SYSTEMS OF MATING 



25 



which takes the successively smaller values, after the initial generation, 



0, 1/2, 5/16, 21/128, 85/1024,... 



for m — 0, 1, 2, 3, 4, . . ., when c — 1/2 and q = 1. 



The ratios of the probabilities of heterozygotes in successive generations tends 

 toward a constant as m increases. For large m, 



^m + i/^m = I — c, approximately. 

 The probability of heterozygosity in any advanced cycle is, approximately, a fraction, 

 1 — c, of the probability of heterozygosity in the preceding cycle. When c = 1/2, the 

 loss tends to be 1/2. 



Fig. 6. Probability of incrosses for the cross-intercross system. 

 1.0 



0.8 



0.6 



PROBABILITY 



m 



0.4 

 0.2 



0.0 



2 3 4 



CYCLE m 

 The probability of incrosses p m for the cross-intercross system, starting with q = 1, for 

 five selected values oft = 1/10, 2/10, 3/10, 4/10, 5/10. 



After the cross-intercross system has been in effect for several cycles, the incrosses 

 will be increasing at a steady rate exactly balanced by the rate of decrease of the crosses 

 and backcrosses. This rate may be found by finding the characteristic root of the 

 determinant made up of the q and r rows and columns of the cycle matrix (table 7). 



The desired root is 



Aj = 1 — c. 



Table 7 

 Cycle matrix of the cross-intercross system 



