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F Chazalon

S Rabouille

P Hartmann

A Sciandra

O Bernard

A Dynamical Model to study the Response of Microalgae to Pulse Amplitude Modulated Fluorometry

On-line monitoring growth of microalgal based processes is a challenging issue. Pulse Amplitude Modulated (PAM) fluorometers, used to closely monitor the physiological state of photosystems, do not provide an estimation of the growth rate, a critical information for culture management. We designed a model to represent the relation between the fast dynamics of photosynthesis and the slower process of cell growth in microalgae as a function of light. This model provides a synthetic view of photosystem II photochemistry and accounts for the main two states (open and closed) of photosystem II reaction centres as well as the following electron transport chain. The model is used to analyse the link between a very fast process (the transition between closed and open states), an intermediate one (the filling of the quinone-plastoquinone pool) and a slow process (growth rate fluctuations). Experiments were conducted on the Haptophyceae Tisochrysis lutea. Model parameters were calibrated on the measured fluorescence data. A slow-fast analysis is presented to describe the system dynamics. Results provide new insights for understanding and interpreting PAM measurements.

INTRODUCTION

Microalgae are microscopic photosynthetic organism with increasing biotechnological applications (Mata et al. 2011). Their composition offers very diverse high value compounds in the fields of pharmaceutics, cosmetics or food, as well as the potential production of biofuel [START_REF] Chisti | Biodiesel from microalgae[END_REF]). Yet so far, phototrophic microorganisms have been less exploited than bacteria or yeast, mostly because their growth-which is directly driven by photosynthesis--strongly depends on environmental conditions.

On-line monitoring of microalgal-based bioprocesses is thus a crucial challenge [START_REF] Bernard | Hurdles and challenges for modelling and control of microalgae for CO 2 mitigation and biofuel production[END_REF]Mairet et al. 2012). Although quite accurate, deriving the growth rate from cell counts or dry biomass weight measurements is costly, time consuming, and not immediate. Comparatively, real-time photosynthetic activity can be obtained by measuring microalgae fluorescence with a non-invasive, sensitive and fast method [START_REF] Govindjee | Sixty-three years since Kautsky: Chlorophyll a fluorescence[END_REF]. Unfortunately, the rate of photosynthesis is not a direct, experimental proxy of the growth rate. Better comprehension of these two processes can be expected by a modelling analysis at the time scale of the photosystem dynamics.

Photosynthesis initiates in photosystems (PS), the elementary bricks of the photosynthetic apparatus, in which photons are converted into chemical energy. This process is very fast, typically in the order of milliseconds. Photons absorbed by the photosystem antenna turn it into an excited state. Three distinct paths of de-excitation are possible to bring the reaction centre back to the ground state: (i) re-emission of a photon (fluorescence); (ii) initiation of photosynthesis through a series of photochemical reactions involving electrons transport in the cell membrane, called photochemical quenching [START_REF] Maxwell | Chlorophyll fluorescence -a practival guide[END_REF]; (iii) non-photochemical quenching through, e.g., thermal dissipation. The term "quenching" refers to any process lowering fluorescence [START_REF] Krause | Chlorophyll fluorescence and photosynthesis: the basics[END_REF]. Pulse Amplitude Modulated (PAM) fluorometers [START_REF] Quick | Studies of the induction of chlorophyll fluorescence in Barley protoplast. I. Factors affecting the observation of oscillations in the yield of chlorophyll fluorescence and the rate of oxygen evolution[END_REF]Schreiber, 1986) excite photosystems and measure the resultant fluorescence. Two kinds of photosystems are present on cells: type I (PSI) and type II (PSII). Fluorescence emission from PSI is independent from the state of the reaction centre [START_REF] Butler | Energy distribution in the photochemical apparatus of photosynthesis[END_REF], so that fluorescence variations can be attributed to PSII alone. We will work under this hypothesis, and the model we will derive will represent the state of PSII.

The goal of the present study is to use a model in order to gain more information from PAM measurements. The model represents the excitation of PSII centres in response to light and their consequent fluorescence dynamics. In particular, the model is used to analyze the links between a very fast process (the PSII photosynthetic yield) and a slow one (the cell growth rate). Experimental data, acquired on cultures of Tisochrysis lutea growing exponentially, are used for model calibration. Qualitative and quantitative analyses of the model are then performed.

PAM OPERATION

During the photochemical quenching process, chlorophyll a molecules transfer their excitation to the reaction centre P 680 (RC2) of PSII. A succession of oxidation-reduction steps reduces the first quinone Q A (figure 1) and the photosystem closes: energy can no more be transferred to RC2 until Q A is reoxidized by the downstream electrons acceptors Q B and PQ. The corresponding energy transfer through the electron transport chain eventually leads to CO 2 fixation. The irradiance applied to the microalgae in a PAM results from the sum of three elementary light signals: (i) a constant, background irradiance at a chosen intensity to create an ambient light field which will partly close the reaction centres; (ii) brief saturating pulses whose very high intensity closes all reaction centres and (iii) a pulsed, light with very weak intensity (typically, lower than 1 µE.m -2 .s -1 ). All three induce fluorescence, but while the first two are said "actinic" as they trigger photosynthesis, the third one is the measuring light, whose crenel shape allows for the detection of fluorescence capacity variations in the PAM by signal filtering.

MATERIAL AND METHODS

Species considered

The unicellular photosynthetic eukaryote Tisochrysis lutea [START_REF] Bendif | On the description of Tisochrysis lutea gen. nov. sp. nov. and Isochrysis nuda sp. nov. in the Isochrysidales, and the transfer of Dicrateria to the Prymnesiales (Haptophyta)[END_REF]) was used for the experiments. Cultures were grown at 27°C under a light intensity of 400 µE.m -2 .s -1 . Fluorescence monitoring was performed on subsamples from the cultures taken in the exponential phase of growth.

Experimental procedures

Fluorescence measurements were conducted with a Multicolor PAM (Walz, Effeltrich, Germany) using a blue excitation light. Samples were diluted in filtered sea water and incubated in the dark for twenty minutes prior to measurement. The excitation protocol used is described in figure 2. Fluorescence is recorded for increasing levels of actinic light, and two saturating pulses are applied at each irradiance level.

Fig. 2. Excitation protocol applied to the sample in order to calibrate the model.

MODEL DESIGN

The fluorescence model

After the reception of a photon, PSII undergoes several excitation phases depending on the oxidation (or reduction) state of the donor and acceptor molecules. In the present model, these phases are represented in a simplified manner by only two states: The fraction A, representing open photosystems, and the fraction B, representing the closed photosystems. Contrary to other existing models [START_REF] Eilers | Dynamic behaviour of a model for photosynthesis and photoinhibition[END_REF]Peeters 1993, Han, 2002) we do not explicitly represent the dynamics of damaged and inhibited states of PSII following the reception of excess photons. However, due to the short time scales of measurements within a PAM (a few minutes), we will consider a dynamics of PSII deactivation due to light stress. The total number of non deactivated PSII is given by n, which decreases depending on the received light I:

n D n ⋅ ⋅ - = 0 α & (1)
where D is the cumulative damage to the photosystem:

I D = &
. By abuse of notation, A will be called the proportion of open PSII (in the total number of non inhibited states), the total number of open PSII being nA. Closed PSII (of proportion B=1-A, and of number nB) are associated to various level of quinone and plastoquinone pool oxidation. Hence, we gathered quinones and plastoquinones in a pool receiving electrons from the B state, and the degree of reduction of this pool is denoted q. The pool is normalized, meaning that when q is 1, the maximum electron carrying capacity has been reached. The conceptual scheme is represented on figure 3.

Fig. 3. Model conceptual scheme. Dashed and solid lines represent qualitative and quantitative relationships between variables, respectively

The photon flux closes reaction centres (transition from A to B) while their re-opening (transition from B to A) depends on the downstream flux of electrons through pool (q). Equation (2) expresses the dynamics of A:

( ) ( ) q B A I A - ⋅ ⋅ + ⋅ - = 1 α γ & (2)
where α tunes the return from state B to A, this transfer being higher when electrons have been used and q is close to zero. The function γ controls the transfer rate from the state A to B. Since γ(I)/I is decreasing with I, we assume the following function:

( ) q k q B q µ β - - ⋅ ⋅ = 1 & (3) The term ( ) q B - ⋅ ⋅ 1
β represents the rate of electrons filling pool q. The energy flux is mainly used in the Calvin cycle and leads to CO 2 fixation, i.e. biomass growth. The growth rate, denoted µ therefore modulates the rate at which electrons are consumed in chemical reactions. In our model, we assume that the fraction of light energy dissipated under non photochemical quenching (mainly heat) is constant. Constant β controls the refill rate of quinone/plastoquinone, while the rate of electron use is associated to constant k. In order to represent the (slow) resulting changes in the growth rate, we introduced the following growth dynamics:

µ α α µ ⋅ - ⋅ = 2 1 q & (4)
Electrons departing from the pool q stimulate the growth rate. Finally, the fluorescence for a given state (A,q) is the sum of a constant background fluorescence and a fluorescence due to the impossibility of state B to use the excess of photonic energy:

I F B n I A F ⋅ + ⋅ ⋅ ⋅ = 0 1
Where F 0 is the fluorescence obtained when photosystems are all open. Constant A 1 is the fluorescence rate per unit of actinic light.

