In genetics, mapping functions are used to model the relationship between map distances (measured in map units or centimorgans) 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.
[3][4] Few mapping functions are used in practice other than Haldane and Kosambi.
[5] The main difference between them is in how crossover interference is incorporated.
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:
Therefore, the function cannot approximate recombination frequencies beyond short distances.
[7] 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;[5] but using this assumption allows Haldane to model the mapping function using a Poisson distribution.
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.
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).
[8] 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.
[5] 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.