Alfred Russel Wallace : Alfred Wallace : A. R. Wallace :
Russel Wallace : Alfred Russell Wallace (sic)

The Method of Organic Evolution (S510: 1895)

Editor Charles H. Smith's Note: Published in two parts in the 1 February 1895 and 1 March 1895 numbers of Fortnightly Review. Original pagination indicated within double brackets. To link directly to this page connect with:

[[p. 211]]  I.

    The modern doctrine of organic evolution may be said to date from the great French naturalist Buffon, who, more than a hundred years before the publication of the Origin of Species, clearly indicated his belief in the mutability of specific and generic forms, although, owing to the power of the Church in his day, he was often obliged to veil his opinions under the guise of hypotheses, which, as they were opposed to religion of course could not be true. Yet he occasionally speaks very plainly, as when he says:--

    "Nature, I maintain, is in a state of continual flux and movement;"

and again--

    "What cannot Nature effect with such means at her disposal? She can do all except either create matter or destroy it. These two extremes of power the Deity has reserved for Himself only; creation and destruction are the attributes of His omnipotence. To alter and undo, to develop and renew--these are powers which He has handed over to the charge of Nature."

    Dr. Erasmus Darwin held similar views, which he developed at great length, and in doing so, anticipated many of the arguments afterwards elaborated by the celebrated Lamarck, that changes in species were caused both by the direct action of the environment, by the use and exercise by animals of their several organs, and more especially by the effects of effort and desire leading to the development of parts and organs calculated to gratify those desires. The great French naturalists Geoffrey and Isidore St. Hilaire adopted these views with certain modifications, as did a limited number of German naturalists; while they were popularly set forth with much knowledge and literary skill by the late Robert Chambers in his Vestiges of Creation. Somewhat later the general theory of evolution was explained and illustrated by Herbert Spencer with so much power and completeness as to compel its acceptance by most thinkers; but neither he, nor any of the great writers who had gone before him, had been able to overcome the difficulty of explaining the process of organic evolution, since no one had been able to show how the wonderful and complex adaptations of living things to their environment could have been produced by means of known laws and through causes proved to exist and to be of sufficient potency. Alike for naturalists, for men of science in general, and for students in philosophy, the method of organic evolution remained an insoluble problem.

    Considering that this state of opinion prevailed up to the very date [[p. 212]] of publication of the Origin of Species, the effect produced by that work was certainly marvellous. A considerable body of the more thoughtful naturalists at once accepted it as affording, if not a complete solution, yet a provisional theory, founded upon incontrovertible facts of nature, demonstrating a true cause for specific modification, and affording a satisfactory explanation of those countless phenomena of adaptation which every preceding theory had been powerless to explain. Further consideration and discussion only increased the reputation of the author and the influence of his work, which was still further enhanced by his Animals and Plants under Domestication, published nine years later; and when this had been fully considered--about twelve years after the publication of the Origin--a large proportion of naturalists in every part of the world, including many of the most eminent, had accepted Darwin's views, and acknowledged that his theory of Natural Selection constituted--to use his own words--"the main but not the exclusive means of modification." The effect of Darwin's work can only be compared with that of Newton's Principia. Both writers defined and clearly demonstrated a hitherto unrecognised law of nature, and both were able to apply the law to the explanation of phenomena and the solution of problems which had baffled all previous writers.

    Of late years, however, there has arisen a reaction against Darwin's theory as affording a satisfactory explanation of organic evolution. In America, especially, the theories of Lamarck are being resuscitated as of equal validity with natural selection; while in this country, besides a considerable number of Lamarckians, some influential writers are introducing the conception of there being definite positions of organic stability, quite independent of utility and therefore of natural selection; and that those positions are often reached by discontinuous variation, that is, by spurts or sudden leaps of considerable amount, which are thus "competent to mould races without any help whatever from the process of selection, whether natural or sexual."1 These views have been recently advocated in an important work on variation,2 which seems likely to have much influence among certain classes of naturalists; and it is because I believe such views to be wholly erroneous and to constitute a backward step in the study of evolution that I take this opportunity of setting forth the reasons for my adverse opinion in a manner likely to attract the attention not only of naturalists but of all thinkers who are interested in these problems.

    Before proceeding to this special discussion it may be well to illustrate briefly the essential difference between the theories of [[p. 213]] Darwin and those of his predecessors and opponents, by a few examples of those cases of adaptation which are insoluble by all other theories, but of which natural selection gives an intelligible explanation.

    The Darwinian theory is based on certain facts of nature which, though long known to naturalists, were not understood in their relations to each other and to evolution. These facts are: variation, rapid multiplication, and the resulting struggle for existence and survival of the fittest. Variation is the fundamental fact, and its extent, its diversity, and its importance are only now becoming fully recognised. Observation shows that when large numbers of individuals of common species are compared there is a considerable amount of variability in size, form, colour, in number of repeated parts and other characters. Further, that each separate part, which has been thus compared, varies, so that it may be safely asserted that there is no part or organ that is not subject to continual variation. Again, all these variations are of considerable amount--not minute, or infinitesimal, or even small, as they are constantly asserted to be. And, lastly, the parts and organs of each individual vary greatly among themselves, so that each separate character, though sometimes varying in correlation with other characters, yet possesses a considerable amount of independent variability. The amount of the observed variation is so great that in fifty or a hundred adult individuals of the same sex, collected at the same time and place, the difference of the extreme from the mean value of any organ or part is usually from one-tenth to one-fourth, sometimes as great as one-third of the mean value, with usually a perfect gradation of intervening values.

    The multiplication of individuals of all species is so great and so rapid that only a small proportion of those born each year can possibly survive; hence the struggle for existence, the result of which is that, on the average, those individuals which are in any way ill-fitted for the conditions of existence die, while those better fitted live. The struggle is of varied character and intensity--either with the forces of nature, as cold, drought, storms, floods, snow, &c.; with other creatures, in order to escape being devoured, or to obtain food, whether for themselves or for their offspring; or with their own race in the competition for mates and for the means of existence; while as regards all these forms of struggle mental and social qualities are often as important as mere physical perfection, and sometimes much more important. The fact already stated, of the large amount of variability in most species, has been thought by some to show either that there can be no such severe struggle as has been suggested, or that the characters which vary so much can be of little importance to the species, and cannot therefore determine [[p. 214]] survival. But in making this objection two considerations have been overlooked. In the first place we always compare adults, and an enormous amount of destruction has already taken place during the earlier stages of life. The adults, therefore, are already a selected group. In the second place, the struggle is very largely intermittent, owing both to the occurrence only at long intervals of the most adverse meteorological conditions, while the diversity of these conditions leads in each case to the selection of a different characteristic. An exceptionally severe winter will destroy all which are deficient in one set of characters, while a long drought, or scarcity of some particular kind of food, will weed out those deficient in another set of characters. Thus, in any one year there will exist numbers of individuals which are doomed to speedy destruction under some one of the special adverse conditions which are constantly recurring; and it is this, probably, that explains why there is so much individual variation continually present, although the central or typical form remains unchanged for very long periods. This typical form is that which, under existing conditions, survives all the periodical or secular adverse changes, during which the outlying, or extreme variations of whatever kind, are sooner or later eliminated. It is for want of giving full weight to the essentially intermittent nature of the struggle for existence that so many writers fail to grasp its full significance, and continually set forth objections and difficulties which have no real importance.

