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Malecot's method of coancestry
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Malecot's method of coancestry : ウィキペディア英語版
Malecot's method of coancestry
Malecot's coancestry coefficient, f, refers to an indirect measure of genetic similarity of two individuals which was initially devised by the French mathematician Gustave Malécot.
f is defined as the probability that any two alleles, sampled at random (one from each individual), are identical copies of an ancestral allele. In species with well-known lineages (such as domesticated crops), f can be calculated by examining detailed pedigree records. Modernly, f can be estimated using genetic marker data.
== Evolution of inbreeding coefficient in finite size populations ==
In a finite size population, after some generations, all individuals will have a common ancestor : f \rightarrow 1 .
Consider a non-sexual population of fixed size N, and call f_i the inbreeding coefficient of generation i. Here, f means the probability that two individuals picked at random will have a common ancestor. At each generation, each individual produces a large number k \gg 1 of descendants, from the pool of which N individual will be chosen at random to form the new generation.
At generation n, the probability that two individuals have a common ancestor is "they have a common parent" OR "they descend from two distinct individuals which have a common ancestor" :
:f_n = \frac + \fracf_
: \approx \frac+ (1-\frac)f_.
This is a recurrence relation easily solved. Considering the worst case where at generation zero, no two individuals have a common ancestor,
:f_0=0, we get
:f_n = 1 - (1- \frac)^n.
The scale of the fixation time (average number of generation it takes to homogenize the population) is therefore
: \bar= -1/\log(1-1/N) \approx N.
This computation trivially extends to the inbreeding coefficients of alleles in a sexual population by changing N to 2N (the number of gametes).

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