Mendel's Law

    In order to understand what follows it is absolutely necessary that the reader should have a general acquaintance with the present state of knowledge in regard to the Mendelian principle. The original paper is not easily accessible, but it has been reprinted in 'Flora,' 1901, and is about to appear in Ostwald's 'Klassiker der exakten Wissenschaften.' An English translation was published in the 'Journ. Roy. Hortic. Soc.,' 1901. We venture, however, to give a brief outline of the history and progress of the discovery, which is the more necessary as our own views and modes of expression do not agree wholly with those of other writers on the subject.

   It may be premised that the first publication of the re-discovery was made in 1900 by de Vries, {*Footnote: De Vries, 'Comptes Rendus,' March 26, 1900, and 'Ber. deut. Bot. Ges.,' xviii, 1900, p. 83; ibid., p. 435; 'Rev. gen. Bot.,' 1900, p. 257.} and almost simultaneously by Correns {* Footnote: Correns, 'Ber. deut. Bot. Ges.,' xviii, 1900, p. 158; 'Bot. Ztg.,' 1900, p. 232.} and Tschermak {* Footnote: Tschermak, 'Ztschr. f. d. landw. Versuchswesen in Oesterr.,' 1900, 3, p. 465}. There can be no doubt that the appearance of this group of papers constitutes at length a definite advance both in the general study of the physiology of reproduction and in the particular problem of the nature of Species.

    In 1865 Gregor Mendel published his discovery. His experiments are described in considerable detail, and the resulting law is stated with emphasis and precision. He at once perceived and lucidly enunciated what he regarded as the essential truth underlying the observed facts. A reader of this paper can hardly fail to recognise its masterly quality. By some strange chance it was ignored, and excepting a casual reference in Focke's 'Pflanzen-Mischlinge' (p. 110) there appears to be no allusion in [the] literature to this remarkable performance. It is a fortunate circumstance that we need feel no hesitation in now accepting Mendel's account; for even if the original paper were such as to admit of doubt, the re-discovery comes to us with a large body of fresh evidence, the simultaneous work of three independent observers, confirming Mendel on the main points.

   Mendel states that, like other investigators, he had been struck by the regularity with which offspring of certain hybrids reproduce the pure ancestral forms. But owing, as he supposes, to the complex nature of the cases studied and to want of accurate statistics, the precise facts had never been ascertained. Accordingly he set himself to work out some case from which every confusing element should is far as possible be excluded. After several trials he chose the varieties of Pisum sativum as best suited to his purpose.  

 Besides other advantages, this species is well known to have the exceptional merit of being habitually self-fertilised, in N. Europe at least. From the many varieties of peas he first chose pairs of varieties, for crossing, in such a way that the members of each pair differed from each other in respect of one definite character. Of such pairs of characters he chose seven, namely:

As to the first two characters the result of the experiment is seen as soon as the cross-bred seeds are ripe; but to study the other five characters it is of course necessary to plant the seeds and grow the plants to maturity. On such examination it was found that in the case of each pair of characters one only was manifested in every crossbred individual, to the total, or almost total, exclusion of the opposite character. The character which thus prevails is, in Mendel's terminology, the dominant (D), the character which is suppressed, being recessive (R). In the above enumeration of characters the dominant is placed first in each pair. Reciprocal crosses gave identical results. Briefly, then, D x R or R x D gave offspring which in appearance are all practically D.

    The next generation is obtained by allowing the cross-bred plants, DR, to fertilise themselves. The result of such self-fertilisation is, according to Mendel, that the next generation instead of being uniform like their parents, breaks up into the two original forms. This takes place in such a way that there are on the average three dominants to one recessive.

    The recessives are thenceforth not only apparently but actually pure, and if allowed to fertilise themselves give rise to recessives only, for any number of generations.

    The dominants, on the contrary, though they may look alike, can, if allowed to fertilise themselves, be shown to consist of 

•  (a) individuals which are pure dominants, and on self-fertilisation give rise to dominants only; and 
  

•  (b) individuals which are cross-breds, and give rise on self-fertilisation to a mixture of dominants and recessives, again in the proportion of three to one as before.

The pure dominants (a) are to the cross-bred dominants (b) as one to two.

    The whole result, therefore, of self-fertilising the cross-breds is really IDD :2DR : IRR, though apparently the proportion is 3D: IR, because DR plants are not to the eye distinguishable from pure D.{* Footnote omitted} The mixed offspring obtained by self-fertilising DR plants of this second generation consist again of D, DR, and R in the same proportions, and so on at each succeeding generation.

    Mendel worked with considerable numbers, and it is impossible to doubt the general accuracy of his conclusions. In the case of some of the pairs of characters (notably the 5th) the evidence is much less clear than in the case of others, and it seems possible that in such cases unascertained disturbances may be at work; but on the whole the results, as average results, are clear. The purity of the pure dominants and pure recessives resulting from the self-fertilisation of the cross-breds was tested in the case of characters 1 and 2 to the sixth generation, for characters 3 and 7 to the fifth generation, and for characters 4, 5, and 6 to the fourth generation.

     Mendel interprets his facts as follows : -- They point to the conclusion that in the cross-bred each of its pollen-grains and each of its egg cells is either pure dominant or pure recessive, {* Footnote: In what follows such forms are spoken of as "extracted" dominants, or "extracted" recessives.} and that on the average there are equal numbers of each kind for each sex. If the assortment of pollen-grains and egg-cells is then supposed to take place it random, the most probable percentage result is 25D female x D male, 25D female x R male, 25R female x D male, and 25R female x R male. As D x R does not differ from R x D, we have therefore 25D : 50DR : 25R. But as cross-breds resemble dominants in appearance, the apparent result is 3D : 1R at each successive self-fertilisation of cross-breds.

    Mendel next proceeded to cross pairs of varieties differing in respect of two characters; for example, a variety having seeds round and yellow, with a variety having seeds angular and green; and also pairs of varieties differing in three characters; for example, a variety characterised by seeds round, yellow, and in grey-brown skins, with a variety having seeds angular, green, and in white skins. 

    The numerical results of these experiments are set out at length, and are too long to repeat. Briefly the result in all cases was that the dominant characters alone appeared in the first cross. When these were self-fertilised, in the case of two differentiating characters, four different kinds of seeds resulted, namely, round yellow, angular yellow, round green, and angular green. In the case of three differentiating characters these were similarly combined in the eight possible combinations. In both sets of experiments the numbers of individuals and their constitution, as tested by the seeds they were capable of producing on self-fertilisation, were consistent with the hypothesis arrived at in the case of varieties differing in respect of one character, namely, that each male, and female cell of the cross-bred is pure in respect of one character of each pair of characters, and is capable of transmitting this character to the exclusion of the opposite character; that the reproductive cells are, in the cross-breds, of as many kinds as there are possible combinations of pure characters (taken two or three together, as the case may be); and, finally, that each kind is represented in the cross-breds on the average in equal numbers.

    Mendel next tested the truth of the hypothesis that both male and female cells were similarly differentiated, by crossing the first crosses with pure D and pure R forms respectively, finding, as he expected, that DR x D gives the ratio 1DD : 1DR, and that DR x R gives on the average the ratio l DR : 1 RR. Both sets of germ-cells are therefore similarly differentiated.{*Footnote omitted}

    It must be understood that this condensed statement does no justice to the lucidity and completeness of Mendel's account of his facts, and of the reasoning based on them. With regard to the numbers, it may be said that, though there is a good deal of irregularity, yet taken together they plainly bear out the law as a statement of average results.

     De Vries {*Footnote: C. R., 1900, March 26; 'Ber. deut. Bot. Ges.,' 18, 1900, p. 83.} working with pairs of varieties belonging to a diversity of genera and species, found that in a large number of cases one of the varietal characters was definitely dominant, prevailing in the first crosses to the exclusion of the recessive character. In several of these cases the offspring of the cross-breds fertilised inter se were mixed dominants and recessives in proportions fairly agreeing with Mendel's law. In the case of two colour varieties of Papaver somniferum, the constitution of the resulting dominants was investigated, and shown to be also according to the law. In certain cases also the purity of the recessives was tested and found to be complete.

    De Vries' first announcement was followed almost immediately by the appearance of a paper by Correns, {Footnote: 'Ber. deut. Bot. Ges.,' 18, 1900, p. 158} giving an account of some years' work with peas, repeating Mendel's experiments and confirming them as regards the colour of the seeds.

    Correns stated that he has tested the purity of the pure dominants and pure recessives to the third generation, and be has kindly informed us that a fourth generation is equally pure.

    In addition to these, Tschermak has given an account {*Footnote: 'Ztsch. f. d. landw. Versuchswesen in Oesterr.,' 3, 1900, p. 465; continued later, ibid., 4,1901, p. 641, and 'Ber. deut. Bot. Ges.,' 19,1901, p. 35} of simultaneous investigations also carried out on varieties of peas. This last paper is an elaborate memoir giving in addition valuable information on several points not directly relating to the present subject.

     Tschermak worked with many varieties of peas, and though he obtained several results not wholly consistent with Mendel's law, and some actually conflicting evidence, the general tenour of his work is confirmatory. He gives, in particular, results as to the crossing of cross-breds with one or other of the pure forms.

     It is an obvious corollary from Mendel's law that the cross-bred crossed with the recessive parent should give seeds of the dominant and recessive colours in equal numbers. On the other hand, the cross-bred crossed with the dominant should give dominants only (of which half should be pure and half cross-bred in composition). Tschermak's numbers though insufficient for a thorough test, are in fair harmony with Mendel's hypothesis. He believes also that there is evidence that yellow is more decidedly dominant over green, than the rounded character is over the wrinkled, and on this point further experiments are required.

