February 3-7 > Confirmed Invited speakers

Lectures by:

• Vincent Calvez (ICJ, Universite de Lyon 1, FRANCE)
  • Title: Propagation phenomena in kinetic equations (chemotactic waves and transport-reaction waves).
    
  • Abstract: I will present old and new results about wave propagation in partial differential equations for biology. I will focus on kinetic equations with application to chemotactic waves of bacteria, and more generally reaction-transport equations describing persistent motion of individuals at the mesoscopic scale. Further applications and perspectives will be given.
    
• Marie Doumic (MAMBA, Inria Paris, FRANCE)
  • Title: Inverse problems in structured population dynamics: combining deterministic and stochastic approaches
  • Abstract: The aim of this course is an introduction to the inverse problem consisting in estimating the division features of the population and selecting the most convenient "structuring" variable, i.e. the variable which best characterizes the division. We call "division features" on the one hand the division rate, rate at which individuals of the population divide, and on the other hand the so-called "division kernel", which characterizes how from a given value for the parent the structuring variable is distributed in offspring. We shall first give a quick overview of the models and their application domains, detailing the correspondence between the population view and the "microscopic" individual based models (modelled by stochastic branching processes). We shall then focus on the inverse problem consisting in the estimation of the division rate. This is a key step in the calibration and selection of the models, and also a bridge between the (deterministic) population and the (stochastic) individual viewpoints. We apply these methods to the bacterial division cycle in three types of models: age-structured (the renewal equation) as a toy model, size-structured and the recent "incremental" model. A more ill-posed problem is the joint estimation of the fragmentation rate and kernel in a pure fragmentation framework; this will be detailed first theoretically, and then applied to protein fibrils fragmentation, a key feature of many neurodegenerative diseases. All this leads us to the question of model selection - which can be formulated as: how to be certain of what is the real "structuring" variable? This a very natural question since structured population models are often purely empirical, so that assessing their validity on the basis of quantitative results represents an important challenge of mathematical biology.
• Benoı̂te de Saporta (IMAG, Université de Montpellier, FRANCE)
  
  • Title: Stochastic modelling for population dynamics: simulation and inference
  • Abstract: The aim of this course is to present some examples of stochastic models suitable for population dynamics.
    The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a a slow time-scale corresponding to the jumps. I'll present different biological systems that can be modelled by PDMPs, explain how they can be simulated.
    The second part will focus on random models for cell division when the whole branching population is taken into account. I'll present two data sets from biological experiments trying to determine whether cell division is symmetric or not. I'll explain how statistic tools can help answer this question.
    
• Sebastian Schreiber (DEEP, UC Davis, USA)
  • Title: Stochastic Population Dynamics: Persistence, Extinction, and Quasi- stationarity
  • Abstract: A long standing question in biology is "what are the minimal conditions to ensure the long-term persistence of a population, or to ensure the long-term coexistence of interacting species?" The answers to this question are essential for identifying mechanisms that maintain biodiversity. Mathematical models play an important role in identifying potential mechanisms and, when coupled with data, can determine whether or not a given mechanism is operating in a specific population or community. For over a century, nonlinear difference and differential equations have been used to identify mechanisms for population persistence and species coexistence. These models, however, fail to account for intrinsic and extrinsic random fluctuations experienced by all populations. In this mini-tutorial, I will give an overview on models for accounting for both forms of stochasticity, analytical and numerical methods for studying the dynamics of these models, and theoretical and numerical challenges for future research. The overview will focus on discrete-time models: (i) random maps on compact metric spaces to account for extrinsic noise due environmental fluctuations, and (ii) Markov chains on countable state spaces to account for intrinsic noise due to populations consisting of a finite number of individuals. The models, methods, and challenges will be illustrated with data-based models of checkerspot butterflies, California annual plant communities, chaotic beetles, and more.