September 15, 2024

• 9:00 - 9:45 am EDT

  In Search of Markov Solutions

  11th Floor Lecture Hall

  • Speaker
  • Vivek Borkar, IIT Bombay, India

  • Session Chair
  • Arnab Ganguly, Louisiana State University

  Abstract

  This talk will summarise recent contributions to two strands of research - mimicking one dimensional marginals of random processes by Markov processes, and selecting a Markov family of solutions for degenerate diffusions with non-unique solutions (also known as Markov selection).

  • Video
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EDT

  Estimating Rare Event Probabilities in Reflecting Brownian Motion

  11th Floor Lecture Hall

  • Speaker
  • Kevin Leder, University of Minnesota

  • Session Chair
  • Arnab Ganguly, Louisiana State University

  Abstract

  Reflecting Brownian motion (RBM) is a stochastic process that behaves like a Brownian motion in the interior of its domain and is pushed into the interior whenever it reaches the boundary of its domain. RBM’s in the positive orthant were first introduced by Harrison and Reiman 1981, and arise naturally in a wide variety of settings, e.g., heavy traffic queueing networks. A difficult question that has received a significant amount of attention is identifying the asymptotics for tail probabilities associated with RBM in the positive orthant. In this work we focus on the specific tail probability that a stable RBM started near the origin exits a large box before returning to the origin. We develop particle based algorithms to estimate this probability. Using results of Dean and Dupuis 2008 we are able to develop algorithms that efficiently estimate this tail probability in two dimensions. In three and higher dimensions, we are not able to construct an efficient estimator, but we do construct estimators that are provably superior (in an asymptotic sense) to standard Monte Carlo. Numerical results show the benefits of our algorithm to standard Monte Carlo. This is based on joint work with Xin Liu and Zicheng Wang.

  • Video
• 11:30 am - 12:15 pm EDT

  Reflecting Diffusions in Curved Nonsmooth Domains

  11th Floor Lecture Hall

  • Speaker
  • Cristina Costantini, University of Chieti-Pescara

  • Session Chair
  • Arnab Ganguly, Louisiana State University

  Abstract

  Reflecting diffusions arise in many applications: from stochastic networks, to singular stochastic control, to the motion of physical particles, etc.. In many examples the domain in which the reflecting diffusion is to be confined is nonsmooth or the direction of reflection varies nonsmoothly: in these cases it is not obvious that a reflecting diffusion with the prescribed direction of reflection exists and is uniquely characterized. After reviewing the literature, in which the works by Dupuis and Ishii play a central role, I will discuss how a recent ergodic theorem for inhomogeneous killed Markov chains allows to extend the 1993 Dupuis and Ishii results to some new classes of domains and directions of reflection. In particular one can obtain existence and uniqueness of a semimartingale reflecting diffusion in a piecewise smooth domain in dimension 2, possibly with cusps, under optimal conditions on the directions of reflection, and one can uniquely characterize obliquely reflecting Brownian motion in some piecewise smooth cones. The talk is based on joint works with T.G. Kurtz.

  • Video
• 12:30 - 2:00 pm EDT

  Lunch/Free Time
• 2:00 - 2:45 pm EDT

  Using Weak Convergence Methods to Establish Exit Time Asymptotics for a Small Noise Infinite-dimensional System

  11th Floor Lecture Hall

  • Speaker
  • David Lipshutz, Flatiron Institute

  • Session Chair
  • Tao Pang, North Carolina State University

  Abstract

  Dynamical systems with small noise arise in a wide variety of applications. In such applications, we'd like to know how long it takes the small noise system to escape stable equilibra of the corresponding deterministic system. For finite-dimensional systems, these "exit times" are typically established by proving large deviation principles that are uniform over compact sets. However, for infinite-dimensional systems, bounded sets are no long compact and this approach does not naturally extend. Here, in the context of a small noise stochastic delay differential equation with strong solutions whose natural state space is infinite-dimensional, we show how the weak convergence method that was pioneered by Paul Dupuis can be used to prove a large deviation principle that is uniform over bounded sets. In turn, this enables us to prove exit time asymptotics for the small noise stochastic delay differential equation.
• 3:00 - 3:45 pm EDT

  Renormalized relative entropies and an H-theorem for interacting diffusions on sparse graphs

  11th Floor Lecture Hall

  • Speaker
  • Kavita Ramanan, Brown University

  • Session Chair
  • Tao Pang, North Carolina State University

  Abstract

  We consider a class of conditional McKean-Vlasov processes that arise in the study of interacting Langevin diffusions on regular trees. We establish an H-theorem that characterizes the long-time behavior of these processes. Specifically, we show that a certain function that arises when taking the limit of certain renormalized relative entropies serves as a global Lyapunov function for the associated measure flow. We also provide counterexamples to highlight some subtleties in the approach, and discuss some open problems. This is joint work with Kevin Hu.