PAM measurements

The PAM performs two fluorescence measurements: F + at the light I + δI and F -at I (δI is the measurement light):

( ) ( )

I I F B I I A F δ δ + ⋅ + ⋅ + ⋅ = + 0 1 I F B I A F ⋅ + ⋅ ⋅ = - 0 1
Finally, the information which is given is Model equations, expressed with variable B=1-A, read:

( ) ( ) ( ) ( ) n D n I D q q k q B q q B B I B ⋅ ⋅ - = = ⋅ - ⋅ = - - ⋅ ⋅ = - ⋅ ⋅ - - ⋅ = 3 2 1 1 1 1 α µ α α µ µ β α γ

DYNAMICS ANALYSIS

Quantitative analysis of the model for a constant growth rate

We studied the model dynamic behaviour in the case of a constant µ. This simplification is reasonable as both B and q vary much faster than µ. The nullcline for q is given by: ( )

* * * 1 q q k B - ⋅ ⋅ = β µ (a)
The nullcline for B is given by, The equilibrium results from the intersection of the two nullclines. This equilibrium is unique. Indeed, at the equilibrium point we get: Property: the equilibrium (B*, q*,µ*) of the subsystem (B, q,µ) is globally asymptotically stable on the physical domain.

( ) ( ) ( ) * * * 1 q I I q q k ⋅ - + = - ⋅ ⋅ ⋅ α α γ γ β
Sketch of the proof: first note that variables B and q are both bounded between 0 and 1: Variable µ is also lower bounded. Since q<1, we have The bounds of these variables define the (convex) physical domain. Moreover, if we consider the change of variable ρ = 1-q, the system (B, ρ, q) is competitive in the sense that the extradiagonal terms of the Jacobian matrix are all non positive.

The computation of the Jacobian matrix at steady states shows that the equilibrium is locally stable.

As a consequence, for this three dimensional system, if there is a single locally stable equilibrium in the physical domain in which the system stays, this equilibrium is globally stable [START_REF] Smith | Monotone Dynamical Systems[END_REF].

Simulation of the response to a flash in presence of actinic light: a slow fast analysis

Here we focus on the subsystem (B,q), assuming a constant growth rate (the dynamics of the growth rate is slower than that of B and q). We first show that it is a slow fast system of the type:

With the parameter choice from Table 1, we get the following equations:

For I ≥ 200, θ = 0.1 and there is a 10 times faster dynamics for C than for q.

The behaviour of the system can then be analysed as a response to the classical PAM measurement protocol. Darkincubation is first performed to fully reduce (re-open) all reaction centres and let electrons drain away from pools, so that initially B=0 (all the reaction centres are open) and q=0 (no electron in the plastoquinone pool). An example of dynamics following light stimulations is presented in figure 5. A sub-saturating actinic light of 200 µE.m -2 .s -1 is applied; the system (q, B) moves along path (1) and reaches the equilibrium corresponding to this new irradiance level. This is first done by rapidly reaching the slow manifold:

The dynamics of the system then reduces to: , Then q goes towards its equilibrium, continuously increasing. Since B(q) is an increasing function of q, during this period on the slow manifold, B is also increasing. Then, a saturating flash is applied (2), B rapidly increases and reaches a new pseudo equilibrium so a new slow manifold value is reached for I=3000 µE.m -2 .s -1 . The new value obtained for B(q) is then very close to 1. Since the flash is brief, q hardly changes in the meantime. After the flash (3), B rapidly decreases to reach its new value B(q). Variable q still slowly increases towards its equilibrium (the plastoquinone pool is filling up). Finally, B and q decrease (4) until they reach back the equilibrium point corresponding to the constant, 200 µE.m -2 .s -1 ambient irradiance. This slow-fast dynamics is characteristics of the measured response of fluorescence as a response to constant lightflash -constant light (figure 2). The model was calibrated using experimental data obtained in an experiment where multiple excitations have been made

(table 1). The results are then compared to new experimental data.

The experimental fluorescence and the fluorescence from the model simulation are compared on Figure 6. Two saturating pulses have been applied firstly in dark condition and then in the case of five increasing light levels. After each level of sub-saturating actinic light, the intensity of light comes back to 0.05 µE.m -2 .s -1 (measuring light).

The maximum fluorescence level from the flashes diminishes through time in the case of both the simulation and the experiment. The levels of fluorescence decrease through time after the application of actinic sub-saturating light, especially in the case of the last levels of fluorescence.

DISCUSSION

The model describes experimental data with fair accuracy, and in particular the fluorescence levels following application of saturating pulses. The decrease in fluorescence after a flash is mainly due to the combination of both the natural decrease in B under lower light and the destruction of a fraction of reaction centres due to the succession of flashes of high intensity (dynamics of n). This could also be represented by a variation in the amount of energy dissipated through non photochemical quenching. Fluorescence equilibria obtained for different sub-saturating, actinic light levels are relatively well described by the model. The slope of the simulated, last three levels are not as pronounced as in the experiment. The last levels of fluorescence resulting from the actinic sub-saturating light level showed a decrease through time. This could be explained by the progressive activation of carbon fixation processes (photochemical quenching). This may result from a change in the growth rate µ, which is poorly described by the model and which may lead to an increased demand in electrons, thus reducing more rapidly the fluorescence. This part of the model must probably be validated using microalgae sampled from cultures with different growth rates. Coherency between these growth rates and parameter µ in the model must be checked. The model could then be used to inverse the problem and estimate µ from the dynamics of fluorescence. The model will then be used to design an observer in order to estimate the growth rate µ from the measurements of the fluorescence response to series of flashes, and thus provide a simple way to monitor the status of a microalgal culture.

Fig. 1 .

 1 Fig. 1. Decomposition of the photochemical reaction steps. Chl a: chlorophyll a; P 680 : reaction centre, Pheo: Pheophytin molecule; Q A and Q B : quinones A and B; PQ: plastoquinone; Y z : a tyrosine molecule; OEC: Oxygen Evolving Complex; P: PSII; D and A: electron donors and acceptors.

  , K I and γ ~ are constants, with ε << K I . The dynamics of the quinone/plastoquinone pool is then:

  1 (all reaction centres are closed), the PAM response is called F m . And for B = 0 (all reaction centres are open), F D = F 0 .

µ

  Which strictly positive. Moreover, It can be checked that:, showing that 1 is between the two roots of the equation. Finally, since π(0) < 0, only one root is in the physical domain [0,1].

Fig. 4 .

 4 Fig. 4. Phase plane of the model for I = 100 µE.m -2 s -1 including the simulation of some trajectories starting from different initial points (C,q). The black cross represents the equilibrium point. Arrows show the direction of the model trajectories. Black numbers are the coordinates of the initial points and the equilibrium.

Fig. 5 .

 5 Fig. 5. Representation of variables trajectories during a flash, in presence of actinic light. The black cross represent the equilibrium point for I = 100 µE.m -2 .s -1 . Arrows show the direction of model trajectories. The successive steps are represented by green numbers. 5.3. Model calibration/parameter identificationTable 1. Parameter values

Fig. 6 .

 6 Fig. 6. Variation of experimental (blue curve) and simulated (green curve) fluorescences through time. Blue dashes locate the maximum of fluorescence in the experimental data.

  proposed a synthetic view of the photosynthetic apparatus dynamics. The model involves three different scale of variation: a fast one for the direct response to the absorbed photons, an intermediate one for the filling of the quinone/plastoquinone pool and a slow one for the microalgal growth rate. The qualitative behaviour of the model was analysed and fairly matches the known response of fluorescence to a light pulse. The model has been calibrated based on PAM measurements on Tisochrisis galbana. More work remains to be done to better describe the dynamics of the growth rate µ.

& & & & &

Acknowledgements: this work was supported by the ANR-13-BIME-004 Purple Sun.


