Information about Linkage Disequilibrium
Linkage disequilibrium is a term used in the study of population genetics for the non-random association of alleles at two or more loci, not necessarily on the same chromosome. It is not the same as linkage, which describes the association of two or more loci on a chromosome with limited recombination between them. Linkage disequilibrium describes a situation in which some combinations of alleles or genetic markers occur more or less frequently in a population than would be expected from a random formation of haplotypes from alleles based on their frequencies. Non-random associations between polymorphisms at different loci are measured by the degree of linkage disequilibrium (LD). A comparison of different measures is provided by[1]
Linkage disequilibrium is generally caused by genetic linkage and the rate of recombination; mutation rate; random drift or non-random mating; and population structure. For example, some organisms may show linkage disequilibrium (such as bacteria) because they reproduce asexually and there is no recombination (r=0) to break down the linkage disequilibrium: D'=(1-r)D.
It may be instructive to study genetic equilibrium, and its application in the Hardy-Weinberg principle.
The International HapMap Project enables the study of LD in human populations online. The Ensembl project integrates HapMap data and such from dbSNP in general with other genetic information.Linkage disequilibrium measure,
Formally, if we define pairwise LD, we consider indicator variables on alleles at two loci, say 
. We define the LD parameter 
as:
Here
denote the marginal allele frequencies at the two loci and 
denotes the haplotype frequency in the joint distribution of both alleles.
Various derivatives of this parameter have been developed. In the genetic literature the wording "two alleles are in LD" usually means to imply 
. Contrariwise, linkage equilibrium, denotes the case 
.
From there one can determine the frequency of each of the alleles:
if the two loci and the alleles are independent from each other, then one can express the observation A1B1 as "A1 must be found and B1 must be found". The table above lists the frequencies for
, and 
, hence the frequency of 
, 
, equals according to the rules of elementary statistics 
.
A deviation of the observed frequencies from the expected is referred to as the linkage disequilibrium parameter, introduced by Robbins (1918)[2] and named by Lewontin and Kojima (1960)[3] and commonly denoted by a capital D as defined by
. It is vividly presented in the following table.
When extending these formula for diploid cells rather than investigating the gametes/haplotypes directly, the laid out principle prevails, the recombination rate between the two loci
and 
must be taken into account, though, which is commonly denoted by the letter 
.
is nice to calculate with but has the disadvantage of depending on the frequency of the alleles inspected. This is evident since frequencies are between 0 and 1. There can be no observed if any locus has an allele frequency 0 or 1 and is maximal when frequencies are at 0.5. Lewontin (1964) suggested normalising D by dividing it with the theoretical maximum for the observed allele frequencies. Thus 
when 
When 
, 
.
is given by the smaller of 
and 
. 
is given by the larger of 
and 
Another value is the correlation coefficient as also laid out in the initial paragraphs of this page, denoted as
. This however is not adjusted to the loci having different allele frequencies. If it was, 
, the square root of 
if given the sign of would be equivalent to 
[4]
Another statistic used in a selective neutrality test is Tajima's D, to decide whether the mean number of differences between pairs of DNA sequences is compatible with the observed number of segregating sites in a sample.
These are summary statistics (i.e. descriptive statistics summarizing the pattern of genetic diversity) that are computed from diploid samples of DNA sequences and which assume that the gametic phase is known.
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Natural selection is the process by which favorable traits that are heritable become more common in successive generations of a population of reproducing organisms, and unfavorable traits that are heritable become less
..... Click the link for more information.
Linkage disequilibrium is generally caused by genetic linkage and the rate of recombination; mutation rate; random drift or non-random mating; and population structure. For example, some organisms may show linkage disequilibrium (such as bacteria) because they reproduce asexually and there is no recombination (r=0) to break down the linkage disequilibrium: D'=(1-r)D.
It may be instructive to study genetic equilibrium, and its application in the Hardy-Weinberg principle.
The International HapMap Project enables the study of LD in human populations online. The Ensembl project integrates HapMap data and such from dbSNP in general with other genetic information.
Linkage disequilibrium measure,
Formally, if we define pairwise LD, we consider indicator variables on alleles at two loci, say . We define the LD parameter as:
Here
denote the marginal allele frequencies at the two loci and denotes the haplotype frequency in the joint distribution of both alleles.
Various derivatives of this parameter have been developed. In the genetic literature the wording "two alleles are in LD" usually means to imply . Contrariwise, linkage equilibrium, denotes the case .
Linkage disequilibrium measure, D
If inspecting the two loci A and B with two alleles each—a two-locus, two-allele model—the following table denotes the frequencies of each combination:| Haplotype | Frequency |
| |
 |  |
 |  |
 |  |
From there one can determine the frequency of each of the alleles:
| Allele | Frequency |
 |  |
 |  |
 |  |
 |  |
if the two loci and the alleles are independent from each other, then one can express the observation A1B1 as "A1 must be found and B1 must be found". The table above lists the frequencies for
, and , hence the frequency of , , equals according to the rules of elementary statistics .
