LECTURE XXVIII

THE GENERAL SIGNIFICANCE OF AMPHIMIXIS

Twofold import of amphimixis—It conditions the continual changing of individuality—Analogy from game of cards—The germ-plasm is at once variable and persistent—The two roots of individual variation: germinal selection and new combinations of the ids—'Harmonious' adaptation conditions amphimixis—Difference between adaptation and mere variation—Is a 'direct' use of amphimixis to be insisted upon?—Ceaseless intervention of personal selection in the lineage of the germ-plasm—Far-reaching effects of personal selection—Fixing of the arrangements for amphimixis in the course of generations of species—Increase of the constancy of a character with its duration—Characters in the same species variable in different degrees—The upper and under surfaces of Kallima—Wild plants brought under cultivation do not at first vary—Amphimixis very ancient, therefore very firmly established—Does amphimixis bring about equalization (Hatschek, Haycraft, Quetelet)?—Galton's frequency curves—Ammon's free scope for variations—De Vries' asymetrical curves of frequency.

We have already made ourselves familiar with the process which in unicellular organisms is called conjugation and in multicellular organisms fertilization, and we have seen that its most obvious significance lay in the fact that through it the germ-plasms of two individuals are united. Since, according to our view, this germ-plasm or idioplasm is the bearer of the hereditary tendencies of the organism concerned, the mingling or amphimixis of two germ-plasms brings together the hereditary tendencies of two individuals, and the organism whose development is derived from this mingled germ-plasm must therefore exhibit traits of both parents, and must to a certain extent be made up of the traits of both. This is one result attained by amphimixis.

But we went further than this, and saw that there is a second result implied in amphimixis, namely, that the individual character of the germ-plasm is being continually altered by new combinations of the ids contained in it. We inferred from what I believe to be the demonstrated hypothesis that the germ-plasm is composed of ids, that its reduction to half the original mass must mean a reduction of the ids to half the number, and as the ids contain primary constituents which are individually different, this must effect a new arrangement, a new mingling of these individual peculiarities. The reduction of the germ-plasm to half, that is, the diminution of the number of its ids to half, is a phenomenon generally associated with amphimixis, and has been established in the case of all animals which have hitherto been investigated, and of all the most carefully studied plants, and finally, it has been shown to be very probable in unicellular organisms, for the processes of conjugation in Infusorians and many other Protozoa include phenomena very similar to those of reducing division in the higher animals. The prediction made on theoretical grounds has here been verified by observation, and it is obvious that the assumption of ids, that is, of units in the germ-plasm which are handed on from one generation to the succeeding one, involves a reduction of their number in each amphimixis. Without this the number of ids would be doubled at each amphimixis, and would therefore gradually amount to something enormous. We see therefore why this normally recurrent reduction of ids before each amphimixis was established in the course of evolution, and we see that it inevitably involves that a new combination of ids should be associated with each amphimixis.

If nothing persists unless it be purposeful, that is, necessary, what is the meaning of the fact that arrangements for amphimixis occur over almost the whole known domain of life, from the very simple organisms up to the highest, in unicellular and multicellular organisms, in plants and animals alike? Why is it that this arrangement has been departed from only in a few small groups of forms, while it occurs everywhere else, in almost every generation, so indissolubly associated with reproduction that it has even been regarded—with a lack of clearness—as itself a form of reproduction, and is even now generally called 'sexual reproduction'? And why is it that in many organisms, especially lowly ones, it is not associated with every reproduction, though it recurs at regular or irregular intervals? Such a universal arrangement must undoubtedly be of fundamental importance, and we have to ask wherein this importance lies. That is the problem to the solution of which we must now apply ourselves.

So much we may say at once: The significance of amphimixis cannot be that of making multiplication possible, for multiplication may be effected without amphimixis in the most diverse ways—by division of the organism into two or more, by budding, and even by the production of unicellular germs. Even though these last are usually in various ways so organized that they must undergo amphimixis before they can develop into new organisms, yet there are numerous germ-cells which are not subject to this condition (e.g. spores), and there are—as we have seen—many germ-cells, adapted for amphimixis, which always, or in certain generations, or even only occasionally, emancipate themselves from this condition under certain external influences: I refer to egg-cells which develop parthenogenetically.

