Gilles Chabert
email: gilles.chabert@emn.fr

Luc Jaulin
email: luc.jaulin@ensieta.fr

Hull Consistency Under Monotonicity

We prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example.

Introduction

Solving constraint problems with real variables has been the subject of significant developments since the early 90's (see [START_REF] Benhamou | Continuous and interval constraints[END_REF] for a comprehensive survey). One of the key contribution is the concept of hull consistency, which is the counterpart of bound consistency in discrete constraint programming, as Definition 1 shows below. Let us briefly trace the history. The underlying concepts of interval propagation appeared first in several pioneering papers [START_REF] Cleary | Logical Arithmetic[END_REF][START_REF] Hyvönen | Constraint Reasoning Based on Interval Arithmetic[END_REF][START_REF] Older | Extending Prolog with Constraint Arithmetic on Real Intervals[END_REF][START_REF] Hyvönen | Constraint Reasoning Based on Interval Arithmetic-The Tolerance Propagation Approach[END_REF] while consistency techniques for numerical CSP were formalized a few years later in [START_REF] Lhomme | Consistency Techniques for Numeric CSPs[END_REF][START_REF] Benhamou | Applying Interval Arithmetic to Real, Integer and Boolean Constraints[END_REF]. A theoretical comparative study of consistencies was then conducted in [START_REF] Collavizza | A Note on Partial Consistencies over Continuous Domains Solving Techniques[END_REF][START_REF] Delobel | Comparing Partial Consistencies[END_REF]. Finally, hull consistency was made operational in [START_REF] Benhamou | Revising Hull and Box Consistency[END_REF][START_REF] Granvilliers | Progress in the Solving of a Circuit Design Problem[END_REF] where the famous HC4 algorithm is described. Since hull consistency is based on the bound consistency of every isolated constraint, enforcing hull consistency in the general case (i.e., for arbitrary nonlinear equations) is a NP-hard problem [START_REF] Kreinovich | Computational complexity and feasibility of data processing and interval computations[END_REF]. On the practical side, this results into the inability to give a sharp enclosure when variables occur more than once in the expression of a constraint. This happens, in particular, with HC4. We show that hull consistency can be enforced in polynomial time if the functions involved are all monotone. Monotonicity follows the very intuitive idea that a function varies either in the same direction as a variable or in the opposite one (see Definition 2). It turns out that usual functions, i.e., built with arithmetic operators (+,-,×,/) and elementary functions (sin, exp, etc.) are analytic and therefore most of the time strictly monotone. In rigorous terms, most of the time means that, unless the function is flat (or defined piecewise), the set of points that do not satisfy local strict monotonicity is of measure zero (in the sense of measure theory). As a consequence, if a better contraction (or filtering) can be achieved under monotonicity, branch & prune algorithms should take advantage of it. Monotonicity has been considered from the beginning of interval analysis [START_REF] Moore | Interval Analysis[END_REF], but with a motivation slightly different from ours. One of the most fundamental issues of interval analysis is the design of inclusion functions [START_REF] Jaulin | Applied Interval Analysis[END_REF], i.e., methods for computing an enclosure of the range of a function on any given box. Of course, the sharper the better. Now, an optimal inclusion function (i.e., a method for computing the exact range on any box) can be built straightforwardly for monotone functions (see §2). Hence, the main matter since that time has been to devise efficient way to detect monotonicity of a function f over a box [x]. One simple way to proceed is by checking that the gradient does not get null in [x] which, in turn, requires an inclusion function for the gradient. The latter can then be based either on a direct interval evaluation, Taylor forms or the monotonicity test itself in a reentrant fashion (leading to the calculation of second derivatives, and so on). Surprisingly enough, monotonicity has never been used so far in the design of contractors. Remember that, although related, computing a sharp enclosure for {f (x), x ∈ [x]} and for {x ∈ [x] | f (x) = 0} are quite different goals. As we already said, getting an optimal enclosure with a monotone function f is straightforward in the first case. But it is not so in the second case, especially when x is a vector of variables. Algorithm 1 below will provide an answer. In the following, we first define properly the different concepts. The main result, a monotonicity-based polytime optimal contractor for a constraint, is then presented. Finally, we highlight the practical benefits of this contractor with a simple example.

Notations and definitions

We consider throughout this paper a constraint satisfaction problem (CSP) with a vector of n real variables x 1 , . . . , x n . Domains of variables are represented by real intervals and a Cartesian product of intervals is called a box. Intervals and boxes will be surrounded by brackets, e.g., [x]. If [x] is a box, x -and x + will stand for the two opposite corners formed by the lower and upper bound respectively of each components (see Figure 2). Hence, x - i and x + i will stand for the lower and upper bound respectively of the interval

[x] i . The width of an interval [x] (width[x]) is x + -x -.
Furthermore, given a mapping f on R n , we shall denote by {f = 0} the constraint f (x) = 0 viewed as the set of all solution tuples, i.e.,

{f = 0} := {x ∈ R n | f (x) = 0}.
We can now give a definition of hull consistency.