Maha Chalhoub
email: m.chalhoub@brgm.fr

Mikael Philippe

Yves Coquet

A Field Experiment to Assess the Influence of Heat and Mass Transfer at the Soil Surface on Shallow Ground Heat Exchanger Performances

Keywords: heat transfer, energy balance, Shallow Ground Heat Exchanger, soil moisture

Prediction of soil thermal regime is still a difficult task for design of ground-coupled heat pump system units (GCHP). A Field experiment was carried out to study the near-surface and moisture transport effects on soil temperature distribution. Energy balance components at the soil surface was monitored using a meteorological station, that included a pyrgeometer and a pyranometer to measure short and far infrared radiation, and using two heat flux plates installed in the soil at a depth of 0.08 m to measure ground heat fluxes. A 2.5 m deep trench has been dug in order to (i) characterize soil hydraulic and thermal properties at different depths and (ii) install tensiometers and thermocouples allowing continuous measurements of soil water tension and soil temperature. We observed that variations of soil properties along the profile as well as compaction influenced soil thermal properties. Results showed that temporal variations of soil heat flux at 8 cm depth closely followed those of available energy (net radiation), vertical turbulent heat fluxes (latent and sensible fluxes) near the soil's surface.

INTRODUCTION

Shallow geothermal energy sector is continuing to grow at a higher than expected rate: more than 66.000 ground-coupled heat pump system units (GCHP) are installed worldwide annually. 80 % of these installed units are domestic [START_REF] Lund | Direct utilization of geothermal energy[END_REF]. Knowledge of ground temperature distribution is a key parameter for design of GCHPs, such as to define the possible geometrical configurations, and also for their performance enhancement [START_REF] Florides | Review Ground heat exchangers -A review of systems, models and applications[END_REF]). Prediction of soil thermal regime is still a difficult task. This is mainly because that soil temperature near the surface is a property that changes spatially and temporally in response to numerous factors. For this, a test facility has been carried out in Orleans, France since 2008 to optimize performance of shallow geothermal energy systems [START_REF] Marchio | An Evaluation of Ground Thermal Properties Measure Accuracy by Thermal Response of Horizontal Ground Heat Exchangers[END_REF]. The test facility was equipped with GHE of various geometries: horizontal ground heat exchangers (HGHE), coil-shaped GHE and borehole heat exchangers (BHE). The Scientific objectives of this facility are to improve understanding interactions with the surrounding soil (e.g. climatic parameters, geological properties, soil cover) and to determine the performances of new types of ground heat exchangers.

Near-surface and moisture transport effects on soil temperature distribution are usually neglected or have been addressed by relying on extreme simplifications during the design and sizing of shallow ground heat exchangers such as horizontal ground heat exchangers (HVAC&R Research, 2011). The present study aims to investigate at field scale, near-surface processes related to ground temperature variation during soil wetness and dryness to allow a better design of shallow ground heat exchangers

EXPERIMENTAL SET UP

Soil temperature is governed by two kinds of processes: (a) energy exchange/transfer at earth-atmosphere boundary (b) heat propagation within the soil which can vary substantially with moisture content. The former one determines the energy quantity stored in the soil, the latter one control how energy is distributed once inside the soil [START_REF] Saito | Effects of meteorological models on the solution of the surface energy balance and soil temperature variations in bare soils[END_REF][START_REF] Smits | Thermal conductivity of sands under varying moisture and porosity in drainage-Wetting Cycles[END_REF].

For this, continuous measurements of parameters needed to fully evaluate energy and moisture balance were carried out in situ at the geothermal energy test facility to investigate energy transfer between soil and atmosphere and study the thermal and moisture regimes. Figure 1 shows the test facility where these measurements have been processed.

Energy balance components at the soil surface were monitored using a meteorological station and heat flux plates (Figure 2). The net short radiation is measured with an albedometer composed of two pyranometers, mounted back-to-back, model LP PYRA 05, one looking upward (sky) and one downward (earth). The upward pyranometer measures the incident global radiation (direct radiation + diffuse radiation) striking the ground, while the downward one, measures the global radiation reflected from the ground. The incoming far infrared radiation is measured with Pyregeometer, model LP PIRG 01 (DeltaOHM S.R.L.).The outgoing longwave radiation was measured using the soil surface temperature Ts(εσ(T S + 273.16) 4 ) measured at 0.03m, where ε is the emissivity of grass cover (e =0.9) and σ is Stefan Boltzmann's constant (σ = 5.67x10-8 WK-4m-2) Soil heat flux is measured by two heat flux plates Hukseflux Self-Calibrating plates (Campbell Sci, type HFP01SC) installed in the soil at a depth of 0.08 m. The self-calibration corrects the errors due to thermal conductivity differences between the sensor and the surrounding medium, temperature variations, and slight sensor instabilities.

At a 2 m height, the air relative humidity and temperature (Figure 2a) are measured respectively with capacitive humidity and a Platinum temperature sensors (100Ω @0°C) (Delta-OHM, model HD9008TRR).

A 2.5 m deep trench has been dug in order to (i) characterize soil hydraulic and thermal properties at different depths and (ii) install tensiometers and thermocouples allowing continuous measurements of soil water tension and soil temperature (Fig. 2). Tensiometers (two at each depth) were installed at the 20, 45, 100 and 140 cm depths. Soil temperatures, T, are measured by thermocouples type T at depths of 00.3, 0.06, 0.14, 0.2, 0.3, 0.5, 1 and 1.5m (two thermocouples for each 0.03 and 0.06 m depth). Measurements are recorded every ten minutes Soil hydraulic and thermal properties and soil physico-chemical characteristics were measured at the time the thermocouple probes and tensiometers were installed. Soil samples were extracted at 4 depths: 10-20cm, 40-50 cm, 90-105 cm, 145-155 cm and 195-205 cm, coinciding with soil distinct horizons. Three replicate profiles were taken for each measurement to provide a better idea of the within-plot variability.

Soil water retention curves of the soil were measured with the pressure plate apparatus using 50 cm3soil cores. Average bulk density profiles were measured by sand replacement method (AFNOR, 1996 -NF P 94-061-3) using soil cores of 5 cm by 8.4-cm diameter. The hydraulic conductivity -water potential relation was measured with a disc infiltrometer at different matrix potentials from -10 cm up to -0.5 cm (using the multipotential method of Ankeny et al. ( 1991)) [START_REF] Coquet | Caractérisation hydrodynamique des sols à l'aide de l'infiltromètre à disque. Aspects théoriquesetpratiques[END_REF].

Undisturbed soil samples (10 cm length by 11 cm diameter; with three replicates per depth) were taken at different depths (10-20cm, 40-50 cm, 90-105 cm, 1145-155 cm and 195-205 cm) to determine the soil thermal properties. Volumetric heat capacity (Cv, MJ.m-3.°C-1 ), thermal conductivity (k, W.m-1.°C-1) and gravimetric water content were determined for each sample. The given measurements were conducted using an ISOMET 2114 thermal conductivity instrument (Applied Precision Ltd., Slovakia), portable measuring apparatus, and by means of a surface probe at room temperature and according ASTM D 5334-08 et ASTM D 5930-09 methods. Three measurements were made at each depth. The grass cover is mowed regularly, has a mean weight of 0.12 m and a mean leaf area index, LAI, 2.88 (FAO, with LAI=24*0.12).

RESULTS

The monitoring data were used to investigate the interactions between heat transfer and saturated/unsaturated moisture transport caused by solar radiation, rainfall, evapo-transpiration and water table so as to determine the key processes controlling ground temperature and moisture distribution.

Based on particle size distribution, the soil is sandy; the main physico-chemical characteristics are described in Table 1. Low organic matter contents ranging from 1 to 2 %, were found in the middle and deep layers. Soil contained large proportion of gravels (between 33 and 46%) then we classify it at "gravelly soils" (Poesen and Lavee, 1994). Higher concentrations of gravels at the soil surface compared to the soil horizons below (between 33 and 46%). Subsurface layers are more compacted and have less organic matter, compared to surface layers, therefore contain less pore space. Soil porosity was calculated from measured bulk density. High bulk density is an indicator of low soil porosity (Figure 3a,b) and water holding capacity. The top layer (Figure3b), 10-20 cm, had larger water retention than deep layers mainly in the range of macropores (pF 0 -pF 1.5). The highest mobile water content is observed in the 10-20 cm layer and the lowest in the deep layers.In the range of micropores (pF 2.2 -pF 4.5), the water retention curve of this layer showed changes in the slope tending to converge in the micro pore range. The amount of larges pores decreased with depth, but the volume of fine pores (i.e. the volumetric water content between pF1.2 and 4.2) seems equal along the profile. This is related to the fact that the soil texture did not change with soil compaction, therefore, the amount of micro pores remain constant [START_REF] Kutilek | The influence of uniaxial compression upon pore size distribution in bi-model soils[END_REF]. As the bulk density increases with depth, the pore volume decreases, resulting in a decrease of saturated hydraulic conductivity (Figure 3c).

