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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 stay together during meiosis, and are thus genetically linked. Alleles for genes on different chromosomes are usually not linked, due to independent assortment of chromosomes during meiosis.

Because there is some crossing over of DNA when the chromosomes segregate, alleles on the same chromosome can be separated and go to different daughter cells. There is a greater probability of this happening if the alleles are far apart on the chromosome, as it is more likely that a cross-over will occur between them.

The relative distance between two genes can be calculated using the offspring of an organism showing two linked genetic traits, and finding the percentage of the offspring where the two traits do not run together. The higher the percentage of descendants that does not show both traits, the further apart on the chromosome they are.

Among individuals of an experimental population or species, some phenotypes or traits occur randomly with respect to one another in a manner known as independent assortment. Today scientists understand that independent assortment occurs when the genes affecting the phenotypes are found on different chromosomes or separated by a great enough distance on the same chromosome that recombination occurs at least half of the time.

An exception to independent assortment develops when genes appear near one another on the same chromosome. When genes occur on the same chromosome, they are usually inherited as a single unit. Genes inherited in this way are said to be linked, and are referred to as "linkage groups." For example, in fruit flies the genes affecting eye color and wing length are inherited together because they appear on the same chromosome.

But in many cases, even genes on the same chromosome that are inherited together produce offspring with unexpected allele combinations. This results from a process called crossing over. At the beginning of normal meiosis, a chromosome pair (made up of a chromosome from the mother and a chromosome from the father) intertwine and exchange sections or fragments of chromosome. The pair then breaks apart to form two chromosomes with a new combination of genes that differs from the combination supplied by the parents. Through this process of recombining genes, organisms can produce offspring with new combinations of maternal and paternal traits that may contribute to or enhance survival.

Genetic linkage was first discovered by the British geneticists William Bateson and Reginald Punnett shortly after Mendel's laws were rediscovered.

The observations by Thomas Hunt Morgan that the amount of crossing over between linked genes differs led to the idea that crossover frequency might indicate the distance separating genes on the chromosome. Morgan's student Alfred Sturtevant developed the first genetic map, also called a linkage map.

Sturtevant proposed that the greater the distance between linked genes, the greater the chance that non-sister chromatids would cross over in the region between the genes. By working out the number of recombinants it is possible to obtain a measure for the distance between the genes. This distance is called a genetic map unit (m.u.), or a centimorgan and is defined as the distance between genes for which one product of meiosis in 100 is recombinant. A recombinant frequency (RF) of 1 % is equivalent to 1 m.u. A linkage map is created by finding the map distances between a number of traits that are present on the same chromosome, ideally avoiding having significant gaps between traits to avoid the inaccuracies that will occur due to the possibility of multiple recombination events.

Linkage mapping is critical for identifying the location of genes that cause genetic diseases. In an ideal population, genetic traits and markers will occur in all possible combinations with the frequencies of combinations determined by the frequencies of the individual genes. For example, if alleles A and a occur with frequency 90% and 10%, and alleles B and b at a different genetic locus occur with frequencies 70% and 30%, the frequency of individuals having the combination AB would be 63%, the product of the frequencies of A and B, regardless of how close together the genes are. However, if a mutation in gene B that causes some disease happened recently in a particular subpopulation, it almost always occurs with a particular allele of gene A if the individual in which the mutation occurred had that variant of gene A and there have not been sufficient generations for recombination to happen between them (presumably due to tight linkage on the genetic map). In this case, called linkage disequilibrium, it is possible to search potential markers in the subpopulation and identify which marker the mutation is close to, thus determining the mutation's location on the map and identifying the gene at which the mutation occurred. Once the gene has been identified, it can be targeted to identify ways to mitigate the disease.

A linkage map is a genetic map of a species or experimental population that shows the position of its known genes and/or genetic markers relative to each other in terms of recombination frequency, rather than as specific physical distance along each chromosome.

A genetic map is a map based on the frequencies of recombination between markers during crossover of homologous chromosomes. The greater the frequency of recombination (segregation) between two genetic markers, the farther apart they are assumed to be. Conversely, the lower the frequency of recombination between the markers, the smaller the physical distance between them. Historically, the markers originally used were detectable phenotypes (enzyme production, eye color) derived from coding DNA sequences; eventually, confirmed or assumed noncoding DNA sequences such as microsatellites or those generating restriction fragment length polymorphisms (RFLPs) have been used.

Genetic maps help researchers to locate other markers, such as other genes by testing for genetic linkage of the already known markers.

A genetic map is not a physical map or gene map.

## LOD score method for estimating recombination frequencyEdit

The LOD score (logarithm (base 10) of odds, also called logit by mathematicians) is a statistical test often used for linkage analysis in human populations, and also in animal and plant populations. The test was developed by Newton E. Morton. Computerized LOD score analysis is a simple way to analyze complex family pedigrees in order to determine the linkage between Mendelian traits (or between a trait and a marker, or two markers).

