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{{short description|Unit for measuring genetic linkage}}
In [[genetics]], a '''centimorgan''' (abbreviated '''cM''') or '''map unit''' ('''m.u.''') is a unit for measuring [[genetic linkage]].  It is defined as the distance between [[chromosome]] positions (also termed [[locus (genetics)|loci]] or [[genetic marker|markers]]) for which the expected average number of intervening [[chromosomal crossover]]s in a single generation is 0.01.  It is often used to infer distance along a chromosome. However, it is not a true physical distance.

== Relation to physical distance==
The number of [[base pair]]s to which it corresponds varies widely across the [[genome]] (different regions of a chromosome have different propensities towards [[chromosomal crossover|crossover]]) and it also depends on whether the [[meiosis]] in which the crossing-over takes place is a part of [[oogenesis]] (formation of female gametes) or [[spermatogenesis]] (formation of male gametes).

In humans one centimorgan corresponds to about 1 [[Megabase|Mb]] (1,000,000 [[base pair]]s or [[nucleotide]]s) on average.<ref>{{cite web |title = Terms and Definitions |author = Office of Rare Diseases Research |publisher = [[National Institutes of Health]] |url = http://rarediseases.info.nih.gov/Glossary.aspx?acronym=False#C |url-status = dead |archive-url = https://web.archive.org/web/20120717121400/http://rarediseases.info.nih.gov/Glossary.aspx?acronym=False#C |archive-date = 2012-07-17 }}</ref><ref>{{cite book |first1 = Harvey |last1 = Lodish |first2 = Arnold |last2 = Berk |first3 = Paul |last3 = Matsudaira |first4 = Chris A. |last4 = Kaiser |first5 = Monty |last5 = Krieger |first6 = Matthew P. |last6 = Scott |first7 = Lawrence |last7 = Zipursky |first8 = James |last8 = Darnell |title = Molecular Cell Biology |edition = 5th |publisher = W. H. Freeman |location = San Francisco |year = 2004 |pages = [https://archive.org/details/molecularcellbio00harv/page/396 396] |isbn = 0-7167-4366-3 |quote = ...in humans 1 centimorgan on average represents a distance of about 7.5x10E5 base pairs |url-access = registration |url = https://archive.org/details/molecularcellbio00harv/page/396 }}</ref> The relationship is only rough, as the physical chromosomal distance corresponding to one centimorgan varies from place to place in the genome, and also varies between males and females since recombination during gamete formation in females is significantly more frequent than in males. Kong et al. calculated that the female genome is 4460 cM long, while the male genome is only 2590 cM long.<ref>{{cite journal |first1 = Augustine |last1 = Kong |first2 = Daniel F. |last2 = Gudbjartsson |first3 = Jesus |last3 = Sainz |first4 = Gudrun M. |last4 = Jonsdottir |first5 = Sigurjon A. |last5 = Gudjonsson |first6 = Bjorgvin |last6 = Richardsson |first7 = Sigrun |last7 = Sigurdardottir |first8 = John |last8 = Barnard |first9 = Bjorn |last9 = Hallbeck |first10 = Gisli |last10 = Masson |first11 = Adam |last11 = Shlien |first12 = Stefan T. |last12 = Palsson |first13 = Michael L. |last13 = Frigge |first14 = Thorgeir E. |last14 = Thorgeirsson |first15 = Jeffrey R. |last15 = Gulcher |first16 = Kari |last16 = Stefansson |title = A high-resolution recombination map of the human genome. |journal = Nature Genetics |date = 10 June 2002 |volume = 31 |issue = 3 |pages = 241–247 |pmid = 12053178 |doi = 10.1038/ng917 }}</ref>

In contrast,  in ''[[Plasmodium falciparum]]'' one centimorgan corresponds to about 15 [[Kilobase|kb]]; markers separated by 15,000 nucleotides have an expected rate of chromosomal crossovers of 0.01 per generation.

Note that non-[[Synteny|syntenic]] genes (genes residing on different chromosomes) are inherently unlinked, and cM distances are not applicable to them.

