ELIMINATING FEEBLEMINDEDNESS 



Ten Per Cent of American Population Probably Carriers of Mental Defect — If 



Only Those Who Are Actually Feebleminded Are Dealt with, It 



Will Require More Than 8,000 Years to Eliminate the 



Defect New Method of Procedure Needed 



R. C. PUNNETT 



Fellcw of Gonville and Cains College, Arthur Balfour Professor of Genetics in the 



University oj Cambridge, England 



IX AX article on "Hidden Feeble- 

 mindedness," which appeared in the 

 JoiRNAL OF Heredity for May, 

 1^>17, Dr. E. M. East raises a point 

 of great practical imijortance for stu- 

 dents of eugenics. Briefly, it amounts 

 to this: if we know the proportion of 

 individuals exhibiting a simple recessive 

 character in a given population, can we 

 decide what jjroportion of the dominants 

 is heterozygous!" Under certain condi- 

 tions, the required answer can be 

 readily and easily obtained. Some 

 years ago, G. H. Hardy' showed that a 

 mixed population containing p homo- 

 zygous dominants, r recessives, and 2q 

 heterozygous dominants was in stable 

 equililjrium when the equation pr = q- 

 was satisfied. It was assumed that 

 there was random mating and equal 

 fertility among the different classes. 

 Hardy further showed that if the 

 condition of equilibrium were u])sct 

 through some disturbing agency the 

 pojmlation would rapidly fall into a 

 new pH)sition of equilibrium which would 

 be maintained in the absence of an\- 

 fresh disturbance. If we know that 

 one of the two classes of homozygotes 

 is less numerous than the other we 

 can simjjlify the equation by considering 

 the less numerous class as unity. Let 

 us suppose that the recessives are less 

 numerous than the homozygous domin- 

 ants so that p = xr where x is some 

 number greater than one. Then if 

 r=l, the ecjuation pr = q'^ l)ecomes 

 x = q^, and for an ])0])ulation in ec|uilib- 

 rium the number of hetcrozygotes 

 (2q) = 2>ix. The total i)opulation thus 



consists of the three classes: homozy- 

 gous dominants, hetcrozygotes, and 

 recessives in the relati\'e proportions 

 x: 2\jx:\. Now if we know the j^ercent- 

 age of recessives in the total population, 

 we can easily calculate the relative 

 numbers of the three classes. For 

 instance, in the case at issue, Dr. East 

 states that the proj)ortion of feeble- 

 minded in the pojmlation of the L^nited 

 States is 3 per 1,000, or 1 in ?>i?>. Here 

 therefore : 



:. (\lx^\Y-= m 



V'-v-hl = N/,V.3 

 V.\= 17.25 

 2V.v= i\.':> 



In other words, the proi)ortion of hcter- 

 oz3^gotes in such a population is rnthcr 

 more than 10%. The proportion is 

 somewh^ higher than the 7% arrived 

 at by Dr. East, though we must remem- 

 ber that he considers his result to 

 understate rather than to overstate the 

 facts. 



In making the al)ove estimation of the 

 proportion of hetcrozygotes, certain 

 assum])tions have been made. Like 

 conditions must hold with regard to the 

 birth rate and death rate of the difTercnt 

 classes, the distribution of the factors 

 must be similar in both se.xes, and there 

 must be no selective mating. Further, 

 the ])o]nilation at any given moment 

 must be su])])osed to be in eciuilil)rium 

 or very nearly so. In the jiaper cited 

 above. Hardy showed that if a state of 

 ec|uilibrium were upset by some dis- 

 turbing agent, a new state of equilibrium 



» Science, July, 1908. 

 464 



