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.
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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.
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" :
What is the source of the above formula? Is it in a later paper than the 1948 Reference.
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 of gametes).