2G 



Mr. S. M. Jacob. Inbreeding in a [Mar. 18, 



Dividing by 4 (the factor 8st is thus omitted), and collecting like terms, 

 the result is 



(P + ?) 2 [P (4p + q) (A A) + 6 pq (Aa) + q(p+±q) (aa)]. 

 Thus the progeny of brother-sister marriages is 8 st(p + q) 2 multiplied by 



p (4p + q) ( AA) + 6pq (Aa) + q(p + 4q) (act). (1) 

 This last expression gives the relative frequency of the protogenic, hybrid, 

 and allogenic constituents in the offspring. 



The percentage of pure recessives in the offspring of brother-sister 

 marriages is ff(ff + 4 q) ag a g a ^ ns ^ a percentage of ^ s i> in the offspring 

 of unrelated pairs. 



The relative frequency is the ratio of 1 + to unity. This increases 



indefinitely with the ratio p to q, that is with the greater rarity of the 

 allogenic element in the general non-inbreeding population. This result 

 will be seen to hold for the offspring of inbreeding couples, however distantly 

 related. For this reason the discussion of this point will be postponed for 

 fuller consideration when cousin marriages are dealt with. 



The absolute frequency of the allogenic constituent in the offspring of 



brother-sister marriages is ^ + ^(^ , which approaches zero when p/q is very 

 large. 



In the case given by Miss Elderton and Prof. Pearson this ratio is 1 /4. 

 For this value of the ratio, p/q = 1/3 approximately, and the proportion of 

 the allogenic constituent in the non-inbreeding population becomes l/5 - 29. 

 Thus, for an evil which is recessive and obeys the Mendelian formula, its 

 appearance in 25 per cent, of the offspring of brother-sister marriages must 

 be compared with 18*9 per cent, of patent evil in the offspring of non- 

 inbreeding couples. 



3. We will now turn to first cousin marriages. Mr. Snow's Table IV can 

 be shortly written out by collecting like terms in each sibling family, and 

 the same process as that used for obtaining the offspring of brother-sister 

 marriages can be readily applied. The fertility of the first sibling generation 

 when mated to similar first sibling families is taken to be 4t. It is not 

 necessary to give here the reduced table. 



Each constituent in Mr. Snow's Table IV denotes that there are 16.s 

 families, each with 42 members, and these members are brothers and sisters 

 to members of the same family, and first cousins to members of other families 

 in the group. Thus in all there are in each group 64 st individuals who are 

 either brothers and sisters or first cousins. 



