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

  • Kenneth Mather
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.

    66/152 (page 52)
    This is not the same as the variance of the maxi mum likelihood statistic. Now the smaller the variance the more precise the estimate and so the more efficient the statistic. The maximum likelihood statistic has the smallest possible variance and so is always 100 per cent efficient. The efficiency of any other statistic may conveniently be expressed as the ratio of the variance of the maximum likelihood statistic to the variance of the statistic in question. In the case of Imai's data the efficiency is then 8P(1 - P)(2 + P) (1 + 6 P + 4P 2 )(1 + 2 P) P was found to be 0-4835 and so the efficiency is 0*8505 or 85-05 per cent. Where the value of P is J, i.e. p is \ in the absence of linkage, the efficiency of the statistic in question is 1. It is thus fully efficient for the detection of linkage, and so the use of % 2 for this purpose is justified. Where the linkage value is small the efficiency of this particular statistic is very low and will lead to the most misleading results. With no recombination, p = 0, the efficiency is zero. As an example of the trouble which the use of inefficient statistics leads to, we may consider the estimation of the recombination fraction in some F 2 data showing tight linkage of two factors. Ex. 9. The data are on the segregation of the two factors, G,g and L,1 in an F 2 of Primula sinensis (De Winton and Haldane, 1936). The factors were in the coupling phase and the following segregation was observed : TABLE 14 GL Gl gL gl Total Observed . 977 16 19 360 1,372 Expected . ~ (2 + P) ~ (1 - P) ~ (1 - P) \P where P = (1 — p) 2 .