RULES AND RATIOS OF INHERITANCE 21 5 



This yields for the constitution of the generation F2 the 

 following: 



9ABAB + lABAb -f lABaB + iSABab + lAbab + 

 laBab -|- 9abab 



Since the capital letters represent dominant characters, the 

 characters A, B, a and b will be manifested in F2 in the fol- 

 lowing proportions : 



29AB + lAb + laB + 9ab 



In case crossing-over (or exchange) occurs equally in 

 both sexes, the constitution of the F2 generation will be given 

 by the product of the two expressions : 



(9AB + lAb + laB + 9ab) (9AB + lAb + laB + 9ab) 



This yields for the constitution of the F2 generation indi- 

 viduals of different genotypes in the following proportions: 



81ABAB + iSABAb + iSABaB + i62ABab +iAbAb 

 + 2AbaB + iSAbab + laBaB + iSaBab + Siabab 



If we classify these as to whether they manifest the char- 

 acters' represented by A, B, a or b, we find the proportions 

 to be as follows : 



281AB + i9Ab + i9aB + 8iab 



The method of computing the results may be generalized 

 as follows : 



Call the two pairs of dominant genes AA and BB, the two 

 pairs of recessive genes aa and bb. Then the one parent has 

 the two chromosomes A — B and A — B, the other parent 

 a — b and a — b (see figure 45). The individuals of Fi then 

 all have the two chromosomes A — B and a — b. 



Let r = the exchange (or cross-over) ratio (the propor- 

 tion of cases in which the chromosomes exchange genes, in 

 the germ cells produced by Fi ) . 



