Materials for the Study of Variation Treated with Especial Regard to Discontinuity in the Origin of Species

have attempted to solve it by starting from the lumbar plexus, while others have begun from the brachial. In the case of Birds this question is reduced to an absurdity. Which vertebra of a Pigeon, which has 15 cervical vertebrae, is homologous with the first dorsal of a Swan which has 26 cervicals ? To decide these questions the only possible appeal is to the facts of Variation, and judged by these facts the whole inquiry comes to an end, for it is seen at once that the expectation is founded on a wrong conception of the workings of Variation. No one, as has been said above, would attempt such an inquiry if the series were undifferentiated, for this individuality would not be expected in such a Series ; but to suppose that it does exist in a differentiated Series of parts, is to suppose that with Differentiation the ordinal individuality of the members has become fixed beyond revision. This supposition the Study of Variation will dispel.

Here, as in the preceding case of the theoretical doctrine of Serial Homology, the current view is far too simple and far too human. Though the methods of Nature are simple too, yet their simplicity is rarely ours. In these subjective conceptions of Homology and of Variation, we have allowed ourselves to judge too much by human criterions of difficulty, and we have let ourselves fancy that Nature has produced the forms of Life from each other in the ways which we would have used, if we had been asked to do it. If a man were asked to make a wax model of the skeleton of one animal from a wax model of the skeleton of another, he would perhaps set about it by making small additions to and subtractions from its several parts ; but the natural process differs in one great essential from this. For in Nature the body of one individual has never been the body of its parent, and is not formed by a plastic operation from it ; but the new body is made again new from the beginning, just as if the wax model had gone back into the melting-pot before the new model was begun.

Before ending this preliminary consideration of Merism it is right that we should see other aspects of the matter. What follows is put forward in no sense as theory or doctrine, but simply as suggesting a line of thought which should be in the minds of any who may care to pursue the subject further or to study the evidence. It is perhaps only when it is seen in connexion with its possible developments that the magnitude of the subject can be fully felt.

In the treatises on Comparative Anatomy which belong especially to the beginning of this century, the idea constantly recurs that the series of segments of a metarnerically segmented form do in some sort represent a series of individuals which have not detached themselves from each other. Seen in the light of the Doctrine of Descent this resemblance or analogy has been taken as a possible indication that the segmented forms may actually have had some such phylogenetic history as this. By similar reasoning the Metazoa have been spoken of as "Colonies" of Protozoa. Now though we need not allow ourselves to be drawn away into these and other barren speculations as to phylogeny, we may still note the substance of fact which underlies them. For it is now recognized that between the process by which the body of a iYa/,s is metamerically segmented, and that by which it divides into a chain of future " individuals," no line can be drawn : that the process of budding, or of stabilization, by which one form gives rise to a number of detached individuals, is often indistinguishable from the process by which a near ally gives rise to a connected colony, and that the two processes may even be interchangeable in the same form ; finally that the process of division of a fertilized ovum by the first cleavage plane may be in some essentials comparable with the division of a Protozoon into two new individuals. All these are now commonplaces of Natural History.

With what justice these considerations may have been applied to the problems of phylogeny we need not now inquire, but to the interpretation of the facts of Variation they have an application which ought not to be neglected. If, then, as is admitted, there is a true analogy between the process by which new organisms may arise asexually by Division, and the process by which ordinary Meristic Series are produced, it follows that Variation, in the sense of difference between offspring and parent, should find an analogy in Differentiation between the members of a Meristic Series. Applied to the case of asexual reproduction there seems no good reason for denying this analogy. It is of course an undoubted fact that in the asexual reproduction of many forms Variation is rare, though the sexually produced offspring of the same forms are very variable. In plants this is familiar to everyone, though the extension of the same principle to animals rests chiefly on inference. Nevertheless in plants budvariation, both Meristic and Substantive, happens often, and the division of a plant into two dissimilar branches may well be compared to the production of dissimilar offspring by one parent. : indeed, if the processes of Division are admitted to be fundamentally the same, this conclusion can scarcely be escaped.

In one more aspect this subject may be considered with profit. It is, as we have seen, believed that the division of an ovum into two segmentation-spheres is not a process essentially different from the division of certain Protozoa into two " individuals." In conceiving the manner of Variation in such Protozoa we have little or no fact to guide us, but this much is obvious : that for the introduction of a variety as the offspring of a given species, it is necessary either that the two parts into which the unicellular organism divided should have varied equally, and that the division should thus be a symmetrical division (in the full sense of qualitative as well as formal symmetry) ; or that the division should be asymmetrical, the resulting parts being dissimilar, in which case one may conceivably belong to the type arid the other be a Variety. If Variation has ever occurred in the reproduction of animals of this class it must have occurred on one or both of these plans.

