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 An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. ::"The chrom ...

sampled Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population – complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of so ...

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 A genetic marker is a gene or DNA sequence with a known location on a chromosome that can be used to identify individuals or species. It can be described as a variation (which may arise due to mutation or alteration in the genomic loci) that can be ...

data.

Evolution of inbreeding coefficient in finite size populations

In a finite size

population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...

, after some generations, all individuals will have a

common ancestor Common descent is a concept in evolutionary biology applicable when one species is the ancestor of two or more species later in time. All living beings are in fact descendants of a unique ancestor commonly referred to as the last universal comm ...

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_

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

\approx  \frac+ (1-\frac)f_.

This is a

recurrence relation In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...

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

2N

(the number of

gametes A gamete (; , ultimately ) is a haploid cell that fuses with another haploid cell during fertilization in organisms that reproduce sexually. Gametes are an organism's reproductive cells, also referred to as sex cells. In species that produce ...

References

Bibliography

*{{cite book , last=Malécot , first=G. , title=Les mathématiques de l'hérédité , location=Paris , publisher=Masson & Cie , year=1948 Classical genetics

Evolution of inbreeding coefficient in finite size populations

See also

References

Bibliography