A hierarchical Dirichlet process mixture model for haplotype reconstruction from multi-population data

The perennial problem of "how many clusters?" remains an issue of substantial interest in data mining and machine learning communities, and becomes particularly salient in large data sets such as populational genomic data where the number of clusters needs to be relatively large and open-ended. This problem gets further complicated in a co-clustering scenario in which one needs to solve multiple clustering problems simultaneously because of the presence of common centroids (e.g., ancestors) shared by clusters (e.g., possible descents from a certain ancestor) from different multiple-cluster samples (e.g., different human subpopulations). In this paper we present a hierarchical nonparametric Bayesian model to address this problem in the context of multi-population haplotype inference. Uncovering the haplotypes of single nucleotide polymorphisms is essential for many biological and medical applications. While it is uncommon for the genotype data to be pooled from multiple ethnically distinct populations, few existing programs have explicitly leveraged the individual ethnic information for haplotype inference. In this paper we present a new haplotype inference program, Haploi, which makes use of such information and is readily applicable to genotype sequences with thousands of SNPs from heterogeneous populations, with competent and sometimes superior speed and accuracy comparing to the state-of-the-art programs. Underlying Haploi is a new haplotype distribution model based on a nonparametric Bayesian formalism known as the hierarchical Dirichlet process, which represents a tractable surrogate to the coalescent process. The proposed model is exchangeable, unbounded, and capable of coupling demographic information of different populations.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS225 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Haplotype inference in crossbred populations without pedigree information

<p>Abstract</p> <p>Background</p> <p>Current methods for haplotype inference without pedigree information assume random mating populations. In animal and plant breeding, however, mating is often not random. A particular form of nonrandom mating occurs when parental individuals of opposite sex originate from distinct populations. In animal breeding this is called <it>crossbreeding </it>and <it>hybridization </it>in plant breeding. In these situations, association between marker and putative gene alleles might differ between the founding populations and origin of alleles should be accounted for in studies which estimate breeding values with marker data. The sequence of alleles from one parent constitutes one haplotype of an individual. Haplotypes thus reveal allele origin in data of crossbred individuals.</p> <p>Results</p> <p>We introduce a new method for haplotype inference without pedigree that allows nonrandom mating and that can use genotype data of the parental populations and of a crossbred population. The aim of the method is to estimate line origin of alleles. The method has a Bayesian set up with a Dirichlet Process as prior for the haplotypes in the two parental populations. The basic idea is that only a subset of the complete set of possible haplotypes is present in the population.</p> <p>Conclusion</p> <p>Line origin of approximately 95% of the alleles at heterozygous sites was assessed correctly in both simulated and real data. Comparing accuracy of haplotype frequencies inferred with the new algorithm to the accuracy of haplotype frequencies inferred with PHASE, an existing algorithm for haplotype inference, showed that the DP algorithm outperformed PHASE in situations of crossbreeding and that PHASE performed better in situations of random mating.</p

Empirical vs Bayesian approach for estimating haplotypes from genotypes of unrelated individuals

BACKGROUND: The completion of the HapMap project has stimulated further development of haplotype-based methodologies for disease associations. A key aspect of such development is the statistical inference of individual diplotypes from unphased genotypes. Several methodologies for inferring haplotypes have been developed, but they have not been evaluated extensively to determine which method not only performs well, but also can be easily incorporated in downstream haplotype-based association analyses. In this paper, we attempt to do so. Our evaluation was carried out by comparing the two leading Bayesian methods, implemented in PHASE and HAPLOTYPER, and the two leading empirical methods, implemented in PL-EM and HPlus. We used these methods to analyze real data, namely the dense genotypes on X-chromosome of 30 European and 30 African trios provided by the International HapMap Project, and simulated genotype data. Our conclusions are based on these analyses. RESULTS: All programs performed very well on X-chromosome data, with an average similarity index of 0.99 and an average prediction rate of 0.99 for both European and African trios. On simulated data with approximation of coalescence, PHASE implementing the Bayesian method based on the coalescence approximation outperformed other programs on small sample sizes. When the sample size increased, other programs performed as well as PHASE. PL-EM and HPlus implementing empirical methods required much less running time than the programs implementing the Bayesian methods. They required only one hundredth or thousandth of the running time required by PHASE, particularly when analyzing large sample sizes and large umber of SNPs. CONCLUSION: For large sample sizes (hundreds or more), which most association studies require, the two empirical methods might be used since they infer the haplotypes as accurately as any Bayesian methods and can be incorporated easily into downstream haplotype-based analyses such as haplotype-association analyses