   Subsequently a paper by Correns {*Footnote: 'Bot. Cblt.,' 1900, 43, p. 97} has appeared describing his experiments with a glabrous [without hairs] and a hoary form of garden stock (Matthiola incana), and giving results as to these varieties, tested by self-fertilisation, and also by recrossing the cross-breds with them parental forms. In this, as in each of the other papers, there are many points which call for separate notice and discussion, but the facts taken together are in fairly close agreement with the expectation given by Mendel's law, though the discrepancies are decidedly greater in this case than in the others. The case happens to be one which had also formed a subject of our experiments, and the various questions raised by the facts will be discussed in connection with the statement of our results.

    Lastly, Professor Correns has also published {*Footnote: 'Biblioth. Bot.,' 1901, Heft 53} an elaborate and important memoir on the results obtained in crossing varieties of maize. Some of these results are of a complex character, but the essential fact of the truth of Mendel's law in its application to many of these cases was fully established.

From the striking differences between these varieties in several characters, notably in the constitution of the endosperm, whether round starchy (dominant) or wrinkled and sugar-containing (recessive), this case is a most attractive subject for such experiments.

    In the characters of the endosperm in maize de Vries {*Footnote: 'Rev. gen. Bot.,' 12, 1900, p. 270} also demonstrated the truth of Mendel's law. As regards the colour varieties, Correns showed many complications to exist owing to the fact that the general appearance of the seed depends partly on maternal and partly on embryonic elements; and in some of the characteristics there are other confusing factors owing to fluctuations in the intensity of the dominance.

     The above is a brief sketch of a vast mass of observations all tending to the same conclusion, and the truth of the law enunciated by Mendel is now established for a large number of cases of most dissimilar characters, beyond question.

Let us now shortly distinguish what is essential in the new discovery from what is not. The fact that in the cross-bred one character, in appearance, dominated to the exclusion of the other is not of the essence of Mendel's discovery. Tschermak, for instance, saw some exceptions to this rule in Pisum. Among the Matthiola crosses here described, and among those originally made by Trevor Clarke {*Footnote: 'Rep. Intern. Hort. Exhib. And Bot. Congr.,' 1866, p. 142. As a sequel will show, this appearance is otherwise explicable.} the hoary form seems to be not exclusively dominant. Correns saw considerable fluctuations in the dominance of the colours of maize. It is practically certain some of the poultry cases about to be described exhibit the same phenomenon. In fact, generally speaking, there are good reasons for thinking that in numerous instances purity of gametes may occur without either character exhibiting dominance.

   There is also some reason for supposing that alterations in dominance may be affected by changes in conditions (see p. 136), and possibly even by differences in the state of the parents, though the only considerable body of evidence relating to these points, obtained by Vernon {* Footnote: Vernon, H. M., 'Phil. Trans.,' B, 1898, vol. 164, p. 465} in Echinid crossing, still needs repetition and confirmation.

     The essential part of the discovery is the evidence that the germ cells or gametes produced by cross-bred organisms may in respect of given characters be of the pure parental types and consequently incapable of transmitting the opposite character: that when such pure similar gametes of opposite sexes are united together in fertilisation, the individuals so formed, and their posterity, are free from all taint of the cross; that there may be, in short, perfect or almost perfect discontinuity between these germs in respect of one of each pair of opposite characters.

    Doubt might naturally be felt as to the acceptance of a proposition so far-reaching, but it is impossible to see any other possible interpretation of the facts. The pure dominant and pure recessive members of each generation are not merely like, but identical with the pure parents, {*Footnote: Correns, in maize, has found an apparent change in the degree of dominance of certain characters in the "extracted" variety.} and their descendants obtained by self-fertilisation are similarly pure. If they are pure, surely the male and female elements of which they composed must also be pure.

     In another part of this Report we propose to discuss the bearing of these remarkable facts, and to show some of the conclusions to which they point. It will be seen that they provide satisfactory interpretations, of some of those redoubtable paradoxes which have hitherto been so mysterious to all evolutionists.

    We may now proceed to the description of our own experiments. [Parts I and II omitted]

PART III

THE FACTS OF HEREDITY IN THE LIGHT OF MENDEL'S DISCOVERY

    As was stated in the introduction to this paper, with the discovery of the Mendelian principle the problem of evolution passes into a new phase. It is scarcely possible to overrate the importance of this discovery. Every conception of biology which involves a knowledge of the physiology of reproduction must feel the influence of the new facts, and, in their light, previous ideas of heredity and variation, the nature of specific differences, and all that depends on those ideas must be reconsidered, and in great measure modified.

     If we turn to any former description of breeding experiments we generally perceive at once that the whole account must be re-stated in terms of Mendel's hypothesis, and that the discussions and arguments based on former hypotheses are now meaningless. As an illustration we may take the account which Darwin gives of his experiments with peloric Antirrhinum {*Footnote: * 'Animals and Plants,' vol. 2, p. 46, ed. 1885}. He crossed the peloric form with the normal and vice versa. 

    The first crosses were all indistinguishable from the normal or zygomorphic form. These were allowed to fertilise themselves, and gave a crop consisting of 88 normals, 2 intermediates, and 37 perfectly peloric. He discusses these results on the hypothesis that the normal plant has a "tendency" to become peloric, and the peloric a "tendency" to become normal, "so that we have two opposed latent tendencies in the same plants. Now with the crossed Antirrhinums the tendency to produce normal or irregular flowers, like those of the common Snapdragon, prevailed in the first generation; whilst the tendency to pelorism, appearing to gain strength by the intermission of a generation, prevailed to a large extent in the second set of seedlings. How it is possible for a character to gain strength by the intermission of a generation will be considered in the chapter on pangenesis."

    Now, of course, we can perceive that the zygomorphic form is dominant and the peloric recessive, and that the arguments based on other hypotheses have no longer any significance. It would be a useful task to go similarly through the literature of breeding and translate the results into Mendelian terms. Such an exercise would show that the change which must now come over the conceptions of biology can only be compared with that which in the study of physical science followed the revelations of modern chemistry.

    The outcome of such a revision of current conceptions it is impossible to foresee, but we propose in the present paper to consider some of the more important questions which are immediately raised.

     To denote the new conceptions some new terms are needed. Several have already been suggested by Correns, but in practice we have not found his terminology altogether convenient, or that it meets the new requirements. Correns proposes the terms "heterodynamous" and "homodynamous" to express that an organism is dominant or not dominant in respect of a given character. There are unfortunately objections to the use of these terms, though in some respects they are very suitable. 

•  First, they are in use by Weismann and his followers in quite different senses, as Correns states. 
  
  

•  Secondly, it is not clear whether they are to be applied to the variety, the individual, or the character.

 Besides these objections, it is fairly clear that dominance is a phenomenon presenting various degrees of intensity; and while the single phenomenon of dominance is well expressed by that word itself, other conditions probably consist of various phenomena which are not conveniently denoted by one word.

   Correns' terms "homoogonous" and "schizogonous" cannot as yet be used with precision to mean more than breeding "true" and not breeding "true," and, for reasons given later, the metaphor of splitting may be incorrect.

    The terms also "halb-identisch" and "conjugirte" as applied to characters, are already fairly well expressed by the words in perfect or in imperfect correlation, which are already well understood. It would be confusing to introduce the metaphor of conjugation to denote these ideas.

   But while doubting whether this terminology already suggested will be found adequate, we do not propose at present to substitute new terms for the same phenomena. In our view, there are other conceptions arising from the Mendelian discoveries for which brief expressions are absolutely required, and for these we suggest the following terminology.

   In the introduction (p. 6) we attempted to distinguish precisely the essential fact discovered by Mendel, and to separate it from other subordinate appearances. We may now briefly recall and amplify that reasoning, showing how we propose to denote the several phenomena.

By crossing two forms exhibiting antagonistic characters, cross-breds were produced. The generative cells of these cross-breds were shown to be of two kinds, each being pure in respect of one of the parental characters. This purity of the germ-cells, and their inability to transmit both of the antagonistic characters, is the central fact proved by Mendel's work. We thus reach the conception of unit-characters existing in antagonistic pairs. Such characters we propose to call allelomorphs,{*Footnote omitted} and the zygote formed by the union of a pair of opposite allelomorphic gametes, we shall call a heterozygote. Similarly, the zygote formed by the union of gametes having similar allelomorphs, may be spoken of as a homozygote. 

    Upon a wide survey, we now recognise that this first principle has an extensive application in nature. We cannot as yet determine the limits of its applicability, and it is possible that many characters may really be allelomorphic, which we now suppose to be "transmissible" in any degree or intensity. On the other hand, it is equally possible that characters found to be allelomorphic in some cases may prove to be non-allelomorphic in others.

    It will be of great interest to determine how far the purity of the germ cells in respect of allelomorphic characters is an absolute rule, or whether there are exceptional cases in which such purity may be impaired. That such exceptions may arise is indeed almost certain from the evidence of "mosaic" fruits in Datura, where it was shown (p. 23) that the otherwise pure extracted recessives (thornless) showed exceptionally a thorny patch or segment. Unless this is an original sport on the part of the individual, such a phenomenon may be taken as indicating that the germ-cells may also have been mosaic. {*Footnote omitted}

   Indeed all that we know of the occurrence and distribution of variation among repeated parts, would lead us to expect such a possibility with confidence. This is a question we can analyse no further. Were it possible to do so, it might be a real help towards getting a picture of the actual process of heredity.