Returning to the segmentation of the Metazoan ovum we have the well-known results of Roux and others, shewing that, in certain species, the first1 cleavage-plane divides the body into the future right and left halves. In such cases then on the analogy of the Protozoon, the right and left halves of the body are in a sense comparable with the two young Protozoa, and though each half is hemi-symrnetrical, it is in this way the equivalent of a separate organism. This suggestion, which is an old one, receives support from many facts of Meristic Variation, especially from the mode of formation of homologous Twins and "double Monsters" which are now shewn almost beyond doubt, to arise from the division of one ovum'. But besides the evidence that each half of the body may on occasion develop into a whole, evidence will be given that one half may vary in its entirety, independently of the other half. Such Variation may be one of sex, taking the form of Gynandromorphy, so well-known among Lepidoptera, in which the secondary sexual characters of one side are male, those of the other being female ; or it may happen that the difference between the two sides is one of size, the limbs and organs of one side being smaller than those of the other ; or lastly the Variation between the two sides may be one that has been held characteristic of type and variety or even of so-called species and species3.

These matters have been alluded to here as things which a student of the facts of Variation will do well to bear in mind. It is difficult to see the facts thus grouped without feeling the 1 Often it is the second cleavage-plane (if any) which corresponds with the future middle line. 2 The well-known evidence relating to this subject will be spoken of later. The view given above, which is now very generally received, finds support in the striking observations of DRIESCH, lately published (Zt. f. iv. Zool., 1891, LIII. p. 160). Working with eggs of Echinus, Driesch found that if the first two segmentationspheres were artificially separated, each grew into a separate Pluteus ; if the separation was incomplete, the result was a double-monster, united by homologous surfaces. Similar experiments attended by similar results have since been made on AmpJnoxus by E. B. WILSON, Anat. Anz., vn. 1892, p. 732.

3 Evidence of such abrupt Variation between the two sides of the body belongs for the most part to the Substantive group. possibility that the resemblance between the two sides of a bilaterally symmetrical body may be in some essentials the same as the resemblance between offspring of the same parent, or to use an inclusive expression, that the resemblance between the members of a Meristic Series may be essentially the same as the resemblance and relationship between the members of one family ; that the members of a row of teeth in the jaw, of a row of peas in a pod, of a chain of Salps, or even a litter of pigs, all resulting alike from the processes of Division, may stand to each other in relationships which though different in degree may be the same in kind.

If reason shall appear hereafter for holding any such view as this, the result to the Study of Biology will be profound. For if it shall ever be possible to solve the problem of Symmetry, which may well be a mechanical one, we shall thus have laid a sure foundation from which to attack the higher problem of Variation, and the road through the mystery of Species may tl.u- be found in the facts of Symmetry. From the subject of Merism and the thoughts which it suggests, we now pass to another matter. The first limitation by which we proposed to group Variations was found in the characters which they affect : the second relates to the magnitude, or as I shall call it, the Continuity of the variations themselves. And though for many a conception has no value till it be cast in some finite mould, my aim will be rather to describe than to define the meaning of the term Continuity as applied to Variation. In dealing with a subject of this obscurity, where the outlines are doubtful, an exact mapping of the facts cannot be made and ought not to be attempted; but I trust that from the present indications, vague though they are, some larger and more definite conception of Discontinuity in Variation may shape itself hereafter by a process of natural growth. For this reason I shall as far as possible avail myself of examples rather than of general expressions, whether inclusive or exclusive.

To those who have studied the recent works of Galton, the conceptions here outlined will be familiar. In the chapter on "Organic Stability" in Xntnrul Inheritance, the matter has been set forth with charming lucidity, and what follows will serve chiefly to illustrate the manner in which the facts of Natural History correspond with the suggestions there made. In the ease of most species it is a matter of common knowledge that though no two individuals are identical, there are many which in the aggregate of their characters nearly approach each other, constituting thus a normal, from which comparatively few differ widely. In such a species the magnitude of these differences is proportional to the rarity of their occurrence. Now this, which is a matter of common experience, has been shewn by Galton to be actually true of several quantities which in the case of Man are capable of arithmetical estimation. In the cases referred to it has thus been established that these quantities when marshalled in order give rise to a curve which is a normal curve of Frequency of Error. Taking for instance the case of stature, Galton's statistics shew that for a given community there is a mean stature, and the distribution of the statures of that community around the mean gives rise to a Curve of Error. In this case the individuals of that community in respect of stature form one group. Now in the case of a collection of individuals which can be separated into two species, there is some character in respect of which, when arranged by their statistical method, the individuals do not make one group but two groups, and the distribution of each group in respect of that character cannot be arranged in one Curve of Error, though it may give rise to two such curves, each having its respective mean. For example, if in a community tall individuals were common and short individuals were common, but persons of medium height were rare, the measurements of the Stature of such a community when arranged in the graphic method would not form one Curve of Error, though they might and probably would form two. There would thus be a normal for the tall breed, and a normal for the short breed. Such a community would, in respect of Stature, be what is called dimorphic.

