MBI Videos

Videos by 2011

  • Toward a grand unified theory of copepods
    Nicholas Record
    Pelagic copepods are the dominant mesozooplankton in much of the world's oceans. They form a crucial link in the transfer of energy from primary production to upper trophic levels, and they are a significant contributor to vertical carbon flux through migration and fecal pellets. Much effort has gone into studying the effects of climate change on individual species. T...
  • Modeling of Microbial Biofilms and Mats
    Isaac Klapper
    No description available....
  • Predicting the behavior of ocean ecology in a changing climate: from simple theory to global climate models
    Irina Marinov
    Climate driven changes to the physical structure of the ocean will modify oceanic temperature, light, and nutrients, essential ingredients for the growth of ocean phytoplankton. In turn, resulting changes in phytoplankton growth and community structure will affect export production, deep ocean carbon storage, and ultimately atmospheric carbon.
    The questions I work on a...
  • Title coming soon
    Keith Promislow
    No description available....
  • Brine-biogeochemistry interactions in Sea Ice
    Martin Vancoppenolle
    The polar oceans have already experienced significant ecosystem shifts associated with sea ice retreat. Earth system models suggest that major changes in marine ecosystems and biogeochemistry will keep on going through the 21st century. However, future projections of the polar oceans are subject to some of the largest uncertainties. Among the sources of uncertainty is the ...
  • Phytoplankton growth in oligotrophic oceans: Weakly nonlinear theory
    Arjen Doelman
    In this talk, we will consider the problem of bifurcating DCMs under nutrient-light co-limitation from a weakly nonlinear point of view. In particular, we will work with the plankton-nutrient model in one spatial dimension introduced in A. Zagaris's talk and investigate the weakly nonlinear stability problem for these bifurcating DCMs.

    The most intrigui...
  • Phytoplankton growth in oligotrophic oceans: Linear theory
    Antonios Zagaris
    In this talk, we will present analytic results concerning phytoplankton growth under nutrient-light co-limitation. The model we employ consists of two reaction-advection-diffusion PDEs for the plankton and nutrient concentrations and incorporates self-shading effects.

    In the first part of this talk, we will work with a single spatial dimension (depth) and lo...
  • Paleo-perspective of the development of sea ice and related biota in the Arctic Ocean
    Leonid Polyak
    The Arctic environment is experiencing a rapid change due to the ongoing climate warming, with an especially high rate of temperature increase in the Arctic. The core of this change is the cryosphere destruction: an abrupt decrease in sea ice extent and volume, intensified glacier melting, and degradation of the permafrost. These processes profoundly affect the entire Arct...
  • Overview of CO2 dynamics within sea ice
    Bruno Delille
    No description available....
  • The spatio-temporal spread of infectious diseases
    Julien Arino

    Infectious diseases have been spreading across vast distances for milenia as a result of the movement of both human and animal hosts. In the past, both types of hosts had limited movement ranges, and one observed travelling waves of infection slowly expanding across space. Nowadays, the movement of humans has considerably accelerated and expanded, so that one observes a...

