Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.

https://bioinformatics.cs.vt.edu/~easychair/HusonBryant_MBE_2006.pdf

Application of Phylogenetic Networks in Evolutionary Studies

Phylogenetic analyses are central to many research areas in biology and typically involve the identification of homologous sequences, their multiple alignment, the phylogenetic reconstruction and the graphical representation of the inferred tree. The Phylogeny.fr platform transparently chains programs to automatically perform these tasks. It is primarily designed for biologists with no experience in phylogeny, but can also meet the needs of specialists; the first ones will find up-to-date tools chained in a phylogeny pipeline to analyze their data in a simple and robust way, while the specialists will be able to easily build and run sophisticated analyses. Phylogeny.fr offers three main modes. The ‘One Click’ mode targets non-specialists and provides a ready-to-use pipeline chaining programs with recognized accuracy and speed: MUSCLE for multiple alignment, PhyML for tree building, and TreeDyn for tree rendering. All parameters are set up to suit most studies, and users only have to provide their input sequences to obtain a ready-to-print tree. The ‘Advanced’ mode uses the same pipeline but allows the parameters of each program to be customized by users. The ‘A la Carte’ mode offers more flexibility and sophistication, as users can build their own pipeline by selecting and setting up the required steps from a large choice of tools to suit their specific needs. Prior to phylogenetic analysis, users can also collect neighbors of a query sequence by running BLAST on general or specialized databases. A guide tree then helps to select neighbor sequences to be used as input for the phylogeny pipeline. Phylogeny.fr is available at: http://www.phylogeny.fr/

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00324099/document

Phylogeny.fr: robust phylogenetic analysis for the non-specialist

Evolution of Protein Molecules

Gene families are growing rapidly, but standard methods for inferring phylogenies do not scale to alignments with over 10,000 sequences. We present FastTree, a method for constructing large phylogenies and for estimating their reliability. Instead of storing a distance matrix, FastTree stores sequence profiles of internal nodes in the tree. FastTree uses these profiles to implement Neighbor-Joining and uses heuristics to quickly identify candidate joins. FastTree then uses nearest neighbor interchanges to reduce the length of the tree. For an alignment with N sequences, L sites, and a different characters, a distance matrix requires O(N2) space and O(N2L) time, but FastTree requires just O(NLa + N) memory and O(Nlog (N)La) time. To estimate the tree's reliability, FastTree uses local bootstrapping, which gives another 100-fold speedup over a distance matrix. For example, FastTree computed a tree and support values for 158,022 distinct 16S ribosomal RNAs in 17 h and 2.4 GB of memory. Just computing pairwise Jukes–Cantor distances and storing them, without inferring a tree or bootstrapping, would require 17 h and 50 GB of memory. In simulations, FastTree was slightly more accurate than Neighbor-Joining, BIONJ, or FastME; on genuine alignments, FastTree's topologies had higher likelihoods. FastTree is available at http://microbesonline.org/fasttree.

/pdf/fasttree-computing-large-minimum-evolution-trees-with-eo2tre5l8r.pdf

FastTree: Computing Large Minimum Evolution Trees with Profiles instead of a Distance Matrix

Over the last decade, methods have been developed for the reconstruction of gene trees that take into account the species tree. Many of these methods have been based on the probabilistic duplication-loss model, which describes how a gene-tree evolves over a species-tree with respect to duplication and losses, as well as extension of this model, e.g., the DLRS (Duplication, Loss, Rate and Sequence evolution) model that also includes sequence evolution under relaxed molecular clock. A disjoint, almost as recent, and very important line of research has been focused on non protein-coding, but yet, functional DNA. For instance, DNA sequences being pseudogenes in the sense that they are not translated, may still be transcribed and the thereby produced RNA may be functional.

/pdf/gene-pseudogene-evolution-a-probabilistic-approach-19wppxwjp4.pdf

Gene-pseudogene evolution: a probabilistic approach

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

Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximations

The debate over the prevalence of lateral gene transfers (LGTs) has been intense.There is now to a large extent consensus around the view that LGT is an important evolutionary force as well as rega ...

/pdf/detecting-lgts-using-a-novel-probabilistic-modelintegrating-2bzyecyjbl.pdf

Detecting LGTs using a novel probabilistic modelintegrating duplications, LGTs, losses, rate variation,and sequence evolution

An intertwine of two graphs H and H′ is a graph G such that G contains both H and H′ as minors, but no proper minor of G contains both H and H′ as minors. We give an upper bound on the size of an intertwine of two given planar graphs. For two planar graphs H and H′, the bound is triply exponential in O(m5) where m≤max(¦V(H)¦, ¦V(H′)¦). We also give an upper on the size of an intertwine of two given trees T and T′. This bound is exponential in O(m3 log m) where m≤max(¦V(T)¦, ¦V(T′)¦). Let O1 be the set of obstructions for a minor closed family L1 and O2 the set of obstructions for a minor closed family L2. It is a natural to ask the following question: how do we given O1 and O2 compute the obstructions for L1∩L2 and L1 ∪ L2. Both these sets of obstructions are known to be finite, and to obtain the obstructions for L1∩ L2 is easy. However, to compute the obstructions for L1∪ L2 is hard. Our upper bound enables us to given O1 and O2 compute a bound on the size of any obstruction for L1 ∪ L2 whenever L1 and L2 are families of planar graphs.

The Size of an Interwine

Background: Lateral gene transfer (LGT) is an evolutionary process that has an important role in biology. It challenges the traditional binary tree-like evolution of species and is attracting incre ...

/pdf/probabilistic-inference-of-lateral-gene-transfer-events-2m0mdbobuj.pdf

Jens Lagergren

Papers

Gene-pseudogene evolution: a probabilistic approach

Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximations

Detecting LGTs using a novel probabilistic modelintegrating duplications, LGTs, losses, rate variation,and sequence evolution

The Size of an Interwine

Probabilistic inference of lateral gene transfer events.