply split combs are typical heterozygotes the slightly split combs are a complex of 2 or more units, one of which is "single comb." But that this is not the explanation follows for two reasons: first, that even in the F₁ generation slightly split combs are obtained, and, second, that the offspring of the cup combs are much more variable than those of slightly split combs (70 to 90 per cent median). What is strikingly true is that, from 50 per cent up, as the proportion of the median element in the parents increases the percentage of single-combed offspring rises.

The matter may be looked at in another light. Median comb is dominant over its absence. Typically, we should expect F₁ to show a single comb; the Y comb that we actually get is a heterozygous condition due to the failure of the median comb to dominate completely. Typically we should expect F₂ to reveal 75 per cent single combs, of which 1 in 3 is homozygous and 2 in 3 are heterozygous. Owing to the failure of single comb always to dominate completely in the heterozygotes, we expect to find some of the 75 per cent with the Y comb. When in the parents dominance has been very incomplete in the heterozygote (as is the case in the 0 per cent to 40 per cent median-combed parents) we find it so in the offspring also and all heterozygotes show a Y comb of some type. But when in the parents dominance has been strong in the heterozygote (50 per cent to 90 per cent) it is so in the offspring also and only a part of the heterozygotes show the Y comb; the others show the single comb and thus swell the numbers of the single-combed type. The only objection to this explanation is found in the reduction in the percentages of the no-median type. Thus, adding together the homozygous and heterozygous median-combed offspring and comparing with the non-median-combed, we find these ratios:

There is a great deviation from 25 per cent in the "non-median" offspring of the 90 per cent parents, but in this particular case the total number of offspring is not large, and the deviation has a greater chance of being accidental. Altogether this explanation of the varying per cents of single comb on the ground of inheritance of varying potency in dominance seems best to fit the facts of the case.

From the foregoing facts and considerations we may conclude that the Y comb represents imperfect dominance of median over no-median comb; that there is a fluctuation in the potency of the dominance, so that the proportion of the median element varies from 0 to over 90 per cent; that the more potent the dominance of median element is in any parents the more complete will be the dominance in the offspring and the smaller will be the percentage of imperfectly dominant, or Y-combed, offspring. Dominance varies quantitatively and the degree of dominance is inheritable.

The index of heredity may be readily obtained in the familiar biometric fashion from table 9. This I have calculated and found to be 0.301 ± 0.002. This agrees with Pearson's theoretical coefficient of correlation between offspring and parent. The index is larger than it would otherwise be because it is measured with an average of the parents and these parents assortatively mated. But this instance is, in any case, an interesting example of strong inheritance of a quantitative variation.

What, it may be asked, is the relation of these facts to the general principle that inheritance is through the gametes? Why, when a gamete with the median element unites with a gamete without that element, does the zygote develop a soma that in some cases shows a nine-tenths median and sometimes a one-tenth median element? We have seen that the Y comb is a heterozygous form due to imperfection of dominance of the median element; but why this variation in the perfection of the median element? This is probably a piece of the question, why any dominance at all. We find, in general, that the determiner of a well-developed organ dominates in the zygote over the determiner of a slightly developed condition of that organ or its obsolete condition. It is as though there were in the zygote an interaction between the strong and the weak form of the determiner, and the strong won; but sometimes the victory is imperfect. In the specific case of comb the interaction between median and no-median leads to a modification, weakening, or imperfection of the median element, and this weakening varies in degree. Sometimes the weakening is inappreciable—when the comb is essentially single; sometimes it is great, and the result is a comb in which the median element is reduced to one-half; sometimes, finally, the determiner of median comb is so completely weakened by its dilution with "no-median" as not to be able to develop, and we have the cup comb with only a trace of the median element. Nevertheless, such a cup comb is heterozygous and produces both single-combed and Polish-combed germ-cells. Thus the variation in the extent of the median comb seems to point to variations in relative potency of the median comb over its absence.

The possession of extra toes is a character that crops out again and again among the higher, typically 5-toed vertebrates. Many cases have been cited in works on human and mammalian teratology (cf. Bateson, 1904, and Schwalbe, 1906), and it is recognized that this abnormality is very strongly inherited in man. Bateson and Saunders, and Punnett (1902 and 1905), Hurst (1905), and Barfurth (1908), as well as myself in my earlier report, have demonstrated the inheritableness of the character in poultry. Bateson and Punnett (1905, p. 114) say: "The normal foot, though commonly recessive, may sometimes dominate over the extra-toe character, and this heterozygote may give equality when bred with recessives, just as if it were an ordinary DR." Altogether, the inheritance of extra-toe diverges so far from typical Mendelian results as to deserve further study.

A. TYPES OF POLYDACTYLISM.

There are two main types of polydactylism: that in which the inner toe (I) of the normal foot is replaced by 2 simple toes, and that in which it is replaced by two toes, of which the mediad is simple and the laterad is divided distally. The former type is characteristic of the Houdans; the latter is usually associated with the Silkies. Both conditions are, however, found in both races. The simplest condition is seen in many Houdans of my strain. It consists of 2 equal, medium-sized toes (I' and I") lying close together and parallel to or slightly convex towards each other. This condition indicates that the 2 toes, together, are to be regarded as the equivalent of the normal single toe occupying the same position. The 2 toes are, I conjecture, derived from the single toe by splitting. The first series of changes consists of the increase in length of the lateral element (I") and a corresponding decrease of the median element (I'). In the last term of the series there are only 4 toes on the foot, but the inner toe is not like the normal inner toe of poultry, but is a much elongated I".

In the Silkie, also, the series begins with 2 small, closely-applied toes (I' and I"). But when there are only 2 toes the lateral one is usually much the larger. Typically this lateral toe is, as stated, split, so that the nail is double, and the degree of splitting is variable, in extreme cases involving half or more than half of the toe. A second series of changes consists of the gradual reduction of toe I' (often concomitantly with an increase in I") which may end in its entire disappearance and thus reduce the number of toes to 5, but these are not equivalent to the 5 toes of the Houdans, since the extra Houdan toes are I', I", and those of the reduced Silkie are I"a and I"b. Finally, in Silkies, the inner toe (I') may split (more or less completely), and thus the 7-toed condition arises. Moreover, in Houdans I have on one or two occasions found the lateral element (I") bifid distally, resembling perfectly the typical condition found in the Silkies.

A simple nomenclature is suggested for these various types of extra-toes. The simple double-toed condition, as found commonly in Houdans, may be called the duplex type (D). The loss of I' gives the reduced duplex (D'). The case of split I", as commonly seen in the Silkie, is the triplex type (T); with the loss of I' this becomes the reduced triplex (T', not duplex!). The 7-toed condition of Silkies may be called the quadruplex type (Q); the combination split I' and single I" gives the reduced quadruplex (Q').[3]

The reduction that leads to the loss of I' consists of a loss of phalanges, as Bateson (1904) has already pointed out. It seems probable that the reduction affects first the proximal phalanges, since the distal nail-bearing phalanx is the last to disappear.

B. RESULTS OF HYBRIDIZATION.

In hybrids of both classes the greatest number of toes occurring on one foot never exceeds the greatest number possessed by its parents; indeed, the most polydactyl hybrids of the F₁ generation of Silkies never have as many as 6 toes on one foot. This result is not to be explained as due to a regression towards the 4-4-toed condition, but rather as due to the intermediate condition of the heterozygote. For 80 per cent of the hybrids show either the typical or the reduced D type on one or both feet, although neither parent exhibits these types.

We have next to consider the results of mating together the F₁ hybrids. Table 11 gives the results of all matings of this sort.