Whether the variations observed in a population of organisms are fluctuations or mutations can only be determined by experiment. Let us suppose that we are dealing with a human population, and that the variation studied is that of stature. Let the men with statures considerably over the mean value marry the women who are correspondingly tall, then it will be found that the children from these unions will, when grown up, exhibit a stature which is greater than that of the whole population, but not so great as that of their parents—that is, regression towards the mean of the whole population takes place.

This is shown in the above diagram, where the lines above and below the mean one indicate the proportion (relative to the value or frequency of the mean) of people of each grade of stature. The latter is proportional to the distance from the mean measured along the vertical line, distances below this line indicating statures below the mean, and vice versa.

If, on the other hand, the men and women with statures considerably below the mean marry, their children will ultimately exhibit statures which are greater than that of their parents, but which are less than that of the whole population. Regression again occurs, but in the opposite direction, and such a case would be represented by the above diagram reversed. Continued selection of this kind would lead to an immediate increase in the mean stature (or the opposite, if the “sign” of the selection were reversed) in one or two generations, but after that the amount of change would be very small, while if the selection were to cease the race produced would slowly revert to the mean, which is characteristic of the whole population from which it arose. It is very important to grasp this result of the practical and theoretical study of heredity—the selection of the ordinary variations shown by a general population leads at once to a small change in the mean value of the character which is selected, but continued selection thereafter makes very little difference to this result, while the race slowly reverts to the value of that from which it arose on the cessation of the selection.

Races which “breed true” do, of course, exist; thus the mean height of the Galloway peasant is greater than that of the Welsh. In the cases of “pure races”—that is, races which breed true with respect to one or more characters, we have to deal with another kind of variation, one which shows no tendency to revert to the value from which it arose. Let the observed variability of stature in a human population be represented by the frequency distribution A, and let the individuals at N—that is, those in which the stature was greater than the mean by the deviation ON—intermarry. It might then happen that the variability of the offspring of these unions would be represented by the frequency distribution B, in which the value of the mean is also that of the stock, at N, from which the race originated. It does not matter now from what variants in B a progeny of the third generation arises: the mean height of the latter will be that of the pure race. In this case the individuals from which the pure race originated (those at N in A) have exhibited a mutation. The stature of the individuals of this new race will continue to exhibit fluctuating variations, and the range of this variability may be as much as that of the stock from which it arose, but the mean stature of the new race will continue to be that of the original mutants.

It is well known that de Vries himself considered fluctuating variations and mutations as something quite different. The former he considered as nothing new, only as augmentations or diminutions of something previously existing; and he regarded fluctuations as due to the action of the environment, following in their distribution the laws of chance.30 Mutations, on the other hand, were something quite new. Now future analysis of variability will not, we think, bear out the validity of this distinction. It is far more likely that a fluctuation is a variation which is the result of some causes the action of which is variable. (We are regarding variability now as subject to “causation” in the physical sense, for only by so regarding it can we attempt its analysis). As a rule this process results in a fluctuation, but if its extent, or degree of operation, exceeds a certain “critical value” a mutation is produced. We may, following the example of the physicists, illustrate this by a “model.”

This model is a modification of Galton’s illustration of the degrees of stability of a species. It is a disc of wood rolling on its periphery. We divide it into sectors, and the arcs ab, cd, ef, and gh have all the same radius, 10, 20, 30, and 40. Then we flatten the sectors bc, de, fg, and ha, so that their radii are greater than are those of the other arcs. Now let us cause the disc to roll about the point 8 as a centre. It will oscillate backwards and forwards about a mean position 8. Let us think of these oscillations as fluctuations.

Suppose, however, that we cause the disc to roll a little more violently, so that it oscillates until either of the points 3 or 4 are perpendicularly beneath the centre O. In either of these positions the disc is in a condition of “unstable equilibrium,” and an infinitesimal increase in the extent of an oscillation will cause it to roll beyond the points 3 or 4. But if it does pass either of these critical points it will begin to oscillate about either of the new centres 5 or 7, thus rolling on one of the arcs, ha or de. This assumption of a new condition of stability we may compare with the formation of a mutation.

