The fixation index (F
ST) is a measure of
population differentiation
Human genetic variation is the genetic differences in and among populations. There may be multiple variants of any given gene in the human population (alleles), a situation called polymorphism.
No two humans are genetically identical. Even m ...
due to
genetic structure
Genetic structure refers to any pattern in the genetic makeup of individuals within a population.
Genetic structure allows for information about an individual to be inferred from other members of the same population. In trivial terms, all popul ...
. It is frequently estimated from
genetic polymorphism
A gene is said to be polymorphic if more than one allele occupies that gene's locus within a population. In addition to having more than one allele at a specific locus, each allele must also occur in the population at a rate of at least 1% to gen ...
data, such as
single-nucleotide polymorphism
In genetics, a single-nucleotide polymorphism (SNP ; plural SNPs ) is a germline substitution of a single nucleotide at a specific position in the genome. Although certain definitions require the substitution to be present in a sufficiently lar ...
s (SNP) or
microsatellites. Developed as a special case of
Wright's F-statistics
In population genetics, ''F''-statistics (also known as fixation indices) describe the statistically expected level of heterozygosity in a population; more specifically the expected degree of (usually) a reduction in heterozygosity when compared ...
, it is one of the most commonly used statistics in
population genetics
Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...
.
Definition
Two of the most commonly used definitions for F
ST at a given locus are based on 1) the variance of
allele frequencies
Allele frequency, or gene frequency, is the relative frequency of an allele (variant of a gene) at a particular locus in a population, expressed as a fraction or percentage. Specifically, it is the fraction of all chromosomes in the population that ...
between populations, and on 2) the probability of
Identity by descent
A DNA segment is identical by state (IBS) in two or more individuals if they have identical nucleotide sequences in this segment. An IBS segment is identical by descent (IBD) in two or more individuals if they have inherited it from a common a ...
.
If
is the average frequency of an allele in the total population,
is the variance in the frequency of the allele between different subpopulations, weighted by the sizes of the subpopulations, and
is the variance of the allelic state in the total population, F
ST is defined as
:
Wright's definition illustrates that F
ST measures the amount of genetic variance that can be explained by population structure. This can also be thought of as the fraction of total diversity that is not a consequence of the average diversity within subpopulations, where diversity is measured by the probability that two randomly selected alleles are different, namely
. If the allele frequency in the
th population is
and the relative size of the
th population is
, then
:
Alternatively,
:
where
is the probability of identity by descent of two individuals given that the two individuals are in the same subpopulation, and
is the probability that two individuals from the total population are identical by descent. Using this definition, F
ST can be interpreted as measuring how much closer two individuals from the same subpopulation are, compared to the total population. If the
mutation rate
In genetics, the mutation rate is the frequency of new mutations in a single gene or organism over time. Mutation rates are not constant and are not limited to a single type of mutation; there are many different types of mutations. Mutation rates ...
is small, this interpretation can be made more explicit by linking the probability of identity by descent to
coalescent times: Let T
0 and T denote the average time to coalescence for individuals from the same subpopulation and the total population, respectively. Then,
:
This formulation has the advantage that the expected time to coalescence can easily be estimated from genetic data, which led to the development of various estimators for F
ST.
Estimation
In practice, none of the quantities used for the definitions can be easily measured. As a consequence, various estimators have been proposed. A particularly simple estimator applicable to DNA sequence data is:
:
where
and
represent the
average number of pairwise differences between two individuals sampled from different sub-populations (
) or from the same sub-population (
). The average pairwise difference within a population can be calculated as the sum of the pairwise differences divided by the number of pairs. However, this estimator is biased when sample sizes are small or if they vary between populations. Therefore, more elaborate methods are used to compute F
ST in practice. Two of the most widely used procedures are the estimator by Weir & Cockerham (1984),
or performing an
Analysis of molecular variance Analysis of molecular variance (AMOVA), is a statistical model for the molecular algorithm in a single species, typically biology, biological. The name and model are inspired by ANOVA. The method was developed by Laurent Excoffier, Peter Smouse and ...
. A list of implementations is available at the end of this article.
Interpretation
This comparison of genetic variability within and between populations is frequently used in applied
population genetics
Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...
. The values range from 0 to 1. A zero value implies complete
panmixis
Panmixia (or panmixis) means random mating. A panmictic population is one where all individuals are potential partners. This assumes that there are no mating restrictions, neither genetic nor behavioural, upon the population and that therefore all ...
; that is, that the two populations are interbreeding freely. A value of one implies that all genetic variation is explained by the population structure, and that the two populations do not share any genetic diversity.
