Section: New Results

Applications

Modelling and control of Anaerobic Membrane BioReactors (AMBR)

Participants : Claude Lobry, Jérôme Harmand.

The advanced control of AMBR is a new problem since most plants are working under aerobic mode. However, using anaerobic systems present the advantages of allowing the valorization of the biogas produced. However, the main drawback of such processes is the membrane fouling phenomenon which is difficult to control. Models including a number of new variables, such as the Soluble Microbial Product (SMP) that are recognized to play an important role in the membrane fouling, are needed. Furthermore, the integration of models describing the biological phenomena together with the fouling of membranes must be developed. Such objectives are at the heart of the PhD thesis of Boumediene Benyahia and are realized within the framework of the TREASURE project (cf. Section 8.1.5 ).

Observers for investigating microbial ecology problems

Participants : Jérôme Harmand, Alain Rapaport.

One of the most important challenges in microbial ecology is to determine the ecological function of dominant microbial populations in their environment. In the framework of the PhD thesis of Maxime Dumont, we proposed a generic method coupling fingerprinting and mathematical tools to achieve the functional assigning of bacteria detected in microbial consortia (cf. [14] ). This approach was tested on a nitrification bioprocess where two functions carried out by two different communities could be clearly distinguished. The mathematical theory of observers of dynamical systems has been used to design a dynamic estimator of the active biomass concentration of each functional community from the available measurements on nitrifying performance. Then, the combination of phylotypes obtained by fingerprinting that best approximated the estimated trajectories of each functional biomass was selected through a random optimization method. By this way, a nitration or nitration function was assigned to each phylotype detected in the ecosystem by means of functional molecular fingerprints. The results obtained by this approach were successfully compared with the information obtained from 16S rDNA identification. This original approach can be used on any biosystem involving n successive cascading bioreactions performed by n communities.

Modelling and control of cascade biosystems to mimick batch wine making processes

Participants : Jérôme Harmand, Alain Rapaport, José Fernandez.

Wine making processes are operated in batch mode during which the physiological state of yeasts used for converting sugar into alcohol evolves. In particular, at the initial step the biological process is mainly the growth of biomass, while at the end of the batch (when there is almost no nitrogen nor sugar anymore), the main biological process is characterized by an activity without growth. In these different process stages, the yeasts are in very different physiological states. Because the process is operating in batch mode, it is difficult for biologists to study these different microbial states. Thus, a configuration of continuous reactors in series has been proposed to mimic the behavior of a batch process as a set of steady-state points along the reactor cascade. The steady state in each chemostat corresponds to a state at a given time (characterized by the progress of the reaction) in the batch process. In order to control the steady states to be mimicked, it is necessary to model this process and to develop an appropriate time-optimal control strategy in order to leave the possibility to the user to choose the interesting yeast physiological states to be studied. This work is part of the PhD thesis of José Fernandez in the framework of the CAFE European project (see Section 7.2 ).

Modelling and simulating terrestrial plant ecological dynamics

Participants : Fabien Campillo, Audrey Dubourg.

We propose individual-based models (IBMs) for prairial plant dynamics. We propose models of dynamics of a simplified grassland ecosystem, then develop simulation techniques for these models and finally establish their mathematical properties. The ecosystem is a community of individuals (ramets) linked by connections (stems). This ecosystem relies on resources (nitrates) and can store a portion of these resources. We propose different individual-based models coupled with continuous models for the available resources and the stored resources, in this case the individual is the ramet; or the available resources only, in this case the individual is the ramet or the rhizome [46] .

Modelling and inferring agricultural dynamics

Participants : Fabien Campillo, Angelo Raherinirina.

This work is supported by the AUF and is done in collaboration with the University of Fianarantsoa in Madagascar and with Dominique Hervé (IRD, Fianarantsoa, Madagascar).

To study the dynamics of agricultural plots on the edge of primary forest we use Markov chains models. The problem of identification of the transition matrix is ill-posed since the underlying dynamics is not at equilibrium and most states are transient, hence maximum likelihood approaches are not feasible. We adopt a Bayesian approach and work in collaboration with specialists of agricultural dynamics to limit the size of the parameter space.

Modelling for soil ecosystems

Participants : Ihab Haidar, Jérôme Harmand, Alain Rapaport.

In cooperation with the UMR Eco&Sols (Montpellier) and INRA Theix, we study the impact of a spatial structure in microbial activity. Several numerical models have already been developed for the geochemical transfers in soil. Most of them are based on a spatial discretization by elementary volumes, but are not well suited for biotic/abiotic interactions, because most of the time it is not possible to consider that the mobility of micro-organisms in each elementary volume is different from the one of their chemical nutrients. In the framework of Haidar's PhD thesis, we have begun to study theoretically the impact of diffusion among simple motifs of elementary volumes, considering each of these volumes as a chemostat. For the moment, the study has concerned motifs of two or three reactors at steady state.

Decision making tools for the management of natural resources

Participant : Alain Rapaport.

A small part of the activity of the team concerns the bio-economics of natural resources at the decision maker scale, with the help of control theoretic and optimization tools. We distinguish two kinds of natural resources:

• No or weak seasonality-dependency in the reproduction (fisheries, food crops, ...). Typically, the models are in continuous time. We have studied theoretically the benefit of the creation of protected areas, assuming that the reproduction rate is improved in absence of harvesting, in terms of viability analysis of the economics of the exploitation [22] ;

• Strong seasonality-dependency in the reproduction (forests, water tables, ...). The models are usually in discrete time. We have studied theoretically the benefit of an alternative use of the space allocated to the exploitation of resources with slow growth mature, in terms of discounted utility over a large time horizon [30] .