Is multiple-sequence alignment required for accurate inference of phylogeny?

A survey of k-mer methods and applications in bioinformatics

The rapid progression of genomics and proteomics has been driven by the advent of advanced sequencing technologies, large, diverse, and readily available omics datasets, and the evolution of computational data processing capabilities. The vast amount of data generated by these advancements necessitates efficient algorithms to extract meaningful information. K-mers serve as a valuable tool when working with large sequencing datasets, offering several advantages in computational speed and memory efficiency and carrying the potential for intrinsic biological functionality. This review provides an overview of the methods, applications, and significance of k-mers in genomic and proteomic data analyses, as well as the utility of absent sequences, including nullomers and nullpeptides, in disease detection, vaccine development, therapeutics, and forensic science. Therefore, the review highlights the pivotal role of k-mers in addressing current genomic and proteomic problems and underscores their potential for future breakthroughs in research.

An alignment-free method for detection of missing regions for phylogenetic analysis

Phylogenetic tree estimation using conventional approaches usually requires pairwise or multiple sequence alignment. However, sequence alignment has difficulties related to scalability and accuracy in case of long sequences such as whole genomes, low sequence identity, and in presence of genomic rearrangements. To address these issues, alignment-free approaches have been proposed. While these methods have demonstrated promising results, many of these lead to errors when regions are missing from the sequences of one or more species that are trivially detected in alignment-based methods. Here, we present an alignment-free method for detecting missing regions in sequences of species for which phylogeny is to be estimated. It is based on counts of k-mers and can be used to filter out k-mers belonging to regions in one species that are missing in one or more of the other species. We perform experiments with real and simulated datasets containing missing regions and find that it can successfully detect a large fraction of such k-mers and can lead to improvements in the estimated phylogenies. Our method can be used in k-mer based alignment-free phylogeny estimation methods to filter out k-mers corresponding to missing regions.

Quantifying the uncertainty of assembly-free genome-wide distance estimates and phylogenetic relationships using subsampling

Computing distance between two genomes without alignments or even access to assemblies has many downstream analyses. However, alignment-free methods, including in the fast-growing field of genome skimming, are hampered by a significant methodological gap. While accurate methods (many k-mer-based) for assembly-free distance calculation exist, measuring the uncertainty of estimated distances has not been sufficiently studied. In this paper, we show that bootstrapping, the standard non-parametric method of measuring estimator uncertainty, is not accurate for k-mer-based methods that rely on k-mer frequency profiles. Instead, we propose using subsampling (with no replacement) in combination with a correction step to reduce the variance of the inferred distribution. We show that the distribution of distances using our procedure matches the true uncertainty of the estimator. The resulting phylogenetic support values effectively differentiate between correct and incorrect branches and identify controversial branches that change across alignment-free and alignment-based phylogenies reported in the literature.

Multiple genome alignment in the telomere-to-telomere assembly era

With the arrival of telomere-to-telomere (T2T) assemblies of the human genome comes the computational challenge of efficiently and accurately constructing multiple genome alignments at an unprecedented scale. By identifying nucleotides across genomes which share a common ancestor, multiple genome alignments commonly serve as the bedrock for comparative genomics studies. In this review, we provide an overview of the algorithmic template that most multiple genome alignment methods follow. We also discuss prospective areas of improvement of multiple genome alignment for keeping up with continuously arriving high-quality T2T assembled genomes and for unlocking clinically-relevant insights.

Genome-wide alignment-free phylogenetic distance estimation under a no strand-bias model

While alignment has been the dominant approach for determining homology prior to phylogenetic inference, alignment-free methods can simplify the analysis, especially when analyzing genome-wide data. Furthermore, alignment-free methods present the only option for emerging forms of data, such as genome skims, which do not permit assembly. Despite the appeal, alignment-free methods have not been competitive with alignment-based methods in terms of accuracy. One limitation of alignment-free methods is their reliance on simplified models of sequence evolution such as Jukes-Cantor. If we can estimate frequencies of base substitutions in an alignment-free setting, we can compute pairwise distances under more complex models. However, since the strand of DNA sequences is unknown for many forms of genome-wide data, which arguably present the best use case for alignment-free methods, the most complex models that one can use are the so-called no strand-bias models. We show how to calculate distances under a four-parameter no strand-bias model called TK4 without relying on alignments or assemblies. The main idea is to replace letters in the input sequences and recompute Jaccard indices between k-mer sets. However, on larger genomes, we also need to compute the number of k-mer mismatches after replacement due to random chance as opposed to homology. We show in simulation that alignment-free distances can be highly accurate when genomes evolve under the assumed models and study the accuracy on assembled and unassembled biological data.

Availability and implementation

Our software is available open source at https://github.com/nishatbristy007/NSB.

Supplementary information

Supplementary data are available at Bioinformatics Advances online.

Alignment-Free Analysis of Whole-Genome Sequences From Symbiodiniaceae Reveals Different Phylogenetic Signals in Distinct Regions

Dinoflagellates of the family Symbiodiniaceae are predominantly essential symbionts of corals and other marine organisms. Recent research reveals extensive genome sequence divergence among Symbiodiniaceae taxa and high phylogenetic diversity hidden behind subtly different cell morphologies. Using an alignment-free phylogenetic approach based on sub-sequences of fixed length k (i.e. k-mers), we assessed the phylogenetic signal among whole-genome sequences from 16 Symbiodiniaceae taxa (including the genera of Symbiodinium, Breviolum, Cladocopium, Durusdinium and Fugacium) and two strains of Polarella glacialis as outgroup. Based on phylogenetic trees inferred from k-mers in distinct genomic regions (i.e. repeat-masked genome sequences, protein-coding sequences, introns and repeats) and in protein sequences, the phylogenetic signal associated with protein-coding DNA and the encoded amino acids is largely consistent with the Symbiodiniaceae phylogeny based on established markers, such as large subunit rRNA. The other genome sequences (introns and repeats) exhibit distinct phylogenetic signals, supporting the expected differential evolutionary pressure acting on these regions. Our analysis of conserved core k-mers revealed the prevalence of conserved k-mers (>95% core 23-mers among all 18 genomes) in annotated repeats and non-genic regions of the genomes. We observed 180 distinct repeat types that are significantly enriched in genomes of the symbiotic versus free-living Symbiodinium taxa, suggesting an enhanced activity of transposable elements linked to the symbiotic lifestyle. We provide evidence that representation of alignment-free phylogenies as dynamic networks enhances the ability to generate new hypotheses about genome evolution in Symbiodiniaceae. These results demonstrate the potential of alignment-free phylogenetic methods as a scalable approach for inferring comprehensive, unbiased whole-genome phylogenies of dinoflagellates and more broadly of microbial eukaryotes.

