38 



Mr. S. M. Jacob. Inbreeding in a 



[Mar. 18, 



a selective infantile death rate, unfavourable to albinos and deaf mutes, and 

 that, consequently, the conditions of albinism and deaf-mutism are really of 

 more frequent occurrence than would appear from a count of the population 

 at any single instant. 



If this is so, Table II shows that there will be a great reduction in the 

 calculated number of deaf mute and albinotic persons who are the offspring 

 of a consanguineous parentage. 



Another point to be noticed is that Table II has been formed on the 

 assumption that first cousin marriage alone has a greater rate of production 

 of allogenic characters than the non-inbreeding population, whereas some of 

 the excess rate is due to second cousin and other consanguineous marriages. 

 As a matter of fact, if X 2 be the second cousin marriage rate, and g 2 the 

 proportion of allogenic element produced by it, and if A3, g s , be the same 

 functions for third cousin marriages and so on, then equation (12) becomes 



and this equation leads to a larger value of z than (12). 



Thus (13) determines a smaller value of c x than (12). Hence if the second 

 and third cousin rates were taken into account the values given in Table II 

 for A-iCi/E would to some extent be reduced. 



The second and third cousin marriage rates being almost wholly unknown, 

 it has not been feasible to allow for them. But part of the discrepancy 

 noted between calculation and observation can be explained in this way. 



9. Finally, it is important to tabulate the relative rates of production of 

 allogenic element by first cousin parents and by the non-related parents, 

 when there is a given frequency of occurrence of the allogenic element in 

 the population at large. The percentage of first cousin marriage is again 

 taken to have values from 1 to 5. 



The rates of production of the allogenic element by first cousin and non- 

 consanguineous marriages are respectively (l+giz)/(l + z 2 ) and 1/(1 + ; 2 ), 

 where z is given by equation (12). The relative rate of production is thus 



simply 1+giz, where g x = 4 Jg7— 1) ' ThiS h&S beGn calculated for 16s = 4 

 and s =oc , and the results are given in Table III. 



This table shows that while for a pure recessive which occurs in more 

 than 1 per cent, of the general population, a first cousin marriage is at 

 most not more than twice as likely to produce this constituent in its offspring 

 than a non-consanguineous marriage, in the case of a very rare recessive 

 constituent with a frequency, say, of 1 in 20,000, first cousins are from 



fliX-i+/7aX2 + </3*3 + - -A 

 100 E / 



: j +1 -i = a 



(13) 