If amphimixis is not a universal preliminary condition of reproduction, wherein lies the necessity for its general occurrence among living organisms?

We have already learned that there are two results produced without exception by amphimixis; one of these is the antecedent reduction of the original number of ids by one half, and the consequent new combination of ids which results from this; the other is the union of two such halved germ-plasms from two different individuals. The first we may, with Hartog, compare to the removal of half of a pack of cards previously mixed, the second to the combination of two such halves from different packs. The first process brings nothing new into the complex of primary constituents, but rather removes a part—larger or smaller—of its characters: not necessarily exactly half of these, since each individual kind of id may be represented by doubles or multiples. But the reduction simplifies the composition of the germ-plasm, and might by itself, through the struggle of the ids in ontogeny, lead to a resultant different from the parent, that is, to a new individuality. Through the second process, however, new individual traits are of necessity added, and make the resultants still more markedly diverse, that is, if the ids of both parents attain to expression in the struggle of ontogeny, and this, as we have already seen, is usually the case, though not always and certainly not always in all parts. Thus amphimixis, together with the preparatory reduction of the ids, secures the constant recurrence of individual peculiarities through the ceaseless new combinations of individual characters already existing in the species.

When sixteen years ago I first inquired into the actual and ultimate significance of sexual reproduction, I thought I had found it in this ceaseless production of new individualities. This seemed to me a sufficient reason for the introduction of amphimixis into nature, since the difference between individuals is the basis of the process of selection, and thus the basis of all the transformations of organisms, which we may refer to natural or sexual selection. Now these differences of selection-value are—as I believed then, and do still—not only by far the most frequent organic changes, but also the most important, since they not only initiate, but control new lines of evolution. Therefore I still regard amphimixis as the means by which a continual new combination of variations is effected a process without which the evolution of this world of organisms so endlessly diverse in form and so inconceivably complex, could not have taken place.

But I do not regard this amphimixis as the real root of variation itself, for that must depend not on a mere exchange of ids, but rather upon a variation of the ids. The ids of a worm of the primitive world could not without variation now make up the germ-plasm of an elephant, even if it be true that mammals are descended from worms. The ids must have been meanwhile transformed times without number by the modification, degeneration, and new formation of determinants. Amphimixis, that is, the union of two germ-plasms, does not of itself cause variation of the determinants, it only arranges the ids (the ancestral plasms) in ever-new combinations. If the origin of variation were limited to that alone, a transmutation of species and genera would only be possible on a very limited scale; there could at most be a narrow circle of variations, just as in the example already given of the packs of cards; even if the taking away and mixing up of the halves were repeated a thousand times, a definite though undoubtedly large number of card-combinations would in the long run recur again and again. But the case is different with the germ-plasm and amphimixis, where there is an infinitely more varied series of results, because the individual cards—the ids—are variable, even between one time of sifting and shuffling and another, and therefore infinitely productive of variety in the course of numerous repetitions of the shuffling.

I have been frequently and persistently credited with maintaining that the germ-plasm is invariable—a misunderstanding of my position, due perhaps to a somewhat too brief and terse statement which I made at an earlier period (1886). I had described the germ-plasm as 'a substance of great power of persistence,' and as varying with difficulty and slowly, basing this statement upon the age-long persistence of many species in which the specific constitution of the germ-plasm must have remained unchanged. The idea of 'germinal selection,' of a ceaseless struggle between the 'primary constituents' of the germ, and of the resulting continual slight and invisible rising and falling of individual characters, had not yet dawned upon me, nor had I at that time formulated the conception of 'determinants.' I was even doubtful at that time whether development, heredity, and variation were not interpretable on the assumption of an undifferentiated substance without primary constituents. But at no time was I unaware that the whole phyletic evolution of the organic world is only conceivable on the assumption of continual variation of the germ-plasm, that it actually depends upon this, even if these variations come about with exceeding slowness, and are thus in a certain sense 'difficult.'

