MENDELISM AND BIOMETRY 231 



Consequently Pearson's treatment of the subject does 

 not justify his statement that the Mendelian theory 

 gives a rigid value for the coefficients of parental cor- 

 relation for all races and characters a conclusion 

 which he regards as fatal to this theory, because the 

 coefficients for different characters and races, as found 

 statistically, show considerable individual differences, 

 and seem to cluster round a value considerably higher 

 than that indicated by his elaboration of the theory of 

 the pure gamete. Yule thereupon discusses a somewhat 

 more general case, and considers the inheritance of a 

 length made up of a number of distinct segments, each 

 of which is determined by an independent pair of 

 allelomorphs. Supposing each segment to take the 

 length a, b, or c, according as the corresponding proto- 

 zygote, heterozygote, or allozygote is present, Yule 

 arrives at an equation from which the correlation 

 between parent and offspring may be found. From 

 that equation the following results are deducible : 



If there is dominance i.e., if a = 6, or b = c, the corre- 

 lation coefficient is the same as that found by Pearson 

 i.e., one-third. 



But if the heterozygote always gives rise to a 

 length exactly intermediate between those due to 

 the respective homozygotes, the correlation is found 

 to be one-half. 



Cases of partial dominance will give an intermediate 

 value. Consequently, according to the degree of 

 imperfection of dominance, and without assuming any 

 other disturbing circumstances, values of parental 

 correlation varying from 0-33 to 0-5 are to be expected 



