Spline Methods for the Comparison of Physical and Genetic Maps

The first genetic maps were constructed by linkage analysis. Physical mapping techniques, such as radiation hybrids and complete sequencing, produce a different picture. For the purposes of population genetics, clinical genetics, and genetic epidemiology, it is important to harmonize and amalgamate existing genetic and physical maps. Among other things, comparisons of the two kinds of maps promotes better understanding of the wide variation in local recombination rates per unit physical length of DNA. The current paper presents methods for estimating recombination intensity as a function of physical distance along a chromosome. Genetic map distance is the integral of intensity. We derive fast reliable estimation algorithms based on a Poisson process model, penalized likelihoods, and cubic spline interpolation. Our methods provide a rigorous and statistically sound foundation for comparing physical and genetic maps. To illustrate the possibilities, we apply the methods to published recombination data on CEPH families and the complete sequences of chromosomes 21 and 22. Our results are in good agreement with previous studies and the biological data.