    We are now in a position to estimate the efficiency of Darwin's theory in explaining the wondrous and complex adaptations that abound in the organic world, as compared with that of Lamarck or of his modern supporters. And first let us take the simple case of the adaptation of fleshy and juicy fruits to be eaten by birds, causing what seems at first sight an injury to the species, but which is really most beneficial, inasmuch as it leads to the wide dispersal of the seeds, and greatly aids in the perpetuation of the plants which produce such fruits. To what possible direct action of the environment can we impute the production of fleshy or juicy pulp, with attractive colour, and with small, hard-coated seeds, in the innumerable fruits which are devoured by birds, through whose bodies the seeds pass in a state fitted for germination? There is here a combination of characters calculated to a certain end, a definite adaptation. If we suppose that in an early stage of development ancestral fruits which happened to be a little softer than others were eaten by birds, how could that circumstance increase the softness, develop juice, and produce colour in future generations of the trees or bushes that sprang from the seeds so dispersed? And if we assume that these several characteristics are positions of "organic stability," acquired through accidental variation, we have to ask why the [[p. 215]] several kinds of variation occurred together, or why neither of them occurred in the numerous species in which to be eaten by birds would be injurious instead of beneficial?

    But if we begin at the same stage and apply the Darwinian theory we find that the whole process is easy of explanation. It is an observed fact that fruits vary in softness, juicyness, and colour, and seeds in the hardness or hairyness of their integuments. Any variation of primitive fruits in either of these directions would therefore be beneficial, by attracting birds to eat them and so disperse the seeds that they might reach suitable stations for development and growth. Such favourable variations would therefore be preserved, while the less favourable perished.

    Now ask the same questions as to the production of the innumerable modes of dispersal of seeds by the wind, from the simple compressed form and dilated margins of many small seeds, to the winged seeds of the ash and maple, and the wonderful feathery parachute of the thistle and the dandelion. Or again, inquire as to the wonderful springed-fruits which burst so as to scatter the small seeds, as in some of the balsams; or yet again, as to the sticky glands of the sundews, and the small water-traps of the bladder-wort; and a hundred other equally strange adaptations to some purpose of use to the species, but whose development has no relation whatever to any possible direct action of the environment, though all of them are explicable as the result of the successive preservation of such variations as are known to occur, acting at various intervals, and by means of successive modifications, during the whole period of the development of the group from some remote ancestral form.

    The modern advocates of Lamarckism content themselves with such simple cases as the strengthening or enlarging of organs by use, the hardening of the sole of the foot by pressure, or the enlarging of the stomach by the necessity for eating large quantities of less nutritious food. These, and many other similar modifications, may doubtless be explained by the direct action of conditions, if we admit that the change thus produced in the individual is transmitted to the offspring. That such changes are transmitted has, however, not yet been proved, and a considerable body of naturalists reject such transmission as improbable in itself, and at all events as not to be assumed without full and sufficient proof. But even if accepted it will not help us to explain the very great number of important adaptations which, like those already referred to, are quite unrelated to any direct action of the environment. Having thus cleared away some preliminary misconceptions, and stated in briefest outline the main features of the law of natural selection, we may proceed to consider the objections of those modern writers to whose works we have already referred.

    [[p. 216]] Mr. Bateson's large and important volume consists mainly of an extensive collection of cases of variation of a particular kind, which have been met with throughout the whole animal kingdom, and have been recorded in all parts of the world. These are arranged systematically under nearly nine hundred numbered headings, and are in many cases well illustrated by characteristic figures. The character and morphological relations of these variations are often very fully discussed with great knowledge and acuteness, and some original views are set forth which are of interest both to morphologists and physiologists. So far as this part of the work is concerned the present writer would feel himself quite incompetent to criticise it, but would welcome it as presenting in a convenient form a great body of interesting and little-known facts. But the book goes far beyond this. The first words of the preface tell us that "This book is offered as a contribution to the study of the problem of Species;" and in a lengthy introductory and shorter concluding chapters this problem is discussed in some detail, with the view of discrediting the views held by most Darwinians; while a new theory, founded upon the facts given in the body of the work, is set forth as being a more probable one. It is therefore necessary to give some account of the nature of the facts themselves, as well as of the particular theories they are held to support.

    Darwin distinguished two classes of variations, which he termed "individual differences" and "sports." The former are small but exceedingly numerous, the latter large but comparatively rare, and these last are the "discontinuous variations" of Mr. Bateson to which reference has been already made. Darwin, while always believing that individual differences played the most important part in the origin of species, did not altogether exclude sports or discontinuous variations, but he soon became convinced that these latter were quite unimportant, and that they rarely, if ever, served to originate new species; and this view is held by most of his followers. Mr. Bateson, however, seems to believe that the exact contrary is the fact, and that sports or discontinuous variations are the all-important, if not the exclusive, means by which the organic world has been modified. Such a complete change of base as to the method of organic evolution deserves, therefore, to be considered in some detail.

    The difficulty which seems to have struck Mr. Bateson most, and which he declares to be of "immense significance," is, that while specific forms of life form a discontinuous series, the diverse environments on which these primarily depend shade into each other insensibly, and form a continuous series (p. 5). Further on, this objection is again urged in stronger language: "We have seen that the differences between Species are Specific, and are differences of [[p. 217]] 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 in any sense the directing cause of Specific differences, which by the Theory of Natural Selection they should be" (p. 16). Again, at p. 69, he urges that the essential character of species is that they constitute a discontinuous series, and he asks--"Is it not then possible that the Discontinuity of Species may be a consequence and expression of the Discontinuity of Variation?" He then states, that on the received hypothesis, "Variation is continuous, and the Discontinuity of Species results from the operation of Selection." This, however, is not quite a correct statement of the received hypothesis if "discontinuous" is used in Mr. Bateson's sense, as including every change of colour which is not by minute gradation, and every change in number of repetitive parts--as of vertebræ, or of the joints of an antenna, or the rings of a worm--which is not by a gradation of the part from a minute rudiment. Such changes of colour or in the number of parts are admitted by all Darwinians as, in many cases, constituting a part of that individual variation on which modification of species depends. It is, however, on the supposed rejection of this class of variations by Darwinians that he bases what he terms "an almost fatal objection" to their theory.

