220 



Prof. K. Pearson. 



[Mar. 19, 



therefore, of the apparent contradiction between such experiments as those 

 of Mr. Darbishire and the theoretical development of the Mendelism which 

 they profess to establish ? 



It does not seem hard to account for the divergence. Experiments such 

 as those of Mr. Darbishire do not deal with a population as a whole, and 

 consider the contributions to the next generation of all its components 

 supposed to be mated at random. I feel quite certain that if Mr. Darbishire 

 makes the requisite crosses in due proportions, and does not weight with 

 differential fertility, he will find that ancestry does matter. That it does 

 matter is just as good a proof of Mendelism as Mr. Darbishire's proof in the 

 simpler case that it has not any effect. If he fails to find its influence, then 

 he will have refuted Mendelian theory. 



To illustrate my point, take a population distribution which would follow 

 from crossing two pure races with respectively dominant and recessive 

 characters represented by the letters D and E, Suppose the hybrids to 

 cross at random, then the population will remain absolutely stable with the 

 permanent formula 



(DD) + 2(DE) + (EE). 

 Now suppose this to cross with itself or with 



(DD) + 2(DE) + (EE). 



Table I gives the scheme of offspring with their parents. This population 

 of 16 individuals of 6 different types of parentage now crosses with itself. 

 The result is a population of 256 individuals showing 15 types of grand- 

 parentage. This is exhibited in Table II. If Mr. Darbishire's principle 

 that ancestry is of no importance were correct, then the differences in type 

 of these grandparents would not be of any significance. 



Table I. 



• 



Parents. 



Offspring. 



DD. 



DR, 



RR, 



DD, DD 



1 







DD, DR 



2 



2 





DD, RR 





2 





DR, DR 



1 



2 



1 



DR, RR 





2 



2 









1 



