GENETIC BASIS 25 



ditional units for length, (2) those with 1 additional unit, 

 (3) those with 2, (4) those with 3, and (5) those with 4. 



The AAB'B' genotype, for instance, has 2 genes for addi- 

 tional length. It will produce leaves of the same size class 

 as do A'A'BB and AA'BB' , each of which also has 2 genes 

 from the larger parent. If we collect the various genotypes 

 into the 5 size classes and summarize our expectation, we ob- 

 tain the following: 



genes for additional length 1 



1 li U (I iC A 



2 u u u u 6 ■ 



o a (I i( ti A 



4 u (I a ti 1 



16 



In other words, we shall expect about one sixteenth of the 

 second-generation hybrids to be as small as the small parent, 

 and another sixteenth to be as large as the large parent. 

 About one quarter of the population will be intermediate be- 

 tween the small parent and the Fi, and another quarter will 

 in turn be intermediate between the large parent and Fi. 

 More than a third of the second-generation plants (He) 

 will be the same length as the Fi. 



In Table 2 are shown the expected distributions for 3 gene 

 differences and for 4 gene differences and the general for- 

 mulae for any number of differences. It will be noted that 

 with an increase in the number of genes affecting a character 

 the number of possible genotypes increases exponentially, 

 as does all the possible number of intermediates between the 

 tw^o parental extremes. 



As we consider larger and larger numbers of independent 

 genes all affecting the same character, the chances of getting 

 individuals that resemble either parent become less and less. 

 With only 10 genes there is only 1 chance in 1,000,000 of 

 getting an F2 plant like one of the parents ; with 20 independ- 

 ent genes the chances are 1 in 1,000,000,000,000. At the 



