Report on the mini-symposium on Nonlinear Population Dynamics

This mini-symposium was part of the conference Theory and Mathematics in Biology and Medicine 1999 Vrije Universiteit Amsterdam, The Netherlands, June 29 - July 3, 1999.

This mini-symposium was announced in the continuation research proposal for NLS Population dynamics and epidemics financially supported by the NWO priority program `Nonlinear Systems, Population dynamics, including epidemiology'. Sessions organizers were Martin Boer (VU now CPRO, Wageningen) and Markus. Kirkilonis (CWI, UU and now Heidelberg Germany). The reseach projects of Martin ( Ph.D. student Dept. of Theoretical Biology VU) and Markus (post-doc with the CWI) were supported by the NLS priority program. Martin Boer is finishing his Ph.D. thesis entitled: The dynamics of tri-trophic food chains. Markus was involved in the development of theory and numerical bifurcation analysis of models of physiologically structured populations. To that end he wrote the computer package called BASE, a modularly designed tool for 'Bifurcation Analysis of Structured Equations'.

Two invited speakers gave a rather broad introduction into the scientific field of nonlinear population dynamics. In parallel sessions oral contributions were presented. Furthermore there was a well attended poster-session.

Abstracts of the contributions of the invited speakers:

David Rand, University of Warwick, Mathematics Institute, Coventry CV4 7AL UK
e-mail: dar@maths.warwick.ac.uk

In this talk I propose to discuss population dynamics with a particular emphasis on recent trends and future perspectives. In the first part I will concentrate on ecology, evolutionary theory and epidemiology and my discussion will include individual-based systems, spatial ecologies, populations of structured individuals and invasion. In the second part I want to consider some examples from microbial and molecular biology such as viral systems, T-cell receptors and cell signalling. On the one hand I want to demonstrate that population dynamics is crucial to an understanding of many biological phenomena of real current interest and on the other hand I want to draw attention to the way in which new mathematical techniques can aid understanding of population dynamics.

Hal Smith, Arizona State University, Mathematics, Tempe, AZ 85287, USA
e-mail: halsmith@asu.edu Coauthor(s): Mary Ballyk, Don Jones

A mathematical model for microbial growth and competition for limiting nutrient and for limited wall attachment sites in a plug flow reactor will be presented. The model is an adaptation of a model, due to Rolf Freter for cstr, to examine the effect of wall attachment of bacteria in the mammalian gut on the stability of the natural microflora of the gut to invasion. We will present both analytical and numerical results which bear on such questions as 'for what gut residence times and cell doubling times can the bacteria persist?', 'how can many strains coexist in the gut?' 'when does a potential invader have a competitive edge over a resident strain?'.

All abstracts are still available on: http://toranaga.bio.uva.nl/~aroos/.
The oral presentations:

• Nelly Noykova, Parameter and State Sensitivity in a Five Order Model of Anaerobic Digestion in Continuous Stirred Bioreactor
• Tatiana Sazykina, An ecosystem model with the optimal feeding behavior of a predator - a pseudoequilibrium regime
• Nour Eddine Elhoussif, A deterministic size structured population model with reproduction at a specified size
• Julien Arino, Size structured models for the chemostat; comparison with experiments Vladas Skakauskas On age-sex-space-structured population dynamics model with random mating and females' pregnancy
• Idriss El Akili, Modelisation of the spatio-temporal dynamics of immune anti-tumor cytotoxic reactions
• Mark Pernarowski, Controllability of excitable cells
• Tanya Kostova, Non-periodic Oscillations in Two-Patch Systems
• Maria-Josefina Hernandez, Bifurcations and Catastrophes in Conditional Outcomes of Population Interactions
• Suzanne Touzeau, Stability of a stage-structured population model with a generalized stock-recruitment function
• Linda Rass, Exploting model similarities to describe stochastic convergence results
• Serge Chernyshenko, Mathematical Modelling of Ecological Successions: Approach on the Base of M. Eigen's Hypercycle
• Valery Kirzhner, On finiteness of the equilibria set under selection in a system of multiallele loci
• Hartmut Schwetlick, Propagation of disturbances in multidimensional nonlinear transport models
• Yoh Iwasa, Pollen-Coupling of Forest Trees, Forming Synchronized and Periodic Reproduction out of Chaos
• Jean-Luc Gouzé, Global behaviour of periodically forced loop systems: example of a class of model for algal growth
• Manmohan Singh, Predator-Prey Models with Diffusion Based on Luckinbill's Experiment with Didinium and Paramecium
• Nico Stollenwerk Testing nonlinear stochastic models on empirical algae mass time series
• Bernard Cazelles, Intermittent rarity and On-Off intermittency in population dynamics
• Sergei V. Petrovskii, The Wave of Chaos: A New Mechanism of Pattern Formation in Spatio-Temporal Population Dynamics
• Mick Roberts, A simple parasite model with complicated dynamics

Poster contributions:

• Mohamed Benkherourou, From Mechanical Characterization of Fibrin Gels To Quantification of Endothelial Cell Traction Forces
• Faina Berezovskaya, `Travelling waves' and `pulsing patterns' in population models with autotaxis
• Carlos A. Braumann, Conditions for population steady-states in random environments
• Nikola Buric, Time-delay effects in a minimal model of the immune response
• Derik Castillo-Guajardo, Effect of stage-structure on stability of host-parasitoid interactions
• Michael Deakin, A Generalised Multistage Logistic Population Model
• Tiago Domingos, A General Approach to the Modelling of Trophic Chains
• Vasiliy Govorukhin, One Model of Active Migrations: Qualitative Investigation
• Michael Grinfeld, Modelling IGP and GLP in age-structured populations
• Fabrice Heiser, A Predator-Prey in a Heterogeneous Environment
• Barbara Hellriegel, Factors influencing the complex dynamics and variable composition of mixed hybridogenetic populations
• Adam Kleczkowski, Plants competition in a changing environment
• Ryusuke Kon, The Effect of Evolution to Host-Parasite Systems
• Abraham Korol, Complex Dynamics Manifested by a Multilocus Genetic System upon Cyclical Selection
• Nicholas Kositski, Self-control of Proliferation-diferentiation Proceses in Cell Population Dynamics
• Mayer Landau, Transition rules between various coexisting equilibrium states in a cardiac Non Pacemaker cel
• Pierre Magal, Evaluation of the eel flux during the migration for the reproduction
• Alexander B. Medvinsky, Fish school walks and plankton patchiness as a result of plankton- fish interactions
• Andrey Morgulis, Wave phenomena in the model of a spatially active population.
• Thorsten Mëller, Analysis of non-linear dynamical systems: estimating parameters and model selection
• Vikas Rai, On the Determinstic Description of Population Dynamics
• Akiko Satake, A Globally Coupled Map Model for Synchronized Reproduction in Beech Forests - Pollen-Coupling of Trees Creates Coherent Dynamics out of Chaos
• Pekka Vainiomäki, The Application of Ergodic Theory to Discrete Time Systems with Stochastic Perturbations
• Andrew White, Explaining the colour of power spectra in chaotic ecological models
• Sergio Furtado dos Reis, Dispersal on small spatial scales: Waves, neighborhoods of interaction and non-locality