The EM Algorithm and the Rise of Computational Biology

In the past decade computational biology has grown from a cottage industry with a handful of researchers to an attractive interdisciplinary field, catching the attention and imagination of many quantitatively-minded scientists. Of interest to us is the key role played by the EM algorithm during this transformation. We survey the use of the EM algorithm in a few important computational biology problems surrounding the "central dogma"; of molecular biology: from DNA to RNA and then to proteins. Topics of this article include sequence motif discovery, protein sequence alignment, population genetics, evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

An artificial neural network for estimating haplotype frequencies

The problem of estimating haplotype frequencies from population data has been considered by numerous investigators, resulting in a wide variety of possible algorithmic and statistical solutions. We propose a relatively unique approach that employs an artificial neural network (ANN) to predict the most likely haplotype frequencies from a sample of population genotype data. Through an innovative ANN design for mapping genotype patterns to diplotypes, we have produced a prototype that demonstrates the feasibility of this approach, with provisional results that correlate well with estimates produced by the expectation maximization algorithm for haplotype frequency estimation. Given the computational demands of estimating haplotype frequencies for 20 or more single-nucleotide polymorphisms, the ANN approach is promising because its design fits well with parallel computing architectures

Reconstructing the evolutionary history of the radiation of the land snail genus Xerocrassa on Crete based on mitochondrial sequences and AFLP markers

Sauer J, Hausdorf B. Reconstructing the evolutionary history of the radiation of the land snail genus Xerocrassa on Crete based on mitochondrial sequences and AFLP markers. BMC Evolutionary Biology. 2010;10(1): 299.Background: A non-adaptive radiation triggered by sexual selection resulted in ten endemic land snail species of the genus Xerocrassa on Crete. Only five of these species and a more widespread species are monophyletic in a mitochondrial gene tree. The reconstruction of the evolutionary history of such closely related species can be complicated by incomplete lineage sorting, introgression or inadequate taxonomy. To distinguish between the reasons for the nonmonophyly of several species in the mitochondrial gene tree we analysed nuclear AFLP markers. Results: Whereas six of the eleven morphologically delimited Xerocrassa species from Crete are monophyletic in the mitochondrial gene tree, nine of these species are monophyletic in the tree based on AFLP markers. Only two morphologically delimited species could not be distinguished with the multilocus data and might have diverged very recently or might represent extreme forms of a single species. The nonmonophyly of X. rhithymna with respect to X. kydonia is probably the result of incomplete lineage sorting, because there is no evidence for admixture in the AFLP data and the mitochondrial haplotype groups of these species coalesce deeply. The same is true for the main haplotype groups of X. mesostena. The nonmonophyly of X. franciscoi might be the result of mitochondrial introgression, because the coalescences of the haplotypes of this species with some X. mesostena haplotypes are shallow and there is admixture with neighbouring X. mesostena. Conclusion: The most likely causes for the nonmonophyly of species in the mitochondrial gene tree of the Xerocrassa radiation on Crete could be inferred using AFLP data by a combination of several criteria, namely the depth of the coalescences in the gene tree, the geographical distribution of shared genetic markers, and concordance with results of admixture analyses of nuclear multilocus markers. The strongly subdivided population structure increases the effective population size of land snail species and, thus, the likelihood of a long persistence of ancestral polymorphisms. Our study suggests that ancestral polymorphisms are a frequent cause for nonmonophyly of species with a strongly subdivided population structure in gene trees