Individual-Based Modelling Techniques Organised By Alexander Anderson

Modelling pattern formation in interacting cell systems
with cellular automata

Andreas Deutsch
Technische Universitaet Dresden, Germany
deutsch@zhr.tudresden.de

Examples of interacting cell systems are life cycles of bacteria or social amoebae, embryonic tissue formation, wound healing or tumour growth and metastasis. Mathematical models of spatio-temporal pattern formation can offer insight into the principles of cooperativity in interacting cell systems which can not be explained at the single cell level.

Typical modelling attempts focus on a macroscopic perspective, i.e. the models describe the spatio-temporal dynamics of cell concentrations. A modelling alternative are cell-based models in which the fate of each individual cell can be tracked. Cellular automata are discrete dynamical systems and can be used as cell-based models. Here, we analyze pattern formation in cellular automaton models of actively moving and interacting discrete cells. Model applications are in particular bacterial pattern formation and avascular tumour growth.

Modelling Chick Limb Development

James Glazier
Indiana University, USA
glazier@indiana.edu

Coauthor(s): Mark Alber, George Hentschel, Stuart Newman, Gabor Forgacs and Jesus Izaguirre

We discuss a variety of approaches to modelling early stage development of mesenchymal condensation and chondrogenesis in the chick limb. Methods to be discussed incluse classical reaction diffusion modelling, cellular automaton modeling and the Extended (or Cellular) Potts Model.

Stochastic models of growth and reproduction for individual
organisms

Roger Nisbet
University of California, Santa Barbara, USA
nisbet@lifesci.ucsb.edu

Coauthor(s): Masami Fujiwara and Bruce E Kendal

One important feature of individual-based population models is the ability to take account of variability in the growth, reproduction and survival probability of individual organisms. Formulating stochastic models of organismal growth involves confronting the issue that for many animals, length increases monotonically, while weight may increase or decrease in response to changes in energy acquisition from food and expenditure for growth maintenance and reproduction. Modelling this situation requires dynamic energy budget (DEB) models that have explicit representation of energy reserves.

We review the predictions for growth, reproduction and survival, from DEB models with forcing functions that represent fluctuating food environments. For the DEB model of S.A.L.M. Kooijman, environmental stochasticity typically leads to enhanced growth and reduced reproduction. We present analytic approximations that capture many of the essential features of this variability in individual performance. These approximations can guide the formulation of statistical models that will be used to model fish growth in stressed environments. We speculate on the implications of our findings for the population size distributions of fish in California coastal wetlands.