Predicting recombination frequency from map distance

Abstract

Map distance is one of the key measures in genetics and indicates the expected number of crossovers between two loci. Map distance is estimated from the observed recombination frequency using mapping functions, the most widely used of those, Haldane and Kosambi, being developed at the time when the number of markers was low and unobserved crossovers had a substantial effect on the recombination fractions. In contemporary high-density marker data, the probability of multiple crossovers between adjacent loci is negligible and different mapping functions yield the same result, that is, the recombination frequency between adjacent loci is equal to the map distance in Morgans. However, high-density linkage maps contain an interpretation problem: the map distance over a long interval is additive and its association with recombination frequency is not defined. Here, we demonstrate with high-density linkage maps from humans and stickleback fishes that the inverse of Haldane or Kosambi mapping functions fail to predict the recombination frequency from map distance, and show that this is because the expected number of crossovers is not sufficient to predict recombination frequency. We formulate a piecewise function to calculate the probability of no crossovers between the markers that yields more accurate predictions of recombination frequency from map distance. Our results demonstrate that the association between map distance and recombination frequency is context-dependent and no universal solution exists. We anticipate that our study will motivate further research on this subject to yield a more accurate mathematical description of map distance in the context of modern data.