In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary relationship accurately depends on the model of sequence evolution, the substitution rate, divergence times and the method used to infer phylogenetic history. A particularly challenging problem for phylogenetic methods arises when a rapid divergence event occurred in the distant past. We analyse an idealised form of this problem in which the terminal edges of a symmetric four--taxon tree are some factor ($p$) times the length of the interior edge. We determine an order $p^2$ lower bound on the growth rate for the sequence length required to resolve the tree (independent of any particular branch length). We also show that this rate of sequence length growth can be achieved by existing methods (including the simple `maximum parsimony' method), and compare these order $p^2$ bounds with an order $p$ growth rate for a model that describes low-homoplasy evolution. In the final section, we provide a generic bound on the sequence length requirement for a more general class of Markov processes.
The use of fossil evidence to calibrate divergence time estimation has a long history. More recently Bayesian MCMC has become the dominant method of divergence time estimation and fossil evidence has been re-interpreted as the specification of prior distributions on the divergence times of calibration nodes. These so-called "soft calibrations" have become widely used but the statistical properties of calibrated tree priors in a Bayesian setting has not been carefully investigated. Here we clarify that calibration densities, such as those defined in BEAST 1.5, do not represent the marginal prio…
Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular the fossilized birth-death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within tw…
Here we introduce a general class of multiple calibration birth-death tree priors for use in Bayesian phylogenetic inference. All tree priors in this class separate ancestral node heights into a set of "calibrated nodes" and "uncalibrated nodes" such that the marginal distribution of the calibrated nodes is user-specified whereas the density ratio of the birth-death prior is retained for trees with equal values for the calibrated nodes. We describe two formulations, one in which the calibration information informs the prior on ranked tree topologies, through the (conditional) prior, and the ot…
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters, such as divergence times and population sizes, they form a generative process of molecular sequence evolution. Early work on computational methods for phylogenetic network inference focused exclusively on reticulations and sought networks with the fewest number of reticulations to fit the data. As processes such as incomplete lineage sorting (ILS) could be at …
Most approaches to prediction of protein function from primary structure are based on similarity between the query sequence and sequences of known function. This approach, however, disregards the occurrence of gene duplication (paralogy) or convergent evolution of the genes. The analysis of correlated proteins that share a common domain, taking into consideration the evolutionary history of genes under study may provide a more reliable annotation of predicted proteins with unknown function. A computer program that enables real-time comparison of 'gene trees' with 'species trees' was developed.…
A classic problem in computational biology is constructing a phylogenetic tree given a set of distances between n species. In most cases, a tree structure is too constraining. We consider a circular split network, a generalization of a tree in which multiple parallel edges signify divergence. A geometric space of such networks is introduced, forming a natural extension of the work by Billera, Holmes, and Vogtmann on tree space. We explore properties of this space, and show a natural embedding of the compactification of the real moduli space of curves within it.
The inability to resolve deep node relationships of highly divergent/rapidly evolving protein families is a major factor that stymies evolutionary studies. In this manuscript, we propose a Multiple Sequence Alignment (MSA) independent method to infer evolutionary relationships. We previously demonstrated that phylogenetic profiles built using position specific scoring matrices (PSSMs) are capable of constructing informative evolutionary histories(1;2). In this manuscript, we theorize that PSSMs derived specifically from the query sequences used to construct the phylogenetic tree will improve t…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence i…
We give a non-technical introduction to convergence-divergence models, a new modeling approach for phylogenetic data that allows for the usual divergence of species post speciation but also allows for species to converge, i.e. become more similar over time. By examining the $3$-taxon case in some detail we illustrate that phylogeneticists have been "spoiled" in the sense of not having to think about the structural parameters in their models by virtue of the strong assumption that evolution is treelike. We show that there are not always good statistical reasons to prefer the usual class of tree…
The reconstruction of phylogenetic trees from discrete character data typically relies on models that assume the characters evolve under a continuous-time Markov process operating at some overall rate $λ$. When $λ$ is too high or too low, it becomes difficult to distinguish a short interior edge from a polytomy (the tree that results from collapsing the edge). In this note, we investigate the rate that maximizes the expected log-likelihood ratio (i.e. the Kullback--Leibler separation) between the four-leaf unresolved (star) tree and a four-leaf binary tree with interior edge length $ε$. For a …
We present a model for evolving agents using both genetic and cultural inheritance mechanisms. Within each agent our model maintains two distinct information stores we call the genome and the memome. Processes of adaptation are modeled as evolutionary processes at each level of adaptation (phylogenetic, ontogenetic, sociogenetic). We review relevant competing models and we show how our model improves on previous attempts to model genetic and cultural evolutionary processes. In particular we argue our model can achieve divergent gene-culture co-evolution.