Accurate Inference of Tree Topologies from Multiple Sequence Alignments Using Deep Learning

Reconstructing the phylogenetic relationships between species is one of the most formidable tasks in evolutionary biology. Multiple methods exist to reconstruct phylogenetic trees, each with their own strengths and weaknesses. Both simulation and empirical studies have identified several "zones" of parameter space where accuracy of some methods can plummet, even for four-taxon trees. Further, some methods can have undesirable statistical properties such as statistical inconsistency and/or the tendency to be positively misleading (i.e. assert strong support for the incorrect tree topology). Recently, deep learning techniques have made inroads on a number of both new and longstanding problems in biological research. In this study, we designed a deep convolutional neural network (CNN) to infer quartet topologies from multiple sequence alignments. This CNN can readily be trained to make inferences using both gapped and ungapped data. We show that our approach is highly accurate on simulated data, often outperforming traditional methods, and is remarkably robust to bias-inducing regions of parameter space such as the Felsenstein zone and the Farris zone. We also demonstrate that the confidence scores produced by our CNN can more accurately assess support for the chosen topology than bootstrap and posterior probability scores from traditional methods. Although numerous practical challenges remain, these findings suggest that the deep learning approaches such as ours have the potential to produce more accurate phylogenetic inferences.

LMAP_S: Lightweight Multigene Alignment and Phylogeny eStimation

Background

Recent advances in genome sequencing technologies and the cost drop in high-throughput sequencing continue to give rise to a deluge of data available for downstream analyses. Among others, evolutionary biologists often make use of genomic data to uncover phenotypic diversity and adaptive evolution in protein-coding genes. Therefore, multiple sequence alignments (MSA) and phylogenetic trees (PT) need to be estimated with optimal results. However, the preparation of an initial dataset of multiple sequence file(s) (MSF) and the steps involved can be challenging when considering extensive amount of data. Thus, it becomes necessary the development of a tool that removes the potential source of error and automates the time-consuming steps of a typical workflow with high-throughput and optimal MSA and PT estimations.

Results

We introduce LMAP_S (Lightweight Multigene Alignment and Phylogeny eStimation), a user-friendly command-line and interactive package, designed to handle an improved alignment and phylogeny estimation workflow: MSF preparation, MSA estimation, outlier detection, refinement, consensus, phylogeny estimation, comparison and editing, among which file and directory organization, execution, manipulation of information are automated, with minimal manual user intervention. LMAP_S was developed for the workstation multi-core environment and provides a unique advantage for processing multiple datasets. Our software, proved to be efficient throughout the workflow, including, the (unlimited) handling of more than 20 datasets.

Conclusions

We have developed a simple and versatile LMAP_S package enabling researchers to effectively estimate multiple datasets MSAs and PTs in a high-throughput fashion. LMAP_S integrates more than 25 software providing overall more than 65 algorithm choices distributed in five stages. At minimum, one FASTA file is required within a single input directory. To our knowledge, no other software combines MSA and phylogeny estimation with as many alternatives and provides means to find optimal MSAs and phylogenies. Moreover, we used a case study comparing methodologies that highlighted the usefulness of our software. LMAP_S has been developed as an open-source package, allowing its integration into more complex open-source bioinformatics pipelines. LMAP_S package is released under GPLv3 license and is freely available at https://lmap-s.sourceforge.io/.

Graph Theory-Based Sequence Descriptors as Remote Homology Predictors

Alignment-free (AF) methodologies have increased in popularity in the last decades as alternative tools to alignment-based (AB) algorithms for performing comparative sequence analyses. They have been especially useful to detect remote homologs within the twilight zone of highly diverse gene/protein families and superfamilies. The most popular alignment-free methodologies, as well as their applications to classification problems, have been described in previous reviews. Despite a new set of graph theory-derived sequence/structural descriptors that have been gaining relevance in the detection of remote homology, they have been omitted as AF predictors when the topic is addressed. Here, we first go over the most popular AF approaches used for detecting homology signals within the twilight zone and then bring out the state-of-the-art tools encoding graph theory-derived sequence/structure descriptors and their success for identifying remote homologs. We also highlight the tendency of integrating AF features/measures with the AB ones, either into the same prediction model or by assembling the predictions from different algorithms using voting/weighting strategies, for improving the detection of remote signals. Lastly, we briefly discuss the efforts made to scale up AB and AF features/measures for the comparison of multiple genomes and proteomes. Alongside the achieved experiences in remote homology detection by both the most popular AF tools and other less known ones, we provide our own using the graphical-numerical methodologies, MARCH-INSIDE, TI2BioP, and ProtDCal. We also present a new Python-based tool (SeqDivA) with a friendly graphical user interface (GUI) for delimiting the twilight zone by using several similar criteria.

Alignment-free inference of hierarchical and reticulate phylogenomic relationships

We are amidst an ongoing flood of sequence data arising from the application of high-throughput technologies, and a concomitant fundamental revision in our understanding of how genomes evolve individually and within the biosphere. Workflows for phylogenomic inference must accommodate data that are not only much larger than before, but often more error prone and perhaps misassembled, or not assembled in the first place. Moreover, genomes of microbes, viruses and plasmids evolve not only by tree-like descent with modification but also by incorporating stretches of exogenous DNA. Thus, next-generation phylogenomics must address computational scalability while rethinking the nature of orthogroups, the alignment of multiple sequences and the inference and comparison of trees. New phylogenomic workflows have begun to take shape based on so-called alignment-free (AF) approaches. Here, we review the conceptual foundations of AF phylogenetics for the hierarchical (vertical) and reticulate (lateral) components of genome evolution, focusing on methods based on k-mers. We reflect on what seems to be successful, and on where further development is needed.

Gilbert MT, Bafna V, Mirarab S. Skmer: assembly-free and alignment-free sample identification using genome skims

The ability to inexpensively describe taxonomic diversity is critical in this era of rapid climate and biodiversity changes. The recent genome-skimming approach extends current barcoding practices beyond short markers by applying low-pass sequencing and recovering whole organelle genomes computationally. This approach discards the nuclear DNA, which constitutes the vast majority of the data. In contrast, we suggest using all unassembled reads. We introduce an assembly-free and alignment-free tool, Skmer, to compute genomic distances between the query and reference genome skims. Skmer shows excellent accuracy in estimating distances and identifying the closest match in reference datasets.