Definition 1 (Hull consistency). Let P be a constraint satisfaction problem involving a vector x of n variables and let [x] be the domain of x. P is said to be hull consistent if for every constraint c and for all i (1 ≤ i ≤ n), there exists two points in [x] which satisfy c and whose i th coordinates are x - i and x + i respectively.

The key property of hull consistency lies in the combination of local reasoning and interval representation of domains. This concept brought a decisive improvement to the traditional Newton-based numerical solvers that were basically only able to contract domains globally.

Definition 2 (Monotonicity). A mapping f : R → R is increasing over an interval [x] if ∀a ∈ [x], ∀b ∈ [x] a ≤ b =⇒ f (a) ≤ f (b). A mapping f : R → R is decreasing if -f is increasing, and monotone if it is either decreasing or increasing. A mapping f : R n → R is increasing (resp. decreasing, monotone) over a box [x] if ∀x ∈ [x] and ∀i, 1 ≤ i ≤ n, x i → f (x 1 , . . . , xi-1 , x i , xi+1 , . . . , xn ) is increasing (resp. decreasing, monotone) over [x] i .
Strict monotonicity is satisfied when formulas hold with strict inequalities.

Let f : [y] ⊆ R → R be an increasing function. For any interval [x] ⊆ [y],
the infimum and the supremum of f on [x] are f (x -) and f (x + ). Hence, the following interval function:

[x] → [f (x -), f (x + )]
is an optimal inclusion function for f . This result easily generalizes to monotone multivariate functions, by a componentwise repetition of the same argument.

Main result

Enforcing hull consistency on a CSP boils down to enforcing bound consistency on every isolated constraint (cf. Definition 1). Giving an optimal contractor for a single constraint is thus the main issue, which we shall address below. We shall even focus on an equation f (x) = 0 (inequalities will be discussed further). Consider first the univariate case (f has a single variable) and assume that f is differentiable. The set {f = 0} can easily be bracketed by an interval Newton iteration (see, e.g., [START_REF] Moore | Interval Analysis[END_REF] for details on the operations involved):

[y] ← ỹ -f (ỹ)/[f ′ ]([y]) ∩ [y]
where [f ′ ] is a (convergent) inclusion function for f ′ and ỹ any point in [y] such that f (ỹ) = 0. Henceforth, we assume that a procedure univ newton(f, [x], ε) is available. This procedure returns an interval [y] such that both [y -, y -+ ε]

and [y +ε, y + ] intersect {f = 0}. It can refer to any implementation of the univariate interval Newton iteration, such as the one given in [START_REF] Hansen | Global Optimization using Interval Analysis[END_REF].

Let us state the complexity. As noticed in the introduction, an analytic function is locally either strictly monotone or flat. Thus, it makes sense to assume strict monotonicity when dealing with complexity. The interval Newton iteration has a quadratic rate of convergence [START_REF] Alefeld | Interval Analysis: Theory and Applications[END_REF], i.e., the width of [y] at every step is up to a constant factor less than the square of the width at the previous step. However, the quadratic rate is only achieved when the iteration is contracting, i.e., when ỹ -

f (ỹ)/[f ′ ]([y]) ⊆ [y]
. While this condition is not fulfilled, the progression can be slow, as the following figure illustrates:

mi n slo pe m ax slo pe

[x] l (0) l (1) l (2) l (3) • • •
Fig. 1: Slow progression of the Newton iteration (with the left bound as point of expansion). The maximum slope on the interval [x] (on the right side) is repeatedly encompassed in the interval computation of the derivative, which explains the slow progression. The successive lower bounds of the interval [x] are l (0) , l (1) , . . ..

When the point of expansion ỹ is the midpoint of [y]

, the width of the interval is at least divided by two (this is somehow a way to interleave a dichotomy within the Newton iteration). Thus, the worst-case complexity of univ newton with the midpoint heuristic is O(log(w/ε)), where w is the width of the initial domain.

Finally, note that if f is not differentiable (or if no convergent inclusion function is available for f ′ ), one can still resort to a simple dichotomy and achieve the same complexity. The general algorithm (called OCTUM: optimal contractor under monotonicity) that works with a multivariate mapping f : R n → R is given below. Note that univ newton is called on the restriction of f to (axis-aligned) edges of the input box [x]. Since (n -1) coordinates are fixed on an edge, the restriction is indeed a function from R to R.

