304 



On the Mathematical Theory of Evolution. [Mar. 5, 



Turning now to Equations (iii) and (iv), I note that r , <r , and r (J 2 

 are multiplied by the small quantities /> and 1 — (c^/a - ™) 2 , and that r„ 

 and a m only differ from r p and a T by quantities of the order p. 

 Hence, neglected to a first approximation /> 2 , we can use the value r pt 

 already known, for r in (iii) and (iv) and the value a u already 

 known for «7 i* 1 we thus deduce — 



M : — M = o-08i fr . 



ff, — a = —0-008". 



These are the effects of reproductive selection on the height of 

 women. We thus see that the effect is to render women less 

 variable, and to raise their mean height. The quantities are very 

 small, but it must be remembered that the process is secular. Thus, 

 supposing reproductive selection to have been unchecked by natural 

 selection, say, for forty generations, the mean height of women, 

 neglecting small quantities of the second order, would have been 

 raised about 3j inches. A factor which would alter stature by about 

 3 inches in 1000 years is clearly capable of producing very consider- 

 able results in the long periods during which evolution may be sup- 

 posed to have been at work. In the case of both mean and standard 

 deviation the changes from wives to daughters (0 - 25 / '' and 0*044") 

 are, in the only statistics at present available, far more considerable 

 than the above values ; but, it must be remembered, that other 

 causes than reproductive selection are at work, such as shrinkage 

 with age and the greater physical training of the young women of 

 to-day. 



(5) I have only been able to measure, so far, the actual value of 

 the correlation between fertility and any organ in the case of stature 

 in women. It would, doubtless, be more sensible in other cases, e.g., 

 pelvic measurements. But there are certain considerations which 

 may be referred to here, and which will suggest how important — at 

 any rate in the case of man — it is to take into consideration the 

 influence of reproductive selection. 



From considering the fertility of man, in England and in Denmark, 

 I conclude that 25 per cent, of the mated population produce one- 

 half the next generation. This is the gross fertility. Allowing for 

 the selective death-rate — which I knew only for Denmark — 27 per 

 cent, of the mated population produced half the next generation. In 

 other words, although natural selection tends to counteract reproduc- 

 tive selection by a death-rate which, it may be shown, rises continu- 

 ously and uniformly with increased fertility, yet, in the case of civilised 

 man, it is totally ineffectual as against reproductive selection. If we 

 allow for the portion of the population which remains unmarried, we 

 are well within the mark if we say that less than 25 per cent, of one 

 generation produce more than half of the next generation. Correla- 