The method is described in greater detail by Strachan and Read [1]. Briefly, it works as follows:

1. Establish a pedigree
2. Make a number of estimates of recombination frequency
3. Calculate a LOD score for each estimate
4. The estimate with the highest LOD score will be considered the best estimate

The LOD score is calculated as follows:

\begin{align} LOD = Z & = \log{10} \frac{ \mbox{probability of birth sequence with a given linkage value} }{ \mbox{probability of birth sequence with no linkage} } \\ & = \log{10} \frac{(1-\theta)^{NR} \times \theta^R}{ 0.5^{(NR + R)} } \end{align}

NR denotes the number of non-recombinant offspring, and R denotes the number of recombinant offspring. The reason 0.5 is used in the denominator is that any alleles that are completely unlinked (e.g. alleles on separate chromosomes) have a 50% chance of recombination, due to independent assortment.

Theta is the recombinant fraction, that is to say it is equal to R / (NR + R)

In practice, LOD scores are looked up in a table which lists LOD scores for various standard pedigrees and various values of recombination frequency.

By convention, a LOD score greater than 3.0 is considered evidence for linkage. (A score of 3.0 means the likelihood of observing the given pedigree if the two loci are not linked is less than 1 in 1000). On the other hand, a LOD score less than -2.0 is considered evidence to exclude linkage. Although it is very unlikely that a LOD score of 3 would be obtained from a single pedigree, the mathematical properties of the test allow data from a number of pedigrees to be combined by summing the LOD scores.

## Recombination frequencyEdit

Recombination frequency (θ) is the frequency that a chromosomal crossover will take place between two loci (or genes) during meiosis. Recombination frequency is a measure of genetic linkage and is used in the creation of a genetic linkage map. A centimorgan (cM) is a unit that describes a recombination frequency of 1%.

During meiosis, chromosomes assort randomly into gametes, such that the segregation of alleles of one gene is independent of alleles of another gene. This is stated in Mendel's Second Law and is known as the law of independent assortment. The law of independent assortment always holds true for genes that are located on different chromosomes, but for genes that are on the same chromosome, it does not always hold true.

As an example of independent assortment, consider the crossing of the pure-bred homozygote parental strain with genotype AABB with a different pure-bred strain with genotype aabb. A and a and B and b represent the alleles of genes A and B. Crossing these homozygous parental strains will result in F1 generation offspring with genotype AaBb. The F1 offspring AaBb produces gametes that are AB, Ab, aB, and ab with equal frequencies (25%) because the alleles of gene A assort independently of the alleles for gene B during meiosis. Note that 2 of the 4 gametes (50 %)—Ab and aB—were not present in the parental generation. These gametes represent recombinant gametes. Recombinant gametes are those gametes that differ from both of the haploid gametes that made up the diploid cell. In this example, the recombination frequency is 50% since 2 of the 4 gametes were recombinant gametes.

The recombination frequency will be 50% when two genes are located on different chromosomes or when they are widely separated on the same chromosome. This is a consequence of independent assortment.

When two genes are close together on the same chromosome, they do not assort independently and are said to be linked. Whereas genes located on different chromosomes assort independently and have a recombination frequency of 50%, linked genes have a recombination frequency that is less than 50%.

As an example of linkage, consider the classic experiment by William Bateson and Reginald Punnett. They were interested in trait inheritance in the sweet pea and were studying two genes—the gene for flower color (P, purple, and p, red) and the gene affecting the shape of pollen grains (L, long, and l, round). They crossed the pure lines PPLL and ppll and then self-crossed the resulting PpLl lines. According to Mendelian genetics, the expected phenotypes would occur in a 9:3:3:1 ratio of PL:Pl:pL:pl. To their surprise, they observed an increased frequency of PL and pl and a decreased frequency of Pl and pL (see table below).

Bateson and Punnett experiment
Phenotype and genotypeObservedExpected from 9:3:3:1 ratio
Purple, long (P_L_)284216
Purple, round (P_ll)2172
Red, long (ppL_)2172
Red, round (ppll)5524

Their experiment revealed linkage between the P and L alleles and the p and l alleles. The frequency of P occurring together with L and with p occurring together with l is greater than that of the recombinant Pl and pL. The recombination frequency cannot be computed directly from this experiment, but intuitively it is less than 50%.

The progeny in this case received two dominant alleles linked on one chromosome (referred to as coupling or cis arrangement). However, after crossover, some progeny could have received one parental chromosome with a dominant allele for one trait (eg Purple) linked to a recessive allele for a second trait (eg round) with the opposite being true for the other parental chromosome (eg red and Long). This is referred to as repulsion or a trans arrangement. The phenotype here would still be purple and long but a test cross of this individual with the recessive parent would produce progeny with much greater proportion of the two crossover phenotypes. While such a problem may not seem likely from this example, unfavorable repulsion linkages do appear when breeding for disease resistance in some crops.

When two genes are located on the same chromosome, the chance of a crossover producing recombination between the genes is directly related to the distance between the two genes. Thus, the use of recombination frequencies has been used to develop linkage maps or genetic maps.