SYSTEMS OF MATING 



13 



desire to know the probability of matings between like homozygotes, i.e., of incrosses 

 in any generation n. Assume further that the probabilities of various types of matings in 

 the generation w(G n ) are: 



_ (AA x AA\ 

 Incrosses: r | = p., 



\aa x aa J 



Crosses: P (AA x aa) = q n , 



(AA x Aa\ 



Backcrosses : P 



(AA x Aa\ 

 \aa x Aa) 



yaa x Aa} 

 Intercrosses: P (Aa x Aa) = v n , 



where each mating type also includes the reciprocal mating, if any. The incrosses 

 each produce one type of progeny, AA or aa, like the parents, and following the system 

 of mating brother by sister, these produce one type of mating, incrosses, in the next 

 generation. The crosses produce one type of progeny Aa, unlike the parents, and 

 one type of mating, intercrosses, in the next generation. The backcrosses each 

 produce two types of progeny AA and Aa, or aa and Aa, with probabilities 1 /2 and 

 1/2, and so produce three types of matings, incrosses, backcrosses, and intercrosses, 

 in the ratios 1/4:1/2:1/4. Finally, the intercrosses produce three kinds of progeny 

 AA, Aa, and aa in the ratio 1/4:1/2:1/4 which yield incrosses, crosses, backcrosses, 

 and intercrosses in the ratios 1/8:1/8:1/2:1/4. 



Table 4 

 Generation matrix for the brother-sister inbreeding system 



Pn 



q n 



Pn + 1 



q n +i 



r n + l 

 On + 1 



The probabilities of mating types in G n + 1 may conveniently be shown as func- 

 tions of the probabilities in G n in a generation matrix, as in table 4. The 

 probabilities may be written as equations: 



Pn + 1 =Pn + (l/4)r.+ (l/8)»„ 



?» + i = (1/8K, 



(l/2)r n + (1/2K, 



v n + i = 1n + (l/4)r n + (1/4X. 



