Haplotype Inference on Pedigrees with Recombinations, Errors, and Missing Genotypes via SAT solvers

The Minimum-Recombinant Haplotype Configuration problem (MRHC) has been highly successful in providing a sound combinatorial formulation for the important problem of genotype phasing on pedigrees. Despite several algorithmic advances and refinements that led to some efficient algorithms, its applicability to real datasets has been limited by the absence of some important characteristics of these data in its formulation, such as mutations, genotyping errors, and missing data. In this work, we propose the Haplotype Configuration with Recombinations and Errors problem (HCRE), which generalizes the original MRHC formulation by incorporating the two most common characteristics of real data: errors and missing genotypes (including untyped individuals). Although HCRE is computationally hard, we propose an exact algorithm for the problem based on a reduction to the well-known Satisfiability problem. Our reduction exploits recent progresses in the constraint programming literature and, combined with the use of state-of-the-art SAT solvers, provides a practical solution for the HCRE problem. Biological soundness of the phasing model and effectiveness (on both accuracy and performance) of the algorithm are experimentally demonstrated under several simulated scenarios and on a real dairy cattle population.Comment: 14 pages, 1 figure, 4 tables, the associated software reHCstar is available at http://www.algolab.eu/reHCsta

Methods and Algorithms for Inference Problems in Population Genetics

Inference of population history is a central problem of population genetics. The advent of large genetic data brings us not only opportunities on developing more accurate methods for inference problems, but also computational challenges. Thus, we aim at developing accurate method and fast algorithm for problems in population genetics. Inference of admixture proportions is a classical statistical problem. We particularly focus on the problem of ancestry inference for ancestors. Standard methods implicitly assume that both parents of an individual have the same admixture fraction. However, this is rarely the case in real data. We develop a Hidden Markov Model (HMM) framework for estimating the admixture proportions of the immediate ancestors of an individual, i.e. a type of appropriation of an individual\u27s admixture proportions into further subsets of ancestral proportions in the ancestors. Based on a genealogical model for admixture tracts, we develop an efficient algorithm for computing the sampling probability of the genome from a single individual, as a function of the admixture proportions of the ancestors of this individual. We show that the distribution and lengths of admixture tracts in a genome contain information about the admixture proportions of the ancestors of an individual. This allows us to perform probabilistic inference of admixture proportions of ancestors only using the genome of an extant individual. To better understand population, we further study the species delimitation problem. It is a problem of determining the boundary between population and species. We propose a classification-based method to assign a set of populations to a number of species. Our new method uses summary statistics generated from genetic data to classify pairwise populations as either \u27same species\u27 or \u27different species\u27. We show that machine learning can be used for species delimitation and scaled for large genomic data. It can also outperform Bayesian approaches, especially when gene flow involves in the evolutionary process

Haplotype estimation in polyploids using DNA sequence data

Polyploid organisms possess more than two copies of their core genome and therefore contain k>2 haplotypes for each set of ordered genomic variants. Polyploidy occurs often within the plant kingdom, among others in important corps such as potato (k=4) and wheat (k=6). Current sequencing technologies enable us to read the DNA and detect genomic variants, but cannot distinguish between the copies of the genome, each inherited from one of the parents. To detect inheritance patterns in populations, it is necessary to know the haplotypes, as alleles that are in linkage over the same chromosome tend to be inherited together. In this work, we develop mathematical optimisation algorithms to indirectly estimate haplotypes by looking into overlaps between the sequence reads of an individual, as well as into the expected inheritance of the alleles in a population. These algorithm deal with sequencing errors and random variations in the counts of reads observed from each haplotype. These methods are therefore of high importance for studying the genetics of polyploid crops. </p

Global haplotype partitioning for maximal associated SNP pairs

<p>Abstract</p> <p>Background</p> <p>Global partitioning based on pairwise associations of SNPs has not previously been used to define haplotype blocks within genomes. Here, we define an association index based on LD between SNP pairs. We use the Fisher's exact test to assess the statistical significance of the LD estimator. By this test, each SNP pair is characterized as associated, independent, or not-statistically-significant. We set limits on the maximum acceptable proportion of independent pairs within all blocks and search for the partitioning with maximal proportion of associated SNP pairs. Essentially, this model is reduced to a constrained optimization problem, the solution of which is obtained by iterating a dynamic programming algorithm.</p> <p>Results</p> <p>In comparison with other methods, our algorithm reports blocks of larger average size. Nevertheless, the haplotype diversity within the blocks is captured by a small number of tagSNPs. Resampling HapMap haplotypes under a block-based model of recombination showed that our algorithm is robust in reproducing the same partitioning for recombinant samples. Our algorithm performed better than previously reported models in a case-control association study aimed at mapping a single locus trait, based on simulation results that were evaluated by a block-based statistical test. Compared to methods of haplotype block partitioning, we performed best on detection of recombination hotspots.</p> <p>Conclusion</p> <p>Our proposed method divides chromosomes into the regions within which allelic associations of SNP pairs are maximized. This approach presents a native design for dimension reduction in genome-wide association studies. Our results show that the pairwise allelic association of SNPs can describe various features of genomic variation, in particular recombination hotspots.</p

Using an evolutionary algorithm and parallel computing for haplotyping in a general complex pedigree with multiple marker loci

<p>Abstract</p> <p>Background</p> <p>Haplotype reconstruction is important in linkage mapping and association mapping of quantitative trait loci (QTL). One widely used statistical approach for haplotype reconstruction is simulated annealing (SA), implemented in SimWalk2. However, the algorithm needs a very large number of sequential iterations, and it does not clearly show if convergence of the likelihood is obtained.</p> <p>Results</p> <p>An evolutionary algorithm (EA) is a good alternative whose convergence can be easily assessed during the process. It is feasible to use a powerful parallel-computing strategy with the EA, increasing the computational efficiency. It is shown that the EA can be ~4 times faster and gives more reliable estimates than SimWalk2 when using 4 processors. In addition, jointly updating dependent variables can increase the computational efficiency up to ~2 times. Overall, the proposed method with 4 processors increases the computational efficiency up to ~8 times compared to SimWalk2. The efficiency will increase more with a larger number of processors.</p> <p>Conclusion</p> <p>The use of the evolutionary algorithm and the joint updating method can be a promising tool for haplotype reconstruction in linkage and association mapping of QTL.</p

Rapid haplotype inference for nuclear families

Hapi is a new dynamic programming algorithm that ignores uninformative states and state transitions in order to efficiently compute minimum-recombinant and maximum likelihood haplotypes. When applied to a dataset containing 103 families, Hapi performs 3.8 and 320 times faster than state-of-the-art algorithms. Because Hapi infers both minimum-recombinant and maximum likelihood haplotypes and applies to related individuals, the haplotypes it infers are highly accurate over extended genomic distances.National Institutes of Health (U.S.) (NIH grant 5-T90-DK070069)National Institutes of Health (U.S.) (Grant 5-P01-NS055923)National Science Foundation (U.S.) (Graduate Research Fellowship

ISHAPE: new rapid and accurate software for haplotyping

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