Heredity and Continuous Variation
It has been to a certain extent assumed in the preceding pages that both parents are alike, or, if different, that they have an equal influence on the offspring. This may be true in many cases for certain characteristics. Thus a son from a tall father and a short mother may be intermediate in height, or if the father is white and the mother black, the children are mulattoes. But other characters rarely or never blend. In such cases the offspring is more like one or the other parent, in which case the inheritance is said to be exclusive. Thus if one parent has blue eyes and the other black, some of the children may have black eyes and others blue. There are also cases of particular inheritance where there may be patches of color, some like the color of one parent, some like that of the other parent. The latter two kinds of inheritance will be more especially considered in the subsequent part of this chapter; for the present we are here chiefly concerned with blended characters.
How much in such cases does each parent contribute to the offspring? This has been expressed by Galton in his law of ancestral heredity. This law takes into account not only the two parents, but also the four grandparents, and the eight great-grandparents, etc. There will be 1024 in the tenth generation. These 1024 individuals may be taken as a fair sample of the general population, provided there has not been much interbreeding. Are we then to look upon the individual as the fused or blended product of the population a few generations back? If this were true, should we not expect to find all the individuals of a community very much alike, except for the fluctuating variations close around the mode?
As a result of his studies on the stature of man, and on the coat color of the Basset hounds, Galton has shown that the inheritance from the parents can be represented by the fraction 1/2; that is one-half of the peculiarities of the individual comes from the two parents. The four grandparents together count for 1/4 of the total inheritance, the great-grandparents 1/8, and so on, giving the series 1/2, 1/4, 1/8. Pearson, taking certain other points into consideration, believes the following series more fully represents the inheritance from the ancestors, .3, .15, .075, .0375, etc. He concludes that, “if Darwinism be the true view of evolution, i.e. if we are to describe evolution by natural selection combined with heredity, then the law which gives us definitely and concisely the type of the offspring in terms of the ancestral peculiarities is at once the foundation stone of biology and the basis upon which heredity becomes an exact branch of science.”
The preceding statements give some idea of what would occur in a community in which no selection was taking place. The results will be quite different, although the same general law of inheritance will hold, if selection takes place in each generation. If, for instance, selection takes place, the offspring after four generations will have .93 of the selected character, and without further selection will not regress, but breed true to this type.[[22]] “After six generations of selection the offspring will, selection being suspended, breed true to under two per cent divergence from the previously selected type.”
[22]. In this statement the earlier ancestors are assumed to be identical with the general type of the population.
If, however, we do not assume that the ancestors were mediocre, it is found that after six generations of selection the offspring will breed true to the selected type within one per cent of its value. Thus, if selection were to act on a race of men having a mode of 5 feet 9 inches, and the 6-foot men were selected in each generation, then in six generations this type would be permanently established, and this change could be effected in two hundred years.[[23]]
[23]. Quoted from Pearson’s “Grammar of Science.”
Thus we have exact data as to what will happen on the average when blended, fluctuating variations are selected. Important as such data must always be to give us accurate information as to what will occur if things are left to “chance” variations, yet if it should prove true that evolution has not been the outcome of chance, then the method is entirely useless to determine how evolution has occurred.
More important than a knowledge of what, according to the theory of chances, fluctuating variations will do, will be information that would tell us what changes will take place in each individual. In this field we may hope to obtain data no less quantitative than those of chance variations, but of a different kind. A study of some of the results of discontinuous variation will show my meaning more clearly.