Now that I understand these processes more clearly, my opinion is that the roots of all heritable variation lie in the germ-plasm, and furthermore, that the determinants are continually oscillating hither and thither in response to very minute nutritive changes, and are readily compelled to variation in a definite direction, which may ultimately lead to considerable variations in the structure of the species, if they are favoured by personal selection, or at least if they are not suppressed by it as prejudicial. But selection is continually keeping watch over both kinds of variation, and if the conditions of life do not further the variation or do not even allow it to persist, selection eliminates everything that lessens the purity of the specific type, everything that transgresses the limits of utility, or that might endanger the existence of the species. Thus we understand how the germ-plasm may be variable, and yet at the same time remain unvaried for thousands of years, how it is ready and able to furnish any variation that is possible in a species if that is required by external circumstances, and yet is able to preserve the characters of the species in almost absolute constancy through whole geological ages; in short, how it can be at once readily variable and yet slow to vary.

The importance which amphimixis thus has in connexion with the adaptation of organisms lies, if I mistake not, in the necessity for co-adaptation, that is, in the fact that in almost all adaptations it is not merely a question of the variation of a single determinant, but of the correlated variations of many—often very numerous—determinants, of 'harmonious adaptation,' as we have already said. Many-sided adaptation of this kind seems to me impossible without a continually recurrent sifting and recombining of the germ-plasms, and this can only be effected by amphimixis.

It may be objected that, apart from amphimixis, variation can be brought about in many parts of an organism, as in purely asexual reproduction. A plant, for instance, may vary when it is transferred to a strange soil or climate; and even in that case the variations seem to be harmonious, at least the harmony of the parts is so far maintained that the plant continues to flourish, at any rate under cultivation. A plant species may be incited by abundant nourishment to gigantic growth, and caused to vary in many of its parts, and the abundant food may even directly affect the germ-plasm so that all or some of these variations may become hereditary; and yet this is far from being a case of adaptation, it is merely a case of simultaneous variations, and it is questionable whether they will make the continued existence of the plant under the new conditions possible or not. It might easily happen, for instance, that the plant, though it became larger and bore more abundant blossoms, would be sterile, and therefore unfitted for continued existence in a natural state. Variations are not necessarily adaptations; the latter can never come about solely through direct influence upon the germ-plasm. What direct influence upon the germ-plasm could, for instance, make the hind-legs of a mammal long and strong and the fore-legs short and weak? Obviously neither an increase nor decrease in the food-supply, nor a higher or lower temperature—in short, no direct influence, because all these affect the germ-plasm as a whole, and therefore cannot possibly influence two homologous groups of determinants in opposite directions.

This, it seems to me, is only possible when amphimixis brings about in one individual a favourable coincidence of the chance germinal variations of the determinants of the fore- and hind-limbs; and just as it is with the two variations in this simple hypothetical case, so it will be in the actual processes of adaptation where there are involved numerous—we know not how numerous—variations essential to a 'harmonious adaptation.'

It need not be objected that the very number of variations necessary to a 'harmonious adaptation' makes its occurrence impracticable; for it is the complete harmony of the parts that makes the adaptation, and without this the individual was only imperfectly adapted, and therefore incapable of survival. It is certainly not mathematically demonstrable that this is the case, but as the whole process of transformation which makes an old adaptation into a new one begins with minimal fluctuations of the determinants, which must first be brought by germinal selection to the level of selection-value, and must then be subject to personal selection, so the whole process goes on so gradually and by such small steps that the harmony of the parts is maintained by functional adaptation during the individual life in a great number of individuals. But these are just the individuals which survive in the struggle for existence, and at the same time possess at every stage of the process the best combination of favourably varying determinants. As these favourable variations are, in consequence of germinal selection, not mere isolated variations of fluctuating importance, but variations in a definite direction, the whole process of variation must persist in every single part in the direction imposed upon it by personal selection. But since at every reducing division the ids of the germ-cells are brought down to half their number, a possibility is offered for gradually removing the unfavourable ids from the germ-plasm of the species, since the descendants resulting from the most unfavourable id-combinations always perish, and so from generation to generation the germ-plasm gets rid of its unfavourably varying ids, and the most propitious combinations afforded by amphimixis are preserved, till ultimately there remain only those combinations which are varying appropriately, or at least only those in which the appropriately varying determinants are in the majority, and so have controlling influence.

Logically this deduction is undoubtedly indisputable, from the standpoint of the germ-plasm theory; but whether it may be regarded as a sufficient reason for the introduction of amphimixis, and for its extremely tenacious persistence throughout the course of the long and intricate phylogeny, cannot be maintained without special investigation.