To ease the description of the algorithm, we will assume that the multivariate function f is increasing (according to Definition 2). Once the algorithm is understood, considering the other possible configurations makes no difficulty and just require a case-by-case adaptation. Lines 1 to 5 initializes the two vectors x ⊖ and x ⊕ that correspond to the vertices where f is minimized and maximized respectively. When f is increasing, x ⊖ and x ⊕ are just aliases for x -and x + .

Line 6 checks that the box [x] contains a solution (and otherwise, the algorithm returns the empty set). The main loop relies on the following fact (see Figure 2) that will be proven below. Remember that f is assumed to be increasing and that [x] contains at least one solution. The minimum of x i when x describes the solutions inside [x] is then either reached (1) on the edge where all the other variables are instantiated to their upper bound x + j or (2) on the face where x i = x - i (which means that no contraction can be made).

face e d g e edge

x - x + x 1 x 3 x 2 {f = 0} x e 1 (x - 1 , •, •) (•, x + 2 , x + 3 )
Fig. 2: The first component of the solutions inside the box either reaches its minimum on the face (x - 1 , •, •) or on the edge (•, x + 2 , x + 3 ).

Furthermore, as soon as the minimum for a component x i is met on an edge, the solution on this edge makes all x + j (j = i) consistent in the domain of the j th variable. To skip useless filtering operations for the upper bounds of the remaining variables, we use a flag named sup in the algorithm (see lines 17 and 18). Finally, when univ newton is called, either the lower or upper bound of the resulting interval is considered, depending on which bound of [x] i is contracted (see lines 15 and 16 or 21 and 22). This ensures that no solution is lost. Filtering the upper bound of x i is entirely symmetrical. The complexity of OCTUM is O(n × log( width[x] ε )), where width[x] stands for max 1≤i≤n width[x] i . It can be qualified as a pseudo-linear complexity. The OCTUM algorithm can be very easily extended to an inequality f (x) ≤ 0 or f (x) ≥ 0 by simply skipping narrowing operations on y - i or y + i respectively. The completeness and optimality of OCTUM relies on the following proposition. Proposition 1. Let f : R n → R be a continuous increasing mapping and

[x] a box such that {f = 0} ∩ [x] = ∅. Given i, 1 ≤ i ≤ n put: x i := inf{x i , x ∈ {f = 0} ∩ [x]}.
Then, one of the two options holds:

Algorithm 1: OCTUM(f, [x], ε) Input: a monotone function f , a n-dimensional box [x], ε > 0 Output: the smallest box [y] enclosing [x] ∩ {f = 0}, up to the precision ε for i = 1 to n do 1 if (f ր xi) then x ⊕ i ← x + i ; // x ⊕ is the vertex where f is maximized 2 else x ⊕ i ← x - i // (f ր xi) means "f is increasing w.r.t. xi" 3 if (f ր xi) then x ⊖ i ← x - i ; // x ⊖ is the vertex where f is minimized 4 else x ⊖ i ← x + i 5 if f (x ⊖ ) > 0 or f (x ⊕ ) < 0 then return ∅ //
[s] ← univ newton(t → f (x ⊕ 1 , . . . , x ⊕ i-1 , t, x ⊕ i+1 , x ⊕ n ), [y]i, ε) 13 if [s] = ∅ then 14 if (f ր xi) then y - i ← s - //
[s] ← univ newton(t → f (x ⊖ 1 , . . . , x ⊖ i-1 , t, x ⊖ i+1 , x ⊖ n ), [y]i, ε) 19 if [s] = ∅ then 20 if (f ր xi) then y + i ← s + 21 else y - i ← s - 22 inf ← true 23 return [y] 24
1. x i = x - i , 2. there exists x ∈ [x] such that x i = x i and for every j = i, x j = x + j .

Proof. Let x * be a solution point in [x] minimizing x i , i.e., f (x * ) = 0 and x * i = x i . If x * i = x - i , the first option holds and we are done. Assume x * i > x - i . If n = 1, the second option holds trivially. If n > 1, consider the following vector:

x := (x + 1 , . . . , x + i-1 , x * i , x + i+1 , . . . , x + n ). We will prove that f (x) = 0. By contradiction, assume f (x) > 0 (f being increasing). Since x i = x * i > x - i , there exists by continuity ε > 0 such that x * i -ε > x - i and f (x-εe i ) > 0 (e i being the i th unit vector). Now, x * is the point in [x] where f gets null with the smallest i th coordinate. Hence, f (x *εe i ) < 0. Since f is continuous, f gets null somewhere on the segment joining x *εe i and xεe i because the sign of f is opposite at the two extremities. Since [x] is convex, the corresponding point is inside [x] and its i th component is x * iε i , which contradicts the fact that x * i is the infimum among the solutions.

