domain: info.info-au math spi sdv

text:
C Baroukh

J P Steyer

O Bernard

B Chachuat
email: b.chachuat@imperial.ac.uk

dynamic Flux Balance Analysis of the Metabolism of Microalgae under a Diurnal Light Cycle

Keywords: Microalgae, Dynamic modelling, dFBA, Metabolism, Photosynthesis, Carbon storage 

Microalgae have received much attention in the context of renewable fuel production, due to their ability to produce in high quantities carbon storage molecules such as lipids and carbohydrates. Despite significant research effort over the last decade, the production yields remain low and need to be optimized. For that, a thorough understanding of carbon storage metabolism is necessary. This paper develops a constrained metabolic model based on the dFBA framework to represent the dynamics of carbon storage in microalgae under a diurnal light cycle. The main assumption here is that microalgae adapt their metabolism in order to optimize their production of functional biomass (proteins, membrane lipids, DNA, RNA) over a diurnal cycle. A generic metabolic network comprised of 160 reactions representing the main carbon and nitrogen pathways of microalgae is used to characterize the metabolism. The optimization problem is simplified by exploiting the right kernel of the stoichiometric matrix, and transformed into a linear program by discretizing the differential equations using a classical collocation technique. Several constraints are investigated. The results suggest that the experimentally observed strategy of accumulation of carbon storage molecules during the day, followed by their depletion during the night may indeed be the optimal one. However, a constraint on the maximal synthesis rate of functional biomass must be added for consistency with the biological observations.

INTRODUCTION

Microalgae are promising organisms in the context of renewable energy since they can grow using light and CO 2 and can store large quantities of lipids and carbohydrates [START_REF] Mata | Microalgae for biodiesel production and other applications: A review[END_REF], which can be converted into biofuels. Despite significant research effort over the last decade, the production yields remain low and need to be further optimized. For that, a thorough understanding of carbon storage metabolism is necessary, which could be achieved using systems biology and metabolic modelling. Indeed, in silico studies of microbial metabolism can help clarify the intracellular mechanisms and identify routes for enhancing the production of certain targeted molecules. There are many examples of successful optimization guided by metabolic modelling [START_REF] Hamilton | Software platforms to facilitate reconstructing genome-scale metabolic networks[END_REF], such as the in silico study of Saccharomyces cerevisae metabolism that led to an increase of up to 25% in the production yield of ethanol on xylose/ glucose mixtures [START_REF] Bro | In silico aided metabolic engineering of Saccharomyces cerevisiae for improved bioethanol production[END_REF].

To understand carbon storage metabolism, it is important to study why such storage exists in the first place. For that, one needs to consider microalgae in the context of their natural habitats. Microalgae either grow in oceans (marine type) or lakes (freshwater type), where the culture media are usually limited by nutrient availability and subject to diurnal cycles. Because sunlight is the primary energy source in microalgae, and energy is required for inorganic carbon assimilation, energy and carbon storage during the day appears to be a necessary strategy to meet the maintenance requirements during the night. Such an accumulation of lipids, carbohydrates or other carbon storage molecules during the day and their subsequent depletion during the night have been observed experimentally in several microalgae species [START_REF] Knoop | Flux Balance Analysis of Cyanobacterial Metabolism: The Metabolic Network of Synechocystis sp. PCC 6803[END_REF][START_REF] Lacour | Diel Variations of Carbohydrates and Neutral Lipids in Nitrogen-Sufficient and Nitrogen-Starved Cyclostat Cultures of Isochrysis Sp[END_REF]). However, it has not been proved (or disproved) so far that this strategy is optimal under a diurnal light cycle. In addition, the amount of carbon stored, its storage form (as carbohydrates, lipids, cyanophycin, glycerol, etc) and its accumulation/depletion kinetics are still not fully understood. In order to provide hints for answering such questions, this paper develops an optimization-based model capable of describing the metabolic behaviour of a generic microalgae species under a diurnal light cycle. This model relies on dynamic Flux Balance Analysis (dFBA) [START_REF] Mahadevan | Dynamic flux balance analysis of diauxic growth in Escherichia coli[END_REF] and uses dynamic optimization. The paper is structured as follows: in section 2, the construction of the model is described, composed of i) metabolic network reconstruction, ii) adaptation of dynamic Flux Balance Analysis in the case of microalgae, iii) model formulation iv) simplification and linearization of the problem and v) numerical solution procedure. Then, in section 3, the model is solved and simulated. Several constraints are investigated and results are discussed and compared to experimental data.

MODEL FORMULATION

Metabolic network

The core carbon and nitrogen metabolic network among the microalgae species whose metabolic network has been reconstructed so far is relatively well conserved (Baroukh et al. 2015a). Here, we use a core metabolic network comprised of 160 reactions, which includes the following metabolic pathways relevant to autotrophy: photophosphorylation, Calvin cycle, pentose phosphate pathway, glycolysis, TCA cycle, oxidative phosphorylation, and synthesis of carbohydrates, lipids, amino acids, nucleotides and chlorophyll. Species-specific pathways, such as the synthesis of secondary metabolites, are not represented since the corresponding fluxes are usually negligible compared with the main pathways, and thus have a small impact on the metabolism. Then, the reactions of macromolecules synthesis (proteins, lipids, DNA, RNA and biomass) are lumped into generic reactions in order to arrive at a rather generic model, which is likely to describe a broad range of microalgae species (Baroukh et al., 2015b). The complete list of reactions and metabolites is available in the supplementary information of [START_REF] Baroukh | DRUM : A New Framework for Metabolic Modeling under Non-Balanced Growth. Application to the Carbon Metabolism of Unicellular Microalgae[END_REF].

dynamic Flux Balance Analysis

Adaptation of the framework to represent accumulation of some metabolites

Dynamic Flux Balance Analysis (dFBA) [START_REF] Mahadevan | Dynamic flux balance analysis of diauxic growth in Escherichia coli[END_REF] is the dynamical extension of Flux Balance Analysis [START_REF] Orth | What is flux balance analysis?[END_REF] for describing the metabolic behaviour of an organism. This framework relies on a quasi-steady state approximation (QSSA), which assumes no accumulation or depletion of intracellular metabolites. In order to represent carbon storage under the form of some intracellular metabolites, we represent the corresponding metabolites as external metabolites here, which are either excreted as products by the cell, or consumed as substrates within the cell. These metabolites are assumed to play no further functional role in the cell besides acting as storage (or buffers).

There are thus two types of intracellular metabolites inside the cell (Fig 1 ): i) those assumed to follow a QSSA (denoted by C), consumed as they are produced ( 𝑑𝐶 𝑑𝑡 = 0) for synthesizing new functional biomass (proteins, DNA, RNA, membrane carbohydrates and lipids); and ii) those assumed to act as carbon storage units (denoted by A), which are not consumed at the same time they are produced. Biomass X is thus divided into two pools: metabolites A and functional biomass B.

Optimization problem formulation

Maximization of the production of biomass (B) over a 24h day/night cycle is chosen as objective function (1.1). The only model input is light (1.8), as all the other nutrients are assumed to be non-limiting. An additional constraint on the quota of A is added to ensure the cyclic behaviour of the

𝑀(0) = 𝑀 0 (1.3) 𝑀 ≥ 0 (1.4) 𝐾 𝐶 . 𝑣(𝑡) = 0 (1.5) 𝑣 𝑖 ≥ 0 𝑓𝑜𝑟 𝑖 ∈ 𝐼𝑟𝑟 (1.6)
𝑣 𝑗 ≤ 𝑣 𝑚𝑎𝑥 for some 𝑗 ∈ {1, . . , 𝑛 𝑣 } (optional)

(1.7)

𝑣 𝐼 = 𝑒𝑓𝑓𝑚𝑎𝑥. 𝐼(𝑡) (1.8) 𝑞𝐴(24ℎ) = 𝐴(24ℎ) 𝐵(24ℎ) = 𝐴(0) 𝐵(0)
= 𝑞𝐴(0) (1.9) with: i) 𝑀, the vector of external metabolite concentrations of size 𝑛 𝑀 composed of substrates 𝑆, carbon storage metabolites 𝐴 and biomass 𝐵; ii) 𝑀 0 , the initial concentrations of the metabolites 𝑀;

iii) 𝐾 and 𝐾 𝐶 , the lines of the stoichiometric matrix of the metabolic network corresponding, respectively, to 𝑀 and the intracellular metabolites; iv) 𝑣, the kinetic rate vector of the 𝑛 𝑣 reactions; v) 𝐼𝑟𝑟 ⊂ {1, . . , 𝑛 𝑣 }, the index subset of irreversible reactions; vi) 𝑣 𝑚𝑎𝑥 , the maximal admissible kinetic rates of certain reactions; vii) 𝑒𝑓𝑓𝑚𝑎𝑥, the conversion efficiency of the light input parameter (𝐼(𝑡)) into energy for the reaction of the light phase of photosynthesis (𝑣 𝐼 ); and viii) 𝑞 𝐴 the biomass quota of 𝐴.

Simplification and linearization of the problem 2.3.1 Coordinate transform

Solving the optimization problem (1), involves identifying the 160 fluxes 𝑣(𝑡). In order to linearize the problem, we optimize for the transformed variables 𝑣 ′ = 𝑣. 𝐵 instead of 𝑣.