Against my position the objection has often been urged that an arrangement cannot arise or be maintained through natural selection unless it is of direct use to the individual in which it occurs. Sexual reproduction cannot therefore have been established simply because it advances, or even because it makes possible the adaptations of species, for these adaptations only came about occasionally, perhaps once in a thousand generations or even less frequently; thus the intervening generations could derive no advantage of any kind from the arrangement in question, and therefore, according to the law of the degeneration of unused characters, it must have long since been lost. I mentioned this objection before, but was obliged to postpone a detailed consideration of it until we had discussed germinal selection.

We admit, of course, that characters are only preserved intact as long as they are of advantage sufficient to turn the scale in favour of their possessors, and that they begin to fall from their height of perfection when that is no longer the case; we admit also that new adaptations are not continually necessary, but are so only at intervals of long series of generations, and yet the objection cited seems to me baseless.

Leaving out of account, for the moment, the first introduction of amphimixis, let us deal with it as an existing occurrence, for the tenacious persistence of which we wish to find reasons.

Is it really the case that amphimixis is only of importance in connexion with the new adaptation of a species, and that it has nothing to do with the persistence of the species in the state of adaptation already attained? According to the conception of the processes within the germ-plasm which we have already stated, it is impossible that this should be the case, for continual slight fluctuations are occurring in the determinants in consequence of the fluctuations of the nutritive stream, and these slight variations, plus or minus, do not in many cases equalize one another or counteract one another by turning again in a contrary direction; they go on increasing in the direction in which they have begun. It is only when personal selection opposes them that they come to a standstill, and this can only happen when they attain to selection-value, that is to say, when they reach a level at which they become disadvantageous in the struggle of persons. But as germinal variations of this kind are continually occurring, personal selection must keep continual watch over them, and eradicate them as soon as they have attained selection-value.

Therefore, when a species is most perfectly adapted to its conditions, it would of necessity begin to degenerate if personal selection were not continually guarding it, and setting aside everything that is in excess or deficient as soon as it begins to be prejudicial. But the adaptation of a species does not depend upon one character persisting at its normal level, but on the persistence of very many, and many of these vary simultaneously upwards or downwards, and reach the limit of selection-value at one time or another. If there were no amphimixis, then either all individuals with any excessive variant would be at once eliminated, or the species would go on deteriorating until this excessive variant was so numerously and strongly represented in all its individuals that it would perish through degeneration. But even in the first of these cases the species would drift towards the fate of extinction, because excessive variations do occur even in every asexual generation, and would appear in an increasingly large number of determinants if there were no possibility of rejecting them and eliminating them from the lineage of the species.

This is made possible through the periodic intervention of amphimixis; it is actually effected thereby; and in this way alone the species is kept at its high-water mark of adaptation. It is not necessary to assume that every single determinant which is varying in an unfavourable direction is at once eliminated as soon as it becomes prejudicial, that is, reaches negative selection-value, or—to make use of an expression introduced by Ammon—as soon as it oversteps the boundaries of the 'playground of variations,' the limits within which variations are neither favourable nor unfavourable. But in the course of generations they are unfailingly eliminated, especially when a large number of unfavourably varying determinants are coincident in the germ-plasm. Then the individuals which arise from a germ-plasm thus composed must perish in the struggle for existence, and thus the id-combinations with excessive determinants are eliminated from the germinal constitution of the species. As this is repeated as often as excesses of the ids occur, the species is kept pure.

It might be objected that, through such a continual weeding-out of rebellious determinants, the germ-plasm would become so constant in its constitution that it would ultimately be secure from all such aberrations of it on the part of its determinants, and therefore would in time become quite incapable of diverging from its proper path at all, and would thus no longer require this continual correction through amphimixis.

I do not wish to contradict this conclusion; indeed, I believe that the constitution of the species becomes more and more constant in the way I have indicated, and that an ever more perfect and stable equilibrium of the whole determinant system is thus brought about. It follows that in the course of generations the diverse determinants of the germ-plasm will vary within a progressively shortened radius, and will thus more and more rarely overstep the limits of the 'variation-playground'—and yet I still believe that this justifiable conclusion tells in favour of my interpretation of the utility of the persistence of amphigony once introduced.

