24 



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



The paper also gives a very simple operational notation by which the 

 sibling families in any generation can be at once written down. From this 

 result the offspring of the sibling group in any generation, when these mate 

 endogamously, can be immediately calculated. 



As Mendelism, whether it be finally accepted or rejected, is likely to be 

 a very much debated subject for some time to come, this condensed notation 

 may serve a useful purpose in minimising algebraical labour. Miss Elderton 

 and Prof. Karl Pearson have taken a special case of Mendelian inbreeding,* 

 in which one of the common grandparents of the inbreeding first cousins 

 is a pure recessive, although the occurrence of this pure recessive constituent 

 is assumed to be excessively rare in the population at large. If the 

 recessive constituent is a harmful one this makes first cousin marriages 

 appear in a very unfavourable light. As a matter of fact it will be shown 

 that where the recessive element is of very infrequent occurrence inbreeding 

 greatly increases the relative chances of its appearance in the offspring of 

 consanguineous matings as compared to its frequency in the offspring of 

 unrelated pairs ; but at the same time the absolute frequency becomes 

 smaller and smaller in both cases with increasing rarity of the pure recessive 

 in the general population. 



In the present paper the ancestry of the inbreeding sibling group is always 

 supposed to be a representative sample of the general stable population. 



The plan adopted will be, first of all, to obtain the offspring of brother- 

 sister and first cousin marriages in the direct way, and then to use the 

 operational notation to obtain the offspring of intermarrying nth. cousins. 

 Some numerical results have been calculated, and a comparison made with 

 the available statistics. 



The notation used will be the ordinary, though verbally somewhat 

 inconvenient one in which (AA), (Aa), (act), represent the protogenic, hybrid, 

 and allogenic constituents formed by a single alleloniorphic pair. 



Where only a single pair of allelomorphs is dealt with, the only possible 

 stable form of Mendelian community, in which there is no preferential 

 mating, selective death-rate, or differential fertility, is 

 f (AA) + 2pq (Aa) + <f (aa), 

 where the coefficients give the frequency of the elements which they precede. 



2. In order to obtain the offspring of brother-sister marriages we must take 

 each of the families shown in Table I on p. 41 of Mr. Snow's paper, and, 

 assuming that these first siblings consist of males and females in equal 



* 'Eugenics Laboratory Memoirs,' IV, "On the Measure of the Resemblance of 

 first Cousins." Dulau and Co., 1907. 



