38 STATISTICAL METHODS. 



CHAPTEK Y. 

 SOME APPLICATIONS OF STATISTICAL BIOLOGICAL STUDY. 



The Laws of Variation. Darwin and others have 

 formulated certain laws of variation, such as the law that 

 specific characters are more variable than generic ones ; that 

 highly aberrant characters are more variable than more usual 

 ones ; that males are more variable than females. These laws 

 can be established only by a determination of the Index or 

 Coefficient of Variation in critical cases. 



The causes of variation can be determined only by r 

 quantitative study of the relation between specific change and 

 environmental change, or a knowledge of the degree and fre- 

 quency of sports. 



The effect of selection in causing a greater death rate on 

 one side of the mean than on the other side the production of 

 skewness requires the quantitative method for its complete 

 study. The change in the mode and in the index of skewness 

 measures the progress of the effect of selection. 



The origin of species through geographical segrega- 

 tion can be studied by the determination of place-modes ; that 

 is, the modal condition of specific characters of one and the 

 same species in various localities. The progress of specific 

 differentiation will be measured by the change in place-modes 

 from decade to decade, or by the formation of a binomial curve 

 in the place of a modal one ; and by the gradual separation of 

 the two modes of a binomial curve. 



The definition of species may be improved by being 

 rendered more quantitative. The relative importance of the 

 various criteria used in separating species may be determined 

 by finding that character in which there is least intergrading 

 between the modal condition characteristic of the two races. 

 Thus if for two species or varieties of birds both total length 

 and form of bill show two modes, the better criterion is that 

 in which the modes are farthest apart or in which the inter- 

 grades are fewest. 