Let it be remarked, in the first place, that it is by no means essential to the preservation of a useful institution that it should practically justify its utility in every generation. Although, for instance, the warm winter coat of a species of mammal may be necessary to its survival, it does not disappear at once when a winter happens to occur which is so warm that even individuals with poor pellage can survive. Indeed, several such mild winters might occur in succession, in which there was no weeding-out of the individuals with poor fur, and yet the thickness of the winter fur of the species would not become less fixed, just because this character no longer varies perceptibly in an old-established species which has long been perfectly adapted, and it could only be brought into a state of marked fluctuation very slowly through direct influence on the germ-plasm, or through panmixia. But exactly the same thing is true in regard to the determinants of the reproductive cells, in respect of their adaptation to amphimixis, only very much more emphatically.

Before going further, I should like to show that the conclusion we have just deduced from the theory, namely, that the equilibrium of the determinant system of a species increases in stability with the duration of its persistence, holds good not only for the whole system, but for its individual parts, that is, for the individual characters and adaptations. Experience teaches that characters are the more exactly and constantly transmitted the older they are; generic characters are more constant than species-characters, order-characters more persistent than family-characters—this is implied even in their name. But we are able to show even in relation to the characters of a species that those which have been fixed for a long time are most precisely and purely transmitted; that is, that their determinants are least inclined to overstep the limits of the 'variation-playground' either in an upward or downward direction.

Two groups of facts prove this: first the observed fact that the very different degree of variability which the different species exhibit is by no means common to all the characters of the species in the same measure; for individual characters may be variable or constant in very different degrees.

Many years ago[21] I drew attention to the fact that the different stages in the life-history of insects, especially of Lepidoptera, might be variable in quite different degrees. Thus, for instance, the caterpillar might be very variable, and yet the butterfly which arises from it might be extremely constant. I concluded from this—what probably no one now will dispute—that the various stages may vary phyletically independently of one another, that, for instance, the caterpillar may adapt itself to a new manner of life, a new food-plant, a new means of defence, while the butterfly, unaffected by this, goes on quietly as it was before. Every new adaptation necessarily implies variability, and so the stage which is in process of transformation must have its period of variability, which gradually returns again to greater constancy, and this the more completely the longer the series of generations through which the weeding out of the less well-adapted has endured.

[21] Studien zur Descendenztheorie, Leipzig, 1876.

But it is not only the individual stages of development that may be unequally variable; the same is true of the characters of a species which occur simultaneously. The most striking example of this known to me is the leaf-butterfly, which I have already mentioned many times in the course of these lectures—the Indian Kallima paralecta. In this species the brown and red upper surface is almost alike in colour and marking in all individuals, but the under surface, the colour and marking of which is so deceptively mimetic of a leaf, is variable to such a degree that it is difficult, among a large number of specimens, to find even a few which are as like one another as are the members of species in which the under side is constant. It need not be urged that this is due to the complexity of the marking on the under side. In many of our indigenous butterflies the under side is just as complex in coloration and marking, and nevertheless it is very constant, being almost identical in all individuals, as for instance in Vanessa cardui. In Kallima the great variability of the under surface certainly depends not merely on the fact that the mimetic character has been only recently acquired (phyletically speaking), but chiefly on the fact that the dead leaves to which they approximate are themselves very diverse in appearance, for many are dry, others moist and covered with mould, and that the adaptations have therefore gone in different directions, and as yet, at least, have neither combined to form a single constant type, nor diverged to form two or three distinct types. The various 'leaf-pictures' seem equally effective in concealing the insects from their enemies, and thus there is still a continual crossing and mingling of the different essays at leaf-picturing.

A second group of facts, which indicates that old-established characters have less tendency to overstep the limits of the neutral 'variation-playground,' is to be found in the experience of breeders, and especially that of gardeners who have brought wild plants under cultivation in order to procure varieties.

It has been proved that the wild plants often exhibit no hereditary variations for a long series of generations, notwithstanding the greatly altered conditions of life, but that then a moment comes in which isolated variations crop up, which may then be intensified by the manipulations of the breeder to form sport-species with large conspicuously coloured flowers, or with some other distinctive character. Darwin called this a shattering of the constitution of the plant; but the stable and slowly varying 'constitution' simply means that in old-established and well-adapted species the determinants possess only a very restricted 'variation-playground,' and because of their firmly based harmonious correlation are not easily and never very quickly induced to overstep its limits in any marked degree.

