Trinets encode tree-child and level-2 phylogenetic networks

Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all "recoverable" rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets

Reconstructing Phylogenetic Networks via Cherry Picking and Machine Learning

Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. In this paper, we apply the recently-introduced theoretical framework of cherry picking to design a class of heuristics that are guaranteed to produce a network containing each of the input trees, for practical-size datasets. The main contribution of this paper is the design and training of a machine learning model that captures essential information on the structure of the input trees and guides the algorithms towards better solutions. This is one of the first applications of machine learning to phylogenetic studies, and we show its promise with a proof-of-concept experimental study conducted on both simulated and real data consisting of binary trees with no missing taxa

Genome-wide inference of ancestral recombination graphs

The complex correlation structure of a collection of orthologous DNA sequences is uniquely captured by the "ancestral recombination graph" (ARG), a complete record of coalescence and recombination events in the history of the sample. However, existing methods for ARG inference are computationally intensive, highly approximate, or limited to small numbers of sequences, and, as a consequence, explicit ARG inference is rarely used in applied population genomics. Here, we introduce a new algorithm for ARG inference that is efficient enough to apply to dozens of complete mammalian genomes. The key idea of our approach is to sample an ARG of n chromosomes conditional on an ARG of n-1 chromosomes, an operation we call "threading." Using techniques based on hidden Markov models, we can perform this threading operation exactly, up to the assumptions of the sequentially Markov coalescent and a discretization of time. An extension allows for threading of subtrees instead of individual sequences. Repeated application of these threading operations results in highly efficient Markov chain Monte Carlo samplers for ARGs. We have implemented these methods in a computer program called ARGweaver. Experiments with simulated data indicate that ARGweaver converges rapidly to the true posterior distribution and is effective in recovering various features of the ARG for dozens of sequences generated under realistic parameters for human populations. In applications of ARGweaver to 54 human genome sequences from Complete Genomics, we find clear signatures of natural selection, including regions of unusually ancient ancestry associated with balancing selection and reductions in allele age in sites under directional selection. Preliminary results also indicate that our methods can be used to gain insight into complex features of human population structure, even with a noninformative prior distribution.Comment: 88 pages, 7 main figures, 22 supplementary figures. This version contains a substantially expanded genomic data analysi