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Genetic linkage is the tendency of DNA sequences that are close together on a chromosome to be inherited together during the meiosis phase of sexual reproduction. Two genetic markers that are physically near to each other are unlikely to be separated onto different chromatids during chromosomal crossover, and are therefore said to be more linked than markers that are far apart. In other words, the nearer two genes are on a chromosome, the lower the chance of recombination between them, and the more likely they are to be inherited together. Markers on different chromosomes are perfectly unlinked.

Genetic linkage is the most prominent exception to Gregor Mendel's Law of Independent Assortment. The first experiment to demonstrate linkage was carried out in 1905. At the time, the reason why certain traits tend to be inherited together was unknown. Later work revealed that genes are physical structures related by physical distance.

The typical unit of genetic linkage is the centimorgan (cM). A distance of 1 cM between two markers means that the markers are separated to different chromosomes on average once per 100 meiotic product, thus once per 50 meioses...

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• ✪ Gene mapping | Biomolecules | MCAT | Khan Academy
• ✪ 8H - Physical and genetic linkage and maps
• ✪ Introduction to gene mapping (gene mapping part 1)
• ✪ Genetic Recombination and Gene Mapping
• ✪ GENETIC MAPPING | LINKAGE MAP | CHROMOSOME MAP | PART-1

#### Transcription

- [Voiceover] One of the very interesting things about genetic recombination is that you can actually use genetic recombination to figure out the distance between genes on a chromosome. And if you were to do this to all the genes on a chromosome, you could actually map out the chromosome, figure out exactly where the genes are. And we're going to explore that concept. So we're looking at a pair of homologous chromosomes, and let's just say that the orange chromosome is the paternal chromosome, so it comes from the father, and let's say that the yellow one is the maternal chromosome. And, just to remind ourselves, these are sister chromatids. That means that they are identical chromatids, they have identical genes on them. So those colored circles that I drew represent just some genes that I randomly picked. And you can see that on the two sister chromatids I drew them in the same color, because they are the same. And for that matter, these are also sister chromatids. These two yellow chromatids are also sister chromatids. And I'm just gonna review a bit to give us some context. So normally in the cell, the paternal chromosome would just look something like that, with the centromere middle. And the maternal chromosome would also look something like that. But, during myosis or mitosis, when they replicate, this chromosome will turn into that. So it's gonna duplicate itself and each one of those strands is a sister chromatid. And so the maternal chromosome turns into something that looks like that. But, this is still considered one chromosome. And this is considered one chromosome. And that can be a little bit confusing, because how could this be one chromosome and this also be one chromosome? If this X has double the material as the original strand? And the answer to that question is because we count chromosomes by the amount of centromeres that are present. So this has one centromere, it's considered one chromosome. This X has one centromere, so it's considered one chromosome. However, they're not quite the same. This, on top, is just one chromatid. And the bottom chromosome has ended up with two chromatids. So try not to get confused, even though we're calling this one chromosome, it's really made up of two identical sister chromatids. But anyway, that was a bit of a digression. Let's focus again on our homologous chromosomes. So I picked a couple of genes, that I just put on, and we're gonna focus on three genes in particular. And to make this a bit more real or relevant, let's just say that the green genes represent I don't know, maybe complexion. Maybe like a dark complexion versus a lighter complexion. And on the maternal chromosome, I also drew it in green, to remind us that these are homologous chromosomes, they're homologous alleles, in other words, these are both alleles that code for complexion, but different shades of green, because they're probably different versions. So these green genes also code for complexion. And let's say that this darker purple, or magenta, gene codes for, let's say hair color. So that means that the lighter purple on the maternal chromosome also code for hair color. And then let's say that the blue genes code for eye color. So we have dark blue on the paternal chromosome and light blue on the maternal chromosome. And let's then focus on the sister chromatids where genetic recombination occurs. So these two strands are going to swap genetic information between them. Maybe like a chunk on bottom will swap, maybe something in middle will swap, maybe something on top will swap. Actually, genetic recombination also occurs between sister chromatids. However, sister chromatids are identical so it would be of no consequence. Anyway, so let's look at the two chromatids where genetic recombination is happening. The two that I circled. Let's take a closer look at those. So here are the two chromatids that are going to exchange genetic information and undergo recombination. And I want to ask you a question. So I'm gonna give you two choices. And I want you to try to figure out which one is more likely. So, for the first choice, let's look at the purple and green genes. And the question is, what's the what's more likely? Is it more likely that the purple and green genes undergo recombination? And when I say that, I mean that the genes that are originally on one chromosome separate. So I mean to say that, for example, this purple gene will get separated from that gene, and this lighter purple gene will get separated