METHODS FOR TESTING LINKAGE 59 



In a linkage test, two pairs of genes will commonly be segregating at the same time. 

 Deviations from expectation may be due to faulty segregation of either or both pairs 

 or to failure of random assortment (linkage) between the two pairs. The total ^ 2 , 

 which for four classes has three degrees of freedom, can be partitioned into three in- 

 dependent parts, each with one degree of freedom, one for segregation at each of the 

 two loci, and one for linkage. Table 14 gives the formulas for partitioning the total £ 2 

 for the three common kinds of matings. 



Table 14 

 Formulas for calculation of x 2 for segregation at individual loci, y^-A and x 2 B> 



AND FOR LINKAGE, % 2 L, FOR THREE KINDS OF MATINGS 



Mating 



AB Ab aB ab 



Double backcross 1/4 1/4 1/4 1/4 Z 2 J = (< 



X 2 B = 

 X *L = 



Intercross 9/16 3/16 3/16 1/16 X *A = 



X 2 B = 



X 2 L = 



Single backcross A 3/8 3/8 1/8 1/8 2A = 



intercrossed 



X 2 B = 



The data of Fisher and Snell 379 on the linkage of ruby, ru, and jerker, je, in the 

 mouse may be taken as an example again. From an intercross in repulsion the 

 following data were obtained : 



+ 4- +j e ru + ru J e Total 

 Observed number 86 31 35 5 157 



- Expected proportion 9/16 3/16 3/16 1/16 



(86 4- 31 - 105 - 15) 2 9 



X 2 m = Wl 47T-°- 019 



