A Polynomial-Time Algorithm for Minimizing the Deep Coalescence Cost for Level-1 Species Networks

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.

Classes of explicit phylogenetic networks and their biological and mathematical significance

The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately represented by a phylogenetic tree, and rooted phylogenetic networks that describe such complex processes have been introduced as a generalization of rooted phylogenetic trees. In fact, estimating rooted phylogenetic networks from genomic sequence data and analyzing their structural properties is one of the most important tasks in contemporary phylogenetics. Over the last two decades, several subclasses of rooted phylogenetic networks (characterized by certain structural constraints) have been introduced in the literature, either to model specific biological phenomena or to enable tractable mathematical and computational analyses. In the present manuscript, we provide a thorough review of these network classes, as well as provide a biological interpretation of the structural constraints underlying these networks where possible. In addition, we discuss how imposing structural constraints on the network topology can be used to address the scalability and identifiability challenges faced in the estimation of phylogenetic networks from empirical data.