A Not-So-Long Introduction to Computational Molecular Evolution

In this chapter, we give a not-so-long and self-contained introduction to computational molecular evolution. In particular, we present the emergence of the use of likelihood-based methods, review the standard DNA substitution models, and introduce how model choice operates. We also present recent developments in inferring absolute divergence times and rates on a phylogeny, before showing how state-of-the-art models take inspiration from diffusion theory to link population genetics, which traditionally focuses at a taxonomic level below that of the species, and molecular evolution. Although this is not a cookbook chapter, we try and point to popular programs and implementations along the way.

Phylogenetics Algorithms and Applications

Phylogenetics is a powerful approach in finding evolution of current day species. By studying phylogenetic trees, scientists gain a better understanding of how species have evolved while explaining the similarities and differences among species. The phylogenetic study can help in analysing the evolution and the similarities among diseases and viruses, and further help in prescribing their vaccines against them. This paper explores computational solutions for building phylogeny of species along with highlighting benefits of alignment-free methods of phylogenetics. The paper has also discussed the application of phylogenetic study in disease diagnosis and evolution.

Neisseria genomics: current status and future perspectives

High-throughput whole genome sequencing has unlocked a multitude of possibilities enabling members of the Neisseria genus to be examined with unprecedented detail, including the human pathogens Neisseria meningitidis and Neisseria gonorrhoeae. To maximise the potential benefit of this for public health, it is becoming increasingly important to ensure that this plethora of data are adequately stored, disseminated and made readily accessible. Investigations facilitating cross-species comparisons as well as the analysis of global datasets will allow differences among and within species and across geographic locations and different times to be identified, improving our understanding of the distinct phenotypes observed. Recent advances in high-throughput platforms that measure the transcriptome, proteome and/or epigenome are also becoming increasingly employed to explore the complexities of Neisseria biology. An integrated approach to the analysis of these is essential to fully understand the impact these may have in the Neisseria genus. This article reviews the current status of some of the tools available for next generation sequence analysis at the dawn of the ‘post-genomic’ era.

Homology-Aware Phylogenomics at Gigabase Scales

Obstacles to inferring species trees from whole genome data sets range from algorithmic and data management challenges to the wholesale discordance in evolutionary history found in different parts of a genome. Recent work that builds trees directly from genomes by parsing them into sets of small $k$-mer strings holds promise to streamline and simplify these efforts, but existing approaches do not account well for gene tree discordance. We describe a "seed and extend" protocol that finds nearly exact matching sets of orthologous $k$-mers and extends them to construct data sets that can properly account for genomic heterogeneity. Exploiting an efficient suffix array data structure, sets of whole genomes can be parsed and converted into phylogenetic data matrices rapidly, with contiguous blocks of $k$-mers from the same chromosome, gene, or scaffold concatenated as needed. Phylogenetic trees constructed from highly curated rice genome data and a diverse set of six other eukaryotic whole genome, transcriptome, and organellar genome data sets recovered trees nearly identical to published phylogenomic analyses, in a small fraction of the time, and requiring many fewer parameter choices. Our method's ability to retain local homology information was demonstrated by using it to characterize gene tree discordance across the rice genome, and by its robustness to the high rate of interchromosomal gene transfer found in several rice species.

Phylogenetic Tree Estimation With and Without Alignment: New Distance Methods and Benchmarking

Phylogenetic tree inference is a critical component of many systematic and evolutionary studies. The majority of these studies are based on the two-step process of multiple sequence alignment followed by tree inference, despite persistent evidence that the alignment step can lead to biased results. Here we present a two-part study that first presents PaHMM-Tree, a novel neighbor joining-based method that estimates pairwise distances without assuming a single alignment. We then use simulations to benchmark its performance against a wide-range of other phylogenetic tree inference methods, including the first comparison of alignment-free distance-based methods against more conventional tree estimation methods. Our new method for calculating pairwise distances based on statistical alignment provides distance estimates that are as accurate as those obtained using standard methods based on the true alignment. Pairwise distance estimates based on the two-step process tend to be substantially less accurate. This improved performance carries through to tree inference, where PaHMM-Tree provides more accurate tree estimates than all of the pairwise distance methods assessed. For close to moderately divergent sequence data we find that the two-step methods using statistical inference, where information from all sequences is included in the estimation procedure, tend to perform better than PaHMM-Tree, particularly full statistical alignment, which simultaneously estimates both the tree and the alignment. For deep divergences we find the alignment step becomes so prone to error that our distance-based PaHMM-Tree outperforms all other methods of tree inference. Finally, we find that the accuracy of alignment-free methods tends to decline faster than standard two-step methods in the presence of alignment uncertainty, and identify no conditions where alignment-free methods are equal to or more accurate than standard phylogenetic methods even in the presence of substantial alignment error. [Alignment-free; distance-based phylogenetics; pair Hidden Markov Models; phylogenetic inference; statistical alignment.].

Reconstructing Yeasts Phylogenies and Ancestors from Whole Genome Data

Phylogenetic studies aim to discover evolutionary relationships and histories. These studies are based on similarities of morphological characters and molecular sequences. Currently, widely accepted phylogenetic approaches are based on multiple sequence alignments, which analyze shared gene datasets and concatenate/coalesce these results to a final phylogeny with maximum support. However, these approaches still have limitations, and often have conflicting results with each other. Reconstructing ancestral genomes helps us understand mechanisms and corresponding consequences of evolution. Most existing genome level phylogeny and ancestor reconstruction methods can only process simplified real genome datasets or simulated datasets with identical genome content, unique genome markers, and limited types of evolutionary events. Here, we provide an alternative way to resolve phylogenetic problems based on analyses of real genome data. We use phylogenetic signals from all types of genome level evolutionary events, and overcome the conflicting issues existing in traditional phylogenetic approaches. Further, we build an automated computational pipeline to reconstruct phylogenies and ancestral genomes for two high-resolution real yeast genome datasets. Comparison results with recent studies and publications show that we reconstruct very accurate and robust phylogenies and ancestors. Finally, we identify and analyze the conserved syntenic blocks among reconstructed ancestral genomes and present yeast species.

Alignment-free sequence comparison: benefits, applications, and tools

Alignment-free sequence analyses have been applied to problems ranging from whole-genome phylogeny to the classification of protein families, identification of horizontally transferred genes, and detection of recombined sequences. The strength of these methods makes them particularly useful for next-generation sequencing data processing and analysis. However, many researchers are unclear about how these methods work, how they compare to alignment-based methods, and what their potential is for use for their research. We address these questions and provide a guide to the currently available alignment-free sequence analysis tools.

