Mathematical Contributions to the Theory of Evolution. 163 



"Mathematical Contributions to the Theory of Evolution. VI. 

 Eeproductive or Genetic Selection. Part I. Theoretical." By 

 KARL PEARSON, F.B.S. " Part II. On the Inheritance of Fer- 

 tility in Man." By KARL PEARSOX, F.K.S., and ALICE LEE. 

 " Part III. On the Inheritance of Fecundity in Thoroughbred 

 Race-horses." By KARL PEARSON, F.R.S., with the assist- 

 ance of LESLIE BRAMLEY-MOORE. Received November 14 



Read December 8, 1898. 



(Abstract.) 



1. The object of this memoir is twofold : first, to develop the theory 

 of reproductive or genetic selection* on the assumption that fertility 

 .and fecundity may be heritable characters ; and, secondly, to demon- 

 strate from two concrete examples that fertility and .fecundity actually 

 are inherited. 



The problem of whether fertility is or is not inherited is one of very 

 far reaching consequences. It stands on an entirely different footing 

 to the question of inheritance of other characters. That any other 

 organ or character is inherited, provided that inheritance is not stronger 

 for one value of the organ or character than another, is perfectly con- 

 sistent with the organic stability of a community of individuals. That 

 fertility should be inherited is not consistent with the stability of such a 

 community, unless there be a differential death-rate, more intense for the 

 offspring of the more fertile, i.e., unless natural selection or other factor 

 of evolution holds reproductive selection in check. The inheritance of 

 fertility and the correlation of fertility with other characters are prin- 

 ciples momentous in their results for our conceptions of evolution ; they 

 mark a continual tendency in a race to progress in a definite direction, 

 unless equilibrium be maintained by any other equipollent factors, exhi- 

 bited in the form of a differential death-rate on the most fertile. Such a 

 differential death-rate probably exists in wild life, at any rate until the 

 environment changes and the equilibrium between natural and repro- 

 ductive selection is upset. How far it exists in civilized communities 

 of mankind is another and more difficult problem, which I have par- 

 tially dealt with elsewhere.f At any rate it becomes necessary for the 

 biologist either to affirm or deny the two principles stated above. If 



* I have retained the term " reproductive " selection here, although objection 

 has been raised to it, because it has been used in the earlier memoirs of this series. 

 Mr. G-alton has kindly provided me with "genetic" and "proliferal" selection. 

 The term is used to describe the selection of predominant types owing to the 

 different grades of reproductivity being inherited, and without the influence of a 

 differential death-rate. 



f Essay on Reproductive Selection in ' The Chances of Death and other Studies 

 in Evolution,' vol. 1, p. 63, 



VOL. LXIV. 



