HARDY 6 1 



bases for the co?itribution of genetics to evolutionary thought. 

 Hardy, as a mathej/iaticiaji, did not differentiate between the individ- 

 ual and the genes that individual carries, so he based his calculatioris 

 of frequency on the nmnbers of honiozygotes and heterozygotes in 

 the popidation. Because of the redistribution of genes between iji- 

 dividuals, his first generation, which was made up entirely of ''''pure'" 

 individuals, differs i?j proportio?7S fro?n his second ge?ieratiojj, which 

 ijic hides heterozygotes. Geneticists soo?i recogjiized that the cojj- 

 stancy and stability Hardy observed after his second gejieration ex- 

 isted equally m the transitioji from first to seco7id, if one compares 

 the total number of "^" afid 'V genes in the population, rather than 

 the innnbers of different kinds of individuals. A direct co7isequence 

 of this awareness is the ^^gene-pooV^ concept, which is cojicerned 

 primarily with the total number of genes and their proportions in a 

 population, and not with the appearance of the individuals carrying 

 those genes. From the viewpoint that the number of genes in a gene 

 pool tends to remain stable and unchanging comes the concept of 

 evolution defined as any situatioii which tends to change the propor- 

 tional distribution of genes in a gene pool. Hardy perceived several 

 of the factors that coidd affect the 'proportional distribution, and 

 pointed them out in his cojicluding paragraph. He jnissed one of the 

 prijnary forces, however, i?i that the fruit of Darwiji's thought, 

 fiatural selectioji, is 07mtted. 



The concept of stability of gene proportions in a populatio7i has 

 come to be kfiown as the ^''Hardy-Weifjberg Law,^'' as a conseqitence 

 of another of those dramatic coincidences that were pointed out 

 earlier, for Wei?jberg (Uber den Nachweis des Verebung beim 

 Menschen, 1908) pointed out the same facts at much the same time 

 as did Hardy. This law still forins the core about which the field of 

 population genetics revolves today. 



To THE Editor of Science: i am tors, to get three brachydactylous per- 



reluctant to intrude in a discussion con- sons to one normal." 

 cerning matters of wiiich I have no It is not difficult to prove, however, 



■expert knowledge, and I should have that such an expectation would be 



expected the very simple point which quite groundless. Suppose that Aa is 



I wish to make to have been familiar to a pair of Mendelian characters, A 



biologists. However, some remarks of being dominant, and that in any given 



Mr. Udny Yule, to which Mr. R. C. generation the numbers of pure domi- 



Punnett has called my attention, sug- nants (AA), heterozygotes (Aa), and 



gest that it may still be worth making, pure recessives (aa) are as p:2q:r. 



In the Proceedings of the Royal So- Finally, suppose that the numbers are 



ciety of Medicine (Vol. I., p. 165) Mr. fairly large, so that the mating may be 



Yule is reported to have suggested, as regarded as random, that the sexes are 



a criticism of the Mendelian position, evenly distributed among the three 



that if brachydactyly is dominant "in varieties, and that all are equally fertile, 



the course of time one would expect, A little mathematics of the multiplica- 



in the absence of counteracting fac- tion-table type is enough to show that 



