A characterization of crossover models that possess map functions

Abstract

This paper concerns genetic map functions and a particular probability model for crossovers. S. Karlin and U. Liberman (1979, Adv. Appi. Prob. 11, 479-501) and N. Risch and K. Lange (1979, Biometrics39, 949-963) independently introduced what the former called the count-location (point) process model for crossovers, which leads to a probability model for multilocus recombination under the assumption of no chromatid interference. U. Liberman and S. Karlin (1984, Theor. Popul. Biol. 25, 331-346) later explored the constraints on genetic map functions resulting from the requirement that they be realisable in terms of a probability model for multilocus recombination. In this note we prove that un..