214 MENDELISM 



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, 6, or c, according as the corresponding proto- 

 zygote, heretozygote, 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 = b, 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 

 on the Mendelian theory of inheritance when applied 

 to populations. These figures are calculated on the 

 supposition that there is random mating of the parents, 

 but if there were a tendency for like to mate with like 

 the correlation values would become still higher. Yule 

 therefore concludes that ' there is therefore no diffi- 

 culty in accounting for a coefficient of 0*5 on the 

 theory of segregation, but such a value probably 

 indicates an absence of the somatic phenomenon of 



