300 Method of Calculation for Diallel Crossings 



According to Mr Trachtenberg's supposition the squared standard 

 deviation of a personal value of a parent is 50 times that of the mean 

 for a group of offspring. Now we find here that deviations between 

 observed and theoretical values are on an average more than 400 times 

 as great for parents as for offspring. We must therefore conclude that 

 the supposition is wrong and reject it. 



This result ought to be emphasised because it is a fundamental part 

 of the plan of the experiments with diallel crossings that the environ- 

 mental conditions are kept uniform for all groups of offspring, while 

 on the other hand, for all we know, the parents have developed in 

 quite different environments. Hence there is no reason to expect that 

 their personal values, apart from an unknown constant common to all 

 of them, should coincide with their generative values to the same order 

 of accuracy as we find they do for the offspring. 



• While thus the fundamental idea of Mr Trachtenberg's method of 

 calculation is wrong it is only fair to admit that practically it does not 

 give so bad results, because the 7 parental observations weigh very 

 little as compared with the 12x50 observations of offspring. 



The correct proceeding when introducing the personal values in the 

 calculation is of course to give to each of them a weight of only ^^ of 

 that of the means of a group of offspring. But then the ratio ^^ is 

 somewhat uncertain and has to be determined empirically. 



It has therefore been found preferable to carry out the calculation 

 in two tempi. At first the generative values are calculated according to 

 the method of least squares, fixing an arbitrary value for one of the 

 parents, and secondly the arbitrary zero point of the generative values is 

 determined so as to make the squared differences between generative 

 and personal values a minimum. This method has been followed in 

 some of Dr Johannes Schmidt's publications concerning diallel crossings 

 with trout while in others the second part of the calculation has been 

 omitted as really unessential. 



PRINTED IN ENGLAND BY J. B. PEACE, M.A. 

 AT THE CAMBRIDGE UNIVERSITY PRESS 



