Discontinuous Variation
Galton, in his book on “Natural Inheritance,” points out that “the theory of natural selection might dispense with a restriction for which it is difficult to see either the need or the justification, namely, that the course of evolution always proceeds by steps that are severally minute and that become effective only through accumulation.” An apparent reason, it is suggested, for this common belief “is founded on the fact that whenever search is made for intermediate forms between widely divergent varieties, whether they are of plants or of animals, of weapons or utensils, of customs, religion, or language, or of any other product of evolution, a long and orderly series can usually be made out, each member of which differs in an almost imperceptible degree from the adjacent specimens. But it does not at all follow because these intermediate forms have been found to exist, that they were the very stages that were passed through in the course of evolution. Counter evidence exists in abundance, not only of the appearance of considerable sports, but of their remarkable stability in hereditary transmission.” Comparing such an apparently continuous series with machines, Galton concludes, “If, however, all the variations of any machine that had ever been invented were selected and arranged in a museum, each would differ so little from its neighbors as to suggest the fallacious inference that the successive inventions of that machine had progressed by means of a very large number of hardly discernible steps.”
Bateson, also, in his “Materials for the Study of Variation,” speaks of the two possible ways in which variations may arise. He points out that it has been tacitly assumed that the transitions have been continuous, and that this assumption has introduced many gratuitous difficulties. Chief of these is the difficulty that in their initial and imperfect stages many variations would be useless. “Of the objections that have been brought against the Theory of Natural Selection, this is by far the most serious.” He continues: “The same objection may be expressed in a form which is more correct and comprehensive. We have seen that the differences between species on the whole are Specific, and are differences of kind forming a discontinuous Series, while the diversities of environment to which they are subject are, on the whole, differences of degree, and form a continuous Series; it is, therefore, hard to see how the environmental differences can thus be made in any sense the directing cause of Specific differences, which by the Theory of Natural Selection they should be. This objection of course includes that of the utility of minimal Variations.”
“Now the strength of this objection lies wholly in the supposed continuity of the process of Variation. We see all organized nature arranged in a discontinuous series of groups differing from each other by differences which are Specific; on the other hand, we see the diverse environments to which these forms are subject passing insensibly into each other. We must admit, then, that if the steps by which the diverse forms of life have varied from each other have been insensible,—if, in fact, the forms ever made up a continuous series,—these forms cannot have been broken into a discontinuous series of groups by a continuous environment, whether acting directly as Lamarck would have, or as selective agent as Darwin would have. This supposition has been generally made and admitted, but in the absence of evidence as to Variation it is nevertheless a gratuitous assumption, and, as a matter of fact, when the evidence as to Variation is studied, it will be found to be in a great measure unfounded.”
There is a fair number of cases on record in which discontinuous variations have been seen to take place. Darwin himself has given a number of excellent examples, and Bateson, in the volume referred to above, has brought together a large and valuable collection of facts of this kind.
Some of the most remarkable of these instances have been already referred to and need only be mentioned here. The black-shouldered peacock, the ancon ram, the turnspit dog, the merino sheep, tailless and hornless animals, are all cases in point. In several of these it has been discovered that the young inherit the peculiarities of their parents if the new variations are bred together; and what is more striking, if the new variation is crossed with the parent form, the young are like one or the other parent, and not intermediate in character. This latter point raises a question of fundamental importance in connection with the origin of species.
Darwin states that he knows of no cases in which, when different species or even strongly marked varieties are crossed, the hybrids are like one form or the other. They show, he believes, always a blending of the peculiarities of the two parents. He then makes the following significant statement: “All the characters above enumerated which are transmitted in a perfect state to some of the offspring and not to others—such as distinct colors, nakedness of skin, smoothness of leaves, absence of horns or tail, additional toes, pelorism, dwarfed structure, etc., have all been known to appear suddenly in individual animals or plants. From this fact, and from the several slight, aggregated differences which distinguish domestic races and species from each other, not being liable to this peculiar form of transmission, we may conclude that it is in some way connected with the sudden appearance of the characters in question.”
