Black box variational inference has consistently produced impressive empirical results. Convergence guarantees require that the variational objective exhibits specific structural properties and that the noise of the gradient estimator can be controlled. In this work we study the smoothness and the variance of the gradient estimator for location-scale variational families with non-linear covariance parameterizations. Specifically, we derive novel theoretical results for the popular exponential covariance parameterization and tighter gradient variance bounds for the softplus parameterization. These results reveal the benefits of using non-linear scale parameterizations on large scale datasets. With a non-linear scale parameterization, the smoothness constant of the variational objective and the upper bound on the gradient variance decrease as the scale parameter becomes smaller. Learning posterior approximations with small scales is essential in Bayesian statistics with sufficient amount of data, since under appropriate assumptions, the posterior distribution is known to contract around the parameter of interest as the sample size increases. We validate our theoretical findings through empirical analysis on several large-scale datasets, underscoring the importance of non-linear parameterizations.

We cast the resampling step in particle filters (PFs) as a variational inference problem, resulting in a new class of resampling schemes: variational resampling. Variational resampling is flexible as it allows for choices of 1) divergence to minimize, 2) target distribution to input to the divergence, and 3) divergence minimization algorithm. With this novel application of VI to particle filters, variational resampling further unifies these two powerful and popular methodologies. We construct two variational resamplers that replicate particles in order to maximize lower bounds with respect to two different target measures. We benchmark our variational resamplers on challenging smoothing tasks, outperforming PFs that implement the state-of-the-art resampling schemes.

Mixture variational distributions in black box variational inference (BBVI) have demonstrated impressive results in challenging density estimation tasks. However, currently scaling the number of mixture components can lead to a linear increase in the number of learnable parameters and a quadratic increase in inference time due to the evaluation of the evidence lower bound (ELBO). Our two key contributions address these limitations. First, we introduce the novel Multiple Importance Sampling Variational Autoencoder (MISVAE), which amortizes the mapping from input to mixture-parameter space using one-hot encodings. Fortunately, with MISVAE, each additional mixture component incurs a negligible increase in network parameters. Second, we construct two new estimators of the ELBO for mixtures in BBVI, enabling a tremendous reduction in inference time with marginal or even improved impact on performance. Collectively, our contributions enable scalability to hundreds of mixture components and provide superior estimation performance in shorter time, with fewer network parameters compared to previous Mixture VAEs. Experimenting with MISVAE, we achieve astonishing, SOTA results on MNIST. Furthermore, we empirically validate our estimators in other BBVI settings, including Bayesian phylogenetic inference, where we improve inference times for the SOTA mixture model on eight data sets.

Feature selection is a crucial task in settings where data is high-dimensional or acquiring the full set of features is costly. Recent developments in neural network-based embedded feature selection show promising results across a wide range of applications. Concrete Autoencoders (CAEs), considered state-of-the-art in embedded feature selection, may struggle to achieve stable joint optimization, hurting their training time and generalization. In this work, we identify that this instability is correlated with the CAE learning duplicate selections. To remedy this, we propose a simple and effective improvement: Indirectly Parameterized CAEs (IP-CAEs). IP-CAEs learn an embedding and a mapping from it to the Gumbel-Softmax distributions’ parameters. Despite being simple to implement, IP-CAE exhibits significant and consistent improvements over CAE in both generalization and training time across several datasets for reconstruction and classification. Unlike CAE, IP-CAE effectively leverages non-linear relationships and does not require retraining the jointly optimized decoder. Furthermore, our approach is, in principle, generalizable to Gumbel-Softmax distributions beyond feature selection.

MOTIVATION: Phylogenetic reconstruction is a fundamental problem in computational biology. The Neighbor Joining (NJ) algorithm offers an efficient distance-based solution to this problem, which often serves as the foundation for more advanced statistical methods. Despite prior efforts to enhance the speed of NJ, the computation of the n2 entries of the distance matrix, where n is the number of phylogenetic tree leaves, continues to pose a limitation in scaling NJ to larger datasets. RESULTS: In this work, we propose a new algorithm which does not require computing a dense distance matrix. Instead, it dynamically determines a sparse set of at most O(n log n) distance matrix entries to be computed in its basic version, and up to O(n log 2n) entries in an enhanced version. We show by experiments that this approach reduces the execution time of NJ for large datasets, with a trade-off in accuracy. AVAILABILITY AND IMPLEMENTATION: Sparse Neighbor Joining is implemented in Python and freely available at https://github.com/kurtsemih/SNJ.

