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

Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation

Background: In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation. Methods: For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers. Results: The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers. Conclusions: The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritabilit

Genomic evaluations with many more genotypes

<p>Abstract</p> <p>Background</p> <p>Genomic evaluations in Holstein dairy cattle have quickly become more reliable over the last two years in many countries as more animals have been genotyped for 50,000 markers. Evaluations can also include animals genotyped with more or fewer markers using new tools such as the 777,000 or 2,900 marker chips recently introduced for cattle. Gains from more markers can be predicted using simulation, whereas strategies to use fewer markers have been compared using subsets of actual genotypes. The overall cost of selection is reduced by genotyping most animals at less than the highest density and imputing their missing genotypes using haplotypes. Algorithms to combine different densities need to be efficient because numbers of genotyped animals and markers may continue to grow quickly.</p> <p>Methods</p> <p>Genotypes for 500,000 markers were simulated for the 33,414 Holsteins that had 50,000 marker genotypes in the North American database. Another 86,465 non-genotyped ancestors were included in the pedigree file, and linkage disequilibrium was generated directly in the base population. Mixed density datasets were created by keeping 50,000 (every tenth) of the markers for most animals. Missing genotypes were imputed using a combination of population haplotyping and pedigree haplotyping. Reliabilities of genomic evaluations using linear and nonlinear methods were compared.</p> <p>Results</p> <p>Differing marker sets for a large population were combined with just a few hours of computation. About 95% of paternal alleles were determined correctly, and > 95% of missing genotypes were called correctly. Reliability of breeding values was already high (84.4%) with 50,000 simulated markers. The gain in reliability from increasing the number of markers to 500,000 was only 1.6%, but more than half of that gain resulted from genotyping just 1,406 young bulls at higher density. Linear genomic evaluations had reliabilities 1.5% lower than the nonlinear evaluations with 50,000 markers and 1.6% lower with 500,000 markers.</p> <p>Conclusions</p> <p>Methods to impute genotypes and compute genomic evaluations were affordable with many more markers. Reliabilities for individual animals can be modified to reflect success of imputation. Breeders can improve reliability at lower cost by combining marker densities to increase both the numbers of markers and animals included in genomic evaluation. Larger gains are expected from increasing the number of animals than the number of markers.</p

Evaluation of Haplotype Inference Using Definitive Haplotype Data Obtained from Complete Hydatidiform Moles, and Its Significance for the Analyses of Positively Selected Regions

The haplotype map constructed by the HapMap Project is a valuable resource in the genetic studies of disease genes, population structure, and evolution. In the Project, Caucasian and African haplotypes are fairly accurately inferred, based mainly on the rules of Mendelian inheritance using the genotypes of trios. However, the Asian haplotypes are inferred from the genotypes of unrelated individuals based on population genetics, and are less accurate. Thus, the effects of this inaccuracy on downstream analyses needs to be assessed. We determined true Japanese haplotypes by genotyping 100 complete hydatidiform moles (CHM), each carrying a genome derived from a single sperm, using Affymetrix 500 K Arrays. We then assessed how inferred haplotypes can differ from true haplotypes, by phasing pseudo-individualized true haplotypes using the programs PHASE, fastPHASE, and Beagle. We found that, at various genomic regions, especially the MHC locus, the expansion of extended haplotype homozygosity (EHH), which is a measure of positive selection, is obscured when inferred Asian haplotype data is used to detect the expansion. We then mapped the genome using a new statistic, XDiHH, which directly detects the difference between the true and inferred haplotypes, in the determination of EHH expansion. We also show that the true haplotype data presented here is useful to assess and improve the accuracy of phasing of Asian genotypes

Imputation of Missing Genotypes from Sparse to High Density Using Long-Range Phasing

Related individuals share potentially long chromosome segments that trace to a common ancestor. We describe a phasing algorithm (ChromoPhase) that utilizes this characteristic of finite populations to phase large sections of a chromosome. In addition to phasing, our method imputes missing genotypes in individuals genotyped at lower marker density when more densely genotyped relatives are available. ChromoPhase uses a pedigree to collect an individual's (the proband) surrogate parents and offspring and uses genotypic similarity to identify its genomic surrogates. The algorithm then cycles through the relatives and genomic surrogates one at a time to find shared chromosome segments. Once a segment has been identified, any missing information in the proband is filled in with information from the relative. We tested ChromoPhase in a simulated population consisting of 400 individuals at a marker density of 1500/M, which is approximately equivalent to a 50K bovine single nucleotide polymorphism chip. In simulated data, 99.9% loci were correctly phased and, when imputing from 100 to 1500 markers, more than 87% of missing genotypes were correctly imputed. Performance increased when the number of generations available in the pedigree increased, but was reduced when the sparse genotype contained fewer loci. However, in simulated data, ChromoPhase correctly imputed at least 12% more genotypes than fastPHASE, depending on sparse marker density. We also tested the algorithm in a real Holstein cattle data set to impute 50K genotypes in animals with a sparse 3K genotype. In these data 92% of genotypes were correctly imputed in animals with a genotyped sire. We evaluated the accuracy of genomic predictions with the dense, sparse, and imputed simulated data sets and show that the reduction in genomic evaluation accuracy is modest even with imperfectly imputed genotype data. Our results demonstrate that imputation of missing genotypes, and potentially full genome sequence, using long-range phasing is feasible

