# Related Articles

Background

Biology has increasingly recognized the necessity to build and utilize larger phylogenies to address broad evolutionary questions. Large phylogenies have facilitated the discovery of differential rates of molecular evolution between trees and herbs. They have helped us understand the diversification patterns of mammals as well as the patterns of seed evolution. In addition to these broad evolutionary questions there is increasing awareness of the importance of large phylogenies for addressing conservation issues such as biodiversity hotspots and response to global change. Two major classes of methods have been employed to accomplish the large tree-building task: supertrees and supermatrices. Although these methods are continually being developed, they have yet to be made fully accessible to comparative biologists making extremely large trees rare.

Results

Here we describe and demonstrate a modified supermatrix method termed mega-phylogeny that uses databased sequences as well as taxonomic hierarchies to make extremely large trees with denser matrices than supermatrices. The two major challenges facing large-scale supermatrix phylogenetics are assembling large data matrices from databases and reconstructing trees from those datasets. The mega-phylogeny approach addresses the former as the latter is accomplished by employing recently developed methods that have greatly reduced the run time of large phylogeny construction. We present an algorithm that requires relatively little human intervention. The implemented algorithm is demonstrated with a dataset and phylogeny for Asterales (within Campanulidae) containing 4954 species and 12,033 sites and an rbcL matrix for green plants (Viridiplantae) with 13,533 species and 1,401 sites.

Conclusion

By examining much larger phylogenies, patterns emerge that were otherwise unseen. The phylogeny of Viridiplantae successfully reconstructs major relationships of vascular plants that previously required many more genes. These demonstrations underscore the importance of using large phylogenies to uncover important evolutionary patterns and we present a fast and simple method for constructing these phylogenies.

doi:10.1186/1471-2148-9-37

PMCID: PMC2645364
PMID: 19210768

Background

With current technology, vast amounts of data can be cheaply and efficiently produced in association studies, and to prevent data analysis to become the bottleneck of studies, fast and efficient analysis methods that scale to such data set sizes must be developed.

Results

We present a fast method for accurate localisation of disease causing variants in high density case-control association mapping experiments with large numbers of cases and controls. The method searches for significant clustering of case chromosomes in the "perfect" phylogenetic tree defined by the largest region around each marker that is compatible with a single phylogenetic tree. This perfect phylogenetic tree is treated as a decision tree for determining disease status, and scored by its accuracy as a decision tree. The rationale for this is that the perfect phylogeny near a disease affecting mutation should provide more information about the affected/unaffected classification than random trees. If regions of compatibility contain few markers, due to e.g. large marker spacing, the algorithm can allow the inclusion of incompatibility markers in order to enlarge the regions prior to estimating their phylogeny. Haplotype data and phased genotype data can be analysed. The power and efficiency of the method is investigated on 1) simulated genotype data under different models of disease determination 2) artificial data sets created from the HapMap ressource, and 3) data sets used for testing of other methods in order to compare with these. Our method has the same accuracy as single marker association (SMA) in the simplest case of a single disease causing mutation and a constant recombination rate. However, when it comes to more complex scenarios of mutation heterogeneity and more complex haplotype structure such as found in the HapMap data our method outperforms SMA as well as other fast, data mining approaches such as HapMiner and Haplotype Pattern Mining (HPM) despite being significantly faster. For unphased genotype data, an initial step of estimating the phase only slightly decreases the power of the method. The method was also found to accurately localise the known susceptibility variants in an empirical data set – the ΔF508 mutation for cystic fibrosis – where the susceptibility variant is already known – and to find significant signals for association between the CYP2D6 gene and poor drug metabolism, although for this dataset the highest association score is about 60 kb from the CYP2D6 gene.

Conclusion

Our method has been implemented in the Blossoc (BLOck aSSOCiation) software. Using Blossoc, genome wide chip-based surveys of 3 million SNPs in 1000 cases and 1000 controls can be analysed in less than two CPU hours.

doi:10.1186/1471-2105-7-454

PMCID: PMC1624851
PMID: 17042942

Phylogenetic networks are models of evolution that go beyond trees, incorporating non-tree-like biological events such as recombination (or more generally reticulation), which occur either in a single species (meiotic recombination) or between species (reticulation due to lateral gene transfer and hybrid speciation). The central algorithmic problems are to reconstruct a plausible history of mutations and non-tree-like events, or to determine the minimum number of such events needed to derive a given set of binary sequences, allowing one mutation per site. Meiotic recombination, reticulation and recurrent mutation can cause conflict or incompatibility between pairs of sites (or characters) of the input. Previously, we used “conflict graphs” and “incompatibility graphs” to compute lower bounds on the minimum number of recombination nodes needed, and to efficiently solve constrained cases of the minimization problem. Those results exposed the structural and algorithmic importance of the non-trivial connected components of those two graphs.