MOTIVATION: Copy number variations (CNVs) are common genetic alterations in tumour cells. The delineation of CNVs holds promise for enhancing our comprehension of cancer progression. Moreover, accurate inference of CNVs from single-cell sequencing data is essential for unravelling intratumoral heterogeneity. However, existing inference methods face limitations in resolution and sensitivity. RESULTS: To address these challenges, we present CopyVAE, a deep learning framework based on a variational autoencoder architecture. Through experiments, we demonstrated that CopyVAE can accurately and reliably detect CNVs from data obtained using single-cell RNA sequencing. CopyVAE surpasses existing methods in terms of sensitivity and specificity. We also discussed CopyVAE's potential to advance our understanding of genetic alterations and their impact on disease advancement. AVAILABILITY AND IMPLEMENTATION: CopyVAE is implemented and freely available under MIT license at https://github.com/kurtsemih/copyVAE.

Cell lineage tree reconstruction methods are developed for various tasks, such as investigating the development, differentiation, and cancer progression. Single-cell sequencing technologies enable more thorough analysis with higher resolution. We present Scuphr, a distance-based cell lineage tree reconstruction method using bulk and single-cell DNA sequencing data from healthy tissues. Common challenges of single-cell DNA sequencing, such as allelic dropouts and amplification errors, are included in Scuphr. Scuphr computes the distance between cell pairs and reconstructs the lineage tree using the neighbor-joining algorithm. With its embarrassingly parallel design, Scuphr can do faster analysis than the state-of-the-art methods while obtaining better accuracy. The method's robustness is investigated using various synthetic datasets and a biological dataset of 18 cells.

In this paper, we show how the mixture components cooperate when they jointly adapt to maximize the ELBO. We build upon recent advances in the multiple and adaptive importance sampling literature. We then model the mixture components using separate encoder networks and show empirically that the ELBO is monotonically non-decreasing as a function of the number of mixture components. These results hold for a range of different VAE architectures on the MNIST, FashionMNIST, and CIFAR-10 datasets. In this work, we also demonstrate that increasing the number of mixture components improves the latent-representation capabilities of the VAE on both image and single-cell datasets. This cooperative behavior motivates that using Mixture VAEs should be considered a standard approach for obtaining more flexible variational approximations. Finally, Mixture VAEs are here, for the first time, compared and combined with normalizing flows, hierarchical models and/or the VampPrior in an extensive ablation study. Multiple of our Mixture VAEs achieve state-of-the-art log-likelihood results for VAE architectures on the MNIST and FashionMNIST datasets. The experiments are reproducible using our code, provided https://github.com/Lagergren-Lab/MixtureVAEs.

In variational inference (VI), the marginal log-likelihood is estimated using the standard evidence lower bound (ELBO), or improved versions as the importance weighted ELBO (IWELBO). We propose the multiple importance sampling ELBO (MISELBO), a versatile yet simple framework. MISELBO is applicable in both amortized and classical VI, and it uses ensembles, e.g., deep ensembles, of independently inferred variational approximations. As far as we are aware, the concept of deep ensembles in amortized VI has not previously been established. We prove that MISELBO provides a tighter bound than the average of standard ELBOs, and demonstrate empirically that it gives tighter bounds than the average of IWELBOs. MISELBO is evaluated in density-estimation experiments that include MNIST and several real-data phylogenetic tree inference problems. First, on the MNIST dataset, MISELBO boosts the density-estimation performances of a state-of-the-art model, nouveau VAE. Second, in the phylogenetic tree inference setting, our framework enhances a state-of-the-art VI algorithm that uses normalizing flows. On top of the technical benefits of MISELBO, it allows to unveil connections between VI and recent advances in the importance sampling literature, paving the way for further methodological advances. We provide our code at https://github.com/Lagergren-Lab/MISELBO.

