Part 2

[4] See later. Galton gave a simple diagrammatic representation of his law in _Nature_, 1898, vol. LVII. p. 293.

But already many cases are known to which the rule in any simple form will not apply. Galton points out that it takes no account of individual prepotencies. There are, besides, numerous cases in which on crossing two varieties the character of one variety almost always appears in each member of the first cross-bred generation. Examples of these will be familiar to those who have experience in such matters. The offspring of the Polled Angus cow and the Shorthorn bull is almost invariably polled or with very small loose “scurs.” Seedlings raised by crossing _Atropa belladonna_ with the yellow-fruited variety have without exception the blackish-purple fruits of the type. In several hairy species when a cross with a glabrous variety is made, the first cross-bred generation is altogether hairy[5].

[5] These we now recognize as examples of Mendelian ‘dominance.’

Still more numerous are examples in which the characters of one variety very largely, though not exclusively, predominate in the offspring.

These large classes of exceptions--to go no further--indicate that, as we might in any case expect, the principle is not of universal application, and will need various modifications if it is to be extended to more complex cases of inheritance of varietal characters. No more useful work can be imagined than a systematic determination of the precise “law of heredity” in numbers of particular cases.

Until lately the work which Galton accomplished stood almost alone in this field, but quite recently remarkable additions to our knowledge of these questions have been made. In the year 1900 Professor de Vries published a brief account[6] of experiments which he has for several years been carrying on, giving results of the highest value.

[6] _Comptes Rendus_, March 26, 1900, and _Ber. d. Deutsch. Bot. Ges._ xviii. 1900, p. 83.

The description is very short, and there are several points as to which more precise information is necessary both as to details of procedure and as to statement of results. Nevertheless it is impossible to doubt that the work as a whole constitutes a marked step forward, and the full publication which is promised will be awaited with great interest.

The work relates to the course of heredity in cases where definite varieties differing from each other in some _one_ definite character are crossed together. The cases are all examples of discontinuous variation: that is to say, cases in which actual intermediates between the parent forms are not usually produced on crossing[7]. It is shown that the subsequent posterity obtained by self-fertilising these cross-breds or hybrids, or by breeding them with each other, break up into the original parent forms according to fixed numerical rule.

[7] This conception of discontinuity is of course pre-Mendelian.

Professor de Vries begins by reference to a remarkable memoir by Gregor Mendel[8], giving the results of his experiments in crossing varieties of _Pisum sativum_. These experiments of Mendel’s were carried out on a large scale, his account of them is excellent and complete, and the principles which he was able to deduce from them will certainly play a conspicuous part in all future discussions of evolutionary problems. It is not a little remarkable that Mendel’s work should have escaped notice, and been so long forgotten.

[8] ‘Versuche üb. Pflanzenhybriden’ in the _Verh. d. Naturf. Ver. Brünn_, iv. 1865.

For the purposes of his experiments Mendel selected seven pairs of characters as follows:--

1. Shape of ripe seed, whether round; or angular and wrinkled.

2. Colour of “endosperm” (cotyledons), whether some shade of yellow; or a more or less intense green.

3. Colour of the seed-skin, whether various shades of grey and grey-brown; or white.

4. Shape of seed-pod, whether simply inflated; or deeply constricted between the seeds.

5. Colour of unripe pod, whether a shade of green; or bright yellow.

6. Nature of inflorescence, whether the flowers are arranged along the axis of the plant; or are terminal and form a kind of umbel.

7. Length of stem, whether about 6 or 7 ft. long, or about 3/4 to 1-1/2 ft.

Large numbers of crosses were made between Peas differing in respect of _one_ of each of these pairs of characters. It was found that in each case the offspring of the cross exhibited the character of one of the parents in almost undiminished intensity, and intermediates which could not be at once referred to one or other of the parental forms were not found.

In the case of each pair of characters there is thus one which in the first cross prevails to the exclusion of the other. This prevailing character Mendel calls the _dominant_ character, the other being the _recessive_ character[9].

[9] Note that by these novel terms the complications involved by use of the expression “prepotent” are avoided.

That the existence of such “dominant” and “recessive” characters is a frequent phenomenon in cross-breeding, is well known to all who have attended to these subjects.

By letting the cross-breds fertilise themselves Mendel next raised another generation. In this generation were individuals which showed the dominant character, but also individuals which presented the recessive character. Such a fact also was known in a good many instances. But Mendel discovered that in this generation the numerical proportion of dominants to recessives is on an average of cases approximately constant, being in fact _as three to one_. With very considerable regularity these numbers were approached in the case of each of his pairs of characters.

There are thus in the first generation raised from the cross-breds 75 per cent. dominants and 25 per cent. recessives.

