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 

 lan 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. 



