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THE AMERICAN NATURALIST [Vol. XLV 



D = difference between numerical value of the parent 

 character and the mean of the same character 

 in the offspring. 



In a later report he makes use of this formula "in an 

 attempt to answer the question whether prepotency is in- 

 herited or not." 5 



Now while Waugh deserves all credit for suggesting 

 the need of a coefficient of individual prepotency, I think 

 the formula he proposes can not be justified theoretically 

 nor regarded as practically satisfactory. 



The requirements of a coefficient of individual pre- 

 potency are at least the following : 



(a) The comparison must be made between the off- 

 spring families, not between the individual parent and 

 its offspring. 



(fe) The comparison must be so drawn as to attach 

 importance only to differences significantly greater than 

 the probable errors of random sampling. 



(c) The coefficient expressing prepotency should be 

 relative, i. e., it should be comparable from character to 

 character. 



Proposition (b) and (c) will be granted without argu- 

 ment. In justification of (a) it is only necessary to point 

 out that from the standpoint of the man who wishes to 

 decide which families to continue to propagate and which 

 to burn, the ideal method is one which may be applied to 

 the individuals of any one generation entirely indepen- 

 dently of those of any other. Of course this is not to be 

 interpreted as a recommendation that in the routine work 

 of practical or experimental breeding only one generation 

 should be considered. What is meant is that it is desira- 

 ble to have formulae which permit of a consideration of 

 prepotency on the data of any (offspring) generation 

 independently. Such a formula does not preclude or 

 render inadvisable the study of many ascendant genera- 

 tions. 



