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Originally appearing in Volume V27, Page 912 of the 1911 Encyclopedia Britannica.
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VARIATION AND SELECTION, in biology. Since the publication in 1859 of Charles Darwin's Origin of Species, the theory of evolution of animals and plants (see EVOLUTION) has rested on a linking of the conceptions of variation and selection. Living organisms vary, that is to say, no two individuals are exactly alike; the death-rate and the multiplication-rate are to a certain extent selective, that is to say, on the average, in the long run, they favour certain variations and oppress other variations. Co-operation of the two factors appears to supply a causal theory of the occurrence of evolution; the suggestion of their co-operation and the comparison of the possible results with the actual achievements of breeders in producing varieties were the features of Charles Darwin's theoretical work which made it a new beginning in the science of biology, and which reduced to insignificance all earlier work on the theory of evolution. P. Geddes, J. H. Stirling, E. Clodd and H. F. Osborn have made careful studies of pre-Darwinian writers on evolution, but the results of their inquiries only serve to show the greatness of the departure made by Darwin. Several of the ancients had a vague belief in continuity between the inorganic and the organic and in the modifying or variation-producing effects of the environment. Medieval writers contain nothing of interest on the subject, and the speculations of the earliest of the modern evolutionists, such as C. Bonnet, were too vague to be of value. G. L. L. Buffon, in a cautious, tentative fashion, suggested rather than stated the mutability of species and the influence of the forces of nature in moulding organisms. Immanuel Kant, in his Theory of the Heavens (17J5), foreshadowed a theory of the development of unformed matter into the highest types of animals and plants, and suggested that the gradations of structure revealed by comparative anatomy pointed to the existence of blood relationship of all organisms, due to derivation from a common ancestor. He appeared to believe, however, that the successive variations and modifications had arisen in response to mechanical laws of the organisms themselves rather than to the influence of their surroundings. J. G. von Herder suggested that increase by multiplication with the consequent struggle for existence had played a large part in the organic world, but his theme remained vague and undeveloped. Erasmus Darwin, the grandfather of Charles Darwin, set forth in Zoonomia a much more definite theory of the relation ofvariation to evolution, and the following passage, cited by Clodd, clearly expresses it: " When we revolve in our minds the metamorphoses of animals, as from the tadpole to the frog; secondly, the changes produced by artificial cultivation, as in the breeds of horses, dogs and sheep; thirdly, the changes produced by conditions of climate and season, as in the sheep of warm climates being covered with hair instead of wool, and the hares and partridges of northern climates becoming white in winter; when, further, we observe the changes of structure produced by habit, as shewn especially by men of different occupations; or the changes produced by artificial mutilation and prenatal influences, as in the crossing of species and production of monsters: fourth, when we observe the essential unity of plan in all warm-blooded animals—we are led to conclude that they have been alike produced from a single living filament." G. R. Treviranus, in the beginning of the loth century, laid stress on the indefiniteness of variation, but assumed that some of it was adaptive response to the environment, and some due to sexual crossing. J. B. P. Lamarck was the first author to work out a connected theory of descent and to suggest that the relationships of organic forms were due to actual affinities. He believed that life was an expanding, growing force, and that animals responded to the environment by developing new wants, seeking to satisfy .these by new movements and thus by their own striving producing new organs which were transmitted to their descendants. Variation was in fact a purposive response. In 1813 W. C. Wells definitely propounded the theory of natural selection, but applied it only to certain human characters. In 1831 Patrick Matthew, in the appendix to a book on naval timber and arboriculture, laid stress on the extreme fecundity of nature " who has in all the varieties of her offspring a prolific power much beyond (in many cases a thousandfold) what is necessary to fill up the vacancies caused by senile decay. As the field of existence is limited and pre-occupied, it is only the hardier, more robust, better-suited-tocircumstance individuals, who are able to struggle forward to maturity, these inhabiting only the situations to which they have superior adaptation and greater power of occupancy than any other kind; the weaker and less circumstance-suited being prematurely destroyed. This principle is in constant action; it regulates the colour, the figure, the capacities and instincts; those individuals in each species whose colour and covering are best suited to concealment or protection from enemies, or defence from inclemencies or vicissitudes of climate, whose figure is best accommodated to health, strength, defence and support; whose capacities and instincts can best regulate the physical energies to self-advantage according to circumstances—in such immense waste of primary and youthful life those only come to maturity from the strict ordeal by which nature tests their adaptation to her standard of perfection and fitness to continue their kind by reproduction." G. St Hilaire and afterwards his son Isodore regarded variation as not indefinite but directly evoked by the demands of the environment. L. von Buch laid stress on geographical isolation as the cause of production of varieties, the different conditions of the environment and the segregated interbreeding gradually producing local races. K. E. von Baer and M. J. Schleiden regarded, variation and the production of new or improved structures as an unfolding of possibilities latent in the stock. Robert Chambers, in the once famous Vestiges of Creation, interested and shocked his contemporaries by his denial of the fixity of species and his insistence on creation by progressive evolution, but had no better theory of the cause of variation than to suppose that organisms—" from the simplest and oldest to the highest and most recent " were possessed of " an inherent impulse, imparted by the Almighty both to advance them from the several grades and modify their structure as circumstances required." In 1852 C. Naudin compared the origin of species in nature with that of varieties under cultivation. Herbert Spencer from 1852 onwards maintained the principle of evolution and laid special stress on the moulding forces of the environment which called into being primarily new functions and secondarily new structures. Although the pre-Darwinian writers amongst them invoked nearly every principle that Darwin or his successors have suggested, they failed to carry conviction with regard to evolution, and they neither