Then, by exploiting the right kernel (𝐾 𝐶 . 𝐾𝑒𝑟(𝐾 𝐶 ) = 0) of the stoichiometric matrix 𝐾 𝐶 , the optimization problem simplifies to:

max 𝑢(𝑡) ∫ 𝐵(𝑡)𝑑𝑡 24 0 (2.1) (2) subject to 𝑑𝑀 𝑑𝑡 = 𝑑( 𝑆 𝐴 𝐵 ) 𝑑𝑡 = 𝐾 ′ . 𝑢(𝑡) with 𝐾 ′ = ( 𝐾 𝑆 𝐾 𝐴 𝐾 𝐵 ) . 𝐾𝑒𝑟(𝐾 𝑐 ) (2.2) 𝑀(0) = 𝑀 0 (2.3) 𝑀 ≥ 0 (2.4) 𝐾𝑒𝑟(𝐾 𝐶 ) 𝑖 . 𝑢 ≥ 0 𝑓𝑜𝑟 𝑖 ∈ 𝐼𝑟𝑟 (2.5)
𝐾𝑒𝑟(𝐾 𝐶 ) 𝑗 . 𝑢 ≤ 𝑣 𝑚𝑎𝑥 . B for some 𝑗 ∈ {1, . . , 𝑛 𝑣 } (optional)

(2.6) 𝐾𝑒𝑟(𝐾 𝐶 ) 𝐼 . 𝑢 = 𝑒𝑓𝑓𝑚𝑎𝑥. 𝐼(𝑡). 𝐵(𝑡) (2.7)

𝑞𝐴(24ℎ) = 𝐴(24ℎ) 𝐵(24ℎ) = 𝐴(0) 𝐵(0) = 𝑞𝐴(0) (2.8)
where 𝑣 ′ = 𝐾𝑒𝑟(𝐾 𝐶 ). 𝑢, with 𝑢 ∈ 𝑅 11 . Note that the QSSA constraint (1.5) no longer appears in the optimization problem since it is satisfied by 𝑢 construction.

Discretization

The optimization problem (2) is solved numerically by applying a discretization in the time domain, following a standard orthogonal collocation approach [START_REF] Biegler | Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes[END_REF]

𝑢(𝑡) = ∑ u i,q . 𝐿 𝑞 ( 𝐾 𝑞=1 𝑡 -𝑡 𝑖-1 ℎ ) , 𝑡 𝑖-1 ≤ 𝑡 ≤ 𝑡 𝑖 , 𝑖 = 1. . 𝑁 (3) 𝑑𝑀(𝑡) 𝑑𝑡 = ∑ dM dt i,q . 𝐿 𝑞 ( 𝑡 -𝑡 𝑖-1 ℎ ) 𝐾 𝑞=1 , 𝑡 𝑖-1 ≤ 𝑡 ≤ 𝑡 𝑖 , 𝑖 = 1. . 𝑁 (4)
with 𝐿 𝑞 , 𝑞 = 1. . 𝐾 the Lagrange polynomials:

𝐿 𝑞 (𝑟) = ∏ 𝑟 -𝑟 𝑙 𝑟 𝑞 -𝑟 𝑙 𝐾 𝑙=1 𝑙≠𝑞 (5)
and 𝑡 𝑖 = 𝑖 * ℎ, 𝑖 = 0,1, … , 𝑁 the end-points of the time subintervals.

The metabolites' concentration vector 𝑀 is discretized at each time interval and computed within each time interval by integrating the vector

𝑑𝑀(𝑡) 𝑑𝑡 : 𝑀(𝑡) = 𝑀 𝑖-1 + ℎ. ∑ dM dt i,q ∫ 𝐿 𝑞 (𝑠)𝑑𝑠 𝑡-𝑡 𝑖-1 ℎ 0 𝐾 𝑞=1 , 𝑡 𝑖-1 ≤ 𝑡 ≤ 𝑡 𝑖 , 𝑖 = 1. . 𝑁 (6)
The continuity of the concentrations 𝑀 is enforced by the constraints:

𝑀 𝑖 = 𝑀 𝑖-1 + ℎ. ∑ dM dt i,q ∫ 𝐿 𝑞 (𝑠)𝑑𝑠 1 0 𝐾 𝑞=1 , 𝑖 = 1. . (𝑁 -1) (7)
Using this discretization scheme, the optimal control problem (2) is thus approximated by a linear program (LP) of the form: and 𝑢 𝑖,𝑞 , 𝑖 = 1. . 𝑁, 𝑞 = 1. . 𝐾 correspond to the collocation coefficients in (3), ( 4) and (6). The linear optimization problems (8) is solved using the LP solver Gurobi in Matlab, with the discretization parameters N=48 and K=3. Initial values for the concentrations M and the discretized light intensity input parameter I(t) are taken from [START_REF] Lacour | Diel Variations of Carbohydrates and Neutral Lipids in Nitrogen-Sufficient and Nitrogen-Starved Cyclostat Cultures of Isochrysis Sp[END_REF]. Moreover, the parameter effmax is estimated to be 0.0115𝑚𝑀. ℎ -1 . 𝑚𝑀𝐵 -1 . 𝜇𝐸. 𝑚 -2 . 𝑠 -1 in order to match the experimental observation of roughly a doubling time in 24h. Finally, carbon storage (A) is assumed to be only in the form of carbohydrates (CARB) here. A schematic representation of these assumptions is shown in

𝑓 * =

Numerical solution procedure

NUMERICAL RESULTS AND DISCUSSIONS

Without constraint on 𝑣 𝑚𝑎𝑥

A first case study is conducted by solving (8) without any constraint (2.6) on 𝑣 𝑚𝑎𝑥 . This model predicts an instantaneous consumption of CARB during the first time step (t=0.11h), which leads to an instantaneous synthesis of B (Fig 3A -B). After this, both CARB and B stay constant during the rest of the dark period. During day time (from t=12h to 24h), light then allows to replenish the CARB pool, so as to satisfy the periodicity constraint (2.8) on metabolite storage. The CARB minimal carbon quota is about 17%, a value determined by the maximal light intensity during the day-the availability of light during the day determines how much energy can be produced, and therefore how much CO 2 can be assimilated and how much CARB can be synthesized.

If maximal light intensity increases to 1800 μE.m -2 .s -1 (instead of 1400 μE.m -2 .s -1 ), the CARB minimal quota drops to 0%, suggesting that the amount of carbon stored during the day is indeed related to the maximal light intensity.

A sharp decrease in the concentration 𝑋 of the total carbon biomass is also observed during the first time step (Fig 3C). This is due to the fact that synthesis of B from CARB implies a release of CO 2 by the TCA cycle, which is coupled with oxidative phosphorylation to meet the energy demand (under the form of ATP) in the absence of light. Then, X remains constant until day time, since CARB is no longer consumed and B is no longer produced. During day time, X increases because of CARB synthesis from light and CO 2 . We note that the biomass X nearly doubles over a 24h period, in agreement with the experimental data by [START_REF] Lacour | Diel Variations of Carbohydrates and Neutral Lipids in Nitrogen-Sufficient and Nitrogen-Starved Cyclostat Cultures of Isochrysis Sp[END_REF].

With constraints on the biomass synthesis rate 𝑣 𝐵

A second case study is conducted by solving (8) with a constraint on the maximal synthesis rate 𝑣 𝐵 of the biomass B. Several values of 𝑣 𝐵 lead to different behaviours of the system during night time (Fig 3), and to different optimal values of the cost function (Table 1) in turn. No difference in behaviour is observed during day time, on the other hand.

For values of 𝑣 𝐵 larger than 0.03 µM.h -1 .μMB reach their minimal quota values (and B their maximal quota values) before the end of dark period (Fig 3 A-B). These values are the same as those obtained without maximal rate constraints (Section 3.1). Once these quotas are reached, CARB and B stay constant until day time; then, light replenishes the CARB pool in order to satisfy the periodicity constraint (2.8). The variations in total carbon biomass 𝑋 are also consistent with the conversion rate of CARB into B during night time, and with the rate of CARB synthesis during day time. The experimental data in [START_REF] Lacour | Diel Variations of Carbohydrates and Neutral Lipids in Nitrogen-Sufficient and Nitrogen-Starved Cyclostat Cultures of Isochrysis Sp[END_REF] suggest that certain microalgae species satisfy a maximal rate of biomass synthesis (Fig 3A). These data also suggest that the maximal rate 𝑣 𝐵 might evolve so that the CARB pool nearly reaches its minimal admissible quota value (dictated by light availability during day time) at the end of the dark period (Fig 2, light blue curve). This observation supports the theory stipulating that starch turnover in photosynthetic organisms is regulated so that it is almost, but not completely, exhausted at the end of the dark period [START_REF] Stitt | Starch turnover: pathways, regulation and role in growth[END_REF]. It is also interesting to note that such a behavior results in a productivity loss of about 9% only compared with the optimal productivity in the absence of rate limiting constraints.

On imposing a maximal rate constraint on the nitrate assimilation rate (𝑣 𝑁𝑂3 ≤ 𝑣 𝑚𝑎𝑥 ) and on the carbohydrate consumption rate (𝑣 𝐶𝐴𝑅𝐵 ≤ 𝑣 𝑚𝑎𝑥 ), similar results are obtained: a constraint is mandatory to reproduce the experimental data by [START_REF] Lacour | Diel Variations of Carbohydrates and Neutral Lipids in Nitrogen-Sufficient and Nitrogen-Starved Cyclostat Cultures of Isochrysis Sp[END_REF], and the value of the maximal rate is such that the CARB pool nearly reaches its minimal admissible quota at the end of the dark period. This symmetry between the rate limiting constraints suggests that the activities of different enzymes might become synchronized with each other by evolution pressure. The advantage of such a synchronization could be to minimize the accumulation of intermediate metabolites, besides carbon storage molecules, inside the cells.

An inherent advantage of metabolic modelling is that both the intracellular (metabolic fluxes) and macroscopic (substrate consumption, biomass production) processes can be predicted simultaneously. Although our main focus in this paper has been on macroscopic processes, it is found that the metabolic fluxes predicted by the solution of (8) with maximal rate constraints 𝑣 𝐵 ≤ 0.028 µM.h -1 .μMB -1 are also consistent with available predictions at the macroscopic and metabolic levels (Baroukh et al. 2015b). The dark period is characterized by a heterotrophic-like metabolism, with consumption of carbohydrates, glycolysis in the downward direction and a high respiration rate (Fig 4). During day time, the metabolism is autotrophic-like, characterized by high fluxes in the photosynthesis pathway, and a relative decrease in the magnitude of various other fluxes; upper glycolysis occurs in the glyconeogenic direction to produce the carbohydrates and sugar precursor metabolites (PEP, G6P, R5P) that are necessary for growth. Finally, near the beginning of day time (t=12-15h), the metabolism is mixotrophic-like, namely a mix between autotrophy-like and heterotrophy-like metabolisms, as light is not intense enough yet to meet the carbon and energy growth demands, which are palliated by carbohydrate consumption.