==Relation to the probability of recombination ==
Because [[genetic recombination]] between two markers is detected only if there are an odd number of chromosomal crossovers between the two markers, the distance in centimorgans does not correspond exactly to the probability of genetic recombination. Assuming the [[Genetic map function|Haldane Mapping Function]], eponymously devised by [[J. B. S. Haldane]], the number of chromosomal crossovers is distributed according to a [[Poisson distribution]],<ref>{{cite web |first = Ted |last = Helms |year = 2000 |url = http://www.ag.ndsu.nodak.edu/plantsci/adv_genetics/genetics/mf/mf01.htm |url-status = dead |archive-url = https://web.archive.org/web/20120321211822/http://www.ag.ndsu.nodak.edu/plantsci/adv_genetics/genetics/mf/mf01.htm |archive-date = 2012-03-21 |title = Haldane's Mapping Function |publisher = Department of Plant Sciences, North Dakota State University }}</ref> a genetic distance of ''d'' centimorgans will lead to an odd number of chromosomal crossovers, and hence a detectable genetic recombination, with probability
:<math>\ P(\text{recombination}|\text{linkage of }d\text{ cM}) = \sum_{k=0}^{\infty} \ P(2k + 1 \text{ crossovers}|\text{linkage of }d\text{ cM})</math>
:<math>{} = \sum_{k=0}^{\infty} e^{-d/100} \frac{(d/100)^{2\,k+1}}{(2\,k+1)!} = e^{-d/100} \sinh(d/100) = \frac{1 - e^{-2d/100}}{2}\,,</math>
where sinh is the [[hyperbolic sine]] function.  The probability of recombination is approximately ''d''/100 for small values of ''d'' and approaches 50% as ''d'' goes to infinity.

The formula can be inverted, giving the distance in centimorgans as a function of the recombination probability:
:<math>d=50 \ln\left({\frac{1}{1 - 2 \ P(\text{recombination})}}\right)\,.</math>

<!-- needs confirmation == Shared centimorgans ==
Genealogists often use "shared centimorgans" as a proxy for reciprocal of distance in a family tree, halving with each generational step. So if two individuals differ on average by:
<!-- TODO: add ±σ to each of the following mid-points -->
* 7050 cM, they are identical twins (or actually the same person; 0 steps);
* 3525 cM, they are parent & child (1 step);
* 1762 cM, they are (very likely) grandparent & grandchild, or half siblings (2 steps);
* 881 cM, they are (likely) great grandparent & great grandchild, or half aunt/uncle and half niece/nephew (3 steps);
* 440 cM, they are (probably) great great grand parent & great great grandchild, or half great aunt/uncle & half great niece/nephew, or half cousins (4 steps);
etc. The margin of error increases with each step, so that beyond about 4 steps the ranges overlap to such an extent as to make it difficult to establish how many steps are involved, and beyond about 7 steps any relationship at all is tenuous.

The self/twin figure of 7050 cM corresponds to the sum of the cM lengths of human DNA for males and females.

<!-- needs confirmation
When multiple genetic lines are inherited, they combine as root-sum-of-squares, so that full siblings share around 2493 cM or √2 times as much as half siblings.
-->

Because some recombinations result in unviable gametes, or offspring that cannot themselves reproduce, the observed genetic distances in families tend to be lower (shared cM higher) than predicted by models based purely on physical recombination rates. {{Citation-needed|reason=This seems like sky-is-blue obvious to me, but I defer to the judgement of others as to whether a citation or correction is needed|date=November 2024}}-->

==Etymology==
The centimorgan was named in honor of geneticist [[Thomas Hunt Morgan]] by [[J. B. S. Haldane]].<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 |journal = Journal of Genetics |volume = 8 |pages = 299–309 |quote = It is suggested that the unit of distance in a chromosome as defined above be termed a "morgan," on the analogy of the ohm, volt, etc. Morgan's unit of distance is therefore a centimorgan. (p. 305) }}</ref> Its parent unit, the morgan, is rarely used today.

==See also==

* [[Mutation rate]]

==References==
{{reflist}}

==Further reading==
{{refbegin}}
*{{cite journal |author1 = Xin-Zhuan Su |first2 = Michael T. |last2 = Ferdig |author3= Yaming Huang |author4 = Chuong Q. Huynh |first5 = Anna |last5 = Liu |author6 = Jingtao You |first7 = John C. |last7 = Wootton |first8 = Thomas E. |last8 = Wellems  |title = A genetic map and recombination parameters of the human malaria parasite Plasmodium falciparum |journal = Science |volume = 286 |issue = 5443 |pages = 1351–1353 |date = November 1999 |pmid = 10558988 |doi = 10.1126/science.286.5443.1351 |url = https://zenodo.org/record/1231171 }}
{{refend}}
[[Category:Units of measurement]]
[[Category:Genetics]]
[[Category:Dimensionless units]]