Inferring Haplotypes From Genotypes on a Pedigree With Mutations, Genotyping Errors and Missing Alleles

Abstract

Inferring the haplotypes of the members of a pedigree from their genotypes has been extensively studied. However, most studies do not consider genotyping errors and de novo mutations. In this paper, we study how to infer haplotypes from genotype data which may contain genotyping errors, de novo mutations and missing alleles. We assume that there are no recombinants in the genotype data, which is usually true for tightly linked markers. We introduce a combinatorial optimization problem, called haplotype configuration with mutations and errors (HCME), which calls for haplotype configurations consistent with the given genotypes that incur no recombinants and require the minimum number of mutations and errors. HCME is NP-hard. To solve the problem, we propose a heuristic algorithm, the core of which is an integer linear program (ILP) using the system of linear equations over Galois field GF(2). Our algorithm can detect and locate genotyping errors that cannot be detected by simply checking the Mendelian law of inheritance. The algorithm also offers error correction in genotypes/haplotypes rather than just detecting inconsistencies and deleting the involved loci. Our experimental results show that the algorithm can infer haplotypes with a very high accuracy, and recover 65%-94% of genotyping errors depending on the pedigree topology.

A fast and practical approach to genotype phasing and imputation on a pedigree with erroneous and incomplete information

“…on the accuracy and the performance of our algorithm. Second, we compared reHCstar with MePhase [14], which is a combinatorial approach to a slightly different formulation of the Haplotype Inference problem on pedigrees. Third, we present the evaluation of reHCstar on a complex pedigree of a real bovine population.We tested on such pedigree the soundness of the (r, e)-HC formulation and the ability of reHCstar to handle these instances.…”

“…In this second part, we compared accuracy and performance of reHCstar with another state-of-theart approach for the haplotype inference problem on pedigrees: MePhase [14]. A second approach, PedPhase 3.0 [7], was initially considered.…”

“…To ensure a proper comparison even if our approach and MePhase were designed for slightly different problems, the experimental evaluation is similar to the one described by the authors of MePhase in [14]. Tree pedigrees have been generated using the random generator proposed by Thomas and Cannings [12].…”

“…Moreover, the extraction of genotypes is quite expensive, hence it is performed only on animals of higher commercial value, such as Table 2. Results of the experimental comparison between MePhase [14] and reHCstar. The first column (f ) indicates the average size of nuclear family, the second reports the average number of errors present in the generated haplotype configuration (original errors), the next four columns (and the last one) are defined as the rows of Table 1.…”

“…The formulation naturally arises since recombinations are the most common source of genetic variation. However, the HI problem where mutations were allowed instead of recombinations has been solved by an ILP-based algorithm [14]. An efficient heuristic when both recombinations and mutations are allowed has been presented in [8].…”