THE AMERICAN NATURALIST 



[Vol. L 



genital cataract is so rare (perhaps 1 in 4.000 or 5.000)° that the 

 number of heterozygous individuals in the general population 

 must be relatively low— theoretically not more than 1 : 30. 7 In 

 other words, if congenital cataract were recessive the chances that 

 an affected individual in marrying would get a heterozygous 

 partner and thereby be able to produce affected children would 

 be only one in thirty and the chances that the same thing would 

 happen in several generations in direct descent as occurs repeat- 

 edly in the charts (the case in over 40 different family trees) 

 become extremely remote. We should not then expect families 

 with one cataraetous parent to contain affected children more 

 often than in the above proportion. 8 



2. If congenital cataract were recessive the normal children of 

 a cataraetous parent should themselves produce affected children 

 in half as many cases as do their cataraetous sibs and the total 

 number of affected children produced should be one half as great 

 in the first case as in the second. This expectation follows from 

 the assumption that the original (grandparental) mating was 

 Nn X nn. As a result of such a mating the F 1 generation can 

 be composed only of Nn and nn individuals. Neither of these 

 should produce affected children except when married to an Nn 

 (or an nn), and the chances of such a marriage are as great (or 

 as remote) in the one case as in the other. In other words, an 

 equal number of heterozygous and pure recessive individuals of 

 the F 1 generation should get heterozygous mates. In these few 

 families the expectation for F 2 would then be of a 1 : 3 ratio for 

 the Nn X Nn matings and a 1 : 1 ratio for the Nn X nn, which 

 would obviously give one half as many affected children in the 

 first case as in the second. 



Harman's charts afford sufficient data to settle these points 

 conclusively. In regard to the first point there are 96 cases in 

 which the cataraetous child of a cataraetous parent has himself 



etc. ^Itfe Probably not too low, but if 'the incidence were as much as 1: 100 



i This result is arrived at by the use of a formula similar to one given by 

 Jennings in his paper "The Numerical Eesults of Diverse Systems of 

 Breeding," in Genetics, Vol. 1, No. 1, pp. 53-89. Jennings is not respon- 

 Slb 8Cor r b^ ^ ° f f ° rmUlae in this eonilectioil > but the 7 obviously apply, 

 retinitis pigmentosa in the paper by Usher already referred to. 