  • Questions/panel with morning speakers
    Stephen Ackley, Ken Golden
    No description available....
  • Questions/panel with morning speakers
    Stephen Ackley, Ken Golden
    No description available....
  • The effect of noise on mixed-mode oscillations
    Barbara Gentz
    Many neuronal systems and models display so-called mixed-mode oscillations (MMOs) consisting of small-amplitude oscillations alternating with large-amplitude oscillations. Different mechanisms have been identified which may cause this type of behaviour. In this talk, we will focus on MMOs in a slow-fast dynamical system with one fast and two slow variables, containing a fo...
  • Dynamics of Differential Equations with Multiple State Dependent Delays
    Antony Humphries
    The Mackey-Glass equation is a seemingly simple delay differential equation (DDE) with one fixed delay which can exhibit the full gamut of dynamics from a trivial stable steady state to fully chaotic dynamics, and has inspired decades of mathematical research into DDEs. However, much of that research has focused on equations with fixed or prescribed delays, whereas many bi...
  • Computing 2D invariant manifolds: Can you do this?
    Hinke Osinga
    The Lorenz system is the classical example of a seemingly simple dynamical system that exhibits chaotic dynamics. In fact, there are numerous studies to characterize the complicated dynamics on the famous butterfly attractor. This talk addresses how the dynamics is organized more globally. An important role in this regard is played by the stable manifold of the origin, als...
  • Animal gaits and symmetries of periodic solutions
    Marty Golubitsky
    In the first part of this talk I will briefly describe previous work on quadruped gaits (which distinguishing gaits by their spatio-temporal symmetries). In the second part, I will discuss how the application to gaits has led to results about phase-shift synchrony in periodic solutions of coupled systems of differential equations. This work is joint with David Romano, Yunj...
  • Modeling Neural Networks for Rhythmic Movements
    Ron Harris-Warrick
    Central Pattern Generators (CPGs) are limited neural networks that drive rhythmic behaviors such as locomotion, respiration and mastication. We have been studying the structure, function, and modulation of CPGs, with an emphasis on neuronal and ionic mechanisms that allow flexibility in the output from an anatomically defined network. Both biological and modeling studies s...
  • Exploring the interplay between ecology and evolution of plant-herbivore interactions
    Marc Johnson
    (Co)evolutionary ecologists have long appreciated that ecology drives evolution, and that evolution ultimately shapes the ecological processes and patterns of populations and communities over long periods of time. However, it remains unclear how these two processes interact to affects the ecology, evolution and coevolution of communities over short timescales (e.g. one to ...
  • Probing Membrane Protein Structure and Dynamics by NMR and Single Molecule Fluorescence
    Lukas Tamm
    Structures of membrane proteins have been challenging to solve by any structural technique. We are developing solution NMR spectroscopy as a tool to study the structure and dynamics of membrane proteins, including bacterial outer membrane porins. This class of membrane proteins has proven particularly beneficial for these studies because (i) a larger chemical shift dispers...
  • Red King predators, evolution of mutualistic antagonists and coevolution patterns between mutualists and antagonists
    Claire de Mazancourt
    In this talk I will present several theories related to co-evolution between plants and insects. First I will present a model of predator-prey coevolution, showing that rapid evolution in the predator can lead to prey diversification and a decrease in the number of preys available to the predator. This correspond to a "Red King" scenario, where rapid evolution le...
  • ReplicOpter: A Replicate Optimizer for Flexible Docking
    Julie Mitchell
    We present a computationally efficient method for flexible refinement of docking predictions that reflects observed motions within a protein's structural class. Using structural homologs, we derive deformation models that capture likely motions. The models or "replicates" typically align along a rigid core, with a handful of flexible loops, linkers and tails...
  • Analysis, prediction, and design of viral RNA secondary structures
    Christine Heitsch
    Understanding how biological sequences encode structural and functional information is a fundamental scientific challenge. For RNA viral genomes, the information encoded in the sequence extends well-beyond their protein coding role to the role of intra-sequence base pairing in viral packaging, replication, and gene expression. Working with the Pariacoto virus as a model se...
  • Geometric flow for biomolecular solvation
    Nathan Baker
    Implicit solvent models are important components of modern biomolecular simulation methodology due to their efficiency and dramatic reduction of dimensionality. However, such models are often constructed in an ad hoc manner with an arbitrary decomposition and specification of the polar and nonpolar components. In this talk, we review current implicit solvent models and sug...
  • Pseudo-time coupled smooth interface models for biomolecular solvation calculations
    Shan Zhao
    Recently, we have introduced a differential geometry based model, the minimal molecular surface, to characterize the dielectric boundary between biomolecules and the surrounding aqueous environment. The mean curvature flow is used to minimize a surface free energy functional to drive the surface formation and evolution. More recently, several potential driven geometric flo...
  • In silico modeling of the effects of missense mutations causing mental disorders
    Emil Alexov
    Human DNA sequence differs among individuals and the most common variations are known as single nucleotide polymorphisms, or SNPs. Studies have shown that non-synonymous coding SNPs (nsSNPs - SNPs occurring in protein coding regions which lead to amino acid substitutions) can be responsible for many human diseases or cause the natural differences among the individuals by a...
  • Mathematics in drug design
    Ridgway Scott
    We show how mathematics can help in the complex process of drug discovery. We give an example of modification of a common cancer drug that reduces unwanted side effects. The mathematical model used to do this relates to the hydrophobic effect, something not yet fully understood. The hydrophobic effect modulates the dielectric behavior of water, and this has dramatic effect...
  • Discrete differential geometry of curves and protein structure
    Jack Quine
    Differential geometry of curves uses the Frenet-Serret moving frame. A curve can be defined by scalar quantities of curvature and torsion and these quantities are defined by differentiating the frame. Similar techniques can be used for discrete curves formed by sequences of bonded atoms. The frames are related to molecular frames and are useful in finding protein structure...
  • The Coevolution of Competitors in a Community Context
    Peter Abrams
    Most theoretical work on the evolution of competing species has used models having the minimum number of species (i.e. two), and has not represented either enemies or resources of those two consumer species. Empirical studies of character displacement involve species that share multiple resources, and usually multiple predators as well. Although some prominent experimental...
  • Reciprocal adapations as a key factor in the stabilization of a defensive ant-plant mutualism
    Martin Heil
    Ant-plants are important structural elements in many disturbed tropical ecosystems and the mutualism between plants and their defending ant symbionts is increasingly being used as a model to study general factors that stabilize a horizontally transmitted mutualisms. As these mutualisms must be established anew in every consecutive generation they are particularly prone to ...
  • Measuring coevolutionary selection in plant-insect interactions
    Ben Ridenhour
    No description available....
  • Trait Matching: What does it tell us?
    Bruce Anderson
    Recently, several studies have used the geographic matching of morphological traits (e.g. proboscis versus corolla length) to infer that coevolution has taken place between two interacting organisms. However, geographic trait matching alone is not sound evidence for coevolution because it is not a mandatory end point for coevolutionary relationships, and nor is coevolution...
  • Exploring selection mosaics and coevolution in multiespesific generalized systems
    Jose Gomez
    The geographic mosaic theory of coevolution (GMTC) considers that populations differ in evolutionary dynamics due to spatial variation in selective regimes. According to GMTC, three components of geographic structure drive the overall coevolutionary dynamics of such interactions: selection mosaics, coevolutionary hotspots, and trait remixing. Furthermore, the GMTC suggests...
  • A coevolutionary resolution to the paradox of concave selection?
    Paul Hohenlohe
    The adaptive landscape, long a useful metaphor, is also a rigorous tool for understanding evolution when it is linked to empirical measurements of fitness. However, empirical estimates of fitness surfaces are often concave, implying an evolutionarily unstable situation under general conditions in the short term, and untenable extrapolations to longer-term evolution under t...
  • Coevolution in plant-pollinator networks: the impact of network properties
    Franck Jabot
    In many plant-pollinator systems, interactions present a high degree of generalism, so that coevolution should be studied at the community level. Indeed intraspecific trait variation in such systems may both lead to variation in the gains that individuals are drawing from their interactions, and to variation in their choice/attraction of interaction partners. In this contr...
  • Evolution of virulence and mixed infections
    Jacqui Shykoff
    One very robust result of models of host-parasite co-evolution is that under regimes of mixed infection, where different strains of parasites compete for limiting host resources, parasites should evolve higher virulence strategies. This has wide reaching ramifications for optimal parasite strategies, since parasites are seldom alone in exploiting hosts. However, not all in...
  • The consequences of exploitation for plant-pollinator mutualisms
    Emily Jones
    Species exist in complex biotic environments, engaging in a variety of antagonistic and cooperative interactions that contribute to their population and evolutionary dynamics. However, studies tend to concentrate on each pairwise interaction in isolation. By doing so, they may overlook significant feedbacks between the interactions. In this talk, I will focus on plant-poll...
  • Statistical Measures on Residue-Level Protein Structural Properties
    Zhijun Wu
    Structural properties on protein residue-level, such as the distances between two residues and the angles formed by short sequences of residues, can be important for structural analysis and modeling, but they have not been examined and documented in great detail. While these properties are difficult to measure experimentally, they can be statistically estimated based on th...
  • Ions in Channels: important biology ready for mathematical analysis
    Robert Eisenberg
    Ion channels are irresistible objects for biological study because they are the 'nanovalves of life' controlling most biological functions, much as transistors control computers. Channels contain an enormous density of crowded charged spheres, fixed and mobile, and induced polarization charge as well. Direct simulation of channel behavior in atomic detail is diff...
  • Noise sensitivities in systems with delays and multiple time scales
    Rachel Kuske
    Dynamical systems with delayed feedback often exhibit complex oscillations not observed in analogous systems without delay. Stochastic effects can change the picture dramatically, particularly if multiple time scales are present. Then transients ignored in the deterministic system can dominate the long range behavior. This talk will contrast the effects of different noise ...
  • Waves in random neural media
    Stephen Coombes
    The propagation of waves of neural activity across the surface of the brain is known to subserve both natural and pathological neurobiological phenomena. An example of the former is spreading excitation associated with sensory processing, whilst waves in epilepsy are a classic example of the latter. There is now a long history of using integro-differential neural field mod...
  • Geometric singular perturbation theory beyond the standard form
    Peter Szmolyan
    In many biological models multiple time scale dynamics occurs due to the presence of variables and parameters of very different orders of magnitudes. Situations with a clear "global" separation into fast and slow variables governed by singularly perturbed ordinary differential equations in standard form have been investigated in great detail.

