MATHEMATICAL CONTRIBUTIONS TO THE THEORY" OF EVOLUTION. 235 



on the magnitude of the probable errors of the variation constants, and therefore on 

 the size of the selection. Then the system Scr,, So-,, 8o- 3> . . . 8r K , Sr., 3 , Sr, 3 , . . ., is not 

 a system of independent variations, but the changes in variation and correlation are 

 correlated together, since the terms F M , do not generally vanish. We therefore 

 conclude that if a random selection be made out of a population with regard to one 

 organ o-,, there will be tendencies for the variation of all other organs and the 

 correlation between all organs to change also in certain directions, which can be 

 definitely indicated so soon as the general population has been measured, and the 

 effect of the random selection on one organ has been ascertained. What is proved 

 here of random selection will be shown to be true still more intensively for artificial 

 selection,* i.e., every selection of one organ modifies in a correlated manner the 

 variation and correlation of all other organs. It is impossible to alter one organ 

 without altering all other organs and their relation to each other. 



() The remarks in (y) are not only true for a random selection of variation, but 

 equally well apply to selection of sixe. This follows because the terms Q, and O,, do 

 not as a rule vanish. If a random selection of 100 or 1,000 individuals be made out 

 of a general population, then the mean sixe of any organ in this sub-group will 

 probably differ from that of the general population. The result is that the sixe of 

 all other organs, their amounts of variation and correlation, will probably have values 

 differing in definite directions from those of the general population. 



(e) Take two random selections out of a general population ; the probability is that 

 they will have different means for any one organ, and a result will be that they will 

 have correlated systems of changes in the sixes, variations, and correlations of all 

 other organs. In other words, random selection produces a differentiation of all 

 characters, which differentiation will bo the more marked the smaller the random 

 selection. t 



() This principle that a random selection gives a system of correlated changes in 

 the deviations of all the characters of a species seems, to some extent, capable of 

 explaining the small but systematic differences to be found occasionally between 

 closely allied species. It is not necessary to suppose them due to a long process of 

 natural selection acting on a variety of organs ; a small random selection, or possibly 

 a natural selection of one organ, might suffice to produce the systematic differences of 

 character in all organs. 



How far a succession of random selections would give an evolution biassed by the 

 first random selection requires further consideration ; but it seems impossible for the 

 characters of a race to remain fixed under the influence of a heavy but non-selective 

 death-rate. They will vary from year to year, although this systematic change of 



* " Memoir on the Influence of Selection on Correlation." Selection not only modifies correlation, 

 but the selection of one organ can create correlation between organs previously uucorrelated. 



t Continuous artificial selection of an organ produces a still more marked differentiation of all other 

 characters, but this is treated of in another memoir. 



2 H 2 



