New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.Support from the Mathematical Institute, Serbian Academy of Sciences and Arts, are acknowledged for this research

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.EThOS - Electronic Theses Online ServiceMathematical Institute, Serbian Academy of Sciences and ArtsGBUnited Kingdo

Alignment uncertainty, regressive alignment and large scale deployment

A multiple sequence alignment (MSA) provides a description of the relationship between biological sequences where columns represent a shared ancestry through an implied set of evolutionary events. The majority of research in the field has focused on improving the accuracy of alignments within the progressive alignment framework and has allowed for powerful inferences including phylogenetic reconstruction, homology modelling and disease prediction. Notwithstanding this, when applied to modern genomics datasets - often comprising tens of thousands of sequences - new challenges arise in the construction of accurate MSA. These issues can be generalised to form three basic problems. Foremost, as the number of sequences increases, progressive alignment methodologies exhibit a dramatic decrease in alignment accuracy. Additionally, for any given dataset many possible MSA solutions exist, a problem which is exacerbated with an increasing number of sequences due to alignment uncertainty. Finally, technical difficulties hamper the deployment of such genomic analysis workflows - especially in a reproducible manner - often presenting a high barrier for even skilled practitioners. This work aims to address this trifecta of problems through a web server for fast homology extension based MSA, two new methods for improved phylogenetic bootstrap supports incorporating alignment uncertainty, a novel alignment procedure that improves large scale alignments termed regressive MSA and finally a workflow framework that enables the deployment of large scale reproducible analyses across clusters and clouds titled Nextflow. Together, this work can be seen to provide both conceptual and technical advances which deliver substantial improvements to existing MSA methods and the resulting inferences.Un alineament de seqüència múltiple (MSA) proporciona una descripció de la relació entre seqüències biològiques on les columnes representen una ascendència compartida a través d'un conjunt implicat d'esdeveniments evolutius. La majoria de la investigació en el camp s'ha centrat a millorar la precisió dels alineaments dins del marc d'alineació progressiva i ha permès inferències poderoses, incloent-hi la reconstrucció filogenètica, el modelatge d'homologia i la predicció de malalties. Malgrat això, quan s'aplica als conjunts de dades de genòmica moderns, que sovint comprenen desenes de milers de seqüències, sorgeixen nous reptes en la construcció d'un MSA precís. Aquests problemes es poden generalitzar per formar tres problemes bàsics. En primer lloc, a mesura que augmenta el nombre de seqüències, les metodologies d'alineació progressiva presenten una disminució espectacular de la precisió de l'alineació. A més, per a un conjunt de dades, existeixen molts MSA com a possibles solucions un problema que s'agreuja amb un nombre creixent de seqüències a causa de la incertesa d'alineació. Finalment, les dificultats tècniques obstaculitzen el desplegament d'aquests fluxos de treball d'anàlisi genòmica, especialment de manera reproduïble, sovint presenten una gran barrera per als professionals fins i tot qualificats. Aquest treball té com a objectiu abordar aquesta trifecta de problemes a través d'un servidor web per a l'extensió ràpida d'homologia basada en MSA, dos nous mètodes per a la millora de l'arrencada filogenètica permeten incorporar incertesa d'alineació, un nou procediment d'alineació que millora els alineaments a gran escala anomenat MSA regressivu i, finalment, un marc de flux de treball permet el desplegament d'anàlisis reproduïbles a gran escala a través de clústers i computació al núvol anomenat Nextflow. En conjunt, es pot veure que aquest treball proporciona tant avanços conceptuals com tècniques que proporcionen millores substancials als mètodes MSA existents i les conseqüències resultants

Simulated annealing in the search for phylogenetic trees

I investigate use of the simulated annealing heuristic to seek phylogenetic trees judged optimal according to the principle of parsimony. I begin by looking into the central data structure in phylogenetic research, the tree. I discuss why it is usually necessary to employ a heuristic, rather than an exact method, when seeking parsimonious trees. I summarise different heuristic approaches. I explain how to use the program LVB, written to use simulated annealing in the search for parsimonious trees. I use LVB, with different combinations of values for parameters controlling the annealing search, to re-analyse two DNA sequence data matrices, one of 50 objects and one of 365 objects. Equations to estimate suitable control parameters, on the basis of desired run time and quality of result, are fitted to data obtained by these analyses. Future directions of research are discussed