from that gene. So is it more likely that the purple and green genes recombine? Or the way I like to view it, get separated. Or, is it more likely that the blue and purple genes recombine or get separated? And the way to think about this is, well look at the distance between them. So the distance between the purple and green genes is something like that. So in order for recombination to occur with respect to the purple and green genes, it would have to happen somewhere over here. Or on the other side, it doesn't matter, it doesn't make a difference. So you have this whole distance, whereas if you wanted recombination to occur with respect to the purple and blue genes, you have a very smaller area to work with. It would have to happen somewhere here. So somewhere along this line of the chromosome. So, that means that it's much more likely for recombination to happen with respect to the purple and green genes. That is more likely because you have this entire distance to work with. If these two chromatids swap genetic information anywhere along this stretch of the chromosome, so the green and purple genes will separate and recombine. And the blue and purple genes are less likely to recombine because recombination would have to occur only in this little sliver of chromosome and that's just smaller than the other part of the chromosome that we were looking at. So, we just learned a very important concept and that is that the further apart two genes are, the more likely it is that they will recombine. I'm not actually not sure if that's the proper way to use the word, but I just use it that way. So I'm gonna put it in quotes. And again, when I say recombine, I mean that two chromosomes that were originally on the same, sorry, two genes that were originally on the same chromosome get separated. And then the next thing we learned is that the closer two genes are to each other, I'll abbreviate each other, just e.o., the less likely it is that they will recombine. And now i'm gonna introduce you to some terms. The centimorgan is the unit of measurement that we use to measure distance on a chromosome. And another way to say centimorgan is a genetic map unit. Or, m.u. which stands for map unit. And I'll give you the official definition of a centimorgan, because I think it's important and it kind of ties in distance to what it has to do with recombination. And so a centimorgan is the distance between genes, I'm just gonna abbreviate between like that, for which one product of myosis in 100 is recombinant. And to put that in simpler terms, it means that if two genes are one centimorgan apart, it means that one out of one hundred times, or one percent of the time that myosis happens, those two genes will be recombinant, or separate, or recombine. And we'll actually do an example of this to illustrate what this means. So here we have our two chromatids again and let's just say that the distance between the purple and green genes is 25 map units. Remember, a map unit is the same thing as a centimorgan. And let's say that the distance between the blue and purple genes is six map units. So this is clearly not drawn to scale very well, but it's just an estimate. So let's first focus on the purple and green genes. So if they're 25 map units apart, so remember if two genes are one map unit apart that means that one percent of the time they'll recombine, so these are 25 map units apart, so that means that 25% of the time that myosis happens, recombination will occur with respect to the purple and green genes. So let's see what that looks like. So we're gonna see that in this spot, right over here, the chromatids just swap information, So let's draw what that would look like. So let's draw our paternal chromosome, or at least part of it. And then we'll draw our, actually I'm gonna draw that a little bit higher, because we need more room. So here's our paternal chromosome. And then our maternal chromosome. Or chromatid. And then, since they kind of swapped in this spot, so I'm gonna draw yellow, right over here. That's the part that came from the maternal chromosome. And then I'm gonna draw orange over here. That's the part that came from the paternal chromosome. And now let's fill in our genes. So the blue genes will just stay where they were. So, we just leave them put. And the same goes for the purple genes. But then, we have that piece of maternal chromosome. So we get that hunter green gene over here. And then we get the lime green gene right over here. So this is what I mean by recombination being a separation of genes. So this purple gene and that lime green gene were on the same chromosome before, but they got separated. They're not on the same chromosome any more. And the same applies to these two genes. Now let's look at the blue and purple genes. So they're six map units apart. So that means that 6% of the time that myosis happens, the purple and blue genes will get separated. So, we're gonna see that upwards of this spot, the chromatids swap information. So, let's draw that. So here we'll draw a part of our paternal. that's the paternal chromosome and the maternal one. And they swapped somewhere like over here. So let's fill that in. So that's the part of the maternal chromosome that lands up, sorry, yeah, that's the part of the maternal chromosome that ends up on the paternal one. And the orange over here. And now let's fill in our genes. So lets's first fill in the ones that just stay put. So we have that lime green gene, then we have that hunter green gene. And our purples also stay put. But the blue genes swap chromosomes. So we have our dark blue gene over here and our light blue gene over here. And again, take note of how they swap places, or how the separate. So these two genes were together on the same chromosome before, but not anymore. And the same for these two genes. So let's just tie this back into the bigger concept going on. If we were to do a statistical analysis of how often certain recombinations happen, that can help us map out the genes on a chromosome.