    For m...
  • Periodic orbits in problems with state-dependent delays
    Jan Sieber
    Delays in feedback loops tend to destabilize dynamical systems, inducing self-sustained oscillations or chaos. I will show some typical examples in my presentation. I will also show how one can reduce the study of periodic oscillations in systems with delay to low-dimensional smooth algebraic systems of equations. The approach works also when the delay depends on the state...
  • Stability analysis for stochastic delay differential equations
    Evelyn Buckwar
    Stochastic delay differential equations often arise in biosciences as models involving, e.g., negative feedback terms and intrinsic or extrinsic noise. Examples of applications range from stochastic models of human immune response systems, neural networks or neural fields to genetic regulatory systems. Stability theory for stochastic delay differential equations is quite w...
  • Numerics for stability analysis of delay systems and population dynamics
    Dimitri Breda
    The plan is to divide the talk in three distinct but related parts.

    First, the question of asymptotic stability for equilibria of delay differential equations is addressed numerically. The proposed method, based on the discretization of the infinitesimal generator of the solution operator semigroup via pseudospectral differentiation, allows to approximate th...
  • Bounded noise: bifurcations of random dynamical systems
    Ale Jan Homburg
    Random dynamical systems with bounded noise can have multiple stationary measures with different supports. Under variation of a parameter, such as the amplitude of the noise, bifurcations of these measures may occur. We discuss such bifurcations both in a context of random diffeomorphisms and of random differential equations.

    References:

