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In [[genetics]], '''mapping functions''' are used to model the relationship between [[Gene mapping|map]]
The simplest mapping function is the '''Morgan Mapping Function''', eponymously devised by [[Thomas Hunt Morgan]]. Other well-known mapping functions include the '''Haldane Mapping Function''' introduced by [[J. B. S. Haldane]] in 1919,<ref>{{Cite journal |last=Haldane |first=J.B.S. |date=1919 |title=The combination of linkage values, and the calculation of distances between the loci of linked factors |url=https://www.ias.ac.in/article/fulltext/jgen/008/04/0299-0309 |journal=Journal of Genetics |volume=8 |issue=29 |pages=299–309}}</ref> and the '''Kosambi Mapping Function''' introduced by [[Damodar Dharmananda Kosambi]] in 1944.<ref>{{Cite journal |last=Kosambi |first=D. D. |date=1943 |title=The Estimation of Map Distances from Recombination Values |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1469-1809.1943.tb02321.x |journal=Annals of Eugenics |language=en |volume=12 |issue=1 |pages=172–175 |doi=10.1111/j.1469-1809.1943.tb02321.x |issn=2050-1420|url-access=subscription }}</ref><ref name=":0">{{Cite book |last1=Wu |first1=Rongling |url=https://books.google.com/books?id=-NlGKOEQuEsC&dq=haldane%20mapping%20function&pg=PA65 |title=Statistical genetics of quantitative traits: linkage, maps, and QTL |last2=Ma |first2=Chang-Xing |last3=Casella |first3=George |date=2007 |publisher=Springer |isbn=978-0-387-20334-8 |___location=New York |pages=65 |oclc=141385359}}</ref> Few mapping functions are used in practice other than Haldane and Kosambi.<ref name=":1" /> The main difference between them is in how [[crossover interference]] is incorporated.<ref name=":3">{{Cite journal |last1=Peñalba |first1=Joshua V. |last2=Wolf |first2=Jochen B. W. |date=2020 |title=From molecules to populations: appreciating and estimating recombination rate variation |url=https://www.nature.com/articles/s41576-020-0240-1 |journal=Nature Reviews Genetics |language=en |volume=21 |issue=8 |pages=476–492 |doi=10.1038/s41576-020-0240-1 |issn=1471-0064|url-access=subscription }}</ref>
== Morgan Mapping Function ==
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=== Overview ===
Two properties of the Haldane Mapping Function is that it limits recombination frequency up to, but not beyond 50%, and that it represents a linear relationship between the frequency of recombination and map distance up to recombination frequencies of 10%.<ref>{{Cite web |title=mapping function |url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100132641 |access-date=2024-04-29 |website=Oxford Reference |language=en
=== Definitions ===
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=== Inverse ===
<math>\ d = -\frac{1}{2} \ln (1-2r)</math>
== Kosambi Mapping Function ==
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=== Formula ===
<math>\ r = \frac{1}{2}
=== Inverse ===
<math>\ d = \frac{1}{2} \tanh^{-1} (2r) = \frac{1}{4}
== Comparison and application ==
Below 10% recombination frequency, there is little mathematical difference between different mapping functions and the relationship between map distance and recombination frequency is linear (that is, 1 map unit = 1% recombination frequency).<ref name=":2" /> When genome-wide SNP sampling and mapping data is present, the difference between the functions is negligible outside of regions of high recombination, such as recombination hotspots or ends of chromosomes.<ref name=":3" />
While many mapping functions now exist,<ref>{{Cite journal |last=Crow |first=J F |date=1990 |title=Mapping functions. |url=https://academic.oup.com/genetics/article/125/4/669/6000769 |journal=Genetics |language=en |volume=125 |issue=4 |pages=669–671 |doi=10.1093/genetics/125.4.669 |issn=1943-2631 |pmc=1204092 |pmid=2204577}}</ref><ref>{{Cite journal |last=Felsenstein |first=Joseph |date=1979 |title=A == References ==
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