propounded a coherent philosophy of variation nor suggested a mechanism by which variations that appeared might give rise to new species. The anticipations of Darwin were little more than formal and verbal. As T. H. Huxley pointed out in his essay on the reception of the Origin of Species in the second volume of Darwin's Life and Letters, " The suggestion that new species may result from the selective action of external conditions upon the variations from their specific type which individuals present—and which we call `spontaneous' because we are ignorant of their causation—is as wholly unknown to the historian of scientific ideas as it was to biological specialists before 1858. But that suggestion is the central idea of the Origin of Species, and contains the quintessence of Darwinism." C. Darwin opened his argument by consideration of plants and animals under domestication. He pointed to the efflorescence of new forms that had come into existence under the protection of man. A multitude of varieties of cultivated plants and domesticated animals existed, and these differed amongst themselves and from their nearest wild allies to an extent that, but for the fact o. their domestication, would entitle them to the systematic rank of species. Some of these changes he sup-posed to have been the result of new conditions, including abundance of food and protection from enemies, but most he attributed to the accumulated results of selective breeding. No doubt such domesticated species might revert, and it has been shown that many do revert when restored to wild conditions, but such reversion is natural if we reflect that the domestic varieties are under the guardianship of man and have been selected according to his whim and advantage. Comparing domesticated varieties with species and varieties in nature, Darwin showed that the distinction between varieties and species was chiefly a matter of opinion, and that the discovery of new linking forms often degraded species to varieties. Species, in fact, were not fixed categories, but halting-places, often extremely difficult to choose, for the surveying mind of the systematist. He considered that a struggle for existence was the inevitable result of the operation of the principle of Malthus in the animal and vegetable worlds. The struggle would be most acute between individuals and varieties of the same species, with the result that " any being, if it vary however slightly, in any manner profitable to itself, under the complex and somewhat varying conditions of life, will have a better chance of surviving, and thus be naturally selected." Under natural selection the less well-adapted forms of life would on the average have a heavier death-rate and a lower multiplication-rate. He did not suggest that every variation and every character must have a " selection value," although he pointed out that, because of our ignorance of animal physiology, it was extremely rash to set down any characters as valueless to their owners. It is even more important to notice that he did not suggest that every individual with a favourable variation must be selected, or that the selected or favoured animals were better or higher, but merely that they were more adapted to their surroundings. With regard to variation, Darwin was urgent in stating his opinion that the laws of variation were not understood and that the phrase " chance " variation was a wholly incorrect expression. He thought it probable that circumstances affecting the reproductive system of the parents had much influence in producing a plastic condition of the progeny. He doubted, but did not exclude, the importance of the direct effect of differences of climate and food and of increased use and disuse, except so far as the individual was concerned, but his opinion as to these Lamarckian factors changed from time to time. He laid much stress on the unity of the organism in every stage of its existence, with the resulting correlation of variations, so that the favouring of one particular variation entailed modifications of correlated structures. He recognized the existenceof the large variations, but he believed these to be of little value in evolution, and he attached preponderating importance to relatively :minute indeterminate variations. On the other hand, he was far from advocating the view that has been pithily expressed as the "selection of the fit from the fortuitous "; he recognized that variations, although perhaps suggested or excited by the environment, were determined by internal causes. He showed how different varieties in a species, or species in a genus, tended to display parallel variation, clearly indicating that the range and direction of variation were limited or determined by the nature of the organism. Alfred Russel Wallace, the co-discoverer of the Darwinian principles, had sent to Darwin early in 1858 an outline of a theory of the origin of species. Darwin found that it was, in all essential respects, identical with his own theory at the exposition of which he had been working for many years. With an unselfish generosity which must always shine in the history of science, and indeed of the human race, Darwin proposed at once to communicate his correspondent's essay to the Linnaean Society of London, but was persuaded by his friends to send with it an outline of his own views. Accordingly, on the same evening, in July 1858, both communications were made to the Linnaean Society. When Wallace found how much more fully Darwin was equipped for expounding the new views, he exhibited an unselfish modesty that fully re-paid Darwin's generosity, henceforth described himself as a follower of Darwin, entitled his most important publication on the theory of evolution Darwinism, and did not issue it' until 1889, long after the world had given full credit to Darwin. In most respects his ideas were closely parallel with those of Darwin. He believed that species had been formed by means of natural selection. He insisted that the great powers of increase of all organisms led to a tremendous struggle for existence, and that variability extended to every part and organ of every organism; that the variability was large in amount in proportion to the size of the part affected, and occurred in a considerable proportion of the individuals of those large and dominant species which might be supposed to be breaking up into new species. He pointed to the changes wrought on domesticated organisms by the artificial selection of similar variations, and drew the inference that there must be parallel occurrences under wild nature. In the sphere of nature, with its vast numbers and constant pressure, not every more favoured individual would survive, nor every surviving individual be the more favoured, but throughout the changes and chances there would be a constant and important bias in favour of the individuals more fitted to their conditions. Wallace, however, brought into his scheme a factor excluded by Darwin. He believed that behind the natural world lay a spiritual world, irruptions from which had disturbed the natural sequence of causation, certainly in the production of the higher emotional and mental qualities of man, probably in the appearance of self-consciousness, and possibly in the first origin of life. It is to be remembered that the origin of species by the modification of pre-existing species,—in fact, the doctrine of organic evolution; although first. made credible by Darwin and Wallace, does not depend upon their theory of the relation of natural selection to variation. The theory of evolution is supported by a great :range of evidence, much of which was first collected by Darwin, and which has been enormously increased by subsequent workers excited by his genius. Such evidence relates to the facts of classification, structure, development, and geographical and geological distribution. It now remains to examine in closer detail the further knowledge that has been gained with regard to variation and the bearing of that on the Darwinian posit'on. Magnitude of Variation.