All this is merely a conceptual physical model of a process about which we know nothing at all. It is meant to illustrate the view that the organisation of a plant or animal is not something absolutely fixed and invariable. The organism in respect of each recognisable and measurable character oscillates about a point of stability, that is to say exhibits fluctuating variations about the mean value of this character. If the stability of the organisation is upset, so that it oscillates, or fluctuates about a new centre, that is, if the variations deviate in either direction from a new “type” or mean, a mutation has been established. A mutation is not, therefore, necessarily a large departure from “normality.” It is not necessarily a “discontinuous variation,” nor a “sport” nor a “freak.” It is essentially a shifting of the mean position about which the variations exhibited by the organism fluctuate.

Such a mutation will, in general, involve the creation of an “elementary species.” We have considered only one character, say stature, in the above discussion, but it generally happens that the assumption of a new centre of stability involves all the characters of the mutating organism. An elementary species therefore differs a little in respect of all its characters from the species from which it arose, or from the other elementary species near which it is situated. This is what we do usually find in the cases of the “races,” or “local varieties,” of any one common species of plant or animal. That we do not recognise that most, or perhaps all, of the species known to systematic biology are really composed of such local races is merely because such results involve an amount of close investigation such as has not generally been possible except in the few cases studied with the object of proving such variability; or in the case of those species which are studied with great attention to detail because of their economic importance. Thus the herrings of North European seas can be divided into such races, and it is possible for a person possessing great familiarity with these fishes to identify the various races or elementary species—that is, to name the locality from which the fish were taken—by considering the characteristics in respect of which the herrings of one part of the sea differ from those of other parts.

The term “variety” has rather a different connotation in systematic biology from that which is included by the term “elementary species.” The meaning of the latter is simple and clear. Two or more elementary species are assemblages of organisms, in each of which assemblages the mean positions about which the various characters fluctuate is different. The term “variety” cannot so easily be defined. The progeny of two different species (in the sense of the term as it is usually applied by systematists) may be called a hybrid variety of one or other of the parent species. In the case of the ordinary species of zoology such a hybrid would, in general, be infertile, or if it did produce offspring these would be infertile. In the case of ordinarily bred offspring from parents of the same species a large deviation from the parental characters might be a malformation, or the result of some irregularity of development. An “atavistic” variation we may regard as the reappearance of some character present in a more or less remote ancestor. Thus dogfishes and skates are no doubt descended from some elasmobranch fish which possessed an anterior dorsal fin. This fin persists in the dog-fishes, but has been lost in the skates and rays. Yet it may appear in the latter fishes as an atavistic variation.

In a variety (following de Vries’ analysis) a character which disappears is not really lost: it is only suppressed, and it still exists in a latent form. Some flowers are coloured, for instance, but there may be varieties in the species to which they belong in which the flowers are colourless. It may not be quite correct, in the physical sense, to say that the colour has been lost, but we may put it in this way. These flowers are then coloured and colourless varieties of the same species. Colour or lack of colour is not, however, fixed in the variety, for the individual plant bearing colourless flowers also bears in its organisation the potentiality of producing coloured flowers. The petals of a flower may be smooth or covered with hairs, and in the same stock both of these varieties may occur. But we must not speak of the presence or absence of hairs as constituting a difference of kind: the smooth-petalled flowers might be regarded as containing the epidermal rudiments of hairs. So also coloured and colourless flowers may be regarded as containing the same kinds of pigment, but these pigments are mixed in different proportions. Such a view enables us to look upon these contrasting characters in the same way as we look upon fluctuating variations, that is, as quantitative differences in the value of the same character.

Such a suppression of a character is not really a loss. An organism belonging to an elementary species in which, say, monochromatic flowers are usually produced may produce flowers which are striped. The progeny of the plant may still produce monochromatic flowers, but we must think of it as also possessing the potentiality of producing striped flowers. In the terminology of Mendelism the characters are dominant and recessive ones.

In discussing Mendelian varieties we consider the manner in which two contrasting characters—one present in the male parent and one in the female—are transmitted to the offspring. The characters in question may be the tallness of the male parent and the contrasting shortness of the female; or the brown eyes of the male and the blue eyes of the female; or the brown skin of the female parent and the white skin of the male one. These characters may be inherited in two ways: either they may be blended or they may remain distinct in the offspring. The children of the brown mother and the white father are usually coloured in some tint intermediate between those of the parents. The mulatto hybrid is fertile with either of the parent races, and again the offspring may take a tint intermediate between those of the parents, and so on through a number of generations. But somewhere in this series the concealed or recessive brown colour may appear in all its completeness, showing that it has been present in the organisations of all the intervening generations. The progeny of a tall male parent and a short female parent are not, in general, intermediate in stature between the parents; some of them may be tall and others short. The children of a brown-eyed mother and a blue-eyed father do not usually have eyes in which the colours of the parental eyes are blended: they are blue-eyed or brown-eyed. The contrasting characters are spoken of as dominant and recessive: if tallness is transmitted to offspring, which may nevertheless produce dwarf offspring, the latter character is said to be recessive to tallness. The contrasting characters of the parents therefore remain distinct in the progeny, some of the latter exhibiting the one character and some the other; while it may happen that the one character or the other may be segregated, so that it only appears in, and is transmitted by, the offspring. There are numerical relationships between the numbers of the offspring in which the contrasting characters appear.

