EVOLUTION 



485 



that the third column giving the variabilities only becomes 

 approximately correct when the selection is very stringent 

 round the type. 



Turning now to the second case, in which we are 

 ignorant of the mid-parents beyond the nth generation and 

 cannot assert that they were mediocre, we can deduce an 

 expression for the average offspring of the form — - 



where e^^, 6.-,, e.^ . . . e„ are numerical constants, no longer 



but varying with the number of 



ill 



2' 4' S 



2"> 



equal to 



generations 



Their values are the following :- 



during which selection has taken place. 



Table of Pedigree Stock 



Now the results here appear even more remarkable than 

 in the previous table. We see that after six generations 

 of selection the selected individuals will, without further 

 selection, breed true to the selected type within nearly i 

 per cent of its value. But their variability about this type is 

 only some 1 1 per cent less than the racial variability before 

 selection. Thus the tendency to vary has been preserved, 

 while the type has been permanently, and it may be pro- 

 foundly, modified. These results appear well in accordance 

 not only with breeders' experience, but with our observa- 

 tions of nature. 



If selection were to act upon our 5' g" Englishmen, 

 and the 6' among them were the type best fitted to 

 survive, then with fairly stringent selection it would not 

 take more than six generations to produce a type sensibly 