    *...
  • Phase Models for Oscillators with Time Delayed Coupling
    Sue Ann Campbell
    We consider a network of inherently oscillatory neurons with time delayed connections. We reduce the system of delay differential equations to a phase model representation and show how the time delay enters into the reduced model. For the case of two neurons, we show how the time delay may affect the stability of the periodic solution leading to stability switching between...
  • Cross-currents between Biology and Mathematics on Models of Bursting
    Arthur Sherman
    I will trace the history of models for bursting, concentrating on square-wave bursters descended from the Chay-Keizer model for pancreatic beta cells. The model was originally developed on a biophysical and intutive basis but was put into a mathematical context by John Rinzel's fast-slow analysis. Rinzel also began the process of classifying bursting oscillations base...
  • Math to Bio and Bio to Math
    John Guckenheimer
    The interchange between dynamical systems theory with biology has had lasting impact upon both. As biology becomes increasingly quantitative, this relationship is likely to strengthen still further. This lecture will review my experience as a mathematician working at the interface with biology, emphasizing the role of multiple time scales in biological models. It will also...
  • No Title Available
    Jean-Louis Deneubourg
    No description available....
  • Generalized Poisson Nernst-Planck equations for ion channel transport: Numerical schemes and modified models
    Qiong Zheng
    As a mean-field continuum model, Poisson Nernst-Planck (PNP) theory is an efficient computational tool for the study of ion transport phenomenon in the biological systems such as ion channels, which are important in the cell survival and the regulation of cellular activity. The present talk reports advanced numerical schemes and modified PNP models for ion channels. Based ...
  • Modeling ion size effects with density functional theory of fluids
    Dirk Gillespie
    Theories like Poisson-Nernst-Planck that model ions as point charge are very useful in many applications. However, when ions are near highly-charged binding sites on proteins or inside ion channels, the size of the ions produces first-order effects because the ions' concentration is very large and/or because the ions are in a crevice or pore that is not much wider tha...
  • Fluid Assisted Charge Transport: Mathematical Consistency of the Navier-Stokes/Poisson-Nernst-Planck Model
    Joseph Jerome
    The Navier-Stokes/Poisson-Nernst-Planck model assumes significance because of its connection to the electrophysiology of the cell, including neuronal cell monitoring and microfluidic devices in biochip technology. The model has also been used in other applications, including electro- osmosis. The steady model is especially important in ion channel model- ing, because the c...
  • Quantum dynamics in continuum for proton channel transport
    Duan Chen
    Proton transport across membranes is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysical model for the understanding of atomic level mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model numerous ...
  • Molecular meshing and continuum modeling
    Benzhuo Lu
    Continuum modeling can be a proper choice to overcome the limitations on time and length scales of all-atom biomolecular simulations. The main concerns in this area are the model's accuracy and the numerical techniques/implementation. Besides, the molecular surface/volume meshing is also an unavoidable issue in many cases. I'll talk about our works on calculation...
  • Folding of Lipid Monolayers Containing Lung Surfactant Proteins SP-B1-25 and SP-C Studied via Coarse-Grained Molecular Dynamics Simulations
    Ron Larson
    We utilize the MARTINI coarse-grained force field to simulate lipid monolayers during the compression and re-expansion, to determine the effect of monolayer components on lung surfactant functioning. Our simulated monolayers contain pure dipalmitoylphosphatidylcholine (DPPC) and DPPC mixed with palmitoyloleoylphosphatidylglycerol (POPG), palmitic acid (PA), and/or peptides...
  • Factors Controlling Plankton Ecology
    David Thomas
    No description available....
  • Ecological Modeling
    Alan Hastings
    Some underlying issues of modeling in ecology
    2 species predator prey dynamics and analysis
    Aquatic ecological systems - basic issues
    NPZ modeling basics
    NPZ "applications" and extensions...
  • Dynamic-clamp studies of neuronal synchronization
    John White
    Coherent neuronal activity is ubiquitous and presumably important in brain function. I will review my group's experimental studies of the mechanisms underlying coherent activity using dynamic clamp technology, which allows us to perform virtual-reality-inspired experiments in neurons in vitro. Using these techniques and mathematical tools from dynamical systems theory...
  • Predation, competition and infection in a noisy environment
    Horst Malchow
    Biological invasions including the spread of infectious diseases have strong ecological and economical impacts. The perception of their often harmful effects has been continuously growing both in sciences and in the public. Mathematical modelling is a suitable method to investigate the dynamics of invasions, both supplementary to and initiating eld studies as well as cont...
  • Patchy Invasion: Exotic Spread of Exotic Species or a Paradigm Shift?
    Sergei Petrovskii
    Biological invasion admittedly consists of a few distinctly different stages such as exotic species introduction, establishment and geographical spread. Each of the stages has its own specific mechanisms and implications, which require application of specific research approaches. In my talk, I focus on the challenges arising during the stage of the geographical spread. A w...
  • Spatiotemporal Dynamics Behind Invasions In Cyclic Populations
    Jonathan Sherratt
    In populations with cyclic dynamics, invasions typically generate either regular (periodic) spatiotemporal oscillations, spatiotemporal chaos, or a mixture of the two. I will present examples of these behaviours in numerical simulations of invasions. I will then describe how to determine which of the behaviours will occur, as a function of ecological parameters. The charac...
  • The effect of disease on invasions
    Frank Hilker
    Why do some exotic species thrive so successfully once they have been introduced to a new environment? One of the reasons most frequently called upon is the enemy release hypothesis, which explains the inordinate success of introduced species by the lack of pressure from co-evolved natural enemies. In this talk, I consider the situation that the new environment changes in ...
  • Invasion speeds and sensitivity analysis in variable environments
    Hal Caswell
    Invasion speeds can be calculated from matrix integrodifference equation models that incorporate stage-specific demography and dispersal. These models also permit the calculation of the sensitivity and elasticity of invasion speed to changes in demographic and dispersal parameters. Such calculations have been used to understand the factors determining invasion speed and to...
  • Stochastic logistic model with environmental noise
    Brian Dennis
    The logistic model is the quintessential model of invasion. The fundamental idea of the logistic is "something replacing something else": vegetative cover replacing empty space, biomass replacing nutrient, infected individuals replacing uninfected ones, DVD households replacing VHS households. Biological mechanisms producing logistic growth are analogous to an au...
  • Confronting perfect models with imperfect data using data cloning
    Subhash Lele
    Modeling population dynamics is essential to study ecological populations whether for maintaining the existing populations (e.g. Population Viability Analysis) or for controlling spread of invasive species. Meta-population dynamics that takes into account of immigration and emigration also plays an important role in studying spread of invasive species. Systems of ordinary ...
  • Optimal control of invasive models
    Suzanne Lenhart
    Optimal control will discussed as a tool to find intervention strategies in models for invasive species. Examples of optimal control of discrete time systems and of systems of ordinary differential equations will be given. Control characterizations and numerical results for models with different types of control intervention actions will be presented. Applications include ...
  • Dynamics and control of Spartina alterniflora and related issues
    Alan Hastings
    I will discuss models that include the kinds of spatial dynamics and control and life history appropriate for this plant. The ideas will focus on developing simple analytic models and using approaches that into account not only control but restoration and bio-economic aspects. Mathematical tools will include linear and quadratic programming in addition to optimization and ...
  • Group discussion: Applying wavespeed models to the real world
    Ingrid Parker
    No description available....
  • Sea Ice Structure and Processes
    Ken Golden
    No description available....
  • Biology/Physics Interface in Sea Ice
    Stephen Ackley
    No description available....
  • Gas Transport thru' Sea Ice
    Jean-Louis Tison
    No description available....
  • Ocean Transport and Mixing
    Emily Shuckburgh