Computational analysis of nascent peptides that induce ribosome stalling and their proteomic distribution in Saccharomyces cerevisiae

Interactions between the ribosomal exit tunnel and the nascent peptide can affect translation elongation rates. While previous studies have already demonstrated the feasibility of such interactions, little is known about the nature of the stalling peptide sequences and their distribution in the proteome. Here we ask which peptide sequences tend to occupy the tunnel of stalled ribosomes and how they are distributed in the proteome. Using computational analysis of ribosome profiling data from S. cerevisiae, we identified for the first time dozens of short stalling peptide sequences and studied their statistical properties. We found that short peptide sequences associated with ribosome stalling tend significantly to be either over- or underrepresented in the proteome. We then showed that the stalling interactions may occur at different positions along the length of the tunnel, prominently close to the P-site. Our findings throw light on the determinants of nascent peptide-mediated ribosome stalling during translation elongation and support the novel conjecture that mRNA translation affects the proteomic distribution of short peptide sequences.

Diversification of Rosaceae since the Late Cretaceous based on plastid phylogenomics

Phylogenetic relationships in Rosaceae have long been problematic because of frequent hybridisation, apomixis and presumed rapid radiation, and their historical diversification has not been clarified. With 87 genera representing all subfamilies and tribes of Rosaceae and six of the other eight families of Rosales (outgroups), we analysed 130 newly sequenced plastomes together with 12 from GenBank in an attempt to reconstruct deep relationships and reveal temporal diversification of this family. Our results highlight the importance of improving sequence alignment and the use of appropriate substitution models in plastid phylogenomics. Three subfamilies and 16 tribes (as previously delimited) were strongly supported as monophyletic, and their relationships were fully resolved and strongly supported at most nodes. Rosaceae were estimated to have originated during the Late Cretaceous with evidence for rapid diversification events during several geological periods. The major lineages rapidly diversified in warm and wet habits during the Late Cretaceous, and the rapid diversification of genera from the early Oligocene onwards occurred in colder and drier environments. Plastid phylogenomics offers new and important insights into deep phylogenetic relationships and the diversification history of Rosaceae. The robust phylogenetic backbone and time estimates we provide establish a framework for future comparative studies on rosaceous evolution.

String kernels for protein sequence comparisons: improved fold recognition

BACKGROUND

The amino acid sequence of a protein is the blueprint from which its structure and ultimately function can be derived. Therefore, sequence comparison methods remain essential for the determination of similarity between proteins. Traditional approaches for comparing two protein sequences begin with strings of letters (amino acids) that represent the sequences, before generating textual alignments between these strings and providing scores for each alignment. When the similitude between the two protein sequences to be compared is low however, the quality of the corresponding sequence alignment is usually poor, leading to poor performance for the recognition of similarity.

RESULTS

In this study, we develop an alignment free alternative to these methods that is based on the concept of string kernels. Starting from recently proposed kernels on the discrete space of protein sequences (Shen et al, Found. Comput. Math., 2013,14:951-984), we introduce our own version, SeqKernel. Its implementation depends on two parameters, a coefficient that tunes the substitution matrix and the maximum length of k-mers that it includes. We provide an exhaustive analysis of the impacts of these two parameters on the performance of SeqKernel for fold recognition. We show that with the right choice of parameters, use of the SeqKernel similarity measure improves fold recognition compared to the use of traditional alignment-based methods. We illustrate the application of SeqKernel to inferring phylogeny on RNA polymerases and show that it performs as well as methods based on multiple sequence alignments.

CONCLUSION

We have presented and characterized a new alignment free method based on a mathematical kernel for scoring the similarity of protein sequences. We discuss possible improvements of this method, as well as an extension of its applications to other modeling methods that rely on sequence comparison.

Additive methods for genomic signatures

Background

Studies exploring the potential of Chaos Game Representations (CGR) of genomic sequences to act as “genomic signatures” (to be species- and genome-specific) showed that CGR patterns of nuclear and organellar DNA sequences of the same organism can be very different. While the hypothesis that CGRs of mitochondrial DNA sequences can act as genomic signatures was validated for a snapshot of all sequenced mitochondrial genomes available in the NCBI GenBank sequence database, to our knowledge no such extensive analysis of CGRs of nuclear DNA sequences exists to date.

Results

We analyzed an extensive dataset, totalling 1.45 gigabase pairs, of nuclear/nucleoid genomic sequences (nDNA) from 42 different organisms, spanning all major kingdoms of life. Our computational experiments indicate that CGR signatures of nDNA of two different origins cannot always be differentiated, especially if they originate from closely-related species such as H. sapiens and P. troglodytes or E. coli and E. fergusonii. To address this issue, we propose the general concept of additive DNA signature of a set (collection) of DNA sequences. One particular instance, the composite DNA signature, combines information from nDNA fragments and organellar (mitochondrial, chloroplast, or plasmid) genomes. We demonstrate that, in this dataset, composite DNA signatures originating from two different organisms can be differentiated in all cases, including those where the use of CGR signatures of nDNA failed or was inconclusive. Another instance, the assembled DNA signature, combines information from many short DNA subfragments (e.g., 100 basepairs) of a given DNA fragment, to produce its signature. We show that an assembled DNA signature has the same distinguishing power as a conventionally computed CGR signature, while using shorter contiguous sequences and potentially less sequence information.

Conclusions

Our results suggest that, while CGR signatures of nDNA cannot always play the role of genomic signatures, composite and assembled DNA signatures (separately or in combination) could potentially be used instead. Such additive signatures could be used, e.g., with raw unassembled next-generation sequencing (NGS) read data, when high-quality sequencing data is not available, or to complement information obtained by other methods of species identification or classification.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1157-8) contains supplementary material, which is available to authorized users.

Exploring lateral genetic transfer among microbial genomes using TF-IDF

Many microbes can acquire genetic material from their environment and incorporate it into their genome, a process known as lateral genetic transfer (LGT). Computational approaches have been developed to detect genomic regions of lateral origin, but typically lack sensitivity, ability to distinguish donor from recipient, and scalability to very large datasets. To address these issues we have introduced an alignment-free method based on ideas from document analysis, term frequency-inverse document frequency (TF-IDF). Here we examine the performance of TF-IDF on three empirical datasets: 27 genomes of Escherichia coli and Shigella, 110 genomes of enteric bacteria, and 143 genomes across 12 bacterial and three archaeal phyla. We investigate the effect of k-mer size, gap size and delineation of groups on the inference of genomic regions of lateral origin, finding an interplay among these parameters and sequence divergence. Because TF-IDF identifies donor groups and delineates regions of lateral origin within recipient genomes, aggregating these regions by gene enables us to explore, for the first time, the mosaic nature of lateral genes including the multiplicity of biological sources, ancestry of transfer and over-writing by subsequent transfers. We carry out Gene Ontology enrichment tests to investigate which biological processes are potentially affected by LGT.

