On Counting the Number of Consistent Genotype Assignments for Pedigrees

Consistency checking of genotype information in pedigrees plays an important role in genetic analysis and for complex pedigrees the computational complexity is critical. We present here a detailed complexity analysis for the problem of counting the number of complete consistent genotype assignments. Our main result is a polynomial time algorithm for counting the number of complete consistent assignments for non-looping pedigrees. We further classify pedigrees according to a number of natural parameters like the number of generations, the number of children per individual and the cardinality of the set of alleles. We show that even if we assume all these parameters as bounded by reasonably small constants, the counting problem becomes computationally hard (#P-complete) for looping pedigrees. The border line for counting problems computable in polynomial time (i.e. belonging to the class FP) and #P-hard problems is completed by showing that even for general pedigrees with unlimited number of generations and alleles but with at most one child per individual and for pedigrees with at most two generations and two children per individual the counting problem is in FP

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

Estimate haplotype frequencies in pedigrees

BACKGROUND: Haplotype analysis has gained increasing attention in the context of association studies of disease genes and drug responsivities over the last years. The potential use of haplotypes has led to the initiation of the HapMap project which is to investigate haplotype patterns in the human genome in different populations. Haplotype inference and frequency estimation are essential components of this endeavour. RESULTS: We present a two-stage method to estimate haplotype frequencies in pedigrees, which includes haplotyping stage and estimation stage. In the haplotyping stage, we propose a linear time algorithm to determine all zero-recombinant haplotype configurations for each pedigree. In the estimation stage, we use the expectation-maximization (EM) algorithm to estimate haplotype frequencies based on these haplotype configurations. The experiments demonstrate that our method runs much faster and gives more credible estimates than other popular haplotype analysis software that discards the pedigree information. CONCLUSION: Our method suggests that pedigree information is of great importance in haplotype analysis. It can be used to speedup estimation process, and to improve estimation accuracy as well. The result also demonstrates that the whole haplotype configuration space can be substituted by the space of zero-recombinant haplotype configurations in haplotype frequency estimation, especially when the considered haplotype block is relatively short

Haplotype inference in general pedigrees with two sites

<p>Abstract</p> <p>Background</p> <p>Genetic disease studies investigate relationships between changes in chromosomes and genetic diseases. Single haplotypes provide useful information for these studies but extracting single haplotypes directly by biochemical methods is expensive. A computational method to infer haplotypes from genotype data is therefore important. We investigate the problem of computing the minimum number of recombination events for general pedigrees with two sites for all members.</p> <p>Results</p> <p>We show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem and therefore can be solved by an <it>O</it>(2<it>^k</it> · <it>n</it>²) exact algorithm, where <it>n</it> is the number of members and <it>k</it> is the number of recombination events.</p> <p>Conclusions</p> <p>Our work can therefore be useful for genetic disease studies to track down how changes in haplotypes such as recombinations relate to genetic disease.</p

On Counting the Number of Consistent Genotype Assignments for Pedigrees

Consistency checking of genotype information in pedigrees plays an important role in genetic analysis and for complex pedigrees the computational complexity is critical. We present here a detailed complexity analysis for the problem of counting the number of complete consistent genotype assignments. Our main result is a polynomial time algorithm for counting the number of complete consistent assignments for non-looping pedigrees. We further classify pedigrees according to a number of natural parameters like the number of generations, the number of children per individual and the cardinality of the set of alleles. We show that even if we assume all these parameters as bounded by reasonably small constants, the counting problem becomes computationally hard (#P-complete) for looping pedigrees. The border line for counting problems computable in polynomial time (i.e. belonging to the class FP) and #P-hard problems is completed by showing that even for general pedigrees with unlimited number of generations and alleles but with at most one child per individual and for pedigrees with at most two generations and two children per individual the counting problem is in FP

