Accelerating Parallel Maximum Likelihood-Based Phylogenetic Tree Calculations Using Subtree Equality Vectors

Since 2020, the SARS-CoV-2 virus has infected billions of people and spread to 185 countries. The virus spreads by making new copies of its genome inside human cells and exploits the cells’ machinery to synthesise viral proteins it needs to infect further cells. Each time the virus copies its genetic material there’s a chance that the replication process introduces an error to the genetic sequence. Over time, these mutations accumulate which can give rise to new variants with different properties. These new variants, originating from a common ancestor, may spread faster or be able to evade immune systems that have learnt to recognise previous variants. To understand where new variants of SARS-CoV-2 come from and how related they are to each other, scientists build family trees called ‘phylogenetic trees’ based on similarities in the genetic sequences of different variants of the virus. Looking at these trees researchers can track how a variant spreads geographically, and also attempt to identify new worrying variants that might lead to a new wave of infections. The scale of the COVID-19 pandemic together with the global effort by clinicians and researchers to sequence SARS-CoV-2 genetic material means a library of over 13 million SARS-CoV-2 genomes now exists, making it the largest such collection for any organism. Although phylogenetic trees of viruses have been studied for a long time, exploring the SARS-CoV-2 library presents technical and practical challenges due to its sheer size. Sanderson has developed an open-source web tool called Taxonium that allows users to explore phylogenetic trees with millions of sequences. With help from collaborators at the University of California, Santa Cruz, Sanderson built a website called Cov2Tree, that uses the Taxonium platform to allow immediate access to an expansive tree of all publicly available SARS-CoV-2 sequences. Cov2Tree enables users to visualise all SARS-CoV-2 genomes in a birds-eye view akin to a ‘Google Earth for virus sequences’ where anyone can zoom in on a related family of viruses down to the level of individual sequences. This can be used to compare variants and follow geographic spread. Using Taxonium, scientists can explore how virus sequences are related to each other. They can also see the individual mutations that have occurred at each branch of the tree, and can search for sequences based on mutation, geographical location, or other factors. Interestingly, a trend appearing in the SARS-CoV-2 phylogenetic tree is the emergence of identical mutations at different branches of the tree without a common origin. These mutations may be a result of convergent evolution, a phenomenon that occurs when a mutation appears independently in different variants as it confers an advantage to the virus making such mutations more likely to persist. This means that scientists may be able to expect certain mutations to appear in more distantly related variants if they have appeared independently in several different variants already. Overall, Taxonium is an important tool for monitoring SARS-CoV-2 genomes, but it also has broader applications. The tool can be used to browse phylogenetic trees of other viruses and organisms. Furthermore, the Taxonium website offers a way to browse a tree of life, with images and links to Wikipedia. The SARS-CoV-2 library might be the largest now, but in the future even bigger datasets will likely be available, highlighting the importance of tools like Taxonium.

This paper proposes the application of parallelization techniques for solving the unit commitment problem (UCP) on NOWs (networks of workstations). A modified parallel dynamic programming method that takes advantage of NOWs is presented. Our algorithm performs better than the general parallel dynamic programming algorithm for UCP. In order to demonstrate the usefulness of our technique, we apply our parallel programs in some case studies. Studies reveal that our parallel dynamic programming algorithm has the potential to enhance the dynamic control of unit commitment in real time situations.

Inference of phylogenetic trees comprising hundreds or even thousands of organisms based on the maximum likelihood method is computationally intensive. We present simple heuristics which yield accurate trees for synthetic as well as real data and significantly reduce execution time. Those heuristics have been implemented in a sequential, parallel, and distributed program called RAxML‐II, which is freely available as open source code. We compare the performance of the sequential program with PHYML and MrBayes which—to the best of our knowledge—are currently the fastest and most accurate programs for phylogenetic tree inference based on statistical methods. Experiments are conducted using 50 synthetic 100 taxon alignments as well as nine real‐world alignments comprising 101 up to 1000 sequences. RAxML‐II outperforms MrBayes for real‐world data both in terms of speed and final likelihood values. Furthermore, for real data RAxML‐II requires less time (a factor of 2–8) than PHYML to reach PHYML's final likelihood values and yields better final trees due to its more exhaustive search strategy. For synthetic data MrBayes is slightly more accurate than RAxML‐II and PHYML but significantly slower. The non‐deterministic parallel program shows good speedup values and has been used to infer a 10 000‐taxon tree comprising organisms from the domains Eukarya, Bacteria, and Archaea. Copyright © 2005 John Wiley & Sons, Ltd.