CONCLUSION

In this paper, we have presented a DFBA generic model of microalgae under a diurnal light cycle. In order to account for carbon storage, we have adapted the dFBA framework by separating the pool of intracellular metabolites into two categories: those metabolites following a classical QSSA (𝐶) and those subject to accumulation (𝐴). Our main assumption here is that microalgae can adapt their metabolism in order to optimize functional biomass production (proteins, membrane lipids, DNA, RNA) over a diurnal cycle. Moreover, for improved numerical tractability, we have reduced the optimization problem by exploiting the right kernel of the stoichiometric matrix, and transformed into an LP by discretizing the differential equations using orthogonal collocation.

Several maximal rate constraint scenarios have been tested, which concur to show that the experimentally observed pattern of accumulating carbon storage molecules during day time, followed by their depletion during night time is an optimal strategy. However, a constraint on maximal synthesis rate of functional biomass must be added to reflect biological observations. A constraint on maximal carbohydrate consumption rate or a constraint on nitrate assimilation rate has been shown to be equivalent. Finally, light availability during the day has been shown to determine how much carbon is stored.

Future work will consist in implementing other carbon storage molecules in the model (lipids, glycerol, cyanophycin, …) to study the impact of the nature of the storage molecule on the dynamic behaviour of the metabolism and on the quantity stored. Implementation of several carbon storage molecules and addition of isodensity constraints or maximal cell volume will also be tested, to study whether these constraints could explain the repartition between several carbon storage molecules. Experimental validation on several species of microalgae will also be considered. 2) subject to the maximal rate constraint 𝑣 𝐵 ≤ 0.028 µM.h - 1 .μMB -1 . X-axis: Time (h). Y-axis: Fluxes value (µM.h -1 .μMB -1 ).

  ., Steyer, J.-P., Bernard, O., Chachuat, B. (2016). Dynamic flux balance analysis of the metabolism of microalgae under a diurnal light cycle. IFAC-PapersOnLine. Presented at 11. IFAC Symposium on Dynamics and Control of Process Systems -DYCOPS-CAB 2016 , Trondheim, NOR (2016-06-06 -2016-06-08). DOI : 10.1016/j.ifacol.2016.07.285

Fig. 1 .

 1 Fig. 1. Adaptation of dFBA taking carbon storage into account:A. Schematic view of an organism metabolism, in which substrates (S) are converted, via intermediates metabolites (green and orange dots), into products (P) or biomass (X) (mainly composed of proteins (Prot), DNA, RNA, membrane carbohydrates and lipids (Mbm)). B. Schematic view of an organism metabolism after application of classical QSSA (no accumulation of intracellular metabolites). Substrates (S) are directly converted into products (P) or biomass (X). C. Schematic view of an organism metabolism, accounting for carbon storage. There are two types of intracellular metabolites: i) those assumed to follow a QSSA (C, green dots); and ii) those assumed to act as carbon storage units (A, orange dots). Biomass X is thus divided into two pools: metabolites A and functional biomass B -mainly composed of proteins (Prot), DNA, RNA, membrane carbohydrates and lipids (Mbm). D. Schematic view of an organism metabolism after application of QSSA, when taking into account carbon storage. Substrates (S) are directly converted into products (P), functional biomass (B) or indirectly converted into products (P), functional biomass (B) via carbon storage metabolites (A). metabolism (1.9), along with an optional constraint on the maximal kinetic rate (1.7). A formulation of dFBA optimization problem is as follows: max 𝑣(𝑡) ∫ 𝐵(𝑡)𝑑𝑡 24 0

  . The time interval [0;24h] is divided into N equally sized intervals, each of length ℎ = 24ℎ 𝑁 . Each time interval contains 𝐾 collocation points 𝑟 𝑞 ∈ [0; 1], 𝑞 ∈ {1; … ; 𝐾}, 𝑟 𝑞 chosen as the zeros of the Legendre polynomial of degree 𝐾 here. The flux variable 𝑢(𝑡) and time derivatives of the metabolite concentrations 𝑑𝑀(𝑡) 𝑑𝑡 are discretized according to a Lagrange interpolation scheme:

  ., Steyer, J.-P., Bernard, O., Chachuat, B. (2016). Dynamic flux balance analysis of the metabolism of microalgae under a diurnal light cycle. IFAC-PapersOnLine. Presented at 11. IFAC Symposium on Dynamics and Control of Process Systems -DYCOPS-CAB 2016 , Trondheim, NOR (2016-06-06 -2016-06-08). DOI : 10.1016/j.ifacol.2016.07.285

Fig. 2 .

 2 Fig. 2. A schematic view of the model. CO 2 assimilation is driven by light energy. This available carbon is then converted via the metabolic network into carbohydrates (CARB) and biomass (B). CARB can also synthesize B. Total biomass X is composed of B and CARB. Light intensity follows a representative day/night cycle at Narbonne, France during summer (Lacour et al. 2012).

Fig. 3 .

 3 Fig. 3. Simulation results for several constraints Grey: Light intensity. Dark blue: without constraint on 𝑣 𝑚𝑎𝑥 . Others: with onstraints (µM.h -1 .μMB -1 ) on the biomass synthesis rate 𝑣 𝐵 (Green: 0.06, Purple: 0.03, Light blue: 0.028, Red: 0.025) A. Biomass (B) carbon quota. Dots: experimental data from Lacour et al. (2012) from duplicates. B. Carbohydrates (CARB) carbon quota. C. Total carbon biomass X.

  -1 (Fig 3 green and purple curves), CARB are no longer consumed instantaneously (Fig 3A), which shows that the maximal rate constraints are limiting (active) in the LP problem. CARB Comment citer ce document : Baroukh, C., Steyer, J.-P., Bernard, O., Chachuat, B. (2016). Dynamic flux balance analysis of the metabolism of microalgae under a diurnal light cycle. IFAC-PapersOnLine. Presented at 11. IFAC Symposium on Dynamics and Control of Process Systems -DYCOPS-CAB 2016 , Trondheim, NOR (2016-06-06 -2016-06-08). DOI : 10.1016/j.ifacol.2016.07.285

  ., Steyer, J.-P., Bernard, O., Chachuat, B. (2016). Dynamic flux balance analysis of the metabolism of microalgae under a diurnal light cycle. IFAC-PapersOnLine. Presented at 11. IFAC Symposium on Dynamics and Control of Process Systems -DYCOPS-CAB 2016 , Trondheim, NOR (2016-06-06 -2016-06-08). DOI : 10.1016/j.ifacol.2016.07.285

Fig. 4 .

 4 Fig. 4. Metabolic fluxes prediction of the optimization model (2) subject to the maximal rate constraint 𝑣 𝐵 ≤ 0.028 µM.h - 1 .μMB -1 . X-axis: Time (h). Y-axis: Fluxes value (µM.h -1 .μMB -1 ).

Table 1 . Optimal objective values Constraint (µM.h -1 .μMB -1 )

 1 For smaller values of 𝑣 𝐵 (Fig 3 red curve), the system may no longer reach a steady-state before day time. This is due to the fact that 𝑣 𝐵 has a low enough value to prevent the CARB pool to reach its minimal admissible quota, as dictated by light availability during day time. Like in previous simulations, light replenishes the CARB pool during day time (periodicity constraint (2.8)) and the variations in total carbon biomass 𝑋 are consistent with the rate conversion of CARB into B during night time, and with the rate of CARB synthesis during day time.

		Objective value	% of best
		(mMB.j -1 )	objective value
	None	4.128	1
	𝑣 𝐵 ≤ 0.06	3.957	95.9
	𝑣 𝐵 ≤ 0.03	3.782	91.6
	𝑣 𝐵 ≤ 0.028	3.758	91.0
	𝑣 𝐵 ≤ 0.025	3.713	90.0


Priscila Duarte Malanski
email: priscila-duarte.malanski@inra.fr

Nathalie Hostiou
email: nathalie.hostiou@inra.fr

Stéphane Ingrand
email: stephane.ingrand@inra.fr

WS4 -Transformations in work organizations in farms

Keywords: Pathways of evolution, work, wage earner, dairy farm

Enlargement of farms in association with the decrease in the family workforce are inducing the development of permanent wage earners. In dairy farms, permanent wage earners have been recruited to carry out milking in particular. Studies show that human resource management practices can help farmers to retain wage earners in farms, but the authors do not take into account changes in wage earners' work over time. Our hypothesis is that dynamic aspects in work content are crucial for wage earners, because they give them some perspective and good reasons to stay. In this paper, we analyze the evolution of permanent wage earners' work in dairy farms according to a human resource management approach. Individual interviews were carried out with farmers and permanent wage earners who work in specialized or diversified dairy farms. Five pathways of evolution of wage earners' work were identified as well five variables and categories were identified to describe the pathways of evolution according to the assignment of tasks and versatility/specialization.

Introduction

Structural changes in livestock are impacting work conditions; farms become larger and more modern, inducing an increase in labor productivity [START_REF] Dedieu | Vingt ans de recherche-développement sur le travail en élevage: acquis et perspectives[END_REF]. In the same time, even if the family workforce remains important, wage earners are becoming more common in family farms [START_REF] Dufour | Le travail dans les exploitations d'élevage bovin laitier est-il toujours conjugal?[END_REF][START_REF] Nettle | Farmers growing farmers: the role of employment practices in reproducing dairy farming in Australia[END_REF][START_REF] Chmieliński | Changes in population and labour force in family farming in Poland[END_REF][START_REF] Pluvinage | L'exploitation agricole, entre famille et entreprise: 60 ans de débats et d'itinéraire de recherche personnel[END_REF][START_REF] Nowak | The effect of human capital on labour productivity of farms in Poland[END_REF]. In France, permanent wage earners are responsible for 17% of work in farms (AWU), they represent 16% of active agricultural population working in almost 67 000 farms [START_REF] Agreste | Enquête structure et recensement agricole: Population agricole, formation et recherche[END_REF]. Permanent wage earners are taking an increasing place in dairy farms to carry out milking, which requires a large, highly skilled and regular workforce [START_REF] Porter | What Dairy Employees Think About Their Jobs[END_REF][START_REF] Stup | Relationships Between Selected Human Resource Management Practices and Dairy Farm Performance[END_REF].

