4 GENETIC STOCKS AND BREEDING METHODS 



NOTATIONS AND DEFINITIONS 



Three autosomal loci of diploid, sexually reproducing organisms such as mice 

 will be designated by the symbols: a-locus, ZMocus, and r-locus. The a-locus is any 

 locus whose heterozygosity is in question as a given breeding system advances from 

 generation to generation. The ZMocus is the locus of a dominant mutation ; the r-locus, 

 that of a recessive mutation. The D and r mutations are called the genes of interest. 

 The alleles at these three loci will be denoted as Aja, Djd, and R/r, and the genotypes 

 by AA, Aa, aa; DD, Dd, dd; and RR, Rr, rr. The relative frequency (i.e., probability) 

 of Aa will be denoted by h. 



The mating types are of four kinds : 



Incrosses: A A x A A and aa x aa, matings of like homozygotes, 



Crosses : AA x aa, matings of unlike homozygotes, 



Backcrosses: AA x Aa and aa x Aa, matings of homozygote and heterozygote, 



Intercrosses: Aa x Aa, matings of heterozygotes. 



When the terms incrosses, crosses, backcrosses, and intercrosses appear in lower-case 

 letters, they refer to the locus with questionable heterozygosity. When they appear in 

 small capitals, incrosses, crosses, backcrosses, intercrosses, they refer to the locus 

 of interest. The last three of these terms are in general use. 



The relative frequencies or probabilities of the mating types will be denoted by 

 p, q, r, . . ., v with the definition varying slightly from system to system. In general, p 

 will be used to denote the frequency of incrosses (AA x A A and aa x aa), the maxi- 

 mizing of which is the objective of all of the systems of breeding, except random mating. 

 A subscript n (or m) denotes generation n (or cycle m). G (or C) will stand for genera- 

 tion (or cycle). G, P, A, etc. are matrices. P will designate probability. 



The probability of crossing over between the a-locus with questionable heterozy- 

 gosity and the D- or r-locus carrying the mutation of interest will be denoted by c. 

 To avoid a troublesome complication in notation, for any two loci, c will be treated as 

 equal in the two sexes. 



The probability of heterozygosity at the a-locus in generation n (or cycle m) will be 

 denoted by h n (or h m ). In all cases, as p n increases, h n decreases. As will be seen, h n 

 is a function of the probabilities of backcrosses and intercrosses in each system of mating. 



SYSTEMS OF BREEDING 



Relatively few of the systems developed by breeders of domestic and laboratory 

 mammals are used frequently enough to warrant exposition here. Parent-offspring 

 inbreeding, line breeding, or systems which use first, second, or third cousins will not be 

 described. The systems included are, with the exception of random mating, all 

 regular systems which permit the development of sequence equations to relate the 

 probabilities of incrosses, etc., of one generation to those of the next. Irregular 



