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The real spectrum compactification of character varieties: characterizations and applications

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We announce results on a compactification of general character varieties that has good topological properties and give various interpretations of its ideal points. We relate this to the Weyl chamber … length compactification and apply our results to the theory of maximal and Hitchin representations.

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Date Published: No date defined

Publication Type: Unpublished

High-Performance approaches for Phylogenetic Placement, and its application to species and diversity quantification

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In recent years, advances in high-throughput genetic sequencing, coupled with the ongoing exponential growth and availability of computational resources, have enabled entirely new approaches in the … biological sciences. It is now possible to perform broad sequencing of the genetic content of entire communities of organisms from individual environmental samples. Such methods are particularly relevant to microbiology. The field was previously largely constrained to the study of those microbes that could be cultured in the laboratory (i.e., in vitro), which represents a small fraction of the diversity observed in nature. In contrast to this, high-throughput sequencing now enables the collection of genetic sequences directly from a microbiome in its natural environment (i.e., in situ). A typical goal of microbiome studies is the taxonomic classification of the sequences contained in a sample (the queries). Phylogenetic methods are commonly used to determine detailed taxonomic relationships between queries and well-trusted reference sequences from previously classified organisms. However, due to the high volume (106 to 109) of query sequences produced by high-throughput sequencing based microbiome sampling, accurate phylogenetic tree reconstruction is computationally infeasible. Moreover, currently used sequencing technologies typically produce short query sequences that have limited phylogenetic signal, causing instability in the inference of comprehensive phylogenies. Another common goal of microbiome studies is to quantify the diversity within a sample, as well as between multiple samples. Phylogenetic methods are commonly used for this task as well, typically involving the inference of a phylogenetic tree comprising all query sequences, or a clustered subset thereof. Again, as with taxonomic identification, analyses based on this kind of tree inference may result in inaccurate results, and/or be computationally prohibitive. In contrast to comprehensive phylogenetic inference, phylogenetic placement is a method that identifies the phylogenetic context of a query sequence within a trusted reference tree. Such methods typically regard the reference tree as immutable, that is the reference tree is not altered before, during, or after the placement of a query. This allows for the phylogenetic placement of a query sequence in linear time with respect to the size of the reference tree. When combined with taxonomic information for the reference sequences, phylogenetic placement therefore allows to identify a query. Further, phylogenetic placement enables a wealth of additional post-analysis procedures, allowing for example the association of microbiome characteristics with clinical diagnostic properties. In this thesis I present my work on designing, implementing, and improving EPA-ng, a high-performance implementation of maximum likelihood phylogenetic placement. EPA-ng is designed to scale to billions of input query sequences and to parallelize across thousands of cores in both shared, and distributed memory environments. It also improves the single-core processing speed by up to 30 times compared to its closest direct competitors. Recently, we have introduced an optional feature to EPA-ng that allows for placement into substantially larger reference trees, using an active memory management approach that trades memory for execution time. Additionally, I present a massively parallel approach to quantify the diversity of a sample, based on phylogenetic placement results. the resulting tool, called SCRAPP, combines state-of-the-art methods for maximum likelihood phylogenetic tree inference and molecular species delimitation to infer a species count distribution on a reference tree for a given sample. Furthermore, it employs a novel approach for clustering placement results, allowing the user to reduce the computational effort.

Author: Pierre Barbera

Date Published: No date defined

Publication Type: Doctoral Thesis

Empirical Numerical Properties of Maximum Likelihood Phylogenetic Inference

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Phylogenetic trees represent hypothetical evolutionary relationships between organisms. Approaches for inferring phylogenetic trees include the Maximum Likelihood (ML) method. This method relies on … numerical optimization routines that use internal numerical thresholds. We analyze the influence of these thresholds on the likelihood scores and runtimes of tree inferences for the ML inference tools RAxML-NG, IQ-Tree, and FastTree. We analyze 22 empirical datasets and show that we can speed up the tree inference in RAxML-NG and IQ-Tree by changing the default values of two such numerical thresholds. Using 15 additional simulated datasets, we show that these changes do not affect the accuracy of the inferred phylogenetic trees. For RAxML-NG, increasing the likelihood thresholds lh_epsilon and spr_lh_epsilon to 10 and 103 respectively results in an average speedup of 1.9 ± 0.6. Increasing the likelihood threshold lh_epsilon in IQ-Tree results in an average speedup of 1.3 ± 0.4. In addition to the numerical analysis, we attempt to predict the difficulty of datasets, with the aim of preventing an unnecessarily large number of tree inferences for datasets that are easy to analyze. We present our prediction experiments and discuss why this task proved to be more challenging than anticipated.

Author: Julia Haag

Date Published: No date defined

Publication Type: Master's Thesis

Algorithms, load balancing strategies, and dynamic kernels for large-scale phylogenetic tree inference under Maximum Likelihood

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Phylogenetics, the study of evolutionary relationships among biological entities, plays an essential role in biological and medical research. Its applications range from answering fundamental questions, … such as understanding the origin of life, to solving more practical problems, such as tracking pandemics in real time. Nowadays, phylogenetic trees are typically inferred from molecular data, via likelihood-based methods. Those methods strive to find the tree that maximizes a likelihood score under a given stochastic model of sequence evolution. This work focuses on the inference of species as well as gene phylogenetic trees. Species evolve through speciation and extinction events. Genes evolve through events such as gene duplication, gene loss, and horizontal gene transfer. Both processes are strongly correlated, because genes belong to species and evolve within their genomes. One can deploy models of gene evolution and to exploit this correlation between species and gene evolutionary histories, in order to improve the accuracy of phylogenetic tree inference methods. However, the most widely used phylogenetic tree inference methods disregard these phenomena and focus on models of sequence evolution only. In addition, current maximum likelihood methods are computationally expensive. This is particularly challenging as the community faces a dramatically growing amount of available molecular data, due to recent advances in sequencing technologies. To handle this data avalanche, we urgently need tools that offer faster algorithms, as well as efficient parallel implementations. In this thesis, I develop new maximum likelihood methods, that explicitly model the relationships between species and gene histories, in order to infer more accurate phylogenetic trees. Those methods employ both, new heuristics, and dedicated parallelization schemes, in order to accelerate the inference process. My first project, ParGenes, is a parallel software pipeline for inferring gene family trees from a set of per-gene multiple sequence alignments. For each input alignment, it determines the best-fit model of sequence evolution, and subsequently searches for the gene family tree with the highest likelihood under this model. To this end, ParGenes uses several state-of-the-art tools, and runs them in parallel using a novel scheduling strategy. My second project, SpeciesRax, is a method for inferring a rooted species tree from a set of unrooted gene family trees. SpeciesRax strives to find the rooted species tree that maximizes the likelihood score under a dedicated model of gene evolution, that accounts for gene duplication, gene loss, and horizontal gene transfer. In addition, I introduce a new method for assessing the confidence in the resulting species tree, as well as a novel method for estimating its branch lengths. My third project, GeneRax, is a novel maximum likelihood method for gene family tree inference. GeneRax takes as input a rooted species tree as well as a set of (per-gene) multiple sequence alignments, and outputs one gene family tree per input alignment. To this end, I introduce the so-called joint likelihood function, which combines both, a model of sequence evolution, and a model of gene evolution. In addition, GeneRax can estimate the pattern of gene duplication, gene loss, and horizontal gene transfer events that occured along the input species tree.

Author: Benoit Morel

Date Published: No date defined

Publication Type: Doctoral Thesis

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