Part 3

But suppose that instead of individuals presenting one character in differing intensities, two individuals breed together distinguished by characters which we know to be mutually exclusive, such as _A_ and _B_. Here again we may speak of the individuals producing the gametes as _A_ and _B_, and the resulting zygote as _AB_. What will _AB_ be like? The population here again may consist of many like _A_ and like _B_. These two forms may have been breeding together indiscriminately, and there may have been many or few of either type in the pedigree of either _A_ or _B_.

Here again Galton applied his method with remarkable success. Referring to the progenitors of _A_ and _B_, determining how many of each type there were in the direct pedigree of _A_ and of _B_, he arrived at the same formula as before, with the simple difference that instead of expressing the probable average intensity of one character in several individuals, the prediction is given in terms of the probable number of _A_’s and _B_’s that would result on an average when particular _A_’s and _B_’s of known pedigree breed together.

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[16], 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[17] the wisdom of which can scarcely be questioned.

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

[17] 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[18], 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_.

[18] 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[19]. These “reversionary” mice bred together produce the parental tame types, some other types, and “reversionary” mice again.

[19] See von Guaita, _Ber. naturf. Ges. Freiburg_ X. 1898 and XI. 1899, quoted by Professor Weldon (see later).

From what has been said it will now be clear that the applicability of the Mendelian hypothesis has, intrinsically, nothing whatever to do with the question of the inheritance being _blended_ or _alternative_. In fact, as soon as the relation of zygote characters to gamete characters is appreciated, it is difficult to see any reason for supposing that the manifestation of characters seen in the zygotes should give any indication as to their mode of allotment among the gametes.

On a previous occasion I pointed out that the terms “Heredity” and “Inheritance” are founded on a misapplication of metaphor, and in the light of our present knowledge it is becoming clearer that the ideas of “transmission” of a character by parent to offspring, or of there being any “contribution” made by an ancestor to its posterity, must only be admitted under the strictest reserve, and merely as descriptive terms.

* * * * *

We are now presented with some entirely new conceptions:--

(1) The purity of the gametes in regard to certain characters.

(2) The distinction of all zygotes according as they are or are not formed by the union of like or unlike gametes. In the former case, apart from Variation, they breed true when mated with their like; in the latter case their offspring, collectively, will be heterogeneous.

(3) If the zygote be formed by the union of dissimilar gametes, we may meet the phenomenon of (_a_) dominant and recessive characters; (_b_) a blend form; (_c_) a form distinct from either parent, often reversionary[20].

[20] This fact sufficiently indicates the difficulties involved in a superficial treatment of the phenomenon of reversion. To call such reversions as those named above “returns to ancestral type” would be, if more than a descriptive phrase were intended, quite misleading. It is not the ancestral _type_ that has come back, but something else has come in its guise, as the offspring presently prove. For the first time we thus begin to get a rationale of “reversion.”

But there are additional and even more significant deductions from the facts. We have seen that the gametes are differentiated in respect of pure characters. Of these pure characters there may _conceivably_ be any number associated together in one organism. In the pea Mendel detected at least seven--not all seen by him combined in the same plant, but there is every likelihood that they are all capable of being thus combined.

Each such character, which is capable of being dissociated or replaced by its contrary, must henceforth be conceived of as a distinct _unit-character_; and as we know that the several unit-characters are of such a nature that any one of them is capable of independently displacing or being displaced by one or more alternative characters taken singly, we may recognize this fact by naming such unit-characters _allelomorphs_. So far, we know very little of any allelomorphs existing otherwise than as _pairs_ of contraries, but this is probably merely due to experimental limitations and the rudimentary state of our knowledge.

In one case (combs of fowls) we know three characters, _pea_ comb, _rose_ comb and _single_ comb; of which _pea_ and _single_, or _rose_ and _single_, behave towards each other as a pair of allelomorphs, but of the behaviour of _pea_ and _rose_ towards each other we know as yet nothing.

We have no reason as yet for affirming that any phenomenon properly described as _displacement_ of one allelomorph by another occurs, though the metaphor may be a useful one. In all cases where _dominance_ has been perceived, we can affirm that the members of the allelomorphic pair stand to each other in a relation the nature of which we are as yet wholly unable to apprehend or illustrate.

To the new conceptions already enumerated we may therefore add

(4) _Unit-characters_ of which some, _when once arisen by Variation_, are alternative to each other in the constitution of the gametes, according to a definite system.

From the relations subsisting between these characters, it follows that as each zygotic union of allelomorphs is _resolved_ on the formation of the gametes, no zygote can give rise to gametes collectively representing more than _two_ characters allelomorphic to each other, apart from new variation.

From the fact of the existence of the interchangeable characters we must, for purposes of treatment, and to complete the possibilities, necessarily form the conception of an _irresoluble base_, though whether such a conception has any objective reality we have no means as yet of determining.

We have now seen that when the varieties _A_ and _B_ are crossed together, the heterozygote, _AB_, produces gametes bearing the pure _A_ character and the pure _B_ character. In such a case we speak of such characters as _simple_ allelomorphs. In many cases however a more complex phenomenon happens. The character brought in on fertilisation by one or other parent may be of such a nature that when the zygote, _AB_, forms its gametes, these are not individually bearers merely of _A_ and _B_, _but of a number of characters themselves again integral_, which in, say _A_, behaved as one character so long as its gametes united in fertilisation with others like themselves, but on cross-fertilisation are resolved and redistributed among the gametes produced by the cross-bred zygote.