Phylogenetics is a classical methodology in computational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of development of cancer. The exponential size of the tree space is unfortunately a formidable obstacle for current Bayesian phylogenetic inference using Markov chain Monte Carlo based methods since these rely on local operations. And although more recent variational inference (VI) based methods offer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy, a remarkably fast VI based algorithm for approximate posterior inference in an \textit{augmented tree space}. VaiPhy produces marginal log-likelihood estimates on par with the state-of-the-art methods on real data, and is considerably faster since it does not require auto-differentiation. Instead, VaiPhy combines coordinate ascent update equations with two novel sampling schemes: (i) \textit{SLANTIS}, a proposal distribution for tree topologies in the augmented tree space, and (ii) the \textit{JC sampler}, the, to the best of our knowledge, first ever scheme for sampling branch lengths directly from the popular Jukes-Cantor model. We compare VaiPhy in terms of density estimation and runtime. Additionally, we evaluate the reproducibility of the baselines. We provide our code on GitHub: \url{https://github.com/Lagergren-Lab/VaiPhy}.

MOTIVATION: DNA methylation plays a key role in a variety of biological processes. Recently, Nanopore long-read sequencing has enabled direct detection of these modifications. As a consequence, a range of computational methods have been developed to exploit Nanopore data for methylation detection. However, current approaches rely on a human-defined threshold to detect the methylation status of a genomic position and are not optimized to detect sites methylated at low frequency. Furthermore, most methods use either the Nanopore signals or the basecalling errors as the model input and do not take advantage of their combination. RESULTS: Here, we present DeepMP, a convolutional neural network-based model that takes information from Nanopore signals and basecalling errors to detect whether a given motif in a read is methylated or not. Besides, DeepMP introduces a threshold-free position modification calling model sensitive to sites methylated at low frequency across cells. We comprehensively benchmarked DeepMP against state-of-the-art methods on Escherichia coli, human and pUC19 datasets. DeepMP outperforms current approaches at read-based and position-based methylation detection across sites methylated at different frequencies in the three datasets. AVAILABILITY AND IMPLEMENTATION: DeepMP is implemented and freely available under MIT license at https://github.com/pepebonet/DeepMP. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Identifying the interrelations among cancer driver genes and the patterns in which the driver genes get mutated is critical for understanding cancer. In this paper, we study cross-sectional data from cohorts of tumors to identify the cancer-type (or subtype) specific process in which the cancer driver genes accumulate critical mutations. We model this mutation accumulation process using a tree, where each node includes a driver gene or a set of driver genes. A mutation in each node enables its children to have a chance of mutating. This model simultaneously explains the mutual exclusivity patterns observed in mutations in specific cancer genes (by its nodes) and the temporal order of events (by its edges). We introduce a computationally efficient dynamic programming procedure for calculating the likelihood of our noisy datasets and use it to build our Markov Chain Monte Carlo (MCMC) inference algorithm, ToMExO. Together with a set of engineered MCMC moves, our fast likelihood calculations enable us to work with datasets with hundreds of genes and thousands of tumors, which cannot be dealt with using available cancer progression analysis methods. We demonstrate our method's performance on several synthetic datasets covering various scenarios for cancer progression dynamics. Then, a comparison against two state-of-the-art methods on a moderate-size biological dataset shows the merits of our algorithm in identifying significant and valid patterns. Finally, we present our analyses of several large biological datasets, including colorectal cancer, glioblastoma, and pancreatic cancer. In all the analyses, we validate the results using a set of method-independent metrics testing the causality and significance of the relations identified by ToMExO or competing methods.

Identification of mutations of the genes that give cancer a selective advantage is an important step towards research and clinical objectives. As such, there has been a growing interest in developing methods for identification of driver genes and their temporal order within a single patient (intra-tumor) as well as across a cohort of patients (inter-tumor). In this paper, we develop a probabilistic model for tumor progression, in which the driver genes are clustered into several ordered driver pathways. We develop an efficient inference algorithm that exhibits favorable scalability to the number of genes and samples compared to a previously introduced ILP-based method. Adopting a probabilistic approach also allows principled approaches to model selection and uncertainty quantification. Using a large set of experiments on synthetic datasets, we demonstrate our superior performance compared to the ILP-based method. We also analyze two biological datasets of colorectal and glioblastoma cancers. We emphasize that while the ILP-based method puts many seemingly passenger genes in the driver pathways, our algorithm keeps focused on truly driver genes and outputs more accurate models for cancer progression.

