A mathematically tractable family of genetic mapping functions with different amounts of interference

By extension of the argument of Kosambi (1944), a family of mapping functions can be derived, which has a parameter regulating the intensity of interference. Different values of this parameter yield the Haldane (1919) and Kosambi mapping functions as special cases. The parameter is the coincidence coefficient for nearby small intervals. The family includes mapping functions for negative interference. A simple rule for combining recombination fractions in adjacent intervals is also obtained.