METHODS FOR TESTING LINKAGE 75 



of the recombination proportions may be large enough to make the method of sum or 

 difference unreliable. A linkage test using all three loci simultaneously is then 

 advisable. The least frequent class of recombinations obtained from this kind of 

 mating is then assumed to be the double recombinant class. An example will make the 

 reasoning clear. 



Falconer and Sobey 345 give data on a cross involving Rex (Re), Trembler (Tr), and 

 shaker-2 (sh-2) in the mouse. The cross was ReTr + j+ -{-sh-2 x + +sh-2j + +sh-2, 

 and the following offspring, grouped in complementary classes, were obtained : 



ReTr +16 + Tr + 3 



+ + sh-2 28 Re + sh-2 8 



ReTr sh-2 1 + Trsh-2 



+ + + 1 Re + + 0. 



The three recombination proportions are therefore : 



Re - Tr U + ° = 0.193, 

 57 



2 + 

 Tr - sh-2 -^r- = 0.035, 

 57 



11+2 

 R e - s h-2 ~T = 0.228. 



57 



Since 0.193 + 0.035 = 0.228 the order appears to be Re - Tr - sh-2. In this 

 calculation the assumption is made that the two recombination classes which did not 

 occur, + Tr sh-2 and Re + + , would require two recombinations each, and that the 

 recombinations in the Tr-sh-2 interval require only single recombinations. This is a 

 reasonably safe assumption, since, assuming no interference, the probability of double 

 recombinations is 0.193 x 0.035 = 0.007. Interference, which undoubtedly exists, 

 would make this probability even smaller. It is therefore very unlikely that the two 

 recombinations between Tr and sh-2 would have been found if the order were Re — 

 sh-2 — Tr and they were indeed double recombinants. 



STOCKS FOR TESTING LINKAGE 



For the efficient testing of linkage of new mutations in any organism, it is desirable 

 to have multiple-gene stocks so designed as to cover the greatest length of the known 

 linkage map with the smallest number of crosses. The task will be greater for organisms 

 with greater length of the known linkage map, and will increase as more of the linkage 

 map becomes known. This increase may be partly offset, however, by the discovery 

 of more suitable marker genes (for example, dominants to replace recessives) which 

 increase the efficiency of any one test. 



Multiple-gene stocks for testing linkage in the mouse were first developed by Snell 



