58 



CHAPTER 8 



Measurement of the variability of a trait 

 can be made statistically as follows: the 

 mean, m (the simple arithmetic average), is 

 found. The variance, v (the measure of vari- 

 ability), is determined for a group of measure- 

 ments by determining the difference between 

 each measurement and the mean, squaring 

 this difference in each case, adding all the 

 values obtained, and dividing the total by 

 1 less than the number of measurements in- 

 volved. (The square root of v is called the 

 standard deviation.) With a given sample 

 size, other things being equal, the greater 

 the variance the smaller the number of gene 

 pairs involved. Detailed statistical proce- 

 dures for utilizing variance may be found in 

 any standard text on elementary statistical 

 methods. 



Let us next consider the effect of dominance 

 upon the expression of quantitative traits, as 

 revealed partly by considering its effect on 

 qualitative traits. When a qualitative trait 

 is determined by 1, 2, or 3 pairs of genes not 

 showing dominance, there are, as in Figure 

 8-1, 3, 5, or 7 possible phenotypic classes, 

 respectively. However, as a result of dom- 

 inance the number of classes is reduced, as 

 you will recall from the discussion in Chap- 

 ter 7 and Figure 7-2. Since our estimate of 

 the number of gene pairs responsible for a 

 phenotype is directly connected with the 

 number of phenotypic classes, the number 

 of gene pairs involved in a quantitative trait 

 will be underestimated where there is dom- 



inance. This is important since many genes 

 show complete or partial dominance. 



In fact, one can construct a hypothetical 

 case where two pairs of genes with dominance 

 can give much the same phenotypic result as 

 one pair with no dominance. Suppose gene 

 A (as AA or Aa) adds 2 units of effect while 

 its recessive allele a (as aa) adds only 1 unit; 

 suppose B (as BB or Bb) subtracts 1 unit of 

 effect while its recessive allele b (as bb) has 

 no effect at all. Then a 2-unit individual 

 {AA bb) mated with a 0-unit one {aa BB) will 

 give all intermediate 1-unit Fi{AaBb). The 

 F2 from the mating of the Fi can be derived 

 by a branching track shown in Figure 8-2. 

 The phenotypic ratio obtained in F2 of 

 3 : 10 : 3 might be, in practice, difficult to 

 distinguish from the 1:2:1 ratio obtained 

 from crossing monohybrids showing no 

 dominance. 



There is a second effect of dominance upon 

 inheritance of quantitative traits which can 

 be illustrated by means of two crosses in- 

 volving the genes just described. In the 

 first, two 0-unit individuals are crossed, 

 aa Bb X aa Bb, yielding % aa B- (0 unit) and 

 %aabb (1 unit). Here the parents, being at 

 one extreme (0 units), 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 par- 

 ents are at the other extreme (2 units) but pro- 

 duce offspring which, on the average, are less 



% A. 



% B 



Va b b 



9/16 A_B, 



(1 unit) 



3/16 A_bb (2 units) 



FIGURE 8-2. Results of crossing to- 

 gether the diliyhrids described in tlie 

 text. 



V4 a a 



3/16 a a B_ (0 units) 



l/16a a b b (1 unit) 



