12 GENETIC STOCKS AND BREEDING METHODS 



form the frequencies into multipliers for the diagonal matrix, A, of the G matrix roots. 

 The roots of the G matrix are also useful in that one of them, called the characteristic 

 root, measures the rate of decrease of the frequency of nonincross matings. This 

 root also can be used to calculate the approximate number of generations required to 

 reach a given proportion of incross matings. 



In the subsequent discussion, these principles will be applied to the six systems of 

 mating mentioned above. 



BROTHER-SISTER INBREEDING SYSTEM 



The system of brother-sister inbreeding is used when it is desired to reduce the 

 genetic (i.e., genotypic) variability at all loci. The probability h of heterozygosity 



Fig. 1. The brother-sister inbreeding system. 



GENERATION 

 n 







CO 

 CO 

 CO 

 CO 



B 



at any locus a is to become as small as possible. Figure 1 shows three ways of repre- 

 senting the system in a diagram. In the following analysis of the system reference is 

 made only to autosomal loci. In the case of sex-linked loci, brother-sister inbreeding 

 also reduces the probability of heterozygosity in the homogametic sex, and, if there is 

 crossing over between the sex chromosomes, in the heterogametic sex. The analysis 

 differs in details from that for autosomal loci. 



Assume that Aja are alleles at the a-locus and that the a-locus is autosomal. We 