   But besides the strictly allelomorphic or Mendelian distribution of characters among the gametes (with or without mosaics), we can imagine three other possible arrangements.

 By a sufficiently wide survey, illustrations of each of these systems and of intermediates between them, will doubtless be found, and the classification of gametic differentiation according to these several types, in respect of various characters, in various species, will be a first step towards the construction of a general scheme of heredity.

    In gametic variation we thus meet in fact the same series of possibilities with which we have been familiar in the variation of zygotic organisms.

     The second fact observed by Mendel is that each heterozygote produces on an average equal numbers of gametes bearing each allelomorph of each pair. This is only enunciated as an average result. Unfortunately, the determinations of the results for individuals are still few, but from those that have been made, and even from the few recorded by Mendel himself (p. 13), we see that the fluctuations are so great, that we must suspect some special sources of disturbance. 

    Contributing to the average result of 3: 1 as between round and wrinkled peas, he mentions as extremes 43: 2, 14: 15 ; and between yellow and green 20 : 19 and 32 : 1. It is obvious that this suggests either that there has been, for some cause, selection among the germ-cells originally equal in numbers, or that the numbers were originally unequal, or that the assortment of male and female germs was not governed by pure chance. Probably a series of individual determinations when seriated would throw light on the nature of these remarkable fluctuations which have been observed in almost all the subjects studied. From what we already know (see p. 121), in respect of the output of the two kinds of gametes, it is fairly certain that fluctuations take place, corresponding probably with changes in health, age, and other conditions.

    From analogy -- an unsafe guide in these fields -- and from what is known of discontinuous variation in general, we incline to the view that even though the figures point to a sharp discontinuity between dominant and recessive elements, we shall ultimately recognise that the discontinuity between these elements need not be universally absolute. 

    We may expect to find individuals, and perhaps breeds or strains, and even individual gonads or groups of gonads, in which the discontinuity is less sharp even in respect of these very characters; similarly, for such units definite departures from statistical equality between D and R germs may be expected. In Pisum, for instance, we cannot be far out in considering an average of 50 per cent. D and 50 per cent. R as a close approximation to the truth for both male and female cells, but there is nothing yet which proves even here that the discontinuity must be always and absolutely complete.

    Similarly, we are not compelled to accept the proposition that germ-cells of each allelomorph always exist, on an average, in equal numbers. The proofs of the two propositions are unfortunately as yet interdependent. The purity of the extracted recessives and dominants has been tested, and we can in such cases accept it as a fact: the universal purity of the gametes we cannot test. For, any dominant which gives rise to a recessive offspring, we should class as a cross-bred, because cross-breds are like dominants in appearance. Similarly, any partially impure recessive would be classed as a cross-bred. If the number of germs of each kind borne by the cross-bred is sensibly unequal, or the discontinuity between them sensibly lessened, we can perceive a result, but we shall not know to which cause to ascribe it. The statistical method unfortunately cannot distinguish between the two causes in such a case. Readers of Mendel's paper will be aware that he laid down no universal rule as to the absolute purity of gametes, but merely pointed out that his results were explicable on the hypothesis of such purity.

     The statistics, however, are not so precise as to compel us to accept both that the germs of the cross-breds are always pure, and that they are always produced on an average in equal numbers.

    The next point arising immediately out of Mendel's work concerns the characters of the heterozygote. In the Pisum cases the heterozygote normally exhibits only one of the allelomorphs clearly, which is therefore called the dominant. It is, however, clear from what we know of cross-breeding, that such exclusive exhibition of one allelomorph in its totality is by no means a universal phenomenon. Even in the pea it is not the case that the heterozygote always shows the dominant allelomorph as clearly and in the same intensity as the pure dominant, and speaking generally, heterozygotes, though in numerous instances readily referable to one or other of the allelomorphic types, exhibit those types in a more or less modified form.

    Besides these, there are undoubtedly cases in which the heterozygote may show either of the allelomorphs, though one is commonly dominant. In the poultry crosses it was shown that the usually recessive foot-character (want of extra toe) may appear in the cross-bred. The want of dominance of hoariness in Matthiola seen in exceptional cases is a wholly different phenomenon (see pp. 45 and 79).

    From the analogy of poultry, it is scarcely doubtful that polydactylism in man is also allelomorphic to the normal, and here from the tables of heredity already recorded, {*Footnote: * For examples see Fackenbeim, 'Jen. Zt' xxii, p. 343} there is good evidence that both the normal and the polydactyle offspring of one polydactyle parent can transmit the polydactylism; in other words, the heterozygote may exhibit either allelomorph. Cases of the same phenomenon can indeed be multiplied. It must, however, be remembered that what is accepted as evidence of alternative inheritance, is not a proof that the dominance of either allelomorph is imperfect. This can only be known for certain when it has already been established that individuals showing either of the two allelomorphs can, when mated with an individual showing the same allelomorph, produce both allelomorphs among their offspring.{*Footnote omitted}

   This leads to a point of great importance to the evolutionist. We have been in the habit of speaking of a variation as discontinuous, in proportion as, between it and other forms of the species, intermediates are comparatively scarce when all breed freely together. In all cases of allelomorphic characters we can now give a more precise meaning to this description. It must now be recognised that such a population consists, in respect of each pair of allelomorphs, of three {*Footnote: Four, if reciprocal heterozygotes are not identical} kinds of individuals, namely, homozygotes containing one allelomorph, homozygotes containing the other allelomorph, and heterozygotes compounded of both. The first two will thus always form discontinuous groups, and the degree to which the heterozygotes form a connecting group, will depend on whether one allelomorph regularly or chiefly dominates in the heterozygote, or the allelomorphic characters completely or partially blend in the heterozygote. Such discontinuity will in fact primarily depend not on the blending or non-blending of the characters, as hitherto generally assumed, but on the permanent discontinuity or purity of the unfertilised germ-cells.

    It will be of great interest to study the statistics of such a population in nature. If the degree of dominance can be experimentally determined, or the heterozygote recognised, and we can suppose that all forms mate together with equal freedom and fertility, and that there is no natural selection in respect of the allelomorphs, it should be possible to predict the proportions of the several components of the population with some accuracy. Conversely, departures from the calculated result would then throw no little light on the influence of disturbing factors, selection, and the like.

    From the circumstance that dominance of either character is no essential accompaniment of allelomorphism, it must be determined whether the proportions of the two kinds of gametes produced by the heterozygote will vary with its individual character. Bearing on this question the experiments are very few. The determination from statistical study of zygotes must be exceedingly difficult, seeing that both resulting forms may be heterozygous. The ratio in which the heterozygotes are distributed in the second generation need not be the same as it was in the first, and unless this can be determined it will be almost impossible to get further with this particular inquiry.

   Another difficulty will be found in the possibility that when the first cross-bred generation gives a mixture, the forms showing the usually recessive character (both in this and subsequent generations) may be pure recessives as regards their own gametes also (false hybrids of Millardet, see p. 154) though heterozygous in origin. To solve these difficulties before the gametes can be microscopically differentiated may be still impossible.

    We have now simple and convincing explanations of many facts hitherto paradoxical.

    I. Heterozygous Forms. It has long been known to breeders that certain forms cannot be fixed by selection indefinitely continued. In other words, when the most perfect examples of such forms are bred together, though they produce some offspring like themselves, they have also a large number which do not resemble them.

    A case of this kind is seen in breeding crested canaries. The kind of crest desired for exhibition can, according to canary-fanciers, be produced most easily by mating crested birds with non-crested, or plain-heads as they are called. If it be supposed that the crested character is usually dominant, we have a simple explanation. When, crested birds are bred together a number of birds are produced whose crests are coarse and stand up, and others [are produced] without crests. The latter are the recessives; the former we may suppose to be the pure dominants. 

    What the fancier wants is a crest composed of long feathers lying evenly down over the head. These may be the heterozygotes, and consequently cannot breed true or be fixed by selection. Such birds bred together, give many plain-heads, and birds with coarse crests. Fanciers hold that the plain-heads needed for crest-breeding should be themselves crest-bred, i.e., from families which have had crests among them. On the view here suggested this is probably a superstition, though one can easily see how it may have arisen.

    If two crested birds are bred together it is advised that they should have imperfect crests, in all probability another form of the heterozygote. {*Footnote: An account of these facts is given in Blakiston, Swaysland, and Wiener's 'Canaries and Cage Birds,' p. 128. When birds with good crests are bred together the recessive "plain-head" is often produced, a fact which has been exaggerated by various writers into the statement that the offspring of crests are always plain-heads, or even always bald}.

    Another case, to which our attention was called by Mr. G. Thorne, of Broxbourne, is that of the Golden Duckwing Game Fowl. This colour can be produced by crossing Black-Reds with Silver Duckwing; but on attempting to breed the Golden Duckwing true, the colour breaks up again into its components. {*Footnote: See also Lewis Wright, 'Book of Poultry,' 1886, pp. 289 and 356}.

     Probably the impossibility of fixing certain colours in Pigeons also illustrates the same phenomenon. Such forms have hitherto been regarded as exhibiting "instability." Of this instability there is now a satisfactory account.