A complex disease has, by definition, multiple genetic causes. In theory, these causes could be identified individually, but their identification will likely benefit from informed use of anticipated interactions between causes. In addition, characterizing and understanding interactions must be considered key to revealing the etiology of any complex disease. Large-scale collaborative efforts are now paving the way for comprehensive studies of interaction. As a consequence, there is a need for methods with a computational efficiency sufficient for modern data sets as well as for improvements of statistical accuracy and power. Another issue is that, currently, the relation between different methods for interaction inference is in many cases not transparent, complicating the comparison and interpretation of results between different interaction studies. In this paper we present computationally efficient tests of interaction for the complete family of generalized linear models (GLMs). The tests can be applied for inference of single or multiple interaction parameters, but we show, by simulation, that jointly testing the full set of interaction parameters yields superior power and control of false positive rate. Based on these tests we also describe how to combine results from multiple independent studies of interaction in a meta-analysis. We investigate the impact of several assumptions commonly made when modeling interactions. We also show that, across the important class of models with a full set of interaction parameters, jointly testing the interaction parameters yields identical results. Further, we apply our method to genetic data for cardiovascular disease. This allowed us to identify a putative interaction involved in Lp(a) plasma levels between two 'tag' variants in the LPA locus (p = 2.42 ⋅ 10-09) as well as replicate the interaction (p = 6.97 ⋅ 10-07). Finally, our meta-analysis method is used in a small (N = 16,181) study of interactions in myocardial infarction.

BACKGROUND: Lateral gene transfer (LGT) is an evolutionary process that has an important role in biology. It challenges the traditional binary tree-like evolution of species and is attracting increasing attention of the molecular biologists due to its involvement in antibiotic resistance. A number of attempts have been made to model LGT in the presence of gene duplication and loss, but reliably placing LGT events in the species tree has remained a challenge. RESULTS: In this paper, we propose probabilistic methods that samples reconciliations of the gene tree with a dated species tree and computes maximum a posteriori probabilities. The MCMC-based method uses the probabilistic model DLTRS, that integrates LGT, gene duplication, gene loss, and sequence evolution under a relaxed molecular clock for substitution rates. We can estimate posterior distributions on gene trees and, in contrast to previous work, the actual placement of potential LGT, which can be used to, e.g., identify "highways" of LGT. CONCLUSIONS: Based on a simulation study, we conclude that the method is able to infer the true LGT events on gene tree and reconcile it to the correct edges on the species tree in most cases. Applied to two biological datasets, containing gene families from Cyanobacteria and Molicutes, we find potential LGTs highways that corroborate other studies as well as previously undetected examples.

Cancer is a leading cause of death worldwide and represents one of the biggest biomedical research challenges of our time.Tumor progression is caused by somatic evolution of cell populations.Cancer cells expand because of the accumulation of selectively advantageous mutations, and expanding clones give rise to new cell subpopulations with increasingly higher somatic fitness (Fig 1).In the 1970s, Nowell and others established this somatic evolutionary view of cancer [1].Today, computational biologists have the opportunity to take advantage of large-scale molecular profiling data in order to carve out the principles of tumor evolution and to elucidate how it manifests across cancer types.Analogous to other evolutionary studies, mathematical modeling will be key to the success of understanding the somatic evolution of cancer [2].In general, cancer research involves a range of clinical, epidemiological, and molecular approaches, as well as mathematical and computational modeling.An early and very successful example of mathematical modeling was the work of Nordling [3] and of Armitage and Doll [4].In the 1950s, long before cancer genome data was available, they analyzed cancer incidence data and postulated, based on the observed age-incidence curves, that cancer is a multistep process.In search of these rate-limiting events, cancer progression was then linked to the accumulation of genomic alterations.Since then, the evolutionary perspective on cancer has proven useful in many instances, and the mathematical theory of cancer evolution has been developed much further.However, little clinical benefit could be gained from this approach so far.Much of evolutionary modeling in general, and of cancer in particular, has remained conceptual or qualitative, either because of strong simplifications in the interest of mathematical tractability or lack of informative data.Next-generation sequencing (NGS) technologies and their various applications have changed this situation fundamentally [5].Today, cancer cells can be analyzed in great detail at the molecular level, and tumor cell populations can be sampled extensively.Driven by this technological revolution, large numbers of high-dimensional molecular profiles of tumors, and even of individual cancer cells, are collected by cancer genome consortia, as well as by many individual labs.Large catalogs of cancer genomes, epigenomes, transcriptomes, proteomes, and other molecular profiles are generated to assess variation among tumors from different patients (intertumor heterogeneity) as well as among individual cells of single tumors (intratumor heterogeneity).These data hold the promise not only of new cancer biology discoveries but also of progress in cancer diagnostics and treatment.Analyzing these complex data and interpreting them in the context of ongoing somatic evolution, disease progression, and treatment response is a major challenge, and the prospects to