However, farmers have some difficulties in managing wage earners in many aspects, such as difficulties in hiring, in delegating tasks and avoiding staff turnover. Agricultural advisors and researchers try to better understand these difficulties, to give advice and to develop tools, such as ensuring the successful integration of a wage earner in farm activities [START_REF] Depoudent | Faciliter l'intégration d'un nouveau salarié[END_REF], or helping the farmer to prepare his replacement by a wage earner in some tasks [START_REF] Frappat | Salariat et remplacement en exploitations laitières face au défi du recrutement[END_REF], or defining farmer practices to make a more attractive workplace [START_REF] Nettle | Farmers growing farmers: the role of employment practices in reproducing dairy farming in Australia[END_REF]. Certainly, these studies enabled some progress to be made, but frequently they are focused on the farmer, and not, or too little, on the wage earner and his work.

In management science, authors show that human resource management (HRM) practices contribute to retaining wage earners in farms and to improving farm profitability by improving the wage earners' work conditions [START_REF] Porter | What Dairy Employees Think About Their Jobs[END_REF][START_REF] Stup | Relationships Between Selected Human Resource Management Practices and Dairy Farm Performance[END_REF][START_REF] Nettle | Farmers growing farmers: the role of employment practices in reproducing dairy farming in Australia[END_REF][START_REF] Ullah | The Impact of Strategic Human Resource Management Practices on Australian Dairy Farm Performance[END_REF]. One of HRM practices is the work organization of wage earners in farms by assignment of tasks according to the wage earners' profile and skills [START_REF] Hutt | Organizing the human resource: A review of centralization, decentralization and delegation in agricultural business management[END_REF][START_REF] Porter | What Dairy Employees Think About Their Jobs[END_REF]. Assignment of tasks is an important action to decide and to organize the work at farm level and define the tasks that the wage earner has to carry out and his responsibilities [START_REF] Hutt | Organizing the human resource: A review of centralization, decentralization and delegation in agricultural business management[END_REF][START_REF] Vafaï | Délégation et hiérarchie[END_REF]. Most tasks carried out by wage earners in dairy farms in France are milking in the first place, and then the feeding of animals and maintenance of farm equipment [START_REF] Beguin | Composition et organisation des collectifs de travail des exploitations laitières de Picardie[END_REF]. The profile and skills of the wage earner are strongly linked to the tasks he carries out [START_REF] Everaere | La polyvalence et ses contradictions, in 18ème Congrès de l'AISLF[END_REF][START_REF] Attia | Factors Affecting the Development of Workforce Versatility[END_REF]. Wage earners have different profiles in swine farms. For example, specialized wage earners carry out important technical tasks such as artificial insemination, some veterinary care and technical control of animal production; versatile wage earners carry out routine tasks such as cleaning buildings and feed distribution [START_REF] Depoudent | Salariat en élevage porcin: synthèse de quatre études bretonnes[END_REF].

Even if those studies describe the work of wage earners, they do not take into account the dynamic aspects of work, such as changes in the division of work, changes in the rhythm of work and how interactions at farm level make changes in work organization over time. As farms change, we assume that the work of permanent wage earners in dairy farms may change over time as well. Therefore, understanding the evolution of wage earners' work in the farm may contribute to defining strategies to avoid staff turnover and to face changes in dairy farms. Our aim is to produce knowledge about how permanent wage earners' work organization evolves in dairy farms after their recruitment, to identify different types of evolution and to identify the relevant variables to analyze these evolutions.

Material and methods

We adopted an inductive method to analyze the evolution of wage earners' work. We conducted a literature review and an exploratory study with 14 wage earners working in 8 dairy farms in the Center of France (Auvergne).

Data collection and data analysis

Our methodology was implemented in three steps. The first step concerned data collection and individual analyses carried out as follows: 1) individual interviews with eight farmers about farm trajectory, division of tasks over time, composition of teamwork, wage earner recruitment; 2) integral transcription of interviews; 3) interview codification with software Nvivo 10 to build a data base; 4) construction of farm pathway to have a chronological point of view of farm changes; 5) writing a monograph for each farm to identify variables that describe the evolution of task assignment.

The second step was based on a second interview with wage earners : 1) to complete data of the first interview about division of tasks and about changes between interviews, if any (farm, teamwork and division of tasks); 2) to identify changes in tasks carried out over time, reasons for these changes and their consequences on the work (routine, tasks carried out and rhythm of work); 3) integral transcription; 4) to identify complementary variables that describe assignment of tasks and versatility/specialization. The third step concerned transversal analysis based on data collected during the two previous steps. We first identified some profiles based on a classification of tasks carried out by wage earners according to the three levels of system management defined by [START_REF] Brossier | Gestion de l'exploitation agricole familiale: éléments théoriques et méthodologiques[END_REF]: operational, tactical and strategic. The operational level concerns technical tasks to maintain the functioning of a dairy farm, like milking, feeding distribution and maintenance of farm equipment; the tactical level concerns technical tasks to adjust and plan the functioning at operational level, like veterinary care and identification of cows in heat; the strategic level concerns tasks that define and guide the characteristics of the dairy system over time, like selection of the characteristics of a breeding bull for reproduction. Then, we assigned each profile to categories defined by [START_REF] Everaere | La polyvalence et ses contradictions, in 18ème Congrès de l'AISLF[END_REF]: i) task specialist: the wage earner carries out one task; ii) job specialist: the wage earner carries out several tasks in one job; for example, the wage earner who only works with animal husbandry carrying out milking and feeding; iii) versatile worker: the wage earner carries out several tasks in different jobs, for example the wage earner who works with animal husbandry and vegetable production. Finally, we combined the previous steps to describe the diversity of the evolution of wage earners' work. The first list of variables and categories was constructed comparing the two most different monographs. This first list was progressively modified by comparison between other monographs. Variables and categories were identified and regrouped until the point where they describe noteworthy characteristics of pathway of evolution of wage earners' work. In a fourth step, we used a graphic representation [START_REF] Bertin | La graphique et le traitement graphique de l'information[END_REF] to identify the different pathways of evolution of wage earners' work. We described different pathways obtained by using trigger events [START_REF] Mendez | Processus: concepts et méthode pour l'analyse temporelle en sciences sociales[END_REF] that promote changes in the pathways.

Description of wage earners and dairy systems

The sample of 14 wage earners is composed of 9 men and 5 women, from 22 to 50 years old. They were recruited between 1998 and 2014. The majority are full-time workers (n=7) working 40 h/week; 3 wage earners are full-time workers working in employer group (they work 15h/week in the sampled farms); 4 wage earners are part-time workers working 25 h/week.

The wage earners work in 8 dairy farms that are larger than the average in Auvergne, center of France, with 150 ha on average as against 62 ha in Auvergne [START_REF] Agreste | Deux vaches nourrices pour une vache laitière sur les herbages auvergnats[END_REF]. The average number of dairy cows in our farm sample is twice that of the regional average (83 dairy cows as against 36 dairy cows in Auvergne) [START_REF] Agreste | Deux vaches nourrices pour une vache laitière sur les herbages auvergnats[END_REF], except for one (n°8), with 12 dairy cows, but with a large herd of 250 dairy goats (Table 1).

Results

Assignment of tasks to wage earners

We identified an important difference in tasks carried out by wage earners at recruitment and the tasks carried out since their recruitment. The tasks carried out by wage earners at recruitment are milking (Milkg), cheese production (CheeP), feed distribution (FeeD), manure spreading (ManSp), grassland maintenance (GrassM), silage (Sil), haymaking (Haym), harvesting (Harv) and maintenance of farm equipment (EquipM). All these tasks are linked to the operational level of the dairy system.

Over time, more tasks are carried out by some wage earners: declaration of birth calves (SBCal), support to calving (SCalv), support to artificial insemination (SAI), declaration of insemination (StIn), simple veterinary care (SVetC), identification of cows on heat (ICowH) and selection of breeding bull (SBull). All these new tasks are linked with the tactical level of the dairy system, except selection of breeding bull which is linked to the strategy level of the dairy system ( Figure 1).

Figure 1. Differences between tasks and number of tasks carried out by hired workers at recruitment and currently.

We observe both quantitative and qualitative changes in the tasks carried out by wage earners since recruitment. The quantitative change is about the "number of tasks carried out", indicating the evolution of the quantity of tasks assigned to a wage earner since his recruitment. The results show that 11 wage earners carried out more tasks over time and only 3 wage earners carried out the same number of tasks since their recruitment. Therefore, assignment of more and more tasks to the wage earner is a common decision for farmers, especially for milking and feed distribution at operational level.

The qualitative change concerned the upgrade in the level of tasks carried out. Thus, the "nature of tasks carried out", indicates the evolution of the type of tasks carried out by wage earners since their recruitment. Three categories were identified: 1) increasing tasks of execution and responsibilitythis concerns tasks at operational level and tactical level or concerns all levels of the dairy system; 2) increasing tasks of executionthis concerns tasks at operational level; 3) stablethere is no change in the nature of tasks carried out. Five wage earners are in the first category; two of them carry out tasks at all levels of the dairy system and three wage earners carry out tasks at operational and tactical levels. The other wage earners are distributed between the second category (n=6) and the third category (n=3) (Figure 2).

Three categories were identified concerning "frequency of tasks' execution": 1) increasing daily taskswith more tasks carried out every day, like milking or identification of cows on heat; 2) increasing regular taskswith more tasks carried out systematically according to regular periods except daily tasks, like milking every week-end or haymaking every summer; 3) increasing occasional tasks with more rarely tasks carried out by the wage earner, the case of wage earners who usually do not do the milking, but sometimes they can do. Almost half of the wage earners have carried out more daily tasks (n=6), the other wage earners have carried out more regular tasks (n=4) or occasional tasks (n=4).

Wage earner profile: between specialization and versatility

Versatility/specialization is the second dimension to analyze the evolution of wage earners' work. We have identified two variables linked to this dimension. The first variable, "variation between tasks carried out", shows the evolution of the level of work assignment since recruitment. Two categories were identified: 1) between jobsthe tasks carried out by wage earners belong to two jobs or more, like the wage earner who works with animal husbandry and vegetable production; he can carry out milking and harvesting; 2) intra jobthe tasks carried out by a wage earner belong to one job, like the wage earner who works with animal husbandry; he can carry out milking and feeding. The distribution of wage earners between these two categories is almost equal; the first category has 8 wage earners and the second category has 6 wage earners.