    A more complex instance of this may be the Andalusian fowl. The colour is a blue-grey mixed with dull black. The breed will not continue true to colour. Though a considerable proportion of Andalusians are produced, a number will be hatched which are too dark or too light in various ways and proportions. Selecting the best Andalusians effects nothing, and the constancy does not increase, There is, therefore, a strong probability that the Andalusian is a heterozygote, though, doubtless, of a complex nature (cf. p.144). Its gametes do not fully correspond to it, and its colour must be produced by a combination of dissimilar allelomorphs.

    A point of great practical and theoretical importance would be the determination whether the increased vigour so commonly observed in the offspring of some crosses is, or is not, correlated with the union of dissimilar allelomorphs. Hitherto we have spoken of all the offspring of crossing as "crosses," alike. We must now recognise that when heterozygotes are bred together their offspring may not be crosses at all. The great vigour seen in the first cross is known, not rarely, to decline in the next generation bred from them, and it may be possible to see whether such vigour was in reality associated with the union of any recognisably dissimilar allelomorphs.

    The existence of forms which are exclusively heterozygous leads to the contemplation of another possibility. In the heterozygotes we have spoken of, both sexes of course bear gametes transmitting each allelomorph. If, however, one allelomorph were alone produced by the male and the other by the female we should have a species consisting only of heterozygotes.

    So long as the heterozygotes bred together, the offspring in such a case would come true, but a proof that they were heterozygotes would be obtained by crossing them with another species or variety. It would then be found that reciprocal crosses would not give the same result. That this is actually the case we know in certain instances, of which the most familiar amongst animals is perhaps that of the Mule (Mare x Jackass) and the Hinny (She-ass x Stallion), {*Footnote: A good description of the differences between these forms is given by Cornevin, 'Traite de Zootechnie,' 1891, p. 641} and amongst plants the hybrids of Digitalis. {*Footnote: See Focke, 'Pflanzenmischlinge,' 1881, p. 322; and Gartner, 'Bastarderzeugung,' 1849, p. 225. Other examples are given by Gartner, ibid.; and by Swingle and Webber, 'Year-book Dept. Agric.,' 1897, p. 401}.

     In most treatises on crossing other cases are referred to, and though probably many of them are based on experiments insufficiently repeated, there can be no doubt many are authentic. Gartner {*Footnote: Loc. cit., p, 228} acutely observes that the phenomenon of dissimilarity between the results of reciprocal crosses is more likely to be found among dioecious forms.

   2. Selection and the Phenomenon of Dominance. We have seen that the want of fixity in certain forms, though continually selected, may at once be explained by the hypothesis that they are heterozygous only, and have no gametes corresponding to them. Another illustration of the failure of selection is the constant recurrence of a particulate "rogue" in the best strains. Seed is never taken from such rogues. Every year they may be pulled up as soon as detected, but they continuallv reappear.

   The hypothesis that such a "rogue" is a recessive form may give a complete explanation of this phenomenon in many cases. Selection from individuals of known fertilisation would at once test the truth of this view, and might provide a means of producing a pure strain once and for all from the pure dominants.

     It is well known that some of the best modern beardless wheats which have been raised of late years by crossing distinct varieties will give a small proportion of bearded plant. This is, of course, called "reversion" to a bearded ancestor used in the original cross.

    From the experiments of Rimpau, {*Footnote: 'Landw. J. B.,' 20} we find that when bearded and beardless varieties are crossed, beadlessness is dominant, and the bearded character is recessive. By subsequent breeding a form is produced with a desirable character, and after a few years of selection it is found to give this character with sufficient purity and it is put on the market. It may be a bearded or a beardless form, but if the latter, the chances are that it will always produce a certain proportion of bearded plants. {*Footnote: Such a variety is Garton's Red King.} This may happen in every case where there has been a promiscuous selection of many dominant plants, for any one of these may be a heterozygote and bear in each year both dominant and recessive germs.

    The fact that the hornless breeds of goats still give some horned offspring is probably referable to the same cause. The point is of course not certain, but from the analogy of cattle (see p. 140) we may anticipate that the hornless form is dominant. In the polled breeds of cattle, which are never promiscuously selected, the polled character has naturally been easily fixed pure, but in goats selection among the ewes has been probably to a large extent promiscuous.

    The phenomenon is without doubt occurring very widely in nature. To it we may perhaps attribute the undiminished persistence of some weakly varieties, which are unceasingly exterminated by natural or artificial selection without ever leaving offspring. Cases have only to be looked for to be found in abundance. We may note the paradox that, for anything we know to the contrary, a recessive allelomorph may even persist as a gamete without the corresponding homozygote having ever reached maturity in the history of the species.  

 It would be premature to trace out the deductions to which this suggestive fact points, but we see at once that it may give the true account of the phenomenon that domesticated forms constantly give rise to varieties not met with in the wild state, a fact often ascribed, on insufficient grounds, to the action of changed conditions in producing greater variability.

    It will be clear -- a point which may have some economic importance -- that in any such case the recessive "rogue" can be eliminated by selection from individual plants or animals, breeding only from those which give no recessives on being self-fertilised, if hermaphrodite. If the organism be dioecious the process will be more elaborate, for it will be first necessary to test for recessive allelomorphs by fertilising with a recessive, and afterwards to fertilise those that gave no recessive offspring, with a dominant similarly proved to be free from recessive influence. Nevertheless it is certain that by this process alone can a strain of pure dominants be readily made.

    "Purity" then acquires a new and more precise meaning. An organism resulting from an original cross is not necessarily pure when it has been raised by selection from parents similar in appearance for an indefinite number of generations. It is only pure when it is compounded of gametes bearing identical allelomorphs, and such purity may occur in any individual raised from cross-bred organisms.

    An organism can be strictly defined as genetically pure if all its gametes when united with similar gametes reproduce the parent identically; and in practice the only way in which such purity can, by one breeding, be tested, is by crossing the organism in question with pure recessives.

    There are also other classes of cases where progressive selection fails not only to fix a particular variety but to diminish the proportion of "rogues" beyond a fairly definite limit. We may first consider how far the principle of dominance may give an acceptable account of such cases.

   In his most valuable book, 'Die Mutationstheorie,' 1901, Professor de Vries devotes a chapter to the consideration of such phenomena, pointing out in a number of cases that progressive and continued selection has failed to fix a particular character. He draws the conclusion that such characters distinguish "half-races," as he calls them, which cannot be bred pure.

   The cases taken are many-leaved clovers, a polypetalous Ranunculus, several plants with variegated foliage, and the biennial forms of certain species. Selection in each case at first rapidly increases the proportions in which the selected form appears among the offspring, but soon a maximum effect is produced which is not surpassed.

    Now in each of these examples fertilisation was left to insects, and though seed was saved from individual plants, it is not in dispute that cross-fertilisation between them occurred. In Mendelian terms some might be pure D, some pure R, and some DR. Supposing dominance complete, eradication of the pure R forms annually does not extinguish them, for by the breeding of the DR forms inter se they will be continually reproduced.

    There are no doubt many overlying complications in each of these cases, as, for instance, the probability that dominance is in these instances imperfect, but these will not change the main result. The case of the biennial plants is especially interesting, as here we have strong indications that treatment and conditions may determine which character shall appear. For example, de Vries quotes the evidence of the Sugar Beet, a plant of great economic importance, to the breeding of which much attention has been devoted.

    The plant which forms the large sugar-bearing axis is a biennial and does not flower until it has made the sugar-store. But from the best seed which has for generations been saved from such plants only, there arises a small percentage of an annual form which runs to seed without making a thick root at all. After years of selection the proportion of such rogues is not diminished. 

    Now, if it could be supposed that the annual is recessive and the biennial dominant, this is partly explained. On selection, seeds are taken from dominants only. But some of these will be pure dominants and others will be heterozygotes bearing both allelomorphs. The latter will, each year, give rise to a certain number of pure recessives, compounded of two recessive gametes. In the first years of selection, the proportion of recessives will be diminished rapidly by choosing seed from dominants only, but further promiscuous selection of dominants, unless continued for an indefinite time, will not altogether remove the recessives, for they arise from the dominants themselves. {*Footnote: It is of course only a conjecture that the biennial form is dominant in these cases, but, owing to the great importance of the subject, it seems worth while to call the attention of those interested to the possibility. Among the many investigations already made on the Beet, it does not appear that the simple experiment has been tried of seeing if the annual or biennial form can be bred true from individual plants fertilised under proper precautions. Still less has the possibility of dominance been investigated. The only evidence known to us is that of Rimpau, that when the annual Beta vulgaris was grown near the cultivated form, it bore two seeds which proved biennial, and fifty-eight which were annuals. Rimpau conjectures that the two were crosses with the cultivated form, in which, as we should now say, the latter was dominant. But B. patula, an annual, emasculated and fertilised by cultivated Beets promiscuously, gave annuals only. Here there is a cross with another species, and the evidence is of doubtful application}.

    But in these forms it is well known that several kinds of treatment, exposure of the young plants to frost, over-crowding, heavy manuring, and forcing, will greatly increase the proportion of "runners." In the ease of Oenothera de Vries has made some very convincing experiments, clearly proving this fact, and Rimpau has done the same for the Beet, showing that the number of "runners" can thus be greatly increased. There are then some which are biennial in any case, some which are biennial or annual according to treatment, and some which are in any case annual. This is strongly suggestive of the three Mendelian classes.

    De Vries has also experimented by selection from the annual plants, getting of course a higher proportion of annuals. But it must be remembered that in order to prove that the annual character is recessive, and that it can, as such, be fixed by one selection, it is necessary to ascertain first that the plant chosen is not what de Vries calls a "facultative" annual -- on this hypothesis, a DR -- and secondly that it has not been cross-fertilized, particulars not yet forthcoming.