    Part 2 of a two-part introduction to the mathematics of ocean dynamics, transport and mixing....
  • Ocean Dynamics
    Emily Shuckburgh
    Part 1 of a two-part introduction to the mathematics of ocean dynamics, transport and mixing....
  • Intoductions and questions/panel with morning speakers
    Alan Hastings
    Panel discussion with morning speakers David Thomas and Alan Hastings...
  • Phytoplankton Role, Growth, and Fate
    Walker Smith
    No description available.......
  • Questions/panel with morning speakers
    Arjen Doelman, Walker Smith, Walker Smith
    No description available....
  • Questions/panel with morning speakers
    Arjen Doelman, Walker Smith, Walker Smith
    No description available....
  • Questions/panel with morning speakers
    Arjen Doelman, Walker Smith, Walker Smith
    No description available....
  • Coevolution and community complexity
    Sharon Strauss
    Our best examples of coevolution come from simplified interactions, but communities are rarely simple. Are complex communities less coevolved, or is coevolution just harder to recognize? I discuss coevolution and community complexity in light of both natural and invaded systems....
  • Questions/panel with morning speakers
    Nicole Lovenduski, Jean-Louis Tison, Jean-Louis Tison
    No description available....
  • Questions/panel with morning speakers
    Nicole Lovenduski, Jean-Louis Tison, Jean-Louis Tison
    No description available....
  • Questions/panel with morning speakers
    Nicole Lovenduski, Jean-Louis Tison, Jean-Louis Tison
    No description available....
  • Phytoplankton-Nutrient Modeling
    Arjen Doelman
    No description available.......
  • Sex-Biased Dispersal and the Speed of Two-Sex Invasions
    Mike Neubert
    Population models that combine demography and dispersal are important tools for forecasting the spatial spread of biological invasions. Current models describe the dynamics of only one sex (typically females). Such models cannot account for the sex-related biases in dispersal and mating behavior that are typical of many animal species. In this lecture, I will construct a t...
  • Swarms as smart architects: understanding construction dynamics in ant colonies
    Guy Theraulaz
    The amazing abilities of social insects to solve their everyday-life problems, also known as swarm intelligence, have received a considerable attention the past twenty years. Among their collective behaviors, nest building is certainly the most spectacular. Not only the characteristic scale of the nests is typically much larger than the size of the individuals, but some of...
  • Audience and information transfer in ant societies
    Claire Detrain
    The ant society is a dynamic network of interacting nestmates of which individual decision rules lead to adaptive and functional patterns at the collective level. The non-linearity of relationships between workers makes those societies displaying properties characterizing other complex systems such as a high sensitivity to the number and/or rates of interactions between sy...
  • Evolutionary Constraints on Social Organization from Disease Risks
    Nina Fefferman
    As social insects have evolved division of labor and colony organization to accomplish tasks necessary to their survival, their social and collaborative environment should make them more and more susceptible to risk from infectious disease. Since they haven't been forced to extinction yet, they're clearly doing something right. Some have evolved individual physio...
  • Organization and regulation of work in the social insect colony
    Jennifer Fewell
    Division of labor, the way in which social groups distribute work among their individual members, is a product of self organization and selection. A basic system of division of labor can be produced even in artificial associations of normally solitary individuals and fits simple rules of interaction. In social insect colonies, however, the process of division of labor refl...
  • Cohesive Swarm Behavior With Information Flow Constraints
    Kevin Passino
    Bacteria, bees, and birds often work together in groups to find food. A group of mobile wheeled robots can be designed to coordinate their activities to achieve a goal. Networked cooperative autonomous air vehicles are being developed for commercial and military applications. In order for such multiagent systems to succeed it is often critical that they can both maintain c...
  • Swarm guidance in Apis florea: making decisions on the fly?
    Mary Myerscough
    Nest site selection and swarm guidance in swarms of Apis mellifera are well studied, both observationally and theoretically, but not nearly so much is known about decision-making behaviour in other species of Apis. The Asian red dwarf honey bee, Apis florea, is an open-nesting honey bee, found in Southeast Asia, India and parts of the Middle East whose nest is a single com...
  • Collective decision making by honey bees
    Thomas Seeley
    I will review what is known about one of the most enchanting forms of collective animal behavior: the skillful choice of a new home by a swarm of honey bees. The challenge has been to understand how the 1.5 kilograms of bees in a swarm, like the 1.5 kilograms of neurons in a brain, are organized so that even though each individual has limited information and limited intell...
  • Network topology and the evolution of collective migration
    Naomi Leonard
    Agent-based dynamical models have been used successfully to reproduce a range of observed collective behaviors in biological groups. In these models, agents interact with one another and it has been shown that the topology of the interaction network plays a significant role in emergent outcomes and performance at the level of the group. An important challenge is to underst...
  • Engineering Self-Organizing Systems
    Radhika Nagpal
    Biological systems, from embryos to social insects, get tremendous mileage by having vast numbers of cheap and unreliable individuals cooperate to achieve complex goals. We are also rapidly building new kinds of distributed systems with similar characteristics, from multi-modular robots and robot swarms, to vast sensor networks. Can we engineer collective systems to achiev...
  • Variational Principles and Control of Collective Behavior
    P. S. Krishnaprasad
    Geometric methods in control theory have had a useful role in the investigation of dynamics of collectives. In this talk, we build on models from this theory to sketch recent progress in understanding small networks governed by interaction strategies associated with pursuit. We extend these ideas to a broader array of variational principles in networks of interacting syste...
  • Workshop 4: Insect Self-organization and Swarming Lecture 5
    Craig Tovey
    No description Available....
  • Multi-Level Modeling and Distributed Control for Miniature Robotic Swarms
    Alcherio Martinoli
    In this talk, I will first highlight the challenges related to the design, control, modeling, performance evaluation, and optimization of distributed, mobile, resource-constrained robotic systems. In particular, I will describe a specific distributed control method based on multiple modeling levels which has provided up to date interesting results in several case studies c...
  • Adaptive network models of swarm dynamics
    Cristian Huepe
    I will present a simple adaptive network model describing recent insect swarming experiments. By exploiting an analogy with human decision-making models and considering network-like interactions, this model captures the experimental dynamics using a low dimensional system of equations that permits analytical investigation. It reproduces several characteristic features of s...
  • Models and Data for Invasive Spread Across Lake Networks
    Mark Lewis
    In this talk I will outline a recent interdisciplinary effort to model and understand the spread of invasive copepods across lake networks in North America. This 5-year project, developed through the Canadian Aquatic Invasive Species Network (CAISN), tracked the invasion status of approximately 500 interconnected lakes in the Canadian shield. Here the invader, spiny waterf...
  • Marine bioinvasion in the network of global shipping connections
    Bernd Blasius
    Transportation networks play a crucial role in human mobility, the exchange of goods, and the spread of invasive species. With 90% of world trade carried by sea, global shipping provides one of the most important modes of transportation. Shipping also constitutes the world largest transportation vector for marine bioinvasion, transferring accidentally numerous species arou...
  • Effects of endogenous vs exogenous sources of spatial heterogeneity on population stability and persistence
    Karen Abbott
    Invasive species can be heavily influenced by spatial heterogeneity in the landscape through which they are spreading. This heterogeneity may be endogenous (that is, patchiness in the distribution of the invader itself, or heterogeneity in other species due directly to interactions with the invader) or it may be exogenous (such as patchy resources or heterogenous climatic ...
  • Integrodifference equations for invasive species - some recent developments
    Frithjof Lutscher
    Integrodifference equations provide a very natural general framework to model the spread of invasive species if the species in question has a clearly distinct growth and dispersal phase during its life cycle. Many insect species satisfy this description, in particular where climate imposes strong seasonality.

