288 maine agricultural experiment station. i914 



Studies on Inbreeding, iv. on a General Formula eor 



THE Constitution of the A^th Generation of a 



Mendelian Population in which all Mat- 



iNGs Are of a Brother x Sister.* 



In this paper it is shown that if we let 



On-i denote the number of AA families in the n — ith genera- 

 tion, and 



Pn-i denote the number of AA-\-Aa families in the n — ith 

 generation, and 



Qn-i denote the number of Aa families in the 11 — ith genera- 

 tion, and 



Rn-i denote the number of AA and 2Aa and aa families m the 

 n — Ith generation, and 



Un-i denote the number of Aa-\-aa families and 



Vn-i denote the number of aa families. , 



Then the families in the wth generation will be given by the 



following relations of the coefficients. 



Studies on Inbreeding, v. Inbreeding and Relationship 

 Coefficients.** 



The object of this paper is to call attention to the fact that 

 inbreeding of considerable degree may exist in the entire ab- 

 sence of any kinship between the two individuals bred together, 

 and to bring forward a method of separately measuring what 

 proportion of the observed inbreeding in a particular case is due 

 to kinship of the parents, and what to earlier ancestral redupli- 

 cation. A proposed coefficient of relationship is described, and 

 its application illustrated by concrete cases. 



*This is an abstract of a paper bearing the same title by Raymond 

 Pearl, published in the American Naturalist, Vol. XL,VIII pp. 491-494. 



**This is an abstract of a paper bearing the same title by Raymond 

 Pead, published in the American Naturalist, Vol. XLVIII, pp. 513-523. 