Parallel Computing on a network of workstations (NOW) is receiving a lot of attention from the research community. However, there is still a lack of tools for developing and running parallel applications on a NOW environment. In this paper, we develop and implement an object-oriented parallel programming system that facilitates the implementation of parallel applications on a NOW environment. In our programming system, a conceptual model, named Synchronous Object Model, is provided to help programmers write parallel programs. The object model makes use of the inherent parallel nature of an object-oriented model to express parallelism. In addition, an object-oriented framework is included into our programming system that reduces the size of parallel programs through code reuse and design reuse. Our system design further takes advantage of the underlying hardware architecture of the NOW environment to maximize performance by integrating multicast and load balancing support, and this is illustrated through experimental results.

Highly accurate estimation of phylogenetic trees for large data sets is difficult, in part because multiple sequence alignments must be accurate for phylogeny estimation methods to be accurate. Coestimation of alignments and trees has been attempted but currently only SATé estimates reasonably accurate trees and alignments for large data sets in practical time frames (Liu K., Raghavan S., Nelesen S., Linder C.R., Warnow T. 2009b. Rapid and accurate large-scale coestimation of sequence alignments and phylogenetic trees. Science. 324:1561-1564). Here, we present a modification to the original SATé algorithm that improves upon SATé (which we now call SATé-I) in terms of speed and of phylogenetic and alignment accuracy. SATé-II uses a different divide-and-conquer strategy than SATé-I and so produces smaller more closely related subsets than SATé-I; as a result, SATé-II produces more accurate alignments and trees, can analyze larger data sets, and runs more efficiently than SATé-I. Generally, SATé is a metamethod that takes an existing multiple sequence alignment method as an input parameter and boosts the quality of that alignment method. SATé-II-boosted alignment methods are significantly more accurate than their unboosted versions, and trees based upon these improved alignments are more accurate than trees based upon the original alignments. Because SATé-I used maximum likelihood (ML) methods that treat gaps as missing data to estimate trees and because we found a correlation between the quality of tree/alignment pairs and ML scores, we explored the degree to which SATé's performance depends on using ML with gaps treated as missing data to determine the best tree/alignment pair. We present two lines of evidence that using ML with gaps treated as missing data to optimize the alignment and tree produces very poor results. First, we show that the optimization problem where a set of unaligned DNA sequences is given and the output is the tree and alignment of those sequences that maximize likelihood under the Jukes-Cantor model is uninformative in the worst possible sense. For all inputs, all trees optimize the likelihood score. Second, we show that a greedy heuristic that uses GTR+Gamma ML to optimize the alignment and the tree can produce very poor alignments and trees. Therefore, the excellent performance of SATé-II and SATé-I is not because ML is used as an optimization criterion for choosing the best tree/alignment pair but rather due to the particular divide-and-conquer realignment techniques employed.

Dominant trends in parallel and distributed computing (parallel computers, parallel algorithms) aim to connect a number of powerful workstations (WS) based on single personal computers (PC) or symmetrical multiprocessor system (SMP) to solve complex problems in a parallel way. Typical representatives of these trends are network of workstation (NOW) and Grid as a high integrated network of NOW modules. In relation to it there is a bad need of unified modelling in traditionally evolved parallel computing and distributed computing as two separate research disciplines. Likewise current trends in high performance computing (HPC) aim to use NOW modules based on SMP parallel computers as cheaper alternatives to the traditionally used massive parallel multiprocessors or supercomputers and to profit from unifying modelling in parallel and distributed computing too. To exploit the parallel processing capability of such cluster, any application program must be paralleled. A way how to do it (decomposition model) belongs to a most important step in developing process of effective parallel algorithm. This article at first discusses the development of effective (optimised) iterative parallel algorithms (IPA) to solve partial differential equations (PDE). By carefully choosing an illustrative typical problem of PDE (Laplace equation) the proposed research has demonstrated the most important complexities in the process of complete modelling of substantial complexities and their optimisation in order to develop an effective PA. Such approach could be used as illustrative example for a complete modelling and effective solution of even other more complex PDE´s in a parallel way.