    Early applications of integrodifference equations...
  • Moving in the crowd: Ants hold the key to traffic chaos
    Audrey Dussutour
    Many animals take part in flow-like collective movements. In most species, however, the flow is unidirectional. Ants are one of the rare group of organisms in which flow-like movements are predominantly bidirectional. This adds to the difficulty of the task of maintaining a smooth, efficient movement. Yet, ants seem to fare well at this task. Do they really? And if so, how...
  • Self-organization in Insect Societies: past, present and future
    Nigel Franks
    The application of self-organization theory to social insect studies is, for the most part, barely 20 years old. It has been remarkably successful because much of the new thinking and modelling that self-organization theory has brought to social insect studies has been very provocative, sometimes naive, and often oversimplifying; yet it has, almost invariably, lead to new ...
  • Optimality theory in collective behaviour
    James Marshall
    Twenty years ago, the case for optimality theory in evolutionary biology was set out in a review by Geoff Parker and John Maynard Smith. Thinking of what idealised animals should do if they are behaving optimally has informed behavioural ecology since its inception. With some exceptions, the study and theory of collective behaviour seems to be much more more mechanistic. T...
  • A Primer of Swarm Equilibria
    Andrew Bernoff
    We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the continuum population density. Equilibrium solutions are extrema of an energy functional, and satisfy a Fredholm integral equation. We find conditions for the extrema t...
  • From swarms to cannibalism to obesity: lessons from locusts
    Stephen Simpson
    Locust plagues are one of the most infamous insect scourges, invading vast areas of Africa, Asia, Australia and the Americas. The reason that locusts form plagues is that they have an extraordinary capacity to change from shy, green, harmless grasshoppers into brightly coloured, swarming creatures when they experience crowding. This remarkable change can occur within the l...
  • Modeling flocks and swarms
    Leah Edelstein-Keshet
    I will summarize some work on the link between individual behaviour and the dynamics of the swarm/flock. I will highlight two projects:

