1896. REPRODUCTIVE SELECTION. 323 



could not cover had they been based solely on the usual or normal 

 theory of correlation. 



(3) By simply forming the means for any organ (or characteristic) 

 for mates and for parents, we can ascertain from Equation (i) if 

 there is or is not any sensible correlation between that organ (or 

 characteristic) and fertility. Equation (ii) enables us to verify the 

 value found for p, since 07, and <r m are easily calculated when we 

 know the distribution of fertility. If the correlation were normal 

 S (x z y') would be zero, and this term, it may reasonably be expected, 

 will never be very large. When p has been found from Equation (i), 

 then Equations (iii) and (iv) give us M x — M and o^ — cr 0> or the 

 measures of reproductive selection in its action on the mean and 

 variation of successive generations. 



(4) I have applied these results to the only case — that of man — in 

 which statistics are at present available. 



I find for upwards of 4,000 families, principally of Anglo-Saxon 

 race, = 0-692, and for 1,842 families of Danish race, v = 0-652. 

 This, considering difference of race, is a very satisfactory agreement. 

 In the next place, there appears to be a significant difference 0-278" 

 between the mean height of mothers of daughters and the mean 

 height of wives. Thus, we have pva- m = 0-278", and since <r m = 2*303", 

 it follows that pv = 0*121. Now, the coefficient of variation for 

 fertility in daughters is not quite the same, but still very nearly 

 the same as that for fertility in general. We therefore find that 

 p = 0-175 to 0-186, according as we use the first or second value of 

 v given above. We may accordingly conclude that there is a sensible 

 correlation {circa 0-18) between fertility and height in the mothers of 

 daughters. 



Turning now to Equations (iii) and (iv), I note that r 0t o- 0> and r 2 

 are multiplied by the small quantities p and 1 — (a-p'<T m ) 2 , and that r 

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

 Hence, neglected to a first approximation p-, we can use the value Yp f 

 already known, for r in (iii) and (iv) and the value <r lt already 

 known for o- in (iii), we thus deduce — 



M 1 -M =o-o8i". 



o-j — cr = — 0'Oo8". 



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 

 3^ inches. A factor which would alter stature by about 3 inches in 

 1,000 years is clearly capable of producing very considerable results 

 in the long periods during which evolution may be supposed to have 

 been at work. In the case of both mean and standard deviation the 



2 a 2 



