, 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.
In a finite size population, after some generations, all individuals will have a common ancestor :
means the probability that two individuals picked at random will have a common ancestor.
At each generation, each individual produces a large number
individual will be chosen at random to form the new generation.
This is a recurrence relation easily solved.
Considering the worst case where at generation zero, no two individuals have a common ancestor, 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