The assignment of tasks determines the wage earners' profile. We have identified three different profiles at recruitment. The first profile is a "task specialist", in our sample 4 wage earners only carried out milking, thus they are milking specialists. The second profile is a "job specialist", the majority of wage earners of our sample have this profile at recruitment, 2 of them are animal husbandry technician, 3 wage earners are cheesemakers and 2 wage earners are agricultural equipment operators. The third profile is a "versatile worker". Three wage earners in our sample have this profile; they carried out tasks that belong to an animal husbandry technician and an agricultural equipment operator.

Over time, the wage earner's profile has changed. The "task specialist" profile has disappeared, however the number of animal husbandry technicians increased to "job specialist" profile. The "versatility" profile has the most important increase over time (Figure 3). Changes in wage earners' profile have been constructed over time as described for the second variable, "evolution of job". This variable qualifies the change in wage earner job profile after recruitment. Three categories were identified: suddenly, progressive and stable. For the first category, "suddenly", the wage earner starts to carry out tasks that he does not expect to do because these tasks are incompatible with his job profile at recruitment. This is the case of six wage earners. Two of them were recruited to carry out tasks as agricultural machine operator, but over time they started to do milking and feed distribution, which are tasks of an animal husbandry technician. Two wage earners were recruited as cheesemakers; over time, one wage earner started to sell cheese in the local market; this is a task linked to commercialization. The other wage earner started to milk, a task of an animal husbandry technician. One wage earner was recruited as a versatile worker to carry out tasks as agricultural equipment operator and animal husbandry technician. Over time he started to carry out tasks as a cheesemaker. Thus, his versatility was improved because he carries out tasks in three jobs. One wage earner was recruited to milking, but throughout time he started do carry out tasks in two different jobs, agricultural equipment operator and animal husbandry technician. For the second category, "progressive", tasks that the wage earner started to carry out after his recruitment belong to the same job. This is the case of 5 wage earners; three of them carried out milking at recruitment and over time carried out simple veterinary care and identified cows on heat, tasks carried out by an animal husbandry technician. The others were recruited as versatile workers to carry out tasks as agricultural equipment operator and animal husbandry technician. Over time the number of tasks carried out in both jobs increased the versatility of these wage earners. For the third category, stable, there is no change in tasks assigned and no change of job profile (Table 2).

Synthesis: 5 pathways of evolution of wage earners' work

Five pathways of evolution of wage earners' work were identified (Table 3). The three variables that most distinguish the pathways are: number of tasks carried out, variation of task assignment and nature of tasks carried out.

Table 4. Illustration of 5 pathways of evolution of wage earners' work according to the combination of 14 wage earners (lines) and 5 variables (column), each category describes changes in wage earners' work since recruitment (one color represents one category per variable).

Type of pathway Wage earner

Number of tasks carried out

Variation of task assignment

Evolution of job

Nature of tasks carried out

Frequency of task execution

The wage earner becoming a farmer

4 1 1 1 1 2 8 1 1 1 1 2
The executor that can do occasional replacement

14 1 1 1 2 3 9 1 1 1 2 3 1 1 1 1 2 3 2 1 1 1 2 3 The versatile worker to regular replacement 3 1 1 2 2 2 5 1 1 2 2 2
Becoming a high-skill technician

6 1 2 2 1 1 7 1 2 2 1 1 10 1 2 2 1 1
Staying an executor

11 2 2 3 3 1 12 2 2 3 3 1 13 2 2 3 3 1
The wage earner becoming a farmer: two wage earners are concerned by this pathway that characterizes an increase in versatility with tasks carried out on the three levels of dairy system (operational, tactical, strategic). Most tasks carried out are execution tasks on an operational level and responsibility tasks on a technical level such as milking, feed distribution, spreading manure, hay making, simple veterinary care and identification of cows in heat. The objective is to maintain the operational level running and to adjust or regulate how the operational level runs. However, the wage earner started to carry out some responsibility tasks on a strategic level, such as choosing the breeding bull. One wage earner was recruited as a versatile worker and became a farmer. The other wage earner was recruited to milking, but he evolved to versatile worker and is a potential candidate to become a farmer in the farm where he currently works. This pathway represents the increasing accountability of the wage earner in the whole dairy farm.

The executor that can do occasional replacement: four wage earners were identified in this pathway that characterizes a transition from job specialist on the operational level to a versatile worker for occasional replacement. All the tasks carried out are execution tasks to maintain the operational level running. In daily work, the wage earner carried out several tasks on one kind of job, however he may carry out execution tasks of other workers in the case of an unexpected event or sickness. This is the case of four wage earners. Two of them were recruited to carry out tasks as agricultural equipment operator, like manure spreading, silage, haymaking, harvesting and maintaining farm equipment. Over time they can replace the farmer on milking. The other two wage earners were recruited as cheesemakers. One of them started to milk the cows with one of the two farmers and the other one started to sell cheese in the local market.

The versatile worker for regular replacement: two wage earners were identified in this pathway that represents the increase of versatility on the operational level to regular replacement. All the tasks carried out are execution tasks on the operational level to maintain the operational level running. In daily work, the wage earner carried out several tasks on different jobs, however he regularly carried out execution tasks of other workers. This pathway represents the increasing flexibility of wage earners' work that in its turn gives flexibility to the rhythm of teamwork. This is the case of two wage earners recruited as versatile workers to carry out tasks like feed distribution, spreading manure and harvesting. Over time they started to carry out milking with the farmer or another wage earner, especially on weekends, but during the week milking is a task carried out by the farmer or another wage earner.

Becoming a high-skill technician: three wage earners were identified in this pathway that represents the evolution of a task specialist at operational level to job specialist at operational and tactical levels for the accomplishment of daily tasks at both levels. The tasks carried out are execution tasks on the operational level to keep the operational level running, and responsibility tasks at tactical level to adjust or regulate how the operational level runs. This pathway represents the increase in technical accountability of the wage earner. The three wage earners identified in this pathway were recruited to carry out milking. Over time, they carried out other tasks such as feed distribution, identification of cows in heat and simple veterinary care. Thus, they became animal husbandry technicians.

Staying an executor: three wage earners were identified in this pathway that represents the evolution of the stable pathway of a job specialist with several execution tasks at the operational level of a dairy system. The accountability of the wage earner is to carry out important daily tasks to keep the operational level running, such as milking or feed distribution. Their profile does not evolve because the number of tasks that they carry out is stable over time. The three wage earners identified in this pathway are full-time workers at the same farm. One of them is a cheesemaker and the others are animal husbandry technicians.

For all the pathways, the time of permanence in the farm after recruitment is not an explicative factor of stability or changes in pathways. We observed a wage earner in the "staying an executor" pathway who has worked for 5 years in the same farm; he has a stable pathway, he still carries out the same tasks as a cheesemaker. But a wage earner in the pathway "the wage earner becoming a farmer" who has worked for 1 year in the farm has significant changes in his pathway; he has started to carry out milking and currently he is a versatile worker who has carried out important tasks such as selection of breeding bull with the farmer.

Seven elements were identified as trigger events that explain wage earners' pathways (Figure 4). All the factors are linked with changes in different aspects of a dairy system. About structural changes, we identified two trigger events such as increase in herd size (Herd+) and increase in land (Land+). These events acted to change the pathways of six wage earners. Technical changes in a dairy farm also contribute to changing the pathways; we identified two trigger events such as technical management (Tech Manag) and changes of equipment (Equip), each trigger event acted to change the pathway of one wage earner. Finally, changes in teamwork have promoted changes in pathways; we identified three trigger events: departure of worker (Team-), arrival of worker (Team+) and workers with health problems (Health); they changed the pathway of twelve wage earners. Sometimes trigger events can combine to promote changes. Trigger events acted in all wage earners' pathways, except in the case of the three wage earners on the executor pathway where no change was identified in the dairy farm.

Discussion and conclusion

Five pathways of evolution of permanent wage earners' work in dairy farms were identified by taking into account the human resource management approach in work organization; five noteworthy variables were identified to describe the pathways of evolution according to assignment of tasks and versatility/specialization. The specificities of our approach are the analysis of work organization in dairy farms by evolutional and individual perspective, highlighting changes in quantitative and qualitative characteristics of wage earners' work, as well the consequences of changes at dairy farm level in work at individual level. Most approaches and methodologies developed to analyze work organization in livestock systems highlight technical practices over a year to describe work organization at farm level [START_REF] Dedieu | Organisation du travail dans les systèmes d'activités complexes: Intérêt et limites de la méthode Bilan Travail[END_REF]Madelrieux et al., 2009).

We have observed growing versatility of wage earners, which confirms that versatility of permanent wage earners in dairy farms is a profile wanted by farmers as shown by [START_REF] Dupré | Spécificités du salariat permanent en élevage laitier de montagne: une première approche dans les Alpes du Nord[END_REF]. Three pathways represent the versatile wage earners. Two of them are "the executor that can do occasional replacement" and "the versatile worker to regular replacement". In both cases the versatility of a wage earner gives flexibility in teamwork organization to keep running the operational level of a dairy farm, which confirms that versatility is one strategy to improve flexibility in work organization [START_REF] Mundler | Flexibilité du travail en agriculture : méthodes d'observation et évolutions en cours[END_REF]. But the tasks to carry out replacement of farmers have to be simple and repetitive to facilitate the replacement, thus stimulating versatility only for replacement reasons has a negative effect on the development of high skills and competencies of wage earners [START_REF] Everaere | La polyvalence et ses contradictions, in 18ème Congrès de l'AISLF[END_REF]. The third pathway with increase in versatility is "the wage earner becoming a farmer". In this case, versatility is a way to train a wage earner and develop several technical and managerial skills in the entire dairy farm management. Our result accorded with the results of Madelrieux et al., (2009) about permanent wage earners with this profile who attempt to have their own farm in the future, and farmers test the permanent wage earner to become an associate farmer.

In the other way, we have observed two pathways of wage earner specialization. For "becoming a high-skill technician" pathway, specialization has been reinforced by a growth of technical responsibilities to monitor herd health and reproduction. However, [START_REF] Brasier | Farm-Level Human Resource Management: An Opportunity for Extension[END_REF] identified that for some farmers there is no difference between the milker and animal husbandry technician profiles, while monitoring herd health and reproduction are complementary tasks of milkers. In the case of "staying an executor" pathway, the specialization has been retained by the stability of execution tasks such as milking and cheese-making.