Darwin has, incidentally, raised here a question of the most far-reaching import. If it should prove true, as he believes, that inheritance of this kind of discontinuous variation is also discontinuous, and that we do not get the same result when distinct species are intercrossed, or even when well-marked domestic races are interbred, then he has, indeed, placed a great obstacle in the path of those who have tried to show that new species have arisen through discontinuous variation of this sort.
If wild species, when crossed, give almost invariably intermediate forms, then it may appear that we are going against the only evidence that we can hope to obtain if we claim that discontinuous variation, of the kind that sports are made of, has supplied the material for evolution. If, furthermore, when distinct races of domesticated animals are crossed, we do not get discontinuous inheritance, it might, perhaps, with justness be claimed that this instance is paralleled by what takes place when wild species are crossed. And if domesticated forms have been largely the result of the selection of fluctuating variations, as Darwin believes, then a strong case is apparently made out in favor of Darwin’s view that continuous variation has given the material for the process of evolution in nature. Whether selection or some other factor has directed the formation of the new species would not, of course, be shown, nor would it make any difference in the present connection.
Before we attempt to reach a conclusion on this point let us analyze the facts somewhat more closely.
In the first place, a number of these cases of discontinuous variation are of the nature of abnormalities. The appearance of extra fingers or toes in man and other mammals is an example of this sort. This abnormality is, if inherited at all, inherited completely; that is, if present the extra digit is perfect, and never appears in an intermediate condition, even when one of the parents was without it. The most obvious interpretation of this fact is that when the material out of which the fingers are to develop is divided up, or separated into its component parts, one more part than usual is laid down. Similarly, when a flower belonging to the triradiate type gives rise to a quadriradiate form,—as sometimes occurs,—the new variation seems to depend simply on the material being subdivided once more than usual; perhaps because a little more of it is present, or because it has a somewhat different shape. My reasons for making a surmise of this sort are based on certain experimental facts in connection with the regeneration of animals. It has been shown in several cases that it is possible to produce more than the normal number of parts by simply dividing the material so that each part becomes more or less a new whole, and the total number of parts into which the material becomes subdivided is increased. It seems not improbable that phenomena of this sort have occurred in the course of evolution, although it is, of course, possible that those characters that define species do not belong to this class of variation. To take an example. There are nine neck-vertebræ in some birds, but in the swan the number is twenty-five. We cannot suppose that the ancestor of the swan gradually added enough materially to make up one new vertebra and then another, but at least one new whole vertebra was added at a time; and we know several cases in which the number of vertebræ in the neck has suddenly been increased by the addition of one more than normal, and the new vertebra is perfectly formed from the first.
In cases of this sort we can easily understand that the inheritance must be either of one kind or the other, since intermediate conditions are impossible, when it comes to the question of one or not one; but if one individual had one and another six vertebræ, then it would be theoretically possible for the hybrid to have three.
This brings us to a question that should have been spoken of before in regard to the inheritance of discontinuous variation. It sometimes occurs that a variation, which appears in other respects to be discontinuous, is inherited in a blended form. Thus the two kinds of variation may not always be so sharply separated as one might be led to believe. There may be two different kinds of discontinuous variation in respect to inheritance, or there may be variations that are only to a greater or a less extent inherited discontinuously; and it seems not improbable that both kinds occur.
This diversion may not appear to have brought us any nearer to the solution of the difficulty that Darwin’s statement has emphasized, except in so far as it may show that the lines are not so sharply drawn as may have seemed to be the case. The solution of the difficulty is, I believe, as follows:—
The discontinuity referred to by Darwin relates to cases in which only a single step (or mutation) has been taken, and it is a question of inheritance of one or not one. If, however, six successive steps should be taken in the same direction, then when such a form is crossed with the original form, the hybrid may inherit only three of the steps and stand exactly midway between the parent forms; or it may inherit four, or five, or three, or two steps and stand correspondingly nearer to the one or to the other parent. Thus while it may not be possible to halve a single step (hence one-sided inheritance), yet when more than one step has been taken the inheritance may be divided. There is every evidence that most of the Linnæan (wild) species that Darwin refers to have diverged from the parent form, and from each other, by a number of successive steps; hence on crossing, the hybrid often stands somewhere between the two parent forms. On this basis not only can we meet Darwin’s objection, but the point of view gives an interesting insight into the problem of inheritance and the formation of species.
