Section: New Results

Fields of application

Bioenergy

Modeling of microalgae production

Participants : Olivier Bernard, Antoine Sciandra, Frédéric Grognard, Philipp Hartmann, Rafael Muñoz-Tamayo, Ghjuvan Grimaud, Charlotte Combe, 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 [18] , [17] , [48] and support model development. These experiments have been carried out in the Lagrangian simulator (SEMPO), 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 [58] . 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 [24] .

This work is done in collaboration with Amélie Talec, Thomas Lacour, and Christophe Mocquet (CNRS-Océanographic Laboratory of Villefranche-sur-Mer).

Modeling the effect of temperature

The effect of temperature on microalgae has been represented by adapting the CTMI model developed for bacteria [115] . The proposed model [14] , [28] , was able to correctly represent the growth response to temperature for 15 different species. A procedure for model calibration and estimation of the parameter uncertainties was specially developed, allowing to gather experimental data from various sources. It was shown that different strains of the same species have a very similar response to temperature fluctuations. Moreover, for low light intensities, a simple model can represent both effects of light and temperature [14] .

Modeling light distribution within a photobioreactor

The light distribution within a photobioreactor was estimated thanks to a multi photon Monte-Carlo simulation. From measurements of absorption and scattering properties, it was thus possible to extrapolate and validate the light distribution within a photobioreactor or a raceway.

Modeling lipid accumulation

We have proposed a new model for lipid production by microalgae which describes the fate of the CO${}_2$ incorporated during photosynthesis [10] . This model describes the accumulation of neutral lipids (which can be turned into biofuel), carbohydrates and structural carbon. It has been calibrated and validated with experimental data. This model highlights and explains the phenomenon of hysteresis in lipid production which has been experimentally verified. It has been extended to account for light/dark cycles [96] .

Modeling a microalgae production process

The integration of different models developed in the group [72] , [96] , [10] ,[14] 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 [72] . 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 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 [109] , [110] . This model is used to predict lipid production in the perspective of large scale biofuel production.

Coupling growth of microalgae with hydrodynamics

Participants : Olivier Bernard, Antoine Sciandra, Philipp Hartmann, Charlotte Combe.

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 [13] . 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 [37] [92] . 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 [93] .

Optimization of microalgae production

Participants : Olivier Bernard, Antoine Sciandra, Frédéric Grognard, Rafael Muñoz-Tamayo.

Numerical optimization

Using the detailed model for raceway systems, we assessed strategies for optimal operation in continuous mode [109] . 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 reach biomass productivities very near to the 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.

Analytical optimization

Optimization strategies were based on simple microalgae models : first, biomass production has been optimized in a constant light environment [104] , yielding results emphasizing the importance of the optical depth of the reactor. In a second work, we focused on the optimal operating conditions for the biomass productivity under day/night cycles using Pontryiagin's maximum principle (assuming a periodic working mode) [61] [90] .

CO${}_2$ fixation by microalgae

Participants : Olivier Bernard, Antoine Sciandra, Ghjuvan Grimaud.

Experimental work

We have run experiments to observe the response of a population of microalgal cells to various periodic light/dark or nitrate signals. The measurements show the synchronicity of the cells for some conditions. These experiments support the hypothesis that uptake of nitrogen stops during cell division [24] .

Modeling cell cycle

On this basis, we have developed a structured model representing the development of microalgal cells through three main phases of their cell cycle: G1, G2 and M. The model is made of three interdependent Droop models [107] . The model was validated through extensive comparison with experimental results in both condition of periodic light forcing and nitrogen limitation. The model turns out to accurately reproduce the experimental observations [107] .

Calcification of coccolithophorids

The effect of CO${}_2$ partial pressure increase on photosynthesis and calcification of the calcareous microalgae Emiliania huxleyi have been experimentally observed. It results in an increase of the coccolith size together with a decrease in the calcification rate [25] .

Three models accounting for the possible coupling between photosynthesis and calcification [75] were included in an ocean model; they account for settling and predation by grazers, and a bloom of coccolithophorids was simulated [76] , [77] .

Nitrogen fixation by nitrogenotrophs

The fixation of nitrogen by Croccosphera watsonii was represented with a macro metabolic model [60] [89] . 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, remain 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 [12] , [43] , [42] .

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

Design of ecologically friendly plant production systems

Controlling plant pests

Participants : Frédéric Grognard, Ludovic Mailleret, 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] [111] . It had allowed to unveil the crucial influence of within-predator density dependent processes, and especially negative density dependence. In particular, we concluded that pest control is more efficiently achieved through the frequent introduction of small populations of natural enemies as compared to larger and rarer ones. 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 [55] .

Connected experimental research is also being pursued in the laboratory on trichogramma spp. which tends to show positive density dependence because of demographic stochasticity [32] , and the PhD thesis of Thibaut Morel Journel (UMR ISA) has just started on this topic.

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 [118] . From the biological control point of view, this makes it possible to sustain natural enemies populations able to fight pests at the onset of pest attacks. Moreover, when supplied with different food types, generalists organisms are expected to thrive. Alternative prey, banker plants or more generally habitat enhancement based biological control strategies are thus becoming popular IPM (Integrated Pest Management) methods [112] . Although it has clear advantages, the simultaneous presence of various food sources also has important drawbacks: feeding on different food sources means that a given individual cannot feed on each food source at the same moment. This distraction effect thus potentially reduces the overall predation pressure imposed by the natural enemy population, and the interaction between the demographic response of the predator population and individual behavior is complex. To investigate such questions, we developed and analyzed behavioral-demographic population models taking into account the negative density dependent character of most generalist biocontrol agents. We found out that predator distraction effects can dominate the demographic response of the predator populations, potentially disrupting pest control [120] . An additional conclusion of our study, is that higher predator densities can actually bring about lesser pest suppression. Such results question current biological control practices, and show that, counter-intuitively, recording a lot of predators within fields does not ensure efficient pest control.

