66 GENETIC STOCKS AND BREEDING METHODS 



Table 18 



Calculation of D and I p for detection of linkage between ru ANDJe in the mouse 

 (Using data of Fisher and Snell. 379 ) 



... Offspring 



Mating — JJ = 



Parents type + + +je ru + ruje 2 ns Total I p 



I C n 151 54 45 20 270 



s -4/9 4/3 4/3 -4 i p 16/9 



ns -67.111 72.000 60.000 -80.000 -15.111 480.000 



1R » 86 31 35 5 157 



s 4/9 -4/3 -4/3 4 i p 16/9 



ns 38.222 -41.333 -46.667 20.000 -29.778 279.111 



B C n 120 103 89 122 434 



s -2 2 2-2 i p 4 



ns -240.000 206.000 178.000 -244.000-100.000 1,736.000 



B R n 9 9 10 12 40 



s 2-2-2 2 i p 4 



7u 18.000 -18.000 -20.000 24.000 4.000 160.000 



-140.889 2,655.111 



I = intercross, B = double backcross, C = coupling, R = repulsion, n = number, s = score 



The deviation is highly significant and linkage must therefore be said to exist. 



It is desirable now to estimate p. A fortunate property of D and I v allows them to 

 be used to obtain a first estimate of/>. For small values of D it can be shown that 



/ = D 



P ~Po 



and 



D 



p = p + y> approximately, 



where p is the value of p assumed in calculating D, and p is the exact maximum 

 likelihood estimate of p calculated from the same data. In the above example the 

 improved estimate of/) is therefore 



p = ■= + Djl p = 0.500 - 0.053 = 0.447- 



The standard error of this estimate is 



SE ' - W ~ 5T53 " °- 019 - 



Recombination between ru andjV is thus 44.7 + 1.9 per cent. 



The quantity p estimated in this way is very close to the exact estimate for depart- 

 ures from one half of this magnitude. For large departures from one half it will be 

 necessary to obtain a more exact estimate. For this purpose the first estimate of p 

 could be used to calculate a second set of scores and i p which could then be used to get 



