Multipoint approximations of identity-by-descent probabilities for accurate linkage analysis of distantly related individuals

We propose an analytical approximation method for the estimation of multipoint identity by descent (IBD) probabilities in pedigrees containing a moderate number of distantly related individuals. We show that in large pedigrees where cases are related through untyped ancestors only, it is possible to formulate the hidden Markov model of the Lander-Green algorithm in terms of the IBD configurations of the cases. We use a first-order Markov approximation to model the changes in this IBD-configuration variable along the chromosome. In simulated and real data sets, we demonstrate that estimates of parametric and nonparametric linkage statistics based on the first-order Markov approximation are accurate. The computation time is exponential in the number of cases instead of in the number of meioses separating the cases. We have implemented our approach in the computer program ALADIN (accurate linkage analysis of distantly related individuals). ALADIN can be applied to general pedigrees and marker types and has the ability to model marker-marker linkage disequilibrium with a clustered-markers approach. Using ALADIN is straightforward: It requires no parameters to be specified and accepts standard input files.