A first experiment

Consider the problem of characterizing the set of points (x, y) in [-3, 0] × [0, 3] satisfying f (x, y) = 0 with f (x, y) = x 2 y 2 -9x 2 y + 6xy 2 -20xy -1.

Let us compare OCTUM with three other standard generic contractors (namely HC4 [START_REF] Benhamou | Revising Hull and Box Consistency[END_REF][START_REF] Granvilliers | Progress in the Solving of a Circuit Design Problem[END_REF], BOX [START_REF] Benhamou | CLP(intervals) revisited[END_REF][START_REF] Van Hentenryck | Solving Polynomial Systems Using a Branch and Prune Approach[END_REF] and 3B [START_REF] Lhomme | Consistency Techniques for Numeric CSPs[END_REF]) as pruning steps of a classical branch & prune system. We have implemented a very naive method for detecting monotonicity, using an interval evaluation of the gradient that is systematically computed for every box (a better method would be to manage flags w.r.t. each variable in a backtrackable structure, each flag being set incrementally as soon as f is proven to be monotone). Even with this naive implementation, OCTUM yields better results, both in terms of quality (see Figure 3) and quantity (see Table below).

Conclusion

We have proven that hull consistency can be achieved in polynomial time in the case of constraints involving monotone functions. Hull consistency amounts to bound consistency for each isolated constraint. We have given an algorithm called OCTUM that enforces bound consistency for an equation under monotonicity (and explained how to adapt it to inequalities). Hull consistency based on OCTUM can then be programed by simply embedding OCTUM in a classical AC3 propagation loop. A first experiment has illustrated the two nice properties of OCTUM: optimality and (pseudo-)linear complexity.

  (a) Using HC4. (b) Using BOX. (c) Using 3B. (d) Using OCTUM.

Fig. 3 :

 3 Fig. 3: Comparing the monotonicity-based contractor OCTUM with other standard operators. Black surfaces encompass the solutions while grey boxes represent the contracted parts. The thinnest black surface is obtained with OCTUM. Note however the two little marks in (d) that correspond to points where one component of the gradient gets null.

  update lower bound of xi

	15
	16	else y + i ← s + ;	// update upper bound of xi
		sup ← true	// the edge x ⊕ j , j = i, contains a solution

17

if curr sup is false then 18


Stéphanie Boulêtreau
email: stephanie.bouletreau@cict.fr

Mehdi Sellali

Arturo Elosegi

Yvan Nicaise

Yvan Bercovitz

Frédéric Moulin

Olivier Eiff

Sabine Sauvage

José-Miguel Sánchez-Pérez

Frédéric Garabétian

Temporal Dynamics of River Biofilm in Constant Flows: A Case Study in a Riverside Laboratory Flume

Keywords: epilithon, periphyton, bacterial community fingerprinting, community metabolism, experimental flume

A 15-week experiment was performed in a riverside laboratory flume (with diverted river water) to check variations of river biofilm structure (biomass, algal and bacterial compositions) and function (community gross primary production GPP and respiration) under constant flow while water quality went through natural temporal variations. One major suspended matter pulse coinciding with one river flood was recorded after 10 weeks of experiment. Epilithic biofilm first exhibited a 10-week typical pattern of biomass accrual reaching 33 g ash-free dry matter (AFDM) m -2 and 487 mg chlorophyll-a m -2 and then, experienced a shift to dominance of loss processes (loss of 60% AFDM and 80% chlorophyll-a) coinciding with the main suspended matter pulse. Algal diversity remained low and constant during the experiment: Fragilaria capucina and Encyonema minutum always contribute over 80% of cell counts. DGGE banding patterns discriminated between two groups that corresponded to samples before and after biomass loss, indicating major changes in the bacterial community composition. GPP/R remained high during the experiment, suggesting that photoautotrophic metabolism prevailed and detachment was not autogenic (i.e., due to algal senescence or driven by heterotrophic processes within the biofilm). Observational results suggested that silt deposition into the biofilm matrix could have triggered biomass loss.

Introduction

Disturbanc e is a major source of spatial and temporal heterogeneity in the structure and dynamics of natural communities. Among physical processes of disturbance, flow is the main agent of natural disturbance in lotic ecosystems [START_REF] Power | Disturbance and recovery of an algal assemblage following flooding in a Oklahoma stream[END_REF][START_REF] Biggs | Linking scales of flow variability to lotic ecosystem structure and function[END_REF]. The discharge of a river or stream is made up of both the water that exerts forces compared as wind does in terrestrial environments and, any solid particles contained within it. The redistribution of solid particles such as suspended particulate matter (e.g., silt) or larger objects transported by water (e.g., cobbles) can strike and abrade the substratum over which the water flows. As sessile assemblage colonizing pebble surfaces, epilithic biofilms are directly exposed to both increased in flow velocity and material movement.

