400 



Prof. Karl Pearson. 



(8) I venture to think this table of considerable suggestiveness, 

 and will now point out some of the conclusions that may be drawn 

 from it. 



(i) "With a view of reducing the absolute variability of a species it 

 is idle to select beyond the grandparents, and hardly profitable to 

 select beyond parents. The ratio of the variability of pedigree stock 

 to the general population decreases 10 per cent, on the selection of 

 parents, and only 11 per cent, on the additional selection of grand- 

 parents. Beyond this no sensible change is made. We cannot then 

 reduce variability beyond 11 per cent, by the creation of a pedigree 

 stock, i.e., by breeding from selected parents for 2, 3, 4, .... n genera- 

 tions. In some cases of course we appear to decrease variability — 

 for example, if we increase the average size of an organ — for the 

 absolute variability is then a smaller proportion of the actual size, and 

 the relative variability, or coefficient of variation, may thus be steadily- 

 decreased. If Mr. Galton's law be true, then pedigree stock would 

 retain only a slightly diminished capacity for variation about the 

 new type. For example, the absolute variability of men of average 

 height, 69'2 inches, being 2*6 inches, the absolute variability of men 

 of 72 inches, obtained by selecting any number of 6-foot ancestors, 

 would hardly fall short of 2*3 inches.* 



(ii) Two different classes of pedigree stock exist. In the one we 

 start with the general population, and select special characters for 

 1, 2, 3, . . . . n generations. In the other we know the pedigree for 

 I, 2, 3, .... n generations, but have no reason for supposing that 

 before these generations the stock was absolutely identical with the 

 general population. 



In the former case we put for the mid-parents 



lC\ — 7^2 — &3 — — • • • ■ — h n = K, + l — &«+2 = &ao — 0. 



Hence the regression formula is 



The values of Tc /K are tabulated in the last column of the table 

 above in brackets. They give the ratio of character in offspring to 

 character in ancestors, if ancestors of equal fall character have been 

 selected for n generations. We see that in six generations the off- 

 spring will have been raised to within 1*6 per cent, of the selected 

 ancestral character. 



In the latter case we must use the partial regression coefficients 



* The probability of an individual of selected stock differing widely from the- 

 type is of course mucb less than in the general population, because the stock is,, 

 as a rule, far less numerous. 