Let us now apply all this to the institution of amphimixis and amphigony, and it is immediately obvious that these determinants of the germ-plasm which control the characters relating to sexual reproduction must be more stable and less variable than all others which a species possesses, for they are infinitely older. They are older than all species-characters, older than the characters of the genus, of the family, of the class, and indeed of the whole series or phylum to which a higher animal, a vertebrate, for instance, belongs. We cannot wonder, therefore, that amphigony has persisted through hundreds and thousands of generations, even if it had not been reinforced in the germ-plasm during this period by selection. We should rather wonder that an institution so primaeval, and so firmly engrained in the germ-plasm, can ever be departed from, even when its abandonment is to the advantage of the species, as has happened in parthenogenesis.

I have entered upon this long discussion because I believe that we require to appreciate this power of persistence on the part of the sexual determinants before we can explain the general occurrence of amphigony. The occurrence of pure parthenogenesis, unaccompanied by any degeneration of the species, can hardly be understood except on the assumption that the constancy of the species, when it has once been attained, may be preserved without the continual intervention of amphimixis. How long it can be preserved is another question, which it is difficult or impossible to answer, since species exhibiting pure parthenogenesis are rare, and since we cannot tell with certainty how long it is since amphimixis ceased to occur in them. Generally speaking, the answer in regard to the few species which have to be taken into account in this connexion would be 'not long,' but whether this 'not long' signifies hundreds of generations or thousands of generations we must leave undecided. So much only we can say, that in all species of animals in which the male sex has quite died out or has dwindled to a minimal remnant, there are as yet no traces of degeneration to be found, and that even organs which have fallen into disuse and become functionless because amphigony has disappeared, are nevertheless in several cases retained in perfect completeness. I shall return to this subject later on, but in the meantime I wish to work out our conception of the actual efficacy of amphigony or ordinary sexual reproduction, and thereby increase our understanding of its significance and power of persistence.

We have seen that amphigony not only renders possible the novel 'harmonious adaptations' which are continually required, but that it also leads, by a continual crossing of individuals, simultaneously with the elimination of the less fit, to a gradually increasing constancy of the species. This has been regarded by some writers as its sole effect; thus recently by Hatschek, whose view has already been refuted.

Haycraft also finds the significance of amphigony simply in the equalizing or neutralizing of individual differences which it effects. Quetelet and Galton have attempted to show that intercrossing leads to a mean which then remains constant. Haycraft supposes that a species can only remain constant if its individuals are being continually intercrossed, and that otherwise they would diverge and take different forms, because the 'protoplasm' has within itself the tendency to continual variation. The transformation of species is effected by means of this variation tendency, and the persistency and constancy of species which are already adapted to the conditions of their life are secured by the constant intercrossing of the individuals, and the consequent neutralization of individual peculiarities.

Although the cases already mentioned in which great constancy of species is associated with purely parthenogenetic reproduction do not tell in favour of the accuracy of the view just stated, yet the fundamental idea, that amphigony is an essential factor in the maintenance and even in the evolution of species, is undoubtedly sound. We should certainly find neither genera nor species in Nature if amphigony did not exist; but we cannot simply suppose that amphigony and variation are, so to speak, antipodal forces, the former of which secures the constancy of the species, the latter its transformation. In my opinion, at all events, there is no such thing as a 'tendency' of the protoplasm to vary, although there is a constant fluctuation of the characters—dependent on the imperfect equality of the external influences, especially of nutrition. This certainly results, as far as it takes place within the germ-plasm, in a continual upward and downward variation of the hereditary tendencies, and it would lead to increasing dissimilarity of the individuals were it not that amphigony is continually equalizing the differences by a constantly repeated mingling of individuals. Quetelet and Galton have shown that the tendency of this mingling is towards the establishment of a mean; the characters of Man, such as bodily size, fluctuate about a mean, which at the same time shows the maximum of frequency; and the frequency curve of the various bodily sizes assumes a perfectly symmetrical form, so that the average size is the most frequent, and deviations from it upwards or downwards occur more rarely in proportion to the amount of deviation, the largest and the smallest sizes occurring least frequently.