    1. The behaviour of a 2D flock of aquatic birds, and how Ryan Lukeman (former PhD student, now at St FX University) figured out the underlying individual rules
    2. models for social foraging, an ongoing project i...
  • Parallel Work and Parallel Play
    Fred Adler
    In human children, parallel play describes two or more children playing side by side, perhaps using the same toy but for different purposes, and only occasionally modifying their behavior in response to the other. It forms an early stage of social development, following solitary play and generally preceding social and cooperative play.

    If a group of ants wer...
  • The Road from Individual to Group Position to Emergence in Whirligig Swarms
    William Romey
    Emergent patterns of flocks and swarms are at once beautiful and mysterious. We ask ourselves: "How and why do individuals coordinate these complicated maneuvers?" More specifically: how does self organization at lower levels influence emergent properties at higher levels? I will present the results of some of my studies addressing these questions using whirligig...
  • Recombination dynamics and ancestral recombination trees
    Ellen Baake
    I will start with an overview over various models for the dynamics of the genetic composition of populations evolving under recombination. For the deterministic treatment that applies in the infinite-population limit, one has large, nonlinear dynamical systems; for the stochastic treatment required for finite populations, the Moran, or Wright-Fisher model is appropriate.
  • Basic reproduction numbers for reaction-diffusion epidemic models
    Wendi Wang
    The basic reproduction number and its computation formulae are established for epidemic models with reaction-diffusion structures. It is proved that the basic reproduction number provides the threshold value for disease invasion in the sense that the disease-free steady state is asymptotically stable if the basic reproduction number is less than unity and the disease is un...
  • No lecture title available
    Keith Lindsay
    No description available...
  • Evolution of phytoplankton cell size in a variable environment
    Ariane Verdy
    The size of phytoplankton cells determines their competitive ability, sinking rate, and potential to export carbon to the deep ocean. Observations suggest that small phytoplankton species dominate the equatorial and subtropical oceans while larger species are more abundant in subpolar regions. To understand this pattern, we have developed an allometric model for the evolut...
  • Spatio-Temporal Dynamics in Disease Ecology and Epidemiology
    Shigui Ruan
    We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) La...
  • Insecticide resistance and its implications for mosquito and malaria control
    Stephen Gourley
    Mosquitoes can rapidly develop resistance to insecticides, which is a big problem in malaria control. Current insecticides kill rapidly on contact, but this leads to intense selection for resistance because young adults are killed. Of considerable current interest is the possibility of slowing down or even halting the evolution of resistance. Biologists believe that much w...
  • Run for your Life
    Odo Diekmann
    In 1927 Kermack and McKendrick introduced and analyzed a rather general epidemic model (nota bene : their model takes the form of a nonlinear renewal equation and the familiar SIR model is but a very special case !). The aim of this lecture is to revive the spatial variant of this model, as studied in the late seventies by Horst Thieme and myself (see the AMS book 'Sp...
  • Cell migration as a free boundary problem
    Alex Mogilner
    Cells migrate on surfaces by protruding their front through growth of actin networks, retracting the rear by myosin-driven contraction and adhering to the substrate. Recent experimental and modeling efforts elucidated specific molecular and mechanical processes that allow motile cells to maintain constant distances from front to rear and from side to side while maintaining...
  • Fluctuations in a moving boundary description of diffusive interface growth
    Rodolfo Cuerno
    Stochastic generalizations of moving boundary problems appear quite naturally in the continuum description of e.g. solidification problems. Perhaps the simplest example is provided by a so-called one-sided solidification problem in which a condensed (solid) non-diffusing phase grows at the expense of a diluted diffusing phase (vapor or liquid). In this context, noise terms...
  • Propagation of fronts in non homogeneous media and applications in medicine and biology
    Henri Berestycki
    This talk is about fronts and propagation phenomena for reaction-diffusion equations in non-homogeneous media. I will discuss some specific models arising in population dynamics or in medicine where the medium imposes a direction of propagation....
  • (no title available)
    Arshak Petrosyan
    (no description available)...
  • Modeling blood coagulation: recent trends and new ideas
    Antonio Fasano
    Blood coagulation is an extremely complex process which is the result of the action of platelets and of a large number of chemicals going through a chemical cascade. Its aim is the formation of a clot, sealing a wound The clot evolution leads to a free boundary problem. It goes in parallel with the process of clot dissolution (fibrinolysis), taking place with a slower time...
  • Regularity for almost minimizers with free boundary
    Tatiana Toro
    We study the regularity of almost minimizers for the types of functionals analyzed by Alt, Caffarelli and Freidman. Although almost minimizers do not satisfy an equation using appropriate comparison functions we prove several regularity results. For example in the one phase situation we show that almost minimizers are Lipschitz. Our approach reminiscent of the one used in ...
  • The Dynamics of Mucus, or, Why the Stomach does not Digest Itself
    James Keener
    There are a number of interesting and important biological processes that are best modelled as two-phase material mixtures. These include mucin exocytosis and transport, blood clot formation and biofilm formation. These all involve the interplay between flow, physical structure, mechanics and chemistry in a environment with complex dynamic geometry. The mathematical descri...
  • Bridging Scales in Molecular Motor Models: From Single to Multiple Motor Systems
    Peter Kramer
    Recent years have seen increasing attention to the subtle effects on intracellular transport caused when multiple molecular motors bind to a common cargo. We develop and examine a coarse-grained model which resolves the spatial configuration as well as the thermal fluctuations of the molecular motors and the cargo. This intermediate model can accept as inputs either common...
  • Bridging Scales in Molecular Motor Models: From Diffusing Heads to Multiple Steps
    John Fricks
    A stochastic model for variable-length stepping of kinesins engineered with extended neck linkers is developed. This requires consideration of the separation in microtubule binding sites between the heads of the motor at the beginning of a step. It can be shown that the separation is a stationary Markov process and can be included in the calculation of standard experimenta...
  • Cell-free synthetic biology in nanofabricated reaction devices
    David Karig
    The growing field of synthetic biology aims to forward engineer biology both for applications such as energy production, drug production, and bioremediation, as well as for the purpose of furthering the fundamental understanding of natural systems. However, engineering living cells is notoriously difficult due to issues such as mutation, epigenetic variation, fitness effec...
  • Population persistence in the face of demographic and environmental uncertainty
    Sebastian Schreiber
    Populations, whether they be viral particles, bio-chemicals, plants or animals, are subject to intrinsic and extrinsic sources of stochasticity. This stochasticity in conjunction with nonlinear interactions between individuals determines to what extinct populations are able to persist in the long-term. Understanding the precise nature of these interactive effects is a cent...
  • Large-scale behaviour of the spatial Lambda-Fleming-Viot process
    Amandine Veber
    The SLFV process is a population model in which individuals live in a continuous space. Each of them also carries some heritable type or allele. We shall describe the long-term behaviour of this measure-valued process and that of the corresponding genealogical process of a sample of individuals in two cases : one that mimics the evolution of nearest-neighbour voter model (...
  • Impacts of genetics, environment and noise on virus growth
    John Yin
    The dynamics of a virus infection within its host is governed at its earliest stages by processes at the molecular and cellular scale. We are developing cell-culture measurements and computational models to better understand how these and other processes contribute to the early dynamics of virus growth and infection spread. As a model system we study vesicular stomatitis v...
  • Effective population sizes and the canonical equation of adaptive dynamics
    Johan (=Hans) Metz
    Deterministic population dynamical models connect to reality through their interpretation as limits for systems size going to infinity of stochastic processes in which individuals are represented as discrete entities. In structured population models individuals may be born in different states (e.g. locations in space) after which they proceed through their h(eterogeneity)-...
  • Pathogen Extinction in Stochastic Models of Epidemics and Viral Dynamics
    Linda Allen
    In deterministic epidemic models, pathogen extinction in a population is determined by the magnitude of the basic reproduction number R0. In stochastic epidemic models, the probability of pathogen extinction depends on R0, the size of the population and the number of infectious individuals. For example, in the SIS Markov chain epidemic model, if the basic reproduction numb...
  • Kinetic equations in spatial quantitative genetics
    Judith Miller
    We derive kinetic differential or integrodifference equations for the mean and variance or of a quantitative trait as a function of space and time, in some cases recovering known equations and in some cases obtaining new ones that capture effects, such as nonmonotonicity of traveling waves, that can be seen in stochastic simulations. We then reanalyze kinetic equations due...
  • Simple, very simple, and not so simple models of populations lingering around a carrying capacity, and allowing evolutionary branching
    Peter Jagers
    In a toy model of binary splitting branching processes with population size dependence (supercritical below and subcritical above a threshhold, the carrying capacity) the chance of a little population establishing itself in the sense of reaching a band around the carrying capacity is determined, and so is the persistence time of the population. Mutations and competition be...
  • Computational methods for stochastically modeled biochemical reaction networks
    David Anderson
    I will focus on computational methods for stochastically modeled biochemical reaction networks. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. I will show how different computational methods can be...
  • Stochastic processes in the adiabatic limit: applications to biochemistry and population genetics
    Ilya Nemenman
    Stochastic biochemical systems and population genetics models are described by similar mathematical equations, and hence similar phenomena should be observed in both systems. Here we focus on stochastic kinetics with time scale separation. We show how to integrate out the fast degrees of freedom, while rigorously preserving their effects on the fluctuations of slower varia...
  • Random walk distances in data clustering and applications
    Anastasios Matzavinos

    Clustering data into groups of similarity is well recognized as an important step in many diverse applications, including biomedical imaging, data mining and bioinformatics. Well known clustering methods, dating to the 70's and 80's, include the K-means algorithm and its generalization, the Fuzzy C-means (FCM) scheme, and hierarchical tree decompositions...

