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.