Malecot's method of coancestry
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Malecot's coancestry coefficient, 
, refers to an indirect measure of genetic similarity of two individuals which was initially devised by the French mathematician Gustave Malécot
.
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), 
can be calculated by examining detailed pedigree records. Modernly, 
can be estimated using genetic marker data.
.
Consider a non-sexual population of fixed size
, and call 
the inbreeding coefficient of generation 
. Here, 
means the probability that two individuals picked at random will have a common ancestor. At each generation, each individual produces a large number 
of descendants, from the pool of which 
individual will be chosen at random to form the new generation.
At generation
, 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" :
This is a recurrence relation easily solved. Considering the worst case where at generation zero, no two individuals have a common ancestor,
, we get
the scale of the fixation time (average number of generation it takes to homogenize the population) is therefore
This computation trivially extends to the inbreeding coefficients of alleles in a sexual population by changing
to 
(the number a gametes).
, refers to an indirect measure of genetic similarity of two individuals which was initially devised by the French mathematician Gustave MalécotGustave Malécot
Gustave Malécot was a French mathematician whose work on heredity had a strong influence on population genetics.- Biography :...
.
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), can be calculated by examining detailed pedigree records. Modernly, 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 :.Consider a non-sexual population of fixed size
, and call the inbreeding coefficient of generation . Here, means the probability that two individuals picked at random will have a common ancestor. At each generation, each individual produces a large number of descendants, from the pool of which individual will be chosen at random to form the new generation.At generation
, 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" :This is a recurrence relation easily solved. Considering the worst case where at generation zero, no two individuals have a common ancestor,
, we getthe scale of the fixation time (average number of generation it takes to homogenize the population) is therefore
This computation trivially extends to the inbreeding coefficients of alleles in a sexual population by changing
to (the number a gametes).