SYSTEMS OF MATING 



35 



for this system of brother-sister inbreeding with heterozygosis forced by backcrossing. 

 Values of X x for selected values of c have been estimated from repetitive application of 

 the equation 



P n + 1 = GP r 



(2) 



for n = 0, 1, . . . , 11. Until a general solution of equation (7) can be derived for these 

 systems, the equation 



V n = A"V (6) 



cannot be applied. 



Using the above estimate of X l5 however, the number of generations required to 

 obtain a given percentage of incross matings can be estimated. Fort = 1/2, 15 genera- 

 tions of brother-sister inbreeding with heterozygous forced by backcrossing are required 



Fig. 10. Probability of heterozygosity with heterozygosis forced by 



BACKCROSSING. 



hi 



4 6 8 10 12 

 GENERATION, n 



4 6 8 

 GENERATION, n 



10 12 



Top: The probability of heterozygosity, h' n for rr, h" n for Rr, for selected values of 

 c = 0, 1/10,. 3/10, 5/10, for the system of brother-sister inbreeding with heterozygosis forced 

 by backcrossing, starting with q = 1. 



Bottom : The probability of heterozygosity, ti n for rr, h'n for Rr, for selected values of 

 c = 1/10, 3/10, 5/10 for the system of brother-sister inbreeding with heterozygosis forced by 

 backcrossing, starting with t — 1 . 



