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 ½. 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 deviation of the race multiplied by
or by . 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 ½; 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 or by . Such measurements of fraternal correlation in the lower animal as Pearson and his pupils have at present made give values very close to ½. 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 ½ observed in sexually produced brethren (Biometrika, vol. i., 1902); he has obtained a fairly concordant result for the broods of parthenogenetic Daphnia (Proc. Roy. Soc. vol. lxv., 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 ½. 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 of species 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. βαθμός, 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
