MBI Videos

Videos by Workshop 1: New Questions in Probability Theory Arising in Biological Systems

  • A model for evolution in a spatial continuum
    Alison Etheridge
    Classical models for gene flow fail in (at least) three ways. First, they cannot explain patterns in data observed over large scales; second, they predict much more genetic diversity than is observed; and third, they asssume that genetic loci evolve independently. I shall describe, as time permits, results of joint projects with Nick Barton, Nathanael Berestycki, Jerome Ke...
  • Pedigrees, genealogies and genomes
    Nick Barton
    An individual passes on random segments of her genome to future generations: typically, most of the genome is lost, but a small fraction survives, in many copies. This distribution of surviving blocks can be calculated using a branching process argument. Remarkably, after a few tens of generations it has the same form for every individual, with variation in reproductive va...
  • Pedigrees, genealogies and genomes
    Nick Barton
    An individual passes on random segments of her genome to future generations: typically, most of the genome is lost, but a small fraction survives, in many copies. This distribution of surviving blocks can be calculated using a branching process argument. Remarkably, after a few tens of generations it has the same form for every individual, with variation in reproductive va...
  • Noise in the Nervous System
    John White
    One of the principal tasks of the nervous system is to generate internal representations of the world, in order that we might best interpret the present, predict the future, and thus pass our genes to the next generation. For this reason, it seems quite surprising that the nervous system is so noisy. This noise is reasonably well characterized at the level of ion channels ...
  • Noise in the Nervous System
    John White
    One of the principal tasks of the nervous system is to generate internal representations of the world, in order that we might best interpret the present, predict the future, and thus pass our genes to the next generation. For this reason, it seems quite surprising that the nervous system is so noisy. This noise is reasonably well characterized at the level of ion channels ...
  • Cancer causes stable laws
    Rick Durrett
    It is common to use a multitype branching process to model the accumulation of mutations that leads to cancer progression, metastasis, and resistance to treatment. In this talk I will describe results about the time until the first type k (cell with k mutations) and the growth of the type k population obtained in joint work with Stephen Moseley, and their use in evaluating...
  • A simple mutational model that produces diminishing returns epistasis and decelerating fitness trajectories in adaptive walks
    Paul Joyce
    In relating genotypes to fitness, models of adaptation need to be both computation- ally tractable and to qualitatively match observed data. One reason tractability is not a trivial problem comes from a combinatoric problem whereby no matter in what order a set of mutations occurs, it must yield the same fitness. We refer to this problem as the bookkeeping problem. Because...
  • Muller's ratchet with compensatory mutations
    Anton Wakolbinger
    We discuss a Fleming-Viot model whose mutation process is a birth- and death process on the non-negative integers. In this model, new deleterious mutations accumulate at a constant rate per generation, and each mutation decreases the individual fitness by a constant amount. Other than in the classical case of Muller's ratchet, each of the present mutations has a small...
  • Metagenomics and metrics on spaces of probability measures
    Steven Evans
    Metagenomics attempts to sample and study all the genetic material present in a community of micro-organisms in environments that range from the human gut to the open ocean. This enterprise is made possible by high-throughput pyrosequencing technologies that produce a "soup" of DNA fragments which are not a priori associated with particular organisms or with part...
  • Dynamics of the evolving Bolthausen-Sznitman coalescent
    Jason Schweinsberg
    Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the population. This gives rise to a tree-valued stochastic process. We will study this process in the case of populations whose genealogy is given b...
  • Stochastic Dynamics of some Neuron Models
    Priscilla Greenwood
    How does a stochastic process move between the domains of attraction of locally stable points or cycles of an associated deterministic system, and cross unstable cycles? This question arises when we try to quantify the behavior of a neuron in terms of a stochastic neuron model. In the Morris Lecar model, for instance, the much-studied interspike-interval distribution depen...
  • Antibiotic resistance plasmids and spatial structure
    Steve Krone
    Bacterial plasmids are circular extra-chromosomal genetic elements that code for simultaneous resistance to multiple antibiotics and are thought to be one of the most important factors in the alarmingly rapid loss of our arsenal of antimicrobial drugs. Plasmids propagate horizontally by infectious transfer, as well as vertically during cell division. Horizontal transfer re...
  • Identifying separated time scales in stochastic models of reaction networks
    Thomas Kurtz
    For chemical reaction networks in biological cells, reaction rates and chemical species numbers may vary over several orders of magnitude. Combined, these large variations can lead to subnetworks operating on very different time scales. Separation of time scales has been exploited in many contexts as a basis for reducing the complexity of dynamic models, but the interactio...

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