In this paper, we more fully develop the structural importance of non-trivial connected components of the incompatibility and conflict graphs, proving a general decomposition theorem (first presented in Gusfield and Bansal 2005) for phylogenetic networks. The decomposition theorem depends only on the incompatibilities in the input sequences, and hence applies to phylogenetic networks of all types, and to any phenomena that causes pairwise incompatibilities. More generally, the proof of the decomposition theorem exposes a maximal embedded tree structure that exists in the network when the sequences cannot be derived on a perfect phylogenetic tree. This extends the theory of perfect phylogeny in a natural and important way. The proof is constructive and leads to a polynomial-time algorithm to find the unique underlying maximal tree structure. We next examine and fully solve the major open question from Gusfield and Bansal (2005): Is it true that for every input there must be a fully decomposed phylogenetic network that minimizes the number of recombination nodes used, over all phylogenetic networks for the input. We previously conjectured that the answer is yes. In this paper we show that the answer in is no, both for the case that only single-crossover recombination is allowed, and also for the case that unbounded multiple-crossover recombination is allowed. The latter case also resolves a conjecture recently stated in Huson and Klopper (2007) in the context of general reticulation networks. Although the conjecture from Gusfield and Bansal (2005) is disproved in general, we show that the answer to the conjecture is yes in several natural special cases, and establish necessary combinatorial structure that counterexamples to the conjecture must posses. We also show that counterexamples to the conjecture are rare (for the case of single-crossover recombination) in simulated data.

doi:10.1089/cmb.2006.0137

PMCID: PMC2581772
PMID: 18047426

Molecular Evolution; Phylogenetic Networks; Perfect Phylogeny; Ancestral Recombination Graph; Recombination; Gene-Conversion; SNP

Lishout, François Van | Mahachie John, Jestinah M | Gusareva, Elena S | Urrea, Victor | Cleynen, Isabelle | Théâtre, Emilie | Charloteaux, Benoît | Calle, Malu Luz | Wehenkel, Louis | Steen, Kristel Van
Background

Research in epistasis or gene-gene interaction detection for human complex traits has grown over the last few years. It has been marked by promising methodological developments, improved translation efforts of statistical epistasis to biological epistasis and attempts to integrate different omics information sources into the epistasis screening to enhance power. The quest for gene-gene interactions poses severe multiple-testing problems. In this context, the maxT algorithm is one technique to control the false-positive rate. However, the memory needed by this algorithm rises linearly with the amount of hypothesis tests. Gene-gene interaction studies will require a memory proportional to the squared number of SNPs. A genome-wide epistasis search would therefore require terabytes of memory. Hence, cache problems are likely to occur, increasing the computation time. In this work we present a new version of maxT, requiring an amount of memory independent from the number of genetic effects to be investigated. This algorithm was implemented in C++ in our epistasis screening software MBMDR-3.0.3. We evaluate the new implementation in terms of memory efficiency and speed using simulated data. The software is illustrated on real-life data for Crohn’s disease.

Results

In the case of a binary (affected/unaffected) trait, the parallel workflow of MBMDR-3.0.3 analyzes all gene-gene interactions with a dataset of 100,000 SNPs typed on 1000 individuals within 4 days and 9 hours, using 999 permutations of the trait to assess statistical significance, on a cluster composed of 10 blades, containing each four Quad-Core AMD Opteron(tm) Processor 2352 2.1 GHz. In the case of a continuous trait, a similar run takes 9 days. Our program found 14 SNP-SNP interactions with a multiple-testing corrected p-value of less than 0.05 on real-life Crohn’s disease (CD) data.

Conclusions

Our software is the first implementation of the MB-MDR methodology able to solve large-scale SNP-SNP interactions problems within a few days, without using much memory, while adequately controlling the type I error rates. A new implementation to reach genome-wide epistasis screening is under construction. In the context of Crohn’s disease, MBMDR-3.0.3 could identify epistasis involving regions that are well known in the field and could be explained from a biological point of view. This demonstrates the power of our software to find relevant phenotype-genotype higher-order associations.

doi:10.1186/1471-2105-14-138

PMCID: PMC3648350
PMID: 23617239

Epistasis; Multiple testing; maxT; MB-MDR; GWA studies; Crohn’s disease

Background

The perfect phylogeny is an often used model in phylogenetics since it provides an efficient basic procedure for representing the evolution of genomic binary characters in several frameworks, such as for example in haplotype inference. The model, which is conceptually the simplest, is based on the infinite sites assumption, that is no character can mutate more than once in the whole tree. A main open problem regarding the model is finding generalizations that retain the computational tractability of the original model but are more flexible in modeling biological data when the infinite site assumption is violated because of e.g. back mutations. A special case of back mutations that has been considered in the study of the evolution of protein domains (where a domain is acquired and then lost) is persistency, that is the fact that a character is allowed to return back to the ancestral state. In this model characters can be gained and lost at most once. In this paper we consider the computational problem of explaining binary data by the Persistent Perfect Phylogeny model (referred as PPP) and for this purpose we investigate the problem of reconstructing an evolution where some constraints are imposed on the paths of the tree.

Results

We define a natural generalization of the PPP problem obtained by requiring that for some pairs (character, species), neither the species nor any of its ancestors can have the character. In other words, some characters cannot be persistent for some species. This new problem is called Constrained PPP (CPPP). Based on a graph formulation of the CPPP problem, we are able to provide a polynomial time solution for the CPPP problem for matrices whose conflict graph has no edges. Using this result, we develop a parameterized algorithm for solving the CPPP problem where the parameter is the number of characters.

Conclusions

A preliminary experimental analysis shows that the constrained persistent perfect phylogeny model allows to explain efficiently data that do not conform with the classical perfect phylogeny model.

doi:10.1186/1471-2164-15-S6-S10

PMCID: PMC4240218
PMID: 25572381

perfect phylogeny; persistent perfect phylogeny; fixed-parameter complexity

Background

Although comparative modelling is routinely used to produce three-dimensional models of proteins, very few automated approaches are formulated in a way that allows inclusion of restraints derived from experimental data as well as those from the structures of homologues. Furthermore, proteins are usually described as a single conformer, rather than an ensemble that represents the heterogeneity and inaccuracy of experimentally determined protein structures. Here we address these issues by exploring the application of the restraint-based conformational space search engine, RAPPER, which has previously been developed for rebuilding experimentally defined protein structures and for fitting models to electron density derived from X-ray diffraction analyses.