A deviation of the observed frequencies from the expected is referred to as the linkage disequilibrium parameter, introduced by Robbins (1918)[2] and named by Lewontin and Kojima (1960)[3] and commonly denoted by a capital D as defined by
. It is vividly presented in the following table.
| | Total | |
|  |  |  |
|  |  |  |
| Total |  |  |  |
When extending these formula for diploid cells rather than investigating the gametes/haplotypes directly, the laid out principle prevails, the recombination rate between the two loci
and must be taken into account, though, which is commonly denoted by the letter .
is nice to calculate with but has the disadvantage of depending on the frequency of the alleles inspected. This is evident since frequencies are between 0 and 1. There can be no observed if any locus has an allele frequency 0 or 1 and is maximal when frequencies are at 0.5. Lewontin (1964) suggested normalising D by dividing it with the theoretical maximum for the observed allele frequencies. Thus when When , .
is given by the smaller of and . is given by the larger of and
Another value is the correlation coefficient as also laid out in the initial paragraphs of this page, denoted as
. This however is not adjusted to the loci having different allele frequencies. If it was, , the square root of if given the sign of would be equivalent to [4]
Another statistic used in a selective neutrality test is Tajima's D, to decide whether the mean number of differences between pairs of DNA sequences is compatible with the observed number of segregating sites in a sample.
These are summary statistics (i.e. descriptive statistics summarizing the pattern of genetic diversity) that are computed from diploid samples of DNA sequences and which assume that the gametic phase is known.
Analysis Software
- Haploview
- LdCompare[5] — open-source software for calculating LD.
- PyPop
- HelixTree - commercial software with interactive LD plot.
References
1. ^ Devlin B., Risch N. (1995). "A Comparison of Linkage Disequilibrium Measures for Fine-Scale Mapping". Genomics 29: 311-322.
2. ^ Robbins, R.B. (1918). "Some applications of mathematics to breeding problems III". Genetics 3: 375-389.
3. ^ R.C. Lewontin and K. Kojima (1960). "The evolutionary dynamics of complex polymorphisms.". Evolution 14: 458-472.
4. ^ P.W. Hedrick and S. Kumar (2001). "Mutation and linkage disequilibrium in human mtDNA". Eur. J. Hum. Genet. 9: 969-972.
5. ^ Hao K., Di X., Cawley S. (2007). "LdCompare: rapid computation of single- and multiple-marker r2 and genetic coverage". Bioinformatics 23: 252-254.
2. ^ Robbins, R.B. (1918). "Some applications of mathematics to breeding problems III". Genetics 3: 375-389.
3. ^ R.C. Lewontin and K. Kojima (1960). "The evolutionary dynamics of complex polymorphisms.". Evolution 14: 458-472.
4. ^ P.W. Hedrick and S. Kumar (2001). "Mutation and linkage disequilibrium in human mtDNA". Eur. J. Hum. Genet. 9: 969-972.
5. ^ Hao K., Di X., Cawley S. (2007). "LdCompare: rapid computation of single- and multiple-marker r2 and genetic coverage". Bioinformatics 23: 252-254.
See also
Further reading
- Hedrick, Philip W. (2005). Genetics of Populations, 3rd, Sudbury, Boston, Toronto, London, Singapore: Jones and Bartlett Publishers. ISBN 0763747726.
Topics in population genetics | |
|---|---|
| Key concepts | Hardy-Weinberg law • genetic linkage • linkage disequilibrium • Fisher's fundamental theorem • neutral theory |
| Selection | natural • sexual • artificial • ecological |
| Effects of selection on genomic variation | genetic hitchhiking • background selection |
| Genetic drift | small population size • population bottleneck • founder effect • coalescence |
| Founders | R.A. Fisher • J. B. S. Haldane • Sewall Wright |
| Related topics | evolution • microevolution • evolutionary game theory • fitness landscape • genetic genealogy |
| List of evolutionary biology topics | |
Population genetics is the study of the allele frequency distribution and change under the influence of the four evolutionary forces: natural selection, genetic drift, mutation and gene flow. It also takes account of population subdivision and population structure in space.
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For the hard rock band, see .
An allele (Pronounced: /əˈlil/) is a viable DNA (deoxyribonucleic acid) coding that occupies a given locus (position) on a chromosome...... Click the link for more information.
locus (plural loci) is a fixed position on a chromosome, such as the position of a gene or a biomarker (genetic marker). A variant of the DNA sequence at a given locus is called an allele. The ordered list of loci known for a particular genome is called a genetic map.
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Figure 1: A representation of a condensed eukaryotic chromosome, as seen during cell division.]] A chromosome is a single large macromolecule of DNA, and constitutes a physically organized form of DNA in a cell.
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Genetic linkage occurs when particular genetic loci or alleles for genes are inherited jointly. Genetic loci on the same chromosome are physically connected and tend to segregate together during meiosis, and are thus genetically linked.