  • Video

September 16, 2024

• 8:30 - 8:50 am EDT

  Check In

  11th Floor Collaborative Space
• 8:50 - 9:00 am EDT

  Welcome

  11th Floor Lecture Hall

  • Session Chair
  • Brendan Hassett, ICERM/Brown University
• 9:00 - 9:45 am EDT

  Phylogenetic Semidirected Networks and a Tractable Dissimilarity Measure

  11th Floor Lecture Hall

  • Speaker
  • Cécile Ané, University of Wisconsin - Madison

  • Session Chair
  • Hector Banos, California State University San Bernardino

  Abstract

  From many data types, we hope identify the phylogenetic semidirected network that generated the data, but not the rooted network. In the semidirected network, some but not all edges are directed. I will define a general class of semidirected phylogenetic networks, with a stable set of leaves, tree nodes and hybrid nodes. This class includes both rooted phylogenetic trees and networks, and unrooted phylogenetic trees. I will show various fundamental properties for these networks, including how to generalize the ""tree-child"" property from rooted to semidirected networks. I then will define an edge-based representation of semidirected phylogenetic networks, which generalizes the node-based μ-representation of a rooted network by Cardona et al. (2009), and the split-based representation of an unrooted tree. It leads to a dissimilarity between semidirected networks, which can be efficiently computed in near-quadratic time, and extends the widely-used Robinson-Foulds distance on both rooted trees and unrooted trees. This dissimilarity is in fact a distance on the space of tree-child semidirected phylogenetic networks.

  • Video Available Soon
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EDT

  Gene flow processes in phylogenetic networks and their macroevolutionary implications

  11th Floor Lecture Hall

  • Speaker
  • Joshua Justison, Iowa State University

  • Session Chair
  • Laura Kubatko, The Ohio State University

  Abstract

  Gene flow is a highly dynamic suite of processes that includes events like lateral gene transfer, hybridization, and introgression. Even between clades across the Tree of Life, these processes can have different controlling factors and mechanisms that ultimately affect the macroevolutionary patterns we observe. In this talk I will discuss some of the ways that various gene flow processes can be modeled on a macroevolutionary scale. I simulated phylogenetic networks from the birth-death-hybridization process to demonstrate that phylogenetic networks can have drastically different diversification dynamics and topological profiles as we change our underlying assumptions around reticulate patterns. This work emphasizes the need to think critically when choosing an appropriate and fitting model for a given empirical system. This marks an exciting opportunity for biologists to use their system-specific knowledge to model gene flow appropriately and test macroevolutionary hypotheses regarding the role of gene flow to affect diversification and adaptation.
• 11:30 am - 12:15 pm EDT

  Trait Evolution on Two or More Trees

  11th Floor Lecture Hall

  • Speaker
  • James Degnan, University of New Mexico

  • Session Chair
  • Laura Kubatko, The Ohio State University

  Abstract

  Modeling of trait evolution usually assumes a known phylogeny on which traits evolve such as from Brownian Motion or an OU process. It is conceptually not clear if the phylogeny should be a species tree or a gene tree. Here, we develop a model where a trait evolves on two different gene trees. We introduce a parameter p for the contribution of each gene so that a researcher can estimate the proportion of contribution from each. The example is applied to cultivated rice with two genes that strongly influence grain width but have very different topologies.
• 12:30 - 2:30 pm EDT

