Linkage
data calculation (See News Letter 20:18. 1946).
Fisher (Amer. Nat. 80:568578. 1946) has presented a
simple method of scoring linkage data by using maximum likelihood formulas. To
make it readily understood, we have illustrated its application to F_{2}
and F_{3} data commonly encountered in plant material (now ready to be
submitted for publication). The formulas, for the scores (remainders) of
maximum likelihood formulae when p = one half is substituted (50 per cent
recombination), are:
Source of data 
Formulas for scores (c)
at p = one half * 
Information (i) per F_{2}
plant or F_{3} line at p = one half 



Backcross 
2 (a  b c + d) 
4 
F_{2} 
4 (a/9  (b + c)/3 + d) 
16/9 
F_{3} from Ab F_{2}
plants 
4/3 (k  2 j) 
32/9 
F_{3} from aB F_{2}
plants 
4/3 (m  2 l) 
32/9 
F_{3} from AB F_{2}
plants 
4/9 (8e  f  g  h  i) 
128/81 
F_{3} from doubly
heterozygous F_{2} plants 
4 (h  i) 
16 




*Suitable for repulsion,
change signs for coupling. 

By substituting the observed values for a, b, c, d, e, etc., the score for each source of data is obtained.
The total amount of information furnished by the
data is ni, where n is the number of plants or of F_{3} lines and i is
the information per plant or line. Fisher shows that c^{2}/I is
distributed as c^{2}. Each such c^{2}/I value for
each source of data, having one degree of freedom, tests the significance of
the deviation from 50 per cent recombination. Then c^{2}
= (Sc)^{2}/SI tests the deviation from 50 per cent for the pooled data
with one degree of freedom. The difference c^{2} = [S(c^{2}/I)]
 [(Sc)^{2}/SI] ^{ } tests heterogeneity, the degrees of
freedom being (N1) where N is the number of sources of data pooled. For this
test a value of p sufficiently
close to the best estimate of p
should be used. The ratio Sc/SI provides an estimate of the correction to be
applied to p = 0.5 to obtain the
p value which best fits all the
sources of data.
H. H. Kramer
C. R. Burnham