Section: New Results

Fields of application

Bioenergy

Modelling of microalgae production

Participants : Olivier Bernard, Antoine Sciandra, Frédéric Grognard, Philipp Hartmann, Rafael Muñoz-Tamayo, Ghjuvan Grimaud, David Demory, Frédéric Chazalon, Hubert Bonnefond, Jean-Philippe Steyer, Francis Mairet.

Experimental developments

Experiments have been carried out to study the effects of nitrogen limitation on the lipid production in microalgae and support model development. These experiments have been carried out in the Lagrangian simulator, under constant or periodic light and temperature, varying the total amount of light dose in the day. The response in terms of storage carbon (triglycerides and carbohydrates) has been observed.

Other experiments were carried out to reproduce the light percept by a cell in a raceway pond [74] , that is a large-scale raceway-track shaped open-air photobioreactor with circulating medium. An electronic platform was developed to reproduce the flashing light which, from the hydrodynamical studies, is likely to happen in a raceway at the cell scale. The experiments show that the microalgae adapt their pigments to the average light that they have received.

The effect in the cell cycle of both the light periodic signal and a nitrogen limitation were studied. The strong interactions of the interactions between the different phases of the cell cycle through checkpoints was highlighted [104] .

Finally, we have tested the effect of cement flue gas on microalgae growth and demonstrated that this CO${}_2$ source can be used to feed microalgal industrial cultures [33] .

These works have been carried out in collaboration with A. Talec, S. Rabouille, E. Pruvost and C. Combe (CNRS/UPMC -Océanographic Laboratory of Villefranchesur-Mer).

In collaboration with the IFREMER-PBA team (Nantes) we contributed to a study (within the Symbiose project) of the possible associations between microalgae and bacteria to enhance overall productivity [27] .

Metabolism of carbon storage and lipid production

A macroscopic model for lipid production by oleaginous microalgae [10] has been previously proposed. This model describes the accumulation of neutral lipids (which can be turned into biofuel), carbohydrates and structural carbon. We now start to progressively dig deeper in the metabolism, with the objective to better predict carbohydrate and lipid accumulation[37] , [64] .

Modeling the coupling between hydrodynamics and biology

In collaboration with the Inria ANGE team, a model coupling the hydrodynamics of the raceway (based on multilayer Saint Venant system) with microalgae growth was developed [86] . This model is supported by the work of ANGE aiming at reproducing the hydrodynamics of the raceway, with a specific attention to the effect of the paddle wheel on the fluid.

Modeling the photosynthesis response to fast fluctuating light

The impact of the hydrodynamics on the light percept by a single cell was studied thanks to fluid dynamics simulations of a raceway pond [26] . The light signals that a cell experiences at the Lagrangian scale, depending on the fluid velocity, were then estimated. A Droop-Han model was used to assess the impact of light fluctuation on photosynthesis. A new model accounting for photoacclimation was also proposed [46] . Single cell trajectories were simulated by this tool, and the effect on photosynthesis efficiency was assessed using models of photosynthesis [94] . These results were compared to experimental measurements where the high frequency light was reproduced [74] .

Modeling a microalgae production process

The integration of different models developed in the group [81] , [101] , [10] was performed to represent the dynamics of microalgae growth and lipid production in raceway systems, on the basis of the dynamical model developed to describe microalgal growth in a photobioreactor under light and nitrogen limitations. The strength of this model is that it takes into account the strong interactions between the biological phenomena (effects of light and nitrogen on growth, photoacclimation ...), temperature effect [85] ,[31] and the radiative transfer in the culture (light attenuation due to the microalgae).

Using these approaches, we have developed a model which predicts lipid production in raceway systems under varying light, nutrients and temperature [30] . This model is used to predict lipid production in the perspective of large scale biofuel production.

Finally, we provide guidelines for the design of experiments with high informative content that allows an accurate parameter estimation of this model, concerning the effect of temperature and light on microalgae growth. The optimal experiment design problem was solved as an optimal control problem. E-optimal experiments were obtained by using two discretization approaches namely sequential and simultaneous. Simulation results showed the relevance of determining optimal experimental inputs for achieving an accurate parameter estimation [50] .

