Background: The "common disease -common variant" hypothesis and genome-wide association studies have achieved numerous successes in the last three years, particularly in genetic mapping in human diseases. Nevertheless, the power of the association study methods are still low, in particular on quantitative traits, and the description of the full allelic spectrum is deemed still far from reach. Given increasing density of single nucleotide polymorphisms available and suggested by the block-like structure of the human genome, a popular and prosperous strategy is to use haplotypes to try to capture the correlation structure of SNPs in regions of little recombination. The key to the success of this strategy is thus the ability to unambiguously determine the haplotype allele sharing status among the members. The association studies based on haplotype sharing status would have significantly reduced degrees of freedom and be able to capture the combined effects of tightly linked causal variants.
High-throughput single nucleotide polymorphism genotyping assays conveniently produce genotype data for genome-wide genetic linkage and association studies. For pedigree datasets, the unphased genotype data is used to infer the haplotypes for individuals, according to Mendelian inheritance rules. Linkage studies can then locate putative chromosomal regions based on the haplotype allele sharing among the pedigree members and their disease status. Most existing haplotyping programs require rather strict pedigree structures and return a single inferred solution for downstream analysis. In this research, we relax the pedigree structure to contain ungenotyped founders and present a cubic time whole genome haplotyping algorithm to minimize the number of zero-recombination haplotype blocks. With or without explicitly enumerating all the haplotyping solutions, the algorithm determines all distinct haplotype allele identity-by-descent (IBD) sharings among the pedigree members, in linear time in the total number of haplotyping solutions. Our algorithm is implemented as a computer program iBDD. Extensive simulation experiments using 2 sets of 16 pedigree structures from previous studies showed that, in general, there are trillions of haplotyping solutions, but only up to a few thousand distinct haplotype allele IBD sharings. iBDD is able to return all these sharings for downstream genome-wide linkage and association studies.
An efficient rule-based algorithm is presented for haplotype inference from general pedigree genotype data, with the assumption of no recombination. This algorithm generalizes previous algorithms to handle the cases where some pedigree founders are not genotyped, provided that for each nuclear family at least one parent is genotyped and each non-genotyped founder appears in exactly one nuclear family. The importance of this generalization lies in that such cases frequently happen in real data, because some founders may have passed away and their genotype data can no longer be collected. The algorithm runs in O(m 3 n 3 ) time, where m is the number of single nucleotide polymorphism (SNP) loci under consideration and n is the number of genotyped members in the pedigree. This zero-recombination haplotyping algorithm is extended to a maximum parsimoniously haplotyping algorithm in one whole genome scan to minimize the total number of breakpoint sites, or equivalently, the number of maximal zero-recombination chromosomal regions. We show that such a whole genome scan haplotyping algorithm can be implemented in O(m 3 n 3 ) time in a novel incremental fashion, here m denotes the total number of SNP loci along the chromosome.
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