Darwin refers the origin of these secondary sexual characters to processes of selection quite analogous to those of ordinary natural selection, only that in this case it is not the maintenance of the species which is aimed at, but the attainment of reproduction by the single individual. The males are to some extent obliged to struggle for the possession of the females, and every little variation which enables a male to gain possession of a female more readily than his neighbour has for this reason a greater likelihood of being transmitted to descendants. Thus, attractive variations which once crop up will be transmitted to more and more numerous males of the species, and among these it will always be those possessing the character in question in the highest degree which will have the best chance of securing a mate, and so the character will continue to be augmented as long as variations in this direction appear. Two kinds of preliminary conditions, however, must be assumed. As the ordinary natural selection could never have operated but for the fact that in every generation a great many individuals, indeed the majority of them, perish before they have had time to reproduce, so the process of sexual selection could never have come into operation if every male were able ultimately to secure a mate, no matter what degree of attractiveness to the latter he possessed. If the numbers of males and females were equal, so that there was always one female to one male, there could be no choice exercised either by male or female, for there would always remain individuals enough of both sexes, so that no male need remain unmated. But this is not the case: the proportions of the sexes are very rarely as 1 : 1; there is usually a preponderating number of males, more rarely of females. Among birds the males are usually in the majority, still more so among fishes; and among diurnal butterflies there are often a hundred males to one female (Bates), although there seem to be a few tropical Papilionidæ among which the females have rather the preponderance. Darwin called attention to the fact that one could infer the greater rarity of the females even from the pricelists of butterflies issued by the late Dr. Staudinger in connexion with his business, for the females in most species, except the very common ones, are priced much higher than the males, often twice as high. In the whole list of many thousands of species there are only eleven species of nocturnal Lepidoptera in which the males are dearer than the females.