BackgroundCommon existing phylogenetic tree visualisation tools are not able to display readable trees with more than a few thousand nodes. These existing methodologies are based in two dimensional space.ResultsWe introduce the idea of visualising phylogenetic trees in three dimensional hyperbolic space with the Walrus graph visualisation tool and have developed a conversion tool that enables the conversion of standard phylogenetic tree formats to Walrus' format. With Walrus, it becomes possible to visualise and navigate phylogenetic trees with more than 100,000 nodes.ConclusionWalrus enables desktop visualisation of very large phylogenetic trees in 3 dimensional hyperbolic space. This application is potentially useful for visualisation of the tree of life and for functional genomics derivatives, like The Adaptive Evolution Database (TAED).

A heuristic approach to search for the maximum-likelihood (ML) phylogenetic tree based on a genetic algorithm (GA) has been developed. It outputs the best tree as well as multiple alternative trees that are not significantly worse than the best one on the basis of the likelihood criterion. These near-optimum trees are subjected to further statistical tests. This approach enables ones to infer phylogenetic trees of over 20 taxa taking account of the rate heterogeneity among sites on practical time scales on a PC cluster. Computer simulations were conducted to compare the efficiency of the present approach with that of several likelihood-based methods and distance-based methods, using amino acid sequence data of relatively large (5-24) taxa. The superiority of the ML method over distance-based methods increases as the condition of simulations becomes more realistic (an incorrect model is assumed or many taxa are involved). This approach was applied to the inference of the universal tree based on the concatenated amino acid sequences of vertically descendent genes that are shared among all genomes whose complete sequences have been reported. The inferred tree strongly supports that Archaea is paraphyletic and Eukarya is specifically related to Crenarchaeota. Apart from the paraphyly of Archaea and some minor disagreements, the universal tree based on these genes is largely consistent with the universal tree based on SSU rRNA.

Our ability to infer large phylogenetic trees that contain up to tens of thousands of species, gives rise to novel challenges in computational phylogenetics. Phylogenetic accuracy decreases as we add more and more taxa while keeping the number of sites in an alignment fixed. In addition, it is difficult, if not impossible to visually inspect such large phylogenies in order to determine whether they “make sense” or not. So, how can we assess the biological plausibility of a huge phylogeny? Here, we develop an automated plausibility assessment approach and introduce the algorithm Plausibility-Check. Our algorithm tries to determine whether a comprehensive phylogenetic tree T is plausible or not by comparing it to a set of substantially smaller and hence, more trustworthy, reference trees that contain a proper subset of the taxa in T . This is done by calculating and averaging over all topological distances between the small reference trees and the large tree. The most compute-intensive operation is the extracting of the subtrees that are induced by the taxon (sub-)set of a small reference tree in the large tree T . This is a prerequisite for calculating the topological distance between the

Divide-and-conquer is an important technique in parallel programming. However, algebraic data structures do not fit divide-and-conquer parallelism. For example, the usual pointer-based implementation of lists cannot efficiently be divided at their middle, which prevents us from developing list-iterating divide-and-conquer parallel programs. Tree-iterating programs possibly face a similar problem, because trees might be ill-balanced and list-like shapes. This paper examines parallel programming based on balanced trees: we consider balanced-tree structures and develop recursive functions on them. By virtue of their balancing nature, either bottom-up or top-down recursive functions exploit divide-and-conquer parallelism. Our main contribution is to demonstrate the promise of this approach. We propose a way of systematically developing balanced trees from parallel algorithms, and then, we show that efficient parallel programs on them can be developed by equational reasoning powered by Reynolds' relational parametricity. We consider functions that operate either lists or binary trees, and show that our methods can uniformly deal with both cases. The developed parallel programs are purely functional, correct by construction, and sometimes even simpler than known algorithms.