The other case, in which the whole community, grouped according to the degrees in which they display a given character, forms one Curve of Error, may conveniently be called monomorphic in respect of that character. By considering the possible ways in which such a condition of dimorphism may arise in a monomorphic community, one of the uses of the term Discontinuity as applied to Variation will be made clear. Considering therefore some one character alone, in a species which is monomorphic in respect to that character, individuals possessing it in its mean form are common while the extremes are rare ; while if the species is dimorphic the extremes are common and the mean is rare. Now the change from the monomorphic condition to the dimorphic may have been effected with various degrees of rapidity : for the frequency of the occurrence of the mean form may have gradually diminished, while that of the extremes gradually increased, through the agency of Natural Selection or otherwise, in a long series of generations ; or on the other hand the diminution in the relative numbers of the mean individuals may have been rapid and have been brought about in

a few generations by a few large and decisive changes, whether of environment or of organism. Referring to the curve of Distribution formed in the graphic method of displaying the statistics, during the monomorphic period the curve has one apex corresponding with the greatest frequency of one normal form, but in the dimorphic period the curve has two apices, corresponding with the comparative frequency of the two extremes, and the comparative rarity of the mean form. The terms Continuous or Discontinuous are applicable to the process of transition from the monomorphic to the dimorphic state according as the steps by which this change was effected are small or large.

The further meanings of Discontinuous Variation will be explained by the help of examples. The first cases refer to Substantive Variation1, and we may conveniently begin by examining a case of Variation in a character which is easily measured arithmetically. Among beetles belonging to the Lamellicorn family there are numerous genera in which the males may have long horns arising from various parts of the head and thorax2. These horns may be Fio. 1. Side-views of the Lamellicorn beetle, Xylotrupes gideon. Legs uot represented. I, High male, II, Medium male, III, Low male.

1 In referring thus to evidence as to Substantive Variation, I find myself in the difficulty mentioned in the Preface. For it is necessary to allude to matters which cannot be properly treated in this first instalment of facts. In order, however, that the one introductory account may serve for all the evidence together, such allusion is inevitable and I can only trust that full evidence as to Substantive Variation may be produced before long. - For particulars of this subject with illustrations, see Descent of Mail, 1st ed.. vol. I. pp. 369 — 372. A detailed account of this and the succeeding example in the case of the Earwig was given by Mr Brindley and myself in P. '/,. S., 1893.

of very great size, as in the well-known Hercules beetle (Dynastes hercules) and others. The females of these forms are usually without horns. In such genera it is commonly found that the males are not all alike, but some are of about the size of the females and have little or no development of horns, while others are more than twice the size of the females and have enormous horns. These two forms of male are called " low " and " high " males respectively.

In many places in the Tropics such beetles abound, both " high " and " low " males occurring in the same locality. An admirable example of this phenomenon is seen in Xylotrupes gideon, of which a " high," " low," and medium male are shewn in profile in Fig. 1. Of this insect a very large number were kindly given to me by Baron Anatole von Hiigel, who collected them at one time, in one locality, in Java. In this species there is one cephalic and one thoracic horn, placed in the positions shewn in the figure. Fig. 1, I shews a "high" male, II is a medium, and ill a " low " male. In the gathering received there were 342 males. My friend, Mr H. H. Brindley, has made careful measurements of the lengths of the horns of these specimens and has constructed the diagram, Fig. 2. In this each dot represents an individual, and the abscissae shew the measurements of the length of the cephalic horn. For clearness these measurements are represented as of twice the natural size. So far as the numbers go the result shews that the most frequent forms are

FIG. 2. Diagram representing the frequency of the lengtbs of cephalic horn in male Xylotrupes gideon. M, the mean case ; M' the mean value. The abscissae give lengths of cephalic horn in lines. the moderately low and the moderately high, the forms of mean measurement being comparatively scarce. It is true that the numbers are few, but so little heed is paid to phenomena of this kind that material is difficult to obtain and the present opportunity was indeed wholly exceptional1. But taking the evidence for what it is worth, the comparative scarcity of " medium " males in that particular sample is clear, and so far the form is dimorphic, and has two male normals.