—Darwin was well aware that variation ranged from differences so minute as to become apparent only on careful measurement to those large departures from the normal which may be called abnormalities, malformations or monstrosities. He was of the opinion that the summation of minute differences had played a preponderating if not exclusive part in the formation of species. Wallace, whilst insisting that the range of observed and measured variation was much larger in proportion to the size of the organisms or parts of organism affected than was generally believed, leaned to the Darwinian view in excluding' from the normal factors in the origin of species variations of the extrerner ranges of magnitude. Later writers, and in particular W. Bateson and H. de Vries, have urged that as species are discontinuous—that is to say, marked off by structural differences of considerable magnitude—it is more probable that they have arisen from similarly discontinuous variations. De Vries gave the name " mutations " to such considerable variations (it is to be noted that a further concept, that of the mode of origin, has been added to the word mutation, and that the conception of relative size is being removed from it), and Bateson, de Vries and other writers have added many striking cases to those recorded by Darwin. It is doubtful, however, if there is any philosophical basis for distinguishing between variations merely by their magnitude. Differences which at their first appearance are very minute may result in the kind of variations which certainly would be classed as discontinuous. When the cells of the morula stage of an embryo are shaken asunder, each, instead of forming the appropriate part of a single organism, may form a complete new organism. And similarly in the development of a complicated organism, the suppression or doubling of a single cell or group of cells may bring about striking differences in the symmetry of the adult, or the reduction or increase in the number of metameric organs. A slight change in the structure or activity of a gland, by altering the internal secretion, may produce widespread alterations even in an adult organism; and we have good reason to suppose that, if compatible with viability, such minute changes would have even a greater ultimate effect if they occurred in an embryo. Even amongst the extreme advocates of the theory of mutations, the importance of magnitude is being discounted by their suggestion that some of the minute variations which have hitherto been regarded by them as insignificant " fluctuating variations " may be significant mutations. This in effect is to say that not magnitude but something else has to be sought for if we are to pick out amongst observed variations those which may be the material for the differentiation of species. So far as magnitude is concerned, the attack on the Darwinian position has failed, and it is agreed that species may be discontinuous and none the less have been produced from minute variations. Causes of Variation.—Darwin was careful to insist that we did not know the laws of variation, and that when variation was attributed to " chance " no more should be read into the statement than an expression of our ignorance of the causation. It cannot now be doubted that a very large amount of observed variation, and especially of the indefinite variation which is sometimes spoken of as fluctuating variation, and which is usually distributed indefinitely round a mean, is directly associated with or induced by the environment. On various grounds attempts have been made to exclude such variation from the material for the making of species. The variations which de Vries has called mutations, and which were at first associated by Bateson with what he called discontinuous variations as the exclusive source of new species, are now supposed by de Vries to be distinguished from fluctuating variations by their mode of origin. Such mutations are not the product of the environment, but are an outcrop of the constitution of the germinal material of the varying organism, the result either of causes as yet undetected, or of the premutations and eliminations suggested by the work of Mendel (see MENDELISM). These attempts to reject environmental variation rest on several grounds. In the first place the variations in question are " acquired characters." When Darwin and Wallace framed their theories it was practically assumed that acquired characters were inherited, and the continuous slow action of the environment, moulding each generation to a slight extent in the same direction, was readily accepted by a generation inspired by Sir C. Lyell's doctrine of uniformitarianism in geological change, as a potent force. A. Weismann, however, from theoretical considerations and from analysis of supposed cases has at the least thrown doubt on the trans-mission of acquired characters. And so the newer school discard acquired characters and all the Lamarckian factors and leave the board clear for " mutations." Analysis of any acquired character, however, shows that there are two factors involved. The organism is not a passive medium; the amount and nature of the response it makes to the action of environment depends on its own qualities, and these qualities, on any theory of inheritance, pass from generation to generation. Successful organisms, or well-adapted organisms, are those that have responded to the environment, whether by large or small variations, in suitable fashion. It is the character as acquired that affords the opportunity for selection, but the quality of responding to the environment so as to produce that character is transmitted. The conceptions of Weismann afford no ground for rejecting fluctuating variations from the materials for the production of species. In the second place, it has been urged, particularly by de Vries, that experiment and observation have shown that the possible range of fluctuating variation is strictly limited. Breeders, he says, who try to build up qualities by the selection of the fluctuating variations that occur soon find that they reach a maximum beyond which their efforts fail, unless they turn to the more rarely occurring but heritable mutations. Something will be said later in this article as to the limitation of variation; here it is necessary only to say that de Vries is introducing no new idea. It is well known that some races and some organs in plants and animals are extremely variable, and that others are much less variable, and further, that whilst some of these differences may be due to intrinsic