Data distribution and task scheduling for distributed computing of all-to-all comparison problems

This research studied distributed computing of all-to-all comparison problems with big data sets. The thesis formalised the problem, and developed a high-performance and scalable computing framework with a programming model, data distribution strategies and task scheduling policies to solve the problem. The study considered storage usage, data locality and load balancing for performance improvement in solving the problem. The research outcomes can be applied in bioinformatics, biometrics and data mining and other domains in which all-to-all comparisons are a typical computing pattern

Gene order rearrangement methods for the reconstruction of phylogeny

The study of phylogeny, i.e. the evolutionary history of species, is a central problem in biology and a key for understanding characteristics of contemporary species. Many problems in this area can be formulated as combinatorial optimisation problems which makes it particularly interesting for computer scientists. The reconstruction of the phylogeny of species can be based on various kinds of data, e.g. morphological properties or characteristics of the genetic information of the species. Maximum parsimony is a popular and widely used method for phylogenetic reconstruction aiming for an explanation of the observed data requiring the least evolutionary changes. A certain property of the genetic information gained much interest for the reconstruction of phylogeny in recent time: the organisation of the genomes of species, i.e. the arrangement of the genes on the chromosomes. But the idea to reconstruct phylogenetic information from gene arrangements has a long history. In Dobzhansky and Sturtevant (1938) it was already pointed out that “a comparison of the different gene arrangements in the same chromosome may, in certain cases, throw light on the historical relationships of these structures, and consequently on the history of the species as a whole”. This kind of data is promising for the study of deep evolutionary relationships because gene arrangements are believed to evolve slowly (Rokas and Holland, 2000). This seems to be the case especially for mitochondrial genomes which are available for a wide range of species (Boore, 1999). The development of methods for the reconstruction of phylogeny from gene arrangement data has made considerable progress during the last years. Prominent examples are the computation of parsimonious evolutionary scenarios, i.e. a shortest sequence of rearrangements transforming one arrangement of genes into another or the length of such a minimal scenario (Hannenhalli and Pevzner, 1995b; Sankoff, 1992; Watterson et al., 1982); the reconstruction of parsimonious phylogenetic trees from gene arrangement data (Bader et al., 2008; Bernt et al., 2007b; Bourque and Pevzner, 2002; Moret et al., 2002a); or the computation of the similarities of gene arrangements (Bergeron et al., 2008a; Heber et al., 2009). 1 1 Introduction The central theme of this work is to provide efficient algorithms for modified versions of fundamental genome rearrangement problems using more plausible rearrangement models. Two types of modified rearrangement models are explored. The first type is to restrict the set of allowed rearrangements as follows. It can be observed that certain groups of genes are preserved during evolution. This may be caused by functional constraints which prevented the destruction (Lathe et al., 2000; Sémon and Duret, 2006; Xie et al., 2003), certain properties of the rearrangements which shaped the gene orders (Eisen et al., 2000; Sankoff, 2002; Tillier and Collins, 2000), or just because no destructive rearrangement happened since the speciation of the gene orders. It can be assumed that gene groups, found in all studied gene orders, are not acquired independently. Accordingly, these gene groups should be preserved in plausible reconstructions of the course of evolution, in particular the gene groups should be present in the reconstructed putative ancestral gene orders. This can be achieved by restricting the set of rearrangements, which are allowed for the reconstruction, to those which preserve the gene groups of the given gene orders. Since it is difficult to determine functionally what a gene group is, it has been proposed to consider common combinatorial structures of the gene orders as gene groups (Marcotte et al., 1999; Overbeek et al., 1999). The second considered modification of the rearrangement model is extending the set of allowed rearrangement types. Different types of rearrangement operations have shuffled the gene orders during evolution. It should be attempted to use the same set of rearrangement operations for the reconstruction otherwise distorted or even wrong phylogenetic conclusions may be obtained in the worst case. Both possibilities have been considered for certain rearrangement problems before. Restricted sets of allowed rearrangements have been used successfully for the computation of parsimonious rearrangement scenarios consisting of inversions only where the gene groups are identified as common intervals (Bérard et al., 2007; Figeac and Varré, 2004). Extending the set of allowed rearrangement operations is a delicate task. On the one hand it is unknown which rearrangements have to be regarded because this is part of the phylogeny to be discovered. On the other hand, efficient exact rearrangement methods including several operations are still rare, in particular when transpositions should be included. For example, the problem to compute shortest rearrangement scenarios including transpositions is still of unknown computational