![]() He believed, following Darwin (1868), that reversion, which gives rise to this distinction, occurs because only some of the hereditary elements (the patent or personal elements) are expressed, the rest being latent, that is to say, unexpressed but capable of transmission. In this passage Galton distinguishes clearly between the phenotype (personal features) and the genotype (of which every child receives half from each parent). The question I have to solve, in a reasonable and not merely in a statistical way, is, how much less? Therefore the child does not on the average receive so much as one half of his personal qualities from each parent, but something less than a half. Though one half of every child may be said to be derived from either parent, yet he may receive a heritage from a distant progenitor that neither of his parents possessed as personal characteristics. In the Introduction to Natural Inheritance ( Galton, 1889) he framed the problem as follows:Ī second problem regards the average share contributed to the personal features of the offspring by each ancestor severally. This explanation led him to ask how much the child inherited, on average, from each of his ancestors, and hence to formulate the ancestral law. He explained filial regression as resulting from reversion to ancestral values (‘The child inherits partly from his parents, partly from his ancestry’), together with the fact that ancestral values are likely to deviate less from the mean than the mid-parent does. Galton's rather different derivations of the law in 18 are described, and their shortcomings are discussed in the light of these results ( Galton, 1885, 1897). The former equation reduces to Galton's ancestral law when the proportion of latent elements is 0.5, the latter when this proportion is 0.6. The equation representing ancestral contributions to the heritage of the offspring differs from the multiple regression equation for predicting the value of a trait from ancestral values. The resulting law has a free parameter to be empirically estimated which represents the frequency of latent hereditary elements that are not expressed in a particular individual but are capable of transmission to the next generation. ![]() A logical reconstruction of the law is presented based on formalizing Galton's model of heredity outlined in Natural Inheritance ( Galton, 1889). He interpreted this law both as a representation of the separate contributions of each ancestor to the heritage of the offspring and as a multiple regression formula for predicting the value of a trait from ancestral values. ![]() Galton's ancestral law states that the two parents contribute between them on average one-half of the total heritage of the offspring, the four grandparents one-quarter, and so on.
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