Now such a condition may have arisen in several ways. First, in the past history of the species there may have been a time when the males were horned and were monomorphic, the " medium" form being the most frequent, and the present dimorphic condition may have been derived from this, either continuously or discontimiously as described above for the case of Stature. Secondly, the dimorphism may date from the first acquisition of the horns, and this character may perhaps have always been distributed in the dimorphic way. In this case the term Discontinuous would be applicable to the Variation by which the groups of "high" and " low " males have been severally produced. I am not acquainted with evidence as to the course of inheritance in these cases, and I do not know therefore whether both " high" and " low" males may be produced by one mother. If this should be shewn to be the case, it would suggest that the separation of the males into two groups was a case of characters which do not readily blend, and are thus exempt from what Galton has called the Law of Regression2.

In the case of a somewhat similar structure found in the Common Earwig (Forjicula auric ularia) the dimorphism is still more definite. In the autumn of 1892 on a visit to the Fame Islands, a basaltic group off the coast of Northumberland, it was found that these islands teem with vast quantities of earwigs. The abundance of earwigs was extraordinary. They ^^^^ lay in almost continuous sheets under every stone w and tussock, both among the sea-birds' nests 1 B and by the light-keepers' cottages. Among them

FIG. 3. I, High were males of the two kinds shewn in Fig. 3 ; the male, II, Low male one or high male having forceps of unusual length, of Common Earwig the other or low maj being the common form. (Forficula auricu- T . , . , , °. , c laria) from the It appears that the high male is known from many Fame Islands. places in England and elsewhere and that it was made into a distinct species, F. furcipata, by 1 In the Lucanidffi, of which the Stagbeetlc (L. <-ernt«\ is an example, a similar phenomenon occurs, the "high" and "low" males being distinguished by the degree of development of the mandibles. No sufficient number of male Stagbeetles has yet been received to warrant any statement as to the frequency of the various types of males.

STEVENS1 though by later authorities2 the species has not been retained. A large sample of Earwigs collected in a Cambridge garden contained 163 males of which 5 would come into the high class, but the great abundance of high males at the Fames seems to be quite exceptional. With a view to a statistical determination of the frequency of the high and low forms 1000 of these Earwigs were collected by Miss A. Bateson, the whole being taken at random on one day from three very small islands joined to each other at low tide. Of the 1000 specimens 583 proved to be mature males with elytra fully developed, no specimen with imperfect elytra being included in this number3. On measuring the length of the forceps to the nearest half mm. and grouping the results in the graphic method the curve shewn in Fig. 4 was produced. The figures on the

FIG. 4. Curve shewing frequency of various lengths of forceps of male Earwigs (F. auricularia) from the Fame Islands. Ordinates, numbers of individuals: abscissas, lengths of forceps in mm. ordinates here shew the numbers ot individuals, those on the abscissae giving the length of the forceps in millimetres. As there :i For particulars in evidence of the maturity of these specimens see P. Z. S., shewn the smallest length of forceps was 25 mm., and the greatest 9 mm., the greatest frequency being grouped about 3'5 mm. ami 7 mm. respectively. The mean form having forceps of moderate length is comparatively rare. The size of the forceps of the females scarcely varies at all, probably less than 1 mm. in the whole sample.

The number of cases is enough to fairly justify the acceptance of these statistics and it is not likely that a greater number of cases would much alter the shape of the curve. Here, therefore, is a group of individuals living in close communion with each other, high and low, under the same stones. No external circumstance can be seen to divide them, yet they are found to consist of two well-marked groups. Before leaving these examples special attention should be directed to the fact that the existence of a complete series of individuals, having every shade of development between the "lowest" and the " highest " male, does not in any way touch the fact that the Variation may be Discontinuous ; for we are concerned not with the question whether or no all intermediate gradations are possible or have ever existed, but with the wholly different question whether or no the normal form has passed through each of these intermediate conditions. To employ the metaphor which Gal ton has used so well — and which may prove hereafter to be more than a metaphor — we are concerned with the question of the positions of Organic Stability ; and in so far as the intermediate forms are not or have not been positions of Organic Stability, in so far is the Variation discontinuous. Supposing, then, that the "high" and " low " males should become segregated into two species — a highly improbable contingency — these two species would have arisen by Variation which is continuous or discontinuous according to the answer which this question may receive.