Results

A new application of RAPPER for comparative modelling uses positional restraints and knowledge-based sampling to generate models with accuracies comparable to other leading modelling tools. Knowledge-based predictions are based on geometrical features of the homologous templates and rules concerning main-chain and side-chain conformations. By directly changing the restraints derived from available templates we estimate the accuracy limits of the method in comparative modelling.

Conclusion

The application of RAPPER to comparative modelling provides an effective means of exploring the conformational space available to a target sequence. Enhanced methods for generating positional restraints can greatly improve structure prediction. Generation of an ensemble of solutions that are consistent with both target sequence and knowledge derived from the template structures provides a more appropriate representation of a structural prediction than a single model. By formulating homologous structural information as sets of restraints we can begin to consider how comparative models might be used to inform conformer generation from sparse experimental data.

doi:10.1186/1472-6807-8-7

PMCID: PMC2275734
PMID: 18237407

Background

Maximum parsimony phylogenetic tree reconstruction from genetic variation data is a fundamental problem in computational genetics with many practical applications in population genetics, whole genome analysis, and the search for genetic predictors of disease. Efficient methods are available for reconstruction of maximum parsimony trees from haplotype data, but such data are difficult to determine directly for autosomal DNA. Data more commonly is available in the form of genotypes, which consist of conflated combinations of pairs of haplotypes from homologous chromosomes. Currently, there are no general algorithms for the direct reconstruction of maximum parsimony phylogenies from genotype data. Hence phylogenetic applications for autosomal data must therefore rely on other methods for first computationally inferring haplotypes from genotypes.

Results

In this work, we develop the first practical method for computing maximum parsimony phylogenies directly from genotype data. We show that the standard practice of first inferring haplotypes from genotypes and then reconstructing a phylogeny on the haplotypes often substantially overestimates phylogeny size. As an immediate application, our method can be used to determine the minimum number of mutations required to explain a given set of observed genotypes.

Conclusion

Phylogeny reconstruction directly from unphased data is computationally feasible for moderate-sized problem instances and can lead to substantially more accurate tree size inferences than the standard practice of treating phasing and phylogeny construction as two separate analysis stages. The difference between the approaches is particularly important for downstream applications that require a lower-bound on the number of mutations that the genetic region has undergone.

doi:10.1186/1471-2105-8-472

PMCID: PMC2222657
PMID: 18053244

In this paper, we study the problem of constructing perfect phylogenies for three-state characters. Our work builds on two recent results. The first result states that for three-state characters, the local condition of examining all subsets of three characters is sufficient to determine the global property of admitting a perfect phylogeny. The second result applies tools from minimal triangulation theory to the partition intersection graph to determine if a perfect phylogeny exists. Despite the wealth of combinatorial tools and algorithms stemming from the chordal graph and minimal triangulation literature, it is unclear how to use such approaches to efficiently construct a perfect phylogeny for three-state characters when the data admits one. We utilize structural properties of both the partition intersection graph and the original data in order to achieve a competitive time bound.

doi:10.1186/1748-7188-7-26

PMCID: PMC3558378
PMID: 23006612

Perfect phylogeny; Chordal graph; Minimal triangulation; Minimal separator

Background

Haplotype information is useful for various genetic analyses, including
genome-wide association studies. Determining haplotypes experimentally is
difficult and there are several computational approaches that infer haplotypes
from genomic data. Among such approaches, single individual haplotyping or
haplotype assembly, which infers two haplotypes of an individual from aligned
sequence fragments, has been attracting considerable attention. To avoid incorrect
results in downstream analyses, it is important not only to assemble haplotypes as
long as possible but also to provide means to extract highly reliable haplotype
regions. Although there are several efficient algorithms for solving haplotype
assembly, there are no efficient method that allow for extracting the regions
assembled with high confidence.

Results

We develop a probabilistic model, called MixSIH, for solving the haplotype
assembly problem. The model has two mixture components representing two
haplotypes. Based on the optimized model, a quality score is defined, which we
call the 'minimum connectivity' (MC) score, for each segment in the haplotype
assembly. Because existing accuracy measures for haplotype assembly are designed
to compare the efficiency between the algorithms and are not suitable for
evaluating the quality of the set of partially assembled haplotype segments, we
develop an accuracy measure based on the pairwise consistency and evaluate the
accuracy on the simulation and real data. By using the MC scores, our algorithm
can extract highly accurate haplotype segments. We also show evidence that an
existing experimental dataset contains chimeric read fragments derived from
different haplotypes, which significantly degrade the quality of assembled
haplotypes.

