Abstract (1) The population to be considered in this paper is supposed to be initated by a group of s1 individuals with the protogenic constitution (aa), and s3 individuals with the hydrid constitution (Aa), where the mating is given by the simple Mendelian formula: (AA) X (aa) = 4 (Aa). I do not assume at this stage any relation between the gametic constitution of an individual and its somatic character. I propose first to consider the correlation between any ancestor and the resulting array of offspring, when we regard only their gametic constitutions. I assume that all mating in the population is random, i. e. That every possible mating occurs simply in the population, and that there is no differential fertility or selective death-rate. In a paper published in the “Phil. Trans.,’ vol. 203, A, 1904, P. 53 et seq., I have dealt with the correlation between the somatic characters of the ancestry and the offspring in an population of a Mendelian character, more general in that I supposed the character to depend upon n couplets, and not a single Mendelian couplet, less general in that I supposed the population to have arisen from a series of initial hybridisations, and not form a mixture as in the present case of hybrids and numbers of two pure races in any proportions. In that paper I showed (a) that there was correlation between any ancestor and the offspring, (b) that the regression for any ancestor and the offspring was linear, and (c) that the correlations decreased in geometrical progression. These are the chief characteristics of the Law of Ancestral Heredity. It was clear that, judged by somatic characters only. Ancestry was of importance. The result depended on Mendel’s first principle of dominance being absolutely true. The values of the correlations were, how ever, less than those with which biometric work had made us familiar.
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A 1909 study studied this question.