On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo

A roadmap of phylogenomic methods for studying polyploid plant genera

Phylogenetic inference of polyploid species is the first step towards understanding their patterns of diversification. In this paper, we review the challenges and limitations of inferring species relationships of polyploid plants using traditional phylogenetic sequencing approaches, as well as the mischaracterization of the species tree from single or multiple gene trees. We provide a roadmap to infer interspecific relationships among polyploid lineages by comparing and evaluating the application of current phylogenetic, phylogenomic, transcriptomic, and whole-genome approaches using different sequencing platforms. For polyploid species tree reconstruction, we assess the following criteria: (1) the amount of prior information or tools required to capture the genetic region(s) of interest; (2) the probability of recovering homeologs for polyploid species; and (3) the time efficiency of downstream data analysis. Moreover, we discuss bioinformatic pipelines that can reconstruct networks of polyploid species relationships. In summary, although current phylogenomic approaches have improved our understanding of reticulate species relationships in polyploid-rich genera, the difficulties of recovering reliable orthologous genes and sorting all homeologous copies for allopolyploids remain a challenge. In the future, assembled long-read sequencing data will assist the recovery and identification of multiple gene copies, which can be particularly useful for reconstructing the multiple independent origins of polyploids.

Anomalous networks under the multispecies coalescent: theory and prevalence

Reticulations in a phylogenetic network represent processes such as gene flow, admixture, recombination and hybrid speciation. Extending definitions from the tree setting, an anomalous network is one in which some unrooted tree topology displayed in the network appears in gene trees with a lower frequency than a tree not displayed in the network. We investigate anomalous networks under the Network Multispecies Coalescent Model with possible correlated inheritance at reticulations. Focusing on subsets of 4 taxa, we describe a new algorithm to calculate quartet concordance factors on networks of any level, faster than previous algorithms because of its focus on 4 taxa. We then study topological properties required for a 4-taxon network to be anomalous, uncovering the key role of [Formula: see text]-cycles: cycles of 3 edges parent to a sister group of 2 taxa. Under the model of common inheritance, that is, when each gene tree coalesces within a species tree displayed in the network, we prove that 4-taxon networks are never anomalous. Under independent and various levels of correlated inheritance, we use simulations under realistic parameters to quantify the prevalence of anomalous 4-taxon networks, finding that truly anomalous networks are rare. At the same time, however, we find a significant fraction of networks close enough to the anomaly zone to appear anomalous, when considering the quartet concordance factors observed from a few hundred genes. These apparent anomalies may challenge network inference methods.

A global test of hybrid ancestry from genome-scale data

Methods based on the multi-species coalescent have been widely used in phylogenetic tree estimation using genome-scale DNA sequence data to understand the underlying evolutionary relationship between the sampled species. Evolutionary processes such as hybridization, which creates new species through interbreeding between two different species, necessitate inferring a species network instead of a species tree. A species tree is strictly bifurcating and thus fails to incorporate hybridization events which require an internal node of degree three. Hence, it is crucial to decide whether a tree or network analysis should be performed given a DNA sequence data set, a decision that is based on the presence of hybrid species in the sampled species. Although many methods have been proposed for hybridization detection, it is rare to find a technique that does so globally while considering a data generation mechanism that allows both hybridization and incomplete lineage sorting. In this paper, we consider hybridization and coalescence in a unified framework and propose a new test that can detect whether there are any hybrid species in a set of species of arbitrary size. Based on this global test of hybridization, one can decide whether a tree or network analysis is appropriate for a given data set.

