Phylogeny inference under the general Markov model using MST-backbone

MotivationPhylogeny inference via maximum likelihood is NP-hard. Current methods make simplifying assumptions such as stationarity, homogeneity, and time-reversibility for computational ease. The stationarity assumption is violated by empirical observations of GC content evolution, and might systematically bias phylogeny inference. The general Markov model (GM) is a suitable alternative to stationary models because it allows for the evolution of GC content. Related work on the GM model has predominantly focused on inferring unrooted trees using either the log-det distance or phylogenetic invariants.MethodsWe adapted the structural EM framework to perform tree search under the GM model (SEM-GM). Additionally, we implemented a minimum spanning tree framework called MST-backbone to improve the scalability of SEM-GM by constraining search through tree space. MST-backbone(SEM-GM) was used to infer unrooted trees, which are subsequently rooted under the GM model; the latter procedure is called rSEM-GM. We compared our method with RAxML-NG, IQ-TREE, and FastTree on simulated data. We validated our methods on six empirical datasets.ResultsEstimated experimental phylogenies are rooted with high accuracy under the GM model (recall ranging from 80% to 94%). However, virus phylogenies are not realistically rooted, suggesting that the GM model may be overtrained on some empirical datasets. The comparative analysis of simulated data suggests that MST-backbone(SEM-GM) and FastTree scale linearly whereas rSEM-GM, RAxML-NG, and IQ-TREE scale quadratically. The results on empirical data suggest that it is not necessary to use the general time-reversible model for computational ease.Availabilityhttps://github.com/prabhavk/mst-backbone-sem-gmContactprabhav.kalaghatgi@molgen.mpg.deSupplementary informationSupplementary data are available online

HyDe: a Python Package for Genome-Scale Hybridization Detection

The analysis of hybridization and gene flow among closely related taxa is a common goal for researchers studying speciation and phylogeography. Many methods for hybridization detection use simple site pattern frequencies from observed genomic data and compare them to null models that predict an absence of gene flow. The theory underlying the detection of hybridization using these site pattern probabilities exploits the relationship between the coalescent process for gene trees within population trees and the process of mutation along the branches of the gene trees. For certain models, site patterns are predicted to occur in equal frequency (i.e., their difference is 0), producing a set of functions called phylogenetic invariants. In this paper we introduce HyDe, a software package for detecting hybridization using phylogenetic invariants arising under the coalescent model with hybridization. HyDe is written in Python, and can be used interactively or through the command line using pre-packaged scripts. We demonstrate the use of HyDe on simulated data, as well as on two empirical data sets from the literature. We focus in particular on identifying individual hybrids within population samples and on distinguishing between hybrid speciation and gene flow. HyDe is freely available as an open source Python package under the GNU GPL v3 on both GitHub (https://github.com/pblischak/HyDe) and the Python Package Index (PyPI: https://pypi.python.org/pypi/phyde).

Tying Up Loose Strands: Defining Equations of the Strand Symmetric Model

The strand symmetric model is a phylogenetic model designed to reflect the symmetry inherent in the double-stranded structure of DNA. We show that the set of known phylogenetic invariants for the general strand symmetric model of the three leaf claw tree entirely defines the ideal. This knowledge allows one to determine the vanishing ideal of the general strand symmetric model of any trivalent tree. Our proof of the main result is computational. We use the fact that the Zariski closure of the strand symmetric model is the secant variety of a toric variety to compute the dimension of the variety. We then show that the known equations generate a prime ideal of the correct dimension using elimination theory.

Phylogenetic invariants for group-based models

In this paper we investigate properties of algebraic varieties representing group-basedphylogenetic models. We propose a method of generating many phylogenetic invariants. We provethat we obtain all invariants for any tree for the two-state Jukes-Cantor model. We conjecturethat for a large class of models our method can give all phylogenetic invariants for any tree. Weshow that for 3-Kimura our conjecture is equivalent to the conjecture of Sturmfels and Sullivant[22, Conjecture 2]. This, combined with the results in [22], would make it possible to determineall phylogenetic invariants for any tree for 3-Kimura model, and also other phylogenetic models.Next we give the (rst) examples of non-normal varieties associated to general group-based modelfor an abelian group. Following Kubjas [17] we prove that for many group-based models varietiesassociated to trees with the same number of leaves do not have to be deformation equivalent.