But suppose that instead of individuals presenting one character in differing intensities, two individuals breed together distinguished by characters which we know to be mutually exclusive, such as A and B. Here again we may speak of the individuals producing the gametes as A and B, and the resulting zygote as AB. What will AB be like? The population here again may consist of many like A and like B. These two forms may have been breeding together indiscriminately, and there may have been many or few of either type in the pedigree of either A or B.
Here again Galton applied his method with remarkable success. Referring to the progenitors of A and B, determining how many of each type there were in the direct pedigree of A and of B, he arrived at the same formula as before, with the simple difference that instead of expressing the probable average intensity of one character in several individuals, the prediction is given in terms of the probable number of A’s and B’s that would result on an average when particular A’s and B’s of known pedigree breed together.
The law as Galton gives it is as follows:—
“It is that the two parents contribute between them on the average one-half, or (0·5) of the total heritage of the offspring; the four grandparents, one-quarter, or (0·5)2; the eight great-grandparents, one-eighth, or (0·5)3, and so on. Then the sum of the ancestral contributions is expressed by the series
{(0·5) + (0·5)2 + (0·5)3, &c.},
which, being equal to 1, accounts for the whole heritage.”
In the former case where A and a are characters which can be denoted by reference to a common scale, the law assumes of course that the inheritance will be, to use Galton’s term, blended, namely that the zygote resulting from the union of A with a will on the average be more like a than if A had been united with A; and conversely that an Aa zygote will on the average be more like A than an aa zygote would be.
But in the case of A’s and B’s, which are assumed to be mutually exclusive characters, we cannot speak of blending, but rather, to use Galton’s term, of alternative inheritance.
Pearson, finding that the law whether formulated thus, or in the modified form in which he restated it[16], did not express the phenomena of alternative inheritance known to him with sufficient accuracy to justify its strict application to them, and also on general grounds, proposed that the phenomena of blended and alternative inheritance should be treated apart—a suggestion[17] the wisdom of which can scarcely be questioned.
Now the law thus imperfectly set forth and every modification of it is incomplete in one respect. It deals only with the characters of the resulting zygotes and predicates nothing in regard to the gametes which go to form them. A good prediction may be made as to any given group of zygotes, but the various possible constitutions of the gametes are not explicitly treated.