422 CORRADO GINI 



character an intensity equal to 2 and the factors 2 and 4 determine an 

 intensity equal to 3. And let factor 1 be more energetic than factor 2, 

 and therefore dominant, and factor 4 be more energetic than factor 3 and 

 therefore dominant. 



The hybrid of the first generation, which will contain in its chromosome, 

 in a heterozygous condition, factors 1, 2, 3, and 4, will therefore present an 

 intensity of character superior to that of each of its homozygous parents; 

 equal, for instance, to 5 instead of to 2 or 3. Of the hybrids of the second 

 generation, one-half will have the same genetic formula as the hybrids of the 

 first generation, and therefore an intensity of character equal to 5, and 

 the other half will be divided in equal parts between homozygous individ- 

 uals belonging to the type of the other having an intensity of character 

 equal to 3. 



It follows that, in hybrids of the second generation, the superiority pos- 

 sessed by the hybrids of the first generation in the matter of intensity of 

 characters will necessarily be reduced 50 per cent. 



And here let me quote the words of Dr. East and Dr. Jones, to the latter 

 of whom, if I am not mistaken, we owe the theory in question in the form 

 above set forth, which is generally accepted; "The extra growth derived by 

 crossing the two different types has diminished 50 per cent. In the third 

 generation, from a representative sample of the second generation, it can be 

 shown that this excess again diminishes 50 per cent, so that the effect in the 

 average is only 25 per cent as great in this generation as in the first, and so 

 on in subsequent generations, until the effect diminishes to a negligible 

 quantity in about the eighth generation. This is in fair agreement with 

 the actual results obtained by inbreeding maize, as it ought to be, because 

 the development attained by each individual varies directly with the num- 

 ber of heterozygous factors." 1 



Now, as I have already had occasion to remark, 2 the progressive diminu- 

 tion, after the second generation of hybrids, of the heterosis noted in the first 

 generation is not really at all in keeping with the theory above set forth. It 

 seems indeed quite likely that this assertion is due to some misunderstanding 

 or to an arithmetical error. 



It is, indeed, easy to see that, if in the second generation we have 50 per 

 cent of heterozygous individuals, and 25 per cent of homozygous individuals 



1 E. M. East and D. F. Jones: Inbreeding and outbreeding — Their genetic and sociologi- 

 cal significance. (J. B. Lippincott, Philadelphia and London, 1919.) 



2 Cf r. Corrado Gini : Nascita, Evoluzione e Morte delle Nazioni (Libreria del Littono, 

 Rome, 1930). Pp. 101-102, and Corrado Gini, Shiroshi Nasu, Oliver E. Baker and Robert 

 R. Kuczinsky: Population (The University of Chicago Press, Chicago, 111., 1932). 