Results show that to carry out several execution tasks to keep the operational level of the dairy farm running is the principal characteristic of three pathways: staying an executor, the executor that can do occasional replacement and versatile worker to regular replacement. Working for a long time in the same job with repetitive tasks and absence of responsibilities increases the dissatisfaction of wage earners with their work [START_REF] Peltier | La place du travail salarié dans la gestion des exploitations agricoles[END_REF]. Dissatisfaction about work is one factor that stimulates staff turnover [START_REF] Kossivi | Study on Determining Factors of Employee Retention[END_REF][START_REF] Zhang | A Review of Employee Turnover Influence Factor and Countermeasure[END_REF].

We have identified different reasons for the evolution of wage earners' work linked to changes in dairy farms, such as structural changes (enlargement of herd and land), technical changes (technical management and equipment) and teamwork changes (arrival or departure of workers and health problems of workers). The perspectives are to identify how these changes in dairy farms induce the "direction" of evolution of wage earners' work between the pathways identified.

We can conclude that assignment of tasks and versatility/specialization are pertinent dimensions to better describe and understand the evolution of the work of permanent wage earners in changing dairy farms because they qualify the consequences of changes in wage earners' work and identify their role in teamwork. The perspective is to discuss those profiles with farmers and advisory services to validate them and to assess their usefulness for a reflexive process.

Figure 3 .

 3 Figure 3. Changes in wage earners' profile between recruitment and currently.

Figure 4 .

 4 Figure 4. Types of trigger event identified.

Table 1 .

 1 Size of the eight farms of the sample in Auvergne.

	Farm	Production	Farm size (ha)	Number of dairy cows	Number of wage earners
	1	Milk	80	50	1
	2	Milk	115	80	1
	3	Milk	140	90	1
	4	Milk and cereal	260	130	1
	5	Milk	102	80	1
	6	Milk and cheese	115	60	2
	7	Milk and cheese	110	160	3
	8	Milk, cheese (cow and goat) and cereal	292	12	4

Table 3 .

 3 Summary of identified variables per dimension, categories and number of wage earners per category.

	Dimensions	Variables	Categories	Number of wage earner/ category
		Number of tasks	1-Increasing number of tasks	11
		carried out	2-Stable	3
			1-Increasing execution tasks and responsibility tasks	5
	Assignment of tasks	Nature of tasks carried out	2-Increasing execution tasks 3-Stable	6 3
		Frequency of	1-Increasing daily tasks	6
		tasks' execution	2-Increasing regular tasks	4
			3-Increasing occasionally tasks	4
		Variation	1-Between jobs	8
	Versatility/ specialization	between task carry out	2-Intra job 1-Suddenly	6 6
		Evolution of job	2-Progressive	5
			3-Stable	3

Acknowledgements

This studied was conducted with support of Science without Frontiers, from CAPES and Ministry of Education of Brazil. Partners of this work: RMT Travail, Fédération Nationale des Syndicat Exploitant Agricole and the Syndicat Interprofessionnel Saint Nectaire.


est destinée au dépôt

Mechanical feedback between a growing root and a deformable granular medium: extracting physical laws from numerical simulations

Mahmoud Fakih, Jean-Yves Delenne, Farhang Radjai, Thierry Fourcaud

To cite this version:

Mahmoud Fakih, Jean-Yves Delenne, Farhang Radjai, Thierry Fourcaud. Mechanical feedback between a growing root and a deformable granular medium: extracting physical laws from numerical simulations. 4. International Conference on Soil Bio-and Eco-engineering, Jul 2016, Sydney, Australia. 2016, The Use of Vegetation to Improve Slope Stability. hal-01837343

indicator on plant community performance and soil properties to offer the soil protection and reinforcement for the slope stability.

SBEE25 -Mechanical feedback between a growing root and a deformable granular medium: extracting physical laws from numerical simulations M. Fakih, J.Y. Delenne, F. Radjai, and T. Fourcaud1

CIRAD, UMR AMAP, Montpellier, France

Plant roots play a key role in reinforcing soils against erosion and shallow landslides through different chemical (formation of soil aggregate) and physical processes (mechanical reinforcement, water infiltration and water suction).

Managing vegetated slopes on a longterm perspective to avoid soil loss necessitates understanding and quantifying the dynamics of root-soil interaction.

Soil resistance to penetration is a major component that can significantly affect root growth. The impact of soil properties on root growth has been largely studied at the root, plant and vegetation scales, mainly reducing soil properties to a single input variable representing soil impedance. However the mechanical feedback between growing roots and a deformable soil, is still largely unknown. The underlying questions are how the grains are reorganizing under the action of growing roots, and in return how the resulting forces acting on the growing root tips modify its development, including root elongation rate, root shape and ramification.

We started answering these questions in a theoretical way, developing a numerical model of root growth in a granular medium. The model is based on the discrete-element method (DEM). Single roots are modelled using chains of connected spheroline elements. The growth is initiated from a circular element placed at the free surface of a granular bed prepared by random pluviation. This circle plays the role of a meristem, which is constantly replicated at a given rate and pushed forward under the action of elastic forces, generating a line of fixed thickness equal to the diameter of the circle and with prescribed stiffness and bending moment. The orientation of the meristem at every growth step is driven by the dynamics of the whole root under the action of its internal elastic forces and reaction forces exerted by the grains. The preliminary model is two-dimensional, which not allows the pore space to be opened as in a 3D situation, consequently limiting root the penetration. To overcome this limitation, we introduce two different diameters for the grains, i.e. a "real" diameter that is considered to calculate grain-grain mechanical interactions, and a smaller "virtual" diameter to take into account root-grains interactions. The difference between the two diameters corresponds to the width of a gap at contact points through which the roots can pass. The ratio of this gap to the root diameter is considered as a model parameter.

Parametric studies showed the influence of granular structure and root mechanical properties on root trajectories. The analysis of the evolution of reaction forces exerted by grains on the root tip exhibited a broad distribution of the forces experienced by the root apex during a given growth period. This distribution has the same functional form for each root stiffness when forces are normalized by the mean force. It is characterized by a decreasing power law for forces below the mean force, and by an exponential fall-off for forces above the mean force, thus reflecting the broad distribution of forces inside the granular material.

Acknowledgement

This project is supported by Agropolis Fondation under the reference ID 1202-073 through the "Investissements d'avenir" program (Labex Agro: ANR-10-LABX-001-01).


A Bordoni

F Danesi

D Dardevet

D Gille

C Nunes Dos Santos

P Pinto

R Re

D Rémond

DR Shahar

G Vergères

A systematic review to identify gaps that limit translating knowledge on

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A systematic review to identify gaps that limit translating knowledge on dairy products and inflammation into nutritional guidelines The challenge of translating knowledge on food composition into dietary guidelines that promote health is compounded by the process of food digestion. INFOGEST tackles this issue by promoting research on this topic. The digestive system is highly interconnected with the gut microbiota and immune system. Knowledge on digestion must therefore integrate these additional processes in order to link food composition to the nutritional signals finally sensed by the human organism. This issue can be addressed by a backward strategy identifying relevant metabolic signals produced by humans in response to the ingestion of specific foods.

Dairy products are major components of the diet and interact with the gut microbiota and the immune system. Also, inflammation is mechanistically linked to the metabolism of nutrients. As a demonstrator of this backwards strategy, this review therefore identifies gaps in knowledge on the association between dairy product consumption and inflammation.

We conducted a systematic review of the literature (Medline, Scopus) and identified >60 human studies using inflammatory markers in relation to the consumption of dairy products. These studies were critically evaluated using the PRISMA checklist and EFSA guidance for the authorization of health claims. An inflammatory score was determined for each reported data set to allow for a quantitative evaluation of the impact of dairy consumption on inflammation.

Our analysis indicates that dairy products can modulate inflammation in humans. This effect is, however, blurred by the heterogeneity in study designs, the health status of the subjects under study, the type and dosage of the dairy products, and the inflammatory markers measured. Furthermore, the literature is characterized by a large gap of knowledge on the bioavailability of the nutrients potentially mediating these effects.

Future research should better combine food and nutritional sciences to adequately follow the fate of bioactive nutrients along the gastrointestinal and metabolic axes.

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  A. Bordoni, F. Danesi, Dominique Dardevet, D. Gille, C. Nunes dos Santos, Re Pinto R, Didier Remond, Dr Shahar, G. Vergères To cite this version: A. Bordoni, F. Danesi, Dominique Dardevet, D. Gille, C. Nunes dos Santos, et al.. A systematic review to identify gaps that limit translating knowledge on dairy products and inflammation into nutritional guidelines. 3. International Conference on Food Digestion, European Cooperation in Science and Technology (COST). BEL., Mar 2014, Wageningen, Netherlands. hal-02742188


Sandrine Grasteau
email: sandrine.grasteau@tours.inra.fr

Utlwanang Moreri

Julien Fablet

Michèle Tixier-Boichard

Jérémie David

Marie-Hélène Pinard-Van Der Laan

T B Rodenburg

Tatiana Zerjal

S Mignon-Grasteau

M.-H Pinard-Van Der Laan

Heritability of body surface temperature measured by infra-red thermography in laying hens exposed to high temperature conditions

Keywords: heat, genetics, thermography, stress, laying hens

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The past decade was the warmest on record and Earth has been growing warmer over the last 50 years [START_REF] Blunden | State of the climate in 2010[END_REF]. The European Environment Agency estimated that the temperature in Europe will continue to increase by 0.75 to 2.00°C between 2020 and 2050, and that the number of warm days per year will increase by 6 to 10 d every decade (http://www.eea.europa.eu). Animals will thus have to adapt to these higher rearing temperatures. The animal ability to maintain their body temperature within normal range depends on the balance between the thermogenesis and the rate of heat dissipation. Birds respond to high ambient temperatures by reducing their feed consumption to limit feed induced thermogenesis, by increasing evaporative heat loss through panting and by sensible heat loss through convection and radiation (Mount and Monteith, 1974). The latter has the lowest energetic cost and consequently a lower impact on production. It would thus be interesting to check whether some birds have a better capacity to dissipate heat through sensible heat loss associated with non-evaporative cooling at high temperatures. The goal of our project was to study the genetic basis of adaptation of laying hens to moderate heat stress. In this talk, we will discuss how thermography could be used to estimate the genetic ability of hens to adapt to heat, by estimating genetic parameters of surface temperature, a key component of sensible heat loss, in two lines of laying hens exposed cyclically to moderate heat and/or feed stress during the whole production cycle.