     But even if the hypothesis of dominance could be successfully applied to these cases, there are others at first sight similar, where it cannot be thus applied; for example, instances of varieties recessive in their differentiating character, producing annually a small but sensible number of a particular "sport" exhibiting a character already known to be dominant. Here we must suppose either that we meet the phenomenon of an originating variation -- the "mutation" of de Vries: or possibly, which appears to be de Vries' view of half-races -- the output of a certain number of such aberrant gametes is normally incidental to the development of the type-gametes. An objection to the latter deduction in some cases exists in the fact that the "sports" in question may be exceedingly rare, and therefore produced by few individuals only. {*Footnote omitted}

   3. Skipping a generation. That marked individual peculiarities fail to appear in the immediate offspring, but may reappear in a subsequent generation has been often observed, and the fact has taken a great hold on the popular imagination. It has not yet been shown that the distribution of any of these characters among the different generations in any line of descent is other than is to be expected on the hypothesis of pure chance. Nevertheless we have now, in the phenomenon of dominance, a fact which may possibly be a real element in the causation of such appearances, and those who are familiar with statistics of inheritance, in man for example, might usefully study them with the possibility in view. The absence of the character in the first generation may indicate merely that it is recessive, and its reappearance in the next generation may be due to the heterozygote having bred with another individual also bearing the recessive allelomorph.

    4."New" characters may be dominant.  We cannot as yet perceive any properties common to dominant as compared with recessive characters. It will be noted, however, that the view of many naturalists that the phylogenetically older character is prepotent, or, more correctly, dominant, is by no means of universal application. In poultry, for instance, both pea and rose combs are dominant against single [comb], though the latter is almost certainly ancestral; the polydactyle foot is dominant against the normal, though a palpable sport. A point of some interest is that in both wheat and barley the beardless form is dominant, though we naturally, though perhaps incorrectly, regard it as a state normal in the one species, but an innovation in the other.

    In cattle the polled form is dominant over the horned, though the former is a character which in our cattle has certainly arisen since domestication.

    5. Prepotency The conception of dominance avoids certain difficulties which are involved in the use of the term "prepotent." As we now know that the allelomorphs of the several characters may be quite independent, it is confusing to speak of the prepotency of an individual when all that we know is that one or more of its characters is dominant over the contrary character. Of the dominance or prepotency of the whole we know nothing. 

    The diversity of the views which have been at various times expressed as to the respective powers of mother or father to confer special qualities has probably arisen from confusions thus caused. If the term prepotency is to be preserved, it must be applied to characters rather than to organisms, and its use must be restricted to cases in which the character, so qualified, has been actually tested by combination with the contrary allelomorph in one heterozygote.

    We have been accustomed to consider that a variety may be sometimes prepotent in respect of a given character, and sometimes not prepotent. The whole evidence on which this view is based will in many cases now require careful verification, for, as was fully discussed in the case of poultry, such a result may really be due to an unsuspected heterozygote having been sometimes used for the other parent. The evidence, for instance, that, on crossing pea comb and single comb, the offspring may be sometimes pea, and sometimes single, would formerly have been thought a clear proof that pea comb was not always dominant, whereas it is now certain that much fuller evidence is needed to establish this proposition.

   The existence of the so-called "false" hybrids of Millardet (see p. 154) is an even more serious difficulty besetting the conception of prepotency, for here, though the cross-breds are produced by a union of the male and female gametes of two varieties, it is quite uncertain that the characters of both parents are introduced at all. (See p. 155.)

   6. Sex  It is often profitable to compare the phenomena of variation with those of sex, and if the suggestion alluded to in the last paragraph be found true, it is worth reflecting whether the determination of sex may not sometimes be a phenomenon similarly conditioned. 

    7. Reversions  With the Mendelian conception of the heterozygote as a form with its own special "hybrid character," we have a rationale of large numbers of "reversions"; for we already know many cases where heterozygotes do present the characters of putative ancestors. This fact reduces to harmony several groups of results where different experimenters, believing themselves to have worked with similar organisms, have reached seemingly contradictory conclusions. For some have used pure forms and others heterozygotes appearing in their guise.

THE NATURE OF ALLELOMORPHISM

A. Simple Al1elomorphs

   The following list enumerates the principal cases in which the phenomenon of allelomorphism has either been actually proved to exist or may be safely inferred from the published records. {*Footnote: From the evidence of crosses kindly carried out for us by Mr. Leonard Sutton we are able to add the "palm" leaf (palmatifid) and reddish stems of Primula sinensis as dominant characters, while the "fern" leaf (pinnatifid) and purely green stems are recessive characters. March, 1902.} In each of these cases more or less definite dominance of one character has been found, and in this list the dominant character is put first:-

1. Hairiness and absence of hairs (Lychnis).

2. Hoariness and absence of hairs (Matthiola).

3. Felted ears and smooth ears (Wheat). {*Footnote: Rimpau, 'Landw. J. B.,' 20, 1891, p. 346}

4. Prickliness and smoothness of fruits (Datura).

5. Style long and short (Oenothera). {*Footnote: de Vries}

6. Beardless and bearded ears (Wheat and Barley).{*Footnote: Rimpau, loc. cit., pp. 341 and 353. Since this paper was written we have received Tschermak's valuable analysis of the phenomena in regard to wheat, which considerably extends our knowledge of allelomorphism in that species (see Ztsch. fur d. Landw. Versuchswesen in Oester.,' vol. 4, 1901, p. 1029}                          

7. Pointed seed and rounded seed (Maize). {*Footnote: Correns, 'Biblioth. Bot.,' vol. 53, 1901}

8. Round and wrinkled seed (Pisum).

9. Starch endosperm and sugar endosperm (Maize).

10. Inflated (generally hard) pods and constricted (generally soft) pods (Pisum, Phaseolus).

11. Axial distribution of flowers and terminal distribution of flowers (Pisum).

12. Tall habit and dwarf habit (Pisum, Phaseolus), to which, from experiments seen at Messrs. Sutton's, we think we may safely add tall habit and dwarf procumbent habit (known to gardeners as "Cupids") in Sweet Peas (Lathyrus odoratus). {*Footnote: Some distinct exceptions to the rule of dominance of the tall form are already known. {See final note.}}

13. Entire petals and laciniated petals (Chelidoniun majus). {Footnote: de Vries}

14. Normal zygomorphic form and peloric form (Antirrhinum {*Footnote: Darwin, 'An. and Plts.,' ed. 2, vol. 2, p. 45} and probably Linaria. {*Footnote: In the case of Linaria, Naudin found that on crossing a peloric Linaria with a normal one a mixture of normal and peloric plants resulted. As to the origin of the peloric parent there is no information, and consequently it may have been a heterozygote. See Naudin, 'Nouv. Arch. du Mus.,' 1865, I, p. 137}

15. Normal habit and waltzing habit (connected with malformation of the aural labyrinth) (Mouse). {*Footnote: Von Guaita, 'Ber. Natur. f. Ges.,' vol. 10, 1898, p. 317, and vol. 11, 1899, p 131. For reference to this interesting case we are indebted to Professor Correns}

16. Presence and absence of extra toe (Fowl). {*Footnote: The allelomorphisim is not yet fully proved in this case. It is the only obviously meristic character in which there is yet any evidence of allelomorphism}

17. Pea comb and single comb (Fowl).

18. Rose comb and single comb (Fowl).

19. Polled and horned breeds (Cattle and probably Goats). {*Footnote: It is almost certain that absence and presence of horns are allelomorphic characters. In England there are three principal polled breeds of cattle -- the Aberdeen-Angus, Galloway, and the Red Polled. The first two are black, the last red. Between these and the horned breeds crosses are annually made in large numbers. This is especially the case with the Angus, from which great numbers of cross-bred cattle are annually bred for the meat market. These are usually Angus-Shorthorn crosses, but other horned breeds an also occasional used. The cross between a pure Angus and a pure Shorthorn is almost always a blue-grey without horns. Generally the horns are represented by loose corns of horny material, sometimes imbedded in the skin and not rarely hidden by the hair. Such as they are called in the north, are objected to in the pure polled breeds and are mostly absent. [Section omitted]}

20. White shanks and yellow shanks (Fowl).

21. White plumage and general brown coloration (Fowl). {*Footnote: Wh. Dorking x Ind. Game crosses are this year giving exception to dominance of white.-1902}

22. Several coloured forms of flowers and their white varieties.

23. Several colours of fruits and their xanthic varieties (Atropa, Solanum).

24. Several colours of seed coats.

25. Darker and lighter colours of endosperm (Maize).

26. Yellow and green cotyledons (Pisum).

    With regard to seed-colours, Correns has shown that the question is a complex one, depending on several factors. In Maize, especially, the seed-skin and the several parts of the endosperm may all be independently concerned in giving the net result. Each must be considered separately, and in several cases the dominance is imperfect, and blendings may occur. {Footnote: Full details given in Correns' memoir, 'Biblioth. Bot.,' 1901}

    Between various simple allelomorphs correlations may of course occur. A few of these we know already. But in these cases of simple correlation the gametes may each transmit the correlated groups or the opposite allelomorph entire (see case of Matthiola, p. 81).