causes, others can be modified by experiment. As Sir W. T. Thiselton-Dyer has pointed out, what is called " specific stability " is a familiar obstacle to the producer of novelties, but one which he frequently succeeds in breaking down by cultural and other methods. In a survey of the palaeontological history of plants and animals, it is plain that extreme stability and extreme mutability both have occurred, sometimes having persisted for untold ages, sometimes having succeeded one another for varying periods. As yet no solid reason has been alleged for excluding fluctuating variations, on account of their limitation, from the materials for specific change. J. Cossar Ewart and H. M. Vernon have adduced experimental evidence as to the induction of variation by such causes as difference in the ages of the parents, in the maturity or freshness of the conjugating germ cells, and in the condition of nutrition for the embryos. Such cases show in the plainest way the co-operation of external or environmental and internal or constitutional factors. With our present knowledge it is impossible to discriminate between variation that may or that may not be the material for the differentiation of species by scrutinizing either magnitude or probable causation. It is equally impossible to draw an exact line between variation induced by the environment and variation that may be termed intrinsic. Extrinsic and intrinsic factors are involved in every case, although there is a range from instances in which the external factor appears to be extreme to instances where the intrinsic factor is dominant. Even the results of mutilation involve an intrinsic factor, for they range, according to the organ and organism affected, from complete regeneration to the most imperfect healing. In the effects of exercise, of physiological activity and the gross results of such external agencies as food, temperature, climate, light, pressure and so forth the intrinsic factor appears to become more important. The interplay of extrinsic and intrinsic factors also differs with the age of the organism affected: the more nearly adult it may be, the more direct appears to be the influence of the environment; the more nearly embryonic the organism may be, the less direct is the result of a force impressed from without. The old organism is more stable and responds in obvious ways to direct assaults from without; the young organism is at once less stable and more profoundly modified by environmental change, replying in terms less easy to predict from knowledge of the nature and amount of the impinging agency. And finally, there are a series of variations, amongst which no doubt are the mutations of de Vries and the disintegrations and recombinations of the unit factors with which Mendel and his followers have worked, in which the external or environmental factor is most remote from the actual result. Correlated Variation.—Every organism is an individual, its different parts, organs and functions being associated in a degree of intimacy that varies, but that corresponds roughly with the integration of the individual and its place in the ascending scales of animal or vegetable life. One aspect of organic individuality is the correlation of variations, the fact that when one part varies, other parts vary more or less simultaneously. So far, our knowledge of correlation is almost entirely empirical, and the arrangement of the observed facts cannot be brought into exact harmony with our guesses at their causation. Much correlation is the inevitable result of organic structure. The various parts of a living organism affect each other in adult life and during growth. If, for instance, the testes fail to develop normally, the secretion which they discharge into the blood is abnormal in character and amount, with the result that the characters of the remotest parts of the body are more or less profoundly affected. It is now known that similar internal secretions, or hormones, pass into the blood trom every organ and tissue, so reaching and affecting every part of the body. If we reflect on the multitude and complexity of such actions and reactions in operation from the youngest stages to the end of the life of each individual, we cannot be surprised at any correlation. Change in the size of any part or organ, however it may have been produced, must bring with it many others changes, directly or indirectly. A difference in calibre, elasticity or branching of a blood vessel, the smallest variation in a nerve or group of vessel-cells, any anatomical or physiological divergence, is reflected throughout the organism. Much of the character of organisms is due to various symmetries, radial, bilateral, metameric and so forth, and these symmetries arise, partly at least, from the mode of growth by cell division and the marshalling of groups of cells to the places where they are destined to proliferate. Here, again, a variation in the order, nature and number of the divisions, in itself simple, may result in symmetrical or correlated changes in all the progeny of the affected embryonic part. Every new individual starts life (see REPRODUCTION) as a mass of germinal material derived from one or from two parents, but with a coherent individuality of its own. This individuality is the result of the particular selection of qualities it receives from its parents, a selection that obviously differs in different cases, as, save in the case of " identical twins," which are supposed to be the product of a single fertilized ovum, no individual pair of brothers, or pair consisting of brother and sister, are alike. We are still ignorant of the causes that deter-mine the associated selection of inherited qualities that go to the making of any individual. Those who have followed up the work of Mendel believe that the qualities of the new individual are a precise selection from and reconstruction of the parental qualities, and that were complete analysis possible, the characters of the new individual could be predicted with chemical accuracy. On other views of inheritance, there would be required for prediction knowledge not only of the immediate parents but of the whole line of ancestry, with the result that prediction could reach only some degree of probability for any single individual and be accurate only for the average of a sufficient number of individuals. But whatever be the theory of the mode of inheritance, or the mechanism by which the germinal plasm of an individual is made up, it is plain that there is correlation between the various qualities of an individual due to the mode of origin of its germ plasm as a selected individual portion of the parental germ plasm. Observed cases of correlation cover almost every kind ofanatomical and physiological fact, and range from simple cases such as the relation between height of body and length of face to such an unexpected nexus as that between fertility and height in mothers of daughters. The statistical investigation of correlations forms a new branch of biological inquiry, generally termed " Biometrics," inaugurated by F. Galton and carried on by Karl Pearson and the late W. F. R. Weldon. We quote from the article " Variation and Selection," in the tenth edition of this Encyclopaedia, an exposition of the biometric method by Weldon: The characters