METHODS FOR TESTING LINKAGE 73 



The calculation of D using the tabled values of A for p = 0.45 is set out in table 25. 

 The heterogeneity % 2 can then be determined as follows : 



> 0.05 



There is thus no significant heterogeneity among the matings. 



The estimate of the heterogeneity % 2 is not accurate unless the total deviation is 

 small. Tables 19 to 23 may not be sufficiently detailed when an accurate value of % 2 

 is needed, as when the heterogeneity is on the borderline of significance. Allard's 

 tables may supply the appropriate scores, or it may be necessary to calculate them. 

 Table 26 gives formulas for maximum-likelihood scores and values of i p for several 

 common kinds of matings. 



In cases for which no tables of scores are available, it may sometimes be relatively 

 easy to derive maximum-likelihood scores but may be somewhat more difficult to 

 derive formulas for the amount of information per individual, i p . Fortunately there 

 exists an arithmetic method which gives an approximate estimate of the total amount 

 of information, I p , given by the results of any mating or group of matings. Since I p is 

 equal to the second derivative of the logarithm-likelihood expression, it is also equal to 

 the first derivative of the equation, dLjdp = 0. I p is therefore the rate of change of 

 dLjdp with respect to p. If dLjdp has been evaluated for two values of p (p± and p 2 ) 

 close to the exact estimate, to give two values of D, then I p = (D 2 — D 1 )j{p 2 — pi). 

 The value of I p calculated in this way will not be identical to the value calculated from 

 the formula — ][ {mn[(d 2 log m)ldp 2 ]}. The arithmetic method gives the actual amount 

 of information realized in the particular body of data on hand, whereas the formula 

 gives the expected amount of information in bodies of data of this size and value of p. 



LINEAR ORDER OF LOCI 



Having determined that a mutant is linked with another mutant known to be a 

 member of a particular linkage group, one may wish to determine the linear order of 

 the two mutant loci with respect to another locus in the linkage group. For this 

 purpose it may sometimes be sufficient to determine the distance of the new mutant 

 from the other locus. The recombination for A-B, say, should equal either the sum 

 or difference of the recombinations for A-C and B-C, and the linear order easily 

 follows. If, however, any two of the three loci are closely linked, the errors of estimate 