For idealized models such as
Wright's finite island model, F
ST can be used to estimate migration rates. Under that model, the migration rate is
:
,
where is the migration rate per generation, and
is the mutation rate per generation.
The interpretation of F
ST can be difficult when the data analyzed are highly polymorphic. In this case, the probability of identity by descent is very low and F
ST can have an arbitrarily low upper bound, which might lead to misinterpretation of the data. Also, strictly speaking F
ST is not a
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
in the mathematical sense, as it does not satisfy the
triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
This statement permits the inclusion of degenerate triangles, but ...
.
For populations of
plants
Plants are predominantly Photosynthesis, photosynthetic eukaryotes of the Kingdom (biology), kingdom Plantae. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi; however, all curr ...
which clearly belong to the same
species
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
, values of F
ST greater than 15% are considered "great" or "significant" differentiation, while values below 5% are considered "small" or "insignificant" differentiation.
Values for
mammal
Mammals () are a group of vertebrate animals constituting the class Mammalia (), characterized by the presence of mammary glands which in females produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or ...
populations between
subspecies
In biological classification, subspecies is a rank below species, used for populations that live in different areas and vary in size, shape, or other physical characteristics (morphology), but that can successfully interbreed. Not all species ...
, or closely related species, typical values are of the order of 5% to 20%. F
ST between the
Eurasian
Eurasia (, ) is the largest continental area on Earth, comprising all of Europe and Asia. Primarily in the Northern Hemisphere, Northern and Eastern Hemispheres, it spans from the British Isles and the Iberian Peninsula in the west to the Ja ...
and North American populations of the
gray wolf were reported at 9.9%, those between the
Red wolf and
Gray wolf populations at between 17% and 18%. The
Eastern wolf
The eastern wolf (''Canis lycaon'' or ''Canis lupus lycaon'' or ''Canis rufus lycaon'') also known as the timber wolf, Algonquin wolf or eastern timber wolf, is a canine of debated taxonomy native to the Great Lakes region and southeastern Canad ...
, a recently recognized highly admixed "wolf-like species" has values of F
ST below 10% in comparison with both Eurasian (7.6%) and North American gray wolves (5.7%), with the Red wolf (8.5%), and an even lower value when paired with the
Coyote
The coyote (''Canis latrans'') is a species of canis, canine native to North America. It is smaller than its close relative, the wolf, and slightly smaller than the closely related eastern wolf and red wolf. It fills much of the same ecologica ...
(4.5%).
FST in humans
F
ST values depend strongly on the choice of populations.
Closely related ethnic groups, such as the
Danes
Danes ( da, danskere, ) are a North Germanic ethnic group and nationality native to Denmark and a modern nation identified with the country of Denmark. This connection may be ancestral, legal, historical, or cultural.
Danes generally regard t ...
vs. the
Dutch
Dutch commonly refers to:
* Something of, from, or related to the Netherlands
* Dutch people ()
* Dutch language ()
Dutch may also refer to:
Places
* Dutch, West Virginia, a community in the United States
* Pennsylvania Dutch Country
People E ...
, or the
Portuguese
Portuguese may refer to:
* anything of, from, or related to the country and nation of Portugal
** Portuguese cuisine, traditional foods
** Portuguese language, a Romance language
*** Portuguese dialects, variants of the Portuguese language
** Portu ...
vs. the
Spaniards
Spaniards, or Spanish people, are a Romance peoples, Romance ethnic group native to Spain. Within Spain, there are a number of National and regional identity in Spain, national and regional ethnic identities that reflect the country's complex Hist ...
show values significantly below 1%, indistinguishable from panmixia.
Within Europe, the most divergent ethnic groups have been found to have values of the order of 7% (
Lapps vs.
Sardinians
The Sardinians, or Sards ( sc, Sardos or ; Italian and Sassarese: ''Sardi''; Gallurese: ''Saldi''), are a Romance language-speaking ethnic group native to Sardinia, from which the western Mediterranean island and autonomous region of Italy de ...
).
Larger values are found if highly divergent homogenous groups are compared: the highest such value found was at close to 46%, between
Mbuti
The Mbuti people, or Bambuti, are one of several indigenous pygmy groups in the Congo region of Africa. Their languages are Central Sudanic languages and Bantu languages.
Subgroups
Bambuti are pygmy hunter-gatherers, and are one of the old ...
and
Papuans
The indigenous peoples of West Papua in Indonesia and Papua New Guinea, commonly called Papuans, are Melanesians. There is genetic evidence for two major historical lineages in New Guinea and neighboring islands: a first wave from the Malay Arch ...