Conclusions

We develop a novel method for solving the haplotype assembly problem. We also
define the quality score which is based on our model and indicates the accuracy of
the haplotypes segments. In our evaluation, MixSIH has successfully extracted
reliable haplotype segments. The C++ source code of MixSIH is available at
https://sites.google.com/site/hmatsu1226/software/mixsih.

doi:10.1186/1471-2164-14-S2-S5

PMCID: PMC3582441
PMID: 23445519

Haplotype phasing is a well studied problem in the context of genotype data. With the recent developments in high-throughput sequencing, new algorithms are needed for haplotype phasing, when the number of samples sequenced is low and when the sequencing coverage is blow. High-throughput sequencing technologies enables new possibilities for the inference of haplotypes. Since each read is originated from a single chromosome, all the variant sites it covers must derive from the same haplotype. Moreover, the sequencing process yields much higher SNP density than previous methods, resulting in a higher correlation between neighboring SNPs. We offer a new approach for haplotype phasing, which leverages on these two properties. Our suggested algorithm, called Perfect Phlogeny Haplotypes from Sequencing (PPHS) uses a perfect phylogeny model and it models the sequencing errors explicitly. We evaluated our method on real and simulated data, and we demonstrate that the algorithm outperforms previous methods when the sequencing error rate is high or when coverage is low.

doi:10.1186/1471-2105-13-S6-S3

PMCID: PMC3330028
PMID: 22537042

Background

Reconciliation methods compare gene trees and species trees to recover evolutionary events such as duplications, transfers and losses explaining the history and composition of genomes. It is well-known that gene trees inferred from molecular sequences can be partly erroneous due to incorrect sequence alignments as well as phylogenetic reconstruction artifacts such as long branch attraction. In practice, this leads reconciliation methods to overestimate the number of evolutionary events. Several methods have been proposed to circumvent this problem, by collapsing the unsupported edges and then resolving the obtained multifurcating nodes, or by directly rearranging the binary gene trees. Yet these methods have been defined for models of evolution accounting only for duplications and losses, i.e. can not be applied to handle prokaryotic gene families.

Results

We propose a reconciliation method accounting for gene duplications, losses and horizontal transfers, that specifically takes into account the uncertainties in gene trees by rearranging their weakly supported edges. Rearrangements are performed on edges having a low confidence value, and are accepted whenever they improve the reconciliation cost. We prove useful properties on the dynamic programming matrix used to compute reconciliations, which allows to speed-up the tree space exploration when rearrangements are generated by Nearest Neighbor Interchanges (NNI) edit operations. Experiments on synthetic data show that gene trees modified by such NNI rearrangements are closer to the correct simulated trees and lead to better event predictions on average. Experiments on real data demonstrate that the proposed method leads to a decrease in the reconciliation cost and the number of inferred events. Finally on a dataset of 30 k gene families, this reconciliation method shows a ranking of prokaryotic phyla by transfer rates identical to that proposed by a different approach dedicated to transfer detection [BMCBIOINF 11:324, 2010, PNAS 109(13):4962–4967, 2012].

Conclusions

Prokaryotic gene trees can now be reconciled with their species phylogeny while accounting for the uncertainty of the gene tree. More accurate and more precise reconciliations are obtained with respect to previous parsimony algorithms not accounting for such uncertainties [LNCS 6398:93–108, 2010, BIOINF 28(12): i283–i291, 2012].

A software implementing the method is freely available at http://www.atgc-montpellier.fr/Mowgli/.

doi:10.1186/1748-7188-8-12

PMCID: PMC3871789
PMID: 23566548

Evolution; Reconciliation; Gene Tree Correction; Method; Software; Duplication; Transfer; Loss; Nearest Neighbor Interchange

Haplotype phasing represents an essential step in studying the association of genomic polymorphisms with complex genetic diseases, and in determining targets for drug designing. In recent years, huge amounts of genotype data are produced from the rapidly evolving high-throughput sequencing technologies, and the data volume challenges the community with more efficient haplotype phasing algorithms, in the senses of both running time and overall accuracy. 2SNP is one of the fastest haplotype phasing algorithms with comparable low error rates with the other algorithms. The most time-consuming step of 2SNP is the construction of a maximum spanning tree (MST) among all the heterozygous SNP pairs. We simplified this step by replacing the MST with the initial haplotypes of adjacent heterozygous SNP pairs. The multi-SNP haplotypes were estimated within a sliding window along the chromosomes. The comparative studies on four different-scale genotype datasets suggest that our algorithm WinHAP outperforms 2SNP and most of the other haplotype phasing algorithms in terms of both running speeds and overall accuracies. To facilitate the WinHAP’s application in more practical biological datasets, we released the software for free at: http://staff.ustc.edu.cn/~xuyun/winhap/index.htm.

doi:10.1371/journal.pone.0043163

PMCID: PMC3419172
PMID: 22905221

Background

The development, in the last decade, of stochastic heuristics implemented in robust application softwares has made large phylogeny inference a key step in most comparative studies involving molecular sequences. Still, the choice of a phylogeny inference software is often dictated by a combination of parameters not related to the raw performance of the implemented algorithm(s) but rather by practical issues such as ergonomics and/or the availability of specific functionalities.

Results

Here, we present MetaPIGA v2.0, a robust implementation of several stochastic heuristics for large phylogeny inference (under maximum likelihood), including a Simulated Annealing algorithm, a classical Genetic Algorithm, and the Metapopulation Genetic Algorithm (metaGA) together with complex substitution models, discrete Gamma rate heterogeneity, and the possibility to partition data. MetaPIGA v2.0 also implements the Likelihood Ratio Test, the Akaike Information Criterion, and the Bayesian Information Criterion for automated selection of substitution models that best fit the data. Heuristics and substitution models are highly customizable through manual batch files and command line processing. However, MetaPIGA v2.0 also offers an extensive graphical user interface for parameters setting, generating and running batch files, following run progress, and manipulating result trees. MetaPIGA v2.0 uses standard formats for data sets and trees, is platform independent, runs in 32 and 64-bits systems, and takes advantage of multiprocessor and multicore computers.

