Centimorgan

Last updated December 11, 2024

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 loci or markers) for which the expected average number of intervening chromosomal crossovers 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 pairs to which it corresponds varies widely across the genome (different regions of a chromosome have different propensities towards 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 Mb (1,000,000 base pairs or nucleotides) on average.^[1]^[2] 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.^[3]

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

Note that non-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 Haldane Mapping Function, eponymously devised by J. B. S. Haldane, the number of chromosomal crossovers is distributed according to a Poisson distribution,^[4] a genetic distance of d centimorgans will lead to an odd number of chromosomal crossovers, and hence a detectable genetic recombination, with probability

\ P({\text{recombination}}|{\text{linkage of }}d{\text{ cM}})=\sum _{k=0}^{\infty }\ P(2k+1{\text{ crossovers}}|{\text{linkage of }}d{\text{ cM}})

{}=\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}}\,,

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:

d=50\ln \left({\frac {1}{1-2\ P({\text{recombination}})}}\right)\,.

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:

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.

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 ]}

Etymology

The centimorgan was named in honor of geneticist Thomas Hunt Morgan by J. B. S. Haldane.^[5] Its parent unit, the morgan, is rarely used today.

Related Research Articles

Meiosis (; from Ancient Greek μείωσις 'lessening', is a special type of cell division of germ cells in sexually-reproducing organisms that produces the gametes, the sperm or egg cells. It involves two rounds of division that ultimately result in four cells, each with only one copy of each chromosome. Additionally, prior to the division, genetic material from the paternal and maternal copies of each chromosome is crossed over, creating new combinations of code on each chromosome. Later on, during fertilisation, the haploid cells produced by meiosis from a male and a female will fuse to create a zygote, a cell with two copies of each chromosome again.

Chromosomal crossover, or crossing over, is the exchange of genetic material during sexual reproduction between two homologous chromosomes' non-sister chromatids that results in recombinant chromosomes. It is one of the final phases of genetic recombination, which occurs in the pachytene stage of prophase I of meiosis during a process called synapsis. Synapsis begins before the synaptonemal complex develops and is not completed until near the end of prophase I. Crossover usually occurs when matching regions on matching chromosomes break and then reconnect to the other chromosome.

Genetic recombination is the exchange of genetic material between different organisms which leads to production of offspring with combinations of traits that differ from those found in either parent. In eukaryotes, genetic recombination during meiosis can lead to a novel set of genetic information that can be further passed on from parents to offspring. Most recombination occurs naturally and can be classified into two types: (1) interchromosomal recombination, occurring through independent assortment of alleles whose loci are on different but homologous chromosomes ; & (2) intrachromosomal recombination, occurring through crossing over.

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, although the penetrance of potentially deleterious alleles may be influenced by the presence of other alleles, and these other alleles may be located on other chromosomes than that on which a particular potentially deleterious allele is located.

In genetic algorithms and evolutionary computation, crossover, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. Solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions may be mutated before being added to the population.

Mosaicism or genetic mosaicism is a condition in which a multicellular organism possesses more than one genetic line as the result of genetic mutation. This means that various genetic lines resulted from a single fertilized egg. Mosaicism is one of several possible causes of chimerism, wherein a single organism is composed of cells with more than one distinct genotype.

In population genetics, linkage disequilibrium (LD) is a measure of non-random association between segments of DNA (alleles) at different positions on the chromosome (loci) in a given population based on a comparison between the frequency at which two alleles are detected together at the same loci versus the frequencies at which each allele is simply detected at that same loci. Loci are said to be in linkage disequilibrium when the frequency of being detected together is higher or lower than expected if the loci were independent and associated randomly.

<span class="mw-page-title-main">Chromosomal inversion</span> Chromosome rearrangement in which a segment of a chromosome is reversed

An inversion is a chromosome rearrangement in which a segment of a chromosome becomes inverted within its original position. An inversion occurs when a chromosome undergoes a two breaks within the chromosomal arm, and the segment between the two breaks inserts itself in the opposite direction in the same chromosome arm. The breakpoints of inversions often happen in regions of repetitive nucleotides, and the regions may be reused in other inversions. Chromosomal segments in inversions can be as small as 1 kilobases or as large as 100 megabases. The number of genes captured by an inversion can range from a handful of genes to hundreds of genes. Inversions can happen either through ectopic recombination between repetitive sequences, or through chromosomal breakage followed by non-homologous end joining.

A DNA segment is identical by state (IBS) in two or more individuals if they have identical nucleotide sequences in this segment. An IBS segment is identical by descent (IBD) in two or more individuals if they have inherited it from a common ancestor without recombination, that is, the segment has the same ancestral origin in these individuals. DNA segments that are IBD are IBS per definition, but segments that are not IBD can still be IBS due to the same mutations in different individuals or recombinations that do not alter the segment.