Materials and methods

Animals and rearing conditions

Two pure lines used in a 4 way cross of commercial laying hens were used in this study. At 15 weeks of age, each line was dispatched among 6 floor pens of 200 birds. From 28 weeks to 77 weeks of age, half of the pens were submitted to 3 successive cycles of stress, interposed to recovery periods at standard conditions (neutral ambient temperature and commercial feed).The other half of the pens were kept at standard conditions throughout the whole production period. Each cycle of stress was composed of three phases: i) 24 d of "feed stress" (i.e. suboptimal diet), followed by 24 d of recovery; ii) 12 d of "heat stress" followed by 12 d of recovery; iii) 24 d of combined feed and heat stress factors (i.e. 12 d of diet change and 12 d with both diet change and heat stress) followed by 24 d of recovery. Ambient temperature and relative air humidity were on average 28.4°C and 46.9% during heat stress periods (HS) and 19.6°C and 68.8% during thermoneutral periods (TN).

Measures

Thermal pictures of birds were taken at the beginning of the experiment (at 28 wks), at the end of each stress period (at 32, 37, 42, 54, 67and 72 wks) and at the end of each recovery period (at 35, 39, 45, 52, 56, 63 and 70 wks) on all birds for 2 pens per line and on a sample of 50 birds per pen for the remaining 4 pens per line. To take the pictures, birds were placed side-on in a wooden box. When the comb was not clearly visible, a second picture was taken zoomed in on the comb (Figure 1). We used a FLIR B35 camera1 , providing a thermal sensitivity of 0.05°C and an accuracy of 2%. Images were then analyzed with the ThermaCam Pro 2.10 software (© 1997-2010 FLIR systems AB, Sweden). The comb, wing and shank areas were drawn manually, and their mean temperature calculated. Emissivity was set at 0.980 for comb and shank areas and at 0.896 for wing area.

Statistical analyses

Analyses were performed separately for each line. Summary statistics were obtained using PROC MEANS of SAS. An analysis of variance was then performed with PROC GLM of SAS to check which factors were significant. The genetic parameters were estimated using the REML method implemented in the VCE 6.0.2 (Neumaier and Groeneveld, 1998;[START_REF] Groeneveld | VCE User's Guide and Reference Manual Version 6[END_REF]. Taking into account the result of the GLM analysis, two different models were fitted depending on the trait. Model 1 was used for all traits except for comb area in line A which was analyzed with model 2.

(1)

(2) where y ijkl is the body temperature of animal l (N=4465-4481 in line A, 7279-7311 in line B), µ the general mean, P i the fixed effect of pen i (N=1 to 6 for each line), HS j the fixed effect of heat stress treatment j (j= submitted or not submitted to cycles of heat stress), A the covariate of age, AT the covariate of ambient temperature in the pen, RH the covariate of relative air humidity in the pen,  1 ,  2 and  3 the regression coefficients corresponding to the 3 covariates, NP k the fixed effect of the number of pictures taken per bird (N=1 without extra picture comb, 2 with extra picture comb), a l the random direct genetic effect of animal l (N=990 and 1485 for lines A and B, resp.), and e ijkl the residual effect pertaining to animal j.

Results and discussion

Table 1 shows that under HS, temperatures of all areas increased in the same proportions in both lines, the increase being larger for the wing and the comb (+28.9 to +32.6%) than for the shank (+20.6 to +22.5%). It is to note that the increase of temperature in each zone during HS is strongly dependent on the temperature at TN, the former being higher when the latter is lower. At the contrary, variability was reduced under HS, especially for the shank (CV from 10.4 to 11.4% at 19°C, from 3.3 to 3.6% at 29°C). Heritability of surface temperature was close to zero for the wing area, and low but significantly different from zero for the shank and the comb. These values are consistent with previously estimated heritabilities of body temperature (0.06-0.19) or of surface temperature of the comb (0.02-0.21) in broilers and adult layers at TN for body temperature (Tixier-Boichard et al., 1995;[START_REF] Loyau | Thermal manipulation of the embryo modifies the[END_REF][START_REF] De | Genetic variability of metabolic characteristics in chickens selected for their ability to digest wheat[END_REF]. A low heritability for wing area could be expected as this zone is isolated by feathers and plays a less important role in heat dissipation than unfeathered zones. Moreover, as hens aged, their feather coverage deteriorated, and wing surface temperature was a mix of feather and bare skin zones, which makes the measure less reliable. Tixier-Boichard et al. (1995) found a much higher heritability of temperature in adult males than in females (0.49 vs 0.19), which suggests that the measure of the temperature in adult females can be disturbed by the daily variations due to the ovulatory cycle. In our study, measures of temperatures have been done during the whole day, i.e. at different moments of the ovulatory cycle for females measured in the morning or in the afternoon, which probably introduced an additional noise in the measure. There was also a large variability between birds for the comb size, which might lead to differences in the capacity of birds to dissipate heat through this body part. In our study, the shank was the most suitable area to measure accurately on a large number of animals, as required for genetic studies. The genetic correlation between shank and comb temperatures is moderately positive, indicating that, even if they play the same role in heat dissipation, their genetic control is partly different. For the future, standardizing the measure as proposed by Yahav and Giloh (2012) would probably reduce the noise in the measure and would probably lead to higher values of heritability, compatible with selection requirements. Analysis of the remaining pictures will also enable us to have enough data under HS to be able to analyze TN and HS temperatures as different traits and then to assess whether genetic control of surface temperature under HS or under TN are the same.

FLIR Systems Inc.,

SW Parkway Avenue, Wilsonville, OR 97070, USA

physiology and body composition of broiler chickens reared in floor pens without affecting breast meat processing quality. Journal of Animal Science 91: 3674-3685. MOUNT, L.E. and MONTEITH, J.L. (1974) The concept of thermal neutrality heat loss from animals and man. Butterworths, London, UK, 425-439. NEUMAIER, A. and GROENEVELD, E. (1998) Restricted maximum likelihood estimation of covariances in sparse linear models . Genetics Selection Evolution 1:3-26. TIXIER-BOICHARD, M., BOICHARD, D., GROENEVELD, E. and BORDAS, A. (1995) Restricted maximum likelihood estimates of genetic parameters of adult male and female Rhode Island Red chickens divergently selected for residual feed consumption. Poultry Science 74: 1245-1252. YAHAV, S. and GILOH, M. ( 2012) Infrared thermography -Applications in poultry biological research, Dr. Raghu V Prakash (Ed.), InTech, 93-116. 1. Example of thermal pictures of birds with a zoom in on the comb (1a at TN, 1b during HS), and on the whole body (1c at TN, 1d during HS).


Y Huang

D Andueza

J Ballet

L De Oliveira

F Zawadzki

S Prache

Visible spectroscopy on carcass fat to distinguish pasture-fed, concentrate-fed and concentratefinished pasture-fed lambs

Keywords:

The ability to authenticate the method of production of the food products has become a major challenge for scientists and monitoring bodies. This study compared two methods based on the use of visible reflectance spectrum of fat tissues to discriminate pasture-fed (n=76), concentrate-fed (n=79) and concentrate-finished (for 28 days) pasture-fed (n=69) lamb carcasses. The reflectance spectrum of perirenal and subcutaneous caudal fat was measured at slaughter and at 24 h post mortem. The method 1 used an index calculated from the reflectance spectrum data at wavelengths between 450 and 510 nm, whereas the method 2 was performed at wavelengths between 400 and 700 nm. Method 2 yielded higher overall proportion of correctly classified lambs than method 1 (92.9% vs. 64.7%, P<0.0001), regardless of the measurement time and site. The proportion of lambs which were correctly classified using method 2 was 95.6% and 95.9% for measurements made on perirenal fat at slaughter and at 24 h post mortem. This study indicates the importance of the zones of light absorption by carotenoid and haeminic pigments in the discrimination between lambs from three different feeding systems.

L'analyse du spectre de réflectance du tissu adipeux permet de discriminer trois modalités d'engraissement des agneaux : à l'herbe, en bergerie, ou avec une finition en bergerie après pâturage

Résumé. La possibilité d'authentifier le mode de production des animaux à partir de leurs produits est devenue un enjeu majeur pour les scientifiques et les organismes de contrôle. Cette étude a comparé deux méthodes basées sur l'analyse du spectre de réflectance dans le visible du tissu adipeux pour discriminer les agneaux d'herbe, les agneaux de bergerie et les agneaux d'herbe finis en bergerie pendant 28 jours. Les spectres de réflectance du gras périrénal et du gras sous-cutané caudal ont été mesurés à l'abattage et à 24 h post mortem. La méthode 1 a utilisé un indice calculé à partir de la zone du spectre de réflectance comprise entre 450 et 510 nm, alors que la méthode 2 a utilisé l'ensemble du spectre de réflectance entre 400 et 700 nm. La proportion d'agneaux correctement classés a été plus élevée avec la méthode 2 qu'avec la méthode 1 (92,9% vs. 64,7%, P<0.0001), indépendamment du moment et du site de la mesure. La proportion d'agneaux correctement classés par la méthode 2 était de 95,6% et 95,9% pour les mesures effectuées sur le gras périrénal à l'abattage et à 24 h post mortem. Cette étude montre l'importance des zones d'absorption de la lumière par les pigments caroténoïdes et héminiques dans la discrimination entre les trois types d'agneaux.