Nitrogen fixation by nitrogenotrophs

The fixation of nitrogen by Croccosphera watsonii was represented with a macro metabolic model [44] . The main fluxes of carbon and nitrogen are represented in the cell. The accumulation of starch during the day to fuel the nitrogenase working in the absence of oxygen during the night was the key process to explain the nitrogen fixation. The strong influence of the cell cycle was also included in the model. Finally, the model was calibrated and validated with the data of 3 experiments carried out with different duration of the light period and daily dose. The model succeded to efficiently reproduce the experimental data.

This work is done in collaboration with Sophie Rabouille (CNRS-Océanographic Laboratory of Villefranche-sur-Mer).

Including phytoplankton photoadaptation into biogeochemical models

The complexity of the marine ecosystem models and the representation of biological processes, such as photoadaptation, is very challenging to tackle so that their representation remains an open question. We compared several marine ecosystem models with increasing complexity in the phytoplankton physiology representation in order to assess the consequences of the complexity of photoadaptation models in biogeochemical model predictions. Three models of increasing complexity were considered, and the models were calibrated to reproduce ocean data acquired at the Bermuda Atlantic Time-series Study (BATS) from in situ JGOFS (Joint Global Ocean Flux Study) data. It turns out that the more complex models are trickier to calibrate and that intermediate complexity models, with an adapted calibration procedure, have a better prediction capability [15] .

This work is done in collaboration with Sakina Ayata (UPMC-Océanographic Laboratory of Villefranche-sur-Mer).

Control and Optimization of microalgae production

On-line monitoring

Interval observers give an interval estimation of the state variables, provided that intervals for the unknown quantities (initial conditions, parameters, inputs) are known [7] . Several developments were carried out in this direction to improve the design and performances of interval observers. The approach has been applied to estimation of the microalgae growth and lipid production within a production process [28] .

Optimization of the bioenergy production systems

Based on simple microalgae models, analytical optimization strategies were proposed. We first focused on the optimal operating conditions for the biomass productivity under day/night cycles using Pontryiagin's maximum principle (assuming a periodic working mode) [25] .

On the other hand, we assessed strategies for optimal operation in continuous mode using the detailed model for raceways [49] , [30] . Two strategies were developed. The first one resides in solving numerically an optimal control problem in which the input flow rate of the raceway is calculated such that the productivity in microalgae biomass is maximized on a finite time horizon. In the second strategy, we aimed at translating the optimization problem into a regulation problem. We proposed a simple operational criterion that when integrated in a strategy of closed-loop control allows to attain biomass productivities very near to the maximal productivities obtained with the optimal control. We demonstrated that the practical advantages for real implementation makes our proposed controller a suitable control strategy for optimizing microalgae production in raceways.

We also propose a nonlinear adaptive controller for light-limited microalgae culture, which regulates the light absorption factor (defined by the ratio between the incident light and the light at the bottom of the reactor). We show by numerical simulation that this adaptive controller can be used to obtain near optimal productivity under day-night cycles [47] .

Interactions between species

Large scale culture of microalgae for bioenergy involves a huge biodiversity (different mutants, invasion, growth-promoting bacteria [96] ...). Control of such system requires to consider the interactions between the different species.

In the framework of the ANR Facteur 4 project, we propose to drive this competition exploring different strategies in order to select species of interest.

We have proposed an adaptive controller which regulates the light at the bottom of the reactor [48] . When applied for a culture with $n$ species, the control law allows the selection of the strain with the maximum growth rate for a given range of light intensity. This is of particular interest for optimizing biomass production as species adapted to high light levels (with low photoinhibition) can be selected.

Other strategies (e.g. periodic temperature stress) are now under investigation through simulations (in order to design selection experiments that will be performed at LOV) and model analysis.

Finally, in a more theoretical framework, we studied how to select as fast as possible a given species in a chemostat with two species at the initial instant. Using the Pontryagin maximum principle, we have shown that the optimal strategy is to maintain the substrate concentration to the value maximizing the difference between the growth rates of two species [66] .

Design of ecologically friendly plant production systems

Controlling plant pests

Participants : Frédéric Grognard, Ludovic Mailleret, Suzanne Touzeau, Mickaël Teixeira-Alves, Nicolas Bajeux.