    Returning, however, to the supposed overwhelming importance of discontinuous variation, we pass on to the last chapter of the book, headed "Concluding Reflexions," and we read: "The first object of this work is not to set forth in the present a doctrine, or to advertise a solution of the problem of Species," and then follows immediately a further discussion of this very theory of discontinuity, which is set forth as a doctrine, and as a help to the solution of that problem. We are told that the difficulties of the accepted view "have oppressed all who have thought upon these matters for themselves, and they have caused some anxiety even to the faithful"; it is urged that "the Discontinuity of which Species is an expression has its origin not in the environment, nor in any phenomenon of Adaptation, but in the intrinsic nature of organisms themselves, manifested in the original Discontinuity of Variation"; that, "the existence of sudden and discontinuous Variation, that is to say, of new forms having from their first beginning more or less of the kind of perfection that we associate with normality, is a fact that disposes, once and for all, of the attempt to interpret all perfection and definiteness of form as the work of Selection." And then comes the positive statement--"The existence of Discontinuity in Variation is therefore a final proof that the accepted hypothesis is inadequate" (p. 568), and after several more pages of illustration and argument, the final conclusion is [[p. 218]] reached that--"it is quite certain that the distinctness and Discontinuity of many characters is in some unknown way a part of their nature, and is not directly dependent upon Natural Selection at all."

    Before going further it will be well to make a few observations on these very definite and positive conclusions at which Mr. Bateson has arrived; and it must be remembered that this volume deals only with one portion of the subject even of discontinuous variation, which is itself, if we exclude monstrosities, only a small fragment of the whole subject of variation. The impression that will be produced on those who have given special attention to the relations of living organisms to each other and to their inorganic environment, will be that of an academic discussion, dealing to a large extent with words rather than with the actual facts of nature. The author's main point, that species form a discontinuous series, and that specific differences cannot therefore have been produced by any action of the environment, because that environment is continuous--an argument which, as we have seen, he dwells upon and reiterates with emphasis and persistency--rests wholly upon the obvious fallacies that in each single locality the environment of every species found there is the same, and that all change of environment, whether in space or time, is continuous. To take this latter point first, nothing can be more abrupt than the change often due to diversity of soil, a sharp line dividing a pine or heather-clad moor from calcareous hills; or to differences of level, as from a marshy plain to dry uplands; or, for aquatic animals, from the open sea to an estuary, or from a non-tidal stream to an isolated pond. And when, in the course of geological time, an island is separated from a continent, or volcanic outbursts build up oceanic islands, the immigrants which reach such islands undergo a change of environment which is in a high degree discontinuous.

    Even more important, perhaps, is the fact that, everywhere, the environment as a whole is made up of an unlimited number of sub-environments, each of which alone, or nearly alone, affects a single species, as familiarly included in the term, "their conditions of existence." The mole and the hedgehog may live together in the same general environment, yet their actual environments are very different owing to their different kinds of food, habits, and enemies. The same thing applies to the rabbit and the hare, the rook and the crow, the ring-snake and the viper; and still more when we look at animals of greater diversity, as the otter and the badger, the dung-beetle and the cockchafer, and a hundred others that might be quoted. Now, though all these creatures may be found together in the same area, each of them has its own "environment," to which it must be adapted in order to maintain its existence. Many species, however, live, as it were, on the borders of two distinct [[p. 219]] environments, as when they obtain different kinds of food at different periods, being then exposed to different enemies and varied climatic effects. In such cases, it is easy to see that a small modification of structure might enable them advantageously to change their habits, and thus obtain what would be practically a different environment. This is well seen in those closely allied species which have somewhat different modes of life--as the meadow pipit (Anthus pratensis) and the tree pipit (Anthus arboreus)--the former having a long, nearly straight claw to the hind toe, a more slender bill, and a rather greener tinge of colouring, all modifications suited to its different habits and distinct physical surroundings. Here we have an example in nature of how environments, even when continuous as a whole, may become quite discontinuous in relation to two species differing in very slight characters. Darwin dwelt much upon this phenomenon, of new species being formed when any body of individuals seized upon vacant places in the economy of nature, and by means of comparatively slight variations became adapted to it. It is what we see everywhere in the world around us.

    It thus appears that what is evidently supposed to be a very powerful argument leading to the conclusion that discontinuous variations as a class are those which are of vital, if not exclusive importance in the production of new species, entirely breaks down when confronted with the facts of nature. It does not, however, follow that, because an unsound à priori argument has been used to call attention to these variations, and because they have been set before the world in a way to suggest that their importance in relation to the origin of species is a new discovery calculated to revolutionise the study of this branch of biology, they are, therefore, of no value in this connection. We will, therefore, now proceed to consider them on their own merits as possible factors in the process of organic evolution. For this purpose we must briefly indicate the nature of the variations so laboriously recorded in this volume.

    These consist of what are termed meristic variations, that is, variations in the number or position of parts which occur in series, whether linear, bilateral, or radial. Such are the variation in the number of segments of annulosa and arthropoda, such as worms, leeches, centipedes, &c.; in the antennæ and legs of insects; in the vertebræ, ribs, teeth, nipples, limbs, and toes of vertebrates; in the rays of starfish, encrinites, and allied animals. The ocelli and other symmetrical markings on the wings of butterflies are also recorded, as well as numerous malformations when these affect serial or symmetrical organs.

    On carefully looking through the cases of variation in this volume we are struck with the large proportion of them which exhibit more or less deformation or want of symmetry, culminating in the various [[p. 220]] kinds of monstrosity. In Chapter III., on the variations of vertebræ and ribs, we find vertebræ imperfectly divided in snakes and frogs. Numerous cases of abnormalities in human vertebræ are given, usually exhibiting asymmetry or deformation, and similar variations are found in the anthropoid apes, but here there is apparently more of regularity and symmetry. The greatest amount of this kind of variation occurs in the sloths, as might be expected when we consider that they are the most abnormal of mammals as regards the cervical vertebræ. In Chapter VIII. numerous cases of supernumerary mammæ are recorded, almost all of which are unsymmetrical. The variations in the number or form of the horns in sheep, goats, and deer recorded in Chapter XI. show them to be usually more or less irregular.

