Although the distribution of the rods in this manner takes place twice in succession, the normal number is not, as we have already seen, reduced to a quarter, because, long before the occurrence of the first maturing division, a duplication of the rods by means of longitudinal division had taken place, and thus the first division differs from an ordinary division in that the splitting of the rods does not take place during the process of dividing but long beforehand. Only the second maturing division differs from all other nuclear divisions known to us, since it is not associated with any splitting of the rods at all, but conveys half of the existing rods into each daughter-nucleus. It is the time reducing division, through which the number of the rods is reduced to one half[4].
[4] Recent investigations have shown that the reduction of the chromosomes does not always take place exactly in accordance with the scheme here indicated, but that it differs from it in many cases. But as investigations on this point are as yet by no means complete, I need not go into the question further; the ultimate result is the same in any case.
This numerical reduction must, however, have other consequences; it must make the germ-cells of the same individual qualitatively unlike, that is, in relation to their value in inheritance. Let us assume only four chromosomes of the rod-form ('idants') as the nuclear elements of a species, two of which, A and B, come from the mother, and other two, C and D, from the father, the last maturing division may, as far as we can see, result either in removing the combination A and B from C and D, or A and C from B and D, or A and D from B and C; there is thus a possibility of one of six different combinations of rods in any one germ-cell. What is the same thing, six different kinds of germ-cells differing in their hereditary primary constituents may be developed in the same individual. As this new combination, or, as we may call it, neotaxis of the germ-plasm elements, takes place in female as well as in male individuals, there is a possibility that, in fertilization, 6 × 6 = 36 individuals with different primary constituents may arise from the germ-cells of the same two parents. Of course the number of possible combinations increases very considerably in proportion to the normal number of rods, for with eight of these it comes up to 70, and with sixteen to 12,870; the number of individuals differing in their inherited primary constituents would thus be enormous, for each of the 70 or of the 12,870 different hereditary minglings of the ovum could combine in amphimixis with 70 or 12,870 different sperm-cells, so that 70 × 70 and 12,870 × 12,870 offspring individually different in their primary constituents might arise from the same two parents. In Man there are said to be sixteen nuclear rods; so that in his case the last-mentioned number of parental hereditary minglings might occur. This may seem a disproportionately high number as compared with the small number of children of a human pair, but we must not judge from the case of Man alone, and in plants and animals, which we have already discussed, the number of descendants is very much larger, and is often enormous. We saw what significance this apparent extravagance on the part of nature has, for without it adaptation to changed conditions of life would not be possible, since, if only so many were born as could attain to reproduction, no selection of the fittest could take place. The same would be the case if all the young of a species were alike, and even if all the descendants of a single pair were alike, effective selection would be excluded, since only as many individualities could be selected as there were pairs of parents. It is easy to understand that selection works more effectively the larger the number of descendants of a species and the more they differ from each other. The chance that the best possible combination of characters will occur is thereby increased.
Although we cannot calculate how many individuals of different combinations of characters natural selection requires to work upon in order to direct the evolution of the species[5], we can understand that only as large a choice as possible can secure that the best possible adaptations of all parts and organs are brought about and maintained. Precisely in the fact that in every generation such an enormous superfluity of individuals is produced lies the possibility of such intensive processes of selection as must continually take place, if the adaptation of all parts is to be explained. For if among the thousands of descendants of a fertile species each hundred were alike among themselves, these hundreds would have, as far as natural selection was concerned, only the value of a single variant. But such an all-round adaptation as actually exists in the structure of species requires as many variants as possible; it requires that each individual should be a peculiar complex of hereditary characters; that is, that all the fertilized germ-cells of a pair should possess an individually well-marked character.
[5] For this reason I have left the number of id-combinations given above unaltered, though, according to the most recent researches into the processes of maturation, they are probably too high, since every conceivable combination does not actually occur. We are here concerned less with the exact number than with the principle.
The justification of this postulate becomes all the clearer if we take into consideration the male germ-cells as well as the female. Let us think of the enormous number of sperm-cells which are produced by many animals, and indeed by the highest of them—an almost incalculably large number which certainly goes far beyond millions. Let us assume that in Man there may be 12,870 million spermatozoa, then, with sixteen ids, and with an equally frequent occurrence of all possible combinations of germ-plasm—there would be 12,870—there would be a million of each type containing identical germ-plasm. The danger that several ova would be fertilized by identical sperm-cells would be by no means small.
It cannot, therefore, surprise us that other means have been employed by Nature to secure re-groupings of the ids. The simplest means would be, if before each division of the primitive germ-cells the nuclear rods were to divide, and if the split halves were irregularly intermingled, then at the formation of the next nuclear spindle an entirely new arrangement of the halves would result. But in animals, at least, this is certainly not the case; the processes of reduction are restricted to the maturing divisions.
Years ago Ischikawa observed that, in the conjugation of Noctiluca, the nuclei of the two animals become closely apposed, but that they do not fuse, although they behave like a single nucleus in the division which follows. In this case paternal and maternal nuclear substance remain separate ([Fig. 83, vol. i. p. 317]). The same phenomenon has since been repeatedly observed in many-celled animals, first by Häcker, then by Rückert in the Copepods, and afterwards by Conklin in the eggs of a Gastropod (Crepidula). But all these observations referred only to the earlier stages of ovum-segmentation up to twenty-nine cells, and it could not be affirmed that the distinctiveness of the paternal and maternal chromosomes lasted till farther on into the ontogeny. Professor Häcker now informs me, however, that he has been able to trace this separateness in a Copepod (Canthocamptus) not only from the beginning of segmentation on to the primitive genital cell, but also through the divisions of this up to the mother-egg-cell[6]. Thus we may now assume that the paternal and maternal hereditary bodies remain distinct, not only for a time, but throughout the whole development, a fact which confirms our assumption of the independence of the nuclear rods, notwithstanding their apparent breaking-up in the nuclear reticulum of the 'resting' nucleus. This new knowledge throws fresh light in another direction; it proves to us that the remarkable and complicated processes which go on in the nucleus during the maturing divisions have really the significance which I long ago ascribed to them[7], that of effecting the maximum diversity of intermingling of the paternal and maternal hereditary elements. For Häcker has shown that during the second maturation-division the paternal and maternal chromosomes are no longer united each in a special group, but occur scattered about in the nucleus, and subsequently come together again to form two differently combined groups.
[6] Since this was written Häcker has published his results. See Anatom. Anzeiger xv (1902), p. 440.
[7] See my essay, Amphimixis, Jena, 1891.