CONSTITUTION OF THE STATISTICS 



by H, is separable from the effect of differences between the homo- 

 zygous phases of the genes, as measured by D. In the second place, 

 D is compounded of items like d/, and H of items like h^^. The 

 value of D will therefore be the same no matter how the increasing 

 and decreasing allelomorphs of the various genes were associated 

 with one another in the parents. And the value of H will be 

 unaffected by the signs, whether positive or negative, of the h 

 increments, i.e. by the directions of dominance of the individual 

 genes. H is, of course, expected to be O in the absence of dominance 



from all genes, and the ratio . / — provides us with a measure of the 



average dominance of the genes irrespective of whether dominance 

 is in the same direction for all genes or not, and irrespective of the 

 distribution of the genes between the parental lines. It provides us, 

 in fact, with the information about dominance which could not be 

 obtained by a simple comparison of the parental and F^ means. 



Were the variance of Fg the only statistic available it would 

 obviously be impossible to estimate the separate values of D and H. 

 Backcrosses and the F3 generation, however, help us here. They 

 supply us with additional information about D and H, and they 

 may be used in combination with Fg to effect the separation of 

 D and H both from one another and from the non-heritable varia- 

 tion E. Taken separately, the variances of the backcrosses cannot 

 be expressed in terms of D, H and E ; but if we add together the 

 variances of the two backcrosses, one to each parental line, they 

 have the joint value of |DH- |H+ 2E. The environmental com- 

 ponent is, of course, 2E because each backcross must show as much 

 non-heritable variation as the single Fg family of the same size. 



It will be seen from Fig. 17 that the F3 generation is able to provide 

 us with three statistics. These will be derived from (i) the variation 

 between the different F3 families taken as wholes; (2) the variation 

 within the different F3 famiHes; and (3) the relation between the 

 expression of the character in the individual F3 families and their 

 immediate parents in Fg. The statistics which express these relations 

 are: — 



I. The variance of the means of F3 families, which has the value 

 ID+J^H+E. 



83 