    Nearly a hundred pages are devoted to the digits (fingers and toes) of mammals and birds, about one hundred and forty cases of variation being recorded. Almost the whole of these present, more or less, want of symmetry, while a large proportion, as the double-handed and double-footed children, and the six or seven-toed cats, can only be classed as monstrosities.

    In succeeding chapters the variations in the antennæ and leg-joints of insects; in the radial parts of medusæ and encrinites; in the medial structures of fish, insects, molluscs, &c., which become sometimes double; in the eyes and colouration of flatfish; in duplicate or branching legs of insects and crustaceans; in extra limbs of batrachia; and, lastly, double monsters, are all discussed at great length, and are illustrated by a number of very interesting wood-cuts. But almost the whole of these can only be classed as malformations or monstrosities which are entirely without any direct bearing on the problem of the "origin of species."

    Nothing can better show the small value of the book from this, which is the author's own, point of view, than the large amount of space devoted to the various monstrosities of the hands and feet of man and of some of the mammalia. Not only throughout all mammals, but also in the case of birds, reptiles, and amphibia, five is the maximum number of the toes or fingers. These may vary in size or in proportions, they may be reduced in number by coalescence, or by the loss of the lateral digits; they may be strangely modified in form and function, as in the flappers of the whale, or in the wing of the hat, yet never once in the whole long series of land-vertebrates do they exceed five in number. Yet we have six, seven, or eight-fingered, double-handed, or double-footed children; similar malformations in monkeys; six and seven-toed cats; four, five, or six-toed pigs; double-footed birds, and other monstrosities, described at great length, and all their peculiarities discussed in the most minute detail and from various points of view, in a work presented to us as [[p. 221]] "a contribution to the study of the problem of species." Many of these malformations have been observed among animals in a state of nature, and in fact, Mr. Bateson believes that they occur as frequently among wild as among domesticated animals. Considering how rarely the former cases can be observed, they must be everywhere occurring; yet in no one single instance do they seem to have established themselves as a race or local variety on however small a scale. Yet we know that in the case of the six-toed cats, and probably in other cases, they are easily transmissible; and we must, therefore, conclude that all these irregularities and monstrosities are in a high degree disadvantageous, since when subject to free competition with the normal form in a state of nature they never survive, even for a few generations.

    As the volume we are discussing is entirely devoted to variations in the number or position of the serial parts of organisms in relation to the origin of species, it becomes necessary to lay some stress upon the very familiar, but apparently overlooked fact, that, among all the higher types of life at all events, the most stable of all characters, and the most permanent during long periods of evolution, and throughout changes which have led to the production of a marvellous variety and abundance of specific forms, are these very characters of the number and relative positions of serial organs; whence it follows that variations of this kind can only have led to specific changes at enormously long intervals, and that, as a general rule, they can have had nothing whatever to do with the origin of an overwhelming majority of living species.

    First, we have the four limbs of vertebrates, which among all the marvellous variety of form and function, on land, in the water, or in the air, is never exceeded, and appears to have been fixed at a very early stage of the development of the vertebrate type. Equally fixed, and extending through a still vaster range of modifications of specific forms, are the six legs and four wings of true insects, which, as in vertebrates, may be reduced but never increased in number. Still more extraordinary, because less obviously connected with the main structure and functions of the organism, is the limitation and permanence in the number of the subdivisions of limbs and other appendages. There is no obvious reason why in land-vertebrates the divisions of the hand and foot should never exceed five, yet, not only is this number the maximum, but it may be considered the normal number of which all others are reductions, since it still prevails largely in the marsupials, rodents, carnivores, primates, and lizards; and the five-toed land-vertebrates (excluding birds) are probably far more numerous than those with a lesser number.

    In birds there are only four toes as a maximum, and comparatively few have a smaller number. But we have here a peculiarity in the [[p. 222]] numbers of the toe-joints which does not occur in any other vertebrates. These form a series in arithmetical progression, the hind toe having two, and the others three, four, and five joints in regular order; and this rule is very nearly universal, the only exceptions being in some of the swifts and goatsuckers, whose habits render the feet of comparatively little importance, while their general organisation is of a somewhat low type.

    Coming to insects, we again find the legs consisting of a limited number of parts, and, strangely enough, this number is again five--the coxa, trochanter, femur, tibia, and tarsus. The tarsus, however, is subdivided into small movable joints, and these, too, are five as a maximum, but in certain groups are reduced to four, three, or two. The five-jointed tarsus is, however, the most prevalent; and in the enormous order of coleoptera or beetles, comprising at least one hundred thousand described species, fully half belong to families which have the tarsi five-jointed. Even the antennæ, although they vary greatly in the number of joints, yet in numerous large groups comprising many thousands of species, they have the number of joints constant. Another indication of the tendency of serial parts to become fixed in number, is the typical limitation of the cervical or neck vertebræ of mammalia to seven joints. This number is wonderfully constant, being the same in the long necks of the giraffe and camel, and the very short necks of the hippopotamus, porpoise, and mole, the only exceptions in the whole class being some of the sloths, which have from six to ten, often varying in the same species, and the manatee, which has six.

    Now, if we consider the enormous extent of these fixed numerical relations of important parts of the organism in the higher vertebrates and in insects, both as regards the number of living species affected--perhaps ninety-nine per cent. of the whole--and as regards their range in time, throughout the whole of the tertiary and secondary, and even a considerable portion of the palæozoic periods--and if we take account of the vast number of extinct species, genera, and families needful to complete the various lines of descent from the earliest known forms, presenting the same numerical relations to those now living--we shall be able to form some conception, however inadequate, of the overwhelming frequency and importance of variations in the size, form, proportions, and structure of the various parts and organs of the higher animals, as compared with variations in their number. No doubt, in the earlier stages of organic development, numerical variations were more frequent and more important, as they are now among the lower forms of life; but at a very early period in geological history, the main numerical relations of the essential parts of the higher organisms became more or less fixed and stable, and have in many cases remained unchanged through a large [[p. 223]] proportion of the period comprised in the geological record. The four limbs of vertebrates were already established in the fishes of the Devonian period, as were the four wings and six legs of true insects in the cockroaches and archaic orthoptera of the Carboniferous; and almost all subsequent changes have resulted from modifications of these early types. The earliest mammals of which we have sufficient knowledge have the typical five-toed feet, and the earliest birds appear to have had the same progressive series of toe-joints as now prevails.