In many applications one wants to compute conditional probabilities given a Bayesian network. This inference problem is NP-hard in general but becomes tractable when the network has low tree-width. Since the inference problem is common in many application areas, we provide a practical algorithm for learning bounded tree-width Bayesian networks. We cast this problem as an integer linear program (ILP). The program can be solved by an anytime algorithm which provides upper bounds to assess the quality of the found solutions. A key component of our program is a novel integer linear formulation for bounding tree-width of a graph. Our tests clearly indicate that our approach works in practice, as our implementation was able to find an optimal or nearly optimal network for most of the data sets.

BACKGROUND: Distance methods are ubiquitous tools in phylogenetics. Their primary purpose may be to reconstruct evolutionary history, but they are also used as components in bioinformatic pipelines. However, poor computational efficiency has been a constraint on the applicability of distance methods on very large problem instances. RESULTS: We present fastphylo, a software package containing implementations of efficient algorithms for two common problems in phylogenetics: estimating DNA/protein sequence distances and reconstructing a phylogeny from a distance matrix. We compare fastphylo with other neighbor joining based methods and report the results in terms of speed and memory efficiency. CONCLUSIONS: Fastphylo is a fast, memory efficient, and easy to use software suite. Due to its modular architecture, fastphylo is a flexible tool for many phylogenetic studies.

Gene duplication is considered to be a major driving force in evolution that enables the genome of a species to acquire new functions. A reconciliation - a mapping of gene tree vertices to the edges or vertices of a species tree - explains where gene duplications have occurred on the species tree. In this study, we sample reconciliations from a posterior over reconciliations, gene trees, edge lengths and other parameters, given a species tree and gene sequences. We employ a Bayesian analysis tool, based on the probabilistic model DLRS that integrates gene duplication, gene loss and sequence evolution under a relaxed molecular clock for substitution rates, to obtain this posterior. By applying these methods, we perform a genome-wide analysis of a nine species dataset, OPTIC, and conclude that for many gene families, the most parsimonious reconciliation (MPR) - a reconciliation that minimizes the number of duplications - is far from the correct explanation of the evolutionary history. For the given dataset, we observe that approximately 19% of the sampled reconciliations are different from MPR. This is in clear contrast with previous estimates, based on simpler models and less realistic assumptions, according to which 98% of the reconciliations can be expected to be identical to MPR. We also generate heatmaps showing where in the species trees duplications have been most frequent during the evolution of these species.

BACKGROUND: PrIME-GenPhyloData is a suite of tools for creating realistic simulated phylogenetic trees, in particular for families of homologous genes. It supports generation of trees based on a birth-death process and--perhaps more interestingly--also supports generation of gene family trees guided by a known (synthetic or biological) species tree while accounting for events such as gene duplication, gene loss, and lateral gene transfer (LGT). The suite also supports a wide range of branch rate models enabling relaxation of the molecular clock. RESULT: Simulated data created with PrIME-GenPhyloData can be used for benchmarking phylogenetic approaches, or for characterizing models or model parameters with respect to biological data. CONCLUSION: The concept of tree-in-tree evolution can also be used to model, for instance, biogeography or host-parasite co-evolution.

SUMMARY: PrIME-DLRS (or colloquially: 'Delirious') is a phylogenetic software tool to simultaneously infer and reconcile a gene tree given a species tree. It accounts for duplication and loss events, a relaxed molecular clock and is intended for the study of homologous gene families, for example in a comparative genomics setting involving multiple species. PrIME-DLRS uses a Bayesian MCMC framework, where the input is a known species tree with divergence times and a multiple sequence alignment, and the output is a posterior distribution over gene trees and model parameters. AVAILABILITY AND IMPLEMENTATION: PrIME-DLRS is available for Java SE 6+ under the New BSD License, and JAR files and source code can be downloaded from http://code.google.com/p/jprime/. There is also a slightly older C++ version available as a binary package for Ubuntu, with download instructions at http://prime.sbc.su.se. The C++ source code is available upon request. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: PrIME-DLRS is based on a sound probabilistic model (Åkerborg et al., 2009) and has been thoroughly validated on synthetic and biological datasets (Supplementary Material online).