    From the foregoing list it appears that allelomorphism may occur in a great diversity of characters, involving many different physiological factors. In the plants albinism appears to be recessive, but in the case of fowls white plumage is dominant, though not completely so. It does not appear as yet that simple allelomorphism occurs between any two colours, of which neither is xanthic or albino.

B. Compound A11elomorphs

    So far, in all or nearly all the cases we have considered, the dominant and recessive characters are each simple. In other words, when the heterozygotes breed together, they produce dominants and recessives like their parents, heterozygotes like themselves, and no other forms. The gametes therefore respectively bear characters which are the same as those of the varieties which were used to produce the heterozygotes. We have next to consider a numerous and important group of cases in which a character of one of the original parental varieties, after crossing, is itself split up. Of these we will give illustrations.

   1. Sweet Pea. By the great courtesy of Messrs. Sutton and Sons we have been permitted to watch many of the experiments conducted at their nurseries. We cannot sufficiently express our indebtedness for the splendid opportunities of study in these fields thus provided. For the most part these phenomena are not dealt with in the present paper, and amongst many interesting results there witnessed we propose now to refer very briefly to the following only:-

   Sweet Pea (Lathyrus odoratus). Stanley, standard dark maroon or chocolate, with wings similar but somewhat tinged with violet, crossed with Giant White, gave all Giant Purple Invincible, viz., standards as in Stanley, but wings blue. These first crosses self-fertilised, gave Giant White, Giant Purple (without blue wings), Mars (a well-known red variety), Her Majesty (a full magenta, well known), and a form like Her Majesty, but flaked with white. {*Footnote: It is possible, that this complex result does not always occur; for in another case a Giant Rich Purple, very like Stanley, crossed with Giant White, gave seedlings all Giant Rich Purple. These on self-fertilisation gave a mixture of Giant White and Giant Rich Purple again. One plant of each on self-fertilisation gave only offspring like itself.}

    One plant of each was saved and its self-fertilised seed sown. Mars and Her Majesty came true. The Giant White was tested, and it came true also. The Her Majesty flaked with white, however, gave Whites, Her Majesty, and Her Majesty flaked white again. The Giant Purple gave Giant White, Her Majesty, Giant Purples, all two plants of a streaky cream colour.

   The facts point to a higher degree of complexity than we can yet realise, but we see that the first crosses are all alike, though differing from the coloured parent. The same form, or something very like it, was often observed to come in other cases where a blue or purple parent was used in crossing. Now on self-fertilisation the first cross gave a variety of forms. It therefore produced a variety of gametes, not two kinds, but several. Of these forms some, Mars, Her Majesty (Giant White also in all probability), reproduced themselves exactly. Therefore they had only one kind of gamete, and they must be supposed to have been formed by the union of similar gametes. The purples, on the contrary, produced most of the whole series again, showing that they were producing a variety of gametes like the first cross parent itself.

   Her Majesty flaked with white, gave some Her Majesty, some White, some Her Majesty flaked white. Therefore the flaked plants are heterozygotes, formed by the union of a Her Majesty gamete with a white gamete.

    We are then led to the conclusion that the allelomorph transmitting the coloration of Stanley is compound, and that it can be broken up into simpler and possibly component elements. When similar elements, thus extracted, combine in fertilisation, they do not split up again on the formation of gametes. The constituents of the compound allelomorphs may perhaps be spoken of as hypallelomorphs.

    The fact that Stanley did not occur again is another indication that its colour character had been broken up into more than two elements.

    Another fact which may point in the same direction is that the purple formed on the first cross is different from that which recurs in the next generation. In fact, this Giant Purple Invincible results from the union of the whole compound allelomorph of Stanley with that of Giant White. We may suppose that it does not come again, for the reason that the compound allelomorph has been broken up among the gametes borne by the first cross, and that the union of no two of these, or of any of them with white, results in that particular heterozygote form, Giant Purple Invincible. Inasmuch, however, as Giant Purple Invincible, not yet distinguishable from that produced in this cross, is a well-known, and stable form, there must either be gametes corresponding to it {*Footnote: Similarly from other crosses seen at Messrs. Sutton's it is clear that the form called "Painted Lady" may be another heterozygote form, though the same is one of the oldest and most familiar fixed forms. According to Mr. S. B. Dicks, there is good reason to believe the purple and the Painted Lady forms to be the oldest varieties. 'Report of Sweet Pea Conference,' 1900.} or its male and female gametes must be dissimilar and combine in that definite heterozygote, which is most unlikely. Till the experiment has been repeated on a large scale we must not lay much stress on the absence of Purple Invincible after the break tip of the first cross, because in other experiments where White Cupid (a procumbent form) was crossed with Mme. Carnot (a blue), Purple Invincible again resulted together with White Cupid (? the result of imperfect emasculation). These Purple Invincibles, self-fertilised, gave several forms, amongst them Mme. Carnot and some Purple invincibles again. Whether this indicates that the compound allelomorph is not wholly broken up, or that its character may again be synthetically reproduced, cannot yet be said. Corroborative evidence that the blue elements are definitely extracted from the "derived" Her Majesty was seen in the fact that this variety when crossed with various pink and cream kinds gives no blues or purples.

    To the whole subject of the results of crossing Sweet Peas we hope to return when our own experiments are further advanced. The probability is that in this, as in other similar cases of compound allelomorphs, there is a heterozygote form which may be common to several combinations of dissimilar gametes, and it is characteristic of such forms that they may reproduce in appearance some putative ancestor. It is to this class of phenomena that Darwin's famous "reversions on crossing" are probably to be referred.

    2. Poultry. Another example of the splitting up of a compound allelomorph is probably to be seen in the poultry experiments. The first cross between Indian Game and White Leghorns, for instance, is white flecked with a few black or grey feathers, sometimes barred, sometimes irregularly marked with pigment. Such first crosses bred together give some dark birds and some light (see p. 108), the latter being sometimes pure white, sometimes, flecked with black, and sometimes pile (brown and white).

When White Dorkings are crossed with Brown Leghorns the result is very similar; but in each of these cases the dark birds resulting from the inter-breeding of the first crosses are not simply like their dark grand-parent, but belong to several distinct types of coloration such as black, cuckoo, silver-grey, {*Footnote: The appearance of silver-grey in the offspring of first crosses between White Dorking and Brown Leghorn may be attributed to the certainly that White Dorking were related to Silver-grey Dorkings. The colour may, nevertheless, he come front resolution of the Leghorn colour, for it is not peculiar to Dorking, but is known in other breeds, e.g., Game Duckwings.} together with sonic more or less nearly reproducing the dark grand-parental type. The numbers reared are far too small to justify a comprehensive deduction, but that the types of coloration thus produced have some definiteness is quite clear. Whether any of them will breed pure must be unknown till next season. As already stated, some of these colours are already well known as characterising various breeds.

   Until experiments have been carried out with the express object of proving the compound nature of allelomorphic characters and of resolving them into their constituents, we can only gather indications of such phenomena from experiments undertaken for other objects. Of these there are a considerable number which leave little doubt that further examination would disclose such a result. We may mention the observations of von Guaita on mice, from which it appeared that the first cross of albino mice with black-and-white Japanese waltzing mice, gave a grey house-mouse resembling in size, colour, and wildness the wild house-mouse. {*Footnote: Haacke, crossing albinos with grey-and-white Japanese waltzing mice, usually obtained the same result, viz., grey mice, but more rarely black mice. The latter result may be taken as indicating impurity in one or other parent. Vosseler, quoted by von Guaita, obtained greys only. See Haacke, 'Biol. Cblt.,' vol. 15, 1895, p. 45} The first crosses bred together gave albinos, grey mice, black and white, grey and white, and black mice (with the waltzing character distributed among them in proportions closely obeying the Mendelian ratio); of these the albinos produced, with one exception, albinos only when bred together. The grey marked with white, bred together, produced no more blacks or black-and-whites; and the blacks and the black and whites, bred together, gave no more greys, though both descriptions may still give albinos. Facts like these strongly suggest that, with suitable mating, the classes could be shown to consist of the original albino, and a number of forms, some of which would henceforth be pure, while others would be found to be heterozygous.

   3. Another case, possibly of the same nature, is that of the Himalayan rabbit, of which an account is given by Darwin. {*Footnote: 'An. and Plts.,' I, p. 113}

    The literature of pigeon-fancying abounds with information pointing to a similar rationale of the colour phenomena there seen. Formerly the recipes given in such treatises as to the methods of mating to be followed for the production of particular colours would have seemed mere nostrums, but now we can see at least the general basis of fact whence they have been derived.

    The experiments with stocks described (p. 81) give cases probably also analogous. Several forms crossed together all gave purple for the first cross, which on being self-fertilised gave other colours in addition to those of the pure parental forms and that of the first cross.

   This conception of compound allelomorphs is almost the same as that which Mendel himself introduces in speaking of his Phaseolus crosses. {*Footnote: ' Loc. cit., p. 35} His analysis does not, however, seem to be strictly correct, and the subsequent reasoning is consequently obscure and not altogether valid. He says if the colour of the red Phaseolus be made up of A1+ A2 + …, then on crossing with a white form a, hybrid unions are produced, Ala + A2a + etc..

    But it is the group A1A2 . . . which is allelomorphic to a, and the heterozygote is A1A2 ... a, and not Ala + A2a + etc... It cannot be till the crosses form their gametes that the compound allelomorph breaks up.