complexity. Currently, only efficient approximation algorithms are known (e.g. Bader and Ohlebusch, 2007; Elias and Hartman, 2006). Two problems have been studied with respect to one or even both of these possibilities in the scope of this work. The first one is the inversion median problem. Given the gene orders of some taxa, this problem asks for potential ancestral gene orders such that the corresponding inversion scenario is parsimonious, i.e. has a minimum length. Solving this problem is an essential component 2 of algorithms for computing phylogenetic trees from gene arrangements (Bourque and Pevzner, 2002; Moret et al., 2002a, 2001). The unconstrained inversion median problem is NP-hard (Caprara, 2003). In Chapter 3 the inversion median problem is studied under the additional constraint to preserve gene groups of the input gene orders. Common intervals, i.e. sets of genes that appear consecutively in the gene orders, are used for modelling gene groups. The problem of finding such ancestral gene orders is called the preserving inversion median problem. Already the problem of finding a shortest inversion scenario for two gene orders is NP-hard (Figeac and Varré, 2004). Mitochondrial gene orders are a rich source for phylogenetic investigations because they are known for more than 1 000 species. Four rearrangement operations are reported at least in the literature to be relevant for the study of mitochondrial gene order evolution (Boore, 1999): That is inversions, transpositions, inverse transpositions, and tandem duplication random loss (TDRL). Efficient methods for a plausible reconstruction of genome rearrangements for mitochondrial gene orders using all four operations are presented in Chapter 4. An important rearrangement operation, in particular for the study of mitochondrial gene orders, is the tandem duplication random loss operation (e.g. Boore, 2000; Mauro et al., 2006). This rearrangement duplicates a part of a gene order followed by the random loss of one of the redundant copies of each gene. The gene order is rearranged depending on which copy is lost. This rearrangement should be regarded for reconstructing phylogeny from gene order data. But the properties of this rearrangement operation have rarely been studied (Bouvel and Rossin, 2009; Chaudhuri et al., 2006). The combinatorial properties of the TDRL operation are studied in Chapter 5. The enumeration and counting of sorting TDRLs, that is TDRL operations reducing the distance, is studied in particular. Closed formulas for computing the number of sorting TDRLs and methods for the enumeration are presented. Furthermore, TDRLs are one of the operations considered in Chapter 4. An interesting property of this rearrangement, distinguishing it from other rearrangements, is its asymmetry. That is the effects of a single TDRL can (in the most cases) not be reversed with a single TDRL. The use of this property for phylogeny reconstruction is studied in Section 4.3. This thesis is structured as follows. The existing approaches obeying similar types of modified rearrangement models as well as important concepts and computational methods to related problems are reviewed in Chapter 2. The combinatorial structures of gene orders that have been proposed for identifying gene groups, in particular common intervals, as well as the computational approaches for their computation are reviewed in Section 2.2. Approaches for computing parsimonious pairwise rearrangement scenarios are outlined in Section 2.3. Methods for the computation genome rearrangement scenarios obeying biologically motivated constraints, as introduced above, are detailed in Section 2.4. The approaches for the inversion median problem are covered in Section 2.5. Methods for the reconstruction of phylogenetic trees from gene arrangement data are briefly outlined in Section 2.6.3 1 Introduction Chapter 3 introduces the new algorithms CIP, ECIP, and TCIP for solving the preserving inversion median problem. The efficiency of the algorithm is empirically studied for simulated as well as mitochondrial data. The description of algorithms CIP and ECIP is based on Bernt et al. (2006b). TCIP has been described in Bernt et al. (2007a, 2008b). But the theoretical foundation of TCIP is extended significantly within this work in order to allow for more than three input permutations. Gene order rearrangement methods that have been developed for the reconstruction of the phylogeny of mitochondrial gene orders are presented in the fourth chapter. The presented algorithm CREx computes rearrangement scenarios for pairs of gene orders. CREx regards the four types of rearrangement operations which are important for mitochondrial gene orders. Based on CREx the algorithm TreeREx for assigning rearrangement events to a given tree is developed. The quality of the CREx reconstructions is analysed in a large empirical study for simulated gene orders. The results of TreeREx are analysed for several mitochondrial data sets. Algorithms CREx and TreeREx have been published in Bernt et al. (2008a, 2007c). The analysis of the mitochondrial gene orders of Echinodermata was included in Perseke et al. (2008). Additionally, a new and simple method is presented to explore the potential of the CREx method. The new method is applied to the complete mitochondrial data set. The problem of enumerating and counting sorting TDRLs is studied in Chapter 5. The theoretical results are covered to a large extent by Bernt et al. (2009b). The missing combinatorial explanation for some of the presented formulas is given here for the first time. Therefor, a new method for the enumeration and counting of sorting TDRLs has been developed (Bernt et al., 2009a)