Cancer has complex patterns of progression that include converging as well as diverging progressional pathways. Vogelstein's path model of colon cancer was a pioneering contribution to cancer research. Since then, several attempts have been made at obtaining mathematical models of cancer progression, devising learning algorithms, and applying these to cross-sectional data. Beerenwinkel {\em et al.} provided, what they coined, EM-like algorithms for Oncogenetic Trees (OTs) and mixtures of such. Given the small size of current and future data sets, it is important to minimize the number of parameters of a model. For this reason, we too focus on tree-based models and introduce Hidden-variable Oncogenetic Trees (HOTs). In contrast to OTs, HOTs allow for errors in the data and thereby provide more realistic modeling. We also design global structural EM algorithms for learning HOTs and mixtures of HOTs (HOT-mixtures). The algorithms are global in the sense that, during the M-step, they find a structure that yields a global maximum of the expected complete log-likelihood rather than merely one that improves it. The algorithm for single HOTs performs very well on reasonable-sized data sets, while that for HOT-mixtures requires data sets of sizes obtainable only with tomorrow's more cost-efficient technologies.

The incongruency between a gene tree and a corresponding species tree can be attributed to evolutionary events such as gene duplication and gene loss. This paper describes a combinatorial model where so-called DTL-scenarios are used to explain the differences between a gene tree and a corresponding species tree taking into account gene duplications, gene losses, and lateral gene transfers (also known as horizontal gene transfers). The reasonable biological constraint that a lateral gene transfer may only occur between contemporary species leads to the notion of acyclic DTL-scenarios. Parsimony methods are introduced by defining appropriate optimization problems. We show that finding most parsimonious acyclic DTL-scenarios is NP-hard. However, by dropping the condition of acyclicity, the problem becomes tractable, and we provide a dynamic programming algorithm as well as a fixed-parameter tractable algorithm for finding most parsimonious DTL-scenarios.

BACKGROUND: Several bioinformatic approaches have previously been used to find novel sites of ADAR mediated A-to-I RNA editing in human. These studies have discovered thousands of genes that are hyper-edited in their non-coding intronic regions, especially in alu retrotransposable elements, but very few substrates that are site-selectively edited in coding regions. Known RNA edited substrates suggest, however, that site selective A-to-I editing is particularly important for normal brain development in mammals. RESULTS: We have compiled a screen that enables the identification of new sites of site-selective editing, primarily in coding sequences. To avoid hyper-edited repeat regions, we applied our screen to the alu-free mouse genome. Focusing on the mouse also facilitated better experimental verification. To identify candidate sites of RNA editing, we first performed an explorative screen based on RNA structure and genomic sequence conservation. We further evaluated the results of the explorative screen by determining which transcripts were enriched for A-G mismatches between the genomic template and the expressed sequence since the editing product, inosine (I), is read as guanosine (G) by the translational machinery. For expressed sequences, we only considered coding regions to focus entirely on re-coding events. Lastly, we refined the results from the explorative screen using a novel scoring scheme based on characteristics for known A-to-I edited sites. The extent of editing in the final candidate genes was verified using total RNA from mouse brain and 454 sequencing. CONCLUSIONS: Using this method, we identified and confirmed efficient editing at one site in the Gabra3 gene. Editing was also verified at several other novel sites within candidates predicted to be edited. Five of these sites are situated in genes coding for the neuron-specific RNA binding proteins HuB and HuD.