Thermal properties measurements (Figure 4) showed that local soil thermal conductivity and heat capacity measured at each depth were slightly variable. Coefficients of variation of local thermal conductivity calculated from the three replicates were between 23 and 3 % respectively for the 10-15 cm and 195 and 205 cm layers. Variation coefficients of local heat capacity were between 1 and 9 %. Variability in local soil thermal properties can be explained by spatial variation of gravel content. The porosity of soil varies spatially in general and in the presence of gravels, the variability increases because of the range and tortuosity associated with gravel fragments (the differences in the behavior of fine earth and gravels during the process of wetting and drying, poor soil contact in gravelly soils) (Poesen et Lavee, 1994).

Variations (increase/decrease) of measured Cv and k properties as function of water content were greater in samples taken from depth of 10-15cm. k varies from 1.15 to 1.83 W/m/K (59% increase) as volumetric water content increases by 12 % (from 17 to 18 cm3/cm3). However, k varies from 2.04 to 2.15 W/m/K (5% increase) as water content increases by 5% (from 14 to 15 cm3/cm3).

No clear trend emerges from the measured thermal properties as how thermal conductivity varies with depth despite the fact that bulk density increases with depth. Our results are not in accordance with pervious investigations that showed that thermal conductivity increases with increasing density as a result of better particle contact with a decrease in porosity and a greater mass of solids per volume unit (Smits et al., 2009;[START_REF] Nidal | Soil thermal conductivity: Effects of density, moisture, salt concentration, and organic matter[END_REF]. Thermal properties data are scarce and incomplete as thermal conductivity and heat capacity are not measured in a continuous manner at varying soil water contents.

. Figure 5 showed the temporal evolution of soil temperature at different depths. The soil temperature varies differently with depth; the soil temperature of the surface layer is the most affected by atmospheric variations. Diurnal variations are more important at the soil surface than for deeper layers where there are almost no observed diurnal temperature changes. We note that seasonal variations / fluctuations are more pronounced in deeper layers, meaning that these variations might be more critical for the longterm simulations and cannot be neglected. This might be related to the fact that the measured soil properties differed along the profile (with depth). At a given matrix potential the topsoil has higher water content than deeper depths, and then corresponding k and Cv reach higher values. The top layer (Figure3b), 10-20 cm, has larger water retention than deep layers then, thermal inertia proportionally is higher as well, reducing the diurnal temperature fluctuation in the deep layers. A positive correlation (R 2 =0.198) was observed between net radiation and soil heat flux at 8 cm depth (Figure 7a). Soil heat flux is better described when plotted versus net radiation and convective terms (latent and sensible heat flux (R 2 increases from 0.198 to 0.3512), meaning that temporal variations of the soil temperature follow those of available energy, vertical turbulent heat fluxes near the soil's surface being thus not insignificant.

CONCLUSIONS

We can conclude that different soil characteristics along the profile as well as compaction rate influence soil thermal properties.

The topsoil layer (with high porosity and high water content) can store more heat, and, as a result of different soil properties, the atmospheric variations do not affect the soil thermal regime in the same manner along the profile. The thermal properties, conductivity and volumetric heat capacity, increase with water content. We observed that soil heat flux at 8 cm varies in response to changes in radiant, thermal and latent energy exchange processes that take place at the soil-atmosphere interface. Data analyses are still in progress. In the future, recommendations will be proposed to improve the design of shallow ground heat exchangers (e.g. modification of the soil cover, adaptation exchanger implantation depth).

Figure 1 :

 1 Figure 1: (a) Overview of the test facility in France with horizontal ground heat exchangers (HGHE), (b) Three borehole heat exchangers (50 m deep double-U, coaxial exchanger and 100 m deep double-U exchanger) used to understand the influence of hydro-thermal soil properties on heat transfer (c) Coil-shaped GHE made of copper

Figure 3 :

 3 Figure 3: (a) Bulk densities profiles measured at the study site and the percent of total soil volume made up of pore space (Soil porosity (%) = 1-(soil bulk density / 2.65). The default value of 2.65 is the mean particle density of rock with no pore space, (b) and (c) water retention curve and saturated hydraulic conductivity measured at different depths. Water retention curve express the relation between matrix potential and water content.

Figure 4 :

 4 Figure 4: Volumetric heat capacity and thermal conductivity measured in the different layers as a function of water content

Figure 5 :

 5 Figure 5: Soil temperature variations with time and depth (a) seasonal variations, and (b) diurnal variations

Figure 6 :

 6 Figure 6: Diurnal variation in energy balance at the soil-atmosphere interface for the 20th and 21th of February 2014.

Figure 7 :

 7 Figure 7: Scatter graph of the net radiation (Rn) versus the soil heat flux measured at 8cm depth, (b) net radiation minus sensible heat flux (H) and latent heat flux (LE) versus soil heat flux at 8 cm depth.

Table 1 : Main soil physico-chemical characteristics (average value of 3 sampled profiles ± standard deviation)

 1

		10-15cm	40-50cm	95-105cm	145-155cm 190-200cm
	Clay, g.kg -1 dry wt.	60 (5)	59 (7)	72(10)	56(6)	38
	Silt, g.kg -1 dry wt.	98 (10)	89 (11)	43 (4)	50(2)	80
	Sand, g.kg -1 dry wt.	468(21)	421 (21)	560 (73)	508 (27)	425
	Gravel content, g.kg -1 dry wt.	374(15)	430 (25)	325 (69)	386 (27)	457
	OM a , %	3 (0.3)	1 (0.1)	1 (0.1)	1 (0.1)	2
	Bulk density, Mg.m -3	1.58 (0.07) 1.94 (0.27) 2.03 (0.07) 2.13 (0.02) 2.02 (0.02)

a OM: organic matter content Soil characteristics (e.g. bulk density, degree of wetness, soil heat capacity), which govern temperature regime, were monitored at different depths. Bulk density increases with soil depth which can be related to the fact that subsurface layers are more compacted.


Quaternion softmax classifier R. Zeng, J.S. Wu, Z.H. Shao, L. Senhadji, H.Z. Shu

For the feature extraction of RGB colour images, researchers usually deal with R, G and B channels separately to get three feature vectors, and then combine them together to obtain a long real feature vector. This approach does not exploit the relationships between the three channels of colour images. Recently, attentions have been paid to quaternion features, which take the relationships between channels into consideration and seem to be more suitable for representing colour images. However, there are only few quaternion classifiers for dealing with quaternion features. To meet this requirement, in this paper, we propose a new quaternion classifier, namely, quaternion softmax classifier, which is an extended version of conventional softmax classifier generally defined in complex (or real) domain. We apply the proposed quaternion softmax classifier to two of the most common quaternion features, that is, quaternion principle components analysis (QPCA) feature and colour image pixel feature. The experimental results show that the proposed method performs better than quaternion back propagation neural network (QBPNN) in terms of both accuracy and convergence rate.

Introduction: In recent years, research in the field of machine learning was stimulated by unsupervised feature learning approaches, especially deep learning [START_REF] Charalampous | Sparse Deep-Learning Algorithm for Recognition and Categorisation[END_REF]. Features that are obtained by means of learning algorithm have been widely used in computer vision, language detection, voice recognition and so on. How to classify these features effectively is a challenge.

On the other hand, the theory and application of quaternion or hypercomplex algebra, invented by Hamilton [START_REF] Hamilton | Elements of quaternions[END_REF], has received many attentions in recent years [START_REF] Ell | Hypercomplex Fourier Transforms of Color Images[END_REF][START_REF] Sangwine | Fourier Transforms of Colour Images Using Quaternion or Hypercomplex, Numbers[END_REF][START_REF] Le Bihan | Quaternion Principal Component Analysis of Color Images[END_REF]. Subsequently, Some researchers did studies in quaternion features extraction, for example, Ell and Sangwine [START_REF] Ell | Hypercomplex Fourier Transforms of Color Images[END_REF][START_REF] Sangwine | Fourier Transforms of Colour Images Using Quaternion or Hypercomplex, Numbers[END_REF] used the quaternion Fourier transform to colour image processing, in which they represent colour image pixels using quaternion (i.e. quaternion pixels). Bihan and Sangwine [START_REF] Le Bihan | Quaternion Principal Component Analysis of Color Images[END_REF] proposed quaternion principal component analysis (QPCA) as a new feature extraction method for colour image. Risojevic and Babic [START_REF] Risojevic | Unsupervised Learning of Quaternion Features for Image Classification[END_REF] combined QPCA features with kmeans clustering in real domain for colour image classification, they concluded that QPCA is superior to RGB PCA in colour image features extraction. Other researchers did studies in quaternion features classifiers. Arena et al. [START_REF] Arena | Multilayer Perceptrons to Approximate Quaternion Valued Functions[END_REF] proposed quaternion back propagation neural network (QBPNN), which is probably the most frequently used classifier for quaternion features and performs better than classical real neural network (NN) when dealing with features classification problem. QBPNN also performs better than classical real neural network in chaotic time series prediction [START_REF] Arena | Chaotic time series prediction via quaternionic multilayer perceptrons[END_REF]. Chen et al. [START_REF] Chen | Color Face Recognition Based on Quaternion Zernike Moment Invariants and Quaternion Bp Neural Network[END_REF] represented colour face images by quaternion Zernike moment invariants features, which are then classified by QBPNN.

