Andreas Spillner

Basic Phylogenetic Combinatorics

Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the interrelationship between the principal options for encoding phylogenetic trees: split systems, quartet systems and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and are at the basis of much of phylogenetic data processing. This book highlights how each one provides a unique perspective for viewing and perceiving the combinatorial structure of a phylogenetic tree and is, simultaneously, a rich source for combinatorial analysis and theory building. Graduate students and researchers in mathematics and computer science will enjoy exploring this fascinating new area and learn how mathematics may be used to help solve topical problems arising in evolutionary biology.

Inferring polyploid phylogenies from multiply-labeled gene trees

BackgroundGene trees that arise in the context of reconstructing the evolutionary history of polyploid species are often multiply-labeled, that is, the same leaf label can occur several times in a single tree. This property considerably complicates the task of forming a consensus of a collection of such trees compared to usual phylogenetic trees.ResultsWe present a method for computing a consensus tree of multiply-labeled trees. As with the well-known greedy consensus tree approach for phylogenetic trees, our method first breaks the given collection of gene trees into a set of clusters. It then aims to insert these clusters one at a time into a tree, starting with the clusters that are supported by most of the gene trees. As the problem to decide whether a cluster can be inserted into a multiply-labeled tree is computationally hard, we have developed a heuristic method for solving this problem.ConclusionWe illustrate the applicability of our method using two collections of trees for plants of the genus Silene, that involve several allopolyploids at different levels.

SuperQ: Computing Supernetworks from Quartets

Supertrees are a commonly used tool in phylogenetics to summarize collections of partial phylogenetic trees. As a generalization of supertrees, phylogenetic supernetworks allow, in addition, the visual representation of conflict between the trees that is not possible to observe with a single tree. Here, we introduce SuperQ, a new method for constructing such supernetworks (SuperQ is freely available at www.uea.ac.uk/computing/superq.). It works by first breaking the input trees into quartet trees, and then stitching these together to form a special kind of phylogenetic network, called a split network. This stitching process is performed using an adaptation of the QNet method for split network reconstruction employing a novel approach to use the branch lengths from the input trees to estimate the branch lengths in the resulting network. Compared with previous supernetwork methods, SuperQ has the advantage of producing a planar network. We compare the performance of SuperQ to the Z-closure and Q-imputation supernetwork methods, and also present an analysis of some published data sets as an illustration of its applicability.

PADRE: a package for analyzing and displaying reticulate evolution

UNLABELLEDnRecent advances in gene sequencing for polyploid species, coupled with standard phylogenetic tree reconstruction, leads to gene trees in which the same species can label several leaves. Such multi-labeled trees are then used to reconstruct the evolutionary history of the polyploid species in question. However, this reconstruction process requires new techniques that are not available in current phylogenetic software packages. Here, we describe the software package PADRE (Package for Analyzing and Displaying Reticulate Evolution) that implements such techniques, allowing the reconstruction of complex evolutionary histories for polyploids in the form of phylogenetic networks.nnnAVAILABILITYnPADRE is an open-source Java program freely available from http://www.uea.ac.uk/cmp/research/cmpbio/PADRE.

Untangling a Planar Graph

AbstractA straight-line drawingxa0δ of a planar graphxa0G need not be plane but can be made so by untangling it, that is, by moving some of the vertices ofxa0G. Let shift(G,δ) denote the minimum number of vertices that need to be moved to untanglexa0δ. We show that shift(G,δ) is NP-hard to compute and to approximate. Our hardness results extend to a version of 1BendPointSetEmbeddability, a well-known graph-drawing problem.Further we define fix(G,δ)=n−shift(G,δ) to be the maximum number of vertices of a planar n-vertex graphxa0G that can be fixed when untanglingxa0δ. We give an algorithm that fixes at least n

Computing Phylogenetic Diversity for Split Systems

sqrt{((log n)-1)/loglog n}

Prioritizing Populations for Conservation Using Phylogenetic Networks

nvertices when untangling a drawing of an n-vertex graphxa0G. Ifxa0G is outerplanar, the same algorithm fixes at least n

Consistency of the Neighbor-Net Algorithm

sqrt{n/2}

Metrics on Multilabeled Trees: Interrelationships and Diameter Bounds

nvertices. On the other hand, we construct, for arbitrarily largexa0n, an n-vertex planar graphxa0G and a drawingxa0δG ofxa0G with n

Consistency of the QNet algorithm for generating planar split networks from weighted quartets

ensuremath {mathrm {fix}}(G,delta_{G})leq sqrt{n-2}+1