  Networking Lunch

  Working Lunch - 11th Floor Collaborative Space
• 2:30 - 3:15 pm EDT

  Reconstruction of Ancestral Genomes and Sub-genomes

  11th Floor Lecture Hall

  • Speaker
  • Lingling Jin, University of Saskatchewan

  • Session Chair
  • Sebastien Roch, University of Wisconsin-Madison

  Abstract

  Evolution is a process that involves an organism’s DNA changing over time. Often, this process is driven by external stressors (such as environmental changes, diseases, pests) and/or selective breeding. Recognizing how genomes evolve is of universal biological interest about species origin, survival and adaptation. The fast-increasing number and diversity of sequenced genomes open the door to analyzing the dynamics of evolution at whole-genome resolution. By using a successive ancestral contig construction technique based on statistically conserved syntenic orders of genes, we developed methods to reconstruct chromosome-level ancestral genomes of extant species or subgenomes within a single genome as a result of whole genome doubling/tripling. These methods were applied and verified in many lineages across different studies that improved the scientific knowledge of genome evolution in various biological systems. In the talk, I will first introduce RACCROCHE and SyntenyLink, pipelines for ancestral genome or sub-genome reconstruction, and our research on genome evolution based on genes, their syntenic orders, chromosomal gene co-occurrences, subgenome dominance in gene expressions, novel genomic variations (structural variants and transposable elements) and their relationship with plant phenomics. A particularly important application of this work is to crop species that exhibit rapid rates of evolution. By understanding genome evolution and its impact on plant phenotypes, breeders will be able to make informed decisions on how to breed crops with desired traits.
• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 4:45 pm EDT

  Identifiability and Reconstruction of Phylogenetic Networks

  11th Floor Lecture Hall

  • Speaker
  • Leo van Iersel, Delft University of Technology

  • Session Chair
  • Sebastien Roch, University of Wisconsin-Madison

  Abstract

  Is it possible to reconstruct the correct phylogenetic network if one is given sufficient data? This question has statistical, algebraic, combinatorial and algorithmic sides and has gained quite some interest recently. In this talk, I will discuss recent progress and major open questions related to the identifiability of semi-directed phylogenetic networks under Markov models, the usefulness of quarnets and quadratic phylogenetic invariants, algorithms for constructing the tree of blobs and for constructing level-1 networks, and the elusiveness of level-2.
• 5:00 - 6:30 pm EDT

  Reception

  11th Floor Collaborative Space

September 17, 2024

• 9:00 - 9:45 am EDT

  Inferring Cell Lineage Trees and Differentiation Maps for Organismal Development

  11th Floor Lecture Hall

  • Speaker
  • Benjamin Raphael, Princeton University

  • Session Chair
  • Tandy Warnow, University of Illinois Urbana-Champaign

  Abstract

  The development of a multicellular organism from a single founder cell is the result of a complex process involving growth, death, and differentiation of cells. Recent advances in genome editing and single cell sequencing technologies allow researchers to induce somatic mutations in the genome during development and to simultaneously measure induced mutations and cell state from thousands of cells. In this talk, I will describe two algorithms to infer the developmental process from such dynamic lineage tracing data. First, I will describe Startle (Star tree lineage exploration), an algorithm that reconstructs cell lineage trees from mutations induced during genome editing. Startle models the unique characteristics of the genome editing process using the star homoplasy model to overcome errors and missing data in the measured mutations. Next, I will describe our algorithm Carta to infer a cell differentiation map – a directed graph describing transitions between cell types – from single cell lineage tracing data. Carta models unmeasured progenitor cell types using the concept of a potency set and infers a cell differentiation map that balances the trade-off between the complexity of the cell differentiation map and the number of unobserved cell type transitions on the lineage tree.
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EDT

  Simultaneous reconstruction of phylogenetic trees and transmission trees

  11th Floor Lecture Hall

  • Speaker
  • Caroline Colijn, Simon Fraser University

  • Session Chair
  • Tandy Warnow, University of Illinois Urbana-Champaign

  Abstract

  The utility of whole-genome sequencing for pathogens, and how informative sequence data are for outbreaks, remains unknown, and is important as public health systems around the world decide how much sequencing to undertake for infectious disease surveillance. In this talk, I introduce an MCMC method for simultaneous reconstruction of phylogenetic trees and transmission trees using sequence data for a person-to-person outbreak of an infectious disease. The method is called BREATH: Bayesian Reconstruction and Evolutionary Analysis of Transmission Histories. BREATH's transmission process accounts for a flexible natural history of infection (including a latent period if desired) and a separate process for sampling. It allows for unsampled individuals and for individuals to have diverse within-host infections. BREATH also accounts for the fact that an outbreak may still be ongoing at the time of analysis, using a recurrent events approach to account for right truncation. We perform a simulation study to verify our implementation, and apply BREATH to a previously-described 13-year outbreak of tuberculosis. We find that using a transmission process to inform the phylogenetic reconstruction results in better resolution of the phylogeny (in topology, branch length and tree height) and a more precise estimate of the time of origin of the outbreak. But even with whole-genome sequence data, considerable uncertainty remains about transmission events. An open source implementation of BREATH is available from https://github.com/rbouckaert/transmission as the BREATH package to BEAST 2.
• 11:30 am - 12:15 pm EDT