Quaternion features are superior to real features in representing the colour images, however, the frequently used QBPNN classifier still encounter the problem of low classification accuracy and slow convergence rate. Therefore, quaternion features classifiers with high classification accuracy and fast convergence rate are highly needed. To meet this requirement, in this paper, we propose a new quaternion classifier, namely, quaternion softmax classifier, which is an extended version of the conventional softmax classifier generally defined in real domain.

Quaternion algebra: A quaternion x is a hypercomplex number, which consists of one real part and three imaginary parts as

xx s x (i) ix (j) jx (k) kℚ (1)
Where ℚ denotes quaternion number field, x s , x (i) , x (j) , x (k) ℝ, ℝ denotes the real number field, and i, j and k are three imaginary units obeying the following rules:

i 2  j 2  k 2  ijk  -1, ij  k, jk  i, ki  j, ji  -k, kj  -i, ik  -j.
It should be noted from this that multiplication of quaternion numbers is not commutative. The l 2 norm of quaternion x is defined as

222 2 ( s )( )( )( ) ijk x xxx x   
. The inner product of two quaternions are (x, yx (s) y (s) ,

x (i) y (i) , x (j) y (j) , x (k) y (k) .
Proposed method: Given a label set Y  {1,2,...,r} and a quaternion input pattern x  x 1 , x 2 ,… , x n  ℚ n , the hypothesis to estimate the probability of each label, can be defined as follows:

     1 2 1 2 2 1 1| 1 | T T h T r x r x x r h e pY Hx e pY r e                     (2)
Where θ 1 , θ 2 ,…, θ r ℚ n , θ h = {θ h1 , θ h2 ,..., θ hn }, are the quaternion parameters of this model, and

()() ()() ()() ()() TT T T T hs s hi i h j j hk k h xx x x x ee ei e j e k  
   . The summation term normalizes the distribution of quaternion data, makes its summation to one, to meet the probability criteria.

The cost function of quaternion dataset X  {x 1 , x 2 ,..., x m }, which contains m patterns, is defined as:

    (g) (g) 2 2 11 1 1 log T h T l x mr g r x gh l e JY h m e                      1 ( 3
)
Where 1 is a logical value function, that is, when a true statement is given, 1{}  1, otherwise 1{}  0.

The updates of the quaternion parameters are determined by the gradients of Jθ with respect to the network parameters, then we get θ new  θ old  θ, where θ  Jθθ hq . The quaternion parameters θ hq are updated according to the following equations by gradient descend method: In learning phase of QBPNN and proposed method, we used min-Func matlab toolbox [START_REF] Schmidt | minFunc: Matlab software for unconstrained different iable multivariate optimization[END_REF] for numerical optimization. We set optimized method to 'L-BFGS' for both experiments to search the global minimum. In order to obtain enough accuracy, we set the maximum number of iterations to 300. Learning rate and iteration step are set to default values of toolbox.

  () () () () () 2( ) 2( ) () () () 2 2 1 1 () () 1 () 1 2 2 ,
To clearly illustrate the simulation results, we used the negative logarithm of the cost function (-log J) to describe the evolution of the error with respect to the iteration number.

In quaternion pixels features experiments, every training pattern is normalized by subtracting the mean and dividing by the standard deviation of its elements. For nature images, this corresponds to local brightness and contrast normalization. After normalizing each training picture, the entire training database is processed with a popular method called whitening, which makes the input less redundant (i.e. uncorrelated). Then these processed colour images are represented as a purely imaginary quaternion of the form R•i+G•j+B•k. So we get desired quaternion pixels features to train the classifier. The performance of the proposed algorithm (95.33%) is better than classical QBPNN (92%) for the quaternion pixel features of the noiseless images. As shown in Fig. 1a, our approach exhibits faster convergence rate than QBPNN method. To consider real situation, two kinds of noises (Gaussian and Salt & Pepper) are added to the raw images in the testing process, before using the above method to pre-processing. The standard deviation (STD) of Gaussian noise varies from 5 to 20. The density (D) of Salt & Pepper is changed from 0.02 to 0.05. All experimental results are shown in Table 1.

a b

Fig. 1 The convergence rate using two different methods in QPCA features and colour image pixel features respectively. a The convergence rate of noiseless colour image pixel features b The convergence rate of 30 QPCA features In QPCA features of colour images experiments, the entire database is computed with QPCA [START_REF] Le Bihan | Quaternion Principal Component Analysis of Color Images[END_REF] to get quaternion features. After processing, we have varying quaternion feature for each picture according to the acquirements. Subsequently, every quaternion features of image are put into model in the same manner as above method to test the performance of both classifiers. Both of the proposed method and QBPNN can fit data very well, but the proposed method still performs slightly better. The results are shown in Table 2. The comparisons of two methods in terms of convergence rate are given in Fig. 1b.

Conclusion:

In this paper, we have proposed a new algorithm for classifying quaternion features, namely, quaternion softmax classifier. The results demonstrate that the proposed method outperforms the conventional QBPNN method in quaternion features classification. In deep learning algorithms, autoencoders in real domain, which combines NN and softmax, have achieved good results in classification. The proposed method also has the capacity to propagate back error to QBPNN. It is possible that autoencoders in quaternion field have advantage over conventional one. This is the basis of deep learning in quaternion data filed. In future, we will focus on deep learning of quaternion data.

( 4 )

 4 Results: Two kinds of quaternion features, quaternion pixels features and QPCA features are used to test the capabilities of our proposed quaternion softmax classifier. A set of experiments was performed on the Georgia Tech Face Database where 450 colour face images composed of 30 individuals with 15 images per individual were used. All images were linearly scaled to 40 by 32 pixels. Some examples are shown in Fig. 1. For each individual, the first 10 images were selected as the training set while the rest as the testing set. For comparison purpose, the recognition rate was also tested by the QBPNN method.

Fig. 1

 1 Fig. 1 Nine images of the Georgia Tech Face DatabaseTo compare with the proposed method effectively, the appropriate selection of the parameters used by the QBPNN is required. Most classification problem used 3-layers neural network. The number of input layer units equals to the number of features. The number of output units equals to the number of classes. Assume that N 0 , N 1 , N 2 represent the numbers of input layers, hidden layers, output layers, respectively. The hidden size is 02 NN . The initial weights and bias are set randomly on [u, u], where 01 6/ 1 uN N   . If one of the node values of output layers is 1ijk (in practice we use the value that is closest to 1ijk in terms of Euclidean distance), we suppose the test image belongs to this class. The parameters of proposed method are set randomly on [-0.005, 0.005] for every parts of quaternion.In learning phase of QBPNN and proposed method, we used min-Func matlab toolbox[START_REF] Schmidt | minFunc: Matlab software for unconstrained different iable multivariate optimization[END_REF] for numerical optimization. We set optimized method to 'L-BFGS' for both experiments to search the global minimum. In order to obtain enough accuracy, we set the maximum number of iterations to 300. Learning rate and iteration step are set to default values of toolbox.

Table 1 :

 1 Comparison of classification accuracy performed on the GT colour face database using different methods.

	Noise type		Proposed method (%)	QBPNN (%)
		5	95.33	91.33
	Gaussian	10	92.67	92.67
	noise (STD)	15	91.33	91.33
		20	88	87.33
		0.02	89.33	88.67
	Salt &	0.03	86	86
	Pepper (D)	0.04	84.67	79
		0.05	82	70

Table 2 :

 2 Classification accuracy on QPCA of various feature numbers.

	QPCA features (n)	Proposed method (%)	QBPNN (%)
	15	94	94
	20	96	92.67
	25	98	94
	30	98	96

Acknowledgements: This work was supported by the National Basic Research Program of China under Grant 2011CB707904, by the NSFC under Grants 61201344, 61271312, 11301074, and by the SRFDP under Grants 20110092110023 and 20120092120036, the Project-sponsored by SRF for ROCS, SEM, and by Natural Science Foundation of Jiangsu Province under Grant BK2012329 and by Qing Lan Project. R. Zeng, J.S. Wu, Z.H. Shao and H.Z. Shu (LIST, the Key Laboratory of Computer Network and Information Integration, Southeast University, Nanjing 210096, China; Centre de Recherche en Information Biomédicale Sino-français, Nanjing 210096, China) E-mail: jswu@seu.edu.cn L. Senhadji (INSERM, U 1099, Rennes 35000, France; LTSI, Université de Rennes 1, Rennes 35000, France; Centre de Recherche en Information Biomédicale Sino-français, Rennes 35000, France)


