64 



CHAPTER 5 



3 /4 A- 



% B 



Va bb 



9 /i6 A- B- (1 unit) 



V, 6 A- bb (2 units) 



V4 a a 



% B- 



y 4 bb 



_^ 3 /i6 aa B- (0 units) 



.^ Vi6 aa bb (1 unit) 



figure 5-6. Results of cross- 

 ing together the dihybrids 



described in the text. 



using variance this way in any standard text 

 on elementary statistical methods. 



Consider next the effect of dominance 

 upon the expression of quantitative traits. 

 When a qualitative trait is determined by 

 one. two. or three pairs of heterozygous 

 genes not showing dominance, there are (as 

 in Figure 5-5 ) three, five, or seven possible 

 phenotypic classes, respectively. As a result 

 of dominance, however, the number of 

 classes is reduced (cf. Chapter 4, p. 51). 

 Since the estimated number of gene pairs 

 responsible for a phenotype is directly re- 

 lated to the number of phenotypic classes, 

 the number of gene pairs involved in a quan- 

 titative trait is underestimated whenever 

 dominance occurs. This effect is important 

 because many genes show complete or par- 

 tial dominance. 



One can construct a hypothetical case in 

 which two pairs of genes both showing domi- 

 nance can give much the same phenotypic 

 result as one pair with no dominance. Sup- 

 pose gene A (as AA or Aa) adds 2 units 

 of effect and its recessive allele a (as aa) 

 adds only 1 unit; suppose B (as BB or Bb) 

 subtracts 1 unit of effect and its recessive 

 allele b (as bb) has no effect at all. Then 

 a 2-unit individual {A A bb) mated with a 

 0-unit one (aa BB) will give all intermediate 



1 -unit F| (AaBh). The F_. from the mat- 

 ing of the F] can be derived by a branching 

 track as shown in Figure 5-6. The pheno- 

 typic ratio obtained in F 2 of 3:10:3 might 

 be, in practice, difficult to distinguish from 

 the 1:2:1 ratio obtained from crossing 

 monohybrids showing no dominance. 3 



Dominance has a second effect with re- 

 gard to quantitative traits; this can be illus- 

 trated by means of two crosses involving the 

 genes just described. In the first, two 0- 

 unit individuals are crossed, aa Bb X aa Bb, 

 yielding % aa B- (0 unit) and % aa bb 

 (1 unit). In this case the parents, which 

 are at one phenotypic extreme (0 unit), 

 produce offspring which are, on the average, 

 less extreme (0.25 unit). In the second 

 case, two 2-unit individuals are crossed, 

 Aa bb X Aa bb, yielding % A- bb (2 units) 

 and % aa bb (1 unit). Here the parents 

 are at the other phenotypic extreme (2 units) 

 but produce offspring which are, on the 

 average, less extreme (1.75 units). These 

 results demonstrate regression, the conse- 

 quence of dominance which causes individ- 

 uals phenotypically extreme in either direc- 

 tion to have progeny less extreme. 



Figure 5-7 illustrates the principle of re- 



3 See J. H. Edwards ( 1960). 



