SHORTER ARTICLES AND DISCUSSION 



ON THE RESULTS OF INBREEDING A MENDELIAN 

 POPULATION : A CORRECTION AND EXTENSION 

 OF PREVIOUS CONCLUSIONS 1 



In a recent paper by the present writer on inbreeding, 2 the con- 

 clusion was reached (loc. cit., p. 608) 



that no increase in the proportion of homozygotes in the population 

 (a) Continued self-fertilization. 



(6) Some form of gametic assortative mating which increases the 

 natural probability of like gametes uniting to form zygotes. 



This conclusion is entirely correct as it stands, but also barren, 

 for it overlooks the very essential fact that any sort of inbreed- 

 ing involves in greater or less degree " gametic assortative mat- 

 ing." The mathematical demonstration on page 608 of the paper 

 referred to is also entirely correct so far as it goes, but it stops 

 too soon. Up to the third generation of brother X sister mating 

 starting from a population of complete heterozygotes there is no 

 increase in the proportion of homozygotes beyond that prevailing 

 in a general Mendelian population. In the fourth and later gen- 

 erations there is, however. The blunder, kindly pointed out to 

 me by Professor E. M. East, which in retrospect seems altogether 

 too stupid even to be possible, was in the failure to recognize that 

 after the second generation the constitution of the family would 

 no longer be the same as that of the population. This is the point 

 which makes illegitimate the extension by induction of the results 

 up to the third generation to the generations beyond. 



The general conclusion of the former paper quoted above, 

 should then be as follows : An increase in the proportion of homo- 

 zygotes in the population will follow inbreeding of any sort, 

 though at different rates for different types of inbreeding, 

 because any inbradiny i>u-olr<s homoyamy (or assortative mat- 

 ing) in some degree. 



Having made clear the location and nature of the error I desire 

 now to show in some detail exactly what results follow from con- 



1 Papers from the Biological Laboratory of the Maine Agricultural Ex- 



2 "A Contribution Towards an Analysis of the Problem of Inbreeding," 

 American Naturalist, Vol. XLVII, pp. 577-614, 1913. 



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