Let us now apply all this to the institution of amphimixis and amphigony, and it is immediately obvious that these determinants of the germ-plasm which control the characters relating to sexual reproduction must be more stable and less variable than all others which a species possesses, for they are infinitely older. They are older than all species-characters, older than the characters of the genus, of the family, of the class, and indeed of the whole series or phylum to which a higher animal, a vertebrate, for instance, belongs. We cannot wonder, therefore, that amphigony has persisted through hundreds and thousands of generations, even if it had not been reinforced in the germ-plasm during this period by selection. We should rather wonder that an institution so primaeval, and so firmly engrained in the germ-plasm, can ever be departed from, even when its abandonment is to the advantage of the species, as has happened in parthenogenesis.
I have entered upon this long discussion because I believe that we require to appreciate this power of persistence on the part of the sexual determinants before we can explain the general occurrence of amphigony. The occurrence of pure parthenogenesis, unaccompanied by any degeneration of the species, can hardly be understood except on the assumption that the constancy of the species, when it has once been attained, may be preserved without the continual intervention of amphimixis. How long it can be preserved is another question, which it is difficult or impossible to answer, since species exhibiting pure parthenogenesis are rare, and since we cannot tell with certainty how long it is since amphimixis ceased to occur in them. Generally speaking, the answer in regard to the few species which have to be taken into account in this connexion would be 'not long,' but whether this 'not long' signifies hundreds of generations or thousands of generations we must leave undecided. So much only we can say, that in all species of animals in which the male sex has quite died out or has dwindled to a minimal remnant, there are as yet no traces of degeneration to be found, and that even organs which have fallen into disuse and become functionless because amphigony has disappeared, are nevertheless in several cases retained in perfect completeness. I shall return to this subject later on, but in the meantime I wish to work out our conception of the actual efficacy of amphigony or ordinary sexual reproduction, and thereby increase our understanding of its significance and power of persistence.
We have seen that amphigony not only renders possible the novel 'harmonious adaptations' which are continually required, but that it also leads, by a continual crossing of individuals, simultaneously with the elimination of the less fit, to a gradually increasing constancy of the species. This has been regarded by some writers as its sole effect; thus recently by Hatschek, whose view has already been refuted.
Haycraft also finds the significance of amphigony simply in the equalizing or neutralizing of individual differences which it effects. Quetelet and Galton have attempted to show that intercrossing leads to a mean which then remains constant. Haycraft supposes that a species can only remain constant if its individuals are being continually intercrossed, and that otherwise they would diverge and take different forms, because the 'protoplasm' has within itself the tendency to continual variation. The transformation of species is effected by means of this variation tendency, and the persistency and constancy of species which are already adapted to the conditions of their life are secured by the constant intercrossing of the individuals, and the consequent neutralization of individual peculiarities.
Although the cases already mentioned in which great constancy of species is associated with purely parthenogenetic reproduction do not tell in favour of the accuracy of the view just stated, yet the fundamental idea, that amphigony is an essential factor in the maintenance and even in the evolution of species, is undoubtedly sound. We should certainly find neither genera nor species in Nature if amphigony did not exist; but we cannot simply suppose that amphigony and variation are, so to speak, antipodal forces, the former of which secures the constancy of the species, the latter its transformation. In my opinion, at all events, there is no such thing as a 'tendency' of the protoplasm to vary, although there is a constant fluctuation of the characters—dependent on the imperfect equality of the external influences, especially of nutrition. This certainly results, as far as it takes place within the germ-plasm, in a continual upward and downward variation of the hereditary tendencies, and it would lead to increasing dissimilarity of the individuals were it not that amphigony is continually equalizing the differences by a constantly repeated mingling of individuals. Quetelet and Galton have shown that the tendency of this mingling is towards the establishment of a mean; the characters of Man, such as bodily size, fluctuate about a mean, which at the same time shows the maximum of frequency; and the frequency curve of the various bodily sizes assumes a perfectly symmetrical form, so that the average size is the most frequent, and deviations from it upwards or downwards occur more rarely in proportion to the amount of deviation, the largest and the smallest sizes occurring least frequently.
Thus an equalizing of variations by means of amphimixis really exists, and the question we have to ask is, How does it come about? The case is assuredly not the same as that in which equal quantities of red and white wine are mixed to make a so-called 'Schiller.' This is proved even by the fact that the mixture may turn out quite different even when the wines—the two parents—are alike: for the children of a pair are often dissimilar. And while the 'Schiller' cannot be separated again into red wine and white, this happens often in sexual reproduction, and sometimes to such an extent that the grandchild exactly resembles one or other of the grand-parents, as is most clearly proved in the case of plant-hybrids.
There is thus a deep-seated difference, depending on the fact that what is mingled in amphigony is not simple but composite, not a simple uniform developmental tendency associated with a simple and definite substance, but a combination of several or many developmental tendencies, associated with several equivalent but different material units. These units are the ids or ancestral plasms, and we have seen how they are not only halved by reducing division, but are also arranged in new combinations in amphimixis.
These ids differ very little within the same germ-plasm; in species which have long been established the majority probably only differ in correspondence to the individual differences of the fully-formed organisms, but they are only absolutely alike in the case of two ids which have been formed by the division of a mother-id. Let us disregard this for the moment, and assume that all the ids of a germ-plasm are different: the germ-plasm of a father, A, will be composed of ids A 1-100, that of the mother, B, of the ids B 1-100. But in each mature germ-cell of these two parents only fifty ids are contained, and if we assume that the mingling of the ids is controlled solely by chance, then in the various germ-cells A × B the most diverse combinations of ids may be contained; for instance, A 1, 3, 5, 7, 9, 11, ...to 99, or A 1-10 and 20-30, and 40-50, and so on, and similarly in the germ-cells B. If all germ-cells produced by A and by B attained to development, or even if all the ova succeeded, the thousand or hundred thousand children of this pair would necessarily exhibit every possible mingling of their characters, and each in the same number according to the rules of probability calculations. But it is well known that this does not happen; of the thousands of human ova, for instance, which come to maturity in the course of the life of a female individual more than ten rarely develop, and more than thirty never, and these are determined solely by chance and quite independently of the mixture of ids which they contain. It is thus purely a matter of chance which of the complexes of primary constituents contained in the germ-plasm of an individual are transmitted to descendants, and it is also purely a matter of chance which combination of ids comes to be developed. Therefore we may say that no regular neutralizing of contrasts, either in the primary constituents of the parents or as regards the differences in their characters, can occur. In one case there is a blended inheritance; in another the child takes after the father or after the mother; in a third, and this probably occurs most frequently, the child resembles the father in some characters and the mother in others.
But how then does Galton's curve of frequency of variations come about? Why does the mean of any character occur by far the most frequently, and why does the frequency of a variation diminish regularly in proportion to its approximation to either extreme? To this it is answered: Because the process of mingling through amphigony goes on through numerous generations, and thus an elimination of chance, and the establishment of an average, must be brought about.
But this does not quite suffice to explain matters, for experience shows that asymmetrical frequency-curves of variations also occur, even in species with sexual reproduction. As De Vries has recently shown, there are also 'half-Galton curves,' that is, curves which suddenly break off at their highest point. We must conclude from this that the frequency of the different variations depends not only on their degree, but also on the greater or less facility with which they arise from the constitution of the species.