Computing nearest neighbour interchange distances between ranked phylogenetic trees

Ranked Subtree Prune and Regraft

Phylogenetic trees are a mathematical formalisation of evolutionary histories between organisms, species, genes, cancer cells, etc. For many applications, e.g. when analysing virus transmission trees or cancer evolution, (phylogenetic) time trees are of interest, where branch lengths represent times. Computational methods for reconstructing time trees from (typically molecular) sequence data, for example Bayesian phylogenetic inference using Markov Chain Monte Carlo (MCMC) methods, rely on algorithms that sample the treespace. They employ tree rearrangement operations such as [Formula: see text] (Subtree Prune and Regraft) and [Formula: see text] (Nearest Neighbour Interchange) or, in the case of time tree inference, versions of these that take times of internal nodes into account. While the classic [Formula: see text] tree rearrangement is well-studied, its variants for time trees are less understood, limiting comparative analysis for time tree methods. In this paper we consider a modification of the classical [Formula: see text] rearrangement on the space of ranked phylogenetic trees, which are trees equipped with a ranking of all internal nodes. This modification results in two novel treespaces, which we propose to study. We begin this study by discussing algorithmic properties of these treespaces, focusing on those relating to the complexity of computing distances under the ranked [Formula: see text] operations as well as similarities and differences to known tree rearrangement based treespaces. Surprisingly, we show the counterintuitive result that adding leaves to trees can actually decrease their ranked [Formula: see text] distance, which may have an impact on the results of time tree sampling algorithms given uncertain "rogue taxa".

Leaping through Tree Space: Continuous Phylogenetic Inference for Rooted and Unrooted Trees

Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains challenging. To address this problem, for the first time, we perform both tree exploration and inference in a continuous space where the computation of gradients is possible. This continuous relaxation allows for major leaps across tree space in both rooted and unrooted trees, and is less susceptible to convergence to local minima. Our approach outperforms the current best methods for inference on unrooted trees and, in simulation, accurately infers the tree and root in ultrametric cases. The approach is effective in cases of empirical data with negligible amounts of data, which we demonstrate on the phylogeny of jawed vertebrates. Indeed, only a few genes with an ultrametric signal were generally sufficient for resolving the major lineages of vertebrates. Optimization is possible via automatic differentiation and our method presents an effective way forward for exploring the most difficult, data-deficient phylogenetic questions.

Testing for Phylogenetic Signal in Single-Cell RNA-Seq Data

Phylogenetic methods are emerging as a useful tool to understand cancer evolutionary dynamics, including tumor structure, heterogeneity, and progression. Most currently used approaches utilize either bulk whole genome sequencing or single-cell DNA sequencing and are based on calling copy number alterations and single nucleotide variants (SNVs). Single-cell RNA sequencing (scRNA-seq) is commonly applied to explore differential gene expression of cancer cells throughout tumor progression. The method exacerbates the single-cell sequencing problem of low yield per cell with uneven expression levels. This accounts for low and uneven sequencing coverage and makes SNV detection and phylogenetic analysis challenging. In this article, we demonstrate for the first time that scRNA-seq data contain sufficient evolutionary signal and can also be utilized in phylogenetic analyses. We explore and compare results of such analyses based on both expression levels and SNVs called from scRNA-seq data. Both techniques are shown to be useful for reconstructing phylogenetic relationships between cells, reflecting the clonal composition of a tumor. Both standardized expression values and SNVs appear to be equally capable of reconstructing a similar pattern of phylogenetic relationship. This pattern is stable even when phylogenetic uncertainty is taken in account. Our results open up a new direction of somatic phylogenetics based on scRNA-seq data. Further research is required to refine and improve these approaches to capture the full picture of somatic evolutionary dynamics in cancer.

OUP accepted manuscript

As genomic sequence data become increasingly available, inferring the phylogeny of the species as that of concatenated genomic data can be enticing. However, this approach makes for a biased estimator of branch lengths and substitution rates and an inconsistent estimator of tree topology. Bayesian multispecies coalescent (MSC) methods address these issues. This is achieved by constraining a set of gene trees within a species tree and jointly inferring both under a Bayesian framework. However, this approach comes at the cost of increased computational demand. Here, we introduce StarBeast3—a software package for efficient Bayesian inference under the MSC model via Markov chain Monte Carlo. We gain efficiency by introducing cutting-edge proposal kernels and adaptive operators, and StarBeast3 is particularly efficient when a relaxed clock model is applied. Furthermore, gene-tree inference is parallelized, allowing the software to scale with the size of the problem. We validated our software and benchmarked its performance using three real and two synthetic data sets. Our results indicate that StarBeast3 is up to one-and-a-half orders of magnitude faster than StarBeast2, and therefore more than two orders faster than *BEAST, depending on the data set and on the parameter, and can achieve convergence on large data sets with hundreds of genes. StarBeast3 is open-source and is easy to set up with a friendly graphical user interface. [Adaptive; Bayesian inference; BEAST 2; effective population sizes; high performance; multispecies coalescent; parallelization; phylogenetics.]

Discrete coalescent trees

In many phylogenetic applications, such as cancer and virus evolution, time trees, evolutionary histories where speciation events are timed, are inferred. Of particular interest are clock-like trees, where all leaves are sampled at the same time and have equal distance to the root. One popular approach to model clock-like trees is coalescent theory, which is used in various tree inference software packages. Methodologically, phylogenetic inference methods require a tree space over which the inference is performed, and the geometry of this space plays an important role in statistical and computational aspects of tree inference algorithms. It has recently been shown that coalescent tree spaces possess a unique geometry, different from that of classical phylogenetic tree spaces. Here we introduce and study a space of discrete coalescent trees. They assume that time is discrete, which is natural in many computational applications. This tree space is a generalisation of the previously studied ranked nearest neighbour interchange space, and is built upon tree-rearrangement operations. We generalise existing results about ranked trees, including an algorithm for computing distances in polynomial time, and in particular provide new results for both the space of discrete coalescent trees and the space of ranked trees. We establish several geometrical properties of these spaces and show how these properties impact various algorithms used in phylogenetic analyses. Our tree space is a discretisation of a previously introduced time tree space, called t-space, and hence our results can be used to approximate solutions to various open problems in t-space.