40 



Mr. S. M. Jacob. Inbreeding in a [Mar. 18, 



13 to 28 times more likely to have this pure recessive in their offspring than 

 are non-related couples. 



Were Mendelism completely established as a theory of reproduction 

 applicable to man, and were it shown that good qualities were absolute 

 dominants and bad qualities always recessive, the above result might 

 legitimately be used to show that first cousin marriages are undesirable. 

 But this is not so, and, in particular, it seems probable that dominance is not 

 complete, and that there may be some dominant harmful characters and 

 some useful recessive ones. 



General Conclusions and Limitations. 



10. (i) The not unimportant result has been proved that the more infrequent 

 a pure recessive factor is in any simple stable Mendelian population breeding 

 at random, then this pure recessive is less and less likely to occur in the 

 offspring of any type of marriage, whether consanguineous or not, though 

 at the same time it becomes relatively more and more likely to occur in 

 the offspring of related pairs. In other words, with a less and less 

 frequently occurring pure recessive, the decrease in the appearance of a pure 

 recessive in the offspring of related couples is not so rapid as it is in the 

 case of non-related pairs. 



Precisely the same conclusion applies to the production of the pure 

 dominant. Further, it has been shown that the relative frequency of the 

 appearance of the allogenic constituent in the offspring of related pairs 

 diminishes by about one-half for each grade of cousinship. Hence, if anything 

 can be urged against first cousin marriages as productive of patent recessive 

 qualities, the argument applies with less and less force to cousin marriages of 

 higher grades. 



(ii) The following general proposition throws a good deal of light on this 

 problem of inbreeding in a simple Mendelian population, namely : — 



The offspring of any system of inbreeding, provided there is no selective 

 marriage or death rate or differential fertility, can be expressed in the form 



^(AA) + 1 m (A«) + 2 2 2) [(AA)-2 (A a )+(«a)] ; 



That is to say, the offspring of consanguineous marriage can be expressed as a 

 sample of the general population, together with a part due to the inbreeding 

 factor (AA) - 2 (Aa) + (act). 



To show this, let the offspring of any system of inbreeding consist- 

 of a regrouping of the allelomorphs A and a, such that the term 

 L(AA) + M(Aa) + X (aa) is added to the general population. L, M, X, are 

 functions of p. q. 