## Discovery

Gregor Mendel's Law of Independent Assortment states that every trait is inherited independently of every other trait. But shortly after Mendel's work was rediscovered, exceptions to this rule were found. In 1905, the British geneticists William Bateson, Edith Rebecca Saunders and Reginald Punnett cross-bred pea plants in experiments similar to Mendel's.[1][2] They were interested in trait inheritance in the sweet pea and were studying two genes—the gene for flower colour (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:

Bateson, Saunders, and Punnett experiment
Phenotype and genotype Observed Expected from 9:3:3:1 ratio
Purple, long (P_L_) 284 216
Purple, round (P_ll) 21 72
Red, long (ppL_) 21 72
Red, round (ppll) 55 24

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 p occurring together with l is greater than that of the recombinant Pl and pL. The recombination frequency is more difficult to compute in an F2 cross than a backcross,[3] but the lack of fit between observed and expected numbers of progeny in the above table indicate it is less than 50%. This indicated that two factors interacted in some way to create this difference by masking the appearance of the other two phenotypes. This led to the conclusion that some traits are related to each other because of their near proximity to each other on a chromosome. This provided the grounds to determine the difference between independent and codependent alleles.[citation needed]

The understanding of linkage was expanded by the work of Thomas Hunt Morgan. Morgan's observation 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. The centimorgan, which expresses the frequency of crossing over, is named in his honour.

Thomas Hunt Morgan's Drosophila melanogaster genetic linkage map. This was the first successful gene mapping work and provides important evidence for the chromosome theory of inheritance. The map shows the relative positions of alleles on the second Drosophila chromosome. The distances between the genes (centimorgans) are equal to the percentages of chromosomal crossover events that occur between different alleles.[4]

A linkage map (also known as a genetic map) is a table for a species or experimental population that shows the position of its known genes or genetic markers relative to each other in terms of recombination frequency, rather than a specific physical distance along each chromosome. Linkage maps were first developed by Alfred Sturtevant, a student of Thomas Hunt Morgan.

A linkage 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 further 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 colour) 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.

Linkage maps help researchers to locate other markers, such as other genes by testing for genetic linkage of the already known markers. In the early stages of developing a linkage map, the data are used to assemble linkage groups, a set of genes which are known to be linked. As knowledge advances, more markers can be added to a group, until the group covers an entire chromosome.[5] For well-studied organisms the linkage groups correspond one-to-one with the chromosomes.

A linkage map is not a physical map (such as a radiation reduced hybrid map) or gene map.

Linkage analysis is a genetic method that searches for chromosomal segments that cosegregate with the ailment phenotype through families and is the analysis technique that has been used to determine the bulk of lipodystrophy genes.[6][7] It can be used to map genes for both binary and quantitative traits.[7] Linkage analysis may be either parametric (if we know the relationship between phenotypic and genetic similarity) or non-parametric. Parametric linkage analysis is the traditional approach, whereby the probability that a gene important for a disease is linked to a genetic marker is studied through the LOD score, which assesses the probability that a given pedigree, where the disease and the marker are cosegregating, is due to the existence of linkage (with a given linkage value) or to chance. Non-parametric linkage analysis, in turn, studies the probability of an allele being identical by descent with itself.

