The Amount Of Information And Its Uses

Mather, K. The Measurement of Linkage in Heredity. pgs. 56-68.

"The greater the amount of information concerning the recombination fraction, the greater the precision, or the less the variance, of the estimate, and so it is convenient to define the total amount of information in the data as the inverse of the variance of that statistic obtained by the use of the method of maximum likelihood."

Ip is the amount of information provided by a whole family.

Where i_p is the amount of information provided by a single individual of the family and n is the total number of progeny in a family.

Example

P = 0.241, Vp = 0.0001293, n = 1415.

Mather shows that:

where m is the expected proportion of a phenotype and

dm
dp

ip indicates the amount of information provided by each individual in a particular type of family. ip does not depend on the total number of individuals per family. Let us compare the relative amount of information from each individual derived from different types of families.

Family Type	relativep
Testcross	= 1	1/p(1-p)
F completely classified	= 2	2/p(1-p)
F incomplete dominance	= 2(1-3p + 3p2) =  1-2p + 2p
F complete dominance
coupling:	2(1 - p)(3 - 4p + 2p2) (2 - p)(3 -2p + p2)	2(3 - 4p + 2p2)    p(2 - p)(3 - 2p + p2)
repulsion:	2p(1 + 2p2)    (2 + p2)(1+p)	2(1 + 2p2)    (2 + p2)(1 - p2)

We can see that the amount of information for each type of family depends on the value of p. The F₂ family completely classified has twice as much information per individual as the testcross family.

This graph was developed by plotting ip versus p for different types of families. The testcross provides more information than the F₂ with complete dominance, except when p = 0. Coupling F₂ data provides more information per individual than repulsion F₂ data when there is complete dominance gene action.