    We are thus irresistibly led to the conclusion that, among all the possible forms of variation now occurring, those affecting the number of important serial parts among higher organisms, are those which have the least possible relation to whatever modification of species may now be going on around us, or which has been going on during a large portion of geological time. Yet it is to variations of this nature, a large proportion of which are mere malformations or monstrosities, that the bulky and learned volume we are discussing has been devoted. The author of this book puts forward these malformations and irregularities, mixed up with a proportion of normal variations, under the misleading name of "Discontinuous Variations," as if they were something new, and had been ignorantly overlooked by Darwin and his followers; and he loses no opportunity of telling us how important he thinks they are, what difficulties they enable us to overcome, and how they are the beginnings of the establishment of a sure base for the attack on the problems of evolution. In so doing he has entirely failed to grasp the essential features which characterise at least ninety-nine per cent. of existing species, which are, slight differences from their allies in size, form, proportions, or colour of the various parts or organs, with corresponding differences of function and habits, combined with a wonderful amount of stability in the numerical relations of serial parts, extending sometimes only to genera, but more usually to families, tribes, orders, or even to whole classes of the higher animals. It is differences of the former kind that do actually characterise the great majority of species;3 they affect those organs which vary most frequently and most conspicuously in the individuals of every fresh generation; and they constitute that individual variation on which Darwin always relied as the essential foundation of natural selection, and which his followers have shown to be far more abundant and of far greater amount than he was aware of; and, lastly, they afford amply sufficient material for the continuous production of new forms. Rarely [[p. 224]] in the history of scientific progress has so large a claim been made, and been presented to the world with so much confidence in its being an epoch-making discovery, as Mr. Bateson's idea of discontinuous variation corresponding to and explaining the discontinuity of species: yet more rarely has the alleged discovery been supported by facts which, though interesting in themselves, are for the most part quite outside the general conditions of the complex problem to be solved, and are therefore entirely worthless as an aid to its solution.

    Before leaving this part of the subject we may note the extension of definite numerical relations to plants as well as to animals. In dicotyledons we have a typical five-petalled flower or a corolla with five divisions, a character which prevails in irregular as well as in regular flowers, and often when the stamens are not a multiple of five, as in mallows, bignonias, and many others. Some form of five-parted flower prevails throughout many extensive natural orders, and comprises probably a considerable majority of all dicotyledonous plants. A three or six-parted flower is almost equally a characteristic of monocotyledons, prevailing even among the highly specialised and fantastically formed Orchideæ and Irideæ, thus again demonstrating how large a portion of the specific modifications of organisms are independent of variations in number, but depend wholly upon variations in the size, form, colour, and structure of the various parts and organs.

    Other matters of importance in Mr. Bateson's work, together with some theories recently advanced by Mr. Francis Galton, will be discussed in the concluding portion of this article.

[[p. 435]]  II.

    In the first part of this article the misconception which underlies the main body of Mr. Bateson's work has been discussed in some detail. We will now deal with some of the minor objections to the views of most Darwinians which are to be found in his lengthy Introduction; after which the validity of Mr. Francis Galton's doctrine, as to positions of organic stability (also held by Mr. Bateson), will be considered. And first, we note that he uses the usual misleading terms "minute," "minimal," "imperceptible," and "insensible" (p. 15) as applied to the individual variations on which Darwin relied, although he has himself given figures of beetles and earwigs showing that such variations are enormous--greater, indeed, than in the illustrative cases I have given in my Darwinism.4

    A strong attack is made on the theory of the utility of specific characters. It is admitted that an enormous amount of evidence has been collected, and that "the functions of many problematical organs have been conjectured, in some cases perhaps rightly"--yet he adds, "whole groups of common phenomena are still almost untouched even by conjecture." He tells us that "many suggestions have been made as to the benefits which edible moths may derive from their protective colouration; and as to the reasons why unpalatable butterflies in general are brightly coloured" (p. 11)--but neither here nor elsewhere is any hint given that more than "suggestions" have been advanced. Considering that this is the one branch of the subject in which natural selection has been shown to be an actual working reality in nature by the experiments of Jenner Weir, Butler, Stainton, and Belt, the observations of Bates and Fritz Müller, and especially by the elaborate investigations of Professor Poulton, it was hardly fair to pass the subject by as if nothing had been done but pure conjecture. He also ignores the continuous advance that is being made in determining the utilities of the innumerable modifications in the forms and arrangement of the leaves and other of the non-floral appendages of plants by Kerner, Lubbock, and many other observers; as well as the light thrown on colour and marking as specific characters in the higher animals by the consideration of the value of distinctiveness for purposes of recognition, a character of life-preserving value in the case of many animals, and in all of great importance to reproduction, and an [[p. 436]] essential factor in the differentiation of species. It is, therefore, not correct to say, "But as to the particular benefit which one dull moth enjoys as the result of his own particular pattern of dulness as compared with the closely similar pattern of the next species, no suggestion is made." The suggestion has been made (Darwinism, p. 226), and has been accepted as at all events a good working hypothesis by many naturalists. On this question of the utility of characters which are constant characteristics of the species, but whose utility is not apparent to the casual observer, Mr. Bateson uses very strong language. Referring to the case of two ladybirds, the small Coccinella decempunctata being exceedingly variable, both in colour and spotting, the larger, C. septempunctata, very constant, he says, "To be asked to believe that the colour of C. septempunctata is constant because it matters to the species, and that the colour of C. decempunctata is variable because it does not matter, is to be asked to abrogate reason" (p. 572). I fear that I myself must be in this sad case, for though I have not been asked to believe this unreasonable thing, yet I do believe it! Of course I may be wrong and Mr. Bateson right, but how is it that he is so absolutely sure that he is right?

