328 BIOLOGY OF THE LABORATORY MOUSE 



systems, for example brother-sister mating, the population necessarily 

 breaks up into non-interbreeding lines in each of which there is a limited 

 number of parents in each generation. Under such systems an increasing 

 number of genes will become fixed in any one line. Thus, if genes A and a 

 are both present in the original population, some lines will become fixed 

 so that all individuals in that line are A A, other lines will become fixed 

 for aa, while others may, in a limited period, not yet have become fixed for 

 that particular gene pair. 



This effect of inbreeding is easy to understand for a system as close 

 as brother-sister mating, where, in any one line, there are only two parents 

 for each generation. Merely by chance, matings will occur in which both 

 parents are homozygous for the same gene. Once this has happened all 

 their descendants will be homozygous for that gene so long as they are bred 

 only with each other and no mutation occurs. 



The change in proportion of homozygosis with continued self-fertiliza- 

 tion was given by Jennings (6). The effects of continued brother-sister 

 mating were investigated by Pearl, Fish, Jennings, and Robbins, and are 

 reviewed by Wright (ii). The rate of increase in the proportion of homo- 

 zygosis, and the limit reached, under systems of less intense inbreeding are 

 by no means easy to see. A general method for determining them has been 

 devised by Wright (ii, 17) using his ingenious method of path coefficients. 

 For our purposes it will be sufficient to cite only a few of the results (Fig. 



131)- 



Figure 131 shows that with brother-sister mating (two parents in each 

 generation) the rate of loss of heterozygosis is much more rapid than with 

 double-first-cousin mating (four parents in each generation), although it 

 is considerably slower than that which can be obtained when self-fertiliza- 

 tion (one parent in each generation) is possible. The inbred strains of 

 laboratory mammals have been produced almost exclusively by brother- 

 sister mating. With this system, each generation theoretically loses 

 approximately 19% of its heterozygosis in the succeeding generation 

 (except that the fluctuation is wide of this mark in the first three genera- 

 tions). The actual proportions of heterozygosis in succeeding generations, 

 giving the curve in Fig. 131, are: (i, }4), %, %, ^{q, %2, etc. The propor- 

 tions can be written for any number of generations simply by following the 

 rule that each numerator is the sum of the two preceding, while the denomi- 

 nators double in each successive generation. 



Mating offspring with younger parent, generation after generation, gives 

 the same result as brother-sister mating, with the exception that the average 



