SYSTEMS OF MATING 31 



The backcross generation matrix is 



g 2 = n c 2 \ 



2,(1 -e)\. 

 \0 (\-c) 2 / 



Finally, the intercross generation matrix is 



G 3 = /l c c 2 \ 



(1 -*)")■ 



^0 1 - c 2c{\ - c)j 



Thus, the cycle matrix is 



C = 036^ = /l c 2 {2 - c) 2 (1/2) + (l/2)c 2 (2 - c) 2 \ 



(1-,)* (1/2)(1 - 4 • 



\0 2c(l - c) 2 {2 - c) c{\ - c) 2 (2 - c) J 



From the matrices in table 1 the frequencies of various types of matings in any 

 cycle and the number of generations to reach a given percentage of incross matings can 

 be calculated, remembering that a cycle represents three generations. 



Table 10 



A, A, AND A -1 MATRICES FOR THE CROSS-BACKCROSS-INTERCROSS SYSTEM 



Under the cross-backcross-intercross system, with c = 1/2, 3 cycles (9 generations) 

 are required to exceed 95 per cent incross matings and 4 cycles (12 generations) to 

 exceed 99 per cent. If c = 1/10, 16 cycles (48 generations) and 23 cycles (69 genera- 

 tions) are required to exceed 95 per cent and 99 per cent incross matings. 



It should also be noted that approximately four times as many matings as are 

 required to maintain the stock must be made up in the intercross generation to assure 

 a sufficient supply of the types of matings required. The cost of these extra matings 

 should be borne in mind when the cross-backcross-intercross system is considered for 

 use. 