High performance bioinformatics and computational biology on general-purpose graphics processing units

Bioinformatics and Computational Biology (BCB) is a relatively new multidisciplinary field which brings together many aspects of the fields of biology, computer science, statistics, and engineering. Bioinformatics extracts useful information from biological data and makes these more intuitive and understandable by applying principles of information sciences, while computational biology harnesses computational approaches and technologies to answer biological questions conveniently. Recent years have seen an explosion of the size of biological data at a rate which outpaces the rate of increases in the computational power of mainstream computer technologies, namely general purpose processors (GPPs). The aim of this thesis is to explore the use of off-the-shelf Graphics Processing Unit (GPU) technology in the high performance and efficient implementation of BCB applications in order to meet the demands of biological data increases at affordable cost. The thesis presents detailed design and implementations of GPU solutions for a number of BCB algorithms in two widely used BCB applications, namely biological sequence alignment and phylogenetic analysis. Biological sequence alignment can be used to determine the potential information about a newly discovered biological sequence from other well-known sequences through similarity comparison. On the other hand, phylogenetic analysis is concerned with the investigation of the evolution and relationships among organisms, and has many uses in the fields of system biology and comparative genomics. In molecular-based phylogenetic analysis, the relationship between species is estimated by inferring the common history of their genes and then phylogenetic trees are constructed to illustrate evolutionary relationships among genes and organisms. However, both biological sequence alignment and phylogenetic analysis are computationally expensive applications as their computing and memory requirements grow polynomially or even worse with the size of sequence databases. The thesis firstly presents a multi-threaded parallel design of the Smith- Waterman (SW) algorithm alongside an implementation on NVIDIA GPUs. A novel technique is put forward to solve the restriction on the length of the query sequence in previous GPU-based implementations of the SW algorithm. Based on this implementation, the difference between two main task parallelization approaches (Inter-task and Intra-task parallelization) is presented. The resulting GPU implementation matches the speed of existing GPU implementations while providing more flexibility, i.e. flexible length of sequences in real world applications. It also outperforms an equivalent GPPbased implementation by 15x-20x. After this, the thesis presents the first reported multi-threaded design and GPU implementation of the Gapped BLAST with Two-Hit method algorithm, which is widely used for aligning biological sequences heuristically. This achieved up to 3x speed-up improvements compared to the most optimised GPP implementations. The thesis then presents a multi-threaded design and GPU implementation of a Neighbor-Joining (NJ)-based method for phylogenetic tree construction and multiple sequence alignment (MSA). This achieves 8x-20x speed up compared to an equivalent GPP implementation based on the widely used ClustalW software. The NJ method however only gives one possible tree which strongly depends on the evolutionary model used. A more advanced method uses maximum likelihood (ML) for scoring phylogenies with Markov Chain Monte Carlo (MCMC)-based Bayesian inference. The latter was the subject of another multi-threaded design and GPU implementation presented in this thesis, which achieved 4x-8x speed up compared to an equivalent GPP implementation based on the widely used MrBayes software. Finally, the thesis presents a general evaluation of the designs and implementations achieved in this work as a step towards the evaluation of GPU technology in BCB computing, in the context of other computer technologies including GPPs and Field Programmable Gate Arrays (FPGA) technology

Evolution of gene networks in sex determination.