of individual animals or plants depend upon so many complex conditions, most of which are generally unknown to us, that the statements we can make concerning them are of a peculiar kind. We cannot predict with any exactness the characters of a single unborn individual; but if we consider a large number of unborn individuals, we can predict with considerable accuracy the percentage of individuals which will have the mean character proper to their generation, or will differ from that mean character within any assigned limits. So long as we confine our attention to one or two individuals, we fail to detect any order in the occurrence of variations; but when we examine large numbers we find that it is possible to arrange them in an orderly series, which can be easily and simply described. The series into which we can arrange the results of observing phenomena of complex causation, whether exhibited by living organisms or not, have certain properties in common, which are dealt with by the theory of chance. Many of the properties of such series, and the methods of de-scribing them, are dealt with elsewhere (see PROBABILITY: Law of Error) ; and the frequency with which the mean value or any deviation from the mean value of a character occurs in a race of animals or of plants may probably always be expressed in terms of one or other of the series there described. The theory of chance was applied to the study of human variation by Quetelet; but the most important applications of this theory to biological problems are due in the first instance to Francis Galton, who used the theory of correlation in describing the relation between the deviation of one character in an animal body from the mean proper to its race and that of a second character in the same body (correlation as commonly understood), or between . deviation of a parent from the mean of its generation and deviation of offspring from the mean of the following generation (inheritance). The conceptions indicated by Galton have been extended and added to by Karl Pearson, who has also developed the theory of chance so as to provide a means of describing many series of complex results in a simpler and more accurate way than was hitherto possible. The conception of a race of animals or of plants as a group of individuals capable of being arranged in an orderly series .with respect to the condition of a particular character enables us to define the " type " of that character proper to the race. Table I. shows the number of female swine which had a given number of " Muller's glands " on the right fore leg, in a sample of 2000 swine observed by Davenport in Chicago. If we take the whole number of glands in the series, and divide this by the whole number of swine, we obtain the mean number of glands per swine. For many purposes this is the most convenient " type " of the series. Two Number of Number of Number of Number of Glands. Swine. Glands. Swine. 0 209 5 15 6 134 2 36 7 72 3 482 8 22 IL 4 414 9 8 5 277 10 2 other ways of determining a " type" will be obvious by reference to the diagram, fig. I, in which the observed results are recorded by the thick continuous line, and the form of Pearson's " generalized probability curve " best fitted to represent them by a dotted line. The ordinate of the dotted curve which contains its " centre of gravity " has, of course, for its abscissa the " mean " number of glands; the maximum ordinate of the curve is, however, at 2.98, or sensibly at 3 glands, showing what Pearson has called the " modal" number of glands, or the number occurring most frequently. The ordinate which divides the area of the dotted curve into two equal areas is the median of Galton: it lies in this case nearly at 3.38 glands. The best simple measure of the frequency of deviations from the mean character is the " standard deviation " or " error of mean square " of the system (see article PROBABILITY), in this case equal to 1.68 glands. In cases of nearly symmetrical distribution about the mean, the three " types," the mean, the median and the mode, may sensibly coincide. For example, in Powis's table of the frequency of statures in male Australian criminals between 40 and 5o years of age (Biometrika, vol. i. part 1, p. 41), the mean stature is season by the same plant is an example of differentiation associated 66.91 in., the modal 66.96 in., the median lying between the with time of production; as this kind of differentiation is less familiar than differentiation according to the region of production, it may be well to give an example. In a group of plants of Aster prenanthoides, examined by G. H. Shull (American Naturalist, xxxvi., 1902), the mean number of bracts, ray-florets and disc-florets, and the standard deviation of each, was determined on four different days, with the following result 450 100 zoo 00 too a Sc~IE W Cw~M09 two. In other cases the difference between the three may be considerable. As an example of extreme asymmetry we may take de Vries's record of the frequency with which given numbers of petals occur in a certain race of buttercups. Pearson has shown (Phil. Trans., A., 1893) that this frequency may be closely represented by the curve whose equation is y = 0.2 11225X-0432(7 '3253 - x) 3.142 The curve, and the observations it represents, are drawn in fig. 2. The two are compared numerically in Table 1I. Here the mode is at 4.5 petals, the mean at 5.6 petals, the median lying of course between the two. Numbers of petals . 5 6 7 8 9 10 II Frequency observed. 133 55 23 7 2 2 0 Frequency given by 136.9 48.5 22.6 9.6 3.4 o•8 0.2 Pearson's curve . The distributions represented in figs. I and 2 may be taken as examples of three common forms of series into which the individuals of a race may be arranged with respect to a single character; a comparison of them will show how little can be learnt from a mere statement of racial type, without some knowledge of the way in which deviations from the type are distributed. The variability of structures which are repeated in the body of the same individual (serial homologues) has been studied by Pearson and his pupils with important results. The simplest of such repeated elements are the cells of the tissues, more complex are cell-aggregates, from hairs, scales, teeth and the like, ^p to limbs or metameres in animals, or the ioo leaves and their homologues in plants. Serially homologous structures, borne on the same body, are commonly differentiated into sets, the mean character of a set produced in one part of the body, or during one period of life, differing from the mean character of a set produced in a different region or at a different time. Such differentiation may be measured by determining the correlation between the position or the time of production and the character of the organs produced, the methods by which the correlation is measured being those de-scribed in the article ERROR, LAw OF. An excellent example of structures differentiated according to position is given by the appendages borne on the stein of an ordinary flowering plant—the one or two seed leaves; the stem leaves, which may or may not be differentiated into secondary sets; and the various floral organs borne at the apex of the stem or its lateral branches. The change which often occurs in the mean character and varia- bility of the flowers produced. at different periods of the flowering Sept. 27. Sept. 30. Oct. 4. Oct. 8. Mean No. of bracts . 