Abstract. Driven by the international HapMap project, the haplotype inference problem has become an important topic in the computational biology community. In this paper, we study how to efficiently infer haplotypes from genotypes of related individuals as given by a pedigree. Our assumption is that the input pedigree data may contain de novo mutations and missing alleles but is free of genotyping errors and recombinants, which is usually true for tightly linked markers. We formulate the problem as a combinatorial optimization problem, called the minimum mutation haplotype configuration (MMHC) problem, where we seek haplotypes consistent with the given genotypes that incur no recombinants and require the minimum number of mutations. This extends the well studied zero-recombinant haplotype configuration (ZRHC) problem. Although ZRHC is polynomial-time solvable, MMHC is NP-hard. We construct an integer linear program (ILP) for MMHC using the system of linear equations over the field F (2) that has been developed recently to solve ZRHC. Since the number of constraints in the ILP is large (exponentially large in the general case), we present an incremental approach for solving the ILP where we gradually add the constraints to a standard ILP solver until a feasible haplotype configuration is found. Our preliminary experiments on simulated data demonstrate that the method is very efficient on large pedigrees and can infer haplotypes very accurately as well as recover most of the mutations and missing alleles correctly.

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.

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We study the detection of mutations, sequencing errors, and homologous recombination events (HREs) in a set of closely related microbial genomes. We base the model on single nucleotide polymorphisms (SNPs) and break the genomes into blocks to handle the rearrangement problem. Then we apply a dynamic programming algorithm to model whether changes within each block are likely a result of mutations, sequencing errors, or HREs. Results from simulation experiments show that we can detect 31%–61% of HREs and the precision of our detection is about 48%–90% depending on the rates of mutation and missing data. The HREfinder software for predicting HREs in a set of whole genomes is available as open source (http://sourceforge.net/projects/hrefinder/).

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