    It is not evident how this error of expression came about. Mendel in consequence misses the point that, by the breaking-up of the compound character after the cross, new fixed forms may be produced by union of the elements of the original compound allelomorph, without any admixture from the variety with which the first cross was made. Such pure forms may be represented as A1A1, A2A2, etc., and of these we have already seen instances in the case of the Sweet Peas, Mars and Her Majesty.

    Of the coloured forms appearing as offspring of the first crosses inter-bred, some are compounded of colour-bearing gametes meeting similar or dissimilar colour-bearing gametes, and some (like the Sweet Pea, Her Majesty, flaked with white) of a colour-bearing gamete meeting a white-bearing gamete.

    We have good reason to believe that the compound allelomorph is not in every case resolved into its ultimate constituents when the gametes of the first cross are formed, and indeed we must suppose such imperfect resolution to be present whenever, as in the case of the Sweet Pea, among the resolved forms (White, Mars, Her Majesty) there occur complex heterozygotes like Giant Purple, which can itself produce a series of forms in the next generation. Such a form may be represented as A2A3… a. It is to this class of complex heterozygotes that we conceive the Andalusian fowl to belong.

    It is doubtful whether, and in what sense, we are entitled to regard the whole compound character as one allelomorph. Some justification for this conception is to be found in the fact that in the poultry crosses the light chicks bore to the whole number of dark chicks the proportions of 3 : 1. On the Mendelian hypothesis this must be taken to show that the cross-breds produce on an average white-bearing gametes equal in number to the whole number of colour-bearing gametes, which may bear the colour-allelomorph in various stages of resolution.

    By statistical investigation of such cases it should be possible to determine with some success how the unresolved characters are related to the elementary characters, and to make a scheme of equivalence.

    It is, perhaps, hardly too much to suggest that in a great number of cases the familiar fact so often observed that first crosses bred together give a profusion of new forms may be capable of similar explanation. With such new forms the usual experience is that some breed true from the beginning, while some continue to give rise to other forms, of which some may have already been produced, while others again are new. The cases we have taken are those of colour-varieties, as the facts in those cases are clearer, but their nature is probably not different. It is in this sense that crossing may be truly spoken of as a "cause" of variability, and some picture of that phenomenon is now provided.

   The importance of this reasoning lies in the fact that we can now recognise that these different new forms may be, in their genetic composition, diverse. We are no longer to expect that it is a matter of chance whether each will be able to transmit any of the other forms, but we perceive that this is a question to be determined by actual observation once for all. When such determinations shall have been made on a statistical basis, we shall be able to state precisely the numerical proportions which the gametes of the several classes bear to each other, and hence to determine the actual number of constituents of the compound allelomorph and their relationships to each other. This investigation is now merely a matter for precise quantitative analysis.

    A marked feature in connection with compound allelomorphism {*Footnote: There is no reason for supposing such reversion to be absent in all cases of heterozygotes formed by the union of simple allelomorphs, but the few clear cases known seem to be all cases including compound allelomorphs} is the frequency with which, in such cases, one or more of the heterozygotes present what we have reason to regard as ancestral characters. To such "reversion" we referred in speaking of Sweet Pea crosses. The Sweet Peas produced a flower with purple standard and blue wings, approaching what we may regard as a primitive Sweet Pea. Several white varieties of Stock produce a purple form; many of the crosses with the "half-hoary" type gave fully hoary heterozygotes. The Albino and Japanese mice produce a grey house-mouse as their heterozygote. Why such heterozygotes should show ancestral characters, we do not know; but we can now recognise that such "reversions" are heterozygous mixtures and not constant forms. To speak of such reappearances of ancestral characters as a reappearance of the ancestral form is entirely misleading. These heterozygotes will not breed true, and are ancestral in no real sense. Not only are they heterozygous and in constitution compound, but, as in the Sweet Pea, several different compounds agree in having the same ancestral form as their specific heterozygote.

    It is unfortunate that Darwin's own experiments with poultry and pigeons were so complex that it is now impossible to disentangle the results or to use them for the purposes of these deductions. He records the most complicated unions of birds of different breeds, some homo-, some hetero-zygotes, some exhibiting simple and others compound allelomorphs, and in the statement of results the all-important distinctions between the generations and the offspring of the several individual birds are often not observed.

The facts thus grouped, suggest the following questions. Has a given organism a fixed number of unit-characters? Can we rightly conceive of the whole organism as composed of such unit-characters, or is there some residue -- a basis -- upon which the unit-characters are imposed? We know, of course, that we cannot isolate this residue from the unit-characters. We cannot conceive a pea, for example, that has no height, no colour, and so on; if all these were removed there would be no living organism left. But while we know that all these characters can be interchanged, we are bound to ask is there something not thus interchangeable? And if so, what is it? We are thus brought to face the further question of the bearing of the Mendelian facts on the nature of Species. The conception of Species, however we may formulate it, can hardly be supposed to attach to, allelomorphic or analytical varieties. We may be driven to conceive "Species" as a phenomenon belonging to that "residue" spoken of above, but, on the other hand, we get a clearer conception of the nature of sterility on crossing.

Though some degree of sterility on crossing is only one of the divers properties which may be associated with Specific difference, the relation of such sterility to Mendelian phenomena must be a subject for most careful inquiry. So far as we yet know, it seems to be an essential condition that in these cases the fertility of the cross-bred should be complete. We know no Mendelian case in which fertility is impaired. We may, perhaps, take this as an indication that the sterility of certain crosses is merely an indication that they cannot divide up the characters among their gametes. If the parental characters, however dissimilar, can be split up, the gametes can be formed, and the inability to form gametes may mean that the process of resolution cannot be carried out.  

    In harmony with this suggestion, is the well known experience of hybridisers, that if there is any degree of fertility in the first cross, with subsequent inter-bred generations the fertility may increase. {*Footnote: Focke, 'Pflanzen Mischlinge,' p. 483; Gartner, 'Bastarderzeugung,' pp. 333 and 373}

   Such increase in fertility is generally associated with some greater approximation to one of the parental forms. In terms of our hypothesis, we may conceive this fact as denoting that offspring formed of gametes which have successfully resolved the characters of the heterozygote, and are not bearers of the irresoluble characters, can form their own gametes with less difficulty.

    That the sterility of hybrids is generally connected in some way with inability to form germ-cells correctly, especially those of the male, is fairly clear, and there is in some cases actual evidence that this deformity of the pollen grains of hybrids is due to irregularity or imperfection in the processes of division from which they result. It is a common observation that the grains of hybrid pollen are too large ,or too small, or imperfectly divided from each other. {*Footnote: See e.g., Naudin, 'Nouv. Arch. du Mus.,' 1865, I, p. 95, and Wichura, 'Bastardbefruchtung im Pflanzenreich,' 1865, p. 37. Cases are easy to find.} Such conditions are what we should expect on the hypothesis here suggested.

  However this may be, it would be of the utmost importance to discover at which of the divisions leading to the production of the gametes, the allelomorphic characters are divided. Correns has pointed out that the evidence of maize proves that in that case the two nuclei of the pollen tube must both be transmitters of the same character, for, in the fruit of the first cross between starch and sugar varieties, those seeds which have sugar endosperms produce pure recessive (sugar) offspring. This fact proves therefore that the nucleus which fertilises the embryo and that which fertilises the endosperm, are transmitters of the same character. Therefore, the separation of the characters does not take place in this case when the two generative nuclei divide from each other. 

    Further evidence on this question is wholly wanting. Several attempts are being made by others and by ourselves to determine this point by crossing varieties with recognisably different pollens; but, so far, the desired mixture of dissimilar gametes in our cross-bred has not been satisfactorily observed. As soon as some means shall have been found of making visible that differentiation which we now must exist between the germ-cells of the same heterozygote, a vast field of research will be opened up. Till then, the microscopical appearances accompanying the segregation of the characters must remain unknown, and we are obliged to resort to the cumbrous and protracted method of deduction from the statistical study of the zygotes formed by the union of the several kinds of gametes.

   Variation, especially discontinuous variation, of zygotes is in great measure thrown back on that of the gamete. We perceive, in fact, that the production of dissimilar gametes by one zygote may be compared, to take a rough illustration, to a bud-variation, constantly recurring in each heterozygote. Whether the divisions resulting in the formation of the dissimilar gametes are symmetrical or asymmetrical we cannot yet tell; but as in most cases of discontinuous variation, by sufficient searching, occasional instances, particular individuals or strains, will probably be found where the discontinuity is imperfect. As already pointed out also, the existence of exceptional gametes of a mosaic nature must already be inferred. It is unfortunate that so long as the statistical distribution of the zygotes is the only criterion by which the nature of the gametes can be deduced, even cases of impurity in extracted recessives -- the readiest form in which imperfect differentiation will be seen -- will not suffice to show whether there has been in fact such imperfect differentiation, or only defective dominance.

    With regard to the compound allelomorphs, it must be determined by further investigation whether they similarly can come into existence in their entirety, or whether they are capable of synthesis. At present, though we can perceive the fact that they are capable of decomposition, we know nothing of the reverse process. In the cases (p. 142) we have discussed, it is plainly the simple allelomorph that has discontinuously arisen.  

    Non-Mendelian Cases. In the case of Matthiola and among the poultry, instances have been apparently found of definite departure from Mendel's law (pp. 81-6 and 107). It is certain that these exceptions at all events indicate the existence of other principles which we cannot yet formulate. But besides these cases there are three distinct classes of phenomena met with in breeding to which the Mendelian principles cannot be readily applied. It will be useful to consider briefly how each case departs from these principles, and whether by any modification they can be extended to such cases.

