THE COMBINATION OF LINKAOK VALUES, AND 

 THE CALCULATION OF DISTANCES BETWEEN 

 THE LOCI OF LINKED FACTORS. 



By J. B. S. HALDANE, M.A., 

 Fellow of New College, Oxford. 



(With One Text-figure.) 



On the theory that the degree of linkage between two factors 

 depends on the distance apart of their loci in a chromosome, Morgan 

 and his fellow- workers have taken the distance between two loci .is 

 proportional to the cross-over value ^ of the factors located in them. 

 This theory gives consistent results when the cross-over values are small, 

 but, as recognised by Sturtevant, and by Morgan and Bridg('s(l), is not 

 accurate for larger values. On the reduplication theory Trow(2) h;us given 

 a formula for the combination of linkage values which is shown below 

 to be inaccurate when the linkage is not close. In the present fKiper 

 a more ;iccurate theory of the relations i7iter se of the cross-over values, 

 and of their connexion with the distances apart of the loci of factors in 

 a chromosome, is developed. Some such theory is especially necessary 

 when dealing with a group of factors conUiining few membt'i*s not very 

 closely linked. 



Suppose A, B, C to be three factors whose loci lie in that order in 

 the same chromosome. Let m be the cross-over value for .1 and B, 

 n that for A and C. If the chromosomes were perfectly flexible, so 

 that the fact of their having crossed between A and B did not diminish 

 the probiibility of their crossing again between B and (\ wr sh«uild 

 expect a triply heterozygous organism to j)rodure gamet«*s in th»- f«»l- 



> If zvgot€h of composition AH . ah and Ah . ali ^ive Kametic sfri«-s 



{\-m)Ali.mAh:malt:(\- m) uh and in AH : (1 in) A1> -.{l in) ali .in ah 

 respectively, then m is said to be the croBS-over value for the factor^ A and H. 



