Tree-like reticulation networks--when do tree-like distances also support reticulate evolution?

A distance-based model for convergent evolution

Convergent evolution is an important process in which independent species evolve similar features usually over a long period of time. It occurs with many different species across the tree of life, and is often caused by the fact that species have to adapt to similar environmental niches. In this paper, we introduce and study properties of a distance-based model for convergent evolution in which we assume that two ancestral species converge for a certain period of time within a collection of species that have otherwise evolved according to an evolutionary clock. Under these assumptions it follows that we obtain a distance on the collection that is a modification of an ultrametric distance arising from an equidistant phylogenetic tree. As well as characterising when this modified distance is a tree metric, we give conditions in terms of the model's parameters for when it is still possible to recover the underlying tree and also its height, even in case the modified distance is not a tree metric.

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.

Next-generation cophylogeny: unravelling eco-evolutionary processes

A fundamental question in evolutionary biology is how microevolutionary processes translate into species diversification. Cophylogeny provides an appropriate framework to address this for symbiotic associations, but historically has been primarily limited to unveiling patterns. We argue that it is essential to integrate advances from ecology and evolutionary biology into cophylogeny, to gain greater mechanistic insights and transform cophylogeny into a platform to advance understanding of interspecific interactions and diversification more widely. We discuss key directions, such as incorporating trait reconstruction and considering multiple scales of network organization, and highlight recent developments for implementation. A new quantitative framework is proposed to allow integration of relevant information, such as quantitative traits and assessment of the contribution of individual mechanisms to cophylogenetic patterns.

Tree-metrizable HGT networks

Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if it satisfies the so-called "four point condition", established by Buneman in 1971. While this condition guarantees that a unique tree will display the metric, meaning that the distance between any two leaves can be found by adding the distances on arcs in the path between the leaves, it doesn't exclude the possibility that a phylogenetic network might also display the metric. This possibility was recently pointed out and "tree-metrized" networks - that display a tree metric - with a single reticulation were characterized. In this paper, we show that in the case of HGT (horizontal gene transfer) networks, in fact there are tree-metrized networks containing many reticulations.

Tree-based networks: characterisations, metrics, and support trees

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic tree T, called a base tree, and adding arcs between arcs of T. The class of phylogenetic networks that can be obtained in this way is called tree-based networks and includes the prominent classes of tree-child and reticulation-visible networks. Initially defined for binary phylogenetic networks, tree-based networks naturally extend to arbitrary phylogenetic networks. In this paper, we generalise recent tree-based characterisations and associated proximity measures for binary phylogenetic networks to arbitrary phylogenetic networks. These characterisations are in terms of matchings in bipartite graphs, path partitions, and antichains. Some of the generalisations are straightforward to establish using the original approach, while others require a very different approach. Furthermore, for an arbitrary tree-based network N, we characterise the support trees of N, that is, the tree-based embeddings of N. We use this characterisation to give an explicit formula for the number of support trees of N when N is binary. This formula is written in terms of the components of a bipartite graph.

Distinguishing Between Convergent Evolution and Violation of the Molecular Clock for Three Taxa

We give a non-technical introduction to convergence-divergence models, a new modeling approach for phylogenetic data that allows for the usual divergence of lineages after lineage-splitting but also allows for taxa 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 tree-like. We show that there are not always good statistical reasons to prefer the usual class of tree-like models over more general convergence-divergence models. Specifically, we show many $3$-taxon data sets can be equally well explained by supposing violation of the molecular clock due to change in the rate of evolution along different edges, or by keeping the assumption of a constant rate of evolution but instead assuming that evolution is not a purely divergent process. Given the abundance of evidence that evolution is not strictly tree-like, our discussion is an illustration that as phylogeneticists we need to think clearly about the structural form of the models we use. For cases with four taxa, we show that there will be far greater ability to distinguish models with convergence from non-clock-like tree models. [Akaike information criterion; convergence-divergence models; distinguishability; identifiability; likelihood; molecular clock; phylogeny.].

Which Phylogenetic Networks are Merely Trees with Additional Arcs?

A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on “2-SAT”) that efficiently determines whether or not any given network can be realized in this way. Moreover, the proof provides a polynomial-time algorithm for finding one or more trees (when they exist) on which the network can be based. A number of interesting consequences are presented as corollaries; these lead to some further relevant questions and observations, which we outline in the conclusion.