Genes are information, so information theory is coming to the aid of evolutionary biology

Speciation is central to evolutionary biology, and to elucidate it, we need to catch the early genetic changes that set nascent taxa on their path to species status (Via 2009). That challenge is difficult, of course, for two chief reasons: (i) serendipity is required to catch speciation in the act; and (ii) after a short time span with lingering gene flow, differentiation may be low and/or embodied only in rare alleles that are difficult to sample. In this issue of Molecular Ecology Resources, Smouse et al. (2015) have noted that optimal assessment of differentiation within and between nascent species should be robust to these challenges, and they identified a measure based on Shannon's information theory that has many advantages for this and numerous other tasks. The Shannon measure exhibits complete additivity of information at different levels of subdivision. Of all the family of diversity measures ('0' or allele counts, '1' or Shannon, '2' or heterozygosity, F(ST) and related metrics) Shannon's measure comes closest to weighting alleles by their frequencies. For the Shannon measure, rare alleles that represent early signals of nascent speciation are neither down-weighted to the point of irrelevance, as for level 2 measures, nor up-weighted to overpowering importance, as for level 0 measures (Chao et al. 2010, )2015. Shannon measures have a long history in population genetics, dating back to Shannon's PhD thesis in 1940 (Crow 2001), but have received only sporadic attention, until a resurgence of interest in the last ten years, as reviewed briefly by Smouse et al. (2015).

A Provably Efficient Algorithm for the k-Mismatch Average Common Substring Problem

Alignment-free sequence comparison methods are attracting persistent interest, driven by data-intensive applications in genome-wide molecular taxonomy and phylogenetic reconstruction. Among all the methods based on substring composition, the average common substring (ACS) measure admits a straightforward linear time sequence comparison algorithm, while yielding impressive results in multiple applications. An important direction of this research is to extend the approach to permit a bounded edit/hamming distance between substrings, so as to reflect more accurately the evolutionary process. To date, however, algorithms designed to incorporate k ≥ 1 mismatches have O(n(2)) worst-case time complexity, where n is the total length of the input sequences. On the other hand, accounting for mismatches has shown to lead to much improved classification, while heuristics can improve practical performance. In this article, we close the gap by presenting the first provably efficient algorithm for the k-mismatch average common string (ACSk) problem that takes O(n) space and O(n log(k) n) time in the worst case for any constant k. Our method extends the generalized suffix tree model to incorporate a carefully selected bounded set of perturbed suffixes, and can be applied to other complex approximate sequence matching problems.

The Harvest suite for rapid core-genome alignment and visualization of thousands of intraspecific microbial genomes

Whole-genome sequences are now available for many microbial species and clades, however existing whole-genome alignment methods are limited in their ability to perform sequence comparisons of multiple sequences simultaneously. Here we present the Harvest suite of core-genome alignment and visualization tools for the rapid and simultaneous analysis of thousands of intraspecific microbial strains. Harvest includes Parsnp, a fast core-genome multi-aligner, and Gingr, a dynamic visual platform. Together they provide interactive core-genome alignments, variant calls, recombination detection, and phylogenetic trees. Using simulated and real data we demonstrate that our approach exhibits unrivaled speed while maintaining the accuracy of existing methods. The Harvest suite is open-source and freely available from: http://github.com/marbl/harvest.

ITS2 Secondary Structure Improves Discrimination between Medicinal "Mu Tong" Species when Using DNA Barcoding

DNA barcoding is a promising species identification method, but it has proved difficult to find a standardized DNA marker in plant. Although the ITS/ITS2 RNA transcript has been proposed as the core barcode for seed plants, it has been criticized for being too conserved in some species to provide enough information or too variable in some species to align it within the different taxa ranks. We selected 30 individuals, representing 16 species and four families, to explore whether ITS2 can successfully resolve species in terms of secondary structure. Secondary structure was predicted using Mfold software and sequence-structure was aligned by MARNA. RNAstat software transformed the secondary structures into 28 symbol code data for maximum parsimony (MP) analysis. The results showed that the ITS2 structures in our samples had a common four-helix folding type with some shared motifs. This conserved structure facilitated the alignment of ambiguous sequences from divergent families. The structure alignment yielded a MP tree, in which most topological relationships were congruent with the tree constructed using nucleotide sequence data. When the data was combined, we obtained a well-resolved and highly supported phylogeny, in which individuals of a same species were clustered together into a monophyletic group. As a result, the different species that are often referred to as the herb “Mu tong” were successfully identified using short fragments of 250 bp ITS2 sequences, together with their secondary structure. Thus our analysis strengthens the potential of ITS2 as a promising DNA barcode because it incorporates valuable secondary structure information that will help improve discrimination between species.

Necessary relations for nucleotide frequencies

Genome composition analysis of di-, tri- and tetra-nucleotide frequencies is known to be evolutionarily informative, and useful in metagenomic studies, where binning of raw sequence data is often an important first step. Patterns appearing in genome composition analysis may be due to evolutionary processes or purely mathematical relations. For example, the total number of dinucleotides in a sequence is equal to the sum of the individual totals of the sixteen types of dinucleotide, and this is entirely independent of any assumptions made regarding mutation or selection, or indeed any physical or chemical process. Before any statistical analysis can be attempted, a knowledge of all necessary mathematical relations is required. I show that 25% of di-, tri- and tetra-nucleotide frequencies can be written as simple sums and differences of the remainder. The vast majority of organisms have circular genomes, for which these relations are exact and necessary. In the case of linear molecules, the absolute error is very nearly zero, and does not grow with contiguous sequence length. As a result of the new, necessary relations presented here, the foundations of the statistical analysis of di-, tri- and tetra-nucleotide frequencies, and k-mer analysis in general, need to be revisited.

Efficient representation of uncertainty in multiple sequence alignments using directed acyclic graphs

BACKGROUND

A standard procedure in many areas of bioinformatics is to use a single multiple sequence alignment (MSA) as the basis for various types of analysis. However, downstream results may be highly sensitive to the alignment used, and neglecting the uncertainty in the alignment can lead to significant bias in the resulting inference. In recent years, a number of approaches have been developed for probabilistic sampling of alignments, rather than simply generating a single optimum. However, this type of probabilistic information is currently not widely used in the context of downstream inference, since most existing algorithms are set up to make use of a single alignment.

RESULTS

In this work we present a framework for representing a set of sampled alignments as a directed acyclic graph (DAG) whose nodes are alignment columns; each path through this DAG then represents a valid alignment. Since the probabilities of individual columns can be estimated from empirical frequencies, this approach enables sample-based estimation of posterior alignment probabilities. Moreover, due to conditional independencies between columns, the graph structure encodes a much larger set of alignments than the original set of sampled MSAs, such that the effective sample size is greatly increased.