Optimization of biological control agent introductions

The question of how many and how frequently natural enemies should be introduced into crops to most efficiently fight a pest species is an important issue of integrated pest management. The topic of natural enemies introductions optimization has been investigated for several years [9] [105] , unveiling the crucial influence of within-predator density dependent processes. Because contrarily to predatory biocontrol agents, parasitoids may be more prone to exhibit positive density dependent dynamics rather than negative ones, the current modeling effort concentrates on studying the impact of positive predator-predator interactions on the optimal introduction strategies [72] . Connected experimental research is also being pursued in the laboratory on trichogramma spp. which tends to show positive density dependence because of demographic stochasticity [35] , and the PhD thesis of Thibaut Morel Journel (UMR ISA) has just started on this topic. Non-impulsive positive feedback control of predator-prey systems in that framework was also addressed in [45] .

Food source diversity and classical biological control efficiency using generalist natural enemies

Because generalist biocontrol agents can feed on different food sources like, e.g. a given pest and pollen, they are capable of surviving pest absence within crops and, when supplied with different food types, generalist biocontrol agents are expected to thrive. However, feeding on different food sources means that a given individual cannot feed on each food source at the same moment, which thus potentially reduces the overall predation pressure imposed by the natural enemy population. We exhibited conditions under which the predator distraction effects can dominate the demographic response of the predator populations, potentially disrupting pest control [12] . Such results were at the center of Mickaël Teixeira Alves's PhD thesis.

Plant compensation, pest control and plant-pest dynamics

Introducing a plant compartment into our models, we first focused on plant-insect interactions and showed how the level and timing of the pest invasion and pests control interventions could have important effects on the plant's growth pattern and its final biomass. We then modelled plant compensation, which is the process by which some plants respond positively to recover from the effects of pest injury. We have shown that depending on plants and pests characteristics, as well as the level of pest attack, plant overcompensation may or may not happen [97] .

This work is part of the PhD thesis of Audrey Lebon (Cirad), and done in collaboration with Yves Dumont (Cirad).

Controlling plant pathogens

Participants : Frédéric Grognard, Ludovic Mailleret, Suzanne Touzeau, Elsa Rousseau.

Sustainable management of plant resistance

Because in addition to being eaten, plants can also get sick, we studied other forms of biological control dedicated to fight plant pathogens. One such method is the introduction of plant strains that are resistant to one pathogen. This often leads to the appearance of virulent pathogenic strains that are capable of infecting the resistant plants. It is therefore necessary to develop ways of introducing such resistance into crop production without jeopardizing its future efficiency. Considering plant viruses, we computed the proportion of resistant plants that should be cropped together with the non-resistant ones in a seasonal model, in order to optimize the resistance for production or patrimonial objectives [53] . The study of factors influencing resistance breakdown from the within-plant to the landscape level is the topic of Elsa Rousseau's PhD thesis, with emphasis both on experimental and modelling approaches. Experiments have been held in Avignon to determine the respective impacts of selection and genetic drift on resistance breakdown.

This work is done in collaboration with Frédéric Fabre and Benoit Moury (INRA Avignon).

Eco-evolutionary dynamics of plant pathogens in seasonal environments

Understanding better pathogen evolution also requires to understand how closely related plant parasites may coexist. Indeed, such coexistence is widespread and is hardly explained through resource specialization. We showed that, in agricultural systems in temperate environments, the seasonal character of agrosystems can induce complex plant-pathogens dynamics [98] and is an important force promoting evolutionary diversification of plant pathogens [93] . Plant parasites reproduction mode may also strongly interact with seasonality. In this context, we investigated the influence of cyclical parthenogenesis, i.e. the alternation of sexual and asexual reproduction phases, on the eco-evolutionary dynamics of plant parasites [59] , [60] , [21] .

This work is part of the PhD thesis of Magda Castel (Agrocampus Ouest) and is done in collaboration with Frédéric Hamelin (Agrocampus Ouest).

Biological depollution

Coupling microalgae to anaerobic digestion

Participants : Olivier Bernard, Antoine Sciandra, Jean-Philippe Steyer, Frédéric Grognard, Philipp Hartmann, Francis Mairet.

The coupling between a microalgal pond and an anaerobic digester is a promising alternative for sustainable energy production and wastewater treatment by transforming carbon dioxide into methane using light energy. The ANR Symbiose project is aiming at evaluating the potential of this process [108] , [107] .

