TlIK BIO. METRIC A I. ANALYSIS 



2. The mean of the variances of different F3 families, which has 



thevakie|D+ JH+E. 



3. The covariance of means of F3 famihcs with the measurements 



of the F2 parents, which has the value iDH- JH. 



In a properly designed experiment, the effects of the environment 

 on average manifestation of the character in F3 will bear no corre- 

 lated relation to the effect of the environment on the character in 

 the Fo parent. The covariance, therefore, has no E component. The 

 E component of the variance of F3 means will in general differ from 

 that of the other statistics since the variation of an average value will 

 be influenced to a different extent than that of a single value by 

 the vagaries of the environment. We must thus distinguish between 

 El, the non-heritable component of variation of single individuals, 

 and Eg, the non-heritable component of variation of family means 

 which will usually, though not always, be smaller than E^. The 

 non-heritable component appropriate to individuals, E^, will appear 

 in all the formulae except that for the variance of F3 means, which 

 will contain E2. E^ and Eg can be estimated directly from the 

 variation within the true-breeding parent lines and F^, E^ as the 

 variance of single individuals and E., as the variance of the means 

 of groups containing the same number of individuals as the F3 

 families. 



The Test of Dominance and Linkage 



An example will illustrate the use of these results. The two species 

 o( Antirrliinmn, majus 3.nd gliitinostun, differ in, among other charac- 

 ters, their heights. In a true-breeding strain of majus the average 

 length of the leading shoot was 21-45 inches. No strain o£ glutinosum 

 known to be true-breeding was available, but one which was 

 empirically observed to be no more variable phenotypically than 

 the strain of majus, had leading shoots whose average length was 

 9-12 inches. The F^ between the species gave a mean measurement 

 of 17-08 inches. 



An F2 was raised which showed no segregation of genes with 

 major effects on height, the variation being continuous and 

 depending, presumably, on a polygenic system. The F^ was also 

 backcrossed to both parents, and 19 F3 families were raised by 



84 