The whole question of inheritance has assumed a new aspect; first on account of the work of De Vries in regard to the appearance of discontinuous variation in plants; and secondly, on account of the remarkable discoveries of Gregor Mendel as to the laws of inheritance of discontinuous variations. Mendel’s work, although done in 1865, was long neglected, and its importance has only been appreciated in the last few years. We shall take up Mendel’s work first, and then that of De Vries.
Mendel’s Law[[24]]
[24]. Bateson, in his book on “Mendel’s Principles of Heredity,” has given an admirable presentation of Mendel’s results. I have relied largely on this in my account.
The importance of Mendel’s results and their wide application is apparent from the results in recent years of De Vries, Correns, Tschermak, Bateson, Castle, and others. Mendel carried out his experiments on the pea, Pisum sativum. Twenty-two varieties were used, which had been proven by experiment to be pure breeds. When crossed they gave perfectly fertile offspring. Whether they all have the value of varieties of a single species, or are different subspecies, or even independent species, is of little consequence so far as Mendel’s experiments are concerned. The flower of the pea is especially suitable for experiments of this kind. It cannot be accidentally fertilized by foreign pollen, because the reproductive organs are inclosed in the keel of the flower, and, as a rule, the anthers burst and cover the stigma of the same flower with its own pollen before the flower opens. In order to cross-fertilize the plants it is necessary to open the young buds before the anthers are mature and carefully remove all the anthers. Foreign pollen may be then, or later, introduced.
The principle involved in Mendel’s law may be first stated in a theoretical case, from which a certain complication that appears in the actual results may be removed.
If A represent a variety having a certain character, and B another variety in which the same character is different, let us say in color, and if these two individuals, one of each kind, are crossed, the hybrid may be represented by H. If a number of these hybrids are bred together, their descendants will be of three kinds; some will be like the grandparent, A, in regard to the special character that we are following, some will be like the other grandparent, B, and others will be like the hybrid parent, H. Moreover, there will be twice as many with the character H, as with A, or with B.
If now we proceed to let these A’s breed together, it will be found that their descendants are all A, forever. If the B’s are bred together they produce only B’s. But when the H’s are bred together they give rise to H’s, A’s, and B’s, as shown in the accompanying diagram. In each generation, the A’s will also breed true, the B’s true, but the H’s will give rise to the three kinds again, and always in the same proportion.
Thus it is seen that the hybrid individuals continue to give off the pure original forms, in regard to the special character under consideration. The numerical relation between the numbers is also a striking fact. Its explanation is, however, quite simple, and will be given later.
In the actual experiment the results appear somewhat more complicated because the hybrid cannot be distinguished from one of the original parents, but the results really conform exactly to the imaginary case given above. The accompanying diagram will make clearer the account that follows.
The hybrid, A(B), produced by crossing A and B is like A so far as the special character that we will consider is concerned. In reality the character that A stands for is only dominant, that is, it has been inherited discontinuously, while the other character, represented by B, is latent, or recessive as Mendel calls it. Therefore, in the table, it is included in parentheses. If the hybrids, represented by this form A(B), are bred together, there are produced two kinds of individuals, A’s and B’s, of which there are three times as many A’s as B’s. It has been found, however, that some of these A’s are pure forms, as indicated by the A on the left in our table, while the others, as shown by their subsequent history, are hybrids, A(B). There are also twice as many of these A(B)’s as of the pure A’s (or of the B’s). Thus the results are really the same as in our imaginary case, only obscured by the fact that the A’s and the A(B)’s are exactly alike to us in respect to the character chosen. We see also why there appear to be three times as many A’s as B’s. In reality the results are 1 A, 2 A(B), 1 B.
