THL BIOiMI-TRICAL ANALYSIS 



it ain show us, however. If this fraction departs significantly from 

 zero, then S(h) cannot be zero and at least some of the genes arc 

 showing some dominance in the direction of the departure. 



In Fo the genotypes AA, Aa and aa occur with the relative 

 frequencies |, 2, 4» so that the mean measurement as affected by 

 this gene will be 4d3H- ^h_, — jd^ or Ih^^. Then, taking all genes 

 into account, the mean of Fg will depart from the mid-parent 

 by |S(h). The mean of F3 similarly departs from the mid-parent 

 by 4S(h). We can therefore learn no more about the genes' domi- 

 nance relations from the Fo and F3 means than we can from the 

 Fj mean. 



The information to be gained merely from a study of the means 

 is thus very limited. The different variances and covariances which 

 we can calculate are, however, more helpful. The parental lines and 

 the Fj will show only non-heritable variation. We can consider 

 their variances as including only one component, E. The variance 

 of F2 will, however, contain a heritable portion, to which each gene 

 wdll contribute. The contribution of gene A-a to this variance can 

 be ascertained by fmding the deviations from the mean of the 

 measurements of AA, Aa and aa individuals, squaring them and 

 adding them up. The F2 mean in respect of this gene is Ih,^, so that 

 the deviation of an AA individual will be d^ — ^h^, the deviation 

 of Aa, h.j — ih^, and that of aa, — d^ — Ih^. Now one quarter of 

 the individuals will be AA, one half /It/ and one quarter aa, so that 

 the contribution of gene A-a to the variance of F2 must be: — 



i-a- |hJ2+ i(h, - 4hJ^+ i(- d - il,J2 



The remaining genes in which the parental lines differed will make 

 similar contributions to the variance of Fg. Provided that the genes 

 are unlinked, these contributions will be independent, and the total 

 heritable variation will be the simple sum of the contributions 

 made by the individual genes. Then if we write D = d^'^H- d^^-\- 

 d^^ . . . and H = h^^ -|- h^^ -\- \\^ . . . the heritable variance of 

 Fa becomes |D+ ^H. Since the variance will also contain a non- 

 heritable component, the full formula must be ^D + ^H+ E. 



Two important properties of the variation are revealed by this 

 formula. In the first place, the effect of dominance, as measured 



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