196 Selection and Assortative Mating in Mendelian Population. 



of the dominant and recedent homozygotes. For, if any selected sample of 

 the form pi\ A A) + 2p\q\{ Aa) + q\\aa) be taken from the general population 

 p 2 (AA) + 2z)q(Aa) + q 2 (aa), the parental and fraternal correlations reached 

 when the individuals of the selected sample mate at random within the 

 sample always have the constant value 0"5. 



The investigation next considered the question of assortative mating within 

 a random sample of the general population. Such mating, if positive, increases 

 the parental and sibling regressions as well as the correlations. The ancestral 

 regressions diminish in geometrical progression, the correlations not perfectly, 

 but nearly so. In certain cases the expressions found for the parental and 

 sibling correlations were identical with those reached by the very general 

 methods previously employed by Pearson, and which have no connection 

 whatever with Mendelism, but this can hardly be more than a curious 

 coincidence. 



When we deal with assortative mating within a selected sample, we find 

 the regression of offspring on parent depends upon both the assortative mating 

 and the intensity of selection, and increases as those factors increase. 

 Selection and assortative mating affect the correlations in opposite directions, 

 the decreasing tendency of the former appearing to have the predominating 

 effect in practical cases. The sibling correlation is not raised so much by 

 assortative mating nor reduced so much by selection as is the parental one. 



Fairly similar qualitative results were found throughout for somatic 

 characters, though not so much weight can be given to them as to those for 

 gametic characters. Moreover, it is the latter which agree most closely with 

 observation. It is to the results for gametic characters, therefore, that we 

 must look for theoretical verification for experimental conclusions which, at 

 first sight, appear paradoxical, e.g. the closeness of the resemblance between 

 cousins. 