Phylogeny is both a fundamental tool in biology and a rich source of fascinating modeling and algorithmic problems. Today's wealth of sequenced genomes makes it increasingly important to understand evolutionary events such as duplications, losses, transpositions, inversions, lateral transfers, and domain shuffling. We focus on the gene duplication event, that constitutes a major force in the creation of genes with new function [Ohno 1970; Lynch and Force 2000] and, thereby also, of biodiversity. We introduce the probabilistic gene evolution model , which describes how a gene tree evolves within a given species tree with respect to speciation, gene duplication, and gene loss. The actual relation between gene tree and species tree is captured by a reconciliation, a concept which we generalize for more expressiveness. The model is a canonical generalization of the classical linear birth-death process, obtained by replacing the interval where the process takes place by a tree. For the gene evolution model , we derive efficient algorithms for some associated probability distributions: the probability of a reconciled tree, the probability of a gene tree, the maximum probability reconciliation, the posterior probability of a reconciliation, and sampling reconciliations with respect to the posterior probability. These algorithms provides the basis for several applications, including species tree construction, reconciliation analysis, orthology analysis, biogeography, and host-parasite co-evolution.

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.

BACKGROUND: Evolutionary processes, such as gene family evolution or parasite-host co-speciation, can often be viewed as a tree evolving inside another tree. Relating two given trees under such a constraint is known as reconciling them. Adequate software tools for generating illustrations of tree reconciliations are instrumental for presenting and communicating results and ideas regarding these phenomena. Available visualization tools have been limited to illustrations of the most parsimonious reconciliation. However, there exists a plethora of biologically relevant non-parsimonious reconciliations. Illustrations of these general reconciliations may not be achieved without manual editing. RESULTS: We have developed a new reconciliation viewer, primetv. It is a simple and compact visualization program that is the first automatic tool for illustrating general tree reconciliations. It reads reconciled trees in an extended Newick format and outputs them as tree-within-tree illustrations in a range of graphic formats. Output attributes, such as colors and layout, can easily be adjusted by the user. To enhance the construction of input to primetv, two helper programs, readReconciliation and reconcile, accompany primetv. Detailed examples of all programs' usage are provided in the text. For the casual user a web-service provides a simple user interface to all programs. CONCLUSION: With primetv, the first visualization tool for general reconciliations, illustrations of trees-within-trees are easy to produce. Because it clarifies and accentuates an underlying structure in a reconciled tree, e.g., the impact of a species tree on a gene-family phylogeny, it will enhance scientific presentations as well as pedagogic illustrations in an educational setting. primetv is available at http://prime.sbc.su.se/primetv, both as a standalone command-line tool and as a web service. The software is distributed under the GNU General Public License.

According to current estimates there exist about 20,000 pseudogenes in a mammalian genome. The vast majority of these are disabled and nonfunctional copies of protein-coding genes which, therefore, evolve neutrally. Recent findings that a Makorin1 pseudogene, residing on mouse Chromosome 5, is, indeed, in vivo vital and also evolutionarily preserved, encouraged us to conduct a genome-wide survey for other functional pseudogenes in human, mouse, and chimpanzee. We identify to our knowledge the first examples of conserved pseudogenes common to human and mouse, originating from one duplication predating the human-mouse species split and having evolved as pseudogenes since the species split. Functionality is one possible way to explain the apparently contradictory properties of such pseudogene pairs, i.e., high conservation and ancient origin. The hypothesis of functionality is tested by comparing expression evidence and synteny of the candidates with proper test sets. The tests suggest potential biological function. Our candidate set includes a small set of long-lived pseudogenes whose unknown potential function is retained since before the human-mouse species split, and also a larger group of primate-specific ones found from human-chimpanzee searches. Two processed sequences are notable, their conservation since the human-mouse split being as high as most protein-coding genes; one is derived from the protein Ataxin 7-like 3 (ATX7NL3), and one from the Spinocerebellar ataxia type 1 protein (ATX1). Our approach is comparative and can be applied to any pair of species. It is implemented by a semi-automated pipeline based on cross-species BLAST comparisons and maximum-likelihood phylogeny estimations. To separate pseudogenes from protein-coding genes, we use standard methods, utilizing in-frame disablements, as well as a probabilistic filter based on Ka/Ks ratios.

