56 GENETICS IN RELATION TO AGRICULTURE 
breeding efficiency is such that the regression will be negative—that 
is, away from the mean of the general population—as has been proved 
by Shull, by Emerson and by East in experiments with maize. Further- 
more, Johannsen, Jennings and others have shown that when the indi- 
viduals of a population are alike gametically and their differences are 
due to external conditions only, these differences are not inherited at all 
and regression is perfect. This means that if a number of beans are alike 
gametically, selection of extreme sizes will not shift the mean in either 
direction. 
More recently biometricians have applied the mathematical principle 
involved in Galtonian regression in order to express in absolute terms the 
relative interdependence of characters expressed by correlation coefficients. 
Used in this sense regression is commonly represented by a straight line 
which approximates the largest possible number of the subject means in 
a correlation table. The “regression straight line” is extensively used 
by some authors as a method of representing the relation between the 
absolute values of characters. For excellent illustrations consult Harris 
on body pigmentation and egg production in the domestic fowl. 
Employment and Value of the Statistical Method.—It may be as- 
sumed that biometrical methods are not worth very much if the great 
biological generalities of the biometricians are misleading. Such an 
assumption would also be misleading. Statistical methods are a great 
aid to biologists, but they are only an aid. Trouble has arisen only 
when biological conclusions have been drawn by mathematicians who 
ignored certain biological premises. One can only take out of his 
mathematical mill just what he puts in, but he can take it out in a more 
comprehendible form. If he has made an accurate biological analysis 
mathematics are a help; if he has made no biological analysis mathe- 
matics are a hindrance. Johannsen sums up the whole situation in the 
sentence: ‘‘We must treat genetic facts with mathematics not as mathe- 
matics.” If the beginner is careful of his biological premises, if he is 
certain that the material with which he deals is representative—that he 
has a random sample—if he makes no mathematical deduction unjusti- 
fied by common sense analysis, he will find that the use of mathematics 
will remove many a rough place from his road. Biometry will always be 
an indispensable instrument for the scientific breeder as well as the 
geneticist. The agronomist and pomologist also have need to resort 
to statistical methods in order to reach a satisfactory solution of many 
problems involving variation such as variety testing, seed germination 
tests, investigation of the value of bud selection, etc. Intelligent em- 
ployment of the statistical method insures conservative and reliable con- 
clusions regarding many questions which would otherwise remain in the 
debatable class. 
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