2l6 GENETICS 



Then I - r = the proportion of cases in which there is no 

 exchange. 



Then in the individuals in which exchange occurs (one or 

 both sexes) gametes are produced in the proportions: 



(i-r) AB + r Ab + r aB + (i -r) ab (i) 



If in one sex there is no exchange, the gametes from the 

 individuals of that sex are of but two kinds, in the pro- 

 portions: 



AB + ab (2) 



(Since in these expressions (i) and (2), it is only the 

 relative proportions that are important, either or both may 

 be multiplied through by any convenient factor to make the 

 numbers integral ; the factor need not be the same for both.) 



The proportions of the different types of individuals (zy- 

 gotes) in F2 are obtained by multiplying together the ex- 

 pressions for the proportions of the gametes in the two 

 sexes. That is, the proportions in F2 are, if crossing-over 

 occurs in one sex only : 



[(i-r) AB + r Ab + raB+ (i-r) ab] [AB + ab} (3) 



While if exchange occurs in both sexes, the proportions 

 in F2 are: 



[ ( I - r) AB + r Ab + r aB + ( i - r) ab]^ 



The value of r in case of different pairs of genes is deter- 

 mined by extensive observation of the results of experi- 

 mental breeding. For different pairs of genes of Drosophila, 

 many such values of r are given in the various publications 

 of Morgan, Bridges and Sturtevant. 



5. Parents differing in two gene pairs of the X-chromo- 

 some. — In this case, ratios diverse from those given by auto- 

 somal genes will be produced, owing to the different method 