Understanding the relative contributions of various evolutionary processes—purifying selection, neutral drift, and adaptation—is fundamental to evolutionary biology. A common metric to distinguish these processes is the ratio of nonsynonymous to synonymous substitutions (i.e., dN/dS) interpreted from the neutral theory as a null model. However, from biophysical considerations, mutations have non-negligible effects on the biophysical properties of proteins such as folding stability. In this work, we investigated how stability affects the rate of protein evolution in phylogenetic trees by using simulations that combine explicit protein sequences with associated stability changes. We first simulated myoglobin evolution in phylogenetic trees with a biophysically realistic approach that accounts for 3D structural information and estimates of changes in stability upon mutation. We then compared evolutionary rates inferred directly from simulation to those estimated using maximum-likelihood (ML) methods. We found that the dN/dS estimated by ML methods (ωML) is highly predictive of the per gene dN/dS inferred from the simulated phylogenetic trees. This agreement is strong in the regime of high stability where protein evolution is neutral. At low folding stabilities and under mutation-selection balance, we observe deviations from neutrality (per gene dN/dS > 1 and dN/dS < 1). We showed that although per gene dN/dS is robust to these deviations, ML tests for positive selection detect statistically significant per site dN/dS > 1. Altogether, we show how protein biophysics affects the dN/dS estimations and its subsequent interpretation. These results are important for improving the current approaches for detecting positive selection.

Brassicaceae, one of the most diverse and economically valuable plant families, is distributed all over the world. Previous studies have suggested that Brassicaceae originated and diversified in the Old World. In this study, the phylogenetic relationships of 17 tribes of Brassicaceae from the Qinghai–Tibet Plateau (QTP) and adjacent areas were investigated using nuclear ribosomal internal transcribed spacer (nrITS) and chloroplast DNA sequence data (rbcL and petB‐petD) with maximum likelihood, maximum parsimony, and Bayesian methods. As suggested by both the nrITS and chloroplast DNA trees, Cardaria pubescens (C.A.Mey.) Jarm. (Lepidieae) and Draba lanceolata Royle (Arabideae) should be classified in the Eutremeae and Cardamineae, respectively. Based on over 700 newly sequenced and published nrITS sequences of Brassicaceae, an up‐to‐date comprehensive phylogeny of the family was reconstructed using the maximum likelihood method. In the phylogenetic tree, 10 monophyletic tribes were detected. They were used to clarify the lineage diversification and dispersal patterns of the 10 tribes. The results showed that most of the monophyletic tribes may have originated in different regions of the world, and then dispersed into other regions surrounding the QTP. Rapid lineage diversification rate shifts were detected in several tribes, such as Anastaticeae, which experienced a rapid shift event ∼1.38 Mya, corresponding to the rapid uplift of the QTP, indicating that the recent uplift of the QTP could have promoted diversification in Brassicaceae across and adjacent to the QTP.

he analysis of any hardware or software from the point of view of the actual and possible performance is crucial in the computer world. Huge efforts are made to create newer, better and faster computers and programs while minor design flaws can result in very low performance not even worth the invested money. Many scientists focus their research on the performance analysis of different areas like parallel programs, PC clusters, shared memory architectures, supercomputers, cache performance and so on. Basically, two approaches can be found in this effort. One group of researchers try to create analitical models to calculate the performance and limits “in theory” while the other group implements monitoring tools to collect as much data about real executions as they can and then process this data and find bottlenecks in the performance. The first session of the workshop deals with performance analysis issues of different areas in computer science. The performance of PC clusters is analysed here as well as parallel applications with the need of the power of a teraflop supercomputer. Simulator for low-level interconnection networks is presented as well as mathematical models for parallel programs. Every researcher aims at making possible to the users to improve the performance of their system and their applications. The first paper is “Beowulf Performance in CFD Multigrid Applications” authored by F. Tirado, C. Garcia, R.S. Montereo, M. Prieto and I.M. Llorente. Authors evaluated the performance of a Beowulf-class system from the viewpoint of Computational Fluid Dynamics applications. They used two multigrid solvers to test their PC cluster with different configurations. The results show that, not surprisingly, the best configuration depends on the target application. The second paper presents “SICOSYS: An Integrated Framework for studying Interconnection Network Performance in Multiprocessor Systems” written by V. Puente, J.A. Gregorio and R. Beivide. SICOSYS is a generalpurpose simulator that makes possible the analysis of the interconnection networks of multiprocessor systems. This simulator has been integrated into the RSIM shared-memory-architecture and processor simulator as well as into the SimOS simulator that also includes the effects of an operating system into the simulation. The third paper presents new ideas about “Performance Analysis for Teraflop Computers: A Distributed Automatic Approach” authored by M. Gerndt, A. Schmidt, M. Schulz and R. Wismuller. A new performance analysis system has been designed for the monitoring and analysis of extremely computationally intensive applications on a teraflop computer. In such environment, classical analysis techniques fail because they are not scalable for thousands of processors. This paper presents the design of a new, automatic performance tool that is scalable on teraflop computers using a distributed approach for the analysis process. The fourth paper is the “Execution Time Prediction for Parallel Data Processing Tasks” written by S. Juhasz. This paper presents a mathematical model for execution time prediction in the domain of parallel programs with moderate computational power needs but working on large amount of data. A parallel sorting application is then analysed as an example.