Genetics, a discipline of biology, is the science of heredity and variation in living organisms.

Gene conversion is the process by which one DNA sequence replaces a homologous sequence such that the sequences become identical after the conversion. Gene conversion can be either allelic, meaning that one allele of the same gene replaces another allele, or ectopic, meaning that one paralogous DNA sequence converts another.

Gene mapping or genome mapping describes the methods used to identify the location of a gene on a chromosome and the distances between genes. Gene mapping can also describe the distances between different sites within a gene.

In genetics, a three-point cross is used to determine the loci of three genes in an organism's genome.

Coalescent theory is a model of how alleles sampled from a population may have originated from a common ancestor. In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure, meaning that each variant is equally likely to have been passed from one generation to the next. The model looks backward in time, merging alleles into a single ancestral copy according to a random process in coalescence events. Under this model, the expected time between successive coalescence events increases almost exponentially back in time. Variance in the model comes from both the random passing of alleles from one generation to the next, and the random occurrence of mutations in these alleles.

In genetics, completelinkage is defined as the state in which two loci are so close together that alleles of these loci are virtually never separated by crossing over. The closer the physical location of two genes on the DNA, the less likely they are to be separated by a crossing-over event. In the case of male Drosophila there is complete absence of recombinant types due to absence of crossing over. This means that all of the genes that start out on a single chromosome, will end up on that same chromosome in their original configuration. In the absence of recombination, only parental phenotypes are expected.

Chromosome segregation is the process in eukaryotes by which two sister chromatids formed as a consequence of DNA replication, or paired homologous chromosomes, separate from each other and migrate to opposite poles of the nucleus. This segregation process occurs during both mitosis and meiosis. Chromosome segregation also occurs in prokaryotes. However, in contrast to eukaryotic chromosome segregation, replication and segregation are not temporally separated. Instead segregation occurs progressively following replication.

In genetics, pseudolinkage is a characteristic of a heterozygote for a reciprocal translocation, in which genes located near the translocation breakpoint behave as if they are linked even though they originated on nonhomologous chromosomes.

The Infinite sites model (ISM) is a mathematical model of molecular evolution first proposed by Motoo Kimura in 1969. Like other mutation models, the ISM provides a basis for understanding how mutation develops new alleles in DNA sequences. Using allele frequencies, it allows for the calculation of heterozygosity, or genetic diversity, in a finite population and for the estimation of genetic distances between populations of interest.

In genetics, the crossover value is the linked frequency of chromosomal crossover between two gene loci (markers). For a fixed set of genetic and environmental conditions, recombination in a particular region of a linkage structure (chromosome) tends to be constant and the same is then true for the crossover value which is used in the production of genetic maps.

In genetics, mapping functions are used to model the relationship between map distances and recombination frequencies, particularly as these measurements relate to regions encompassed between genetic markers. One utility of this approach is that it allows one to obtain values for distances in genetic mapping units directly from recombination fractions, as map distances cannot typically be obtained from empirical experiments.

References

↑ Office of Rare Diseases Research. "Terms and Definitions". National Institutes of Health. Archived from the original on 2012-07-17.
↑ Lodish, Harvey; Berk, Arnold; Matsudaira, Paul; Kaiser, Chris A.; Krieger, Monty; Scott, Matthew P.; Zipursky, Lawrence; Darnell, James (2004). Molecular Cell Biology, (5th ed.). San Francisco: W. H. Freeman. pp. 396. ISBN 0-7167-4366-3. ...in humans 1 centimorgan on average represents a distance of about 7.5x10E5 base pairs
↑ Kong, Augustine; Gudbjartsson, Daniel F.; Sainz, Jesus; Jonsdottir, Gudrun M.; Gudjonsson, Sigurjon A.; Richardsson, Bjorgvin; Sigurdardottir, Sigrun; Barnard, John; Hallbeck, Bjorn; Masson, Gisli; Shlien, Adam; Palsson, Stefan T.; Frigge, Michael L.; Thorgeirsson, Thorgeir E.; Gulcher, Jeffrey R.; Stefansson, Kari (10 June 2002). "A high-resolution recombination map of the human genome". Nature Genetics. 31 (3): 241–247. doi:10.1038/ng917. PMID 12053178.
↑ Helms, Ted (2000). "Haldane's Mapping Function". Department of Plant Sciences, North Dakota State University. Archived from the original on 2012-03-21.
↑ Haldane, J.B.S. (1919). "The combination of linkage values and the calculation of distances between the loci of linked factors". Journal of Genetics. 8: 299–309. 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)