These plants were again self-fertilised, and the offspring of each plant separately sown. It next appeared that the offspring of the recessives _remained pure recessive_, and in subsequent generations never produced the dominant again.

But when the seeds obtained by self-fertilising the dominants were examined and sown it was found that the dominants were not all alike, but consisted of two classes, (1) those which gave rise to pure dominants, and (2) others which gave a mixed offspring, composed partly of recessives, partly of dominants. Here also it was found that the average numerical proportions were constant, those with pure dominant offspring being to those with mixed offspring as one to two. Hence it is seen that the 75 per cent. dominants are not really of similar constitution, but consist of twenty-five which are pure dominants and fifty which are really cross-breds, though, like the cross-breds raised by crossing the two original varieties, they only exhibit the dominant character.

To resume, then, it was found that by self-fertilising the original cross-breds the same proportion was always approached, namely--

25 dominants, 50 cross-breds, 25 recessives, or 1_D_ : 2_DR_ : 1_R_.

Like the pure recessives, the pure dominants are thenceforth pure, and only give rise to dominants in all succeeding generations studied.

On the contrary the fifty cross-breds, as stated above, have mixed offspring. But these offspring, again, in their numerical proportions, follow the same law, namely, that there are three dominants to one recessive. The recessives are pure like those of the last generation, but the dominants can, by further self-fertilisation, and examination or cultivation of the seeds produced, be again shown to be made up of pure dominants and cross-breds in the same proportion of one dominant to two cross-breds.

The process of breaking up into the parent forms is thus continued in each successive generation, the same numerical law being followed so far as has yet been observed.

Mendel made further experiments with _Pisum sativum_, crossing pairs of varieties which differed from each other in _two_ characters, and the results, though necessarily much more complex, showed that the law exhibited in the simpler case of pairs differing in respect of one character operated here also.

In the case of the union of varieties _AB_ and _ab_ differing in two distinct pairs of characters, _A_ and _a_, _B_ and _b_, of which _A_ and _B_ are dominant, _a_ and _b_ recessive, Mendel found that in the first cross-bred generation there was only _one_ class of offspring, really _AaBb_.

But by reason of the dominance of one character of each pair these first crosses were hardly if at all distinguishable from _AB_.

By letting these _AaBb_’s fertilise themselves, only _four_ classes of offspring seemed to be produced, namely,

_AB_ showing both dominant characters. _Ab_ " dominant _A_ and recessive _b_. _aB_ " recessive _a_ and dominant _B_. _ab_ " both recessive characters _a_ and _b_.

The numerical ratio in which these classes appeared were also regular and approached the ratio

9_AB_ : 3_Ab_ : 3_aB_ : 1_ab_.

But on cultivating these plants and allowing them to fertilise themselves it was found that the members of the

RATIOS

1 _ab_ class produce only _ab_’s.

3 {1 _aB_ class may produce either all _aB_’s, {2 _or_ both _aB_’s and _ab_’s.

RATIOS

3 { 1 _Ab_ class may produce either all _Ab_’s, { 2 _or_ both _Ab_’s and _ab_’s.

{ 1 _AB_ class may produce either all _AB_’s, { 2 _or_ both _AB_’s and _Ab_’s, 9 { 2 _or_ both _AB_’s and _aB_’s, { 4 _or_ all four possible classes again, namely, { _AB_’s, _Ab_’s, _aB_’s, and _ab_’s,

and the average number of members of each class will approach the ratio 1 : 3 : 3 : 9 as indicated above.

The details of these experiments and of others like them made with _three_ pairs of differentiating characters are all set out in Mendel’s memoir.

Professor de Vries has worked at the same problem in some dozen species belonging to several genera, using pairs of varieties characterised by a great number of characters: for instance, colour of flowers, stems, or fruits, hairiness, length of style, and so forth. He states that in all these cases Mendel’s principles are followed.

The numbers with which Mendel worked, though large, were not large enough to give really smooth results[10]; but with a few rather marked exceptions the observations are remarkably consistent, and the approximation to the numbers demanded by the law is greatest in those cases where the largest numbers were used. When we consider, besides, that Tschermak and Correns announce definite confirmation in the case of _Pisum_, and de Vries adds the evidence of his long series of observations on other species and orders, there can be no doubt that Mendel’s law is a substantial reality; though whether some of the cases that depart most widely from it can be brought within the terms of the same principle or not, can only be decided by further experiments.

[10] Professor Weldon (p. 232) takes great exception to this statement, which he considerately attributes to “some writers.” After examining the conclusions he obtained by algebraical study of Mendel’s figures I am disposed to think my statement not very far out.