In subsequent generations the results are the same as in this one, the A’s giving rise only to A, the B’s to B, and the A(B)’s continuing to split up into the three forms, as shown in our diagram. Mendel found the same law to hold for all the characters he examined, including such different ones as the form of the seed, color of seed-albumen, coloring of seed-coat, form of the ripe pods, position of flowers, and length of stem.
Mendel also carried out a series of experiments in which several differentiating characters are associated. In the first experiment the parental plants (varieties) differed in the form of the seed and in the color of the albumen. The two characters of the seed plant are designated by the capital letters A and B; and of the pollen plant by small a and b. The hybrids will be, of course, combinations of these, although only certain characters may dominate. Thus in the experiments, the parents are AB (seed plant) and ab (pollen plant), with the following seed characters:—
| Seed parent | {A form round | Pollen parent | {a form angular |
| AB | {B albumen yellow | ab | {b albumen green |
When these two forms were crossed the seeds appeared round and yellow like those of the parent, AB, i.e. these two characters dominated in the hybrid.
The seeds were sown, and in turn yielded plants which when self-fertilized gave four kinds of seeds (which frequently all appeared in the same pod). Thus 556 seeds were produced by 15 plants, having the following characters:—
AB 315 round and yellow
Ab 101 angular and yellow
aB 108 round and green
ab 32 angular and green
These figures stand almost in the relation of 9 : 3 : 3 : 1.
These seeds were sown again in the following year and gave:—
From the round yellow seeds:—
AB 38 round and yellow seeds
ABb 65 round yellow and green seeds
AaB 60 round yellow and angular yellow seeds
AaBb 138 round yellow and green, angular yellow and green seeds
From the angular yellow seeds:—
aB 28 angular yellow seeds
aBb 68 angular yellow and green seeds
From the round green seeds:—
Ab 35 round green seeds
Aab 67 round angular seeds
From the angular green seeds:—
ab 30 angular green seeds
Thus there were 9 different kinds of seeds produced. There had been separated out at this time 38 individuals like the parent seed plant, AB, and 30 like the parent pollen plant, ab. Since these had come from similar seeds of the preceding generation they may be looked upon as pure at this time. The forms Ab and aB are also constant forms which do not subsequently vary. The remainder are still mixed or hybrid in character. By successive self-fertilizations it is possible gradually to separate out from these the pure types of which they are compounded.
Without going into further detail it may be stated that the offspring of the parent hybrids, having two pairs of differentiating characters, are represented by the series:—
AB Ab aB ab 2ABb 2aBb 2Aab 2ABa 2AaBb
This series is really a combination of the two series:—
A + 2Aa + a
B + 2Bb + b
Mendel even went farther, and used two parent varieties having three differentiating characters, as follows:—
| ABC seed parent | abc pollen plant |
| { A form round | { a form angular |
| { B albumen yellow | { b albumen green |
| { C seed-coat grey brown | { c seed-coat white |
The results, as may be imagined, were quite complex, but can be expressed by combining these series:—
A + 2Aa + a
B + 2Bb + b
C + 2Cc + c
In regard to the two latter experiments, in which two and three characters respectively were used, it is interesting to point out that the form of the hybrid more nearly approaches “to that one of the parental plants which possesses the greatest number of dominant characters.” If, for instance, the seed plant has short stem, terminal white flowers, and simply inflated pods; the pollen plant, on the other hand, a long stem, violet-red flowers distributed along the stem, and constricted pods,—then the hybrid resembles the seed parent only in the form of the pod; in its other characters it agrees with the pollen plant. From this we may conclude that, if two varieties differing in a large number of characters are crossed, the hybrid might get some of its dominant characters from one parent, and other dominant characters from the other parent, so that, unless the individual characters themselves were studied, it might appear that the hybrids are intermediate between the two parents, while in reality they are only combinations of the dominant characters of the two forms. But even this is not the whole question.
