Studies on variation and selection. 



171 



as easy, if selection in reality changed the germinal bases underlying 

 the character in question. 



We challenge anyone, by selection to change any character in any 

 direction, beyond the range of its modifications, and then to bring it back 

 to its starting-point, beginning ivith one brother and one sister of like 

 grade (or with one plant) and by strictly inbreeding (self-fertilizing) 

 this family (brother to sister, parent to child). The range of modifi- 

 cations of animal characters to be measured by the greatest difference 

 in respect of the character selected, between the two sides (right and 

 left) of the most asymmetrical animal produced. For the whole animal 

 comes frome one zygote. 



IV. Statistical methods in the study of variation. 



A very lamentable error in the selection-experiments of some 

 authors and notably in those of Prof. Castle with Hooded rats, results 

 from the fact, that it is simply taken for granted that the material 

 is genetically pure, and can therefore be treated by statistical methods. 



Now, it may be conceded, that possibly the study of modifi- 

 cations of genetically pure material may be interesting fiom certain 

 points of view (though we can not see how it could ever bring us 

 anywhere biologically) but in material not certainly pure, the method 

 is a very dangerous one, and may readily give very misleading results. 



For as the statistical method concerns itself exclusively with 

 results, and absolutely neglects the causes of variation, it must hope- 

 lessly tangle up these causes, and we could only conceive of a mathe- 

 matician, absolutely callous to the biological problems involved, de- 

 lighting in arranging and manipulating the figures for their own sake. 



For the biologist the statistical method must be the very last 

 resource, a thing to be used only in those cases, where an analysis 

 of causes seems hopelesslj^ impossible, and where the results of these 

 causes have been collected anyhow. For instance in practical cases, 

 such as in the Life-insurance-business.- 



The average grade, to which an organ is developed in two parents 

 has not only not necessarily any relation to the grade this organ has 

 in any one of their children, worse, it even stands in no biological 

 relation to the grade shown by either one of them. 



If anyone tells us, that this horse has four legs, this hen two and that 

 spider eight, and that, therefore, these three animals have an average 

 number of four and two thirds leg, most of us would see that this, 

 though expressing a mathematical truth, has no biological significance. 



