6 GENETIC STOCKS AND BREEDING METHODS 



For each system, the breeder should know the probabilities of the mating types 

 and in particular the probability p of incrosses with respect to the a-locus. He will also 

 want to know the probabilities of the genotypes, particularly the probability h of hetero- 

 zygotes Aa. To evaluate a system he should know the number of generations required 

 to increase p or to decrease h to any desired level. We shall try to answer these questions 

 about the seven systems. 



RANDOM MATING 



The system of random mating is used when preservation of the genetic (i.e., 

 genotypic) variability of a population without change is desired. Random mating 

 will not, in theory, create genetic variability or diminish it. Variability may be 

 created by outcrossing or by mutations. It may be diminished by any scheme of 

 inbreeding. Random mating means that the frequencies of matings of various types 

 are specifiable by the product and addition rules of probability applied to the geno- 

 types. 



Let the probabilities of the three genotypes at the a-locus in G be 



P{AA) = k , 

 ?{Aa) = 2/ , 

 P(afl) = m , 



where k t + 2/, + m t = 1, i = 0, 1, 2,. . ., n, and P(x) means the probability of x. By 

 definition, the gene or allele frequencies are: 



r(A) = x = k + / , 

 P ( fl ) = */o = ! + ™0, 



where x t + y x = 1 , and i = 0, 1 , 2, . . . , n. The mating-type frequencies in G and the 

 genotype frequencies of their progeny in G l are shown in table 2. The probability 



Table 2 

 Mating-type frequencies in g and genotype frequencies of their progeny 



Genotypes in G 1 

 Mating types in G AA Aa aa 



P(AA x AA) = po = k 2 k 2 — 



P(aa x aa) = p " = m Q 2 — m 2 



P(AA x aa) = g = 2k m 

 P(AA x Aa) = r — 4k Q l 

 Y{aa x Aa) — s — 4/ w 

 ?(Aa x Aa) = v = 4/ 2 



The genotype frequencies of G x are related to the mating-type frequencies of G in the random- 

 mating system by the laws of Mendelian genetics. 



