Multiple Alleles; Multigenic Traits, 



63 



individuals to fall out of their phcnotypic 

 class, so to speak, and into the space be- 

 tween classes or into an adjacent phenotypic 

 class. And so, as gene pair number in- 

 creases, classes become more numerous, then 

 indiscrete, resulting finally in a continuum 

 of phenotypes. 



Note also that as the number of gene pairs 

 determining the trait increases, the fraction 

 of all F 2 resembling either P, becomes 

 smaller. Thus, with one pair of genes y 2 

 of F L > are black or white, with two pairs %, 

 with three pairs Y S2 , etc. Consequently, as 

 the number of genes increases from 1 to 20 

 and more, the continuous distribution of 

 phenotypic types gives rise to an F 2 curve 

 which becomes narrower and narrower. In 

 other words, the chance of recovering in F 2 

 any phenotype a given distance off the mean 

 decreases as gene pair number increases. 

 Although it may be relatively easy to identify 

 whether one, two, or three gene pairs cause 

 a given characteristic, it is much more diffi- 

 cult to determine exactly how many pairs 

 are involved whenever more than three are 

 involved. In multigenic cases, measurement 

 of how the population varies relative to the 

 average phenotype can give information as 

 to the approximate number of polygenes 

 involved. 



The variability of a trait can be measured 

 statistically as follows: the mean, m (the 

 simple arithmetic average), is found. The 

 variance, v (the measure of variability from 

 the mean), for a group of measurements is 

 determined by finding the difference between 

 each measurement and the mean, squaring 

 each such difference, adding all the values 

 obtained, and dividing the total by 1 less 

 than the number of measurements involved. 

 With a given sample size, all other things 

 being equal, the greater the variance the 

 smaller the number of gene pairs involved, 

 as would be expected from Figure 5-5. One 

 may find detailed statistical procedures for 



P x P, 



1 



F - >< F , 



F, < 



involving one gene pair 



involving two gene pairs 



-■ill.. 



involving three gene pairs 



involving many gene pairs 



figure 5-5. Dependence of number of pheno- 

 typic classes upon number of gene pairs. 

 Horizontal axis shows classes, vertical axis 

 indicates relative frequencies. 



