Data for the Prohlcni of Evolution in Man. 



317 



on the correlation of fertility and homogamy, I want at once to express 

 my entire disagreement with his view of reproductive selection, if he 

 holds it, as he appears to do,* as a source of divergence or differentia- 

 tion quite independent of natural selection. 



The simple fact is, that if fertility be any function of the organs or 

 relative organs of the parents, having a frequency distribution defined 

 by a normal frequency surface, or by any surface approximating to 

 such a chance distribution, then reproductive selection, whether homo- 

 gamy or any other factor be present, may, under special circumstances, 

 produce a progressive change in a character ; it cannot, unless other 

 factors of evolution, such as natural selection, come into play, produce 

 differentiation. 



2. I shall assume throughout my proof that the frequency distri- 

 butions obey the normal law. Now let one offspring only be taken 

 from each pair of parents, and let the organs in the two parents be 

 + Q'l, m-i + x-2y and in the offspring niz + a*3, where mi, nu, nis, are 

 the respective means ; let a-i, (r.2, 0-3 be the standard deviations of the 

 three organs, and Ou, r.23, r^i, the coefficients of correlation, then the 

 frequency pjSo^i 8a.-2 8xs of a triplet of parents and offspring with organs 

 lying between Xi and Xi -{- 8x1, X2 + ^.^-2, % and x^ + 8xs, respectively, 

 is determined byf 



i- — -. (1 - nr) - 2 (ri2 - r.-iV-^i) 2 (ros - ?3iri2) 



0-3- a-icr2 0-20-3 



X^XiXl 



- 2(r3i - ri2r23) > , 



V30-1 J J 



where X = 1 - - r.>r - rsr + 2 'ri2r23r3i, 



and N = total number of pairs of parents. 



If, instead of the single offspring, we take we have only to 

 replace N in the above results by n'^. 



Now reproductive selection supposes the fertility of a given pair not 

 to be independent of the measure of their organs, in this case of 

 mi -1- Xi and + X2. 



If we suppose n to represent the total fertility of a given pair, we 



* " This dirergence of species takes place quite independently of natural selec- 

 tion, but this principle can always be exerting its action at the same time, whereby 

 the new or modified characteristics produced can, if useful to the species, be accu- 

 mulated and rendel-ed better adapted to the environmental conditions." 'Natural 

 Science,' vol. 11, p. 186. 



t ' Phil. Trans.,' A, vol. 187, p. 287. 



JN 



expt. 



