60 



hooded whites are homozygous for 

 purple, on our '^new we should look 

 for one with round pollen out of 64. 

 Actually, one white hooded plant with 

 round pollen occurred among the 18 

 F2 families, where the hood was re- 

 corded (Nos. 1 and 4). Where ex- 

 pectation demands 1 in 64, experiment 

 gave 2 hooded rounds in 101. 



If, however, the coupling is on the 

 15 : 1 : 1 : 15 basis, the proportion of 

 rounds among the hooded purples and 

 whites should be only 1 in 32- -f- 4, i.e., 

 1 in 256. In No. 6 and its descendants, 

 Nos. 20-27, only one of the 209 hooded 

 purples had round pollen. 



These complicated facts may be 

 summarised thus: From an examina- 

 tion of the families where the hooded 

 standard occurs, it is quite clear that 

 in some of them the coupling of blue 

 factor with long pollen is definitely 

 distributed according to the system 



HARDY 



15:1, and that in others it follows the 

 system 7:1. There are also families 

 which cannot confidently be referred 

 to either class. Since the F2 derived 

 from Bl. Burpee by E.H. round fol- 

 lowed the 7:1 system, the hetero- 

 zygosis between erectness and hood 

 cannot be regarded as the direct cause 

 of the 15:1 distribution. The families 

 showing that distribution came in F3 

 and later generations from this cross, 

 and the 15:1 system seems, therefore, 

 to have been brought into operation 

 by the omission of something which 

 may be supposed to be carried on in 

 those collateral families which follow 

 the 7: 1 system. Scrutiny of the various 

 groups has, however, failed to discover 

 any consistent difference between 

 those of the 7: 1 type and those of the 

 15:1 type. In the case of the Bush X 

 Cupid cross the 15:1 system appeared 

 at once in F^. 



W 



Mendelian Proportions in a Mixed Population 



G. H. HARDY 



Reprinted by publisher's permission from Sci- 

 ence, vol. 28, 1908, pp. 49-50. 



This short paper has more of the air of a kindly old professor 

 gently reprijnanding an irrepressible stude?it inclined to go off half- 

 cocked tha?i that of a major contribution to genetic thought. Hardy 

 had noted the tendency of Ji07i-mathematically inclined biologists to 

 make assumptions a?id draw cojiclusions based upo?i erroneous in- 

 terpretatiojis of the statistics i?i McfidePs work, a?id wrote this letter 

 to the editor of Science to correct these errors. The cojisequences of 

 the paper have been quite far-reaching, however, for it gave rise to 

 the field of population genetics, which fonm o7ie of the primary 



