23 



Inbreeding in a Stable Simple Mendelian Population with Special 

 Reference to Cousin Marriage. 

 By S. M. Jacob, I.C.S., Biometric Laboratory, University College, London. 



(Communicated by Prof. Karl Pearson, F.R.S. Received March 18, — Read 

 May 18, 1911.) 



CONTENTS. 



PAGE. 



1. Introductory 23 



2. Brother-Sister Marriages 24 



3. First Cousin Marriages 26 



4. General Sibling Families 29 



5. nth Cousin Marriages 31 



6. Second Cousin Marriages in Detail 33 



7. Numerical Proportions of Constituents for First Cousin Marriages ... 34 



8. Percentage of Allogenic Offspring which arise from First Cousin 



Marriages 35 



9. Relative Eate of Production of Allogenic Constituents by First 



Cousins and Non-related Pairs 38 



10. Conclusions and Limitations 40 



. 1. The Mendelian theory of the segregation of unit characters, though itjis 

 far, as yet, from being completely demonstrated, offers a simple explanation 

 of some striking features of inheritance. In particular, Mr. E. C. Snow has 

 recently shown* that the gametic correlations for collaterals deducible from 

 the Mendelian hypothesis are in close agreement with the actually observed 

 somatic correlations for man and certain other animals ; or, in other words, 

 that a Mendelian theory of segregation without dominance gives values 

 for collateral resemblance not greatly differing from those found from 

 observation.f 



It seems, therefore, possible that the same theory will throw some light on 

 the problem of inbreeding, or, at any rate, will indicate to what points, on 

 which precise data are at present lacking, statistical encpuiry should be 

 directed. Without these data the Mendelian theory cannot be corroborated 

 or negatived by the methods of the present paper. So far as they go, 

 however, the statistics at present obtainable with regard to consanguinity in 

 the parentage of albinos and deaf mutes are in approximate agreement with 

 the calculated results, although the accuracy of the figures is too uncertain for 

 the application of anything more than a rough criterion. 

 * 'Roy. Soc. Proc.,' B, vol. 83, 1910. 



t Prof. Pearson had previously shown that this result is true for the ancestral relation- 

 ships, ' Roy. Soc. Proc.,' B, vol. 81, 1909. 