In this work, the evolution of sex determination gene networks is inves tigated using a modelling approach. Recent evidence indicates that an in crease in the complexity of interactions has played an important role in gene network evolution. Sex determination mechanisms offer a good model for studying gene network evolution because, among other reasons, they evolve rapidly. In chapter 2, the potential for evolutionary change of the existing Drosophila sex determination gene network is considered. With the aid of a synchronous logical model, theoretical concepts such as a network-specific form of mutation are defined, as well as a notion of functional equivalence between networks. Applying this theoretical framework to the sex deter mination mechanism, it is found that sex determination networks generally exist within large sets of functionally equivalent networks all of which satisfy the sex determination task. These large sets are in turn composed of sub sets which are mutationally related, suggesting a high degree of flexibility is available without compromising the core functionality. The technique for finding functional equivalence between networks suggests a general method for gene network reconstruction, which is explored in chapter 3. Lastly, in chapters 4 and 5, a hierarchical model is presented which integrates popu lation genetics techniques with network dynamics. This model consists of a core population genetics simulation within which parameters such as the sex and fitness of the genotype are calculated from the corresponding network dynamics. The model is used to investigate the early evolution of sex deter mination networks. Following from a hypothesis proposed by Wilkins (1995), the assumption is made that sex determination networks have evolved in a retrograde manner from bottom to top. Starting from the simplest possible ancestral system, based on a single locus, we explore the way in which more complex systems, involving two or three loci, could have evolved

Development of data integration tools within functional genomics

Due to technological advances across all scientific domains, data is generated at an extremely fast pace. This is especially true in biology, where advances in computational and sequencing technologies led to the necessity to develop automated methods for data analysis; thus the field of bioinformatics was born. This thesis focuses on one specific field within bioinformatics - functional genomics. To be precise, in the development of techniques and software for the integration of data to generate novel insights. Indeed, as the amount of knowledge increases, so does the need to integrate it systematically. In this context, the work described herein relates to the integration of multiple resources to improve the functional annotation of proteins, which led to the development of two bioinformatic tools - Mantis and UniFunc. For the downstream integration and analysis of functional predictions, a network annotation tool was developed - UniFuncNet, which, together with the previous tools, enables the efficient functional characterisation of individual organisms or communities

