HEREDITY 205 



the heterozygotes and the homozygotes for the other allele are in the 

 relative proportions p-, ipq and q\ respectively, where p and q are the 

 frequencies of the two alleles so that p -{- q= \ and p or ^ may have any 

 correlative value from o to i. Moreover, if anything occurs to displace the 

 equilibrium, a new equilibrium is reached after a single generation of ran- 

 dom mating. For sex-linked genes, epistatic interactions and other com- 

 plicated cases, equilibrium may be reached more slowly. 



Self-evident as these propositions would appear to be, misunderstandings 

 of them and of their implications are all too frequent in discussions of hu- 

 man heredity. It is often said, for example, that a dominant character in- 

 creases in the general population at the expense of its recessive counter- 

 part until it stands in the ratio of 3:1. This statement has no basis in fact. 

 A recent text states that "albinism is due to a recessive factor, which ex- 

 plains zvhy it is so rare'' (italics mine). Another book, a treatise on handed- 

 ness, proclaims that "left-handedness occurs in 25 per cent, of the popu- 

 lation, which indicates that it is a Meiidelian recessive''' (italics mine). Each 

 of these statements shows a complete lack of understanding of the prin- 

 ciples of equilibrium. 



A recessive character may be common or rare in a population, depend- 

 ing upon the relative abundance or scarcity of the hereditary factor de- 

 termining the character. Split hand, or "lobster claw," in which the hand 

 has only two large fingers, is due to a dominant factor, the normal comple- 

 ment of five fingers being due to its recessive allele, yet the recessive char- 

 acter is the common condition. Recessive characters may occur in various 

 populations in any frequency whatsoever from o to 100 per cent. 



A recent prize-winning essay of the Eugenics Research Association con- 

 tains this remarkable pronouncement: "We are indeed lucky that the men- 

 tal disorders or psychoses are not dominant traits, or we would all be 

 insane by now, according to the laws of heredity." In a recent manuscript 

 on fingerprints which I was requested to read and criticize appeared the 

 following paragraph: 



"Here we have a pattern (arches) which when crossed with another of 

 the same classification, produces its own kind, plus loops and whorls. This 

 reaction seemed to fit the requirements of a character heterozygous in 

 the parents and segregating in the 1:2:1 ratio. A check on the frequency of 

 arches in the general population quickly invalidated such a supposition, 

 however, for it was found that only about 5 per cent, of all patterns are 

 arches. Support for such an idea would require 25 per cent, loops, 50 per 

 cent, arches and 25 per cent, whorls. Some other explanation was there- 

 fore necessary." Here again we have examples of complete misunderstand- 

 ing of gene frequencies and equilibria. 



I have belabored this point because the lack of attention paid to these 

 important considerations has greatly retarded the progress of the study of 