Many studies confirm that flow is the main factor controlling spatial patterns of epilithic biomass among streams [START_REF] Biggs | Patterns in benthic algae of streams[END_REF], temporal patterns in epilithic biomass [START_REF] Biggs | Disturbance in stream periphyton by perturbations in shear stress: time to structural failure and difference in community resistance[END_REF], and heterogeneity in biofilm community composition and biodiversity in streams [START_REF] Besemer | Bacterial community composition of stream biofilms in spatially variable-flow environments[END_REF]. Models applied to long time-series suggested that, in natural conditions, epilithic biomass dynamics can roughly be considered as the result of equilibrium between phototrophic growth and discharge-dependant loss [START_REF] Uehlinger | Periphyton dynamics in a floodprone prealpine river: evaluation of significant processes by modelling[END_REF][START_REF] Boulêtreau | Assessing the importance of a self-generated detachment process in river biofilm models[END_REF][START_REF] Boulêtreau | Identification of a minimal adequate model to describe the biomass dynamics of river epilithon[END_REF]. Models that account for epilithic detachment only considered the effect of fluid forces, using current velocity or discharge as variables [START_REF] Horner | Development of nuisance periphytic algae in laboratory streams in relation to enrichment and velocity[END_REF][START_REF] Momo | A new model for periphyton growth in running waters[END_REF][START_REF] Uehlinger | Periphyton dynamics in a floodprone prealpine river: evaluation of significant processes by modelling[END_REF][START_REF] Saravia | Modelling periphyton dynamics in running water[END_REF]. However, several studies have suggested that epilithon removal during floods is not likely to be explained by water velocity alone [START_REF] Horner | Responses of periphyton to changes in current velocity, suspended sediment and phosphorus concentration[END_REF][START_REF] Uehlinger | Spatial and temporal vairability of the periphyton biomass in a prealpine river (Necker, Switzerland)[END_REF][START_REF] Biggs | Patterns in benthic algae of streams[END_REF][START_REF] Francoeur | Short-term effects of elevated velocity and sediment abrasion on benthic algal communities[END_REF].

Models show that during long and stable inter-flood periods, other factors can interact and produce complex patterns of epilithic biomass. Among processes known to become significant at promoting biomass loss [START_REF] Biggs | Patterns in benthic algae of streams[END_REF] without significant flow events is autogenic sloughing which has rarely been examined in the literature. Autogenic sloughing occurs when parts or clusters of biofilm become thicker, less cohesive and therefore less resistant to floating and drifting, resulting in sloughing of a mature biofilm. Loss of cohesiveness can be consecutive to gas bubble production associated to metabolism activity (photosynthesis or respiration).

We aim to study the evolution of biofilm biomass, community composition and metabolism in a river discriminating the potential effect of changing water flow from other physical or chemical changes due to water flow variations (such as suspended materials, water temperature or nutrient content). To maintain constant flow conditions during a sufficiently long-time period, we studied river biofilm dynamics in an artificial indoor channel.

Methods

Experimental De sign

The experiment was conducted during 4 months in an indoor channel (11 m long, 50 cm wide, 20 cm deep, slope: 1/1000, Fig. 1) located on the right bank of the River Garonne at Toulouse, France (43°35′15′′N-1°26′17′′E). The flume bed and walls are respectively made of opaque PVC 20 mm thick and Plexiglas ® 10 mm thick. The experimental flume from [START_REF] Godillot | Interplay between turbulence and periphyton in rough open-channel flow[END_REF][START_REF] Labiod | The relationship between stream periphyton and near-bed turbulence in rough open-channel flow[END_REF] was adapted for the present study to be run using a partially re-circulating system open to the River Garonne, so that water followed natural physi co-chemical changes, whereas hydraulics were kept constant.