Plant compensation, pest control and plant-pest dynamics

Plant compensation is the process by which plants respond positively to recover from the effects of pest injury on plant growth. It is a common phenomenon, which has been repeatedly reported in various plant taxa during the last thirty years. Of special interest is the overcompensation phenomenon: consecutively to a pest attack, a plant may reach a higher biomass or have a better fitness compared to the no-pest-attack situation [65] . Although this phenomenon has mainly been documented in wild plants [65] it has also been observed on agricultural plants [121] , [113] . To understand better this plant-herbivore interaction and to assess the efficacy of different pest control strategies we built a plant-pest model of plant compensatory growth. We have shown that depending on plants and pests characteristics, plant overcompensation may or may not happen. Moreover, because the model undergoes a backward bifurcation, it is shown that plant overcompensation is also dependent on the level of pest attacks and does not necessarily show up even when the plant-pest couple do have the potential to produce overcompensation [38] .

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, Elsa Rousseau.

Sustainable management of plant resistance

The introduction of plant strains that are resistant to one pathogen often leads to the appearance of virulent pathogenic strains that are capable of infecting the resistant plants. The resistance strain then becomes useless. It is therefore necessary to develop ways of introducing such resistance into crop production without jeopardizing its future efficiency. We did so by choosing the proportion of resistant plants that are mixed with the non-resistant ones. We studied a vector borne pathogen in a seasonal environment, with healthy crop being planted at the beginning of each season and cropped at its end, the pathogen surviving in the environment during the 'winter'. Two strategies have been proposed, one that aims at minimizing the cumulated damage over a 15 years horizon and one that aims at preventing the virulent strain outbreak. We showed that pathogen's fitness cost associated with resistance breakdown was one of the main factors governing damage reduction at the landscape scale, although the optimal resistance deployment also strongly relied on epidemic characteristics and landscape coonnectivity [16] , [51] . The capacity for a virulent virus to establish itself in such an environment, as well as the evolution of the virus characteristics have been studied [59] .

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

Eco-evolutionary dynamics of plant pathogens in seasonal environments

The coexistence of closely related plant parasites is widespread. Yet, understanding the ecological determinants of evolutionary divergence in plant parasites remains an issue. Niche differentiation through resource specialization has been widely researched, but it hardly explains the coexistence of parasites exploiting the same host plant. Most agricultural systems in temperate environments are characterized by the cyclical presence and absence of the crop, due to cropping practices such as harvest and planting. The seasonal character of agrosystems can induce complex plant-pathogens dynamics [19] and is an important force promoting evolutionary diversification of plant pathogens [91] . Plant parasites reproduction mode may 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 [80] . By means of a theoretical approach, we show that an obligate sexual event prior to overseasoning promotes evolutionary divergence in terms of investment into asexual reproduction in plant parasites. Yet, polymorphism may be transient; namely, morphs mostly investing into sexual reproduction may eventually exclude morphs mostly investing into asexual reproduction. Our findings nicely echo with recent population genetics results on Leptosphaeria maculans, the causal agent of the blackleg disease of canola, reporting differential investments into sexual and asexual reproduction both at the global and continental scales.

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 - Anaerobic digestion

Coupling microalgae to anaerobic digestion

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

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 [117] , [116] .

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 optimization [97] , [79] , [20] . 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 [119] (a reference model which considers 19 biochemical reactions) to represent the same dataset. This model, after modification of the hydrolysis step [99] , [100] , [98] has then been used to evaluate process performances (methane yield, productivity...) and stability though numerical simulations.

Life Cycle Assessment of microalgae production

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 [83] .

An analysis of the potential environmental impacts of biodiesel production from microalgae has been carried out using the life cycle assessment (LCA) methodology [94] . 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 [86] , [85] . As a consequence, a new paradigm to transform solar energy (in the large) into transportation biofuel is proposed, including a simultaneous energy production stage.

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 [84] which induces a large digester design and thus more energy to mix and heat it.

Models of ecosystems

Optimality in consumer-resource 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 [66] . We then examined how (resident) predators adopting this optimal behavior would fare when faced with a small population of selfish mutants that would be identical to the resident but would have the freedom to choose a different behavior. We studied the resulting optimal control problem where the mutants maximize their own number of offspring using the knowledge of the resident's behavior, and 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 [52] .

Optimal foraging and residence times variations

Charnov's marginal value theorem (MVT) [81] 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 [49] , [78] .

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

Growth models of zooplankton

Participants : Jean-Luc Gouzé, Jonathan Rault, Eric Benoît.

The model built to describe a zooplankton community is some variant of the McKendrick-Von Foerster Equation. The model includes cannibalism within zooplankton communities and predation on phytoplankton. Dynamic mass budget theory is used in order to describe individual behavior and allows mass conservation. Also we have added phytoplankton dynamics, and we use environmental data as an input for the model. The aim is to compare simulations with data provided by the Laboratoire d'Océanographie de Villefranche (Lars Stemmann). We have also built a discrete size-structured model. Discrete models are less numerically demanding and so can be more easily incorporated into bigger models. Moreover the study of discrete models are often easier than that of continuous ones. We focus our study on the impact of cannibalism within the zooplankton community and show that under some hypotheses, cannibalism can stabilize the equilibrium of the model [29] , [11] . We also address the problem of control of such models (by harvesting or biological control); we obtain results for stabilization of the equilibrium [41] , [11] .