Centimorgan

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, a genetic distance of d centimorgans will lead to an odd number of chromosomal crossovers, and hence a detectable genetic recombination, with probability

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

${\displaystyle =\sum _{k=0}^{\mathrm{\infty }}{e}^{-d/100}\frac{(d/100{)}^{2k+1}}{(2k+1)!}=e^{-d/100}\sinh (d/100)=\frac{1-e^{-2d/100}}{2},}$

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:

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

Etymology

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