    Before proceeding further we may briefly notice that Mr. Bateson seems to imply that the "meristic," or numerical variations, to which he has devoted his volume, are altogether ignored by Darwinians in their adoption of "individual variations" as opposed to "sports" for the main materials on which natural selection works. But this is altogether erroneous. No doubt they would reject nine-tenths of Mr. Bateson's cases as being simply monstrosities, which neither have nor could ever have had any part in the production of new species; but they always recognise that genera, and even species are sometimes characterised by a difference in the number or arrangement of serial parts--as of vertebræ, ribs, teeth, or markings, and that therefore variations of this kind are sometimes, though comparatively very rarely, the material on which natural selection works. As development seems almost always to have proceeded by reduction from large and indefinite numbers of serial parts to the minimum number compatible with the maximum of utility, an increase in number occurring now may be, as is usually considered, a form of reversion, though Mr. Bateson denies that there is any such thing in nature. This diminution in number may have occurred either by a gradual diminution in size and ultimate disappearance, as when limbs of the higher animals have been lost, in whales, the apteryx, snakes, &c.; or it may sometimes have been abrupt, which means that the rudiment of the part ceased to develop at an early embryonic stage. Either mode is quite in harmony with the views of Darwinians, and not very much seems to be gained by terming the former [[p. 437]] "continuous" and the latter "discontinuous," especially when this last term is held to include almost every kind of monstrosity.

    We have now to consider an equally important, though, as I consider, an equally unsubstantial novelty--the view that there are "definite positions of organic stability," which alone are sufficient to mould races "without any help whatever" from natural selection. This view appears to have originated with Mr. Francis Galton, and was first stated in his work on "Natural Inheritance," and again in his Royal Society paper on "Thumb and Finger Marks." The same view is adopted by Mr. Bateson; and in an article on "Discontinuity in Evolution" in Mind (vol. iii., pp. 362, 372) Mr. Galton approves of Mr. Bateson's work, and restates his latest views on the subject, and these I now propose to consider.

    Although Mr. Galton begins by the consideration of races only, that is, of well-marked forms below the value of species, yet later on he applies his theory to the evolution of species and of all higher groups. Speaking of discontinuous or, as he terms it, transilient variation, he says: "A leap has taken place into a new position of stability. I am unable to conceive the possibility of evolutionary progress except by transiliences, for, if they were mere divergences, each subsequent generation would tend to regress backwards towards the typical centre, and the advance which has been made would be temporary and could not be maintained" (l. c., p. 368). Mr. Galton has before implicitly admitted that there is such a thing as natural selection, yet in this passage he reasons as if it had no existence, and that regression to mediocrity would occur just the same with it as without it. For the essence of natural selection is that it preserves and thus increases favourable variations by destroying the unfavourable; but this statement by no means expresses the real power of selection, which may be better illustrated by saying that it destroys about ninety-nine per cent. of the bad and less beneficial variations, and preserves about the one per cent. of those which are extremely favourable. With such an amount of selection how can there be any possible "regression backwards towards the typical centre" when any change in the environment demands an advance in some special direction beyond it as the only means of preserving the race from extinction? Well did Darwin say that unless the universal struggle for existence "be thoroughly ingrained in the mind, the whole economy of nature, with every fact on distribution, rarity, abundance, extinction, and variation will be dimly seen or quite misunderstood." Almost all the misconceptions of popular writers against Darwinism arise from the want of this constantly present recollection; and as capable and instructed writers, such as Mr. Galton and Mr. Bateson, as well as capable but uninstructed writers such as Lord Salisbury, alike suffer [[p. 438]] in this respect, it is needful to again state obvious facts which may serve to drive home the overwhelming importance of this factor in evolution.

    Let us suppose an animal which lives ten years and produces ten young (five pairs) each year, a moderate allowance even for many mammals and birds. A little simple arithmetic will show that if none died for five years there would be 6,480 pairs in place of the one pair, or 6,480 millions in place of one million, as the case might be. But it is evident that such an average rate of increase for all animals could not go on for even one or two years, as no country could supply them with food. We will suppose, then, that only one pair, instead of five, survive each year to breed the next year; but if this goes on for the ten years of the life of the first pair we shall still have 512 pairs instead of each pair, a number which is equally impossible. Let us, then, suppose that only one-fiftieth part of those born survive, that is, that only one individual lives to breed out of five successive broods of ten each; even then, at the end of ten years, we shall have a population two and a half times as great as at first, or, more exactly, if we began with a million individuals, then in ten years we should have 2,593,743. This is probably something like what happens. Forty-nine fiftieths of those born never live to breed, yet the population increases steadily so long as conditions are moderately favourable, the surplus being got rid of at uncertain intervals by recurrent unfavourable conditions, so as to keep the number of individuals on the average about stationary. Looking at it in another way, we find that, beginning with 100 individuals whose offsprings each year amount to 500, of which only 10 survive to breed, then during ten years about 8,000 will have been born, making with the original hundred, 8,100, out of which only the 100 fittest, or nearly the fittest, will survive, to be again weeded out every successive ten years, or thereabouts. Without making some numerical estimate of this kind it is impossible to realise the severity, of the struggle continually going on in nature and the resultant elimination of the unfit. With the above figures (which would have to be enormously greater with many species) we see that for every 80 born only 1 on the average survives to breed. With such an amount of selection it is evident that whenever it happened that the mean point, or "typical centre" of the curve of variation, ceased to be the most advantageous point in relation to the whole conditions of existence, then a new typical centre would rapidly be produced by the elimination of all which diverged from it to any injurious extent. There could not possibly be regression from the new typical centre unless the inevitable survival of the fittest in a rapidly increasing population can be got rid of.

