Haplotypes versus Genotypes on Pedigrees
Genome sequencing will soon produce haplotype data for individuals. For pedigrees of related individuals, sequencing appears to be an attractive alternative to genotyping. However, methods for pedigree analysis with haplotype data have not yet been developed, and the computational complexity of such problems has been an open question. Furthermore, it is not clear in which scenarios haplotype data would provide better estimates than genotype data for quantities such as recombination rates.To answer these questions, a reduction is given from genotype problem instances to haplotype problem instances, and it is shown that solving the haplotype problem yields the solution to the genotype problem, up to constant factors or coefficients. The pedigree analysis problems we will consider are the likelihood, maximum probability haplotype, and minimum recombination haplotype problems.
Two algorithms are introduced: an exponential-time hidden Markov model (HMM) for haplotype data where some individuals are untyped, and a linear-time algorithm for pedigrees having haplotype data for all individuals. Recombination estimates from the general haplotype HMM algorithm are compared to recombination estimates produced by a genotype HMM. Having haplotype data on all individuals produces better estimates. However, having several untyped individuals can drastically reduce the utility of haplotype data.
KeywordsHide Markov Model Genotype Data Pedigree Analysis Haplotype Data Haplotype Allele
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- 1.Barrett, J.C., Hansoul, S., Nicolae, D.L., Cho, J.H., Duerr, R.H., Rioux, J.D., Brant, S.R., Silverberg, M.S., Taylor, K.D., Barmada, M.M., et al.: Genome-wide association defines more than 30 distinct susceptibility loci for crohn’s disease. Nature Genetics 40, 955–962 (2008)CrossRefPubMedPubMedCentralGoogle Scholar
- 7.Geiger, D., Meek, C., Wexler, Y.: Speeding up HMM algorithms for genetic linkage analysis via chain reductions of the state space. Bioinformatics 25(12), i196 (2009)Google Scholar
- 8.Kirkpatrick, B., Halperin, E., Karp, R.M.: Haplotype inference in complex pedigrees. Journal of Computational Biology (2010) (in press)Google Scholar
- 10.Li, J., Jiang, T.: An exact solution for finding minimum recombinant haplotype configurations on pedigrees with missing data by integer linear programming. In: Proceedings of the 7th Annual International Conference on Research in Computational Molecular Biology, pp. 101–110 (2003)Google Scholar
- 15.Thatte, B.D.: Combinatorics of pedigrees (2006)Google Scholar