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. 2011 Apr 19;6(1):10.
doi: 10.1186/1748-7188-6-10.

Haplotypes versus genotypes on pedigrees

Bonnie B Kirkpatrick  1
Affiliations

Haplotypes versus genotypes on pedigrees

Bonnie B Kirkpatrick. Algorithms Mol Biol. .

Abstract

Background: 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.

Results: 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.

Conclusions: 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.

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Figures

Figure 1
Figure 1
Genotype and Haplotype Pedigrees. Genotyped individuals are shaded, and all the individuals are labeled. Individuals 1, 2, and 5 are the founders, and individual 6 is the grandchild of 1 and 2.
Figure 2
Figure 2
Haplotype Pedigrees. Haplotyped individuals are shaded, and individuals have the same labels. For each of the genotyped individuals, i, from the previous figure, the mapping adds a nuclear family containing five new individuals labeled i0, i1, i2, i3, i4.
Figure 3
Figure 3
Predicting Recombinations for Half-Siblings. This is the average accuracy for predictions from a pedigree with two half-siblings and three parents. Five hundred simulation replicates were performed, and the average accuracy of estimates from the haplotype data is superior to those from genotype data. However, as the number of untyped founders increases, in both cases, the accuracy of estimates from haplotype data drop relative to the accuracy from genotype data. The accuracies of genotype and haplotype estimates appear to converge.
Figure 4
Figure 4
Predicting Recombinations for Three Generations. This figure shows accuracy results from a six-individual, three-generation pedigree. Again, five hundred simulation replicates were performed, and the average accuracy of estimates from the haplotype data is superior to those from genotype data. Once again, as the number of untyped founders increases, the accuracy of estimates from haplotype data drop relative to the accuracy from genotype data. The accuracies of genotype and haplotype estimates appear to converge.
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