In a first stage, we developed models for anaerobic digestion of microalgae. Two approaches were used: first, a dynamic model has been developed trying to keep a low level of complexity so that it can be mathematically tractable for optimisation [100] . Considering three main reactions, this model fits adequately the experimental data of an anaerobic digester fed with Chlorella vulgaris (data from INRA LBE). On the other hand, we have tested the ability of ADM1 [109] (a reference model which considers 19 biochemical reactions) to represent the same dataset. This model, after modification of the hydrolysis step [102] has then been used to evaluate process performances (methane yield, productivity...) and stability though numerical simulations.

Life Cycle Assessment

Participants : Olivier Bernard, Jean-Philippe Steyer.

This work is the result of a collaboration with Laurent Lardon and Arnaud Helias of INRA-LBE through the co-supervision of Pierre Collet's PhD thesis [88] .

An analysis of the potential environmental impacts of biodiesel production from microalgae has been carried out using the life cycle assessment (LCA) methodology [95] . This study has allowed to identify the obstacles and limitations which should receive specific research efforts to make this process environmentally sustainable.

This study has been updated and the effects of technological improvements (leading to higher productivities) have been compared to the source of electricity. It turns out that the overall environmental balance can much more easily be improved when renewable electricty is produced on the plant [91] , [90] . As a consequence, a new paradigm to transform solar energy (in the large) into transportation biofuel is proposed, including a simultaneous energy production stage. This motivated the design of the purple sun ANR-project.

These studies have allowed to identify the obstacles and limitations which should receive specific research efforts to make this process environmentally sustainable [65] .

A LCA has been carried out to assess the environmental impact of methane production by coupling microalgae and anaerobic digestion. The study highlights the limitation derived by the low biodegradability of the considered microalgae [89] which induces a large digester design and thus more energy to mix and heat it.

These works have been carried out in collaboration with E. Latrille and B. Sialve (INRA - Laboratory of Environmental Biotechnology, Narbonne).

Models of ecosystems

Optimality/games in population dynamics

Participants : Frédéric Grognard, Ludovic Mailleret, Pierre Bernhard.

Adaptive behavior in seasonal consumer-resource dynamics

In this work we studied the evolution of a consumer-resource (or predator-prey) system with seasonal character of the dynamics. We specified two main parts of the process. First, we considered the system during one season with a fixed length: the prey lay eggs continuously and the predators lay eggs or hunt the prey (choose their behavior) according to the solution of an optimal control problem [76] . We then showed that, in most situations, mutants can take advantage of their low frequency and fare better than the residents. Over the course of a large number of seasons, the mutants replace the residents, only to find themselves applying the original resident behavior [61] .

Optimal foraging and residence times variations

Charnov's marginal value theorem (MVT) [87] is a central tenet of ecological theory. In fragmented environments, the MVT connects the quality and distribution of patches to the optimal time an individual should spend on any patch, and thus the rate of movement in the habitat. Unfortunately, it does not offer explicit predictions regarding how changing habitat quality would affect residence times. In this work, we answer that question in a very general setting, for habitats with homogeneous or heterogeneous patches and with general fitness functions. We then particularize it to the resource consumption framework and indicate how the residence times variations relate to the curvatures of the functional responses,[20] .

This last work is done in collaboration with Vincent Calcagno and Eric Wajnberg (INRA Sophia Antipolis)

The handicap paradox

We have investigated the “handicap paradox” of sexual selection, and more specifically revisited Grafen's mathematical models of Zahavi's “handicap principle”. The paradox is that in many species, male secondary sexual characters that clearly attract the females are so developed as to be a handicap to the male's viability, and therefore should be counter-selected by evolution. Zahavi's explanation, made mathematical by Grafen, is that if this secondary sexual character is a signal to the female of the male's quality that she cannot observe otherwise, if this signal were costless, it could be cheated, a low quality male being induced to mimic the signal of a high quality one. We have cast this problem into a signaling game, using the bayesian equilibrium of game theory. This easily shows that indeed, under mild conditions, at equilibrium the signal should be “costly”. We have developed several models inspired by Grafen, and to a lesser extent Getty, with explicit solutions, and explained why an undesirable feature appeared in Grafen's model (as well as in one of ours) and proposed a model free of this artifact [19] .