Boris Leroy
email: leroy.boris@gmail.com

Isabelle Le Viol

Julien Pétillon

Ecologie

Complementarity of rarity, specialisation and functional diversity metrics to assess community responses to environmental changes, using an example of spider communities in salt marshes

Keywords: Index of Relative Rarity, Community Specialisation Index, Functional Divergence, Grazing, Cutting, Spiders

The study of community responses to environmental changes can be enhanced by the recent development of new metrics useful in applied conservation: relative rarity, ecological specialisation and functional diversity. These different metrics have been critically assessed independently, but are rarely combined in applied conservation studies, especially for less-studied taxa such as arthropods. Here we report how these different metrics can complement each other by using the response of spider communities to environmental changes in salt marshes as an example. Sampling took place using pitfall traps in salt marshes of the Mont St Michel Bay (France) during 2004 and 2007. The sampling design was spatially replicated (3 plots per treatment and 4 traps per plot) and encompassed four habitat treatments: control, sheep grazing, cutting (annual, in summer) and invasion by the plant Elymus athericus. We observed contrasting responses of spider communities to the different treatments: grazing had a negative impact on both rarity and functional diversity but a positive impact on specialisation; cutting had a negative impact on the three metrics; and invasion only had a negative impact on rarity and specialisation. These contrasting responses emphasise the necessity of using different complementary community metrics in such conservation studies. Consequently, rarity-, specialization-, and functional-based indices should be applied simultaneously more frequently, as they potentially provide additional complementary information about communities. Such complementary information is the key to better-informed conservation choices.

Introduction

Addressing responses of biodiversity to environmental changes at the community rather than species level present the advantage of integrating the responses of multiple species and their interactions. Responses of communities can be assessed with different facets (taxonomic, phylogenetic or functional) for which several new indices have been developed (e.g., Devictor et al., 2010;[START_REF] Meynard | Beyond taxonomic diversity patterns: how do α, β and γ components of bird functional and phylogenetic diversity respond to environmental gradients across France?[END_REF][START_REF] Strecker | Defining conservation priorities for freshwater fishes according to taxonomic, functional, and phylogenetic diversity[END_REF]. However, these different facets are still rarely used in applied conservation studies, particularly for less-studied taxa such as arthropods.

The early methods used to assess communities in conservation studies were simple taxonomic diversity metrics such as species richness or abundance (e.g., [START_REF] Prieto-Benítez | Effects of land management on the abundance and richness of spiders (Araneae): A meta-analysis[END_REF]. However these simple metrics only reflect a fraction of the biodiversity and do not take into account the identity of species and their characteristics within and between communities, even though these aspects are crucial to assess biodiversity distribution (α, β components), conservation concerns (rarity), ecosystem functioning (functional traits) and importantly the processes implied in the impact of environmental changes on this biodiversity (biotic and functional homogenisation). Hence, species and communities were attributed values with respect to the conservation goal, for example according to their rarity, or more recently to their functional characteristics. In this study, we focus on recent methodological advances regarding three aspects: rarity, ecological specialisation and functional diversity.

Rarity primarily provides an insight into the facet of species biodiversity that is most at risk of extinction [START_REF] Gaston | Rarity[END_REF], also with respect to the maintenance of vulnerable ecosystem functions [START_REF] Mouillot | Rare species support vulnerable functions in high-diversity ecosystems[END_REF]. Different axes of rarity are usually considered: restricted abundance, restricted geographic distribution and narrow niche breadth. The study of rarity in arthropod communities has recently been improved by the proposal of new indices based on species occurrence [START_REF] Leroy | Improving occurrence-based rarity metrics in conservation studies by including multiple rarity cut-off points[END_REF], which provide the possibility of integrating multiple spatial scales [START_REF] Leroy | Rarity: Calculation of rarity indices for species and assemblages of species. R package version 1[END_REF]. Robust metrics have also been developed to assess the average niche width, i.e. the specialisation of species communities (Devictor et al., 2010a). Using basic predictions from the ecological niche theory, specialist species should indeed be favoured in rather stable environments whereas generalists should be more able to thrive in disturbed habitats [START_REF] Levins | Evolution in Changing Environments: Some Theoretical Explorations[END_REF]). In the same way, species functional traits are increasingly taken into account to provide a better assessment of the functional responses of communities to environmental changes. The study of this facet of biodiversity was improved thanks to the proposal of novel metrics which have been developed and analysed critically (Devictor et al., 2010a;[START_REF] Villéger | New multidimensional functional diversity indices for a multifaceted framework in functional ecology[END_REF]. The loss of functional diversity was a criterion that had been overlooked initially, but is of increasing concern in biological conservation (e.g., Devictor et al., 2010b).

All these distinct approaches were successfully applied on arthropod communities (e.g., [START_REF] Leroy | Integrating multiple scales in rarity assessments of invertebrate taxa[END_REF][START_REF] Penone | Urbanisation effect on Orthoptera: which scale matters?[END_REF] to assess their responses to environmental changes. They have each been critically assessed alone, but how they complement each other in the case of applied conservation remained to be tested. In this paper, we report a case study combining different recently developed metrics (rarity, specialisation, functional diversity) to assess how they complement each other to assess the response of arthropod communities to environmental changes, by using the example of spider communities of salt marshes. The environmental changes are here the replacement of natural vegetation of salt marshes by monospecific stands of the species Elymus athericus [START_REF] Bockelmann | Competitive exclusion of Elymus athericus from a high-stress habitat in a European salt marsh[END_REF], and two management practices likely to limit the spread of this species: annual cutting and sheep grazing. The impact of E. athericus will here be termed as an invasion in accordance with previous work on this species [START_REF] Pétillon | Impact of an invasive plant (Elymus athericus) on the conservation value of tidal salt marshes in western France and implications for management: Responses of spider populations[END_REF].

Salt marshes are of important conservation value because they host stenotopic species due to the constraining environmental conditions [START_REF] Pétillon | Saline stress tolerance partly matches with habitat preference in ground-living wolf spiders[END_REF], and geographically rare species because of the restricted distribution of salt marshes in the western Palearctic [START_REF] Leroy | Integrating multiple scales in rarity assessments of invertebrate taxa[END_REF]. In addition, salt marshes are subject to environmental changes (invasion by E. athericus and management) which often result in the replacement of the single dominant plant species by another [START_REF] Veeneklaas | Spatio-temporal dynamics of the invasive plant species Elytrigia atherica on natural salt marshes[END_REF]. These changes in vegetation in turn modify the structure and composition of arthropod communities [START_REF] Ford | Grazing management in saltmarsh ecosystems drives invertebrate diversity, abundance and functional group structure[END_REF]. The impacts of these environmental changes on salt marsh arthropods are still poorly understood, and results from scarce literature are often contradictive (e.g., [START_REF] Rickert | α-and β-diversity in moth communities in salt marshes is driven by grazing management[END_REF][START_REF] Van Klink | Grazed vegetation mosaics do not maximize arthropod diversity: Evidence from salt marshes[END_REF]. Consequently, we expected the application of distinct community metrics to provide new and complementary information, thus leading to a better understanding of how environmental changes impact communities. For that purpose, we compared the impacts of four treatments (control, invasion, cutting and grazing) on spider communities of salt marshes using community-level indices. Spiders were selected as a model group as they constitute one of the most abundant and diverse groups of arthropods in salt marshes [START_REF] Pétillon | Influence of abiotic factors on spider and ground beetle communities in different salt-marsh systems[END_REF] and for their well-known sensitivity to changes in habitat structure (e.g., [START_REF] Marc | Spiders (Araneae) useful for pest limitation and bioindication[END_REF].

Methods

Sampling design

The impacts of treatments on spider communities were investigated at two sites in the Mont-Saint-Michel Bay (NW France, 48°37'N, 1°34'W), 1 kilometre apart. Four treatments were investigated: control, invasion by E. athericus, vegetation cutting (once a year, in July) and grazing by sheep (on average 50 sheep/ha) [START_REF] Pétillon | Impact of cutting and sheep grazing on ground-active spiders and carabids in intertidal salt marshes (Western France)[END_REF]. Treatments are representative of the main salt-marsh habitats of the Mont St-Michel Bay [START_REF] Pétillon | Impact of cutting and sheep grazing on ground-active spiders and carabids in intertidal salt marshes (Western France)[END_REF], and covered all together 89% of the 4054 hectares of salt marshes (E. athericus-invaded areas: 35%, cutting: 19%, sheep-grazing: 25%, natural vegetation: 10%, data from 2007, Valéry and Radureau, personal communication).

Spider communities were sampled between May and June in 2004 and 2007: the former with control, invasion and cutting treatments, and the latter with control, invasion and grazing treatments. The comparison between treatments was made in similar salt-marsh zones within each site and the only apparent varying factors (at the local and landscape scales) between plots were the presence/absence of management practices (cutting and grazing) or invasion by E. athericus.

