CONSTITUTION OF THE STATISTICS 



the sign of hj, may not be the same as that of h^. The dominances 

 may be reinforcing or opposing one another. 



Two true breeding Hnes raised in a comparable range of environ- 

 ments will have mean phenotypes differing by: — 



2[S(dJ-S(d.)] 



where S(d^) is the smn of the d increments added by all the genes 

 represented by increasing allelomorphs (A, B, etc.) and S(d_) the 

 sum of the increments added by all the genes represented by 

 decreasing allelomorphs (a, b, etc.) in the parent with the larger 

 manifestation of the character. The average of the two lines, the 

 mid-parent as we may call it, will be the zero point from which 

 the h increments can be measured. It is the natural origin of the 

 scale. 



The Fi between the two lines will be uniformly heterozygous for 

 all the genes in which its parents differed and so will differ from the 

 mid-parent by h^+ h^^ • • • == S(h), taking the signs of the various 

 h's into account. Thus S(h) can be zero even though each h is not 

 zero, because of the opposing signs of the h's, or, in genetical terms, 

 because of the opposing dominances. In the same way the parental 

 difference may be zero, i.e. [S(d^) — S(d_)1 = O, no matter 

 what values d^, d^^, etc., may have, because the increasing and 

 decreasing allelomorphs of the different genes may be balanced in 

 the parents. 



The simple comparison of an Fj with its parents is sufficient to 

 establish the dominance relations of a gene in mendelian genetics. 

 But, as we can now see, it is not sufficient to show even the average 

 dominance relations of a polygenic system in biometrical genetics. 

 For if we divide the departure of the Fj mean from the mid-parent 

 by half the parental difference, a ratio which is commonly used 

 to represent the degree of dominance of single genes, we obtain: — 



/ , V „/ , X and this obviously bears no simple relation to the 



s(d^)-S(d_) ^ ^ 



•^ K , , . . 



ratios -t-> -y- and so on. It can vary between zero and an infmitely 



a b 



large value, according to the way in which the increasing and 

 decreasing allelomorphs are distributed betw^een the parents, and the 

 way in which the h's reinforce or oppose one another. One thing 



Elements uj Genetics g I F 