.
Autosomal genetic distances based on classical markers
In their study ''The History and Geography of Human Genes (1994)'', Cavalli-Sforza, Menozzi and Piazza provide some of the most detailed and comprehensive estimates of genetic distances between human populations, within and across continents. Their initial database contains 76,676 gene frequencies (using 120 blood polymorphisms), corresponding to 6,633 samples in different locations. By culling and pooling such samples, they restrict their analysis to 491 populations. They focus on ''aboriginal populations'' that were at their present location at the end of the 15th century when the great European migrations began. When studying genetic difference at the world level, the number is reduced to 42 representative populations, aggregating subpopulations characterized by a high level of genetic similarity.
For these 42 populations, Cavalli-Sforza and coauthors report bilateral distances computed from 120 alleles. Among this set of 42 world populations, the greatest genetic distance observed is between Mbuti Pygmies and Papua New Guineans, where the Fst distance is 0.4573, while the smallest genetic distance (0.0021) is between the Danish and the English. When considering more disaggregated data for 26 European populations, the smallest genetic distance (0.0009) is between the Dutch and the Danes, and the largest (0.0667) is between the Lapps and the Sardinians. The mean genetic distance among the 861 available pairings of the 42 selected populations was found to be 0.1338.. A genetic distance of 0.1338 implies that kinship between unrelated individuals of the same ancestry relative to the world population is equivalent to kinship between half siblings in a randomly mating population. This also implies that if a human from a given ancestral population has a mixed half-sibling, that human is closer genetically to an unrelated individual of their ancestral population than to their mixed half-sibling.
Autosomal genetic distances based on SNPs
A 2012 study based on
International HapMap Project
The International HapMap Project was an organization that aimed to develop a haplotype map (HapMap) of the human genome, to describe the common patterns of human genetic variation. HapMap is used to find genetic variants affecting health, disease ...
data estimated F
ST
between the three major "continental" populations of
Europeans (combined from Utah residents of Northern and Western European ancestry from the CEPH collection and Italians from Tuscany),
East Asians
East Asian people (East Asians) are the people from East Asia, which consists of China, Taiwan, Japan, Mongolia, North Korea, and South Korea. The total population of all countries within this region is estimated to be 1.677 billion and 21% of t ...
(combining Han Chinese from Beijing, Chinese from metropolitan Denver and Japanese from Tokyo, Japan) and
Sub-Saharan Africans (combining
Luhya Luhya or Abaluyia may refer to:
* Luhya people
* Luhya language
Luhya (; also Luyia, Luhia or Luhiya) is a Bantu language of western Kenya.
Dialects
The various Luhya tribes speak several related languages and dialects, though some of them are ...
of Webuye, Kenya,
Maasai Maasai may refer to:
* Maasai people
*Maasai language
* Maasai mythology
* MAASAI (band)
See also
* Masai (disambiguation)
* Massai
Massai (also known as: Masai, Massey, Massi, Mah–sii, Massa, Wasse, Wassil or by the nickname "Big Foot" Mas ...
of Kinyawa, Kenya and
Yoruba
The Yoruba people (, , ) are a West African ethnic group that mainly inhabit parts of Nigeria, Benin, and Togo. The areas of these countries primarily inhabited by Yoruba are often collectively referred to as Yorubaland. The Yoruba constitute ...
of Ibadan, Nigeria). It reported a value close to 12% between continental populations, and values close to
panmixia
Panmixia (or panmixis) means random mating. A panmictic population is one where all individuals are potential partners. This assumes that there are no mating restrictions, neither genetic nor behavioural, upon the population and that therefore all ...
(smaller than 1%) within continental populations.
Programs for calculating FST
*
Arlequin
* Fstat
SMOGDdiveRsity(R package)
hierfstat(R package)
FinePopref> (R package)
*
DnaSP
Modules for calculating FST
*
BioPerl
BioPython
References
Further reading
* Evolution and the Genetics of Populations Volume 2: the Theory of Gene Frequencies, pg 294–295, S. Wright, Univ. of Chicago Press, Chicago, 1969
* A haplotype map of the human genome, The International HapMap Consortium, Nature 2005
See also
*
Genetic distance
Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree of differentiation. Populations with many similar alleles have s ...
External links
BioPerl - Bio::PopGen::PopStats
{{DEFAULTSORT:Fixation Index
Population genetics
Mathematical and theoretical biology