Mots-clés. Authentification -agneau d'herbe -agneaux de bergerie -finition -spectroscopie -ovinsagneau

I -Introduction

Consumers show growing interest in the method of production of their food and growing preference for food products of pasture-based systems of production [START_REF] Prache | Traceability of lamb production systems: carotenoids in plasma and adipose tissue[END_REF]. It is therefore important to be able to authenticate food products from particular production systems. The measurement of the reflectance spectrum of the fat has proven to be of practical interest since it is non-invasive, takes little time and can easily be implemented in the meat industry with a portable spectrophotometer. [START_REF] Prache | Traceability of lamb production systems: carotenoids in plasma and adipose tissue[END_REF] proposed a mathematical analysis of the reflectance spectrum of the fat at wavelengths between 450 and 510 nm (which corresponds to the zone of light absorption by carotenoids) to quantify the intensity of the signature of these pigments and discriminate pasture-fed from stall-fed lamb carcasses. [START_REF] Dian | Methodological developments in the use of visible reflectance spectroscopy for discriminating pasture-fed from concentrate-fed lamb carcasses[END_REF] increased the reliability of the discrimination between pasture-fed and stall-fed lambs by using the full data set of the reflectance spectrum at wavelengths between 400 and 700 nm. However, because of grass shortage during the summer period, pasture-fed lambs are often stallfinished with low-carotenoid diets. The purpose of this study was therefore to further test the reliability of these two spectral methods for discriminating lamb carcasses from less contrasted production systems (pasture-feeding, concentrate-feeding and concentrate-finishing after pasturefeeding).

II -Materials and methods

This study was carried out over 5 years (2008)(2009)(2010)(2011)(2012) at two experimental farms of INRA (Unité Expérimentale des Monts d'Auvergne and Unité Expérimentale des Ruminants de Theix). A total of 224 Romane breed male lambs were used: 76 were fed pasture for at least 60 days (P), 79 were stall-fed concentrate and straw (S) and 69 were fed pasture for at least 60 days followed by an abrupt switch to concentrate and straw indoors (PS) for 28 days. The P and PS lambs grazed pastures that were maintained at a leafy stage and offered ad libitum. The P lambs were fed pasture until slaughter. The PS lambs were expected to gain on average 7.0 kg LW gain (LWG) during the finishing period indoors. Stall-fed lambs were fed ad libitum a commercial concentrate, containing no green vegetative matter, and straw until slaughter. These last feedstuffs were given also to PS lambs during the stall finishing period. The lambs were slaughtered when they had reached a target body condition score of 3 (on a scale of 0 to 5), which was manually assessed by a skilled technician.

The reflectance (R) spectrum of perirenal and subcutaneous caudal fat was measured on all lambs, using a MINOLTA CM-2002 spectrophotometer (D65 illuminant, observer angle 10°). For each tissue, 5 measurements were made at slaughter and at 24 h post mortem. In method 1, the fat reflectance spectrum data were used at wavelengths between 450 and 510 nm to calculate an index quantifying light absorption by carotenoid pigments stored in the fat. The R spectrum was translated to give a reflectance value at 510 nm of zero (TR). On the translated spectrum, the integral value (I450-510) was calculated as follows: I450-510 = [(TR 450/2) + TR 460 + TR 470 + TR 480 + TR 490 +TR 500 + (TR 510/2)] × 10

The integral value was averaged and then linear discriminant analysis was performed, followed by a cross-validation procedure, to classify the fat samples according to feeding treatment, using Minitab software v. 13 (Minitab Inc., Paris).

In method 2, the full R data set at wavelengths between 400 and 700 nm was used. The R data were averaged, then transformed (log (1/R)) and exported into Win ISI II version 1.6 software (Infrasoft International, Port Matilda, PA, USA) for multivariate analysis. The raw R spectra of each tissue representing the three feeding treatments were submitted to discriminant analysis using a partial least squares discriminant analysis (PLS-DA) approach. A principal component analysis (PCA) performed beforehand was used to rank the reflectance spectra from each feeding treatment according to the Mahalanobis distance (H) to the average R spectrum, in order to detect sample outliers (H>3). No outliers were found. The models were tested via a cross-validation procedure, in which 56 randomly chosen samples were temporally removed from the initial data set to be used for validation (i.e. a quarter of all data samples). The PLS-DA model was developed based on the other samples (calibration samples) and used to classify the validation samples. This procedure was repeated four times, i.e. until all data set samples had been used through the validation procedure. The cross-validation error of the models was calculated.

The proportion of correctly classified samples was analyzed using the CATMOD procedure of the SAS (1999) software package using a four-factor model (feeding treatment: P vs. S vs. PS; discrimination method used in the fat: method 1 vs. method 2; site of measurement: perirenal vs. subcutaneous caudal fat; and time of measurement: at slaughter vs. at 24 h post mortem).

III -Results and discussion

The proportion of correctly classified samples using linear discriminant analysis performed on I450-510 (method 1) was 67.1%, 84.8% and 60.9% for P, S and PS lambs, respectively (70.9% on average), when the measurement was made on perirenal fat at slaughter, and 68.4%, 84.8% and 66.7% for P, S and PS lambs, respectively (73.3% on average), when the measurement was made on perirenal fat 24 h post mortem (Fig. 1). This method correctly classified 55.3%, 68.4% and 23.1% of the P, S and PS lambs, respectively (i48.9% on average), when the measurement was made on subcutaneous caudal fat at slaughter, and 76.3%, 69.6% and 50.7% of the P, S and PS lambs, respectively (65.5% on average), when the measurement was made on subcutaneous caudal fat 24 h post mortem. The method 2 allowed for the correct classification of 96.1%, 93.7% and 97.1% of the P, S and PS lambs, respectively (95.6% on average), when the measurement was made on perirenal fat at slaughter, and 96.1%, 98.7% and 92.8% of the P, S and PS lambs, respectively (95.9% on average), when the measurement was made on perirenal fat 24 h post mortem (Fig. 1). This method correctly classified 88.2%, 83.5% and 92.8% of the P, S and PS lambs, respectively (88.2% on average), when the measurement was made on subcutaneous caudal fat at slaughter, and 90.8%, 94.9% and 89.9% of the P, S and PS lambs, respectively (91.9% on average), when the measurement was made on subcutaneous caudal fat 24 h post mortem.

By using all the reflectance spectrum data at wavelengths between 400 to 700 nm, method 2 showed a higher performance (P<0.001) than method 1(Fig. 1), which only used the reflectance spectrum data at wavelengths from 450 to 510 nm to calculate I450-510. Taking both sites, both measurement times and all feeding treatments together, the overall proportion of correctly classified lambs was 64.7% for method 1 and 92.9% for method 2. The proportion of correctly classified lambs also differed between feeding treatments (79.8%, 84.8% and 71.8% for P, S and PS lambs, P<0.0001), measurement sites (83.9% for perirenal and 73.6% for subcutaneous caudal fat, P<0.0001) and measurement times (75.9% at slaughter and 81.6% at 24 h post mortem, P<0.001). Method 2 reliably discriminated the 3 types of lambs when the measurement was made on perirenal fat at slaughter (the proportion of correctly classified lambs ranging between 93.7% and 97.1%) and at 24 h post mortem (the proportion of correctly classified lambs ranging between 92.8% and 98.7%).

The PCA loadings of the two PC axes for perirenal fat measured at 24 h post mortem are shown in Figure 2. PC1 and PC2 axes explained 60% and 24% of variability. The highest loading was situated around 460 to 480 nm for PC1, indicating the importance of carotenoid pigments in the discrimination between the lambs from three different feeding systems. The PC1 and PC2 axes loading values at wavelengths around 420 nm and the PC2 axis loading value at wavelengths around 550-560 nm indicated that haeminic pigments [START_REF] Prache | Les défauts de couleur du tissu adipeux sous-cutané des carcasses d'ovins[END_REF] may also be involved in the discrimination between the lambs from three different feeding systems, as already suggested by [START_REF] Dian | Methodological developments in the use of visible reflectance spectroscopy for discriminating pasture-fed from concentrate-fed lamb carcasses[END_REF].

IV -Conclusions

Using the full set of the reflectance data of the carcass fat in the visible range (at wavelengths between 400 nm to 700 nm) enabled to reliably discriminate lamb carcasses from 3 production systems (pasture-feeding, concentrate-feeding and stall-finishing after pasture). The reliability of the discrimination at best with measurements made on perirenal fat at 24 h post-mortem. The proportion of lambs which were correctly classified using this method was 95.6% and 95.9% for measurements made on perirenal fat at slaughter and at 24 h post mortem. This method is of obvious practical interest for the meat industry, since it is non-invasive, rapidly and easily on-line implemented with a portable spectrophotometer.

Fig. 1 .

 1 Fig. 1. Proportion of correctly classified lambs using method 1 (integral value I450-510, white symbols) and method 2 (full reflectance spectrum data sets at wavelengths between 400 and 700 nm, black symbols) on perirenal and subcutaneous caudal fat measured at slaughter (a) and at 24 h post mortem (b). P: Pasture-fed lambs; S: Stall-fed lambs; PS: Stall-finished pasture-fed lambs

Fig. 2 .

 2 Fig. 2. Loadings for the two principal components axes (PC1 and PC2) for perirenal fat samples measured 24 h post mortem


J-F Louf

G Gu Éna

O Pouliquen

Y Forterre

H Cochard

B Moulia

É Badel

Stem bending induces hydraulic pulse in vascular system : a physical remote signal ?

1 IUSTI Laboratory, FRANCE 2 PIAF Laboratory, FRANCE

*

The perception of mechanical stimuli in the environment is crucial to the survival of all living organisms, and plants make no exception. At the tree scale, the bending of a stem leads to a transient growth response, not only locally but also far away from the stimulated area, suggesting the existence of a long distance signal within the plant network. The nature and mechanism of this long distance signal is not well understood, but it has been suggested that it could result from a purely hydraulic pressure signal, in response to the mechanical bending of the hydrated wood tissue. Recently, such hydro/mechanical coupling have been directly demonstrated in wood and living trees in the PIAF/INRA Laboratory. The objective of our work is to better understand the physical mechanisms responsible for this hydro/mechanical coupling by performing experiments on physical poroelastic beams mimicking stems and branches. To this end, we have designed an original three-dimensional micro-device consisting of a transparent elastomer beam (PDMS) perforated with longitudinal micro-channels and filled with a viscous liquid. The poroelastic response of this biomimetic branch to a sudden bending has then been studied in a closed geometry. The main result of this study is that the bending of the artificial branch generates a global overpressure in the system. This overpressure increases quadratically with the bending deformation, and is controlled by the pore bulk modulus of the media. We propose a simple physical model to explain our measurements and discuss the results in the context of plants.

E-mail address: jean-francois.louf@univ-amu.fr