  Anomalous Phylogenetic Networks under the Coalescent model

  11th Floor Lecture Hall

  • Speaker
  • Hector Banos, California State University San Bernardino

  • Session Chair
  • Tandy Warnow, University of Illinois Urbana-Champaign

  Abstract

  Hybridization plays a crucial role during the evolutionary process of some species. In such cases, phylogenetic trees are insufficient to describe species-level relationships. Phylogenetic networks (also known as admixture graphs in population genetics) are the objects used to represent the evolutionary histories that allow such interactions. The inference of phylogenetic networks from biological data presents many challenges, and methods have been developed under different frameworks and model assumptions to overcome some of these challenges. In this talk, we present a comprehensive overview of existing methods for estimating explicit networks (networks depicting evolutionary history) from biological data. We discuss their distinct model assumptions, framework, hypotheses, and drawbacks.

  • Video Available Soon
• 12:30 - 2:30 pm EDT

  Lunch/Free Time
• 2:30 - 3:30 pm EDT

  Poster Blitz

  - 11th Floor Lecture Hall

  • Session Chair
  • John Rhodes, University of Alaska Fairbanks
• 3:30 - 5:00 pm EDT

  Poster Session/Coffee Break

  Poster Session - 11th Floor Collaborative Space

September 19, 2024

• 9:00 - 9:45 am EDT

  Algorithms for Exploring Reticulate Evolution using Rooted Phylogenetic Networks

  11th Floor Lecture Hall

  • Speaker
  • Daniel Huson, University of Tübingen

  • Session Chair
  • Leo van Iersel, Delft University of Technology

  Abstract

  Unrooted phylogenetic networks are often used to represent evolutionary data when incompatibilities are present. Although rooted phylogenetic networks are better suited for explicitly depicting evolutionary histories that involve reticulate events, they have been rarely used in practice, due to a lack of appropriate methods for their calculation. Here we introduce PhyloFusion, a new fast and easily-applicable method for calculating rooted phylogenetic networks on sets of rooted phylogenetic trees. The algorithm can handle tens of trees on hundreds of taxa, allowing unresolved nodes (which arise when edges with low support are contracted) and missing taxa. We demonstrate how the method can be used to explore the phylogenetic relationships between different Influenza A isolates, based on gene trees built on different genome segments.
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EDT

  Pairwise alignment at arbitrary evolutionary distance

  11th Floor Lecture Hall

  • Speaker
  • Brandon Legried, Georgia Institute of Technology

  • Session Chair
  • Leo van Iersel, Delft University of Technology

  Abstract

  Ancestral sequence reconstruction and phylogenetic reconstruction from present-day states are two important and related problems in computational biology. Multiple sequence alignment is a tertiary task that makes important connections between these two problems. Here, we show that perfect sequence alignment with high probability is possible with a dense enough underlying phylogeny influencing the evolution of genetic sequences. New probabilistic techniques in the evolution of sequences with insertions and deletions are developed, with a view toward more general state spaces. Based on work with Louis Fan, Christine Heitsch, and Sebastien Roch.
• 11:30 am - 12:15 pm EDT

  Generalized Maternal/Paternal Genotype Markov Model for Single-Cell Lineages

  11th Floor Lecture Hall

  • Speaker
  • Julia Chifman, American University

  • Session Chair
  • Leo van Iersel, Delft University of Technology

  Abstract

  The advent of single-cell sequencing provides the ability to model the evolution of somatic cells within individuals. For example, inference of cell phylogenies has the potential to advance our understanding of the variation in the process of tumor progression. Phylogenetic methods have been applied in numerous ways to model the evolution of somatic cells from single-cell DNA data using single-nucleotide variants. Some methods implement a finite-sites Markov model by grouping genotypes in various ways, and such models are the focus of this presentation. Since both the maternal and paternal genomes are passed on to daughter cells during mitosis, it is appropriate to start with a phased model of maternal and paternal sequence evolution using a continuous-time Markov process. However, phased genotypes are not always observed, and only unphased genotypes are available. As a result, it is common to group pairs of heterozygous genotypes into single states, leading to an unphased model. Some methods further lump unphased genotypes, resulting in coarser processes. The process with a smaller state space corresponds to a lumped process of the original phased Markov chain and may or may not be Markovian, depending on restrictions imposed on the generator matrix. The purpose of this presentation is to explore the mathematical formulations of phased and unphased Markov processes. We hope to initiate a discussion about whether restrictions should be placed on the generator matrix when inferring tumor phylogenies in practice.
• 12:30 - 2:30 pm EDT