Most parsimonious haplotype allele sharing determination

<p>Abstract</p> <p>Background</p> <p>The "common disease – common variant" hypothesis and genome-wide association studies have achieved numerous successes in the last three years, particularly in genetic mapping in human diseases. Nevertheless, the power of the association study methods are still low, in particular on quantitative traits, and the description of the full allelic spectrum is deemed still far from reach. Given increasing density of single nucleotide polymorphisms available and suggested by the block-like structure of the human genome, a popular and prosperous strategy is to use haplotypes to try to capture the correlation structure of SNPs in regions of little recombination. The key to the success of this strategy is thus the ability to unambiguously determine the haplotype allele sharing status among the members. The association studies based on haplotype sharing status would have significantly reduced degrees of freedom and be able to capture the combined effects of tightly linked causal variants.</p> <p>Results</p> <p>For pedigree genotype datasets of medium density of SNPs, we present two methods for haplotype allele sharing status determination among the pedigree members. Extensive simulation study showed that both methods performed nearly perfectly on breakpoint discovery, mutation haplotype allele discovery, and shared chromosomal region discovery.</p> <p>Conclusion</p> <p>For pedigree genotype datasets, the haplotype allele sharing status among the members can be deterministically, efficiently, and accurately determined, even for very small pedigrees. Given their excellent performance, the presented haplotype allele sharing status determination programs can be useful in many downstream applications including haplotype based association studies.</p

Genome-Wide Analysis Reveals a Complex Pattern of Genomic Imprinting in Mice

Parent-of-origin–dependent gene expression resulting from genomic imprinting plays an important role in modulating complex traits ranging from developmental processes to cognitive abilities and associated disorders. However, while gene-targeting techniques have allowed for the identification of imprinted loci, very little is known about the contribution of imprinting to quantitative variation in complex traits. Most studies, furthermore, assume a simple pattern of imprinting, resulting in either paternal or maternal gene expression; yet, more complex patterns of effects also exist. As a result, the distribution and number of different imprinting patterns across the genome remain largely unexplored. We address these unresolved issues using a genome-wide scan for imprinted quantitative trait loci (iQTL) affecting body weight and growth in mice using a novel three-generation design. We identified ten iQTL that display much more complex and diverse effect patterns than previously assumed, including four loci with effects similar to the callipyge mutation found in sheep. Three loci display a new phenotypic pattern that we refer to as bipolar dominance, where the two heterozygotes are different from each other while the two homozygotes are identical to each other. Our study furthermore detected a paternally expressed iQTL on Chromosome 7 in a region containing a known imprinting cluster with many paternally expressed genes. Surprisingly, the effects of the iQTL were mostly restricted to traits expressed after weaning. Our results imply that the quantitative effects of an imprinted allele at a locus depend both on its parent of origin and the allele it is paired with. Our findings also show that the imprinting pattern of a locus can be variable over ontogenetic time and, in contrast to current views, may often be stronger at later stages in life

A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on a pedigree

BACKGROUND: When studying genetic diseases in which genetic variations are passed on to offspring, the ability to distinguish between paternal and maternal alleles is essential. Determining haplotypes from genotype data is called haplotype inference. Most existing computational algorithms for haplotype inference have been designed to use genotype data collected from individuals in the form of a pedigree. A haplotype is regarded as a hereditary unit and therefore input pedigrees are preferred that are free of mutational events and have a minimum number of genetic recombinational events. These ideas motivated the zero-recombinant haplotype configuration (ZRHC) problem, which strictly follows the Mendelian law of inheritance, namely that one haplotype of each child is inherited from the father and the other haplotype is inherited from the mother, both without any mutation. So far no linear-time algorithm for ZRHC has been proposed for general pedigrees, even though the number of mating loops in a human pedigree is usually very small and can be regarded as constant. RESULTS: Given a pedigree with n individuals, m marker loci, and k mating loops, we proposed an algorithm that can provide a general solution to the zero-recombinant haplotype configuration problem in O(kmn + k(2)m) time. In addition, this algorithm can be modified to detect inconsistencies within the genotype data without loss of efficiency. The proposed algorithm was subject to 12000 experiments to verify its performance using different (n, m) combinations. The value of k was uniformly distributed between zero and six throughout all experiments. The experimental results show a great linearity in terms of execution time in relation to input size when both n and m are larger than 100. For those experiments where n or m are less than 100, the proposed algorithm runs very fast, in thousandth to hundredth of a second, on a personal desktop computer. CONCLUSIONS: We have developed the first deterministic linear-time algorithm for the zero-recombinant haplotype configuration problem. Our experimental results demonstrated the linearity of its execution time in relation to the input size. The proposed algorithm can be modified to detect inconsistency within the genotype data without loss of efficiency and is expected to be able to handle recombinant and missing data with further extension

