SYSTEMS OF MATING 



33 



in the ratio 1/4: 1/4: 1/4: 1/4 in the next generation. The backcrosses of the third kind 

 likewise produce four kinds of progeny and these yield incrosses, backcrosses of the 

 second kind, backcrosses of the third kind, and intercrosses in the ratio c(\ — c) : 

 c 2 : (1 — c) 2 :c{\ — c). Finally, the intercrosses produce seven kinds of progeny which 

 yield all six kinds of matings in the ratio 



(l/2)c(l -*):(l/4) - (1/2M1 - c):{\j2)c{\ - c) : (1/4) : (1/4) - (l/2)c(l - *):(l/4). 



The linear equations which relate the probabilities of G n + j to the probabilities 

 of G„ are: 



Pn+l = Pn + 



?n + l = 

 r n + 1 = 



s n + 1 = 



*7l+ 1 = 



0» + l = 



where A; = c(\ — c). 



q n + 



kr n + (1/4K + kt n + (1/2) kv n , 



(1/4)(1 -2A:) 0ns 



(1/*K + (l/2)^ n , 



;i -r) 2 r n + (1/4)j, + c\+ (l/4)v n , 



c\+ (1 -c)\+ (1/4)(1 -2/t)^, 



AT n + (1/4K + to; + (i/4)o n , 



Fig. 9. Probability of incrosses with heterozygosis forced by backcrossing. 

 I.Or 1.0 



0.8 



0.6 

 PROBABILITY 



P m 0.4 



0.2h 



0.0 



2 4 6 8 10 

 GENERATION, n 



12 



2 4 6 8 10 



GENERATION. n 



12 



Left: The probability of incrosses for four 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. 



Right: The probability of incrosses p n for three 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. 



Matings in the initial generation may be any of the six types. Two of these are 

 slightly more likely to occur in laboratory populations. First, the mutant allele D may 

 be a semidominant lethal in a noninbred line. When inbreeding is started, the least 

 favorable mating with respect to homozygosity at the a-locus is a cross Ad/ Ad x aDjad, 

 or ad/ad x AD /Ad, i.e., q = 1. The probability p of incrosses increases relatively 

 slowly (figure 9). Second, the mutant allele r may already exist in one inbred strain 