Hydraulic Characteristics

One pump (Selfinox 200/80T, ITT Flygt, France) continuously supplied water from the river to the downstream tank (3300 L) (Fig. 1). One second submerged pump (Omega 10-160-4, Smedegard, Denmark) ran water to the upstream tank (1500 L) through a 100 mm main. The upstream tank fed the downstream tank by gravity. Pumps were robust enough to work equally well with both clear and muddy water. Apparatus to guide (grid) and stabilize (convergent) the flow of water were placed in the inlet reservoir to ensure a quasi uniform entrance flow. Water discharge was measured by an electromagnetic flow meter and water discharge and depth regulated with a sluice gate and a by-pass. A moderate current velocity ± SD (0.225 ± 0.002 m s -1 ) was ensured to limit external shear stress on biofilm and to enhance colonisation [START_REF] Stevenson | Emigration and immigration can be important determinants of benthic diatom assemblages in streams[END_REF][START_REF] Godillot | Interplay between turbulence and periphyton in rough open-channel flow[END_REF]. A water depth h = 10 cm above substratum was maintained to reduce edge effects associated with side boundary layers. The downstream tank was fed by a water discharge of 800 L h -1 thus allowing for a complete turnover of water in the system every 4 h.

Environmental Conditions

River water was treated to exclude macroinvertebrate grazers and fish and to reduce the supply of suspended matter: large particles were eliminated by two centrifugal separators, and the water was then filtered 3 times through 90, 20 and 10 μm pore-sized filters. Using 10 μm filtration prevented the presence of macroorganisms, although seeding by isolated algal cells from the river drift was enabled.

Light was supplied by six 1.5 m long racks of 5 neon tubes, with "daylight" (Philips TLD 58 W) and fluorescent tubes (Sylvania Gro-Lux 58 W, especially designed for enhancing photosynthesis as they emit in the visible red) evenly disposed. Photoperiod was set at 16 hours of day and 8 hours of night. The incident light, measured with a LI-190SA quantum sensor and a LI-1000 data logger (LI-COR Inc. Lincoln, Nebraska) varied between 140 and 180 μmol m -2 s -1 PAR on the channel bottom ensuring photosynthetic activity saturation [START_REF] Bothwell | Influence of natural ultraviolet radiation on lotic periphytic diatom community growth, biomass accrual, and species composition: short-term versus long-term effects[END_REF]. Water temperature, conductivity, pH, dissolved oxygen and turbidity in the upstream tank were measured hourly during the whole experiment (YSI 6600 probe, YSI Incorporated, USA). Furthermore, water was sampled weekly (automatic samplers ISCO 3000) in the upstream tank (flume water) and in the river tank (river water) to assess water composition and compare flume water to river water. Samplers were programmed to collect 500 mL hourly from 7:00 to 6:00, and the 3 samples mixed to give 3 composite samples as chosen to convey daily changes of the water chemistry: the first 8 hours of the day (7:00-14:00), the second 8 hours of the day (15:00-22:00) and the third 8 hours of the night (23:00-6:00).

Substrate Characteristics and Layout

The flume bed was completely covered by 3750 artificial substrata, which mimic natural cobbles. Each substrate consisted of a chemically inert sand-ballasted polyurethane resin hemisphere (37 mm diameter, 20 mm high), a shape and a texture shown to provide good conditions for biofilm adhesion and growth [START_REF] Nielsen | A comparison of periphyton growth on artificial and natural susbtrates in the upper Spokane River[END_REF]. In order to eliminate any possible toxicity (e.g., solvents), substrates were immersed in river water for 3 weeks, then washed with tap water and sterilized by autoclave (120 °C, 20 min) before being positioned side by side in the flume, without any fixation, except at both ends and at the middle of the flum.

Experimental Procedure and Monitoring

Inoculum and Start-up

To collect diverse biofilm communities, pebbles (average size 10 cm 2 ) with biofilm were collected in SW France streams (Oriege, Gave de Pau) and rivers (Garonne, Tarn) displaying a wide range of hydroecological conditions. These pebbles were incubated for a maximum of 3 weeks in a second flume that ran with conditions comparable to those of the experiment. A biofilm suspension was produced by scraping the upper surface of 15 pebbles taken at random with a toothbrush, and adding 1 L of filtered (0.22 μm) water. The biofilm suspension was homogenized (tissue homogenizer) to remove macrofauna and to approach grazer-free conditions. During the 3 first weeks, the flume was run using the closed recirculation: water was renewed weekly, and just after renewal, it was seeded with the prepared biofilm suspension. The first date of seeding phase was defined as the start of the experiment (day 0 of the incubation period).

Water Analyses

Concentrations of ammonium, nitrite, nitrate, phosphate, total phosphorus, silicate and suspended chlorophyll-a were quantified by either manual or continuous-flow colorimetric methods (APHA, 1992). Dissolved organic carbon was measured using a Shimadzu TOC5000 carbon analyzer (Kyoto, Japan). Suspended matter (SM) was measured by weighing the dried matter (105 °C, 4 h) collected by filtration onto a 0.45 μm pore-size membrane filter (Whatman nitrate cellulose membrane). Suspended matter size in the river water was measured once by laser diffraction at the end of the experiment using a laser Mastersizer Micro (Malvern Instruments Ltd, Malvern, UK) without disaggregation pre-treatment.