  Open Problems Lunch

  Working Lunch - 11th Floor Collaborative Space
• 2:30 - 3:15 pm EDT

  TBA

  11th Floor Lecture Hall

  • Speaker
  • Siyu Chen, Princeton University

  • Session Chair
  • Kristina Wicke, New Jersey Institute of Technology
• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 4:45 pm EDT

  A Sequential Monte Carlo approach to the Multispecies Coalescent

  11th Floor Lecture Hall

  • Speaker
  • Paul Lewis, University of Connecticut

  • Session Chair
  • Kristina Wicke, New Jersey Institute of Technology

  Abstract

  Sequential Monte Carlo (SMC, particle filtering) has been used successfully to sample from Bayesian posterior distributions of phylogenetic trees. Our work seeks to apply SMC to the hierarchical Bayesian Multispecies Coalescent (MSC) model. In MSC, the primary distribution of interest is the marginal species tree posterior, which is challenging because the species tree is a hyperparameter that constrains the topology and node heights of the gene trees nested within and is thus only indirectly influenced by the observed sequence data. I will discuss our approach to applying SMC to the MSC model and illustrate with results from simulated as well as empirical datasets.

September 20, 2024

• 9:00 - 9:45 am EDT

  Tree Reconstruction from Multi-state Characters

  11th Floor Lecture Hall

  • Speaker
  • Charles Semple, University of Canterbury

  • Session Chair
  • Julia Chifman, American University

  Abstract

  A central task in evolutionary biology is the construction of phylogenetic trees to represent the ancestral history of a collection of present-day taxa. The data typically used for this task are characters, which describe the attributes of the taxa under consideration. To illustrate, a particular position of aligned DNA sequences is an example of a character. The attributes (states) of this character are the subsets of taxa taking a certain nucleotide at this position. In the context of this task, many questions naturally arise. How do we decide if a collection of characters is compatible (realisable by a single tree)? Does compatibility depend on considering all of the characters in the collection simultaneously or can we do better than that? How many characters does it take to uniquely determine a phylogenetic tree? Does the answer depend on the topology of the tree? If so, how? If the characters have a bounded number of states, how does the number of characters it takes grow with respect to this bound and the number of taxa? In this talk, we investigate these questions, and discuss some old and not so old results.
• 10:00 - 10:45 am EDT

  Phylogenomic Models from Tree Symmetries

  11th Floor Lecture Hall

  • Speaker
  • Colby Long, The College of Wooster

  • Session Chair
  • Julia Chifman, American University

  Abstract

  A model of genomic sequence evolution on a species tree should include not only a sequence substitution process, but also a coalescent process, since different sites may evolve on different gene trees due to incomplete lineage sorting. Chifman and Kubatko initiated the study of such models, leading to the development of the SVDquartets methods of species tree inference. A key observation was that symmetries in an ultrametric species tree led to symmetries in the joint distribution of bases at the taxa. In this talk, we explore the implications of such symmetry more fully, defining new models incorporating only the symmetries of this distribution, regardless of the mechanism that might have produced them. The models are thus supermodels of many standard ones with mechanistic parameterizations. We present phylogenetic invariants for the models, and discuss identifiability of species tree topologies using them.
• 11:00 - 11:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 11:30 am - 12:15 pm EDT

  TBA

  11th Floor Lecture Hall

  • Speaker
  • Arash Jamshidpey, Columbia University

  • Session Chair
  • Julia Chifman, American University
• 12:30 - 1:15 pm EDT

  Algebra and Geometry of Phylogenetic Networks

  11th Floor Lecture Hall

  • Speaker
  • Elizabeth Gross, University of Hawai'i at Mānoa

  • Session Chair
  • Julia Chifman, American University

  Abstract

  Placing a Markov model of evolution on a phylogenetic network gives rise to a statistical model that is particularly amenable to algebraic study by representing it as an algebraic variety. For group-based Markov models, these algebraic varieties are t-varieties with rich combinatorial structure. In this talk, we will present recent results regarding the dimension and defining polynomials of these algebraic varieties. We will then discuss how these properties can be used for establishing identifiability and network inference.
• 1:30 - 3:30 pm EDT

  Lunch/Free Time

September 21, 2024

There are no events currently scheduled for September 21st.