320 l^rof. Karl Pear 



•son. 



s 



Pl-2 = /-T ;;-2— 2 r 2 2 ^ ^ 



P31 



o S 



(viii)- 



PS2 



(ix). 



Results (i) to (ix) contain the whole theory of the influence on 

 evolution of a relation between homogamy and fertility. 



4. General Conclusions. — {a) There is in general a progressive change 

 in the species as a whole, but no divergence or differentiation. 



ih) The change in the second generation (as given by (iii) ) is pre- 

 cisely what we might have anticipated from my theory of biparental 

 inheritance,* assuming that the offspring are those of parents differing 

 from the general population by an amount of the character which is 

 the excess marking parents weighted by their fertility from the general 

 parental population. 



(c) The offspring will be less variable than they would be without a 

 correlation between homogamy and fertility, Le.^ from (vi) 23 is always 

 less than 0-3. 



* ' Eoy. Soc. Proc.,' vol. 58, p. 240, or ' Phil. Trans.,' vol. 187, p. 287. Another 

 interesting relation of this kind is the following one t 



0-3 . / 1 - ^12^ - ^23^ - ^31" + 2r,2r23r3i ^ 2 \/ ^~ ~ ^"^^ ~ ^ ^Pl2P23P31 . 



or the variability of an array of offspring from selected parents is unaltered by the 

 relation between homogamy and fertility — a result which might be a priori 

 expected. 