The LOD score (logarithm (base 10) of odds), developed by Newton Morton,[8] is a statistical test often used for linkage analysis in human, animal, and plant populations. The LOD score compares the likelihood of obtaining the test data if the two loci are indeed linked, to the likelihood of observing the same data purely by chance. Positive LOD scores favour the presence of linkage, whereas negative LOD scores indicate that linkage is less likely. Computerised LOD score analysis is a simple way to analyse 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:

${\displaystyle {\text{LOD}}=Z=\log _{10}{\frac {\text{probability of birth sequence with a given linkage value}}{\text{probability of birth sequence with no linkage}}}=\log _{10}{\frac {(1-\theta )^{NR}\times \theta ^{R}}{0.5^{NR+R}}}}$

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. θ is the recombinant fraction, i.e. the fraction of births in which recombination has happened between the studied genetic marker and the putative gene associated with the disease. Thus, it is equal to R / (NR + R).

By convention, a LOD score greater than 3.0 is considered evidence for linkage, as it indicates 1000 to 1 odds that the linkage being observed did not occur by chance. 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 their LOD scores. A LOD score of 3 translates to a p-value of approximately 0.05,[9] and no multiple testing correction (e.g. Bonferroni correction) is required.[10]

### Limitations

Linkage analysis has a number of methodological and theoretical limitations that can significantly increase the type-1 error rate and reduce the power to map human quantitative trait loci (QTL).[11] While linkage analysis was successfully used to identify genetic variants that contribute to rare disorders such as Huntington disease, it did not perform that well when applied to more common disorders such as heart disease or different forms of cancer.[12] An explanation for this is that the genetic mechanisms affecting common disorders are different from those causing rare disorders.[13]

## Recombination frequency

Recombination frequency is a measure of genetic linkage and is used in the creation of a genetic linkage map. Recombination frequency (θ) is the frequency with which a single chromosomal crossover will take place between two genes during meiosis. A centimorgan (cM) is a unit that describes a recombination frequency of 1%. In this way we can measure the genetic distance between two loci, based upon their recombination frequency. This is a good estimate of the real distance. Double crossovers would turn into no recombination. In this case we cannot tell if crossovers took place. If the loci we're analysing are very close (less than 7 cM) a double crossover is very unlikely. When distances become higher, the likelihood of a double crossover increases. As the likelihood of a double crossover increases we systematically underestimate the genetic distance between two loci.

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 that are double heterozygotes 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 original 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.[citation needed] They were interested in trait inheritance in the sweet pea and were studying two genes—the gene for flower colour (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 genotype Observed Expected from 9:3:3:1 ratio
Purple, long (P_L_) 284 216
Purple, round (P_ll) 21 72
Red, long (ppL_) 21 72
Red, round (ppll) 55 24

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 is more difficult to compute in an F2 cross than a backcross,[3] but the lack of fit between observed and expected numbers of progeny in the above table indicate 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 (e.g. Purple) linked to a recessive allele for a second trait (e.g. round) with the opposite being true for the other parental chromosome (e.g. 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, unfavourable repulsion linkages do appear when breeding for disease resistance in some crops.

The two possible arrangements, cis and trans, of alleles in a double heterozygote are referred to as gametic phases, and phasing is the process of determining which of the two is present in a given individual.

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

However, it is important to note that recombination frequency tends to underestimate the distance between two linked genes. This is because as the two genes are located farther apart, the chance of double or even number of crossovers between them also increases. Double or even number of crossovers between the two genes results in them being cosegregated to the same gamete, yielding a parental progeny instead of the expected recombinant progeny. As mentioned above, the Kosambi and Haldane transformations attempt to correct for multiple crossovers.[14][15]

## Variation of recombination frequency

While recombination of chromosomes is an essential process during meiosis, there is a large range of frequency of cross overs across organisms and within species. Sexually dimorphic rates of recombination are termed heterochiasmy, and are observed more often than a common rate between male and females. In mammals, females often have a higher rate of recombination compared to males. It is theorised that there are unique selections acting or meiotic drivers which influence the difference in rates. The difference in rates may also reflect the vastly different environments and conditions of meiosis in oogenesis and spermatogenesis.[citation needed]

## Meiosis indicators

With very large pedigrees or with very dense genetic marker data, such as from whole-genome sequencing, it is possible to precisely locate recombinations. With this type of genetic analysis, a meiosis indicator is assigned to each position of the genome for each meiosis in a pedigree. The indicator indicates which copy of the parental chromosome contributes to the transmitted gamete at that position. For example, if the allele from the 'first' copy of the parental chromosome is transmitted, a '0' might be assigned to that meiosis. If the allele from the 'second' copy of the parental chromosome is transmitted, a '1' would be assigned to that meiosis. The two alleles in the parent came, one each, from two grandparents. These indicators are then used to determine identical-by-descent (IBD) states or inheritance states, which are in turn used to identify genes responsible for diseases.