Efficient genome ancestry inference in complex pedigrees with inbreeding

Motivation: High-density SNP data of model animal resources provides opportunities for fine-resolution genetic variation studies. These genetic resources are generated through a variety of breeding schemes that involve multiple generations of matings derived from a set of founder animals. In this article, we investigate the problem of inferring the most probable ancestry of resulting genotypes, given a set of founder genotypes. Due to computational difficulty, existing methods either handle only small pedigree data or disregard the pedigree structure. However, large pedigrees of model animal resources often contain repetitive substructures that can be utilized in accelerating computation

Haplotype Inference through Sequential Monte Carlo

Technological advances in the last decade have given rise to large Genome Wide Studies which have helped researchers get better insights in the genetic basis of many common diseases. As the number of samples and genome coverage has increased dramatically it is currently typical that individuals are genotyped using high throughput platforms to more than 500,000 Single Nucleotide Polymorphisms. At the same time theoretical and empirical arguments have been made for the use of haplotypes, i.e. combinations of alleles at multiple loci in individual chromosomes, as opposed to genotypes so the problem of haplotype inference is particularly relevant. Existing haplotyping methods include population based methods, methods for pooled DNA samples and methods for family and pedigree data. Furthermore, the vast amount of available data pose new challenges for haplotyping algorithms. Candidate methods should scale well to the size of the datasets as the number of loci and the number of individuals are well to the thousands. In addition, as genotyping can be performed routinely, researchers encounter a number of specific new scenarios, which can be seen as hybrid between the population and pedigree inference scenarios and require special care to incorporate the maximum amount of information. In this thesis we present a Sequential Monte Carlo framework (TDS) and tailor it to address instances of haplotype inference and frequency estimation problems. Specifically, we first adjust our framework to perform haplotype inference in trio families resulting in a methodology that demonstrates an excellent tradeoff between speed and accuracy. Consequently, we extend our method to handle general nuclear families and demonstrate the gain using our approach as opposed to alternative scenarios. We further address the problem of haplotype inference in pooling data in which we show that our method achieves improved performance over existing approaches in datasets with large number of markers. We finally present a framework to handle the haplotype inference problem in regions of CNV/SNP data. Using our approach we can phase datasets where the ploidy of an individual can vary along the region and each individual can have different breakpoints

PRIMAL: Fast and Accurate Pedigree-based Imputation from Sequence Data in a Founder Population

Founder populations and large pedigrees offer many well-known advantages for genetic mapping studies, including cost-efficient study designs. Here, we describe PRIMAL (PedigRee IMputation ALgorithm), a fast and accurate pedigree-based phasing and imputation algorithm for founder populations. PRIMAL incorporates both existing and original ideas, such as a novel indexing strategy of Identity-By-Descent (IBD) segments based on clique graphs. We were able to impute the genomes of 1,317 South Dakota Hutterites, who had genome-wide genotypes for ~300,000 common single nucleotide variants (SNVs), from 98 whole genome sequences. Using a combination of pedigree-based and LD-based imputation, we were able to assign 87% of genotypes with >99% accuracy over the full range of allele frequencies. Using the IBD cliques we were also able to infer the parental origin of 83% of alleles, and genotypes of deceased recent ancestors for whom no genotype information was available. This imputed data set will enable us to better study the relative contribution of rare and common variants on human phenotypes, as well as parental origin effect of disease risk alleles in >1,000 individuals at minimal cost.</p

A computational method for genotype calling in family-based sequencing data

Background: As sequencing technologies can help researchers detect common and rare variants across the human genome in many individuals, it is known that jointly calling genotypes across multiple individuals based on linkage disequilibrium (LD) can facilitate the analysis of low to modest coverage sequence data. However, genotype-calling methods for family-based sequence data, particularly for complex families beyond parent-offspring trios, are still lacking. Results: In this study, first, we proposed an algorithm that considers both linkage disequilibrium (LD) patterns and familial transmission in nuclear and multi-generational families while retaining the computational efficiency. Second, we extended our method to incorporate external reference panels to analyze family-based sequence data with a small sample size. In simulation studies, we show that modeling multiple offspring can dramatically increase genotype calling accuracy and reduce phasing and Mendelian errors, especially at low to modest coverage. In addition, we show that using external panels can greatly facilitate genotype calling of sequencing data with a small number of individuals. We applied our method to a whole genome sequencing study of 1339 individuals at ~10X coverage from the Minnesota Center for Twin and Family Research. Conclusions: The aggregated results show that our methods significantly outperform existing ones that ignore family constraints or LD information. We anticipate that our method will be useful for many ongoing family-based sequencing projects. We have implemented our methods efficiently in a C++ program FamLDCaller, which is available from http://www.pitt.edu/~wec47/famldcaller.html