THE CALCULATION OF LINKAGE INTENSITIES 1 



Professor R. A. EMERSON 

 Cornell University 



Two methods of estimating the intensity of linkage are 

 in use. One consists of crossing individuals heterozy- 

 gous for two or more linked genes with homozygous re- 

 cessives. This is the more direct method, because the 

 gametic ratio— barring differential viability— is exhibited 

 directly by the zygotic frequencies. The other method 

 employs ordinary F 2 ratios derived from selfing Fj or 

 breeding together like Fj individuals. Here the gametic 

 ratio can only be inferred from the numerical relation of 

 the zygotic classes. The results may be disturbed not 

 only by differential viability, as in the first method, but 

 also by selective fertilization, if that occurs, and may 

 often be materially influenced by chance in random mat- 

 ing where the numbers are small. In fact, this method 

 is so undesirable that it should not ordinarily be used 

 where the other method is practicable. It is true, how- 

 ever, that the mechanical difficulties of crossing certain 

 plants are so great and the number of seeds produced 

 per flower so small that often the ordinary F 2 results are 

 alone available. It is important, therefore, to have a 

 means of calculating gametic ratios from F 2 zygotic 

 numbers. 



Since no direct formulae for calculating gametic ratios 

 from observed F 2 data have heretofore been available, 

 the problem has been attacked in an indirect way. A 

 series of F 2 zygotic ratios has first been calculated from a 

 corresponding series of gametic ratios. Next the ob- 

 served F 2 results have been compared with the eal.-ulnt.-d 

 series, the closest fitting calculated ratio determined, and 

 the corresponding gametic ratio taken as that responsible 

 for the observed F 2 results. 



1 Paper No. 54, Department of Plant Breeding, Cornell University, 

 Ithaca, X. Y. 



411 