Obviously, tallness and dwarfness are not characters which differ in quality: they are different degrees of the same thing. Brown eyes and blue eyes are not necessarily different in quality, for we may think of the same kinds of pigment as being present in the iris but mixed in different proportions. But the terminology of this branch of biology appears to suggest that the contrasting characters are, each of them, something quite different from the other: there are “factors” for “tallness,” “dwarfness,” for blue eyes and brown eyes, and so on. These qualities are called “unit-characters,” and they are supposed to possess much the same individuality in the germ-plasm as the “radicles” of the chemist possess in a compound. Sodium chloride, for instance, is not a blend of sodium and chlorine: the two kinds of atoms do not fuse together but are held together merely. The analogy is, however, very imperfect, for in the chemical molecule the characters are not those of either of the constituents but something quite different, whereas in the Mendelian cross the characters remain distinct, but one of them is patent while the other is latent. In the molecule, however, the atoms are regarded by the chemist as lying beside each other in certain positions, and the Mendelian factors are also spoken of as if they lay side by side in the germ-plasm. This terminology is useful, perhaps necessary, in the work of investigation, but we must not forget that it symbolises, rather than describes, the results of experiment. If the factors are identified with certain morphological structures in the nuclei of the germ-cells, obviously all the objections that may be urged against the Weismannian hypothesis as an hypothesis of development apply also to the Mendelian hypotheses as descriptions of a physical process of the transmission of morphological characters.

It should clearly be understood what is implied in the construction of such a hypothesis. Certain processes are observed to take place when a somatic cell divides: these processes we have regarded as having for their object the exact division of all the parts of the cell into two halves. This process of somatic cell division is modified when a germ cell divides prior to maturation (the process fitting it to become fertilised). Then the cell nucleus divides into four daughter-nuclei. One of these remains in the cell substance which is to become the ovum, and the other three, each of them invested in a minimal quantity of cytoplasm, are eliminated as the “polar bodies.” Also the number of chromosomes in the mother-cell becomes halved, so that the mature ovum, or spermatozoon, possesses only one-half of the number of chromosomes which are present in the ordinary somatic cell. Now let the reader puzzle out for himself what may be meant by this behaviour of the germ cells, and he will certainly see that several interpretations are possible. But suppose that the chromatin consists of an incredibly large number of bodies differing in chemical structure from each other, and occupying definite positions with regard to each other; and suppose that there is a mechanism of unimaginable complexity in the cell capable of rejecting some of these chemically individualised parts, and of “assembling” or arranging the others in much the same way as an engineer assembles the parts of a dynamo when he completes the machine. Then we may regard the hypothetical discrete bodies which form the hypothetical nuclear architecture as the material carriers of Mendelian characters. It is strange that the correspondence of such a logically constructed mechanism with the effects which it would produce if it existed should be regarded as a proof that it does exist, yet biological speculation has actually made use of such an argument. “It seems exceedingly unlikely that a mechanism so exactly adapted to bring it” (the separation from each other of the Mendelian material “factors” of inheritance) “about should be found in every developing germ cell if it had no connection with the segregation of characters that is observed in experimental breeding.” Put quite plainly this argument is as follows: there is a certain segregation to be seen in experimental breeding, and certain processes may be observed to occur in the developing germ cell. Add to these processes many others logically conceivable, and add to the observed material structure of the cell another structure also logically conceivable. Then the assumed mechanism and structure is “exactly adapted” to produce the effects which are to be explained. Therefore the mechanism and structure do actually exist!

