SHORTER ARTICLES AND CORRESPONDENCE 



ON THE PROGRESSIVE INCREASE OF HOMOZYGOSIS 

 BROTHER-SISTER MATINGS 



It has been brought to my attention that the note concerning 

 inbreeding, written at the request of Mr. Phineas W. Whiting to 

 add to his paper on "Heredity of Bristles in the Common Green- 

 bottle Fly, Lucflia Sericata Meig.," which appeared in the Amer- 

 ican Naturalist for June, 1914, might be taken to mean that my 

 data had been sent by Dr. E. M. East to Dr. Raymond Pearl by 

 whom it had been published as his own. I wish to make it clear 

 by a statement of the facts herewith that no such interpretation 

 should be placed upon the note. I was seriously ill at the time 

 and did not submit my manuscript to Dr. Castle or Dr. East for 

 revision, as I should ordinarily have done. In that case no 

 doubt, any ambiguity of statement would have been pointed out 

 to me. 



Mendel, in his original paper, .showed that if equal fertility 

 of all plants in all generations is assumed, and. furthermore, if 

 every plant is always self- fertilized, then in the nth generation 

 the ratio of any allelomorphic pair (A,a) would be 2" — 1 AA: 

 2Aa:2"-^l aa. This statement was generalized in 1912 by East 

 and Hayes 1 for any number of allelomorphic pairs. "The prob- 

 able number of homozygotes and any parfieular elass of heterozy- 

 gotes in any generation r is found by expanding the binomial 

 [1 -j- (2 r — 1) ] " where n represents the number of character 

 pairs involved. The exponent of the first term gives the number 

 of heterozygous and the exponent of the second term the number 

 of homozygous characters." A little later Jennings independ- 

 ently showed how homozygotes are produced from heterozygotes 

 by self-fertilization. 2 



East and Hayes' 1 published no generalized formula for calcu- 

 lating the reduction toward homozygosis through any other type 

 of mating, but that this was thought to be a proper conclusion 

 deducible from the above is shown by the following quotation 

 (P. 21) : 



» U. S. Dept. Agr., Bur. Plant Ind., Bull. No. 243. 

 3 Loc. cit. 



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