Part 7

The law as Galton gives it is as follows:--

“It is that the two parents contribute between them on the average one-half, or (0·5) of the total heritage of the offspring; the four grandparents, one-quarter, or (0·5)^2; the eight great-grandparents, one-eighth, or (0·5)^3, and so on. Then the sum of the ancestral contributions is expressed by the series

{(0·5) + (0·5)^2 + (0·5)^3, &c.},

which, being equal to 1, accounts for the whole heritage.”

In the former case where A and a are characters which can be denoted by reference to a common scale, the law assumes of course that the inheritance will be, to use Galton’s term, blended, namely that the zygote resulting from the union of A with a will on the average be more like a than if A had been united with A; and conversely that an Aa zygote will on the average be more like A than an aa zygote would be.

But in the case of A’s and B’s, which are assumed to be mutually exclusive characters, we cannot speak of blending, but rather, to use Galton’s term, of alternative inheritance.

Pearson, finding that the law whether formulated thus, or in the modified form in which he restated it, did not express the phenomena of alternative inheritance known to him with sufficient accuracy to justify its strict application to them, and also on general grounds, proposed that the phenomena of blended and alternative inheritance should be treated apart--a suggestion the wisdom of which can scarcely be questioned.

In Pearson’s modification the parents contribute 0·3, the grandparents 0·15, the great-grandparents ·075.

See the works referred to above.

Now the law thus imperfectly set forth and every modification of it is incomplete in one respect. It deals only with the characters of the resulting zygotes and predicates nothing in regard to the gametes which go to form them. A good prediction may be made as to any given group of zygotes, but the various possible constitutions of the gametes are not explicitly treated.

Nevertheless a definite assumption is implicitly made regarding the gametes. It is not in question that differences between these gametes may occur in respect of the heritage they bear; yet it is assumed that these differences will be distributed among the gametes of any individual zygote in such a way that each gamete remains capable, on fertilisation, of transmitting all the characters (both of the parent-zygote and of its progenitors) to the zygote which it then contributes to form (and to the posterity of that zygote) in the intensity indicated by the law. Hence the gametes of any individual are taken as collectively a fair sample of all the racial characters in their appropriate intensities, and this theory demands that there shall have been no qualitative redistribution of characters among the gametes of any zygote in such a way that some gametes shall be finally excluded from partaking of and transmitting any specific part of the heritage. The theory further demands--and by the analogy of what we know otherwise not only of animals and plants, but of physical or chemical laws, perhaps this is the most serious assumption of all--that the structure of the gametes shall admit of their being capable of transmitting any character in any intensity varying from zero to totality with equal ease; and that gametes of each intensity are all equally likely to occur, given a pedigree of appropriate arithmetical composition.

Such an assumption appears so improbable that even in cases where the facts seem as yet to point to this conclusion with exceptional clearness, as in the case of human stature, I cannot but feel there is still room for reserve of judgment.

However this may be, the Law of Ancestral Heredity, and all modifications of it yet proposed, falls short in the respect specified above, that it does not directly attempt to give any account of the distribution of the heritage among the gametes of any one individual.

Mendel’s conception differs fundamentally from that involved in the Law of Ancestral Heredity. The relation of his hypothesis to the foregoing may be most easily shown if we consider it first in application to the phenomena resulting from the cross-breeding of two pure varieties.

Let us again consider the case of two varieties each displaying the same character, but in the respective intensities A and a. Each gamete of the A variety bears A, and each gamete of the a variety bears a. When they unite in fertilisation they form the zygote Aa. What will be its characters? The Mendelian teaching would reply that this can only be known by direct experiment with the two forms A and a, and that the characters A and a perceived in those two forms or varieties need not give any indication as to the character of the zygote Aa. It may display the character A, or a, or a character half way between the two, or a character beyond A or below a. The character of Aa is not regarded as a heritage transmitted to it by A and by a, but as a character special and peculiar to Aa, just as NaCl is not a body half way between sodium and chlorine, or such that its properties can be predicted from or easily stated in terms of theirs.

If a concrete case may help, a tall pea A crossed with a dwarf a often produces, not a plant having the height of either A or a, but something taller than the pure tall variety A.

But if the case obeys the Mendelian principles--as does that here quoted--then it can be declared first that the gametes of Aa will not be bearers of the character proper to Aa; but, generally speaking, each gamete will either bear the pure A character or the pure a character. There will in fact be a redistribution of the characters brought in by the gametes which united to form the zygote Aa, such that each gamete of Aa is pure, as the parental gametes were. Secondly this redistribution will occur in such a way that, of the gametes produced by such Aa’s, on an average there will be equal numbers of A gametes and of a gametes.

Consequently if Aa’s breed together, the new A gametes may meet each other in fertilisation, forming a zygote AA, namely, the pure A variety again; similarly two a gametes may meet and form aa, or the pure a variety again. But if an A gamete meets an a it will once more form Aa, with its special character. This Aa is the hybrid, or “mule” form, or as I have elsewhere called it, the heterozygote, as distinguished from AA or aa the homozygotes.

Similarly if the two gametes of two varieties distinguished by characters, A and B, which cannot be described in terms of any common scale (such as for example the “rose” and “single” combs of fowls) unite in fertilisation, again the character of the mule form cannot be predicted. Before the experiment is made the “mule” may present any form. Its character or properties can as yet be no more predicted than could those of the compounds of unknown elements before the discovery of the periodic law.

But again--if the case be Mendelian--the gametes borne by AB will be either A’s or B’s, and the cross-bred AB’s breeding together will form AA’s, AB’s and BB’s. Moreover, if as in the normal Mendelian case, AB’s bear on an average equal numbers of A gametes and B gametes, the numerical ratio of these resulting zygotes to each other will be

1 AA : 2 AB : 1 BB.

This conception was clearly formed by Naudin simultaneously with Mendel, but it was not worked out by him and remained a mere suggestion. In one place also Focke came very near to the same idea (see Bibliography).

We have seen that Mendel makes no prediction as to the outward and visible characters of AB, but only as to the essential constitution and statistical condition of its gametes in regard to the characters A and B. Nevertheless in a large number of cases the character of AB is known to fall into one of three categories (omitting mosaics).

(1) The cross-bred may almost always resemble one of its pure parents so closely as to be practically indistinguishable from that pure form, as in the case of the yellow cotyledon-colour of certain varieties of peas when crossed with green-cotyledoned varieties; in which case the parental character, yellow, thus manifested by the cross-bred is called “dominant” and the parental character, green, not manifested, is called recessive.

(2) The cross-bred may present some condition intermediate between the two parental forms, in which case we may still retain the term “blend” as applied to the zygote.

Such an “intermediate” may be the apparent mean between the two parental forms or be nearer to one or other in any degree. Such a case is that of a cross between a rich crimson Magenta Chinese Primrose and a clear White, giving a flower of a colour appropriately described as a “washy” magenta.

(3) The cross-bred may present some form quite different from that of either pure parent. Though, as has been stated, nothing can be predicted of an unknown case, we already know a considerable number of examples of this nature in which the mule-form approaches sometimes with great accuracy to that of a putative ancestor, near or remote. It is scarcely possible to doubt that several--though perhaps not all--of Darwin’s “reversions on crossing” were of this nature.

Such a case is that of the “wild grey mouse” produced by the union of an albino tame mouse and a piebald Japanese mouse. These “reversionary” mice bred together produce the parental tame types, some other types, and “reversionary” mice again.