Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

 
Session Overview
Session
MS177, part 1: Algebraic and combinatorial phylogenetics
Time:
Tuesday, 09/Jul/2019:
10:00am - 12:00pm

Location: Unitobler, F011
30 seats, 59m^2

Presentations
10:00am - 12:00pm

Algebraic and combinatorial phylogenetics

Chair(s): Marta Casanellas (Universitat Politècnica de Catalunya), Jane Coons (North Carolina State University), Seth Sullivant (North Carolina State University)

Since late eighties, algebraic tools have been present in phylogenetic theory and have been crucial in understanding the limitations of models and methods and in proposing improvements to the existing tools. In this session we intend to present some of the most recent work in this area.

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

An Introduction to Algebraic and Combinatorial Phylogenetics

Jane Coons
North Carolina State University

The purpose of this talk is to provide participants with the necessary background information to attend the subsequent talks in this session. As such, we will discuss preliminary definitions and key results in the field of mathematical phylogenetics. In particular, we will discuss results concerning tree and network combinatorics and introduce some important phylogenetic models. We will also describe the algebraic methods that have been used to understand these models.

 

Inferring species networks from gene trees

Elizabeth S. Allman, Hector Baños, John Rhodes
University of Alaska Fairbanks

Phylogenetic trees for different genes from the same taxa often differ from one another, with incomplete lineage sorting and hybridization considered to be two of the most important biological reasons underlying this discordance. Inferring a hybridization network that shows species relationships from a set of gene trees is made difficult by the confounding of these two sources of conflicting signal. We present a new algorithm for this inference problem, under the Network Multispecies Coalescent model of these processes on a level-1 network. Building on a number of combinatorial insights, the topological species network estimator is statistically consistent with reasonable running time for moderate size data sets. Analyses of several simulated and empirical datasets indicate its practical value.

 

Algebraic versus semi-algebraic conditions for phylogenetic varieties

Marina Garrote-López
BGSMath and Universitat Politècnica de Catalunya

It is common to model evolution adopting a parametric statistical model which allows to define a joint probability distribution at the leaves of phylogenetic trees. When these models are algebraic, one is able to deduce polynomial relationships between these probabilities, and the study of these polynomials and the geometry of the algebraic varieties that arise from them can be used to reconstruct phylogenetic trees. However, not all points in these algebraic varieties have biological sense. In this talk, we would like to discuss the importance of studying the subset of these varieties with biological sense and explore the extent to which restricting to these subsets can provide insight into existent methods of phylogenetic reconstruction. One of our main focuses is to understand and describe these subsets of points that come from positive parameters. We are interested in the algebraic and semi-algebraic conditions that describe them and in knowing which of these conditions are relevant for topology inference. The projection into these subsets can be seen as an optimization problem and can be solved using nonlinear programming algorithms. As these algorithms do not guarantee a global solution, we use a different approach that allows us to find a global optimum. Numerical algebraic geometry and computational algebra play a fundamental role here. We will show some results on trees evolving under groups-based models and, in particular, we will explore the long branch attraction phenomenon.

 

Trait evolution on two gene trees

James Degnan
The University of New Mexico

Models of trait evolution use a phylogenetic tree to determine the correlation structure for traits sampled from a set of species. Typically, the phylogenetic tree is estimated from genetic data from many loci, and a single tree is used to model the trait evolution, for example by assuming that the mean trait value follows a Brownian motion on the tree. Here, we model trait evolution by assuming that there are two genetic loci influencing the trait. In this case separate evolutionary trees (called gene trees) can occur for the two loci. We model the correlation structure as arising from a linear combination of Brownian motions on the two trees, and develop a model to estimate the proportion of trait evolution contributed by each gene.