and 



SYSTEMS OF MATING 7 7 



V n = A n V , and for n = 12, 



A 12 = / 1.835 x 10- 1 



8.311 x 10- 5 



1.526 x 1 







V 12 = /7.859 x 10 2 

 6.772 x lO' 7 

 5.960 x 10" 8 



p 12 = A" *V 12 =: /0.8923X , i.e., p 12 = 0.8923 



0.0060 \ q 12 = 0.0060 



0.0629 I r 12 = 0.0629 



^0.0389/ v 12 = 0.0389. 



This corresponds with the value of/> 12 in figure 2, and the other values also agree with 

 results gained by repetitive application of equation (2) . 



To calculate the generations required to obtain a given percentage of incross 

 matings, formula (10) is used, which gives us an approximation: 



n log Xi ^ log b u - log (1 - a0 

 for ai = 0.95, 



^ log 1.3708 - log 0.05 = 

 " = log 0.8090 ~ ' * 



Therefore it is estimated that 16 generations will be required to give 95 per cent incross 

 matings. Checking, we find that 



p 16 = 0.9539, 

 and 



p lb = 0.9430. 



Repeating the calculations for a 2 = 0.99, 



^ log 1.3708 -log 0.01 _ 

 " = log 0.8090 



and 



p 2i = 0.9915, 



whereas 



p 23 = 0.9895. 



Thus, .16 generations of brother-sister inbreeding are required to obtain 95 per 

 cent incross matings, and 24 generations to obtain 99 per cent. 



Dozens of strains of mice have been inbred by means of brother-sister matings. 

 A few examples are A/J, AKR/J, BALB/cJ, C57BL/6J, DBA/2J, and C3HeB/FeJ. 

 For a complete listing, refer to Committee 220 and Snell and Staats. 1254 



