In population genetics, F-statistics (also known as fixation indices) describe the level of heterozygosity in a population; more specifically the degree of (usually) a reduction in heterozygosity when compared to Hardy-Weinberg expectation. F-statistics can also be thought of as a measure of the correlation between genes drawn at different levels of a (hierarchically) subdivided population. This correlation is influenced by several evolutionary processes, such as mutation, migration, inbreeding, natural selection, or the Wahlund effect, but it was originally designed to measure the amount of allelic fixation owing to genetic drift.
The concept of F-statistics was developed during the 1920s by the American geneticist Sewall Wright, who was interested in inbreeding in cattle. However, because complete dominance causes the phenotypes of homozygote dominants and heterozygotes to be the same, it was not until the advent of molecular genetics from the 1960s onwards that heterozygosity in populations could be measured.
The value for F is found by solving the equation for F using heterozygotes in the above inbred population. This becomes one minus the observed number of heterozygotes in a population divided by its expected number of heterozygotes at Hardy–Weinberg equilibrium:
where the expected value at Hardy–Weinberg equilibrium is given by
|Genotype||White-spotted (AA)||Intermediate (Aa)||Little spotting (aa)||Total|
From this, the allele frequencies can be calculated, and the expectation of f(AA) derived:
The different F-statistics look at different levels of population structure. FIT is the inbreeding coefficient of an individual (I) relative to the total (T) population, as above; FIS is the inbreeding coefficient of an individual (I) relative to the subpopulation (S), using the above for subpopulations and averaging them; and FST is the effect of subpopulations (S) compared to the total population (T), and is calculated by solving the equation:
Consider a population that has a population structure of two levels; one from the individual (I) to the subpopulation (S) and one from the subpopulation to the total (T). Then the total F, known here as FIT, can be partitioned into FIS (or f) and FST (or θ):
This may be further partitioned for population substructure, and it expands according to the rules of binomial expansion, so that for I partitions:
A reformulation of the definition of F would be the ratio of the average number of differences between pairs of chromosomes sampled within diploid individuals with the average number obtained when sampling chromosomes randomly from the population (excluding the grouping per individual). One can modify this definition and consider a grouping per sub-population instead of per individual. Population geneticists have used that idea to measure the degree of structure in a population.
Unfortunately, there is a large number of definitions for Fst, causing some confusion in the scientific literature. A common definition is the following:
where the variance of is computed across sub-populations and is the expected frequency of heterozygotes.
F can be used to define effective population size.
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