PhyloCoalSimulations: A Simulator for Network Multispecies Coalescent Models, Including a New Extension for the Inheritance of Gene Flow

We consider the evolution of phylogenetic gene trees along phylogenetic species networks, according to the network multispecies coalescent process, and introduce a new network coalescent model with correlated inheritance of gene flow. This model generalizes two traditional versions of the network coalescent: with independent or common inheritance. At each reticulation, multiple lineages of a given locus are inherited from parental populations chosen at random, either independently across lineages or with positive correlation according to a Dirichlet process. This process may account for locus-specific probabilities of inheritance, for example. We implemented the simulation of gene trees under these network coalescent models in the Julia package PhyloCoalSimulations, which depends on PhyloNetworks and its powerful network manipulation tools. Input species phylogenies can be read in extended Newick format, either in numbers of generations or in coalescent units. Simulated gene trees can be written in Newick format, and in a way that preserves information about their embedding within the species network. This embedding can be used for downstream purposes, such as to simulate species-specific processes like rate variation across species, or for other scenarios as illustrated in this note. This package should be useful for simulation studies and simulation-based inference methods. The software is available open source with documentation and a tutorial at https://github.com/cecileane/PhyloCoalSimulations.jl.

ANOMALOUS NETWORKS UNDER THE MULTISPECIES COALESCENT: THEORY AND PREVALENCE

Reticulations in a phylogenetic network represent processes such as gene flow, admixture, recombination and hybrid speciation. Extending definitions from the tree setting, an anomalous network is one in which some unrooted tree topology displayed in the network appears in gene trees with a lower frequency than a tree not displayed in the network. We investigate anomalous networks under the Network Multispecies Coalescent Model with possible correlated inheritance at reticulations. Focusing on subsets of 4 taxa, we describe a new algorithm to calculate quartet concordance factors on networks of any level, faster than previous algorithms because of its focus on 4 taxa. We then study topological properties required for a 4-taxon network to be anomalous, uncovering the key role of 32-cycles: cycles of 3 edges parent to a sister group of 2 taxa. Under the model of common inheritance, that is, when each gene tree coalesces within a species tree displayed in the network, we prove that 4-taxon networks are never anomalous. Under independent and various levels of correlated inheritance, we use simulations under realistic parameters to quantify the prevalence of anomalous 4-taxon networks, finding that truly anomalous networks are rare. At the same time, however, we find a significant fraction of networks close enough to the anomaly zone to appear anomalous, when considering the quartet concordance factors observed from a few hundred genes. These apparent anomalies may challenge network inference methods.

Identifiability of local and global features of phylogenetic networks from average distances

Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with likelihood-based methods limits the size of networks that can be handled. Methods based on pairwise distances could offer faster alternatives. We study here the information that average pairwise distances contain on the underlying phylogenetic network, by characterizing local and global features that can or cannot be identified. For general networks, we clarify that the root and edge lengths adjacent to reticulations are not identifiable, and then focus on the class of zipped-up semidirected networks. We provide a criterion to swap subgraphs locally, such as 3-cycles, resulting in indistinguishable networks. We propose the "distance split tree", which can be constructed from pairwise distances, and prove that it is a refinement of the network's tree of blobs, capturing the tree-like features of the network. For level-1 networks, this distance split tree is equal to the tree of blobs refined to separate polytomies from blobs, and we prove that the mixed representation of the network is identifiable. The information loss is localized around 4-cycles, for which the placement of the reticulation is unidentifiable. The mixed representation combines split edges for 4-cycles, regular tree and hybrid edges from the semidirected network, and edge parameters that encode all information identifiable from average pairwise distances.

Recent progress on methods for estimating and updating large phylogenies

With the increased availability of sequence data and even of fully sequenced and assembled genomes, phylogeny estimation of very large trees (even of hundreds of thousands of sequences) is now a goal for some biologists. Yet, the construction of these phylogenies is a complex pipeline presenting analytical and computational challenges, especially when the number of sequences is very large. In the past few years, new methods have been developed that aim to enable highly accurate phylogeny estimations on these large datasets, including divide-and-conquer techniques for multiple sequence alignment and/or tree estimation, methods that can estimate species trees from multi-locus datasets while addressing heterogeneity due to biological processes (e.g. incomplete lineage sorting and gene duplication and loss), and methods to add sequences into large gene trees or species trees. Here we present some of these recent advances and discuss opportunities for future improvements. This article is part of a discussion meeting issue 'Genomic population structures of microbial pathogens'.