  • 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...
  • Challenges for computational vision: From random dots to the wagon wheel illusion
    Leon Glass
    Even understanding the way we perceive very simple images presents a major challenge for both neurophysiologists and computer scientists. In this talk I will discuss two visual effects. In one random dots are superimposed on themselves following a linear transformation. In the second, a rotating disk with radial spokes is viewed under stroboscopic illumination, where the f...
  • A three-dimensional computational model of necrotizing enterocolitis
    Jared Barber
    Necrotizing enterocolitis is a severe inflammatory disease in premature infants that is characterized by wounds in the intestinal wall. The ongoing dynamics of the disease depend upon a complex interplay between the immune system, intestinal bacteria, and intestinal epithelium. We have developed a three-dimensional computational model that examines this complex interplay a...
  • Steady-state invariant genetics: probing the role of morphogen gradient dynamics in developmental patterning
    Marcos Nahmad
    The specification of cell identities during development is orchestrated by signaling molecules named morphogens that establish spatial patterns of gene expression within a field of cells. In the classical view, the interpretation of morphogen gradients depends on the equilibrium morphogen concentrations, but the dynamics of gradient formation are generally ignored. The pro...
  • Computational explorations of cellular blebbing
    Wanda Strychalski
    Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused on cells that use blebbing for migrating through three dimensional fibrous matrices. In particular, metastatic cancer cells have been shown to use ble...
  • Phylogenetic tree models: An algebraic view
    Elizabeth Allman
    Phylogenetics is the branch of biology concerned with inferring evolutionary relationships between currently extant species. For instance, are humans more closely related to chimpanzees or to gorillas on an evolutionary tree? A typical phylogenetic analysis from molecular data might consist of sampling gene sequences from a number of species, aligning them, and performing ...
  • Novel Patterns and Dopamine Modulation in a Model of Working Memory
    Robert McDougal, Robert McDougal
    Working memory is a process for the short-term storage and manipulation of information necessary for complex cognitive tasks. During the performance of working memory tasks, the prefrontal cortex (PFC) exhibits sustained persistent activity and is believed to play a key role in the process. Experiments have demonstrated that working memory performance is modulated by dopam...
  • Novel Patterns and Dopamine Modulation in a Model of Working Memory
    Robert McDougal, Robert McDougal
    Working memory is a process for the short-term storage and manipulation of information necessary for complex cognitive tasks. During the performance of working memory tasks, the prefrontal cortex (PFC) exhibits sustained persistent activity and is believed to play a key role in the process. Experiments have demonstrated that working memory performance is modulated by dopam...
  • A stochastic multi-scale model of fibrinolysis
    Brittany Bannish
    The degradation of blood clots is a tightly regulated process. If the mesh of fibrin fibers securing the clot degrades too slowly, thrombi can form, leading to heart attack or stroke. If the fibrin degrades too quickly, excessive bleeding may occur. We study fibrinolysis (the degradation of fibrin by the main fibrinolytic enzyme, plasmin) using a multi-scale mathematical m...
  • A New Route to Periodic Oscillations in the Dynamics of Malaria Transmission
    Calistus Ngonghala
    A a new SIS model for malaria that incorporates mosquito demography is developed and studied. This model differs from standard SIS models in that the mosquito population involved in disease transmission (adult female mosquitoes questing for human blood) are identified and accounted for. The main focus of this model is disease control. In the presence of the disease, we ide...
  • A game theory approach to infectious disease managemant policy through individual and government investments
    Jing Li
    Government investment in public health management can elicit strong responses from individuals within communities. These responses can reduce and even reverse the expected benefits of the policies. Therefore, projections of individual responses to policy can be important ingredients into policy design. Yet our foresight of individual responses to public health investment r...
  • Models for Semelparity: Dynamics and Evolution
    Jim Cushing
    Discrete time matrix models for the dynamics of structured populations provide one way to study the dynamic consequences of different life history strategies. One fundamental strategy is semelparity. Mathematically, semelparity can be associated with a high co-dimensional bifurcation at R0 = 1 which results in a dynamic dichotomy between persistence equilibrium states (lyi...
  • An eigenvalue optimization problem in Mathematical Ecology
    Alan Lindsay
    Determining whether a habitat with fragmented or concentrated resources is a benefit or hindrance to a species' well-being is a natural question to ask in Ecology. Such fragmentation may occur naturally or as a consequence of human activities related to development or conservation. In a certain mathematical formulation of this problem, one is led to study an indefinit...
  • Asymptotic growth rates underestimate the transient response of a tropical plant population to harvest
    Orou Gaoue
    Over the past two decades, modeling the ecological impacts of harvesting wild plants, as source of food and medicine, has used stationary population growth rate as the metric to measure effects of harvest. In this talk, I show that using asymptotic rather than the transient growth rates may underestimate the effect of harvest and of other disturbances. The transient growth...
  • Exploring the dynamics of CRISPRs: How much can a bacterium remember about viruses that infected it?
    Lauren Childs
    A novel bacterial defense system against invading viruses, known as Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), has recently been described. Unlike other bacterial defense systems, CRISPRs, are virus-specific and heritable, producing a form of adaptive immune memory. Specific bacterial DNA regions, CRISPR loci, incorporate on average 25 copies of un...
  • A stochastic framework for discrete models in systems biology
    David Murrugarra
    This talk will introduce a new modeling framework for gene regulatory networks that incorporates state dependent delays and that is able to capture the cell-to-cell variability. This framework will be presented in the context of finite dynamical systems, where each gene can take on a finite number of states, and where time is also a discrete variable. The state dependent d...
  • 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...