47.41 44'34 43.83 41'92 Standard deviation 5'52 5.15 5.28 4'89 Mean No. of ray-florets 30.77 28.71 28.25 26'34 Standard deviation 3.99 3'57 3'50 3'01 Mean No. disc-florets . 56'43 51.71 49' 16 45.78 Standard deviation 3.99 4'99 4'88 4.78 Notwithstanding this differentiation, the mean character of a series of repeated organs is often constant through a considerable region of the body or a considerable period of time; and the standard deviation of an " array " of repeated parts, chosen from such an area, or within such limits of time, may be taken as a measure of the individual variability of the organism which produces them. If such an array of repeated organs be chosen from the proper region of the body, within proper limits of time, in each of a large series of individuals belonging to a race, and if all the arrays so chosen be added together, a series will be formed from which the racial variability can be determined. Thus a series of arrays of beech leaves, gathered, subject to the precautions indicated, from each of loo beech trees in Buckinghamshire by Professor Pearson, gave 16.1 as the mean number of veins per leaf, the standard deviation of the veins in the series being 1.735. The number of leaves gathered from each tree was 26, and the frequency of leaves with any observed number of veins in the whole series of 2600 leaves was as follows: No. of veins . Io II 12 13 14 15 16 17 18 19 20121 No. of leaves. I 7 34 110 318 479,595 516 307 181 36115 The whole series contains 2600 leaves. If a leaf from this series be chosen at random, it is clearly more likely to have sixteen veins than to have any other assigned number; but if a first leaf chosen at random should prove to have some number of veins other than sixteen, a second leaf, chosen at random from the same series, is still more likely to have sixteen veins than to have any other assigned number. If, however, a series of leaves from the same tree be examined in pairs, the fact that one leaf from the tree is known to possess an abnormal number of veins makes it probable that the next leaf chosen from the same tree will also be abnormal—or, in other words, the fact that leaves are borne by the same tree establishes a correlation between them. Professor Pearson has measured this correlation. Taking each leaf of his series, with an assigned number of veins, he has determined the array of pairs of leaves which can be formed by pairing the chosen leaf with all others from its own tree in succession. The pairs so formed were collected in a table, from which the correlation between the first leaf and the second leaf of a pair, chosen from one tree, could be determined by the methods indicated in the article PROBABILITY. The mean and standard deviation of all first leaves or of all second leaves will clearly be the same as those already determined for the series of leaves; since every leaf in the series is used once as a first member and once as a second member of a pair. The coefficient of correlation is 0.5699, which indicates that the standard deviation of an array is equal to that of the leaves in general multiplied by i — (0.5699)2; and performing this multiplication, we find 1.426 as the standard deviation of an array. The variability of an array of such a table—that is, of any line or column of it—is the mean variability of pairs of leaves, each pair chosen from one tree, and having one leaf of a particular character; it may therefore be taken as a fair measure of the variability of such a tree. We see therefore that while leaves, gathered in equal numbers from each of too trees, are distributed about their mean with a standard deviation of 1.735 veins, the leaves gathered from a single tree are distributed about their mean with a standard deviation of 1.426 veins, the ratio between variability of the race and variability of the individual tree being 1I I - (0.5699)2 =0.822. The correlation between undifferentiated sets of serial homologues, produced by a single individual, is the measure of what Pearson has called homotyposis. In an elaborate memoir on the homotyposis in plants (Phil. Trans., vol. 197 A., 1901), from which the foregoing statements about beech leaves are taken, Pearson has given the correlation between such sets of organs in a large number of plants: he and his pupils have subsequently determined the correlation between structures repeated in the bodies of individual animals. The results obtained are sometimes puzzling, because it is ~^^^^^^~ ^^^^^^^^ 111=1111111111111 =UM MIME U^^^^^^^ 1111111.11111.1 ^^^^^^^^ MI ^^ ^^^^^ ^^^^^^^ ^^^^^^^^ II MEE= ^^^^^ ~^^ ^11^^^^^^ . ^:^^^^^^ ^~U^^^^^ ^^1111^^^^ 111. MN! III II e 1 e v SCALE 0, PlT,9 22 I sometimes difficult to choose the whole series of structures osberved from a region of the body which is not affected by differentiation. In spite of this difficulty, however, the values of the correlation coefficients so far obtained cluster fairly well round the mean value of all of them, which is almost exactly z. From this result it follows (see PROBABILITY) that the standard deviation of the array, which we have taken as a measure of individual variability, is equal to the standard dcviation of the race multiplied by V 1— (2) 2 or by J 2. These results cannot be accepted as final, but they are based on so many investigations of animals and plants, of such widely different kinds, that they may confidently be expected to hold for large classes of organic characters. We may therefore conclude that for large classes of characters, both animal and vegetable, the variability of an individual, as measured by the standard deviation of its undifferentiated but repeated organs, is a constant fraction of the variability of its race, as measured by the standard deviation of the corresponding series of organs produced by all the individuals of its race. Among the most important structures produced in repeated series are the reproductive cells; and Pearson points out that if the variability of animals or of plants be supposed to depend upon that of the germ-cells from which they arise, then the correlation between brothers in the array produced by the same parents will give a measure of the correlation between the parental germ-cells, the determination requiring, of course, the same precautions to avoid the effects of differentiation as are necessary in the study of other repeated organs. After a large series of measurements, involving the most varied characters of human brothers, Pearson has shown that the correlation has a value very nearly equal to i; so that the variability of human children obeys the same law as that of other repeated structures, the standard deviation of an array, produced by the same parents, having an average value equal to the standard deviation of the whole filial generation multiplied by 1— (t) 2 or by 2. Such measurements of fraternal correlation in the lower animal as Pearson and his pupils have at present made give values very close to i. The evidence that the correlation between sexually produced brethren is the same as that existing between the asexually repeated organs on an individual body renders it impossible to accept Weismann's view that one of the results produced by the differentiation of animals and plants into two sexes is an increase in the variability of their offspring. Warren has shown by direct observation that the correlation between brothers among the broods produced parthenogenetically by one of the Aphides has a value not far from the z observed in sexually produced brethren (Biometrika, vol. i., 1902); he has obtained a fairly concordant result for the broods of parthenogenetic Daphnia (Prot. Roy. Soc. vol. ixv., 1899). Finally, Simpson has measured the correlation between the pairs of young produced by the simple asexual division of Paramoecium (Biometrika, vol. i. part 4, 1902), and after some necessary corrections the value he obtains is 0.56, a value which probably does not, if we remember the difficulties of the inquiry, differ very significantly from ;. There is therefore in a large class of cases an indication that the variability of an array of brethren, produced either sexually or asexually, is a constant fraction of the variability of the race to which the brethren belong. Variation and Mendelism.