CONCLUSIONS

The alignment DAG provides a natural way to represent a distribution in the space of MSAs, and allows for existing algorithms to be efficiently scaled up to operate on large sets of alignments. As an example, we show how this can be used to compute marginal probabilities for tree topologies, averaging over a very large number of MSAs. This framework can also be used to generate a statistically meaningful summary alignment; example applications show that this summary alignment is consistently more accurate than the majority of the alignment samples, leading to improvements in downstream tree inference. Implementations of the methods described in this article are available at http://statalign.github.io/WeaveAlign .

The Harvest suite for rapid core-genome alignment and visualization of thousands of intraspecific microbial genomes

Whole-genome sequences are now available for many microbial species and clades, however existing whole-genome alignment methods are limited in their ability to perform sequence comparisons of multiple sequences simultaneously. Here we present the Harvest suite of core-genome alignment and visualization tools for the rapid and simultaneous analysis of thousands of intraspecific microbial strains. Harvest includes Parsnp, a fast core-genome multi-aligner, and Gingr, a dynamic visual platform. Together they provide interactive core-genome alignments, variant calls, recombination detection, and phylogenetic trees. Using simulated and real data we demonstrate that our approach exhibits unrivaled speed while maintaining the accuracy of existing methods. The Harvest suite is open-source and freely available from: http://github.com/marbl/harvest.

Inferring phylogenies of evolving sequences without multiple sequence alignment

Alignment-free methods, in which shared properties of sub-sequences (e.g. identity or match length) are extracted and used to compute a distance matrix, have recently been explored for phylogenetic inference. However, the scalability and robustness of these methods to key evolutionary processes remain to be investigated. Here, using simulated sequence sets of various sizes in both nucleotides and amino acids, we systematically assess the accuracy of phylogenetic inference using an alignment-free approach, based on D₂ statistics, under different evolutionary scenarios. We find that compared to a multiple sequence alignment approach, D₂ methods are more robust against among-site rate heterogeneity, compositional biases, genetic rearrangements and insertions/deletions, but are more sensitive to recent sequence divergence and sequence truncation. Across diverse empirical datasets, the alignment-free methods perform well for sequences sharing low divergence, at greater computation speed. Our findings provide strong evidence for the scalability and the potential use of alignment-free methods in large-scale phylogenomics.

Analysis of dinucleotide signatures in HIV-1 subtype B genomes

Dinucleotide usage is known to vary in the genomes of organisms. The dinucleotide usage profiles or genome signatures are similar for sequence samples taken from the same genome, but are different for taxonomically distant species. This concept of genome signatures has been used to study several organisms including viruses, to elucidate the signatures of evolutionary processes at the genome level. Genome signatures assume greater importance in the case of host-pathogen interactions, where molecular interactions between the two species take place continuously, and can influence their genomic composition. In this study, analyses of whole genome sequences of the HIV-1 subtype B, a retrovirus that caused global pandemic of AIDS, have been carried out to analyse the variation in genome signatures of the virus from 1983 to 2007. We show statistically significant temporal variations in some dinucleotide patterns highlighting the selective evolution of the dinucleotide profiles of HIV-1 subtype B, possibly a consequence of host specific selection.

Causes, consequences and solutions of phylogenetic incongruence

Phylogenetic analysis is used to recover the evolutionary history of species, genes or proteins. Understanding phylogenetic relationships between organisms is a prerequisite of almost any evolutionary study, as contemporary species all share a common history through their ancestry. Moreover, it is important because of its wide applications that include understanding genome organization, epidemiological investigations, predicting protein functions, and deciding the genes to be analyzed in comparative studies. Despite immense progress in recent years, phylogenetic reconstruction involves many challenges that create uncertainty with respect to the true evolutionary relationships of the species or genes analyzed. One of the most notable difficulties is the widespread occurrence of incongruence among methods and also among individual genes or different genomic regions. Presence of widespread incongruence inhibits successful revealing of evolutionary relationships and applications of phylogenetic analysis. In this article, I concisely review the effect of various factors that cause incongruence in molecular phylogenies, the advances in the field that resolved some factors, and explore unresolved factors that cause incongruence along with possible ways for tackling them.

Extraction of high quality k-words for alignment-free sequence comparison

The weighted Euclidean distance (D(2)) is one of the earliest dissimilarity measures used for alignment free comparison of biological sequences. This distance measure and its variants have been used in numerous applications due to its fast computation, and many variants of it have been subsequently introduced. The D(2) distance measure is based on the count of k-words in the two sequences that are compared. Traditionally, all k-words are compared when computing the distance. In this paper we show that similar accuracy in sequence comparison can be achieved by using a selected subset of k-words. We introduce a term variance based quality measure for identifying the important k-words. We demonstrate the application of the proposed technique in phylogeny reconstruction and show that up to 99% of the k-words can be filtered out for certain datasets, resulting in faster sequence comparison. The paper also presents an exploratory analysis based evaluation of optimal k-word values and discusses the impact of using subsets of k-words in such optimal instances.

Molecular phylogenetics before sequences: oligonucleotide catalogs as k-mer spectra

From 1971 to 1985, Carl Woese and colleagues generated oligonucleotide catalogs of 16S/18S rRNAs from more than 400 organisms. Using these incomplete and imperfect data, Carl and his colleagues developed unprecedented insights into the structure, function, and evolution of the large RNA components of the translational apparatus. They recognized a third domain of life, revealed the phylogenetic backbone of bacteria (and its limitations), delineated taxa, and explored the tempo and mode of microbial evolution. For these discoveries to have stood the test of time, oligonucleotide catalogs must carry significant phylogenetic signal; they thus bear re-examination in view of the current interest in alignment-free phylogenetics based on k-mers. Here we consider the aims, successes, and limitations of this early phase of molecular phylogenetics. We computationally generate oligonucleotide sets (e-catalogs) from 16S/18S rRNA sequences, calculate pairwise distances between them based on D₂ statistics, compute distance trees, and compare their performance against alignment-based and k-mer trees. Although the catalogs themselves were superseded by full-length sequences, this stage in the development of computational molecular biology remains instructive for us today.

