Genetic map function

Where d is the distance in map units, the Morgan Mapping Function states that the recombination frequency r can be expressed as $\backslash \; r=d$ . This assumes that one crossover occurs, at most, in an interval between two loci, and that the probability of the occurrence of this crossover is proportional to the map length of the interval.

Where d is the distance in map units, the recombination frequency r can be expressed as:

$\backslash \; r\; =\; \backslash frac\{1\}\{2\}\; [1-(1-2d)]\; =\; d$

The equation only holds when $\backslash frac\{1\}\{2\}\; \backslash geq\; d\; \backslash geq\; 0$ as, otherwise, recombination frequency would exceed 50%. Therefore, the function cannot approximate recombination frequencies beyond short distances.

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%.{{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 }} It also assumes that crossovers occur at random positions and that they do so independent of one another. This assumption therefore also assumes no crossover interference takes place;{{Cite book |title=Mammalian genomics |date=2005 |publisher=CABI Pub |isbn=978-0-85199-910-4 |editor-last=Ruvinsky |editor-first=Anatoly |location=Wallingford, Oxfordshire, UK; Cambridge, MA, USA |pages=15 |editor-last2=Graves |editor-first2=Jennifer A. Marshall}} but using this assumption allows Haldane to model the mapping function using a Poisson distribution.

• r = recombination frequency
• d = mean number of crossovers on a chromosomal interval
• 2d = mean number of crossovers for a tetrad
• e^-2d = probability of no genetic exchange in a chromosomal interval

$\backslash \; r\; =\; \backslash frac\{1\}\{2\}\; (1-e^\{-2d\})$

$\backslash \; d\; =\; -\backslash frac\{1\}\{2\}\; \backslash ln\; (1-2r)$

The Kosambi mapping function was introduced to account for the impact played by crossover interference on recombination frequency. It introduces a parameter C, representing the coefficient of coincidence, and sets it equal to 2r. For loci which are strongly linked, interference is strong; otherwise, interference decreases towards zero. Interference declines according to the linear function i = 1 - 2r.{{Cite book |last1=Hartl |first1=Daniel L. |url=https://books.google.com/books?id=cfvILxY9tCIC&dq=haldane%20mapping%20function&pg=PA168 |title=Genetics: analysis of genes and genomes |last2=Jones |first2=Elizabeth W. |date=2005 |publisher=Jones and Bartlett |isbn=978-0-7637-1511-3 |edition=7th |location=Sudbury, Mass. |pages=168}}

$\backslash \; r\; =\; \backslash frac\{1\}\{2\}\backslash tanh(2d)\; =\; \backslash frac\{1\}\{2\}\backslash frac\{e^\{4d\}-1\}\{e^\{4d\}+1\}$

$\backslash \; d\; =\; \backslash frac\{1\}\{2\}\; \backslash tanh^\{-1\}\; (2r)\; =\; \backslash frac\{1\}\{4\}\backslash ln(\backslash frac\{1+2r\}\{1-2r\})$

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). 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.

While many mapping functions now exist,{{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}}{{Cite journal |last=Felsenstein |first=Joseph |date=1979 |title=A Mathematically Tractable Family of Genetic Mapping Functions with Different Amounts of Interference |url=https://academic.oup.com/genetics/article/91/4/769/5993247 |journal=Genetics |language=en |volume=91 |issue=4 |pages=769–775 |doi=10.1093/genetics/91.4.769 |issn= |pmc=1216865 |pmid=17248911}}{{Cite journal |last1=Pascoe |first1=L. |last2=Morton |first2=N.E. |date=1987 |title=The use of map functions in multipoint mapping |journal=American Journal of Human Genetics |volume=40 |issue=2 |pages=174–183|pmid=3565379 |pmc=1684067 }} in practice functions other than Haldane and Kosambi are rarely used. More specifically, the Haldane function is preferred when distance between markers is relatively small, whereas the Kosambi function is preferred when distances between markers is larger and crossovers need to be accounted for.{{Cite book |url=https://books.google.com/books?id=3Ss-ws2Zm6IC&pg=SA17-PA11 |title=Handbook of computational molecular biology |date=2006 |publisher=CRC Press |isbn=978-1-58488-406-4 |editor-last=Aluru |editor-first=Srinivas |series= |location= |pages=17-10–17-11 |oclc=}}

{{Reflist}}

• Bailey, N.T.J., 1961 Introduction to the Mathematical Theory of Genetic Linkage. Clarendon Press, Oxford.

Category:Equations

Category:Genetics