Mendel points out that, from knowing the characters of the two parent forms (or varieties), one could not prophesy what the hybrid would be like without making the actual trial. Which of the characters of the two parent forms will be the dominant ones, and which recessive, can only be determined by experiment. Moreover, the hybrid characters are something peculiar to the hybrid itself, and to itself alone, and not simply the combination of the characters of the two forms. Thus in one case a hybrid from a tall and a short variety of pea was even taller than the taller parent variety. Bateson lays much emphasis on this point, believing it to be an important consideration in all questions relating to hybridization and inheritance.
The theoretical interpretation that Mendel has put upon his results is so extremely simple that there can be little doubt that he has hit on the real explanation. The results can be accounted for if we suppose that the hybrid produces egg-cells and pollen-cells, each of which is the bearer of only one of the alternative characters, dominant or recessive as the case may be. If this is the case, and if on an average there are the same number of egg-cells and pollen-cells, having one or the other of these kinds of characters, then on a random assortment meeting of egg-cells and pollen-cells, Mendel’s law would follow. For, 25 per cent of dominant pollen grains would meet with 25 per cent dominant egg-cells; 25 per cent recessive pollen grains would meet with 25 per cent recessive egg-cells; while the remaining 50 per cent of each kind would meet each other. Or, as Mendel showed by the following scheme:—
Or more simply by this scheme:—
Mendel’s results have received confirmation by a number of more recent workers, and while in some cases the results appear to be complicated by other factors, yet there can remain little doubt that Mendel has discovered one of the fundamental laws of heredity.
It has been found that there are some cases in which the sort of inheritance postulated by Mendel’s law does not seem to hold, and, in fact, Mendel himself spoke of such cases. He found that some kinds of hybrids do not break up in later generations into the parent forms. He also points out that in cases of discontinuity the variations in each character must be separately regarded. In most experiments in crossing, forms are chosen which differ from each other in a multitude of characters, some of which are continuous and others discontinuous, some capable of blending with their contraries while others are not. The observer in attempting to discover any regularity is confused by the complications thus introduced. Mendel’s law could only appear in such cases by the use of an overwhelming number of examples which are beyond the possibilities of experiment.[[25]]
[25]. This statement is largely taken from Bateson’s book.
Let us now examine the bearing of these discoveries on the questions of variation which were raised in the preceding pages. It should be pointed out, however, that it would be premature to do more than indicate, in the most general way, the application of these conclusions. The chief value of Mendel’s results lies in their relation to the theory of inheritance rather than to that of evolution.
In the first place, Mendel’s results indicate that we cannot make any such sharp distinction as Darwin does between the results of inheritance of discontinuous and of continuous variations. As Mendel’s results show, it is the separate characters that must be considered in each case, and not simply the sum total of characters.
The more general objection that Darwin has made may appear to hold, nevertheless. He thinks that the evolution of animals and plants cannot rest primarily on the appearance of discontinuous variations, because they occur rarely and would be swamped by intercrossing. If Mendel’s law applies to such cases, that is, if a cross were made between such a sport and the original form, the hybrid in this case, if self-fertilized, would begin to split up into the two original forms. But, on the other hand, it could very rarely happen that the hybrid did fertilize its own eggs, and, unless this occurred, the hybrid, by crossing with the parent forms in each generation, would soon lose all its characters inherited from its “sport” ancestor. Unless, therefore, other individuals gave rise to sports at the same time, there would be little chance of producing new species in this way. We see then that discontinuity in itself, unless it involved infertility with the parent species, of which there is no evidence, cannot be made the basis for a theory of evolution, any more than can individual differences, for the swamping effect of intercrossing would in both cases soon obliterate the new form. If, however, a species begins to give rise to a large number of individuals of the same kind through a process of discontinuous variation, then it may happen that a new form may establish itself, either because it is adapted to live under conditions somewhat different from the parent form, so that the dangers of intercrossing are lessened, or because the new form may absorb the old one. It is also clear, from what has gone before, that the new form can only cease to be fertile with the parent form, or with its sister forms, after it has undergone such a number of changes that it is no longer able to combine the differences in a new individual. This result will depend both on the kinds of the new characters, as well as the amounts of their difference. This brings us to a consideration of the results of De Vries, who has studied the first steps in the formation of new species in the “mutations” of the evening primrose.