## References

1. ^ Lobo, Ingrid; Shaw, Kenna. "Discovery and Types of Genetic Linkage". Scitable. Nature Education. Retrieved 21 January 2017.
2. ^ Bateson, W; Saunders, ER; Punnett, RC (18 May 1904). Reports to the Evolution committee of the Royal Society. London: Harrison and Sons, Printers. Retrieved 21 January 2017.
3. ^ a b Fisher, RA; Balmukand, B (July 1928). "The estimation of linkage from the offspring of selfed heterozygotes". Journal of Genetics. 20 (1): 79–92. doi:10.1007/BF02983317.
4. ^ Mader, Sylvia (2007). Biology Ninth Edition. New York: McGraw-Hill. p. 209. ISBN 978-0-07-325839-3.
5. ^ Griffiths, AJF (2000). An Introduction to Genetic Analysis (7th ed.). W. H. Freeman.
6. ^ Lanktree, Matthew B.; Johansen, Christopher T.; Joy, Tisha R.; Hegele, Robert A. (2010), "A Translational View of the Genetics of Lipodystrophy and Ectopic Fat Deposition", in Bouchard, Claude (ed.), Progress in Molecular Biology and Translational Science, Genes and Obesity, 94, Academic Press, pp. 159–196, doi:10.1016/b978-0-12-375003-7.00006-6, ISBN 9780123750037, PMID 21036325
7. ^ a b Cantor, Rita M. (2013), "Analysis of Genetic Linkage", in Rimoin, David; Pyeritz, Reed; Korf, Bruce (eds.), Emery and Rimoin's Principles and Practice of Medical Genetics (6th ed.), Academic Press, pp. 1–9, doi:10.1016/b978-0-12-383834-6.00010-0, ISBN 9780123838346
8. ^ Morton NE (1955). "Sequential tests for the detection of linkage". American Journal of Human Genetics. 7 (3): 277–318. PMC 1716611. PMID 13258560.
9. ^ Nyholt, Dale R (August 2000). "All LODs Are Not Created Equal". American Journal of Human Genetics. 67 (2): 282–288. doi:10.1086/303029. PMC 1287176. PMID 10884360.
10. ^ Risch, Neil (June 1991). "A Note on Multiple Testing Procedures in Linkage Analysis". American Journal of Human Genetics. 48 (6): 1058–1064. PMC 1683115. PMID 2035526.
11. ^ Ferreira, Manuel A. R. (2004-10-01). "Linkage Analysis: Principles and Methods for the Analysis of Human Quantitative Traits". Twin Research and Human Genetics. 7 (5): 513–530. doi:10.1375/twin.7.5.513. ISSN 2053-6003.
12. ^ Gusella, James F.; Frontali, Marina; Wasmuth, John J.; Collins, Francis S.; Lehrach, Hans; Myers, Richard; Altherr, Michael; Allitto, Bernice; Taylor, Sherry (1992-05-01). "The Huntington's disease candidate region exhibits many different haplotypes". Nature Genetics. 1 (2): 99–103. doi:10.1038/ng0592-99. ISSN 1546-1718. PMID 1302016.
13. ^ Mark J. Daly; Hirschhorn, Joel N. (2005-02-01). "Genome-wide association studies for common diseases and complex traits". Nature Reviews Genetics. 6 (2): 95–108. doi:10.1038/nrg1521. ISSN 1471-0064. PMID 15716906.
14. ^ Griffiths, AJF; Miller, JH; Suzuki, DT (2000). "Accurate calculation of large map distances, Derivation of a mapping function". An Introduction to Genetic Analysis (7th ed.). New York: W. H. Freeman. ISBN 978-0-7167-3520-5.
15. ^ Griffiths, AJF; Miller, JH; Suzuki, DT (2000). "Accurate calculation of large map distances, Figure 6-4". An Introduction to Genetic Analysis (7th ed.). New York: W. H. Freeman. ISBN 978-0-7167-3520-5. Graph of mapping function from compared to idealised 1-1 equivalence of recombination frequency percentage (RF%) to map units.