That which renders the son similar to the father—the specific organisation—is undoubtedly very stable, and it may persist in the face of a variable environment. But now and then the son differs from the father. The differences may be “accidental” and may not be transmitted further—then we have to deal with an unstable fluctuation; or the differences may be permanent—then we have to deal with a stable mutation. What “produces” a mutation? A change of the environment, it may be said: if so, the mutation is an active change or adaptation of the organism to a change in its surroundings, and this adaptation is a permanent one and is transmitted. Or the mutation may be a spontaneous change of functioning. If this disturbance of the stability of the organisation is general, if it affects all the characters of the organism, we have to deal with the establishment of a new elementary species. But if the disturbance affects only one, or a few characters, then we need not recognise that a new elementary species has come into existence. Men and women remain men and women (in their morphology), although some time or other among the brown eyes characteristic of a race blue eyes may have appeared. The result of the disturbance, in this case, has been to cause one, or a few, of the characters that fluctuate to surpass their limits of stability.

The idea of the elementary species is a clear and simple one. It is a group of organisms connected by ties of blood relationship: all have descended from one pair of ancestors. The individuals exhibit certain characters, all of which are variable. This variability is not cumulative; in generation after generation the individuals of the species display variations which fluctuate round the same mean values. Two or more elementary species may have had the same origin—a common ancestor or ancestors—but the organisms in one species exhibit characters which, although similar in nature to those of the other species, yet fluctuate about different mean values.

This is not the “species” of the systematic biologist. The Linnean or systematic species is a concept which is much more difficult to define: it is a concept indeed which has not any clear and definite meaning, in actual practice.

We often forget how very young the science of systematic biology is, and how intimately its progress has been dependent on that of human invention and industrial enterprise. Physics and mathematics might be studied in a monastic cell, but the study of systematic biology can only be carried on when we have ships and other means of travelling—the means, in short, of collecting the animals and plants inhabiting all the parts of the earth’s surface. Until a comparatively few years ago the fauna and flora of great tracts of land and sea were almost unknown: even now our knowledge of the life of many parts of the earth is scanty and inaccurate. Systematic biology has therefore had to collect and describe the organisms of the earth, and in so doing it has set up the Linnean species of plants and animals. These we may describe as, in the main, categories of morphological structures. The older and more familiar species are clearly defined in this respect: such are cats and dogs, rabbits, tigers, herrings, lobsters, oysters, and so on: the individuals in each of these categories are clearly marked out with respect to their morphology, and the limits of the categories are clearly defined. In all of them the specific organisation has attained a high degree of stability so that the individuals “breed true to type”; and it has also attained a high degree of specialisation, so that it does not fuse with other organisations.

Yet, in the majority of the systematic species of biology, this criterion of specific individuality—this recognition of the isolation of the species from other species—cannot be applied. Very many species have been described from a few specimens only, many from only one. How does a systematist recognise that an organism with which he is dealing has not already been classified? It differs from all other organisms most like it, that is, he cannot identify it with any known specific description. But the differences may be very small, and if he had a number of specimens of the species most nearly resembling it he might find that these differences were less than the limits of variation in this most closely allied species, and he would then relegate it to this category. But if he has to compare his specimen with the “type” one, that is, the only existing specimen on which the species of comparison was founded, the test would be unavailable. The question to be answered is this: are the difference or differences to be regarded as fluctuations, or are they of “specific rank”? Now certainly many systematists of great experience possess this power of judgment, though they might be embarrassed by having to state clearly what were the grounds on which their judgment was based. But on the other hand hosts of species have been made by workers who did not possess this quality of judgment; and even with the great systematists of biology confusion has originated. Slowly, very slowly, the organic world is becoming better known, and this confusion is disappearing.

The species, then, whether it is the systematic group of the biological systems, or the elementary species based on the study of variability and inheritance, is an intellectual construction: an artifice designed to facilitate our description of nature. This is clearly the case with the higher orders of groups in classifications: genera, families, orders, classes, and phyla express logical relationships, or describe in a hypothetical form our notions of an evolutionary process. But species, it may be said, have an actual reality: there are no genera in nature, only species. These categories of organisms really exist; they have individuality, a certain kind of organic unity, inasmuch as the individuals composing them have descended from a common ancestor. Yet just as much may be said of genera, families, and the other groupings. One species originates from another by a process of transmutation: a genus is a group of species which have all had a common origin; a family is a similarly related group of genera, and so on. The higher categories of biological science are intended to introduce order and simplification into the confusion and richness of nature as we observe it, but obviously the concept of the species has the same practical object. Must we then say that there are no species in nature, only individuals? If so, we are at once embarrassed by the difficulty of forming a clear notion of what is meant by organic individuality. Does it not indicate that life on the earth is really integral, and that our analysis of its forms—species, genera, families, and so on—are only convenient ways of dealing actively with all its richness?