Thus an equalizing of variations by means of amphimixis really exists, and the question we have to ask is, How does it come about? The case is assuredly not the same as that in which equal quantities of red and white wine are mixed to make a so-called 'Schiller.' This is proved even by the fact that the mixture may turn out quite different even when the wines—the two parents—are alike: for the children of a pair are often dissimilar. And while the 'Schiller' cannot be separated again into red wine and white, this happens often in sexual reproduction, and sometimes to such an extent that the grandchild exactly resembles one or other of the grand-parents, as is most clearly proved in the case of plant-hybrids.

There is thus a deep-seated difference, depending on the fact that what is mingled in amphigony is not simple but composite, not a simple uniform developmental tendency associated with a simple and definite substance, but a combination of several or many developmental tendencies, associated with several equivalent but different material units. These units are the ids or ancestral plasms, and we have seen how they are not only halved by reducing division, but are also arranged in new combinations in amphimixis.

These ids differ very little within the same germ-plasm; in species which have long been established the majority probably only differ in correspondence to the individual differences of the fully-formed organisms, but they are only absolutely alike in the case of two ids which have been formed by the division of a mother-id. Let us disregard this for the moment, and assume that all the ids of a germ-plasm are different: the germ-plasm of a father, A, will be composed of ids A 1-100, that of the mother, B, of the ids B 1-100. But in each mature germ-cell of these two parents only fifty ids are contained, and if we assume that the mingling of the ids is controlled solely by chance, then in the various germ-cells A × B the most diverse combinations of ids may be contained; for instance, A 1, 3, 5, 7, 9, 11, ...to 99, or A 1-10 and 20-30, and 40-50, and so on, and similarly in the germ-cells B. If all germ-cells produced by A and by B attained to development, or even if all the ova succeeded, the thousand or hundred thousand children of this pair would necessarily exhibit every possible mingling of their characters, and each in the same number according to the rules of probability calculations. But it is well known that this does not happen; of the thousands of human ova, for instance, which come to maturity in the course of the life of a female individual more than ten rarely develop, and more than thirty never, and these are determined solely by chance and quite independently of the mixture of ids which they contain. It is thus purely a matter of chance which of the complexes of primary constituents contained in the germ-plasm of an individual are transmitted to descendants, and it is also purely a matter of chance which combination of ids comes to be developed. Therefore we may say that no regular neutralizing of contrasts, either in the primary constituents of the parents or as regards the differences in their characters, can occur. In one case there is a blended inheritance; in another the child takes after the father or after the mother; in a third, and this probably occurs most frequently, the child resembles the father in some characters and the mother in others.

But how then does Galton's curve of frequency of variations come about? Why does the mean of any character occur by far the most frequently, and why does the frequency of a variation diminish regularly in proportion to its approximation to either extreme? To this it is answered: Because the process of mingling through amphigony goes on through numerous generations, and thus an elimination of chance, and the establishment of an average, must be brought about.

But this does not quite suffice to explain matters, for experience shows that asymmetrical frequency-curves of variations also occur, even in species with sexual reproduction. As De Vries has recently shown, there are also 'half-Galton curves,' that is, curves which suddenly break off at their highest point. We must conclude from this that the frequency of the different variations depends not only on their degree, but also on the greater or less facility with which they arise from the constitution of the species.

This consideration can be readily elucidated with the help of Ammon's exposition, and especially of his graphic representation of the 'playground of variations.' If we think of the indifferent variations occurring in any character of a species as arranged in a series ascending from the smallest to the largest, this line may be regarded as the abscissal-axis, and from it ordinates may be drawn which express the frequency of the variation in question by the differences in their length. If the tips of these ordinates be united, we have the curve of frequency (Fig. 120, A), which according to Galton ought to be symmetrical, and in most cases really is so. Ammon calls the space between the smallest and the largest variations the 'variation-playground,' that is, the playground within which all variations are equally advantageous to the species. This is not co-extensive with the variation-area, for there may be more marked deviations below the beginning or above the upper end of the variation-playground, but these, being disadvantageous, fall under the shears of personal selection. The variation-playground may also be called the area of indulgence of variation, because the variations falling within it are spared from the eliminating activity of selection, or the variation-area of survivors, because on an average only those survive whose variations do not overstep the limits of this area.

