Parsimony optimization of phylogenetic networks

Phylogenetic minimum description length: an optimality criterion based on algorithmic complexity

Phylogenetic minimum description length (PMDL) is proposed as an optimality criterion for phylogenetic analysis. PMDL is based on algorithmic (Kolmogorov) information and the minimum description length principle. This criterion generates natural weighting functions (i.e. not being externally specified) for a diversity of phylogenetic graph, data and model types. PMDL is a generalized criterion that converges on existing forms of inference (i.e. parsimony, likelihood, Bayesian) in specific circumstances. Furthermore, as opposed to existing criteria, PMDL includes graph complexity allowing for the competition of hypotheses with myriad types of phylogenetic graphs (e.g. trees, networks, forests). Owing to its compound nature, PMDL allows for analytical model choice along with phylogenetic graph hypothesis while avoiding over-parameterization. Although uncomputable, heuristic methods are presented for the calculation of upper bounds on the algorithmic information content of a phylogenetic hypothesis. Examples are presented demonstrating the approach.

The tree labeling polytope: a unified approach to ancestral reconstruction problems

Motivation

Reconstructing unobserved ancestral states of a phylogenetic tree provides insight into the history of evolving systems and is one of the fundamental problems in phylogenetics. For a fixed phylogenetic tree, the most parsimonious ancestral reconstruction - a solution to the small parsimony problem - can be efficiently found using the dynamic programming algorithms of Fitch-Hartigan and Sankoff. Ancestral reconstruction is important in many applications including inferring the routes of metastases in cancer, deriving the transmission history of viruses, determining the direction of cellular differentiation in organismal development, and detecting recombination and horizontal gene transfer in phylogenetic networks. However, most of these applications impose additional global constraints on the reconstructed ancestral states, which break the local structure required in the recurrences of Fitch-Hartigan and Sankoff.

Results

We introduce an alternative, polyhedral approach to ancestral reconstruction problems using the tree labeling polytope , a geometric object whose vertices represent the feasible ancestral labelings of a tree. This framework yields a polynomial-time linear programming algorithm for the small parsimony problem . More importantly, the tree labeling polytope facilitates the incorporation of additional constraints that arise in modern ancestral reconstruction problems. We demonstrate the utility of our approach by deriving mixed-integer programming algorithms with a small number of integer variables and strong linear relaxations for three such problems: the parsimonious migration history problem, the softwired small parsimony problem on phylogenetic networks, and the convex recoloring problem on trees. Our algorithms outperform existing state-of-the-art methods on both simulated and real datasets. For instance, our algorithm scales to trace routes of cancer metastases in trees with thousands of leaves, enabling the analysis of large trees generated by recent single-cell sequencing technologies. On a mouse model of metastatic lung adenocarcinoma, the tree labeling polytope allows us to infer simpler migration histories compared to previous results.

Availability

Python implementations of the algorithms provided in this work are available at: github.com/raphael-group/tree-labeling-polytope .

PSA: an effective method for predicting horizontal gene transfers through parsimonious phylogenetic networks

Horizontal gene transfer (HGT) from one organism to another, according to some researchers, can be abundant in the evolution of species. A phylogenetic network is a network structure that describes the HGTs among species. Several studies have proposed methods to construct phylogenetic networks to predict HGTs based on parsimony values. Existing definitions of parsimony values for a phylogenetic network are based on the assumption that each gene site or segment evolves independently along different trees in the network. However, in the current study, we define a novel parsimony value, denoted the p definition, for phylogenetic networks, considering that a gene as a whole typically evolves along a tree. Using Simulated Annealing, a new method called the Phylogeny with Simulated Annealing (PSA) algorithm is proposed to search for an optimal network based on the p definition. The PSA method is tested on the simulated data. The results reveal that the parsimonious networks constructed using PSA can better represent the evolutionary relationships of species involving HGTs. Additionally, the HGTs predicted using PSA are more accurate than those predicted using other methods. The PSA algorithm is publicly accessible at http://github.com/imustu/sap.

Multi-armed bandits, Thomson sampling and unsupervised machine learning in phylogenetic graph search

A phylogenetic graph search relies on a large number of highly parameterized search procedures (e.g. branch-swapping, perturbation, simulated annealing, genetic algorithm). These procedures vary in effectiveness over datasets and at alternative points in analytical pipelines. The multi-armed bandit problem is applied to phylogenetic graph searching to more effectively utilize these procedures. Thompson sampling is applied to a collection of search and optimization "bandits" to favour productive search strategies over those that are less successful. This adaptive random sampling strategy is shown to be more effective in producing heuristically optimal phylogenetic graphs and more time efficient than existing uniform probability randomized search strategies. The strategy acts as a form of unsupervised machine learning that can be applied to a diversity of phylogenetic datasets without prior knowledge of their properties.

PhylogeneticGraph (PhyG) a new phylogenetic graph search and optimization program

We present Phylogenetic Graph (PhyG), an open-source, phylogenetic search tool for diverse data types and graphs, including softwired and hardwired networks, in addition to trees. This allows for analysis of horizontal transfer and hybridization scenarios, as well as the necessary vertical inheritance of trees. PhyG is the successor to POY5 in performing combined data tree-alignment with enhancements in heuristic optimality (up to 7% in example data) and execution time (up to a factor of 200). Input data may exhibit a practically unlimited number of character states in qualitative or sequence (aligned and unaligned) types. Novel graph construction and refinement algorithms have been implemented and integrated into a variety of search procedures. Currently, PhyG implements parsimony and No-Common-Mechanism Likelihood optimization.