224 The TJieory of Ancestral Contributions in Heredity. 



We have the following table for various values of n : — 



No. of grandparents 

 with dominant 

 character. 



Percentages 



of offspring with dominant character. 





n = 10. 



= 4. 



= 2. 



= 1. 



_ i 



— 2- 



1 



— 4- 



1 



lO' 



4 



99 3 



97 



94 



89 



84 



80 



77 



3 



95 



90 



84 



78 



72 



68 



65 



2 



78 



72 



66 



59 



54 



50 



48 



1 



46 



42 



37 -5 



33 



30 



28 



26 























• 















When experimental work is adduced to demonstrate that ancestry has no 

 influence, it will on investigation be found that the writer is : 



(i) Confining his attention, as Mr. Darbishire, to isolated lines of inheritance, 

 with restricted matings ; 



(ii) Asserting that a gametic knowledge of parents is equivalent to a 

 gametic knowledge of ancestry. 



In neither case does the argument touch the ancestral position, which is 

 summed up in the assertions that if we measure inheritance by the resem- 

 blance of somatic characters between offspring and ancestry, then, in a 

 population mating at random : 



The more ancestors of any grade with a given somatic character the more 

 offspring with that character. 



For ancestry of different grades the influence is diminished in geometrical 

 progression at each stage. 



These principles were first deduced empirically from observations and 

 records without any theory as to the mechanism of heredity. If Mendelism 

 be true for any characters in cross-fertilised plants, then these principles 

 hold also for heredity in that plant-population, for they are essential features 

 of the Mendelian theory (and, as a matter of fact, of a good many other 

 determinantal theories). No proof or disproof of them can be directly 

 deduced from Mr. Darbishire's memoir, but since that memoir brings evidence 

 for the truth of Mendelian theory, it indirectly asserts the truth that 

 ancestry is influential, at least in the field where the biometrician expects 

 and asserts it to play a part. This paper contains only another aspect of 

 the results reached in 1904, but it provides in the simple case — the grand- 

 parentage — the actual percentage measures of , the influence of ancestry 

 according to Mendel. Its j ustification is the misinterpretation which is likely 

 to be placed on the statement that " there is nothing like ancestral 

 contributions within the limits of a single unit-character."* 

 * Daibishire, 'Koy. Soc. Proc.,' B, vol. 81, p. 71. 