Previous chapter Next chapter Full AccessProceedings Symposium on Algorithmic Principles of Computer Systems (APOCS)Parallel In-Place Algorithms: Theory and PracticeYan Gu, Omar Obeya, and Julian ShunYan Gu, Omar Obeya, and Julian Shunpp.114 - 128Chapter DOI:https://doi.org/10.1137/1.9781611976489.9PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines, preventing large inputs from being processed. Therefore, it is desirable to design parallel in-place algorithms that use sublinear (or even polylogarithmic) auxiliary space. In this paper, we bridge the gap between theory and practice for parallel in-place (PIP) algorithms. We first define two computational models based on fork-join parallelism, which reflect modern parallel programming environments. We then introduce a variety of new parallel in-place algorithms that are simple and efficient, both in theory and in practice. Our algorithmic highlight is the Decomposable Property introduced in this paper, which enables existing non-in-place but highly-optimized parallel algorithms to be converted into parallel in-place algorithms. Using this property, we obtain algorithms for random permutation, list contraction, tree contraction, and merging that take linear work, O(n1–∊) auxiliary space, and O(n∊ · polylog(n)) span for 0 < · < 1. We also present new parallel in-place algorithms for scan, filter, merge, connectivity, biconnectivity, and minimum spanning forest using other techniques. In addition to theoretical results, we present experimental results for implementations of many of our parallel in-place algorithms. We show that on a 72-core machine with two-way hyper-threading, the parallel in-place algorithms usually outperform existing parallel algorithms for the same problems that use linear auxiliary space, indicating that the theory developed in this paper indeed leads to practical benefits in terms of both space usage and running time. Previous chapter Next chapter RelatedDetails Published:2021eISBN:978-1-61197-648-9 https://doi.org/10.1137/1.9781611976489Book Series Name:ProceedingsBook Code:APOSC21Book Pages:ii + 158

We sought novel evolutionary insights for the highly diverse Saxifragales by constructing a large phylogenetic tree encompassing 36.8% of the species-level biodiversity. • We built a phylogenetic tree for 909 species of Saxifragales and used this hypothesis to examine character evolution for annual or perennial habit, woody or herbaceous habit, ovary position, petal number, carpel number, and stamen to petal ratio. We employed likelihood approaches to investigate the effect of habit and life history on speciation and extinction within this clade. • Two major shifts occurred from a woody ancestor to the herbaceous habit, with multiple secondary changes from herbaceous to woody. Transitions among superior, subinferior, and inferior ovaries appear equiprobable. A major increase in petal number is correlated with a large increase in carpel number; these increases have co-occurred multiple times in Crassulaceae. Perennial or woody lineages have higher rates of speciation than annual or herbaceous ones, but higher probabilities of extinction offset these differences. Hence, net diversification rates are highest for annual, herbaceous lineages and lowest for woody perennials. The shift from annuality to perenniality in herbaceous taxa is frequent. Conversely, woody perennial lineages to woody annual transitions are infrequent; if they occur, the woody annual state is left immediately. • The large tree provides new insights into character evolution that are not obvious with smaller trees. Our results indicate that in some cases the evolution of angiosperms might be conditioned by constraints that have been so far overlooked.