    We are now in a position to discuss Mr. Galton's theory, that there [[p. 439]] are certain variations which possess "organic stability," and that these are the real factors of evolution "without any help whatever from the process of selection." And first, what is the exact character of these stable variations, which form races and ultimately new species by their own inherent force of stability? Is the stability in relation to the actual conditions of the environment or altogether independent of those conditions? If the former, how did it come to be in harmony with them? If this harmonious relation depends upon a mere chance coincidence, we have to consider the comparative rarity of these large or discontinuous variations, and that only a small proportion of them have the alleged character of "stability." Moreover this class of variations is generally a variation in a single part or organ, and Herbert Spencer (as well as many other writers) has argued forcibly that modifications of single characters would in all cases be useless unless accompanied by the correlative modifications of a number of other characters. I have myself shown that in the case of individual variations this is no difficulty, because all characters are varying more or less in every generation, and thus the needful harmonious relation between the different organs or parts can be easily maintained; but in the case of these large and rare variations the difficulty is an overwhelming one. And we must always remember that these alleged "stable" variations, from the first moment of their appearance, cannot possibly escape from the action of natural selection. As, roughly speaking, only about one per cent. of each generation survives to breed, this new form, however stable in itself, cannot become part of that one per cent. unless the particular variation which characterises it is either beneficial or entirely harmless. But in the latter case it is difficult to see what constitutes its superiority over the rest of the species which, year by year, by means of this intensely severe process of elimination, is kept in harmony with the environment. If the stability consists in greater health, vigour, reproductive power, or intelligence, all these qualities have already been developed to the fullest needful extent, and these superior individuals will be selected in the usual way. But if--as a second alternative--these alleged stable variations are supposed to have some kind of inherent stability independent of the environment, then, stability notwithstanding, they would inevitably soon succumb under the terrible eliminating power which year by year leaves only about one per cent. of the most fit to survive. There is really no escape from this dilemma: If your new variety is among the one or two per cent. of the most fit, then it does not need this purely imaginary quality of "organic stability" in order to survive; if it is not among this small body of the most fit--that is, of the best adapted to the whole conditions of existence of the species or race--then, any other quality notwithstanding, it will certainly not survive. [[p. 440]] The term "organic stability" has really no meaning except that of harmonious adaptation to the environment as tested and maintained by natural selection. To talk about new races or species being produced "without any help whatever from natural selection" can, under the actual conditions of the terrestrial universe, only mean that there is an inherent developmental power which modifies organisms in definite ways, and in more perfect harmony with the environment than has been, or can be, brought about by natural selection, thus keeping these modified organisms always ahead of the rest. They may thus be said to be independent of survival of the fittest, because they and their offspring always are the most fit, and therefore always survive! On this theory evolution goes on by the production of new races complete and ready formed, and in perfect harmony with the environment whenever that environment undergoes a change. But no evidence is offered for such an extraordinary developmental power being always at work and always able to produce adaptation to an ever-changing environment. Such a power would be hardly different from the old special creation, or than the pre-ordained harmony of the philosophers; and it would, moreover, have rendered unnecessary and unintelligible that rapid multiplication, and consequent enormous expenditure of life, which now prevails. It would equally render unnecessary that wonderful property of individual variability, whose only use would then be to enable man to improve his domestic animals and cultivated plants. We should thus have two rival systems at work, and we might almost imagine Mr. Sullivan's cosmic spirits--William and James--to be realities, and that each had been experimenting in organic development on our earth in order to see whose scheme was the most satisfactory.5

    As evidence of the actual existence of this hypothetical "organic stability," Mr. Galton adduces the patterns in thumb and finger-marks, which he has so carefully studied. In his Royal Society paper on this subject, he tells us that these marks fall into definite groups and can be systematically classified, and he actually describes and figures twenty-five distinctive patterns arranged under three very distinct classes. He then urges that these fundamentally distinct classes are strikingly analogous to genera in biology, and as the patterns are so insignificant in every way that they can in themselves be neither useful nor ornamental, and can therefore never have been the subjects of selection, they prove, he thinks, "that natural selection has no monopoly of influence in forming genera, but that it could be wholly dispensed with, the internal conditions acting by themselves being amply sufficient to form them." And it is from the case of these finger-marks that he [[p. 441]] considers the reality of positions of organic stability has been proved, and that they are "competent to mould races without any help whatever from the process of selection."

    At first sight this may appear to be sound reasoning, and to be fatal to some of the claims of the Darwinians, but further examination will show that it is a pure fallacy arising from the vague use of terms, and from comparing quite different things as if they were of the same nature. The fallacy depends on applying the terms of classification in systematic biology to groups of single objects which have no real relation with the genera and species of the naturalist. The essential character of a species in biology is, that it is a group of living organisms, separated from all other such groups by a set of distinctive characters, having relations to the environment not identical with those of any other group of organisms, and having the power of continuously reproducing its like. Genera are merely assemblages of a number of these species which have a closer resemblance to each other in certain important and often prominent characters than they have to any other species. It will be more intelligible and more instructive if we confine ourselves to species as the unit of comparison with Mr. Galton's groups of stable finger-patterns, in order to show the fundamental differences between them. And first we see that Mr. Galton classifies the marks themselves, not the individuals who possess the marks. He tells us that the very same general varieties in these marks are found in English, Hindoos, and Negroes, and, presumably in all other races; and, further, that he has "failed to observe any correlation between the patterns and any single personal quality, whether mental or physical." All this is entirely different from either specific or generic characters, whose essential feature is that they are found in every normal individual of the genus or species, and are always correlated with other characters. In his first paper on this subject (in 1890), Mr. Galton said he had reason to believe that the patterns are to some extent hereditary, but that he had no evidence of it; while in his paper on Mind four years later, he could still only say that "they are to be looked upon" as having "a slight tendency towards transmission by inheritance." But the very essence of specific and generic characters is, that they are strictly transmitted by inheritance. Yet again, whatever difference of opinion there may be as to the utility of all the characters which distinguish species, every one will admit that many are useful, and especially that the general assemblage of characters that fit each species for a somewhat different mode of life from its nearest allies, must certainly be useful. But the very essence of Mr. Galton's argument as to these finger-prints is, that they are not and cannot be in any way directly useful. How, then, can the manner in which [[p. 442]] these patterns may be grouped, furnish us with any argument whatever as regards such totally diverse things as generic or specific characters--and still less as regards genera and species themselves?

    The fact is, no doubt, that these patterns are the direct result of the laws of growth of the tissues of the skin. The limited number and definite character of these patterns are probably the mechanical incidental results of these laws, under the ever-varying conditions of development in each individual. A good analogy would be found in snow-crystals, of which about a thousand varieties have been recorded, which may, however, all be grouped under five classes, while each snow-fall usually produces crystals of one class. Here we have the fixed and definite laws of the crystallisation of water, so modified by conditions of moisture, temperature, motion, and perhaps electric state of the atmosphere, as to lead to this wonderful variety of the product, yet always subject to the law of crystalline symmetry and to systematic grouping under definite classes; just as in these finger-prints we have a more limited variety of forms, which also can be grouped under a few classes. But neither the one nor the other has any real bearing upon the problem of the nature and origin of the genera and species of living organisms. A study of the distribution of the stars over the surface of the heavens, or of the interlacing ripple-marks upon the sea-beach, would no doubt show that these objects might also be the subject of classification; and from the point of view of elucidating the origin of species, they would be about as useful, or as worthless, as the study of finger-marks.