Systematic biology is a very matter-of-fact occupation, and one is surprised to find upon reflection how he, in his handling of the concepts of the science, follows the methods of ancient philosophy. In classical metaphysical systems mutability was an illusion. Behind the confusion and change given to sensation there is something that is immutable and eternal. If there is change there is something that changes; or, at least there ought to be something that changes when it is perceived through the mists of sensation, just as the image of a well-known object on the horizon wavers and is distorted by refraction. This immutable reality is the Form or Essence of the Platonic Idea: that which is in some way degraded by its projection into materiality, so that we become aware of it only through our imperfect organs of sense. We do not see the Form itself, but its quality rather, the Form with something added or something taken away from it.

The Form itself is only a phase in a process of transmutation. Everything that exists in time flows or passes into something else. But it is not a momentary or instantaneous view of the flux that we see, but rather a certain aspect of the reality that flows, that in some way expresses the nature of the transmutation from one Form into another. The sculptor represents the motion of a man running by symbolising in one attitude all the actions of body and limbs; so that from our actual, sensible experience or intuition of the movement of the runner we see in the rigid marble all the plasticity of life. The instantaneous photograph shows us a momentary fixed attitude of the runner—an attitude which is strange and unfamiliar. The Idea does not, then, represent a moment of becoming like the photograph, but rather a typical or essential phase of the process of transmutation, just as the sculptor represents in immobile form the characteristic leap forward of the runner. Just as our intuitive knowledge of the actions of our own bodies enables us to read into the characteristic attitude represented in the marble all the other attitudes of the series of movements, so our experience enables us to expand the formal moment of becoming into the action which it symbolises.

This action has a purpose, an intention or design which was contemplated before it began. There is therefore the threefold meaning in the Platonic Idea: (1) an immutable and essential Form of which we perceive only the quality; (2) the characteristic phase in the transmutation of this Form into some other one; and (3) the design or intention of the transmutation.

This was, as Bergson says, the natural metaphysics of the intellect. It was, in reality, the “practical” way of introducing order and simplification into the confusion of the sensible world—all that is presented to us by our intuitions. And in the effort to reduce to order the welter of the organic world biology has followed the same method, so that it represents the species with the threefold significance of the Platonic Idea. That which is expressed in the term species is an assemblage of organisms each of which is defined by an essential form and an essential mode of behaviour—the characters indicated in the specific diagnosis. But organisms are variable, their specific characters fluctuate round a mean, and in saying this we suggest that there is something which varies—there ought to be an essential form from which the observed forms of the individuals deviate, something invariable which nevertheless varies accidentally. This is (1) the quality of the specific idea. So also we never do actually observe the essential individual; what we do see is the embryo, or the young and sexually immature organism, or the sexually mature one, or the senescent one: there is continual change from the time of birth to that of senile decay. This confusion is unmanageable, and for it we substitute the characteristic form and functioning, and that phase in the life-history of the organism which suggests all that the previous phases have led up to, and all that subsequent phases take away. Thus there is contained in our idea of the species (2) the notion of a typical moment in an individual transformation. It is not a “snap-shot” of some moment in the life-history that we make: in identifying a larval form as some species of animal we are identifying it with all the other phases of the life-history.

Since we accept the doctrine of transformism, the specific idea also includes that of an evolutionary process. For the organic world is a flux of becoming, and species are only moments in this becoming. It does not help us to reflect that if the hypothesis of evolution by mutations is true the process is a discontinuous one: mutability is the result of periods of immutability during which the change was germinating, so to speak. In this flux of becoming we seize moments at which the specific form flashes out—not as instantaneous views of the flux, but as aspects of it which suggest the steps, the morphological processes, by which the transmutation of the species has been effected. Thus our specific idea represents not only a phase of becoming in an individual life-history, but also a phase of becoming in an evolutionary history.

Whether we consider this evolutionary movement as the working out of a Creative Thought, or as the development of elements assembled together by design, or as the results of the action of a mechanism working by itself, we must suppose that underlying it there is design, or purpose, or determinism. All is given, therefore, and our comparison between the metaphysical Platonic Idea and the modern concept of the species becomes complete.