Such phenomena are-

• 1. The ordinary blended inheritance of continuous variations.

• 2. Cases in which the form resulting from the first cross breeds true.

• 3. The "false hybrids" of Millardet.

 1. Blended Inheritance. At first sight it seems that cases of continuous variations, blending in their hereditary transmission, form a class apart from those to which Mendel's principles apply. But, though it may well be so, the question cannot be so easily disposed of. The essence of the Mendelian conception is, as we have seen, that each gamete may transmit one allelomorph pure. So long as each heterozygote can only exhibit one, allelomorphic character, the dominant, we can, from a study of the heterozygotes and their offspring, demonstrate the purity of the gametes. 

     But dominance is a distinct and subordinate phenomenon. We readily perceive that the heterozygotes may show either of the parental characters discontinuously, or various blends between them, while the gametes which composed the heterozygotes may still be pure in respect of the parental characters. The degree of blending in the heterozygote has nothing to do with the purity of the gametes.  

   It is, of course, quite possible that the gametes in such cases do in fact vary as continuously as we see the zygotes do, but this cannot yet be affirmed. The great theoretical significance of this question should therefore lead us to suspend judgment for the present.

2. First Crosses Breeding True. With respect to this phenomenon no experiments on a large scale have yet been made. Most examples are recorded in the form that A and B were crossed together and produced a third form, C. The C's were then bred together, and some C's were again produced. We hardly ever are told that in this generation only C's were produced. Generally, however, we do not even know so much. The cases for example given by Darwin,{*Footnote: 'An. and Plts.,' ed. 2, vol. 2, pp. 73-77}are for the most part general statements that certain new and now definite forms, the Swede turnip, for instance, were produced by crossing. Any such case may, therefore, be merely one of the resolution of compound allelomorphs followed by selection of the forms produced by the union of similar component allelomorphs. This, indeed, is probably the true account of most permanent forms produced by crossings.

    There remain, however, a few cases of which Mendel's {*Footnote: Mendel, 'Abh.Ver. Brunn.,' vol. 8, 1869. See also Swingle and Webber, 'Year-book Dept. Agric.,' 1897, p. 393} own crosses among Hieracia are a good example, in which a distinct form, produced by the first cross, has proved able to transmit its characters to its offspring. Of such cases we know very little. We may, perhaps, notice two features as apparently characteristic of these cases. First, that the results of the first cross may show no uniformity; secondly, that there is often a considerable degree of sterility.

    In Correns' terminology such crosses are "homodynamous" and "homoogonous." De Vries speaks of them as "erbungleich." In these instances the new form is able to give off gametes, male and female, carrying its own new character. Such facts plainly indicate a degree of complexity higher than that to which the Mendelian principles can apply, and for the present we have no insight into their nature.

3. Millardet's "False Hybrids." Some allusion must be made to the remarkable results described by Millardet, {*Footnote: 'Mem. Soc. Sci. Bordeaux,' ser. iv, vol. 4, p. 347} which have been the subject of frequent discussion among practical evolutionists. Put briefly, Millardet found that when certain varieties, especially of strawberry, are crossed together, (1) the cross-breds may precisely reproduce the maternal type, without any indication of the paternal characters; (2) in other cases the cross-bred individuals may show either the maternal characters pure (save in one case the colour of fruits) or the paternal characters pure. Seeds from plants thus exclusively reproducing one parental type themselves gave plants again exclusively of that type. To such forms he gives the name "faux hybrides" or "hybrides sans croisement."

   In order to estimate the significance of these facts we ought to know of what variations the pure forms are capable, when bred inter se, without crossing. Upon this point we have as yet no evidence. If we assume that each of the forms used would, if bred pure, transmit its characters regularly to its offspring, then we should have established that the heterozygote produced exclusively gametes, transmitting the character which appeared as "dominant" in itself, and a new order of facts is thus revealed. It is difficult to see any escape from this conclusion, but, on the other hand, if it could be shown that the pure-bred offspring of the one form could themselves exhibit the characters of the other parent used in the cross, we should recognise that the parent forms themselves produced mixed gametes, and in such a case we should expect that, when similar gametes meet in fertilisation, the offspring resulting would breed true. On the whole this explanation is very improbable, but as yet it is not wholly excluded in some of the cases in which Millardet's phenomenon is alleged to have occurred.

    In our experiments with Matthiola, cases were described which, it can scarcely be doubted, are fully proven. The same is true of some of de Vries' instances, {*Footnote: 'Ber. deut,.Bot. Ges.,' 1900, vol. 18, p. 441} notably that of Oenothera Lamarckiana crossed with the cruciata var. of biennis. Possible instances occurred in regard to the combs of poultry (p. 122), though, as there pointed out, a simpler explanation is not altogether excluded in those examples. Such phenomena may perhaps be regarded as fulfilling the conception of Strasburger and Boveri, that fertilisation may consist of two distinct operations, the stimulus to development and the union of characters in the zygote.

Galton's Law of Ancestral Heredity in relation to the new Facts.

   Such a preliminary survey of the phenomena of heredity as we have attempted would be incomplete without some reference to this subject. We note at once that the Mendelian conception of heredity effected by pure gametes representing definite allelomorphs is quite irreconcilable with Galton's conception in which every ancestor is brought to account in reckoning the probable constitution of every descendant. With respect of each allelomorphic pair of characters we now see that only four kinds of zygotes can exist, the pure forms of each character, and the two reciprocal heterozygotes. On Galton's view the number of kinds is indefinite.

   At first sight it may appear that as the two views are quite incompatible, they must relate to different classes of phenomena. In so far as Galton's law relates to continuous variations, with blended inheritance, this may be the case (see p. 152); but in some of the cases following Galton's rule, notably that of the colour of Basset hounds, the colours dealt with are discontinuous. {*Footnote: Pearson ('Roy. Sec. Proc.,' vol. 66, 1900, p. 142) has suggested a distinct formula for these cases of alternative inheritance, which he terms the "Law of Reversion." He urges that such phenomena should be treated separately from those of blended inheritance. Both laws alike are of course based on the numerical composition of the ancestry.} Let us consider what evidence there is in this case that the gametes are not pure tricolour or non-tricolour, as we should now expect them to be. The first question is, does either colour show dominance? If either were dominant it must clearly be the tricolour, and in view of the fact that both tricolour x tricolour, and non-tricolour x non-tricolour are said to have given mixtures, neither colour can be supposed to be exclusively dominant. In this case, therefore, as it is impossible to tell which individuals are pure and which are heterozygotes, Galton's results might possibly have occurred, and the gametes yet be pure. More cannot be said without reference to the actual details out of which the tables were constructed.

    Attention may also be called to the fact that in cases which fully obey Mendel's ratio (and exhibit dominance), two of the commonest matings happen to give the same result as they would do on Galton's expectation, though the latter is founded on wholly different considerations. Mendel, for instance, expects DR x DR to give 3Ds and 1R, and that DR x R will give equal numbers of Ds and Rs. Both these results are, ceteris paribus, to be expected on Galton's law, so that it might need a good deal of experiment to distinguish the two classes of cases. A clear distinction would, however, at once be found by comparing the result of DR x R with that of DR x D.

    Bearing this in mind, and having regard to the considerations mentioned in the paragraph on blended inheritance, it is impossible to avoid the suggestion that Galton's law may be a representation of particular groups of cases which are in fact Mendelian, in the sense, that is, that there may be purity of gametes in respect of allelomorphic characters. In any case it is now certain that Galton's law cannot be accepted as "universally applicable to bisexual descent."

    By any practical breeder this must have been always expected, for he knows that while he can rapidly fix some characters, some never come true at all, and others will not come true with any certainty after long selection. The expectation after simple selection is, in fact, quite different for different characters. Mendel's principle disposes of a great part of these difficulties, for we now know that any recessive character may be fixed at once by selecting recessives, and that this fixity may have nothing to do with the novelty of the character, its "prepotency," etc., and that the heterozygote may never come true.

    Galton's law in fact does not recognise that absolute purity, which is so common a phenomenon in breeding, as it is in nature. The breeder, in hosts of instances, is not, as a matter of fact, constantly troubled by recurrences of forms with which, even in his own practice, his strain has been crossed. Of this the full explanation is now seen; for if two similar gametes meet, their offspring will be no more likely to show the other allelomorph than if no cross had ever taken place.

CONCLUSION

   We have now sketched the principal deductions already attained by the study of cross-breeding, and we have pointed out some of the results now attainable by that method. The lines on which such experiments can be profitably undertaken are now clear and a wide field of research is open.

   The properties of each character in each organism have, as regards heredity and variation, to be separately investigated, and, for the present, generalisation in regard to those properties must be foregone. The outlook, in fact, is not very different from that which opened in chemistry when definiteness began to be perceived in the laws of chemical combination. It is reasonable to infer that a science of Stoechiometry will now be created for living things, a science which shall provide an analysis, and an exact determination of their constituents. The units with which that science must deal, we may speak of, for the present, as character-units, the sensible manifestations of physiological units of as yet unknown nature. As the chemist studies the properties of each chemical substance, so must the properties of organisms be studied and their composition determined.

     To the solution of the practical problems of heredity, and a determination of the laws of breeding both plants and animals, this is the first step. The attainment of these solutions is now only a question of time and patience.

    That the same method will give a key to the nature of specific differences [speciation], we may perhaps fairly hope. Certain it is, that until the several characters are thus disentangled and their variations classified, no real progress with this question can be expected.

End of Paper