Analysis of horizontal genetic transfer in red algae in the post-genomics age

The recently published genome of the unicellular red alga Porphyridium purpureum revealed a gene-rich, intron-poor species, which is surprising for a free-living mesophile. Of the 8,355 predicted protein-coding regions, up to 773 (9.3%) were implicated in horizontal genetic transfer (HGT) events involving other prokaryote and eukaryote lineages. A much smaller number, up to 174 (2.1%) showed unambiguous evidence of vertical inheritance. Together with other red algal genomes, nearly all published in 2013, these data provide an excellent platform for studying diverse aspects of algal biology and evolution. This novel information will help investigators test existing hypotheses about the impact of endosymbiosis and HGT on algal evolution and enable comparative analysis within a more-refined, hypothesis-driven framework that extends beyond HGT. Here we explore the impacts of this infusion of red algal genome data on addressing questions regarding the complex nature of algal evolution and highlight the need for scalable phylogenomic approaches to handle the forthcoming deluge of sequence information.

Alignment-free genome tree inference by learning group-specific distance metrics

Understanding the evolutionary relationships between organisms is vital for their in-depth study. Gene-based methods are often used to infer such relationships, which are not without drawbacks. One can now attempt to use genome-scale information, because of the ever increasing number of genomes available. This opportunity also presents a challenge in terms of computational efficiency. Two fundamentally different methods are often employed for sequence comparisons, namely alignment-based and alignment-free methods. Alignment-free methods rely on the genome signature concept and provide a computationally efficient way that is also applicable to nonhomologous sequences. The genome signature contains evolutionary signal as it is more similar for closely related organisms than for distantly related ones. We used genome-scale sequence information to infer taxonomic distances between organisms without additional information such as gene annotations. We propose a method to improve genome tree inference by learning specific distance metrics over the genome signature for groups of organisms with similar phylogenetic, genomic, or ecological properties. Specifically, our method learns a Mahalanobis metric for a set of genomes and a reference taxonomy to guide the learning process. By applying this method to more than a thousand prokaryotic genomes, we showed that, indeed, better distance metrics could be learned for most of the 18 groups of organisms tested here. Once a group-specific metric is available, it can be used to estimate the taxonomic distances for other sequenced organisms from the group. This study also presents a large scale comparison between 10 methods--9 alignment-free and 1 alignment-based.

Alignment-free phylogenetics and population genetics

Phylogenetics and population genetics are central disciplines in evolutionary biology. Both are based on comparative data, today usually DNA sequences. These have become so plentiful that alignment-free sequence comparison is of growing importance in the race between scientists and sequencing machines. In phylogenetics, efficient distance computation is the major contribution of alignment-free methods. A distance measure should reflect the number of substitutions per site, which underlies classical alignment-based phylogeny reconstruction. Alignment-free distance measures are either based on word counts or on match lengths, and I apply examples of both approaches to simulated and real data to assess their accuracy and efficiency. While phylogeny reconstruction is based on the number of substitutions, in population genetics, the distribution of mutations along a sequence is also considered. This distribution can be explored by match lengths, thus opening the prospect of alignment-free population genomics.

A Markovian analysis of bacterial genome sequence constraints

The arrangement of nucleotides within a bacterial chromosome is influenced by numerous factors. The degeneracy of the third codon within each reading frame allows some flexibility of nucleotide selection; however, the third nucleotide in the triplet of each codon is at least partly determined by the preceding two. This is most evident in organisms with a strong G + C bias, as the degenerate codon must contribute disproportionately to maintaining that bias. Therefore, a correlation exists between the first two nucleotides and the third in all open reading frames. If the arrangement of nucleotides in a bacterial chromosome is represented as a Markov process, we would expect that the correlation would be completely captured by a second-order Markov model and an increase in the order of the model (e.g., third-, fourth-…order) would not capture any additional uncertainty in the process. In this manuscript, we present the results of a comprehensive study of the Markov property that exists in the DNA sequences of 906 bacterial chromosomes. All of the 906 bacterial chromosomes studied exhibit a statistically significant Markov property that extends beyond second-order, and therefore cannot be fully explained by codon usage. An unrooted tree containing all 906 bacterial chromosomes based on their transition probability matrices of third-order shares ∼25% similarity to a tree based on sequence homologies of 16S rRNA sequences. This congruence to the 16S rRNA tree is greater than for trees based on lower-order models (e.g., second-order), and higher-order models result in diminishing improvements in congruence. A nucleotide correlation most likely exists within every bacterial chromosome that extends past three nucleotides. This correlation places significant limits on the number of nucleotide sequences that can represent probable bacterial chromosomes. Transition matrix usage is largely conserved by taxa, indicating that this property is likely inherited, however some important exceptions exist that may indicate the convergent evolution of some bacteria.

DACTAL: divide-and-conquer trees (almost) without alignments

Motivation: While phylogenetic analyses of datasets containing 1000–5000 sequences are challenging for existing methods, the estimation of substantially larger phylogenies poses a problem of much greater complexity and scale.

Methods: We present DACTAL, a method for phylogeny estimation that produces trees from unaligned sequence datasets without ever needing to estimate an alignment on the entire dataset. DACTAL combines iteration with a novel divide-and-conquer approach, so that each iteration begins with a tree produced in the prior iteration, decomposes the taxon set into overlapping subsets, estimates trees on each subset, and then combines the smaller trees into a tree on the full taxon set using a new supertree method. We prove that DACTAL is guaranteed to produce the true tree under certain conditions. We compare DACTAL to SATé and maximum likelihood trees on estimated alignments using simulated and real datasets with 1000–27 643 taxa.

Results: Our studies show that on average DACTAL yields more accurate trees than the two-phase methods we studied on very large datasets that are difficult to align, and has approximately the same accuracy on the easier datasets. The comparison to SATé shows that both have the same accuracy, but that DACTAL achieves this accuracy in a fraction of the time. Furthermore, DACTAL can analyze larger datasets than SATé, including a dataset with almost 28 000 sequences.

Availability: DACTAL source code and results of dataset analyses are available at www.cs.utexas.edu/users/phylo/software/dactal.

Contact:tandy@cs.utexas.edu

Next-generation phylogenomics

Thanks to advances in next-generation technologies, genome sequences are now being generated at breadth (e.g. across environments) and depth (thousands of closely related strains, individuals or samples) unimaginable only a few years ago. Phylogenomics--the study of evolutionary relationships based on comparative analysis of genome-scale data--has so far been developed as industrial-scale molecular phylogenetics, proceeding in the two classical steps: multiple alignment of homologous sequences, followed by inference of a tree (or multiple trees). However, the algorithms typically employed for these steps scale poorly with number of sequences, such that for an increasing number of problems, high-quality phylogenomic analysis is (or soon will be) computationally infeasible. Moreover, next-generation data are often incomplete and error-prone, and analysis may be further complicated by genome rearrangement, gene fusion and deletion, lateral genetic transfer, and transcript variation. Here we argue that next-generation data require next-generation phylogenomics, including so-called alignment-free approaches.