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A haplotype (Greek haploos = simple) is a combination of alleles at multiple linked loci that are transmitted together. Haplotype may refer to as few as two loci or to an entire chromosome depending on the number of recombination events that have occurred between
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For the hard rock band, see .
An allele (Pronounced: /əˈlil/) is a viable DNA (deoxyribonucleic acid) coding that occupies a given locus (position) on a chromosome...... Click the link for more information.
In theory, genetic equilibrium is a state in which a population is not evolving.
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Assumptions For Genetic Equilibrium
- No gene mutations
- Large population size
- Limited-to-no immigration or emagration
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Hardy–Weinberg principle is a relationship between the frequencies of alleles and the genotype of a population. The occurrence of a genotype, perhaps one associated with a disease, stays constant unless matings are non-random or inappropriate, or mutations accumulate.
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The International HapMap Project is an organization whose goal is to develop a haplotype map of the human genome (the HapMap), which will describe the common patterns of human genetic variation.
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Ensembl is a bioinformatics research project precisely a Genome Browser aiming to "develop a software system which produces and maintains automatic annotation on selected eukaryotic genomes".
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dummy variable (also known as indicator or bound variable) is one that takes the values 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.
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For the hard rock band, see .
An allele (Pronounced: /əˈlil/) is a viable DNA (deoxyribonucleic acid) coding that occupies a given locus (position) on a chromosome...... Click the link for more information.
Allele frequency is a measure of the relative frequency of an allele on a genetic locus in a population. Usually it is expressed as a proportion or a percentage. In population genetics, allele frequencies show the genetic diversity of a species population or equivalently the
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A gamete (from Ancient Greek γαμετης; translated gamete = wife, gametes = husband) is a cell that fuses with another gamete during fertilisation (conception) in organisms that reproduce sexually.
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A haplotype (Greek haploos = simple) is a combination of alleles at multiple linked loci that are transmitted together. Haplotype may refer to as few as two loci or to an entire chromosome depending on the number of recombination events that have occurred between
..... Click the link for more information.
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Tajima's D is a statistical test created by and named after the Japanese researcher Fumio Tajima. The purpose of the test is to distinguish between a DNA sequence evolving randomly versus one evolving under a non-random process, including directional selection or balancing
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Haploview[1] is a commonly used bioinformatics software tool which is designed to analyze and visualize patterns of linkage disequilibrium in genetic data. Haploview also provides functionality for performing association studies, choosing tagSNPs[2]
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Hardy–Weinberg principle is a relationship between the frequencies of alleles and the genotype of a population. The occurrence of a genotype, perhaps one associated with a disease, stays constant unless matings are non-random or inappropriate, or mutations accumulate.
..... Click the link for more information.
..... Click the link for more information.
Genetic linkage occurs when particular genetic loci or alleles for genes are inherited jointly. Genetic loci on the same chromosome are physically connected and tend to segregate together during meiosis, and are thus genetically linked.
..... Click the link for more information.
..... Click the link for more information.
In biology, co-adaptation, or coadaptation refers to the mutual adaptation of:
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- Species: see mutualism, symbiosis
- organs: see the evolution of the eye.
- Genes or gene complexes: see Linkage disequilibrium, epistasis
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A genealogical DNA test examines the nucleotides at specific locations on a person's DNA for genetic genealogy purposes. The test results are meant to have no informative medical value and do not determine specific genetic diseases or disorders (see possible exceptions in
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A tag SNP is a representative single nucleotide polymorphisms (SNPs) in a region of the genome with high linkage disequilibrium (the non-random association of alleles at two or more loci).
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Population genetics is the study of the allele frequency distribution and change under the influence of the four evolutionary forces: natural selection, genetic drift, mutation and gene flow. It also takes account of population subdivision and population structure in space.
..... Click the link for more information.
..... Click the link for more information.
Hardy–Weinberg principle is a relationship between the frequencies of alleles and the genotype of a population. The occurrence of a genotype, perhaps one associated with a disease, stays constant unless matings are non-random or inappropriate, or mutations accumulate.
..... Click the link for more information.
..... Click the link for more information.
Genetic linkage occurs when particular genetic loci or alleles for genes are inherited jointly. Genetic loci on the same chromosome are physically connected and tend to segregate together during meiosis, and are thus genetically linked.
..... Click the link for more information.
..... Click the link for more information.
In population genetics, R. A. Fisher's fundamental theorem of natural selection was originally stated as:
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- "The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.
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The neutral theory of molecular evolution (also, simply the neutral theory of evolution) is an influential theory that was introduced with provocative effect by Motoo Kimura in the late 1960s and early 1970s.
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selection. Under selection, individuals with advantageous or "adaptive" traits tend to be more successful than their peers reproductively--meaning they contribute more offspring to the succeeding generation than others do.
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Natural selection is the process by which favorable traits that are heritable become more common in successive generations of a population of reproducing organisms, and unfavorable traits that are heritable become less
..... Click the link for more information.
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