One may naturally ask, How can these results be brought into harmony with the facts of hybridisation hitherto known; and, if all this is true, how is it that others who have carefully studied the phenomena of hybridisation have not long ago perceived this law? The answer to this question is given by Mendel at some length, and it is, I think, satisfactory. He admits from the first that there are undoubtedly cases of hybrids and cross-breds which maintain themselves pure and do not break up. Such examples are plainly outside the scope of his law. Next he points out, what to anyone who has rightly comprehended the nature of discontinuity in variation is well known, that the variations in _each_ character must be _separately_ regarded. In most experiments in crossing, forms are taken which differ from each other in a multitude of characters--some continuous, others discontinuous, some capable of blending with their contraries, while others are not. The observer on attempting to perceive any regularity is confused by the complications thus introduced. Mendel’s law, as he fairly says, could only appear in such cases by the use of overwhelming numbers, which are beyond the possibilities of practical experiment. Lastly, no previous observer had applied a strict statistical method.

Both these answers should be acceptable to those who have studied the facts of variation and have appreciated the nature of Species in the light of those facts. That different species should follow different laws, and that the same law should not apply to all characters alike, is exactly what we have every right to expect. It will also be remembered that the principle is only explicitly declared to apply to discontinuous characters[11]. As stated also it can only be true where reciprocal crossings lead to the same result. Moreover, it can only be tested when there is no sensible diminution in fertility on crossing.

[11] See later.

Upon the appearance of de Vries’ paper announcing the “rediscovery” and confirmation of Mendel’s law and its extension to a great number of cases two other observers came forward almost simultaneously and independently described series of experiments fully confirming Mendel’s work. Of these papers the first is that of Correns, who repeated Mendel’s original experiment with Peas having seeds of different colours. The second is a long and very valuable memoir of Tschermak, which gives an account of elaborate researches into the results of crossing a number of varieties of _Pisum sativum_. These experiments were in many cases carried out on a large scale, and prove the main fact enuntiated by Mendel beyond any possibility of contradiction. The more exhaustive of these researches are those of Tschermak on Peas and Correns on several varieties of Maize. Both these elaborate investigations have abundantly proved the general applicability of Mendel’s law to the character of the plants studied, though both indicate some few exceptions. The details of de Vries’ experiments are promised in the second volume of his most valuable _Mutationstheorie_. Correns in regard to Maize and Tschermak in the case of _P. sativum_ have obtained further proof that Mendel’s law holds as well in the case of varieties differing from each other in _two_ pairs of characters, one of each pair being dominant, though of course a more complicated expression is needed in such cases[12].

[12] Tschermak’s investigations were besides directed to a re-examination of the question of the absence of beneficial results on cross-fertilising _P. sativum_, a subject already much investigated by Darwin, and upon this matter also important further evidence is given in great detail.

That we are in the presence of a new principle of the highest importance is manifest. To what further conclusions it may lead us cannot yet be foretold. But both Mendel and the authors who have followed him lay stress on one conclusion, which will at once suggest itself to anyone who reflects on the facts. For it will be seen that the results are such as we might expect if it be imagined that the cross-bred plant produced pollen grains and egg-cells, each of which bears only _one_ of the alternative varietal characters and not both. If this were so, and if on an average the same number of pollen grains and egg-cells transmit each of the two characters, it is clear that on a random assortment of pollen grains and egg-cells Mendel’s law would be obeyed. For 25 per cent. of “dominant” pollen grains would unite with 25 per cent. “dominant” egg-cells; 25 per cent. “recessive” pollen grains would similarly unite with 25 per cent. “recessive” egg-cells; while the remaining 50 per cent. of each kind would unite together. It is this consideration which leads both Mendel and those who have followed him to assert that these facts of crossing prove that each egg-cell and each pollen grain is pure in respect of each character to which the law applies. It is highly desirable that varieties differing in the form of their pollen should be made the subject of these experiments, for it is quite possible that in such a case strong confirmation of this deduction might be obtained. [Preliminary trials made with reference to this point have so far given negative results. Remembering that a pollen grain is not a germ-cell, but only a bearer of a germ-cell, the hope of seeing pollen grains differentiated according to the characters they bear is probably remote. Better hopes may perhaps be entertained in regard to spermatozoa, or possibly female cells.]

As an objection to the deduction of purity of germ-cells, however, it is to be noted that though true intermediates did not generally occur, yet the intensity in which the characters appeared did vary in degree, and it is not easy to see how the hypothesis of _perfect_ purity in the reproductive cells can be supported in such cases. Be this, however, as it may, there is no doubt we are beginning to get new lights of a most valuable kind on the nature of heredity and the laws which it obeys. It is to be hoped that these indications will be at once followed up by independent workers. Enough has been said to show how necessary it is that the subjects of experiment should be chosen in such a way as to bring the laws of heredity to a real test. For this purpose the first essential is that the differentiating characters should be few, and that all avoidable complications should be got rid of. Each experiment should be reduced to its simplest possible limits. The results obtained by Galton, and also the new ones especially described in this paper, have each been reached by restricting the range of observation to one character or group of characters, and it is certain that by similar treatment our knowledge of heredity may be rapidly extended.