In such a case we call the character _A_ a _compound_ allelomorph, and we can speak of the integral characters which constitute it as _hypallelomorphs_. We ought to write the heterozygote (_A A′ A″_ ...) _B_ and the gametes produced by it may be of the form _A_, _A′_, _A″_, _A‴_,... _B_. Or the resolution may be incomplete in various degrees, as we already suspect from certain instances; in which case we may have gametes _A_, _A′ A″_, _A‴ A″″_, _A′ A″ A^v_,... _B_, and so on. Each of these may meet a similar or a dissimilar gamete in fertilisation, forming either a homozygote, or a heterozygote with its distinct properties.

In the case of compound allelomorphs we know as yet nothing of the statistical relations of the several gametes.

Thus we have the conception

(5) _of a Compound character_, borne by one gamete, transmitted entire as a single character so long as fertilisation only occurs between like gametes, or is, in other words, “symmetrical,” but if fertilisation take place with a dissimilar gamete (or possibly by other causes), resolved into integral constituent characters, each separately transmissible.

Next, as, by the union of the gametes bearing the various hypallelomorphs with other such gametes, or with gametes bearing simple allelomorphs, in fertilisation, a number of new zygotes will be formed, such as may not have been seen before in the breed: these will inevitably be spoken of as _varieties_; and it is difficult not to extend the idea of variation to them. To distinguish these from other variations--which there must surely be--we may call them

(6) _Analytical_ variations in contradistinction to

(7) _Synthetical_ variations, occurring not by the separation of pre-existing constituent-characters but by the addition of new characters.

Lastly, it is impossible to be presented with the fact that in Mendelian cases the cross-bred produces on an average _equal_ numbers of gametes of each kind, that is to say, a symmetrical result, without suspecting that this fact must correspond with some symmetrical figure of distribution of those gametes in the cell-divisions by which they are produced.

* * * * *

At the present time these are the main conceptions--though by no means all--arising directly from Mendel’s work. The first six are all more or less clearly embodied by him, though not in every case developed in accordance with modern knowledge. The seventh is not a Mendelian conception, but the facts before us justify its inclusion in the above list though for the present it is little more than a mere surmise.

* * * * *

In Mendelian cases it will now be perceived that all the zygotes composing the population consist of a limited number of possible types, each of definite constitution, bearing gametes also of a limited and definite number of types, and definite constitution in respect of pre-existing characters. It is now evident that in such cases each several progenitor need not be brought to account in reckoning the probable characters of each descendant; for the gametes of cross-breds are differentiated at each successive generation, some parental (Mendelian) characters being left out in the composition of each gamete produced by a zygote arising by the union of bearers of opposite allelomorphs.

When from these considerations we return to the phenomena comprised in the Law of Ancestral Heredity, what certainty have we that the same conceptions are not applicable there also?

It has now been shown that the question whether in the cross-bred zygotes in general the characters blend or are mutually exclusive is an entirely subordinate one, and distinctions with regard to the essential nature of heredity based on these circumstances become irrelevant.

In the case of a population presenting continuous variation in regard to say, stature, it is easy to see how purity of the gametes in respect of any intensities of that character might not in ordinary circumstances be capable of detection. There are doubtless more than two pure gametic forms of this character, but there may quite conceivably be six or eight. When it is remembered that each heterozygous combination of any two may have its own appropriate stature, and that such a character is distinctly dependent on external conditions, the mere fact that the observed curves of stature give “chance distributions” is not surprising and may still be compatible with purity of gametes in respect of certain pure types. In peas (_P. sativum_), for example, from Mendel’s work we know that the tall forms and the extreme dwarf forms exhibit gametic purity. I have seen at Messrs Sutton’s strong evidence of the same nature in the case of the tall Sweet Pea (_Lathyrus odoratus_) and the dwarf or procumbent “Cupid” form.

But in the case of the Sweet Pea we know at least one pure form of definitely intermediate height, and in the case of _P. sativum_ there are many. When the _extreme_ types breed together it will be remembered the heterozygote commonly exceeds the taller in height. In the next generation, since there is, in the case of extremes, so much margin between the types of the two pure forms, the return of the offspring to the three forms of which two are homozygous and one heterozygous is clearly perceptible.

If however instead of pure extreme varieties we were to take a pair of varieties differing normally by only a foot or two, we might, owing to the masking effects of conditions, &c., have great difficulty in distinguishing the three forms in the second generation. There would besides be twice as many heterozygous individuals as homozygous individuals of each kind, giving a symmetrical distribution of heights, and who might not--in pre-Mendelian days--have accepted such evidence--made still less clear by influence of conditions--as proof of Continuous Variation both of zygotes and gametes?

Suppose, then, that instead of two pure types, we had six or eight breeding together, each pair forming their own heterozygote, there would be a very remote chance of such purity or fixity of type whether of gamete or zygote being detected.