322 



Data for the Prohlan of Evolution in Man. 



of assortative mating in the paper"*^ " Data for the Problem of Evohi- 

 tion in Man. IIL"t 



(d) The parental coefficient of heredity will generally be increased 

 by taking all instead of a single one of the offspring. 



For example, putting = 0, pio-1/5 = p2^2is = t as before, we find 

 for equipotency — 



Pl2 - t2/(1 + T% P31 - PB2 = 7(1 + 2t2)/(1 + T^). 



Thus pzi = rsi \/l +/)i2, 



showing how the spurious coefficient of assortative mating modifies 

 the coefficient of inheritance. 



6. Thus I think it will be clear that Beprodudive Divergence has not 

 an effective existence. More generally Reproductive Selection, unless we 

 suppose al) initio a fertility distribution with two modes (which is not 

 given by homogamy, and wants, in any case, a special explanation), 

 will not produce differentiation. It can produce, as I have often 

 stated, progressive change. So far as I can yet see, differentiation 

 must involve natural selection, and one can only appeal to reproductive 

 selection as a means, but I think an effective means, of maintaining a 

 differentiation already brought about by Darwin's fundamental factor 

 in evolution, 



Mr. Vernon, in his first paper, states that given a relationship 

 between homogamy and fertility, then reproductive divergence "is 

 capable of mathematical demonstration. This we will now proceed to 

 afford " (p. 182). 



In his second paper, he gives what he terms " the mathematical 

 basis of the theory more fully " (p. 404). I venture to thiak that the 

 whole of his treatment is fallacious. In the first paper he neglects the 

 Law of Regression, and he thinks this justifiable, but it is not so. In 



* * Eoy. Soc. Proc.,' Tol. 66, p. 30. 



t Assuming equipotent hereditary influence of father and mother for stature, we 

 have from the above paper — 



p = O-IVSS, = 0-0931, and 



= (Pi2-n2)/{(l-Pi2)(l-V)} = 11-9626. 

 Hence p-[(J\ls = = r = 3"4587. Thus from the equation for,-^ we find 



y = 3-4587 / + ^1 _ + \ 



S V (Ti (To / 



If = + Xi — stature of father, = + x^y = stature of mother, we liave 

 for the relation between fertility and homogamy 



li-9626/Xi_X,y 

 n =■ %e 2 \ o"! (To/ . 



This will suffice to indicate how such relations can be numerically investigatedi 



