The measurement of linkage in heredity / by K. Mather.

  • Mather, Kenneth, 1911-1990.
Date:
[1938]
Catalogue details

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Credit: The measurement of linkage in heredity / by K. Mather. Source: Wellcome Collection.

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    14. THE CALCULATION OF MAXIMUM LIKELIHOOD Ex. 7. Let us consider the estimation of the recombination fraction p in the case of the factors p and t in the poppy (Philp's data). It has been shown in the previous chapter (Ex. 5) that the data give evidence of linkage of these factors. The cross was one of the double heterozygote in the coupling phase to the double recessive ( v — Y All the \PT pt ) gametes from the recessive parent will be pt and so do not enter into our consideration of the problem. The gametes from the heterozygous parent will be of four kinds, two of which are old, or original, combinations and the other two new, or re-, com binations. In this way the expected frequencies shown in Table 11 are arrived at. The corresponding observed numbers are also shown. TABLE 11 PT Pt pT pt Total Observed . 191 36 37 203 467 -n ■ j n.. . n n n,. Expected . --(1 - p) -p -p -(1 — p) n The logarithm likelihood expression is thus L = 191 log (J — \p) + 36 log 37 log (!,p) + 203 log ip) and maximizing by differentiation and equating to zero the equation of estimation becomes : dL_ 191 36 37 203 _ Q dp 1 — p p p 1 — p 73 The solution is p — = 0-1563 or 15-63 per cent. It will be noticed that in the case of the backcross this method of estimation leads to the formula which is in universal use for data of this kind, viz. p = - 2 ^ a '' ] j^or 0,1 in the case of repulsionj