Biofilm and Drift Sampling

Biofilm was sampled in a 5 m long area of the experimental flume, every week after the seeding phase (13 sampling dates). The 3 rows of substrates closer to the walls were not sampled to avoid edge effect. For each sampling, 11 substrates were randomly sampled and kept in sterile vials at 4 °C: six substrates were randomly used for metabolism, and then, for ash-free dry mass (AFDM), 4 substrates for chlorophyll-a and bacterial composition (randomly selected) and 1 substrate for algal composition. Every substrate sampled was replaced with a new one, pink-coloured to avoid sampling in further occasions.

Drifting material was sampled weekly with a 50 μm nylon mesh placed weekly at the end of the flume for 10 minutes. Six samples were taken consecutively during one hour. Material from the 2 first meshes (i.e., 20 minutes, 4 times water renewal time in the flume) was excluded from the analyses, and only the other 4 were processed, to measure the quantity of newly dislodged drifting material (DM and AFDM), after suspending in 0.5 L water.

Metabolism

Biofilm metabolism (primary production and respiration) was measured weekly within 4 hours of sampling, using a rapid respirometer method based on changes in oxygen over time [START_REF] Mcintire | Laboratory studies of periphyton production and community metabolism in lotic environments[END_REF]. Measurements were conducted in 2 transparent Altuglass chambers (18 cm long, 18 cm wide, 5 cm deep, 1.3 L-total volume with pipes, measurement cell and substrates) closed with a 2 cm thick transparent Altuglass lid, filled with filtered water (0.2 μm, Whatman nitrate cellulose membrane), which recirculated at 600 mL min -1 thanks to an aquarium pump. Note that pumping is not intended to recreate the water velocity that prevails in the flume. Three substrates (0.0065 m 2 ) collected in the flume were placed in each chamber, and incubated at the same temperature measured in the flume one hour before. Light was kept constant at 150 μmol m -2 s -1 by means of a Phyto Claude 400 W lamp. Dissolved oxygen within each chamber was monitored using oxygen probes (WTW Oxi340i) over 2 hours every minute. Net community metabolism (in g O 2 m -2 d -1 ) was determined by measuring dissolved oxygen changes over a 30-min period of daylight (maximal slope). Following the incubation, chambers were exposed to the dark and the rate of community respiration (R in g O 2 m -2 d -1 ) (autotrophic and heterotrophic respirations) was determined as the change in oxygen concentration over a 90-min second incubation period (maximal slope). A dark box was used to prevent light penetration into the chambers. This technique allowed incubations to be relatively short in order to reduce containment effects such as nutrient depletion and supersaturation of oxygen that can be problematic when using enclosed chambers to measure metabolism [START_REF] Bott | An evaluation of techniques for measuring periphyton metabolism in chambers. -Can[END_REF]. The gross primary production (GPP in g O 2 m -2 d -1 ) was calculated by adding net community metabolism to community respiration. The net productivity (in g O 2 m -2 d -1 ) was calculated by adding GPP multiplied by the ratio of day hours (16/24) to R. Biomass-specific GPP (mg O 2 (mg chlorophyll-a) -1 d -1 ), biomass-specific R (mg O 2 (mg chlorophyll-a) -1 d -1 ), and biomass-specific net productivity (mg O 2 (mg chlorophyll-a) -1 d -1 ) were calculated by dividing respectively GPP, R and the net productivity by the chlorophyll-a biomass. The ratio of GPP to R (GPP/R) was calculated and used as an integrative parameter of the physiological state of the community [START_REF] Fisher | Energy flow in Bear brook, New Hampshire: an integrative approach to stream ecosystem metabolism[END_REF].

Epilithic and Drift Biomass

Substrates used for metabolism measurement were removed from the chambers and used to determine DM and AFDM biomass. They were dried (80 °C, overnight), weighed (W 1 ) and scraped. One fraction (around 25 mg) of scraped dry matter was weighed before and after combustion (500 °C, overnight) to determine AFDM. Substrates were finally cleaned, dried and weighed (W 2 ) to obtain DM by difference between W 1 and W 2 .

The production of drift biomass was expressed as a percentage of biomass that detached per day, by multiplying drift concentration (g AFDM L -1 ) by the flow (L d -1 ) divided by the total amount of biomass in the flume (g AFDM). The biofilm suspension (collected with meshes) was homogenised (tissue homogenizer) and a 50 mL aliquot of the homogenised biofilm suspension was centrifuged (2300 × g, 20 min). The pellet was dried (80 °C, overnight) and weighed to determine DM, and weighed before and after combustion (500 °C, overnight) to determine AFDM of the drift material.

