Section: Overall Objectives

Build, simulate and analyze new models of microbial ecosystems

We investigate different models of microbial ecosystems at different scales, that are related to various research questions for better understanding, predicting or piloting real plants.

Eight families of problems are covering our modelling activities:

1. study the mathematical properties (equilibriums, stability, limit cycles, bifurcation...) of macroscopic models that distinguish compartments of attached and free bacteria. We are looking for ecological conclusions in terms of coexistence of species.

2. study the mathematical properties of trajectories of a model that switches from a populational representation by differential equations to an individual-based model when the population falls below a given threshold. We expect from this study new insights on validity domains of macroscopic models and quantitative estimations of the variability about average trajectories.

3. build a framework for modelling the chemostat with stochastic processes at a macroscopic scale justified from hypotheses at the individual level. The classical “deterministic” chemostat is expected to be found as an average dynamics for large populations, but second order moments should provide relevant information about the variability about the deterministic approximation.

4. build and simulate IBMs (individual based models) of 1D biofilm and compare the spatial densities of biofilm and planktonic biomass with the numerical solutions of 1D PDE models.

   The output of this study is to propose and justify attachment/detachment terms in the PDE, that are crucial in the determination of the thickness of the biofilm, and that are usually chosen in an heuristic way.

5. compare detailed ecological models of a multi-species community at a fine scale with low-complexity models at a coarser scale, in the spirit of the neutral model. Within a stochastically varying environment (that is assumed to have different impacts on each species), the coarse model could describe in an effective way the interaction between species and environment as a stochastic variability. The goal is to interpret the parameters of the global model in terms of properties of the fine-scale model.

6. study chemostat-like models with multi-resources and nutrient recycling, within the objective of representing microbial activity in soil ecosystems. The goal is to understand the influence of the choice of hypotheses about the growth terms (dependency in terms of product or minimum functions of each resource) and the recycling terms (from the dead biomass or during the division process) on the qualitative behavior of the system and its performances at steady state.

7. investigate the properties of a network of interconnected chemostats and understand the role of the size of the nodes and the connectivity (with the help of the VITELBIO software, see Section 5.1 ).

8. couple numerical simulation of fluids dynamics in tanks with models of biotic/abiotic reactions. Then, we plan to compare the input/output behavior of these models with simple representations of networks of interconnected chemostats (see the previous point).