Conclusions

The metaGA resolves the major problem inherent to classical Genetic Algorithms by maintaining high inter-population variation even under strong intra-population selection. Implementation of the metaGA together with additional stochastic heuristics into a single software will allow rigorous optimization of each heuristic as well as a meaningful comparison of performances among these algorithms. MetaPIGA v2.0 gives access both to high customization for the phylogeneticist, as well as to an ergonomic interface and functionalities assisting the non-specialist for sound inference of large phylogenetic trees using nucleotide sequences. MetaPIGA v2.0 and its extensive user-manual are freely available to academics at http://www.metapiga.org.

doi:10.1186/1471-2105-11-379

PMCID: PMC2912891
PMID: 20633263

Motivation: Full-length DNA and protein sequences that span the entire length of a gene are ideally used for multiple sequence alignments (MSAs) and the subsequent inference of their relationships. Frequently, however, MSAs contain a substantial amount of missing data. For example, expressed sequence tags (ESTs), which are partial sequences of expressed genes, are the predominant source of sequence data for many organisms. The patterns of missing data typical for EST-derived alignments greatly compromise the accuracy of estimated phylogenies.

Results: We present a statistical method for inferring phylogenetic trees from EST-based incomplete MSA data. We propose a class of hierarchical models for modeling pairwise distances between the sequences, and develop a fully Bayesian approach for estimation of the model parameters. Once the distance matrix is estimated, the phylogenetic tree may be constructed by applying neighbor-joining (or any other algorithm of choice). We also show that maximizing the marginal likelihood from the Bayesian approach yields similar results to a profile likelihood estimation. The proposed methods are illustrated using simulated protein families, for which the true phylogeny is known, and one real protein family.

Availability: R code for fitting these models are available from: http://people.bu.edu/gupta/software.htm.

Contact: gupta@bu.edu

Supplementary information: Supplemantary data are available at Bioinformatics online.

doi:10.1093/bioinformatics/btp015

PMCID: PMC2647833
PMID: 19147663

Background

With the rapid development of high-throughput genotyping technologies, efficient methods for identifying linked regions using high-density SNP genotype data have become more and more important. Recently, a deterministic method that works very well on SNP genotyping data has been developed (Lin et al. Bioinformatics 2008, 24(1): 86–93). However, that program can only work on a limited number of family structures. In particular, the results (if any) will be poor when the genotype data for the whole chromosome of one of the parents in a nuclear family is missing.

Results

We have developed a software package (LIden) for identifying linked regions using high-density SNP genotype data. We focus on handling the case where the genotype data for the whole chromosome of one of the parents in a nuclear family is missing. We use the minimum recombinant model for haplotype inference in pedigrees. Several local optimization algorithms are used to infer the haplotype of each individual and determine the linked regions based on the inferred haplotype data. We have developed a more flexible method to combine nuclear families to further refine (reduce the length of) the linked regions.

Conclusion

Our new package (LIden) is efficient software for linked region detection using high-density SNP genotype data. LIden can handle some important cases where the existing programs do not work well. In particular, the new package can handle many cases where the genotype data of one of the two parents is missing for the entire chromosome. The running time of the program is O(mn), where m is the number of members in the family and n is the number of SNP sites in the chromosome. LIden is specifically suitable for handling big sized families. This research also demonstrates another practical use of the minimum recombinant model for haplotype inference in pedigrees.

The software package can be downloaded at .

doi:10.1186/1471-2105-10-216

PMCID: PMC2723091
PMID: 19604391

Background

The large majority of optimization problems related to the inference of distance‐based trees used in phylogenetic analysis and classification is known to be intractable. One noted exception is found within the realm of ultrametric distances. The introduction of ultrametric trees in phylogeny was inspired by a model of evolution driven by the postulate of a molecular clock, now dismissed, whereby phylogeny could be represented by a weighted tree in which the sum of the weights of the edges separating any given leaf from the root is the same for all leaves. Both, molecular clocks and rooted ultrametric trees, fell out of fashion as credible representations of evolutionary change. At the same time, ultrametric dendrograms have shown good potential for purposes of classification in so far as they have proven to provide good approximations for additive trees. Most of these approximations are still intractable, but the problem of finding the nearest ultrametric distance matrix to a given distance matrix with respect to the L∞ distance has been long known to be solvable in polynomial time, the solution being incarnated in any minimum spanning tree for the weighted graph subtending to the matrix.

Results

This paper expands this subdominant ultrametric perspective by studying ultrametric networks, consisting of the collection of all edges involved in some minimum spanning tree. It is shown that, for a graph with n vertices, the construction of such a network can be carried out by a simple algorithm in optimal time O(n2) which is faster by a factor of n than the direct adaptation of the classical O(n3) paradigm by Warshall for computing the transitive closure of a graph. This algorithm, called UltraNet, will be shown to be easily adapted to compute relaxed networks and to support the introduction of artificial points to reduce the maximum distance between vertices in a pair. Finally, a few experiments will be discussed to demonstrate the applicability of subdominant ultrametric networks.