Distances between sequences based on their $k$-mer frequency counts can be used to reconstruct phylogenies without first computing a sequence alignment. Past work has shown that effective use of k-mer methods depends on 1) model-based corrections to distances based on $k$-mers and 2) breaking long sequences into blocks to obtain repeated trials from the sequence-generating process. Good performance of such methods is based on having many high-quality blocks with many homologous sites, which can be problematic to guarantee a priori. Nature provides natural blocks of sequences into homologous re…
We propose a new space of phylogenetic trees which we call wald space. The motivation is to develop a space suitable for statistical analysis of phylogenies, but with a geometry based on more biologically principled assumptions than existing spaces: in wald space, trees are close if they induce similar distributions on genetic sequence data. As a point set, wald space contains the previously developed Billera-Holmes-Vogtmann (BHV) tree space; it also contains disconnected forests, like the edge-product (EP) space but without certain singularities of the EP space. We investigate two related geo…
Graph construction in QUBO-based recursive phylogenetic tree reconstruction
Graduate School of Media and Governance, Keio University（庆应义塾大学媒体治理研究生院）；Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q), Keio University（庆应义塾大学生物学-微生物组-量子研究中心 (WPI-Bio2Q)）；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC), Keio University（庆应义塾大学可持续量子人工智能中心 (KSQAIC)）
The recA/RAD51 gene family encodes a diverse set of recombinase proteins that effect homologous recombination, DNA-repair, and genome stability. The recA gene family is expressed in almost all species of Eubacteria, Archaea, and Eukaryotes, and even in some viruses. To date, efforts to resolve the deep evolutionary origins of this ancient protein family have been hindered, in part, by the high sequence divergence between families (i.e. ~30% identity between paralogous groups). Through (i) large taxon sampling, (ii) the use of a phylogenetic algorithm designed for measuring highly divergent par…
In molecular systematics, evolutionary trees are reconstructed from sequences at the tips under simple models of site substitution. A central question is how much sequence data is required to reconstruct a tree accurately? The answer depends on the lengths of the branches (edges) of the tree, with very short and very long edges requiring long sequences for accurate tree inference, particularly when these branch lengths are arranged in certain ways. For four-taxon trees, the sequence length question was settled for the case of a rapid speciation event in the distant past. Here, we generalize th…
The goal of branch length estimation in phylogenetic inference is to estimate the divergence time between a set of sequences based on compositional differences between them. A number of software is currently available facilitating branch lengths estimation for homogeneous and stationary evolutionary models. Homogeneity of the evolutionary process imposes fixed rates of evolution throughout the tree. In complex data problems this assumption is likely to put the results of the analyses in question. In this work we propose an algorithm for parameter and branch lengths inference in the discrete-ti…
The total-evidence approach to divergence-time dating uses molecular and morphological data from extant and fossil species to infer phylogenetic relationships, species divergence times, and macroevolutionary parameters in a single coherent framework. Current model-based implementations of this approach lack an appropriate model for the tree describing the diversification and fossilization process and can produce estimates that lead to erroneous conclusions. We address this shortcoming by providing a total-evidence method implemented in a Bayesian framework. This approach uses a mechanistic tre…
Aquifex aeolicus is a deep-branching hyperthermophilic chemoautotrophic bacterium restricted to hydrothermal vents and hot springs. These characteristics make it an excellent model system for studying the early evolution of metabolism. Here we present the whole-genome metabolic network of this organism and examine in detail the driving forces that have shaped it. We make extensive use of phylometabolic analysis, a method we recently introduced that generates trees of metabolic phenotypes by integrating phylogenetic and metabolic constraints. We reconstruct the evolution of a range of metabolic…