—The conceptions of the disciples of Mendel, amongst whom W. Bateson is pre-eminent, would appear to simplify the problem of variation, especially on its mechanical and physiological sides. Their experimental work shows that many facts of inheritance correspond with the theory that the essential fabric of an organism is a mosaic of unit characters. Such units frequently occur in pairs, one member of the pair being characterized by the presence, the other by the absence of a problematical body at least comparable with a ferment, the result of the presence or absence being a notable modification of the whole organism or of parts of it. According to their view, in the formation of the germ cells a segregation of the unit pairs occurs—that is to say, the peculiar body or ferment is handed on to one daughter-cell but not to the other. A similar kind of segregation may take place in the formation of the repeated parts of an organism, so that symmetrical repetition may be compared with normal heredity, and be due to the presence of similar factors in the divisions of the embryonic cells, whilst the differentiation of repeated parts may be due to the unequal distribution of such factors and be comparable with variation. On such an interpretation, variation would result from asymmetrical division and normal inheritance from symmetrical division. It is equally clear that there is a broad analogy between the kind of characters on which systematists often have to rely for the separation ofspecies and those which Mendelian workers have shown to behave in accordance with the Mendelian theories of mosaic inheritance with segregation. The analogy possibly may be extended to such cases as the occurrence of flora or fauna with alpine characters on the summits of mountains separated by broad zones of tropical climate. Segregated inheritance may have produced the appropriate combinations which were latent in the capacities of the race, and the exigencies of the environment protected them in the suitable localities. It is to be noticed, however, that the Mendelian conceptions are in no sense an alternative to Darwinism; at the most they would serve to assist in explaining the mechanism of variation, and by enlarging our idea of the factors, increase the rate at which we may suppose selection to work. Limitation of Variations; Orthogenesis.—Darwin and his generation were deeply imbued with the Butlerian tradition, and regarded the organic world as almost a miracle of adaptation, of the minute dovetailing of structure, function and environment. Darwin certainly was impressed with the view that natural selection and variation together formed a mechanism, the central product of which was adaptation. From the Butlerian side, too, came the most urgent opposition to Darwinism. How is it possible, it was said, that fortuitous variations can furnish the material for the precise and balanced adaptations that all nature reveals? Selection cannot create the materials on which it is supposed to operate; the beginnings of new organs, the initial stages of new functions cannot be supposed to have been useful. Moreover, many naturalists, especially those concerned with palaeontology, pointed to the existence of orthogenetic series, of long lines of ancestry, which displayed not a sporadic differentiation in every direction, but apparently a steady and progressive march in one direction. E. D. Cope put such a line of argument-in the most cogent fashion; the course of evolution, both in the production of variations and their selection, seemed to him to imply the existence of an originative, conscious and directive force, for which he invented the term " bathmism " (Gr. /3aBµos, a step or beginning). On the other hand, dislike of mystical interpretations of natural facts has driven many capable naturalists to another extreme and has led them to insist on the " all-powerfulness of natural selection " and on the complete indefiniteness of variation. The apparent opposition between the conflicting schools is more acute than the facts justify. Both sides concur in the position assumed by Darwin, that the word " chance " in such a phrase as " chance variation " does not mean that the occurrences are independent of natural causation and so far undetermined, but covers in the first place our ignorance of the exact causation. The implication of the phrase may go farther, suggesting that there is no connexion between the appearance of the variation and the use to which it may be put. No doubt a large amount of variation is truly indefinite, so that many meaningless or useless variations arise, and in one sense it is a mere coincidence if a particular variation turn out to be useful. But there are several directions in which the field of variation appears to be not only limited but defined in a certain direction. Obviously variations depend on the constitution of the varying organism; a modification, whether it be large or small, is a' modification of an already definite and limited structure. When beetles, or medusae, or cats vary, the range of possible variation is limited and determined by the beetle, medusa or cat constitution, and any possible further differentiation or specialization must be in a sense at least orthogenetic—that is to say, a continuation of the line along which the ancestors of the individual in question have been forced. Darwin himself showed that different species in a genus, or varieties in a species, tended to show parallel variations, whilst comparative anatomy has made known a multitude of cases where allied series of animals or plants show successive stages of parallel but independent variations of important organs and functions. The phenomena of convergence are to some extent other instances of the same kind and supply evidence that organisms, so to say, fall into grooves, that their possibilities of change are defined and limited by their past history. Variation, again, as has been shown in this article, is limited by correlation; as any change involves other changes, the possibilities are limited by the organic whole. Finally, it is important to remember that the fundamental characteristic of a living organism is its power of response to environment, a response or series of responses being necessary in a continuous environment for the normal facies of the organism to appear, and necessary in a shifting environment if the organism is to change suitably and not to perish. A continuous environment both from the point of view of production of variation and selection of variation would appear necessarily to result in a series with the appearance of orthogenesis. The past history of the organic world displays many successful series and these, as they have survived, must inevitably display orthogenesis to some extent; but it also displays many failures which indeed may be regarded as showing that the limitation of variation has been such that the organisms have lost the possibility of successful response to a new environment. Selection and Adaptation.