Fig. 120. A, symmetrical, and B, asymmetrical curve of frequency; after Ammon. U, minimal, O, maximal limit of individual variation. U-O, the 'variation-playground.' M, the mean of variation. H, the greatest frequency or mode of variation.

This implies that variations below U (the lower limit of the area of exemption) and above O (the upper limit) can occur, but do not survive and leave descendants, and we can therefore easily understand why characters, of which different degrees arise with equal ease from the constitution of the species, must gradually develop a symmetrical curve of frequency because of the constant crossing. Obviously those individuals which stand just upon the borders of admissible variation will, other conditions being equal, leave behind them fewer descendants than those which approximate to the middle of the area of exemption; for as the characters concerned can vary in the offspring in both directions, there will always be at the lower end some of the descendants of a pair which will fall below the limits of exemption, and at the upper end some which will rise above it. This will happen even when pairing takes place between parents at the middle or at the other end of the abscissa, for there are always cases of the preponderance of one parent in heredity. A higher percentage of the descendants of individuals on the borderline will therefore be eliminated, and their frequency must therefore be less. Even if at the beginning of the series of observations a condition obtained in which all the ordinates of the area of exemption were equally high, those nearest the boundaries would of necessity very soon become lower, and this in proportion to their distance from the boundary, and the frequency-curve, which at first would be a straight line (according to our assumption, which of course does not tally with natural conditions), would become a symmetrical curve, highest in the middle and falling equally at either side.

Ammon has worked out the hypotheses on which the curve of frequency would become asymmetrical. Firstly, when the fertility is greater towards the upper or lower limit of the area of exemption; secondly, when germinal selection forces the variation in a particular direction, upwards or downwards; and thirdly, 'when natural selection intervenes diversely at the upper or lower limit.' Of these three possibilities the first two must be acknowledged as quite probable, but the third, it seems to me, could only cause a temporary asymmetry of the curve, lasting, that is, only until a state of equilibrium has again been reached; but that may in certain conditions take a long time.

Asymmetrical curves of frequency (Fig. 120, B) therefore arise, for instance, when the intra-germinal conditions (the 'constitution of the species') more easily and therefore more frequently produce extreme variations. In this case the area of exemption can only extend on one side, and must remain in this state. In Caltha palustris, the marsh marigold, we may find, according to De Vries, among a hundred flowers, those with five, six, seven, and eight petals, in the following proportions:—

Petals5678
Number of flowers722161

and thus there is an asymmetrical curve of frequency. But if we take the whole area of variation as the area of exemption, that is, if we assume that it is indifferent for the species whether the flowers have five, six, seven, or eight petals, the preponderance of the five-petalled flowers may have its reason in the fact that it is much easier for five than six or more petals to be produced because of the internal structure of the whole plant.

In this case the maximum of frequency lies at the lower limit of variation, but it may also lie at the upper. Thus, according to De Vries, the blossoms of Weigelia vary, in regard to the number of their petal-tips, in the following manner. Six-tipped corollas were not found, and among 1,145 flowers there were the following proportions:—

Tips of the corolla345
Number of flowers61196888

It is thus clear that amphimixis is an essential factor in the fixing of forms, but that it certainly does not of itself determine these, and that it is not always the average of the variations that is the most frequent, but that the form of the curve of frequency is determined by other factors also, namely, by germinal and personal selection and by the directive control which these exert on variations.

The equalizing effect of amphigony may perhaps be expressed thus: In the case of every new adaptation there is at first a large area of variation, but this gradually decreases owing to a continual restriction on the part of natural selection, until ultimately—when the highest degree of constancy of the character or species has been attained—it only extends very little beyond the 'adaptation-playground' or the 'area of exemption.'

One of the effects of amphimixis is thus to bring about an increasing restriction of the area of variation, or, as we usually say, a constancy of the facies of a given form, a condensation into a species. How far this result is necessary or useful, and therefore how far it may be regarded as accounting for the persistence of amphimixis, we shall discuss in the chapter on the formation of species. My own view is that even the fact that new adaptations are rendered possible through amphimixis and amphigony, the mode of reproduction associated with it, affords in itself a sufficient reason why amphimixis should have been retained when once it had been introduced.