Availability

http://www.dei.unipd.it/~ciompin/main/Ultranet/Ultranet.html

doi:10.1186/1748-7188-8-7

PMCID: PMC3693977
PMID: 23497437

Phylogenetic network; Ultrametric distance; STR data analysis

We have developed a software analysis package, HapScope, which includes a comprehensive analysis pipeline and a sophisticated visualization tool for analyzing functionally annotated haplotypes. The HapScope analysis pipeline supports: (i) computational haplotype construction with an expectation-maximization or Bayesian statistical algorithm; (ii) SNP classification by protein coding change, homology to model organisms or putative regulatory regions; and (iii) minimum SNP subset selection by either a Brute Force Algorithm or a Greedy Partition Algorithm. The HapScope viewer displays genomic structure with haplotype information in an integrated environment, providing eight alternative views for assessing genetic and functional correlation. It has a user-friendly interface for: (i) haplotype block visualization; (ii) SNP subset selection; (iii) haplotype consolidation with subset SNP markers; (iv) incorporation of both experimentally determined haplotypes and computational results; and (v) data export for additional analysis. Comparison of haplotypes constructed by the statistical algorithms with those determined experimentally shows variation in haplotype prediction accuracies in genomic regions with different levels of nucleotide diversity. We have applied HapScope in analyzing haplotypes for candidate genes and genomic regions with extensive SNP and genotype data. We envision that the systematic approach of integrating functional genomic analysis with population haplotypes, supported by HapScope, will greatly facilitate current genetic disease research.

PMCID: PMC137968
PMID: 12466546

Multilocus analysis of single nucleotide polymorphism haplotypes is a promising approach to dissecting the genetic basis of complex diseases. We propose a coalescent-based model for association mapping that potentially increases the power to detect disease-susceptibility variants in genetic association studies. The approach uses Bayesian partition modelling to cluster haplotypes with similar disease risks by exploiting evolutionary information. We focus on candidate gene regions with densely spaced markers and model chromosomal segments in high linkage disequilibrium therein assuming a perfect phylogeny. To make this assumption more realistic, we split the chromosomal region of interest into sub-regions or windows of high linkage disequilibrium. The haplotype space is then partitioned into disjoint clusters, within which the phenotype–haplotype association is assumed to be the same. For example, in case-control studies, we expect chromosomal segments bearing the causal variant on a common ancestral background to be more frequent among cases than controls, giving rise to two separate haplotype clusters. The novelty of our approach arises from the fact that the distance used for clustering haplotypes has an evolutionary interpretation, as haplotypes are clustered according to the time to their most recent common ancestor. Our approach is fully Bayesian and we develop a Markov Chain Monte Carlo algorithm to sample efficiently over the space of possible partitions. We compare the proposed approach to both single-marker analyses and recently proposed multi-marker methods and show that the Bayesian partition modelling performs similarly in localizing the causal allele while yielding lower false-positive rates. Also, the method is computationally quicker than other multi-marker approaches. We present an application to real genotype data from the CYP2D6 gene region, which has a confirmed role in drug metabolism, where we succeed in mapping the location of the susceptibility variant within a small error.

Author Summary

Genetic association studies offer great promise in dissecting the genetic contribution to complex diseases. The underlying idea of such studies is to search for genetic variants along the genome that appear to be associated with a trait of interest, e.g., disease status for a binary trait. One then proceeds by genotyping unrelated individuals at several marker sites, searching for positions where single markers or combinations of multiple markers on the paternally and maternally inherited chromosomes (or haplotypes) appear to discriminate among affected and unaffected individuals, flagging genomic regions that may harbour disease susceptibility variants. The statistical analysis of such studies, however, poses several challenges, such as multiplicity and false-positives issue, due to the large number of markers considered. Focusing on case-control studies, we present a novel evolution-based Bayesian partition model that clusters haplotypes with similar disease risks. The novelty of this approach lies in the use of perfect phylogenies, which offers a sensible and computationally efficient approximation of the ancestry of a sample of chromosomes. We show that the incorporation of phylogenetic information leads to low false-positive rates, while our model fitting offers computational advantages over similar recently proposed coalescent-based haplotype clustering methods.

doi:10.1371/journal.pgen.0030111

PMCID: PMC1913101
PMID: 17616979

Background

Some distance methods are among the most commonly used methods for reconstructing phylogenetic trees from sequence data. The input to a distance method is a distance matrix, containing estimated pairwise distances between all pairs of taxa. Distance methods themselves are often fast, e.g., the famous and popular Neighbor Joining (NJ) algorithm reconstructs a phylogeny of n taxa in time O(n3). Unfortunately, the fastest practical algorithms known for Computing the distance matrix, from n sequences of length l, takes time proportional to l·n2. Since the sequence length typically is much larger than the number of taxa, the distance estimation is the bottleneck in phylogeny reconstruction. This bottleneck is especially apparent in reconstruction of large phylogenies or in applications where many trees have to be reconstructed, e.g., bootstrapping and genome wide applications.

Results

We give an advanced algorithm for Computing the number of mutational events between DNA sequences which is significantly faster than both Phylip and Paup. Moreover, we give a new method for estimating pairwise distances between sequences which contain ambiguity Symbols. This new method is shown to be more accurate as well as faster than earlier methods.