Co-phylog: an assembly-free phylogenomic approach for closely related organisms

With the advent of high-throughput sequencing technologies, the rapid generation and accumulation of large amounts of sequencing data pose an insurmountable demand for efficient algorithms for constructing whole-genome phylogenies. The existing phylogenomic methods all use assembled sequences, which are often not available owing to the difficulty of assembling short-reads; this obstructs phylogenetic investigations on species without a reference genome. In this report, we present co-phylog, an assembly-free phylogenomic approach that creates a ‘micro-alignment’ at each ‘object’ in the sequence using the ‘context’ of the object and calculates pairwise distances before reconstructing the phylogenetic tree based on those distances. We explored the parameters’ usages and the optimal working range of co-phylog, assessed co-phylog using the simulated next-generation sequencing (NGS) data and the real NGS raw data. We also compared co-phylog method with traditional alignment and alignment-free methods and illustrated the advantages and limitations of co-phylog method. In conclusion, we demonstrated that co-phylog is efficient algorithm and that it delivers high resolution and accurate phylogenies using whole-genome unassembled sequencing data, especially in the case of closely related organisms, thereby significantly alleviating the computational burden in the genomic era.

PHYRN: a robust method for phylogenetic analysis of highly divergent sequences

Both multiple sequence alignment and phylogenetic analysis are problematic in the "twilight zone" of sequence similarity (≤ 25% amino acid identity). Herein we explore the accuracy of phylogenetic inference at extreme sequence divergence using a variety of simulated data sets. We evaluate four leading multiple sequence alignment (MSA) methods (MAFFT, T-COFFEE, CLUSTAL, and MUSCLE) and six commonly used programs of tree estimation (Distance-based: Neighbor-Joining; Character-based: PhyML, RAxML, GARLI, Maximum Parsimony, and Bayesian) against a novel MSA-independent method (PHYRN) described here. Strikingly, at "midnight zone" genetic distances (~7% pairwise identity and 4.0 gaps per position), PHYRN returns high-resolution phylogenies that outperform traditional approaches. We reason this is due to PHRYN's capability to amplify informative positions, even at the most extreme levels of sequence divergence. We also assess the applicability of the PHYRN algorithm for inferring deep evolutionary relationships in the divergent DANGER protein superfamily, for which PHYRN infers a more robust tree compared to MSA-based approaches. Taken together, these results demonstrate that PHYRN represents a powerful mechanism for mapping uncharted frontiers in highly divergent protein sequence data sets.

Organizational heterogeneity of vertebrate genomes

Genomes of higher eukaryotes are mosaics of segments with various structural, functional, and evolutionary properties. The availability of whole-genome sequences allows the investigation of their structure as "texts" using different statistical and computational methods. One such method, referred to as Compositional Spectra (CS) analysis, is based on scoring the occurrences of fixed-length oligonucleotides (k-mers) in the target DNA sequence. CS analysis allows generating species- or region-specific characteristics of the genome, regardless of their length and the presence of coding DNA. In this study, we consider the heterogeneity of vertebrate genomes as a joint effect of regional variation in sequence organization superimposed on the differences in nucleotide composition. We estimated compositional and organizational heterogeneity of genome and chromosome sequences separately and found that both heterogeneity types vary widely among genomes as well as among chromosomes in all investigated taxonomic groups. The high correspondence of heterogeneity scores obtained on three genome fractions, coding, repetitive, and the remaining part of the noncoding DNA (the genome dark matter--GDM) allows the assumption that CS-heterogeneity may have functional relevance to genome regulation. Of special interest for such interpretation is the fact that natural GDM sequences display the highest deviation from the corresponding reshuffled sequences.

Multifractal analysis of HIV-1 genomes

Pathogens like HIV-1, which evolve into many closely related variants displaying differential infectivity and evolutionary dynamics in a short time scale, require fast and accurate classification. Conventional whole genome sequence alignment-based methods are computationally expensive and involve complex analysis. Alignment-free methodologies are increasingly being used to effectively differentiate genomic variations between viral species. Multifractal analysis, which explores the self-similar nature of genomes, is an alignment-free methodology that has been applied to study such variations. However, whether multifractal analysis can quantify variations between closely related genomes, such as the HIV-1 subtypes, is an open question. Here we address the above by implementing the multifractal analysis on four retroviral genomes (HIV-1, HIV-2, SIVcpz, and HTLV-1), and demonstrate that individual multifractal properties can differentiate between different retrovirus types easily. However, the individual multifractal measures do not resolve within-group variations for different known subtypes of HIV-1 M group. We show here that these known subtypes can instead be classified correctly using a combination of the crucial multifractal measures. This method is simple and computationally fast in comparison to the conventional alignment-based methods for whole genome phylogenetic analysis.

Genome-based phylogeny of dsDNA viruses by a novel alignment-free method

Sequence alignment is not directly applicable to whole genome phylogeny since several events such as rearrangements make full length alignments impossible. Here, a novel alignment-free method derived from the standpoint of information theory is proposed and used to construct the whole-genome phylogeny for a population of viruses from 13 viral families comprising 218 dsDNA viruses. The method is based on information correlation (IC) and partial information correlation (PIC). We observe that (i) the IC-PIC tree segregates the population into clades, the membership of each is remarkably consistent with biologist's systematics only with little exceptions; (ii) the IC-PIC tree reveals potential evolutionary relationships among some viral families; and (iii) the IC-PIC tree predicts the taxonomic positions of certain "unclassified" viruses. Our approach provides a new way for recovering the phylogeny of viruses, and has practical applications in developing alignment-free methods for sequence classification.

Graphical and numerical representations of DNA sequences: statistical aspects of similarity

New approaches aiming at a detailed similarity/dissimilarity analysis of DNA sequences are formulated. Several corrections that enrich the information which may be derived from the alignment methods are proposed. The corrections take into account the distributions along the sequences of the aligned bases (neglected in the standard alignment methods). As a consequence, different aspects of similarity, as for example asymmetry of the gene structure, may be studied either using new similarity measures associated with four-component spectral representation of the DNA sequences or using alignment methods with corrections introduced in this paper. The corrections to the alignment methods and the statistical distribution moment-based descriptors derived from the four-component spectral representation of the DNA sequences are applied to similarity/dissimilarity studies of β-globin gene across species. The studies are supplemented by detailed similarity studies for histones H1 and H4 coding sequences. The data are described according to the latest version of the EMBL database. The work is supplemented by a concise review of the state-of-art graphical representations of DNA sequences.