1909. ] The Theory of Ancestral Contributions in Heredity. 223 



or its constituents will be proportional to 



(p + q) 2 (DD) + 2 (p + q) (s + q) ( DE) + (s + q) 2 (EE), 



and this ratio is maintained ever afterwards.* 



A little consideration will show that our Table II is obtained by a 

 symbolic process which will not be affected if we replace D by (p 4- q) D 

 and E by (s + q) E, so that to exhibit the results for a Mendelian population 

 of any constituent proportions we have only to multiply all the numbers 

 in any row of offspring of Table II by (2? + g) 2 for a DD grandparent, by 

 (p + q) (s + q) for a DE grandparent, and by (s + q) 2 for an EE grandparent, 

 starting with the stable population which arises after the first random 

 mating. We then reach the following table for the case of classification 

 by somatic characters, where for brevity I write : p + q = ir, s + q = k, and 

 7j- 2 / k 2 = n — ratio of pure dominants to recessives in the stable population. 

 It will be seen that whatever be the proportions of the Mendelian com- 

 ponents in the original population, then a selection of grandparents influences 

 widely the somatic characters of the offspring. 



Whether, therefore, Mendelism be or be not the final word as to inheritance 

 (and I personally, especially in the case of human characters, must continue 

 to suspend my judgment), it is clear that ancestral influence cannot be 

 denied in the ease of an} r population mating at random and inheriting on 

 Mendelian lines. 



Table III. 



TSo. of grandparents with 

 dominant character. 



Percentage of offspring 

 with dominant character. 



4 



+ (> i + 3 ) 







3 



100 (» + l) (2* + 5) 





2(» + 2) 2 



2 



100 + n) (k + ^ 



6{r + 2)- 



1 



100 





2{n + 2) 











* The stability after the first generation is very obvious, but. as far as I know, wasv 

 first stated in print by G. H. Hardy, ' Science/ vol. 28, p. 49. 



