No. 600] SHORTER ARTICLES AND DISCUSSION 755 



would be greater than that of the unaffected and the total num- 

 ber of children would therefore be more than twice as great. 



Danforth, however, after raising this condition does not deter- 

 mine the number of affected children from the affected and un- 

 affected Fj individuals, but calculates the percentages of these 

 two classes of parents which produce at least one affected child. 

 He finds that eighty-six per cent, of the cataractous children of a 

 cataractous parent themselves produce some affected children and 

 thus presumably have mated with heterozygous normals. Of 

 the normal children from the same F 1 generation only ten per 

 cent, produce affected children. If the chances for securing 

 similar mates were the same these percentages should be approxi- 

 mately equal. The relation of ten to eighty-six which does not 

 conform to a one to two ratio as Danforth states that it should 

 necessarily deviates still more widely from a one to one ratio. 



There are two reasons why this deviation from a one to one 

 ratio can be expected in favor of a larger number of affected 

 matings giving affected children than of unaffected matings. 

 The first lies in the fact that matings of affected by heterozygous 

 normals should give a one to one ratio of affected and normal 

 children, whereas the matings of heterozygote by heterozygote 

 should give a ratio of one to three. As was emphasized in our 

 previous publication the only criterion by which it can be deter- 

 mined whether the mates to the two kinds of F x individuals are 

 heterozygotes or homozygotes is the production of at least one 

 affected child. In families with a small number of children the 

 matings which promise a one to one ratio would have a greater 

 chance of producing at least one affected child than matings 

 which promise a ratio of one affected to three unaffected chil- 

 dren. Hence more of the families of the latter than of the 

 former class would be omitted from the data. 



The other reason why the deviation that Danforth obtains can 

 be expected is that which has already been mentioned, namely, 

 that affected individuals are more likely to marry related indi- 

 viduals because of the greater difficulty of obtaining a mate than 

 the unaffected would have. The proportion of heterozygotes in 

 affected strains would be far higher than in the general popu- 

 lation, so that the chances of the two kinds of F x individuals mat- 

 ing with a heterozygous normal would not be equal as Danforth 

 considers them to be. 



It is recognized that these arguments are extremely indefinite 

 and that it is difficult to determine just how much value to give 