Gene tree and species tree reconstruction, orthology analysis and reconciliation, are problems important in multigenome-based comparative genomics and biology in general. In the present paper, we advance the frontier of these areas in several respects and provide important computational tools. First, exact algorithms are given for several probabilistic reconciliation problems with respect to the probabilistic gene evolution model, previously developed by the authors. Until now, those problems were solved by MCMC estimation algorithms. Second, we extend the gene evolution model to the gene sequence evolution model, by including sequence evolution. Third, we develop MCMC algorithms for the gene sequence evolution model that, given gene sequence data allows: (1) orthology analysis, reconciliation analysis, and gene tree reconstruction, w.r.t. a species tree, that balances a likely/unlikely reconciliation and a likely/unlikely gene tree and (2) species tree reconstruction that balance a likely/unlikely reconciliation and a likely/unlikely gene trees. These MCMC algorithms take advantage of the exact algorithms for the gene evolution model. We have successfully tested our dynamical programming algorithms on real data for a biogeography problem. The MCMC algorithms perform very well both on synthetic and biological data.

This paper introduces a combinatorial model that incorporates duplication events as well as lateral gene transfer events (a.k.a. horizontal gene transfer events). To the best of our knowledge, this is the first such model containing both of these events. A so-called dt-scenario is used to explain differences between a gene tree T and species trees S. The model is biologically as well as mathematically sound. Among other biological considerations, the model respects the partial order of evolution implied by S by demanding that the dt-scenarios are We present fixed parameter tractable algorithms that count the minimum number of duplications and lateral transfers, and more generally can compute the set of pairs (t,d) where d is the minimum number of duplications required by any explanation that requires t lateral transfers. This allows us to also compute a weighted parsimony score. We also show how gene loss events can be incorporated into our model. We also give an $NP$-completeness proof which suggests that the intractability is due to the demand that the dt-scenarios be acyclic. When this condition is removed, we can show that the problem is computable in polynomial time via dynamic programming. By generating synthetic gene and species trees via a birth-death process, we explored the capacity of our algorithms to faithfully reconstruct the actual number of events taken place. The results are positive.

Radiation hybrid (RH) mapping is a technique for constructing a physical map describing the locations of n markers on a chromosome of an organism. In [J. Comput. Biol., 4 (1997), pp. 517--533], Ben-Dor and Chor presented new algorithms for the RH problem and gave the first performance guarantees for such algorithms. We improve the lower bounds on the number of experiments in a way that is sufficient for two of these algorithms to give a correct ordering of the markers with high probability. Not only are the new bounds tighter, but our analysis also captures to a much higher extent how the bounds depend on the actual arrangement of the markers. Furthermore, we modify the two algorithms to utilize RH mapping data produced with several radiation intensities. We show that the new algorithms are almost insensitive to the problem of using the correct intensity.

A parameterized version of the Steiner tree problem in phylogeny is defined, where the parameter measures the amount by which a phylogeny differs from "perfection." This problem is shown to be solvable in polynomial time for any fixed value of the parameter.

This paper develops a model for lateral gene transfer events (a.k.a. horizontal gene transfer events) between a set of gene trees T1, T2, …, Tk and a species tree S. To the best of our knowledge, this model possesses a higher degree of biological and mathematical soundness than any other model proposed in the literature. Among other biological considerations, the model respects the partial order of evolution implied by S. Within our model, we identify an activity parameter that measures the number of genes that are allowed to be simultaneously active in the genome of a taxa and show that finding the most parsimonious scenario that reconciles the disagreeing gene trees with the species tree is doable in polynomial time when the activity level and number of transfers are small, but intractable in general. To the best of our knowledge, all other models proposed in the literature assume implicitly that the activity is one. Finally, using a dataset of bacterial gene sequences from [4], our implementations found 5 optimal scenarios; one of which is the scenario proposed by the authors in [4].

We consider the problem of constructing a species tree given a number of gene trees. In the frameworks introduced by Goodman et al. [3], Page [10], and Guigó, Muchnik, and Smith [5] this is formulated as an optimization problem; namely, that of finding the species tree requiring the minimum number of duplications and/ or losses in order to explain the gene trees.

We show that a set of finite graphs of tree-width at most k is recognizable (with respect to the algebra of graphs with an unbounded number of sources) if and only if it is recognizable with respect to the algebra of graphs of tree-width at most k with at most k sources.

An efficient parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel random access machine (CRCW PRAM). This result can be used to construct efficient parallel algorithms for three important classes of problems: MS (monadic second-order) properties, linear EMS (extended monadic second-order) extremum problems, and enumeration problems for MS properties, for graphs of tree width at most w. The sequential time complexity of the tree-composition problem for fixed w is improved, and some implications for this improvement are stated.>