Conclusion

Our novel algorithm for Computing distance estimators provides a valuable tool in phylogeny reconstruction. Since the running time of our distance estimation algorithm is comparable to that of most distance methods, the previous bottleneck is removed. All distance methods, such as NJ, require a distance matrix as input and, hence, our novel algorithm significantly improves the overall running time of all distance methods. In particular, we show for real world biological applications how the running time of phylogeny reconstruction using NJ is improved from a matter of hours to a matter of seconds.

doi:10.1186/1471-2105-8-89

PMCID: PMC1831791
PMID: 17355623

Background

The human leukocyte antigen system (HLA) contains many highly variable genes. HLA genes play an important role in the human immune system, and HLA gene matching is crucial for the success of human organ transplantations. Numerous studies have demonstrated that variation in HLA genes is associated with many autoimmune, inflammatory and infectious diseases. However, typing HLA genes by serology or PCR is time consuming and expensive, which limits large-scale studies involving HLA genes. Since it is much easier and cheaper to obtain single nucleotide polymorphism (SNP) genotype data, accurate computational algorithms to infer HLA gene types from SNP genotype data are in need. To infer HLA types from SNP genotypes, the first step is to infer SNP haplotypes from genotypes. However, for the same SNP genotype data set, the haplotype configurations inferred by different methods are usually inconsistent, and it is often difficult to decide which one is true.

Results

In this paper, we design an accurate HLA gene type inference algorithm by utilizing SNP genotype data from pedigrees, known HLA gene types of some individuals and the relationship between inferred SNP haplotypes and HLA gene types. Given a set of haplotypes inferred from the genotypes of a population consisting of many pedigrees, the algorithm first constructs a weighted similarity graph based on a new haplotype similarity measure and derives constraint edges from known HLA gene types. Based on the principle that different HLA gene alleles should have different background haplotypes, the algorithm searches for an optimal labeling of all the haplotypes with unknown HLA gene types such that the total weight among the same HLA gene types is maximized. To deal with ambiguous haplotype solutions, we use a genetic algorithm to select haplotype configurations that tend to maximize the same optimization criterion. Our experiments on a previously typed subset of the HapMap data show that the algorithm is highly accurate, achieving an accuracy of 96% for gene HLA-A, 95% for HLA-B, 97% for HLA-C, 84% for HLA-DRB1, 98% for HLA-DQA1 and 97% for HLA-DQB1 in a leave-one-out test.

Conclusions

Our algorithm can infer HLA gene types from neighboring SNP genotype data accurately. Compared with a recent approach on the same input data, our algorithm achieved a higher accuracy. The code of our algorithm is available to the public for free upon request to the corresponding authors.

doi:10.1186/1471-2105-11-S11-S10

PMCID: PMC3024871
PMID: 21172045

Background

The identification of functionally important residue positions is an important task of computational biology. Methods of correlation analysis allow for the identification of pairs of residue positions, whose occupancy is mutually dependent due to constraints imposed by protein structure or function. A common measure assessing these dependencies is the mutual information, which is based on Shannon’s information theory that utilizes probabilities only. Consequently, such approaches do not consider the similarity of residue pairs, which may degrade the algorithm’s performance. One typical algorithm is H2r, which characterizes each individual residue position k by the conn(k)-value, which is the number of significantly correlated pairs it belongs to.

Results

To improve specificity of H2r, we developed a revised algorithm, named H2rs, which is based on the von Neumann entropy (vNE). To compute the corresponding mutual information, a matrix A is required, which assesses the similarity of residue pairs. We determined A by deducing substitution frequencies from contacting residue pairs observed in the homologs of 35 809 proteins, whose structure is known. In analogy to H2r, the enhanced algorithm computes a normalized conn(k)-value. Within the framework of H2rs, only statistically significant vNE values were considered. To decide on significance, the algorithm calculates a p-value by performing a randomization test for each individual pair of residue positions. The analysis of a large in silico testbed demonstrated that specificity and precision were higher for H2rs than for H2r and two other methods of correlation analysis. The gain in prediction quality is further confirmed by a detailed assessment of five well-studied enzymes. The outcome of H2rs and of a method that predicts contacting residue positions (PSICOV) overlapped only marginally. H2rs can be downloaded from http://www-bioinf.uni-regensburg.de.

Conclusions

Considering substitution frequencies for residue pairs by means of the von Neumann entropy and a p-value improved the success rate in identifying important residue positions. The integration of proven statistical concepts and normalization allows for an easier comparison of results obtained with different proteins. Comparing the outcome of the local method H2rs and of the global method PSICOV indicates that such methods supplement each other and have different scopes of application.

doi:10.1186/1471-2105-15-118

PMCID: PMC4021312
PMID: 24766829

We present methods to construct phylogenetic models of tumor progression at the cellular level that include copy number changes at the scale of single genes, entire chromosomes, and the whole genome. The methods are designed for data collected by fluorescence in situ hybridization (FISH), an experimental technique especially well suited to characterizing intratumor heterogeneity using counts of probes to genetic regions frequently gained or lost in tumor development. Here, we develop new provably optimal methods for computing an edit distance between the copy number states of two cells given evolution by copy number changes of single probes, all probes on a chromosome, or all probes in the genome. We then apply this theory to develop a practical heuristic algorithm, implemented in publicly available software, for inferring tumor phylogenies on data from potentially hundreds of single cells by this evolutionary model. We demonstrate and validate the methods on simulated data and published FISH data from cervical cancers and breast cancers. Our computational experiments show that the new model and algorithm lead to more parsimonious trees than prior methods for single-tumor phylogenetics and to improved performance on various classification tasks, such as distinguishing primary tumors from metastases obtained from the same patient population.

