36 STATISTICAL METHODS. 



its parent or parents, but only with mean progeny of mean 

 parents. Any group of selected parents is called a parentage, 

 the progeny of a parentage is called a fraternity. 



In uniparental inheritance, as in budding or asexual 

 generation, heredity of any character is measured by the coef- 

 ficient of correlation between the abmodality in a parentage 

 and the abmodality |of the corresponding fraternity. More 

 strictly, since the variability of the character in the second 

 generation, cr z , may (as a result of selection or of environ- 

 mental change) be different from the variability of the char- 

 acter in the first generation, cr ly the index should be taken as 



The probable error of this determination is 



- , in which Pi 2 means the correlation coeffi- 

 n 



cieDt between the filial character and that of the single parent 

 under consideration. 



The variability of the fraternity is to variability of offspring 

 in general as |/1 p 2 is to 1. 



In biparental inheritance, if there is no evidence of 

 assortative mating, or correlation between the two parents in 

 the character in question, the mean abmodality of any frater- 

 nity will be 



cr,_ cr, 



hi = p 3 7i a + PI /i*, 

 cr 2 cr 3 



where h\ = average abmodality of fraternity ; 



7* 2 average abmodality of male parent ; 



h s average abmodality of female parent ; 



p a = correlation coefficient between fraternity and 



female parent ; 

 p 8 = correlation coefficient between fraternity and male 



parent ; 



o-! = standard deviation of fraternity ; 

 cr 2 = standard deviation of male parent ; 

 cr 3 = standard deviation of female parent. 