* * * * *

To the above popular presentation of the essential facts, made for an audience not strictly scientific, some addition, however brief, is called for. First, in regard to the law of Ancestry, spoken of on p. 5. Those who are acquainted with Pearson’s _Grammar of Science_, 2nd ed. published early in 1900, the same author’s paper in _Proc. R. S._ vol. 66, 1900, p. 140, or the extensive memoir (pubd. Oct. 1900), on the inheritance of coat-colour in horses and eye-colour in man (_Phil. Trans._ 195, A, 1900, p. 79), will not need to be told that the few words I have given above constitute a most imperfect diagram of the operations of that law as now developed. Until the appearance of these treatises it was, I believe, generally considered that the law of Ancestral Heredity was to be taken as applying to phenomena like these (coat-colour, eye-colour, &c.) where the inheritance is generally _alternative_, as well as to the phenomena of _blended_ inheritance.

Pearson, in the writings referred to, besides withdrawing other large categories of phenomena from the scope of its operations, points out that the law of Ancestral Heredity does not satisfactorily express the cases of alternative inheritance. He urges, and with reason, that these classes of phenomena should be separately dealt with.

* * * * *

The whole issue as regards the various possibilities of heredity now recognized will be made clearer by a very brief exposition of the several conceptions involved.

If an organism producing germ-cells of a given constitution, uniform in respect of the characters they bear, breeds with another organism[13] bearing _precisely similar_ germ-cells, the offspring resulting will, if the conditions are identical, be uniform.

[13] For simplicity the case of self-fertilisation is omitted from this consideration.

In practice such a phenomenon is seen in _pure_-breeding. It is true that we know no case in nature where all the germ-cells are thus identical, and where no variation takes place beyond what we can attribute to conditions, but we know many cases where such a result is approached, and very many where all the essential features which we regard as constituting the characters of the breed are reproduced with approximate certainty in every member of the pure-bred race, which thus closely approach to uniformity.

But if two germ-cells of dissimilar constitution unite in fertilisation, what offspring are we to expect[14]? First let us premise that the answer to this question is known experimentally to differ for many organisms and for many classes of characters, and may almost certainly be in part determined by external circumstances. But omitting the last qualification, certain principles are now clearly detected, though what principle will apply in any given case can only be determined by direct experiment made with that case.

[14] In all the cases discussed it is assumed that the gametes are similar except in regard to the “heritage” they bear, and that no _original_ variation is taking place. The case of mosaics is also left wholly out of account (see later).

This is the phenomenon of _cross_-breeding. As generally used, this term means the union of members of dissimilar varieties, or species: though when dissimilar gametes[15] produced by two individuals of the same variety unite in fertilisation, we have essentially _cross_-breeding in respect of the character or characters in which those gametes differ. We will suppose, as before, that these two gametes bearing properties unlike in respect of a given character, are borne by different individuals.

[15] The term “gamete” is now generally used as the equivalent of “germ-cell,” whether male or female, and the term “zygote” is here used for brevity to denote the organism resulting from fertilisation.

In the simplest case, suppose a gamete from an individual presenting any character in intensity _A_ unite in fertilisation with another from an individual presenting the same character in intensity _a_. For brevity’s sake we may call the parent individuals _A_ and _a_, and the resulting zygote _Aa_. What will the structure of _Aa_ be in regard to the character we are considering?

Up to Mendel no one proposed to answer this question in any other way than by reference to the intensity of the character in the progenitors, and _primarily_ in the parents, _A_ and _a_, in whose bodies the gametes had been developed. It was well known that such a reference gave a very poor indication of what _Aa_ would be. Both _A_ and _a_ may come from a population consisting of individuals manifesting the same character in various intensities. In the pedigree of either _A_ or _a_ these various intensities may have occurred few or many times. Common experience leads us to expect the probability in regard to _Aa_ to be influenced by this history. The next step is that which Galton took. He extended the reference beyond the immediate parents of _Aa_, to its grandparents, great-grandparents, and so on, and in the cases he studied he found that from a knowledge of the intensity in which the given character was manifested in each progenitor, even for some few generations back, a fairly accurate prediction could be made, not as to the character of any individual _Aa_, but as to the average character of _Aa_’s of similar parentage, in general.