The sampling protocol was designed to be comparable among treatments: within each site, each treatment was applied to three plots during the same sampling period.

Plots had a surface area of 100m² and were spaced 100m apart. Within each plot, ground-dwelling spiders were sampled with four pitfall traps, set up regularly in a square grid and placed 10m part, as this is the minimum distance to avoid interference between traps [START_REF] Topping | Limitations to the use of pitfall traps in ecological studies exemplified by a study of spiders in a field of winter wheat[END_REF]. Traps consisted of polypropylene cups (10 cm diameter, 17 cm deep) containing ethylene-glycol as a preservative. Traps were covered with a raised wooden roof to exclude the rain and were visited weekly, tides permitting (i.e. three times per month during May and June). To summarise, there were 36 traps per site (3 treatments * 3 plots * 4 traps) and thus a total of 72 traps for the whole sampling protocol. To verify the impacts of treatments on vegetation, percentage covers of all plant species were estimated once within a radius of 1m around all traps.

Spider community-level indices

We calculated the average rarity, specialisation, and functional diversity of each community (pitfall trap) using species characteristics obtained from spider datasets (rarity, specialisation), and the literature (hunting strategy).

Data came from i) the western France spider database, and ii) the Catalogue of Spider Species from Europe and the Mediterranean Basin (both datasets were detailed in [START_REF] Leroy | Integrating multiple scales in rarity assessments of invertebrate taxa[END_REF].

Multiscale Index of Rarity

For each spider species, we calculated rarity weights (wMi) according to the method described in [START_REF] Leroy | Integrating multiple scales in rarity assessments of invertebrate taxa[END_REF] (details in Appendix A). These rarity weights integrate information on the occurrence of species at two spatial scales: the western France scale and the western Palearctic scale. Weight values range from 0 to 2. The rarer the species, the higher the weights, with species which are rare at both scales receiving higher rarity weights than species which are rare at a single scale.

The Index of Relative Rarity (IRR) of each pitfall community was then calculated as the average weight of rarity of individuals of all the species of the considered community, and was subsequently normalized to values between 0 (no rare species in the community) and 1 (all individuals of the community belong to species with the maximum rarity weight): IRR = ([Σ(ai × wMi)/N] -wmin)/(wmax -wmin) where ai and wMi respectively are the abundance and rarity weight of the i th species of the community; N is the total number of individuals in the community; and wmin and wmax are the minimum and maximum possible weights, respectively.

Community Specialisation Index

Each species was characterised for habitat specialisation through using the calculation of a Species Specialisation Index (SSI) according to [START_REF] Julliard | Spatial segregation of specialists and generalists in bird communities[END_REF].

To define habitat specialisation, the western France spider database was used. For each species, the frequencies of occurrence in each habitat class were calculated (see details in Appendix B). The coefficient of variation of these frequencies of occurrence (standard deviation/average) as a measure of each Species Specialisation Index (SSI) [START_REF] Julliard | Spatial segregation of specialists and generalists in bird communities[END_REF] was then calculated. The SSI varied between 0.76 (most generalist species) and 4.69 (most specialised species) (Table 1 and Appendix B). The Community Specialisation Index (CSI) of each pitfall community was calculated as the average SSI of the species detected, weighted by local species abundance, as follows: CSI = [Σ(ai SSIi)/N], where ai and SSIi respectively are the abundance and species specialisation indices of species i; and N is the total number of individuals in the community [START_REF] Devictor | Functional biotic homogenization of bird communities in disturbed landscapes[END_REF]. The CSI was then standardised between 0 and 1 in a similar manner to the Index of Relative Rarity [START_REF] Leroy | Improving occurrence-based rarity metrics in conservation studies by including multiple rarity cut-off points[END_REF]; a CSI of 1 means that a community is composed of individuals of the most specialised species of the database, whereas a CSI of 0 means that a community is composed of individuals of the most generalist species.

Functional diversity

The functional diversity of spider communities was calculated on the basis of functional traits related to hunting modes, because of the important impacts of predator hunting modes in ecosystem functioning [START_REF] Schmitz | Effects of predator functional diversity on grassland ecosystem function[END_REF]. We used functional traits at the family level on the basis of the trait matrix of spider families of [START_REF] Cardoso | Global patterns of guild composition and functional diversity of spiders[END_REF]. The Functional Divergence (FDiv) index [START_REF] Villéger | New multidimensional functional diversity indices for a multifaceted framework in functional ecology[END_REF] was calculated in order to take into account both the occupation of functional space by the different families and the relative abundance of families in communities.

Analyses

Because rarity weights and specialisation indices of species describe two axes of rarity, we first analysed their correlation for the sampled species with Pearson's correlation coefficient. Species richness and the three indices (IRR, CSI and FDiv)

were then calculated for each community of spiders of the 72 traps. The FDiv index was calculated for only 58 out of 72 communities, because functional divergence cannot be estimated when communities contain less than three functionally singular species. The effects of treatments on the calculated metrics were then analysed using linear mixed-effects models because of the hierarchical nature of the sampling design.

We fitted linear mixed-effect models with the treatment as a fixed effect, and sites nested in year as random effects. The significance of fixed effects was tested by comparing models with vs. without fixed effects using likelihood ratio tests. We then performed multiple comparisons between treatments with Tukey's post-hoc tests with a correction on probability values by controlling the false discovery rate [START_REF] Benjamini | Controlling the false discovery rate: a practical and powerful approach to multiple testing[END_REF]. Welsh two sample t-tests were used to compare the average abundance between treatments, of several species. Indices were calculated with Rarity version 1.2-1 [START_REF] Leroy | Rarity: Calculation of rarity indices for species and assemblages of species. R package version 1[END_REF] and FD version 1.0-11 [START_REF] Laliberté | FD: measuring functional diversity from multiple traits, and other tools for functional ecology[END_REF]. Linear mixed effect models were performed in R 3.0.2 (R Core Team, 2013) with the package lme4 version 1.0-5 [START_REF] Bates | lme4: Linear mixed-effect models using Eigen and S4. R package version 1[END_REF], and post-hoc tests with the package multcomp version 1.3-1 [START_REF] Hothorn | Simultaneous Inference in General Parametric Models[END_REF].

Results

Samplings

A total of 3826 spiders, representing 31 species, 10 families and 6 functional groups, was collected (Table 1).

Correlation between rarity weights and specialisation indices of species

We observed a positive correlation between rarity weights and specialisation indices of species (Pearson's R = 0.75; P < 0.001; N = 31) (Fig. 1). Nevertheless, some species had very high specialisation values but low rarity weights (e.g., Erigone longipalpis),

or had very high rarity weights but intermediate specialisation values (e.g., Pardosa purbeckensis).

Effects of treatments on communities

We detected a significant treatment effect on all the measured metrics (see Figure 1 and details in Appendix B). The species richness was significantly lower in traps located in invaded plots than in traps associated with other treatments (χ²=13.5, df=3, p=0.004) (Fig. 2A). The relative rarity of communities was significantly higher in control plot traps than in those located in managed or invaded plots (χ²=24.1, df=3, p<0.001) (Fig. 2B). This increase in rarity was associated with a higher mean abundance of the rare species P. purbeckensis in the control treatment than in other treatments (t=5.78, df=31.50, p<0.001) (Table 1). Conversely, although the CSI was significantly higher in the control treatment than under invasion or cutting treatments, the highest CSI was observed in the grazed plots, and was significantly higher than in control and in invaded or cut plots (χ²=24.40, df=3, p<0.001) (Fig. 2C). The higher specialisation under the control compared to invasion and cutting treatments was associated with higher average abundance of specialised species such as P. purbeckensis (t=6.60, df=30.22, p<0.001) and Silometopus ambiguus (t=2.90, df=33.08, p=0.007) (Table 1). On the other hand, the very high specialisation value observed under the grazing treatment was associated to the high abundance of the specialised species E. longipalpis, with on average 13.83±9.76 individuals per trap versus 1.13±2.05 individuals per trap (mean±sd) in other treatments (t=4.49, df=11.20, p<0.001). However, grazing, and to a lesser extent cutting, appeared to have a negative impact on the functional divergence of communities, with a significantly lower FDiv in traps of grazed plots than in those of invaded or control traps (χ²=10.4, df=3, p=0.016) (Fig. 2D). We compared this lower functional diversity to the presence of functional groups under the grazing treatment, and we observed only two dominant functional groups ("Ground hunters" and "Other hunters"), while other treatments were more balanced, with an additional functional group ("Orb web weavers") (Table 1).