    Of course, there are many varieties or races, both among animals and plants, which continually reappear, and which in some cases are known to reproduce their like, and these undoubtedly have an appearance of stability. Such are the light and dark-coloured varieties in many insects and in some mammals and birds; the hairy or smooth varieties of plants; specially banded or coloured land-shells, and many others. Whenever any of these variations are not injurious under the actual conditions of existence of the species, they may persist in considerable numbers, and thus appear to be stable. But others which are comparatively rare may be just as stable organically, as shown by the case of white mice, pigeons, &c., which increase to any extent under domestication. In a wild state they never do so, and the obvious reason is, that either the conspicuous colour, or something correlated with it, is injurious. In flowers white varieties are frequent, and they occur in all degrees of abundance or rarity; and this indicates, in all probability, various degrees of hurtfulness. If in any case the white colour were not at all injurious as compared with that of the type, it would almost always, by the operation of Delbœuf's Law, tend to increase to nearly an equality with the parent form; and as this equality so rarely [[p. 443]] occurs, we must conclude that, in most cases, the variety (of whatever kind) is to some extent injurious.6 From the usually limited number of individuals presenting these discontinuous variations, we may therefore draw an important conclusion which has hitherto been overlooked. It is, that not only do such variations afford no support to the theory of a special "organic stability" capable of producing races, species, and even genera, without any aid from natural selection, but they furnish a strong, if not conclusive, argument against it, since any which did possess such exceptional stability, and were in no degree injurious, would long since have become equal in numbers to the type of the species.

    A few words are here necessary as to the very common misconception that extreme Darwinians do not recognise the importance of the organism itself and of its laws of growth and development, in the process of evolution. For myself, I may say that no one can be more profoundly impressed by the vast range, by the complexity, by the mystery, by the marvellous power of the laws and properties of organised matter, which constitute the very foundation of all life, and which alone render possible its countless manifestations in the animal and vegetable worlds; while those who have read Weissmann's account of the complex processes of development of sperm and germ cells, in his volume on The Germ Plasm, must feel sure that he, at all events, can have no inadequate conception of their importance.

    What Darwinians deny is--as I understand the question--that these laws themselves serve to keep the completed organism in close adaptation to the fluctuating environment, instead of merely furnishing the material which is required for that adaptation. In our view, the fundamental laws of growth and development, through the agency of rapid multiplication and constant variability, provide the material on which natural selection acts, and by means of which it is enabled to keep up the adaptation to the environment (which alone renders continuous life and reproduction possible) during the constant, [[p. 444]] though slow changes, whether inorganic or organic, by which, in the course of ages, the effective environment of each species becomes more or less profoundly modified. Thus, and thus alone, we believe, are new species produced in strict adaptation to the new environment. So far as rendering possible and actually leading to growth, reproduction, and variation, the fundamental laws are supreme. In securing the development of new forms in adaptation to the new environment, natural selection is supreme. Hence arises the real distinction--though we may not always be able to distinguish them--between specific and non-specific or developmental characters. The former are those definite, though slight modifications, through which each new species actually became adapted to its changed environment. They are, therefore, in their very nature, useful. The latter are due to the laws which determine the growth and development of the organism, and therefore they rarely coincide exactly with the limits of a species. The more important of these latter characters are common to much larger groups, as families, orders, or classes, while others, depending partly on complex and fluctuating influences, are variable even within the limits of a species. Of this kind are the finger-prints, which, like many other minute details of form or structure, vary from individual to individual.

    I have now, I think, shown that the two most recent efforts to establish new methods of organic evolution, as either complete or partial substitutes for natural selection--that is, for the survival of the fittest among the individual variations annually produced--have completely failed to establish themselves as having any relation to the actual facts of nature. Mr. Bateson's discontinuous variations were long ago rejected by Darwin as having no important part in the formation of new species, while recent and ever-growing proofs of the generality and the magnitude of individual variability, render these larger and rarer kinds of variation of even less importance than in his time. Mr. Galton's theory of organic stability, which is essential to the success of discontinuous variations, has been shown to be founded upon a comparison of things of a totally dissimilar nature, and, further, to be absolutely unintelligible and powerless unless in strict subordination to natural selection.

    The reason why two writers of such extensive knowledge and undoubted ability have so completely failed in dealing with the great problem of the modification of organic forms, has been clearly indicated during the course of this discussion. It has arisen from the fact that they have devoted themselves too exclusively to one set of factors, while overlooking others which are both more general and more fundamental. These are, the enormously rapid multiplication of all organisms during more favourable periods, and the [[p. 445]] consequent weeding out of all but the fittest in what must be on the whole stationary populations. And, acting in combination with this annual destruction of the less fit, is the periodical elimination under recurrent unfavourable conditions, of such a large proportion of each species as to leave only a small fraction--the very elect of the elect--to continue the race. It is only by keeping the tremendous severity of this inevitable and never-ceasing process of selection always present to our minds, and applying it in detail to each suggested new factor in the process of evolution, that we shall be able to determine what part such factors can take in the production of new species. It is because they have not done this, that the two authors, whose works have been here examined, have so completely failed to make any real advance towards a more complete solution of the problem of the Origin of Species than has been reached by Darwin and his successors.

Notes Appearing in the Original Work

1. Discontinuity in Evolution. By Francis Galton. Mind, vol. iii., p. 367. [[on p. 212]]
2. Materials for the Study of Variation, treated with especial regard to Discontinuity in the Origin of Species. By William Bateson, M.A. 1894 (pp. xv. and 598). [[on p. 212]]
3. Mr. Bateson, however, makes the extraordinary statement that "it is especially by differences of number and by qualitative differences that species are commonly distinguished" (p. 573). Species-makers know too well that, among the higher animals at all events, it is not so! [[on p. 223]]
4. See Proceedings of the Zoological Society, 1892 (p. 59-23), in a paper by W. Bateson and H. H. Brindley. [[on p. 435]]
5. See Strand Magazine, vol. iv. [[on p. 440]]
6. For a statement and popular demonstration of Delbœuf's Law, see Habit and Intelligence, by J. J. Murphy, 2nd Ed., p. 241. Briefly, the law is that, if a species produces a variety, in however small a proportion annually, and if the variety produces its like in the same proportion as does the species, and if it is neither beneficial nor hurtful to the species, then the variety will increase, rapidly at first and more slowly afterwards, till it approaches to equality in numbers with the species. From this law it follows that, as varieties are usually very much less numerous than the species, this must be due to one of the following causes: either (1) the variety has but recently originated, and has not had time to increase; or (2) the variety has ceased to be produced by the species; or (3) it does not reproduce its like so completely as does the species; or (4) it is disadvantageous to the species. The first two suppositions are improbable, and can only account for a very small proportion of the varieties which are greatly inferior in numbers to the species; the other two are antagonistic to any special "organic stability," which must, therefore, in the great majority of cases he rejected as being both unproven and also opposed to the facts. [[on p. 443]]

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