—Although knowledge of variation has become much wider and more definite, the estimation in which natural selection is held has changed very little since Darwin and Wallace first expounded their theories. Variation provides the material for selection, and although opinions may differ as to the nature of that material, the modes by which it comes into existence and their relative values and permanences, there is an increasingly wide consensus of opinion that all such material has to pass through the sieve of natural selection and that the sifted products form new varieties and species, and new adaptations. It appears to be necessary to distinguish between the production of species and the production of adaptation. We have still to admit with Darwin that it is difficult or impossible to assign utility to all the characters that distinguish species, and particularly to those characters by which systematists identify species. The modern tendency for a more complete and detailed separation of individual forms into specific and sub-specific groups, and the immensely larger range of material at the disposal of systematic experts, have combined to make it increasingly difficult to imagine conditions of the environment under which the species of systematists would have been produced by selection. On the other hand, the work of modern systematists shows an extraordinarily exact relation between their species and geographical locality, and the fact of divergent evolution can be almost demonstrated in museum collections when localities have been recorded exactly. The decision as to whether it is the course of variation or the course of selection that has been different in different localities can be made only by the field naturalist and the experimental breeder. With regard to adaptations, it is becoming more and more apparent, as experimental knowledge advances, that it is a fundamental property of every living organism in every stage of its existence to display adaptive response to its environment. To what extent such responses are transmitted to offspring, and what part they play in the formation of the adaptive characters that are conspicuous in many animals, remain dubious, but it is at least clear that natural selection can favour those individuals and those races which show the greatest power of responsive plasticity in the individual. There remains open a wide field for inquiry as to the precise relations between selection and variation on the one hand, and their products, specific differences and adaptive structures, but the advance of know-ledge has supplied no alternative to the Darwinian principles. In the broadest way variation in organisms is primarily the necessary result of the absence of uniformity in the distribution of physical forces on the globe, in fact is a mere necessary response to the variation of inorganic conditions. So, also, in the broadest way, the result of the existence of variation is equally inevitable. Some individuals happen to fit the environment better, or to respond to the environment better, and these on the average will survive their less fortunate neighbours. It is plain that whilst the existence of variation can be demonstrated and the occurrence of evolution established by induction and deduction, the part played by selection must remain largely theoretical. We append, however, again from the late Professor Weldon's article, a summary of the lines on which it seems possible that the actual process of selection may be demonstrated. Selection and its results can be adequately studied only in those cases which admit of statistical tabulation. In any race of animals, the number of young produced in a season is almost always greater than the number which survives to attain maturity; it is not certain that every one of those which become mature will breed, and not all of those which breed contribute an equal number of offspring to the next generation. At every stage some individuals are prevented from contributing to the next generation, and if the continual process of elimination affects individuals possessing any one character more strongly than it affects others, so that a relation is established between individual character and the chance of producing a certain number of young, selection is said to occur. ,We may distinguish broadly two ways by which such selective elimination of individuals from the number of those who contribute to the next generation may occur, viz. a differential destruction, which prevents certain classes of individuals from breeding by killing them, and a series of processes leading to differential fertility among the survivors, without necessarily involving any differential death-rate. A third form of selection, which may affect the composition of the next generation without of necessity involving a differential death-rate or a differential fertility, is assortative mating, or the tendency of those members of one sex which exhibit a particular character to mate only with members of the other sex which exhibit the same or some other definite character. Differential fertility may be induced in either of two ways. Individuals may not be able to pair unless they possess a character which is absent, or insufficiently developed, in some members of the race. The kind of selection involved may then be measured by comparing those animals which pair with the general body of adults. This is what Darwin especially intended to denote by the term " sexual selection." Or, again, individuals of certain character may be able to pair, but the fertility of their union may not be the same as that of unions between individuals with other characters. This kind of selection, called by Pearson " reproductive " or " genetic " selection, may be measured by finding the correlation between the characters of the individuals which pair and the number of young produced. For an attempt to treat the whole problem of differential fertility and assortative mating numerically, see Pearson, The Grammar of Science, and edition, London, 1900. Assortative mating exists when individuals which mate are not paired at random, but a definite correlation is established between the characters of one mate and those of the other. This kind of selection is measured by the correlation between deviation of either mate from the type, and deviation of the other. Pearson has shown that Galton's function has a value of o•28 for stature of middle-class Englishmen and their wives. (P. C. M.)
VARIA (mod. Vicovaro)

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