Discussion

In this paper, we combined different metrics (rarity, specialisation and functional diversity) to analyse how spider communities of salt marshes respond to changes in their environment, whether induced by a biological invasion (Elymus athericus) or by management practices (grazing, cutting). As expected, environmental changes generally had negative impacts on spider communities, which led to decreases in rarity, specialisation and functional diversity of communities. While the general trend was similar among metrics, we observed divergent responses to the relative impacts of treatments between the three measured metrics.

Influence of community composition on metrics

In particular, the most interesting divergence was observed for the effect of grazing treatment. Specialisation was higher in grazed plots than in control plots, whereas the opposite was observed for rarity and functional diversity. This is surprising given the observed positive relationship between rarity weights and specialisation indices at the species level. However, this relationship has exceptions such as the widespread but specialist species E. longipalpis. Incidentally, E. longipalpis was highly abundant in the grazed plot, leading to a divergence between specialisation and rarity indices. This pattern shows that metrics expected to vary conjointly can produce divergent outcomes because of their sensitivity to the composition of communities. This sensitivity is very important to highlight unexpected impacts of environmental changes on communities.

Another important property of the metrics used here is that they are not biased by the species richness or abundance: because the metrics are based on the average trait (rarity, specialisation) of the species in the community, then a species-poor community can have a higher value than a species-rich community [START_REF] Julliard | Spatial segregation of specialists and generalists in bird communities[END_REF][START_REF] Leroy | Improving occurrence-based rarity metrics in conservation studies by including multiple rarity cut-off points[END_REF][START_REF] Villéger | New multidimensional functional diversity indices for a multifaceted framework in functional ecology[END_REF]. If we take the example of the CSI, a community with only a few individuals from very specialised species will have a higher CSI than a community with many individuals of generalist species. Because of this averaging property, a decrease in CSI may result from a decrease of specialists and/or from an increase of generalist species. Typically disturbances are expected to negatively impact specialist species while fostering generalist species, as both predicted by theory and empirically observed (see [START_REF] Devictor | Measuring community responses to large-scale disturbance in conservation biogeography[END_REF]. As a consequence it is expected that changes in community composition resulting from environmental disturbances will generally result in lower CSI values. However, in extreme cases, the reverse might be observed: for example a disturbance corresponding to the extreme values of the abiotic gradient may have positive impacts on only a few specialist species with particular adaptation to this disturbance (e.g., [START_REF] Doxa | Lowintensity agriculture increases farmland bird abundances in France[END_REF], which would thus result in a higher CSI value. Though this is a particular case, it highlights the importance of verifying, as a second step, how community composition changed. This impact is similar on the functional divergence index: the loss of species occupying intermediate functions will increase the functional value. However, this is not relevant in our case study since spider functional groups are strongly divergent; thus, a decrease in abundance of any functional group will decrease the functional value.

To summarise, the three applied metrics accurately synthesise how changes in community composition affect different facets of biodiversity; such changes cannot be detected by species richness alone. However, understanding these changes imply to look at changes in community composition as a second step.

Implications for salt marsh conservation

The indices showed that grazing induced a decrease in the average rarity and functional diversity of communities, but an increase in their specialisation. This pattern is mainly due to the increase in widespread but specialist species such as E.

longipalpis. This positive impact of grazing on specialist species of salt marshes such as E. longipalpis was reported by [START_REF] Ford | Grazing management in saltmarsh ecosystems drives invertebrate diversity, abundance and functional group structure[END_REF], although they did not investigate species rarity. The negative effect of grazing, and to a lesser extent cutting, on functional diversity is clearly due to a reduction in the number of vegetation strata, which negatively impacts spiders living in higher vegetation such as orb web weavers [START_REF] Uetz | Guild structure of spiders in major crops[END_REF]. On the other hand, no significant impact of grazing was detected on species richness alone, unlike [START_REF] Rickert | α-and β-diversity in moth communities in salt marshes is driven by grazing management[END_REF] and van [START_REF] Van Klink | Grazed vegetation mosaics do not maximize arthropod diversity: Evidence from salt marshes[END_REF]. In fact, a negative impact on species richness was only observed for the invaded treatment. We also found higher specialisation and rarity in control plots than in invaded and cut plots, in accordance with a previous study that revealed more continental, non-specialised, spider species in cut or invaded salt marshes [START_REF] Pétillon | Impact of an invasive plant (Elymus athericus) on the conservation value of tidal salt marshes in western France and implications for management: Responses of spider populations[END_REF].

To summarise, our results suggest that undisturbed salt marshes generally support a higher specialisation, rarity and functional diversity than disturbed salt marshes, with the notable exception of the positive impact of grazing on specialised species. To preserve all the facets of spider diversity, we would recommend maintaining the grazing management in areas invaded by E. athericus rather than the cutting treatment.

Conclusion

We therefore showed contrasting responses of spider communities to the different environmental changes (invasion and management measures). These contrasts emphasise the necessity of using different and complementary community metrics in such conservation studies. As a consequence, rarity-, specialization-and functionalbased indices should be more frequently applied together, as they can potentially contribute a wide range of complementary information about species communities.

Such complementary information is the key to better-informed conservation choices.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Average values of indices (A. Species richness, B. Multiscale Index of Relative Rarity, C. Community Specialisation Index, and D. Functional Divergence) and 95% confidence intervals (estimated by linear mixed-effects models (LMMs)) for the four treatments. Different successive letters indicate significant differences in means (revealed by corrected Tukey's post-hoc test on treatment effect following LMMs, with correction for the false discovery rate).

Table 1 .

 1 Multiscale rarity weights, specialisation indices and functional groups of the sampled spider species, and their average ± sd abundance in pitfall traps. The functional groups are based on[START_REF] Cardoso | Global patterns of guild composition and functional diversity of spiders[END_REF].

	Species	Multiscale rarity weights	indices Species specialisation	Functional groups		Abundance ± sd
					Control	Invasion	Cutting	Grazing
	Family Araneidae
	Argiope bruennichi	0.009	1.272	Orb web weavers	0.00±0.00 0.08±0.28	0.00±0.00	0.00±0.00
	Larinioides cornutus	0.004	1.225	Orb web weavers	0.04±0.20 0.08±0.28	0.00±0.00	0.00±0.00
	Neoscona adianta	0.002	1.271	Orb web weavers	0.00±0.00 0.04±0.20	0.00±0.00	0.00±0.00
	Family Clubionidae
	Clubiona stagnatilis	0.144	1.877	Other hunters	0.00±0.00 0.04±0.20	0.00±0.00	0.00±0.00
	Family Dictinidae
	Argenna patula	0.344	3.247	Ground hunters	0.71±1.16	3.29±4.22	0.83±0.83	0.92±1.00
	Family Gnaphosidae
	Drassyllus pusillus	0.031	1.429	Ground hunters	0.04±0.20 0.00±0.00	0.00±0.00	0.00±0.00
	Silometopus ambiguus	0.697	3.164	Other hunters	3.29±3.38	1.58±2.21	0.08±0.29	2.33±1.97
	Zelotes latreillei	0.026	1.749	Ground hunters	0.00±0.00	0.08±0.41	0.08±0.29	0.00±0.00
	Family Linyphiidae
	Agyneta conigera	0.551	4.286	Sheet web weavers 0.00±0.00 0.00±0.00	0.08±0.29	0.00±0.00
	Bathyphantes gracilis	0.012	1.368	Sheet web weavers	0.21±0.51	0.08±0.28	0.17±0.39	0.08±0.29
	Collinsia inerrans	0.525	2.222	Other hunters	0.04±0.20 0.00±0.00	0.00±0.00	0.00±0.00
	Erigone atra	0.010	1.346	Other hunters	0.46±0.78	0.04±0.20	1.50±1.62	0.67±0.89
	Erigone dentipalpis	0.003	1.195	Other hunters	0.17±0.38	0.00±0.00	0.00±0.00	0.00±0.00
	Erigone longipalpis	0.234	4.690	Other hunters	2.50±2.69	0.25±0.53	0.17±0.39	13.83±9.76
	Oedothorax fuscus	0.022	1.224	Other hunters	4.83±6.68	0.04±0.20	4.25±5.14	2.50±1.24
	Oedothorax retusus	0.028	1.353	Other hunters	0.58±0.78	0.04±0.20	5.50±5.89	0.25±0.45
	Pelecopsis parallela	0.051	1.830	Other hunters	0.00±0.00 0.33±0.82	0.42±0.67	0.00±0.00
	Savignia frontata	0.325	3.720	Other hunters	0.00±0.00 0.00±0.00	0.08±0.29	0.00±0.00

Acknowledgements

We thank Simon Potier, Alain Radureau and Vincent Schricke for fruitful discussion, Damien Nouguès and Mathieu de Flores for their contribution in field work and spider identification. Aldyth Nys provided useful editing of the English of an earlier draft. Loïc Valéry provided data on the spatial distribution of treatments. We thank two anonymous reviewers for useful additions in an earlier draft.