The probability that similar haplotypes are identical by descent

The logic of gene mapping in highly penetrant diseases is to find the minimal overlap of haplotypes that are identical by descent (IBD). If the pedigree is unknown, identity by descent of haplotype overlap cannot be established with certainty. In many cases, it is intuitively clear that similar haplotypes are indeed IBD. The logical and statistical evaluation of haplotype overlap requires that probabilities of IBD are substantial. It is, therefore, important to estimate these probabilities. In this paper, we derive a recursive formula for the probability of IBD. Simulations are used to validate the expected values and to study the variability around the expected value. We demonstrate that for populations 1000 generations of age - without bottlenecks - haplotypes of 1 cM consisting of at least five microsatellite markers have a significant probability to be IBD. Likewise, SNP haplotypes of 1 cM should consist of at least nine identical SNP alleles for a similar probability of IBD. Without considering bottlenecks, haplotypes consisting of as few as three SNPs spanning a region of less than 0.01 cM are likely IBD in populations that are 10000 generations of age.