Related papers: When are quarnets sufficient to reconstruct semi-d…
Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted…
Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are…
We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on n taxa from the set of all quartets containing a certain fixed taxon, in O(n^3) time. We also present a more general method which can handle more…
Here we show that deciding whether two rooted binary phylogenetic trees on the same set of taxa permit a cherry-picking sequence, a special type of elimination order on the taxa, is NP-complete. This improves on an earlier result which…
In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely open. For instance, even the asymptotic counting problem for…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple operations on a set of sequences called orthology relations may be employed. In addition to being…
Phylogenetic networks are generalizations of trees that allow for the modeling of non-tree like evolutionary processes. Split networks give a useful way to construct networks with intuitive distance structures induced from the associated…
Phylogenomics commonly aims to construct evolutionary trees from genomic sequence information. One way to approach this problem is to first estimate event-labeled gene trees (i.e., rooted trees whose non-leaf vertices are labeled by…
Polyploidization is an evolutionary process by which a species acquires multiple copies of its complete set of chromosomes. The reticulate nature of the signal left behind by it means that phylogenetic networks offer themselves as a…
It has remained an open question for some time whether, given a set of not necessarily binary (i.e. "nonbinary") trees T on a set of taxa X, it is possible to determine in time f(r).poly(m) whether there exists a phylogenetic network that…
A normal (phylogenetic) network with $k$ reticulations displays $2^k$ phylogenetic trees. In this paper, we establish an analogous result for tree-child (phylogenetic) networks with no underlying $3$-cycles. In particular, we show that a…
Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree…
In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…
This paper introduces the tensor representation of a network, here tensors are the primitive structures of the network. In view of tensor chains, two binary operations on tensor sets are defined: chain addition and reducing. Based on the…
Algebraic techniques in phylogenetics have historically been successful at proving identifiability results and have also led to novel reconstruction algorithms. In this paper, we study the ideal of phylogenetic invariants of the…
Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers…
Phylogenetic trees (i.e. evolutionary trees, additive trees or X-trees) play a key role in the processes of modeling and representing species evolution. Genome evolution of a given group of species is usually modeled by a species…
Orthologous genes, which arise through speciation, play a key role in comparative genomics and functional inference. In particular, graph-based methods allow for the inference of orthology estimates without prior knowledge of the underlying…
We associate root polytopes to directed graphs and study them by using ribbon structures. Most attention is paid to what we call the semi-balanced case, i.e., when each cycle has the same number of edges pointing in the two directions.…