Author Summary

Cancer is an evolutionary system whose growth and development is attributed to aberrations in well-known genes and to cancer-type specific genomic imbalances. Here, we present methods for reconstructing the evolution of individual tumors based on cell-to-cell variations between copy numbers of targeted regions of the genome. The methods are designed to work with fluorescence in situ hybridization (FISH), a technique that allows one to profile copy number changes in potentially thousands of single cells per study. Our work advances the prior art by developing theory and practical algorithms for building evolutionary trees of single tumors that can model gain or loss of genetic regions at the scale of single genes, whole chromosomes, or the entire genome, all common events in tumor evolution. We apply these methods on simulated and real tumor data to demonstrate substantial improvements in tree-building accuracy and in our ability to accurately classify tumors from their inferred evolutionary models. The newly developed algorithms have been released through our publicly available software, FISHtrees.

doi:10.1371/journal.pcbi.1003740

PMCID: PMC4117424
PMID: 25078894

Single nucleotide polymorphisms (SNPs) play a fundamental role in human genetic variation and are used in medical diagnostics, phylogeny construction, and drug design. They provide the highest-resolution genetic fingerprint for identifying disease associations and human features. Haplotypes are regions of linked genetic variants that are closely spaced on the genome and tend to be inherited together. Genetics research has revealed SNPs within certain haplotype blocks that introduce few distinct common haplotypes into most of the population. Haplotype block structures are used in association-based methods to map disease genes. In this paper, we propose an efficient algorithm for identifying haplotype blocks in the genome. In chromosomal haplotype data retrieved from the HapMap project website, the proposed algorithm identified longer haplotype blocks than an existing algorithm. To enhance its performance, we extended the proposed algorithm into a parallel algorithm that copies data in parallel via the Hadoop MapReduce framework. The proposed MapReduce-paralleled combinatorial algorithm performed well on real-world data obtained from the HapMap dataset; the improvement in computational efficiency was proportional to the number of processors used.

doi:10.3390/ijms16011096

PMCID: PMC4307292
PMID: 25569088

SNPs; haplotype; cloud computing; parallel processing; MapReduce

With the advances in high-throughput genotyping technology, the study of quantitative trait loci (QTL) has emerged as a promising tool to understand the genetic basis of complex traits. Methodology development for the study of QTL recently has attracted significant research attention. Local phylogeny-based methods have been demonstrated to be powerful tools for uncovering significant associations between phenotypes and single-nucleotide polymorphism markers. However, most existing methods are designed for homozygous genotypes, and a separate haplotype reconstruction step is often needed to resolve heterozygous genotypes. This approach has limited power to detect nonadditive genetic effects and imposes an extensive computational burden. In this article, we propose a new method, HTreeQA, that uses a tristate semi-perfect phylogeny tree to approximate the perfect phylogeny used in existing methods. The semi-perfect phylogeny trees are used as high-level markers for association study. HTreeQA uses the genotype data as direct input without phasing. HTreeQA can handle complex local population structures. It is suitable for QTL mapping on any mouse populations, including the incipient Collaborative Cross lines. Applied HTreeQA, significant QTLs are found for two phenotypes of the PreCC lines, white head spot and running distance at day 5/6. These findings are consistent with known genes and QTL discovered in independent studies. Simulation studies under three different genetic models show that HTreeQA can detect a wider range of genetic effects and is more efficient than existing phylogeny-based approaches. We also provide rigorous theoretical analysis to show that HTreeQA has a lower error rate than alternative methods.

doi:10.1534/g3.111.001768

PMCID: PMC3284325
PMID: 22384396

phylogeny; quantitative trait loci (QTL); Mouse Collaborative Cross; Mouse Genetic Resource

Background

SNP genotyping arrays have been developed to characterize single-nucleotide polymorphisms (SNPs) and DNA copy number variations (CNVs). Nonparametric and model-based statistical algorithms have been developed to detect CNVs from SNP data using the marker intensities. However, these algorithms lack specificity to detect small CNVs owing to the high false positive rate when calling CNVs based on the intensity values. Therefore, the resulting association tests lack power even if the CNVs affecting disease risk are common. An alternative procedure called PennCNV uses information from both the marker intensities as well as the genotypes and therefore has increased sensitivity.

Results

By using the hidden Markov model (HMM) implemented in PennCNV to derive the probabilities of different copy number states which we subsequently used in a logistic regression model, we developed a new genome-wide algorithm to detect CNV associations with diseases. We compared this new method with association test applied to the most probable copy number state for each individual that is provided by PennCNV after it performs an initial HMM analysis followed by application of the Viterbi algorithm, which removes information about copy number probabilities. In one of our simulation studies, we showed that for large CNVs (number of SNPs ≥ 10), the association tests based on PennCNV calls gave more significant results, but the new algorithm retained high power. For small CNVs (number of SNPs <10), the logistic algorithm provided smaller average p-values (e.g., p = 7.54e - 17 when relative risk RR = 3.0) in all the scenarios and could capture signals that PennCNV did not (e.g., p = 0.020 when RR = 3.0). From a second set of simulations, we showed that the new algorithm is more powerful in detecting disease associations with small CNVs (number of SNPs ranging from 3 to 5) under different penetrance models (e.g., when RR = 3.0, for relatively weak signals, power = 0.8030 comparing to 0.2879 obtained from the association tests based on PennCNV calls). The new method was implemented in software GWCNV. It is freely available at http://gwcnv.sourceforge.net, distributed under a GPL license.

Conclusions

We conclude that the new algorithm is more sensitive and can be more powerful in detecting CNV associations with diseases than the existing HMM algorithm, especially when the CNV association signal is weak and a limited number of SNPs are located in the CNV.

doi:10.1186/1471-2105-12-331

PMCID: PMC3173460
PMID: 21827692