Phylogenetics in the Genomic Era

Molecular phylogenetics was born in the middle of the 20th century, when the advent of protein and DNA sequencing offered a novel way to study the evolutionary relationships between living organisms. The first 50 years of the discipline can be seen as a long quest for resolving power. The goal – reconstructing the tree of life – seemed to be unreachable, the methods were heavily debated, and the data limiting. Maybe for these reasons, even the relevance of the whole approach was repeatedly questioned, as part of the so-called molecules versus morphology debate. Controversies often crystalized around long-standing conundrums, such as the origin of land plants, the diversification of placental mammals, or the prokaryote/eukaryote divide. Some of these questions were resolved as gene and species samples increased in size. Over the years, molecular phylogenetics has gradually evolved from a brilliant, revolutionary idea to a mature research field centred on the problem of reliably building trees. This logical progression was abruptly interrupted in the late 2000s. High-throughput sequencing arose and the field suddenly moved into something entirely different. Access to genome-scale data profoundly reshaped the methodological challenges, while opening an amazing range of new application perspectives. Phylogenetics left the realm of systematics to occupy a central place in one of the most exciting research fields of this century – genomics. This is what this book is about: how we do trees, and what we do with trees, in the current phylogenomic era. One obvious, practical consequence of the transition to genome-scale data is that the most widely used tree-building methods, which are based on probabilistic models of sequence evolution, require intensive algorithmic optimization to be applicable to current datasets. This problem is considered in Part 1 of the book, which includes a general introduction to Markov models (Chapter 1.1) and a detailed description of how to optimally design and implement Maximum Likelihood (Chapter 1.2) and Bayesian (Chapter 1.4) phylogenetic inference methods. The importance of the computational aspects of modern phylogenomics is such that efficient software development is a major activity of numerous research groups in the field. We acknowledge this and have included seven "How to" chapters presenting recent updates of major phylogenomic tools – RAxML (Chapter 1.3), PhyloBayes (Chapter 1.5), MACSE (Chapter 2.3), Bgee (Chapter 4.3), RevBayes (Chapter 5.2), Beagle (Chapter 5.4), and BPP (Chapter 5.6). Genome-scale data sets are so large that statistical power, which had been the main limiting factor of phylogenetic inference during previous decades, is no longer a major issue. Massive data sets instead tend to amplify the signal they deliver – be it biological or artefactual – so that bias and inconsistency, instead of sampling variance, are the main problems with phylogenetic inference in the genomic era. Part 2 covers the issues of data quality and model adequacy in phylogenomics. Chapter 2.1 provides an overview of current practice and makes recommendations on how to avoid the more common biases. Two chapters review the challenges and limitations of two key steps of phylogenomic analysis pipelines, sequence alignment (Chapter 2.2) and orthology prediction (Chapter 2.4), which largely determine the reliability of downstream inferences. The performance of tree building methods is also the subject of Chapter 2.5, in which a new approach is introduced to assess the quality of gene trees based on their ability to correctly predict ancestral gene order. Analyses of multiple genes typically recover multiple, distinct trees. Maybe the biggest conceptual advance induced by the phylogenetic to phylogenomic transition is the suggestion that one should not simply aim to reconstruct “the” species tree, but rather to be prepared to make sense of forests of gene trees. Chapter 3.1 reviews the numerous reasons why gene trees can differ from each other and from the species tree, and what the implications are for phylogenetic inference. Chapter 3.2 focuses on gene trees/species trees reconciliation methods that account for gene duplication/loss and horizontal gene transfer among lineages. Incomplete lineage sorting is another major source of phylogenetic incongruence among loci, which recently gained attention and is covered by Chapter 3.3. Chapter 3.4 concludes this part by taking a user’s perspective and examining the pros and cons of concatenation versus separate analysis of gene sequence alignments. Modern genomics is comparative and phylogenetic methods are key to a wide range of questions and analyses relevant to the study of molecular evolution. This is covered by Part 4. We argue that genome annotation, either structural or functional, can only be properly achieved in a phylogenetic context. Chapters 4.1 and 4.2 review the power of these approaches and their connections with the study of gene function. Molecular substitution rates play a key role in our understanding of the prevalence of nearly neutral versus adaptive molecular evolution, and the influence of species traits on genome dynamics (Chapter 4.4). The analysis of substitution rates, and particularly the detection of positive selection, requires sophisticated methods and models of coding sequence evolution (Chapter 4.5). Phylogenomics also offers a unique opportunity to explore evolutionary convergence at a molecular level, thus addressing the long-standing question of predictability versus contingency in evolution (Chapter 4.6). The development of phylogenomics, as reviewed in Parts 1 through 4, has resulted in a powerful conceptual and methodological corpus, which is often reused for addressing problems of interest to biologists from other fields. Part 5 illustrates this application potential via three selected examples. Chapter 5.1 addresses the link between phylogenomics and palaeontology; i.e., how to optimally combine molecular and fossil data for estimating divergence times. Chapter 5.3 emphasizes the importance of the phylogenomic approach in virology and its potential to trace the origin and spread of infectious diseases in space and time. Finally, Chapter 5.5 recalls why phylogenomic methods and the multi-species coalescent model are key in addressing the problem of species delimitation – one of the major goals of taxonomy. It is hard to predict where phylogenomics as a discipline will stand in even 10 years. Maybe a novel technological revolution will bring it to yet another level? We strongly believe, however, that tree thinking will remain pivotal in the treatment and interpretation of the deluge of genomic data to come. Perhaps a prefiguration of the future of our field is provided by the daily monitoring of the current Covid-19 outbreak via the phylogenetic analysis of coronavirus genomic data in quasi real time – a topic of major societal importance, contemporary to the publication of this book, in which phylogenomics is instrumental in helping to fight disease