502 THE GRAMMAR OF SCIENCE 



three of the most basal for our further knowledge of 

 evolution. 



SUMMARY 



While in the previous chapter we have discussed how variation and selection 

 are to be quantitatively measured, we have in this applied similar methods to 

 other phases of the exact theory of evolution. The possibility of differentia- 

 tion as distinct from mere change of type is seen to depend (i.) on the dis- 

 appearance or non-existence of pangamic mating; (ii.) on the contemporary 

 differentiation of the type of maximum fertility. That the distribution of 

 fertility is not random, and that even in mankind mating is far from pangamic 

 have been quantitatively demonstrated. In order to ascertain how heredity fixes 

 the results reached by selection, we have considered the quantitative treatment 

 of inheritance and illustrated by numerical examples the intensity of heredity. 

 Our methods 'enable us to determine some of the laws of prepotency and 

 dismiss as highly improbable any theory of steady telegonic influence. Ap- 

 plied to fertility we discover that it is an inherited character, and conclude 

 that reproductive selection has far-reaching influence not only on the evolution 

 of types of wild life, but upon important social problems. Dealing with the 

 influence of two parents and afterwards of the entire ancestry, we conclude 

 that any amount of selection will not reduce the variability of a race more 

 than some lo or ii per cent, so far as normal variations are concerned ; this 

 fact, coupled with the previously noted fact that individual variability amounts 

 to some 80 per cent of racial variability, leads us to consider variation as a 

 permanent attribute of living forms which can hardly have been substantially 

 modified since the beginnings of life. In the same manner we find heredity 

 intimately associated with variation in the individual, and not differing very 

 substantially as we pass from one character to a second, or from one to another 

 form of life. We conclude that variation and inheritance rather precede than 

 follow evolution, they are, at present, one fundamental mystery of the vital unit. 

 Of the two kinds of inheritance — the blended and the exclusive— we see that the 

 first leads us up to the great principle of regression and the second to that of 

 reversion. These two factors of evolution, regression and reversion, are 

 shown with much probability to obey simple quantitative laws. Applying the 

 principle of regression in the case of continuously selected stock, we see how 

 the laws of heredity enable us to establish breeds and obtain permanent differ- 

 ences of type, thus selection for six generations will enable us to reach a 

 permanent type with less than 2 per cent divergence from the selected type. 

 Accordingly in rapidly breeding animals the effect of natural selection can 

 exhibit itself with great rapidity, and the myth of degeneration following on 

 panmixia is dissolved. Taking man as a case in which the intra-group- 

 struggle for existence is largely suspended, we have made an endeavour to 

 determine the proportions of the selective and non-selective death-rates. 

 The problem is seen to reduce to that of ascertaining how far inheritance 

 of the duration of life extends. In some 80 per cent of cases we find the 

 death-rate to be selective, and thus conclude that even in man natural 

 selection is an important factor. The difficulties which still meet us in the 