From the consideration of Discontinuity in the Variation of a character, size, which may be readily measured arithmetically, we pass to the more complex subject of Discontinuous Variation in qualities which are not at once capable of quantitative estimation. In this connexion the case of colourvariation may be profitably considered. Nature abounds with examples of colour-polymorphism, and in numerous instances such Variation is discontinuous. Of such discontinuous Variation in colour I shall speak under two heads, considering first variations in colours themselves and

secondly variations in colour-patterns. As it is not proposed to give the evidence as to Substantive Variation in this volume, a few examples must suffice to shew the use of the term Discontinuity as applied to these Colourvariations. I. Colours. The case of the eye-colour of Man may well be mentioned first, as it has been studied statistically by Galton. In this case the facts clearly shewed that certain types of eye-colour are relatively common and that intermediates between these types are comparatively rare. The statistics further shewed that in this respect inheritance was alternative, and that the different types of eye-colour do not often blend in the offspring. " If one parent has a light eye-colour and the other a dark eye-colour, some of the children will, as a rule, be light and the rest dark ; they will seldom be medium eye-coloured, like the children of medium eye-coloured parents.1"

Colour dimorphism of this kind is very common among animals and plants. It is well known, for example, among beetles. Several metallic blue beetles have bronze varieties of both sexes, living together in the same locality. A familiar instance of this dimorphism occurs in the common Phratora vitellince. Again in the Elaterid beetle, Corymbites cupreus, there is a similar dimorphism in both sexes, the one variety having elytra in larger part yellowbrown, while the elytra of the other are metallic blue. This blue variety was formerly reckoned a distinct species, C. ceruginosus. In the latter case I am informed by Dr Sharp, who has had a large experience of this species, that no intermediate between these two varieties has been recorded, and in the case of the Phratora the occurrence of intermediates is very doubtful. An- other common example of colour dimorphism is seen in Telepltorus lividas, the " sailor " of " soldiers and sailors." This beetle may be found in large numbers, about half being slaty in colour (var. dispar), while the remainder have the yellowish colour which coleopterists call " testaceous." Such instances may be multiplied indefinitely. When the whole evidence is examined it will be found that different colours are liable to different discontinuous variations ; as instances may be mentioned black and tan in dogs ; olive-brown or green and yellow in birds, &c.'2: grey and cream-

2 A specimen of the green Eiug Parakeet (Palceornis torquatus) at the Zoological Society's Gardens was almost entirely canary-yellow in 1890. Since that date it has become more and more " ticked " with green feathers. A Green Woodpecker (Picus I'iridis) is described, having the feathers of the rump edged with red instead of yellow, the normally green feathers of the three lower rows of wing-covers and the back were pointed with yellow. J. H. GURNEY, Zoologist, XT. p. 3800. I am indebted to Mr Gurney for the loan of a coloured drawing of this specimen. Another example is described as being entirely canary-yellow, with the exception of a few feathers on the cap, which were purple-red. Die BETTA, Mater, per una fauna Veronese, p. 174. For this reference I am indebted to Prof. Newton. Specimen of Common Bunting whitish yellow. EDWARD, ZooL, (5492 ; Sedge Warbler canaryyellow. BIRD, ZooL, 3632. The Canary itself is a similar case. An Eel gambogeyellow. GURXEY, ZooL, 3599.

colour in mice and cygnets1 ; red and blue in the eggs of many Copepoda2, the tibia? of Locusts3, the hind wings of the Crimson Underwing (Catocala iu//>fn)4, &c. Another case of blue as a variety of scarlet is the familiar one of the flower of the Pimpernel (AiKiyallis arvensix). Discontinuous colour-variation of this kind is one of the commonest phenomena in nature, but to advance the subject materially it is necessary for a large mass of evidence to be produced. This cannot now be attempted, but in order to bring out the close relation between these facts and the problem of Species I propose to dwell rather longer on one special section of the evidence which must serve to exemplify the rest. The case which I propose to take is that of certain yellow, orange, and red pigments. For brevity I shall present the chief facts in the first instance without comment.

1. Cofias edusa (Clouded Yellow) is usually orange-yellow, having a definite pale yellow female variety, helice, which is not recognized as occurring in the male form. A specimen is figured having the right side helice and the left edusa. FITCH, E. A., Entomologist, 1878, XLI. p. 52, PI. fig. 11. This was an authentic specimen, for Mr Fitch tells me that it was taken by his son and seen alive by himself. A specimen having one wing white and the rest orange is recorded by MORRIS, Brit. But., p. 13.