THE BIOMHTRICAL ANALYSIS 



of recombination between the two genes concerned, and all in 

 H similarly depend on (i — ^p)^. It will thus be noted that the 

 effects of linkage of polygenes are expressible independently of the 

 linear order. 



Exactly the same linkage terms appear in D and H in variance 

 of F2, variance of F3 means, and covariance of F2 and F3. But while 

 the same number of linkage terms appears in the D and H of mean 

 variance of Fg's, those in D now depend on (i — 2p)- instead of 



TABLE 7 



THE INHERITANCE OF HEIGHT IN ANTIRRHINUM MAJUS 



X GLUTINOSUM 



The assumption of linkage permits a perfect fit. 



on (i — 2p), and those in H on (i — 2p)- (i — 2p+ 2p-) instead 

 of on (i — 2p)2. We can thus see how linkage may explain the 

 discrepancies in the analysis of the Antirrhinum results. Similarly, 

 although the linkage terms in D of the summed backcross variances 

 are just like those of D in Fg variance, the linkage terms in H of 

 the backcross depend on (i — 2p) as compared with (i — ^p)^- 

 When p = o • 5 for free recombination, all these linkage terms 

 vanish from all statistics and D and H arc constant over the whole 

 range. 



The test of linkage is, therefore, the test of differences in the values 

 of D and H over the various types of family. In the experiment with 

 shoot length in Antirrhinum, D and H should be constant, even with 

 linkage, over variance of F^, variance of F;> means and covariance 



86 



