The inference of gene trees with species trees

Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and because alleles can co-exist in populations for periods that may span several speciation events. Building models describing the relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known, and vice-versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees. In this article we review the various models that have been used to describe the relationship between gene trees and species trees. These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree-species tree models with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a better basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that gene tree-species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of genomic evolution.Comment: Review article in relation to the "Mathematical and Computational Evolutionary Biology" conference, Montpellier, 201

Phase transition in the sample complexity of likelihood-based phylogeny inference

Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which is perhaps the most widely used in phylogenetic practice because of its superior empirical accuracy. At the theoretical level, except for its consistency, that is, the guarantee of eventual correct reconstruction as the size of the input data grows, much remains to be understood about the statistical properties of maximum likelihood in this context. In particular, the best bounds on the sample complexity or sequence-length requirement of maximum likelihood, that is, the amount of data required for correct reconstruction, are exponential in the number, $n$, of tips---far from known lower bounds based on information-theoretic arguments. Here we close the gap by proving a new upper bound on the sequence-length requirement of maximum likelihood that matches up to constants the known lower bound for some standard models of evolution. More specifically, for the $r$-state symmetric model of sequence evolution on a binary phylogeny with bounded edge lengths, we show that the sequence-length requirement behaves logarithmically in $n$ when the expected amount of mutation per edge is below what is known as the Kesten-Stigum threshold. In general, the sequence-length requirement is polynomial in $n$. Our results imply moreover that the maximum likelihood estimator can be computed efficiently on randomly generated data provided sequences are as above.Comment: To appear in Probability Theory and Related Field

Alignment-free phylogenetic reconstruction: Sample complexity via a branching process analysis

We present an efficient phylogenetic reconstruction algorithm allowing insertions and deletions which provably achieves a sequence-length requirement (or sample complexity) growing polynomially in the number of taxa. Our algorithm is distance-based, that is, it relies on pairwise sequence comparisons. More importantly, our approach largely bypasses the difficult problem of multiple sequence alignment.Comment: Published in at http://dx.doi.org/10.1214/12-AAP852 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Global Alignment of Molecular Sequences via Ancestral State Reconstruction

Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on substitution-only models of sequence evolution. In practice these methods are extended beyond this simplified setting with the use of heuristics that produce global alignments of the input sequences--an important problem which has no rigorous model-based solution. In this paper we consider a new version of the multiple sequence alignment in the context of stochastic indel models. More precisely, we introduce the following {\em trace reconstruction problem on a tree} (TRPT): a binary sequence is broadcast through a tree channel where we allow substitutions, deletions, and insertions; we seek to reconstruct the original sequence from the sequences received at the leaves of the tree. We give a recursive procedure for this problem with strong reconstruction guarantees at low mutation rates, providing also an alignment of the sequences at the leaves of the tree. The TRPT problem without indels has been studied in previous work (Mossel 2004, Daskalakis et al. 2006) as a bootstrapping step towards obtaining optimal phylogenetic reconstruction methods. The present work sets up a framework for extending these works to evolutionary models with indels

A Bayesian phylogenetic hidden Markov model for B cell receptor sequence analysis.

The human body generates a diverse set of high affinity antibodies, the soluble form of B cell receptors (BCRs), that bind to and neutralize invading pathogens. The natural development of BCRs must be understood in order to design vaccines for highly mutable pathogens such as influenza and HIV. BCR diversity is induced by naturally occurring combinatorial "V(D)J" rearrangement, mutation, and selection processes. Most current methods for BCR sequence analysis focus on separately modeling the above processes. Statistical phylogenetic methods are often used to model the mutational dynamics of BCR sequence data, but these techniques do not consider all the complexities associated with B cell diversification such as the V(D)J rearrangement process. In particular, standard phylogenetic approaches assume the DNA bases of the progenitor (or "naive") sequence arise independently and according to the same distribution, ignoring the complexities of V(D)J rearrangement. In this paper, we introduce a novel approach to Bayesian phylogenetic inference for BCR sequences that is based on a phylogenetic hidden Markov model (phylo-HMM). This technique not only integrates a naive rearrangement model with a phylogenetic model for BCR sequence evolution but also naturally accounts for uncertainty in all unobserved variables, including the phylogenetic tree, via posterior distribution sampling

Conserved substitution patterns around nucleosome footprints in eukaryotes and Archaea derive from frequent nucleosome repositioning through evolution.

Nucleosomes, the basic repeat units of eukaryotic chromatin, have been suggested to influence the evolution of eukaryotic genomes, both by altering the propensity of DNA to mutate and by selection acting to maintain or exclude nucleosomes in particular locations. Contrary to the popular idea that nucleosomes are unique to eukaryotes, histone proteins have also been discovered in some archaeal genomes. Archaeal nucleosomes, however, are quite unlike their eukaryotic counterparts in many respects, including their assembly into tetramers (rather than octamers) from histone proteins that lack N- and C-terminal tails. Here, we show that despite these fundamental differences the association between nucleosome footprints and sequence evolution is strikingly conserved between humans and the model archaeon Haloferax volcanii. In light of this finding we examine whether selection or mutation can explain concordant substitution patterns in the two kingdoms. Unexpectedly, we find that neither the mutation nor the selection model are sufficient to explain the observed association between nucleosomes and sequence divergence. Instead, we demonstrate that nucleosome-associated substitution patterns are more consistent with a third model where sequence divergence results in frequent repositioning of nucleosomes during evolution. Indeed, we show that nucleosome repositioning is both necessary and largely sufficient to explain the association between current nucleosome positions and biased substitution patterns. This finding highlights the importance of considering the direction of causality between genetic and epigenetic change