OTTENBERG AND BERES 915 



dividuals AR and AA, forming group A. A second mutation occurred later in the 

 same gene to B, giving individuals BR and BB, or group B. The three genes R, A, and 

 B form the group of triple allelomorphs of which R acts as a recessive gene. Inter- 

 marriages of the mutated A and B groups gave AB individuals. There are thus in the 

 four blood groups of Landsteiner only six genetic types, according to Bernstein. 



TABLE VI 

 Genetic Formul.\e of Bernstein 



Group O A B AB 



Genetic types RR AA,AR BB,BR AB 



This new terminology does not affect the original observation of von Dungern and 

 Hirschfeld that A and B do not appear in the children if they are absent in the parents. 

 We have here only a new Mendelian mechanism that in the opinion of its author 

 better fits the facts described by all workers. Furuhata and Kishi' recently have in- 

 dependently proposed a formula which is substantially the same as Bernstein's. 



Bernstein first attempts to show that the two-factor pair theory is untenable be- 

 cause, by calculation, it seems to require in nearly all races a much larger percentage 

 of group AB than the statistical data actually show. Bernstein's method of showing 

 this is to represent the frequency of gene A by the letter p, a by p, B by q, and b by q. 

 Then the frequencies of group O or aabb should be p^ • q^ In a similar manner he cal- 

 culates the expected frequencies of the other groups according to the two-factor hy- 

 pothesis. He derives from these the ratio: 



(A-hAB).(B-FAB)=AB, 



that is, the sum of the frequencies of groups A+AB times the sum of the frequencies of 

 groups B+AB should equal the frequency of AB(on the Hirschfeld theory). 



Working with his multiple-allelomorph hypothesis, Bernstein sets p equal to the 

 frequency of gene A, q to the frequency of gene B, and r to the frequency of gene R. 

 Since these are all the possibilities, it follows that p+q+r=i. He then calculates 

 from the observed frequencies of O, A, B, and AB the values of p, q, and r to find if 

 their sum is equal to i, as it should be. This Bernstein does as follows: 



The frequency of group O (RR) is r^ 

 The frequency of group A (AR,AA) is 2pr-|-p^ 

 The frequency of group B (BR,BB) is 2qr-t-q2 

 The frequency of group AB (AB) is 2pq 



Therefore 



From which 



0+ A = r^-l- 2pr-l-p^ = (r+p)% 

 0+B = r^-l-2qr-|-q' = (r+q)^ . 



q=i-T/0+A, 

 p = i^' 0+B, 

 r=v O, 



'Furuhata, T., and Kishi, T.: Japan Med. World, 7, i. 1927. 



