Linkage data calculation (See News Letter 20:18. 1946).

Fisher (Amer. Nat. 80:568-578. 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 F₂ and F₃ 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 F2 plant or F3 line at p = one half
Backcross	2 (a - b- c + d)	4
F2	4 (a/9 - (b + c)/3 + d)	16/9
F3 from Ab F2 plants	4/3 (k - 2 j)	32/9
F3 from aB F2 plants	4/3 (m - 2 l)	32/9
F3 from AB F2 plants	4/9 (8e - f - g - h - i)	128/81
F3 from doubly heterozygous F2 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 F₃ lines and i is the information per plant or line. Fisher shows that c²/I is distributed as c². Each such c²/I value for each source of data, having one degree of freedom, tests the significance of the deviation from 50 per cent recombination. Then c² = (Sc)²/SI tests the deviation from 50 per cent for the pooled data with one degree of freedom. The difference c² = [S(c²/I)] - [(Sc)²/SI] tests heterogeneity, the degrees of freedom being (N-1) 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