342 



The Journal of Heredity 



chain, with the quaHfication that this 

 must be muhiphed by a corrective term 

 (1 + Fa), in case the common ancestor 

 {A) is himself inbred.* 



It was demonstrated that this coeffi- 

 cient measures accurately the percentage 

 departure from the number of homo- 

 zygous factors in the random-bred 

 stock toward complete homozygosis. 

 If there were for example, 60 per cent 

 homozygosis in the random-bred an- 

 cestral stock, a coefficient of inbreed- 

 ing of 50 per cent means that the in- 

 dividual in question should be homo- 

 zvgous in 80 per cent of his factors. 

 ' The method of calculation may be 

 made clearer by a few examples. Let 

 us take first the simple case in which 

 a mating is made between half brother 

 and sister (Figure la). The sire and 

 dam are connected in only one way. 

 There are two generations in the con- 

 necting chain. S-A-D. As the common 

 ancestor (A) is not himself inbred, 

 the formula is simply (>^)'. The co- 

 efficient of inbreeding is thus 12.5 per 

 cent. 



If the sire is a grandson and the 

 dam a daughter of the common an- 

 cestor (Figure lb), there are three 

 generations between sire and dam and 

 the coefficient is (^-2)'. or 6.25 per 

 cent. 



If now the mating is between full 

 brotherand sister (Figure Ic) ,the lattter 

 are connected by two chains, each con- 

 taining two generations. The formula 

 requires us to find the sum of the con- 

 tributions of each chain. We have then 

 (K)' + ('AY = M or 25 per cent as 

 the coefficient of inbreeding. With two 

 generations of brother-sister mating 

 (Figure 2a), the reader will readily see 

 that sire and dam are connected 



* Letting Fy. and F^ 1)C coefficients for the 

 individual and for a representative common 

 anccster of his sire and dam, and letting 

 n and »' be the number of generations be- 

 tween the sire and dam respectively and their 

 common ancester, we have as the general 

 formula : 



(a) A mating of half brother and sister 

 Fx=12.5%, RsD=25'?'f, 

 P -47.1% 



(b) A mating between grandson and 



daughter 



Fx=6.25%, RsD=12.5%, 



(c) A mating between full brother and 

 sister 

 Fx=25%. RsD=50%, 

 RxT=44.7% 



INBREEDING AND RELATIONSHIP 



Figure 1. The chart shows three cases of 

 inbreeding: mating of half brother and sis- 

 ter, mating between grandson and daughter, 

 and mating of full brother and sister. The 

 coefficient of inbreeding (F^) of the result- 

 ing individual is given, in each case, also the 

 coefficient of relationship between his sire 

 and dam (Rgp), and between X and the 

 ancestor to whom the inbreeding is due 

 (R.^.^). A coefficient of relationship of 50 

 per cent represents that existing between or- 

 dinary brothers and sisters. 



