THE ANALYSIS OF THE RESULTS OF PROFESSOR 

 JOHANNES SCHMIDT'S DIALLEL CROSSINGS 

 WITH TROUT. 



By H. L. TRACHTENBERG, BA. (Cantab.), A.I.A. 



Actuarial Assistant in the Statistical Bepartment of the Medical 

 Research Council. 



In the Journal of Genetics for December, 1919, Professor Johannes 

 Schmidt described an experiment on trout ^ The basis of this experiment 

 was his method of diallel crossings in which each female is crossed with 

 each male, and the character measured was the number of vertebrae. 



In analysing his results, he sought for a " simple rule connecting the 

 number of vertebrae in the offspring with that in the parents." He first 

 distinguished between "the realized purely personal value of a given indi- 

 vidual trout — this value would have been a different one if the individual 

 in question were developed in different environments — and the generative 

 value of the same individual, and that is the value which it imparts to 

 its offspring." He then assumed that " the average for a number of 

 offspring-individuals closely coincides with the average of the generative 

 values of the parents," and proceeded to inquire whether this supposition 

 did agree with the values arrived at in the experiment. He obtained, 

 however, insufficient independent equations for a solution of the problem, 

 and had recourse to an arbitrary assumption to give him the necessary 

 additional equation. This arbitrary assumption is unnecessary. I will 

 demonstrate this, and indicate my alternative process. 



On the basis of his original assumptions Professor Schmidt writes 

 down the twelve equations connecting the offspring averages with the 

 means of the generative values of the parents : 



-^—=61-14, ^^-^— = 61-3o, -^- = 60-b5, etc., 



1 " Eacial Studies in Fishes. III. Diallel Crossiugs with Trout (.S'a^Hto TruttaL.)." By 

 Johs. Schmidt, D.Sc.,. Director of the Carlsberg Physiological Laboratory, Copenhagen. 

 Journal of Genetics, Vol. ix. No. 1, pp. 61 — 67. 



