1896.] 



On the Mathematical Theory of E eolation. 



301 



Stebbing, Rev. Thomas Roscoe Y 



Rede, M.A. Y 



Stewart, Professor Charles, Y 



M.R.C.S. Y 



Tanner, Professor Henry William Y\ 



Lloyd, M.A. 



Tatham, Jolm P. W., M.R.C.P. Y 



Trouton, Professor Frederick Y\ 



Thomas, M.A. 



Turner, Professor Herbert Hall, Y\ 



M.A. 



The following Papers were read 



Waterhouse, James, Colonel. 

 Whymper, Edward, P.R.G.S. 

 Wilson, William B. 

 Wimshnrst, James. 

 Windle, Bertram Coghill Allen, 

 M.D. 



Woodhead, German Sims, M.D. 

 Woodward, Horace Bolingbroke, 

 F.G.S. 



Wynne, William Palmer, D.Sc. 



I. '* Contributions to the Mathematical Theory of Evolution. 

 Note on Reproductive Selection." By Karl Pearson, 

 University College, London. Communicated by F. Galtox, 

 F.R.S. Received February 13, 1896. 



(1) In a recent memoir (" Contributions to the Mathematical 

 Theory of Evolution, III. Regression, Heredity, and Panmixia," now 

 in type for the ' Philosophical Transactions ') I have found ib neces- 

 sary to note the difference in mean and variation of a pop ul alien 

 when (a) the individuals of a sex are taken into account once as 

 mates, (b) when the individuals of a sex are treated as parents or 

 weighted with their fertility. The mean and variation of the popu- 

 lation are supposed to be taken with regard to any organ whatever. 

 If such a difference is found to exist between the variation curves 

 for mates and for parents, then there is a correlation between fertility 

 and the organ (or characteristic) measured. Under the action of 

 heredity there will accordingly be a progressive evolution in this 

 organ, unless this evolution be checked by some other factor of pro- 

 gressive change, e.g., natural selection. In my memoir I term this 

 factor of progressive evolution 'Reproductive Selection* Without 



* The influence of variation in fertility has been considered by Mr. Romanes 

 under the title of ' Physiological Selection,' but the idea he expresses by this term 

 appears to me very different from that of reproductive selection. In mathematical 

 language, Mr. Romanes supposes the fertility curve and the correlation surfaces, 

 owing to some cause or other, to become double-humped ; they may accordingly be 

 resolved into two components, each corresponding to a distinct species. Physio- 

 logical selection thus aims at an explanation of the origin of species. Reproductive 

 selection supposes the fertility curve and correlation surfaces to embrace only 

 homogeneous material, and it can accordingly never give rise to a new species ; it is 

 purely a source of progressive change in the same species. The only approach to a 

 double hump which occurs in the curves of human fertility that I have dealt with 

 is a secondary maximum at absolute infertility, due in all probability to arcifleiuL 



Y 2 