Haplotype association analyses in resources of mixed structure using Monte Carlo testing

<p>Abstract</p> <p>Background</p> <p>Genomewide association studies have resulted in a great many genomic regions that are likely to harbor disease genes. Thorough interrogation of these specific regions is the logical next step, including regional haplotype studies to identify risk haplotypes upon which the underlying critical variants lie. Pedigrees ascertained for disease can be powerful for genetic analysis due to the cases being enriched for genetic disease. Here we present a Monte Carlo based method to perform haplotype association analysis. Our method, hapMC, allows for the analysis of full-length and sub-haplotypes, including imputation of missing data, in resources of nuclear families, general pedigrees, case-control data or mixtures thereof. Both traditional association statistics and transmission/disequilibrium statistics can be performed. The method includes a phasing algorithm that can be used in large pedigrees and optional use of pseudocontrols.</p> <p>Results</p> <p>Our new phasing algorithm substantially outperformed the standard expectation-maximization algorithm that is ignorant of pedigree structure, and hence is preferable for resources that include pedigree structure. Through simulation we show that our Monte Carlo procedure maintains the correct type 1 error rates for all resource types. Power comparisons suggest that transmission-disequilibrium statistics are superior for performing association in resources of only nuclear families. For mixed structure resources, however, the newly implemented pseudocontrol approach appears to be the best choice. Results also indicated the value of large high-risk pedigrees for association analysis, which, in the simulations considered, were comparable in power to case-control resources of the same sample size.</p> <p>Conclusions</p> <p>We propose hapMC as a valuable new tool to perform haplotype association analyses, particularly for resources of mixed structure. The availability of meta-association and haplotype-mining modules in our suite of Monte Carlo haplotype procedures adds further value to the approach.</p

Parsimony-based genetic algorithm for haplotype resolution and block partitioning

This dissertation proposes a new algorithm for performing simultaneous haplotype resolution and block partitioning. The algorithm is based on genetic algorithm approach and the parsimonious principle. The multiloculs LD measure (Normalized Entropy Difference) is used as a block identification criterion. The proposed algorithm incorporates missing data is a part of the model and allows blocks of arbitrary length. In addition, the algorithm provides scores for the block boundaries which represent measures of strength of the boundaries at specific positions. The performance of the proposed algorithm was validated by running it on several publicly available data sets including the HapMap data and comparing results to those of the existing state-of-the-art algorithms. The results show that the proposed genetic algorithm provides the accuracy of haplotype decomposition within the range of the same indicators shown by the other algorithms. The block structure output by our algorithm in general agrees with the block structure for the same data provided by the other algorithms. Thus, the proposed algorithm can be successfully used for block partitioning and haplotype phasing while providing some new valuable features like scores for block boundaries and fully incorporated treatment of missing data. In addition, the proposed algorithm for haplotyping and block partitioning is used in development of the new clustering algorithm for two-population mixed genotype samples. The proposed clustering algorithm extracts from the given genotype sample two clusters with substantially different block structures and finds haplotype resolution and block partitioning for each cluster