To the above popular presentation of the essential facts, made for an audience not strictly scientific, some addition, however brief, is called for. First, in regard to the law of Ancestry, spoken of on p. [5]. Those who are acquainted with Pearson’s Grammar of Science, 2nd ed. published early in 1900, the same author’s paper in Proc. R. S. vol. 66, 1900, p. 140, or the extensive memoir (pubd. Oct. 1900), on the inheritance of coat-colour in horses and eye-colour in man (Phil. Trans. 195, A, 1900, p. 79), will not need to be told that the few words I have given above constitute a most imperfect diagram of the operations of that law as now developed. Until the appearance of these treatises it was, I believe, generally considered that the law of Ancestral Heredity was to be taken as applying to phenomena like these (coat-colour, eye-colour, &c.) where the inheritance is generally alternative, as well as to the phenomena of blended inheritance.
Pearson, in the writings referred to, besides withdrawing other large categories of phenomena from the scope of its operations, points out that the law of Ancestral Heredity does not satisfactorily express the cases of alternative inheritance. He urges, and with reason, that these classes of phenomena should be separately dealt with.
The whole issue as regards the various possibilities of heredity now recognized will be made clearer by a very brief exposition of the several conceptions involved.
If an organism producing germ-cells of a given constitution, uniform in respect of the characters they bear, breeds with another organism[13] bearing precisely similar germ-cells, the offspring resulting will, if the conditions are identical, be uniform.
In practice such a phenomenon is seen in pure-breeding. It is true that we know no case in nature where all the germ-cells are thus identical, and where no variation takes place beyond what we can attribute to conditions, but we know many cases where such a result is approached, and very many where all the essential features which we regard as constituting the characters of the breed are reproduced with approximate certainty in every member of the pure-bred race, which thus closely approach to uniformity.
But if two germ-cells of dissimilar constitution unite in fertilisation, what offspring are we to expect[14]? First let us premise that the answer to this question is known experimentally to differ for many organisms and for many classes of characters, and may almost certainly be in part determined by external circumstances. But omitting the last qualification, certain principles are now clearly detected, though what principle will apply in any given case can only be determined by direct experiment made with that case.
This is the phenomenon of cross-breeding. As generally used, this term means the union of members of dissimilar varieties, or species: though when dissimilar gametes[15] produced by two individuals of the same variety unite in fertilisation, we have essentially cross-breeding in respect of the character or characters in which those gametes differ. We will suppose, as before, that these two gametes bearing properties unlike in respect of a given character, are borne by different individuals.
In the simplest case, suppose a gamete from an individual presenting any character in intensity A unite in fertilisation with another from an individual presenting the same character in intensity a. For brevity’s sake we may call the parent individuals A and a, and the resulting zygote Aa. What will the structure of Aa be in regard to the character we are considering?
Up to Mendel no one proposed to answer this question in any other way than by reference to the intensity of the character in the progenitors, and primarily in the parents, A and a, in whose bodies the gametes had been developed. It was well known that such a reference gave a very poor indication of what Aa would be. Both A and a may come from a population consisting of individuals manifesting the same character in various intensities. In the pedigree of either A or a these various intensities may have occurred few or many times. Common experience leads us to expect the probability in regard to Aa to be influenced by this history. The next step is that which Galton took. He extended the reference beyond the immediate parents of Aa, to its grandparents, great-grandparents, and so on, and in the cases he studied he found that from a knowledge of the intensity in which the given character was manifested in each progenitor, even for some few generations back, a fairly accurate prediction could be made, not as to the character of any individual Aa, but as to the average character of Aa’s of similar parentage, in general.