Wrio-ht: Analysis of Livestock Breeding ^Methods 343 



(a) Two generations of brother-sister mating 



Fx=37.5%, RsD=60%, 



(b) Three generations of brother-sister mating 



Fx=50%, RgD=72.7%, 

 R^v=40.8% 



TWO AND THREE GENERATIONS OF BROTHER-SISTER MATING 



Fi-ure 2 For explanation of symbols see Figure 1. The effects of continued close 

 breeding on 'homozygosis and resemblance due to relationship are analyzed m the text 

 with the help of these diagrams. 



throutrh six independent chains. S-T-D, 

 S-E-D, S-T-U-E-D, S-T-F-E-D, 

 S-E-U-T-D, S-E-F-T-D. The formula 

 is thus 2{y2y + HViY = H or 37.5 

 per cent. 



With three generations of brother- 

 sister mating (Figure 2b) we encounter 

 for the first time ancestors of the sire 

 and dam which are inbred- There are 

 as before two chains of two genera- 

 tions each by which sire and dam are 

 connected through their parents, and 

 in addition, four chains of four gen- 

 erations each, by which they are 

 connected through their grandparents. 



Similarly we hnd eight chains of six 

 generations each tracing to their great- 

 grandparents. The parents of the sire 

 and dam are themselves 25 per cent 

 inbred, having one generation of in- 

 l)reeding back of them. The formula 

 thus becomes 2(>^' X 1.25) + 4(>^)'' 

 _|_ 8(>^)' = 3^. The individual X is 

 50 per cent inbred. The reader will 

 have no difficulty in carrying the re- 

 sults to further generations and dis- 

 covering that the limit under indefinite- 

 ly continued inbreeding is 1, complete 

 homozvgosis. as it should be according 



