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 uiiipareutal 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 

 arid the abmodality Jof the corresponding fraternity. More 

 strictly, since the variability of the character in the second 

 generation, cr 2 , 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,, the index should be taken as 



P 



<T 2 



The probable error of this determination is 



,67450-, /I - p,, 2 



-4/ , m which p 12 means the correlation coem- 



cr 2 n 



cient 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- is to 1. 



In bipareutal 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 



'7 



11 + P-2 fi-3, 



CT 2 0-3 



where 7ii .= average abmodality of fraternity ; 



A 2 = average abmodality of male parent ; 



7i 3 = average abmodality of female parent ; 



p, correlation coefficient between fraternity and 



female parent ; 

 p a = correlation coefficient between fraternity and male 



parent ; 



o-j = standard deviation of fraternity ; 

 <r 2 = standard deviation of male parent ; 

 <r 3 = standard deviation of female parent. 



