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The Theory of Ancestral Contributions in Heredity.. 

 By Karl Pearson, F.R.S. 



(Received March 19,— Read April 22, 1909.) 



Under the above title a paper has recently appeared by Mr. A. D. 

 Darbishire in the ' Roy. Soc. Proc.,' vol. 81, B, p. 61 et seq., giving further 

 experimental evidence with regard to the inheritance of certain characters 

 in peas. The paper is an interesting one, but the method adopted is not, 

 I venture to think, capable of answering the problem which the author set 

 himself. It has been supposed by some Mendelians that the theory of 

 inheritance summed up in the " law of ancestral heredity " was in some way 

 invalidated by investigations such as Mr. Darbishire's, and that opinion 

 consciously or unconsciously seems to be expressed in the paper just 

 referred to. The law of ancestral heredity is embraced in the following 

 statements : — 



(i) In a population breeding without assortative mating the regression line 

 for offspring on any ancestor is linear. 



(ii) The correlations between offspring and the successive grades of 

 ancestry form a progression diminishing geometrically as we ascend to distant 

 grades ; and 



(hi) The general relation of an individual to his ancestry can be closely 

 expressed by the multiple correlation formula. 



In a memoir published in the ' Phil. Trans.,' vol. 203, pp. 53-86, I showed 

 that these principles held for material obeying Mendel's laws — in particular 

 (i) and (ii) hold for the simple case of alternative characters such as are 

 said to occur in the case of peas. 



The only instance that I am aware of in which ancestry does not matter 

 is that in which the geometrical progression is of the form : 



p, p 2 , p 3 , .... 



I treated this case at length in the ' Phil. Trans.,' vol. 187, A, pp. 304-6 

 (1896), remarking that the grandparents were quite indifferent, when the 

 parents had been selected. Unfortunately, this is not true when the 

 correlation coefficients are 



1 1 1 1_ 1 1 1 



3' 2 X 3' 2 2 *3' 2 3X 3' ' 



as is the case with the somatic correlations on the Mendelian theory. In other 

 words, ancestry does matter in the latter theory. What is the explanation, 