For chlorophyll-a determination, biofilm was scraped from the upper surface of 4 substrates with a sterile toothbrush, and suspended in filtered (0.2 μm, Whatman cellulose nitrate membrane) water (50 or 100 mL according to biomass). Suspensions were homogenised (tissue homogenizer) and 10 mL aliquots were centrifuged (12000 × g, 20 min, 4 °C). After removing the supernatant, the 4 pellets were stored at -80 °C, and chlorophyll a measured spectrophotometrically using trichromatic equations [START_REF] Jeffrey | Phytoplankton pigments in oceanography[END_REF] after extraction of the ground pellet (following ul trasonic digestion) with acetone 90% (4 h darkness, room temperature). Four other 10 mL aliquots of biofilm suspensions were centrifuged (12000 × g, 20 min, 4 °C) and, after removing the supernatant, the pellet was kept at -80 °C for the determination of bacterial community composition.

Bacterial Composition

On each occasion, we selected at random three out of the four pellets obtained by centrifugation. DNA was extracted using a MO BIO (USA) Kit on 10-50 mg of biofilm pellets, and quantified by fluorimetry (Fluroskan Ascent II; Labsystems, Helsinki, Finland) (excitation 485 nm, emission 538 nm) using SYBR Green (Sigma-Aldricht, St. Louis, MO, USA; dilution 1:10000). Extracted DNA was amplified by PCR using the universal Bacteria primers 341F-GC and 907R (MUYZER et al., 1997) and 20 ng of template DNA. The PCR products from 3 distinct reactions were pooled and loaded in an acrylamide gel containing a 35 to 70% urea and formamide gradient (100% corresponding to 7 M of urea and 40% of deionised formamide). DGGE (Denaturing Gradient Gel Electrophoresis) was carried out using D-Code Universal Mutation Detection System (BioRad). The 45 samples (3 replicates × 15 dates) were dispatched on 3 gels putting one replicate per gel. The electrophoresis was run for 18 h at 100 V at 60 °C. The gel was stained for 30 min with SYBR Green (Sigma) and gel image captured using a CCD camera and Biocapt software (Vilber Lourmat) and analyzed using Bio 1D software (Vilber Lourmat). DGGE profiles were compared with regard to the presence or absence of bands using the Jaccard similarity index [START_REF] Jaccard | The distribution of flora in the alpine zone[END_REF] and dendrogram construction according to the unweighed pair group method with average means (UPGMA) [START_REF] Michener | A quantitative approach to a problem in classification[END_REF]. Statistical differences between groups determined from the dendrograms were tested using random permutation (Monte Carlo test, 10000 permutations) [START_REF] Kropf | Significance test for comparing complex microbial community fingerprints using pairwise similarity measures[END_REF].

Algal Composition

Biofilm was removed from the upper surface of 1 substrate as for chlorophyll-a determinations. The biofilm suspension was preserved with neutralized glutaraldehyde (1% final concentration) and stored at 4 °C in darkness until examination at 600 to 1000 ×. Taxa were identified to the lowest practical taxonomic level, usually to species but often to genus. For practical reason, nine of 13 samples were selected at random for analysis to observe changes in taxonomic composition.

Results

Water Characteristics

Conductivity, dissolved oxygen and pH (mean ± SD) remained fairly stable within the flume during the experiment (197 ± 21 μS cm -1 , 10.4 ± 1.4 mg L -1 and 8.6 ± 0.2 respe ctively) (Table 1A). Temperature in the flume varied widely during the study, from 8.1 to 20.3 °C. Turbidity averaged 6.5 NTU and exhibited two 3 and 2 day peaks reaching 16 and 19 NTU after 53 and 57 incubation days respectively, followed by one clear 3 day increase on the 66 th incubation day reaching 175 NTU (Table 1A and Fig. 2). At the end of the experiment, most of the suspended particles were fine silt-sized particles (>2 μm and <20 μm) corresponding to 33% of the total SM, coarse silt-sized particles (>20 μm and <50 μm) corresponding to 45% and very fine sand (>50 μm and <100 μm) corresponding to 14%. Clay-sized particles (<2 μm) and fine and medium sand (>100 μm and <500 μm) represented less than 3% and around 5% respectively. As no major failure of the centrifugation/filtration device occurred, particle aggregation, floc formation and drifting of biofilm pieces is likely to explain the unexpected proportion of particles larger than 10 μm.

Concentrations in nitrate, ammonia, nitrite and DOC exhibited similar variations in both river and flume waters (Table 1B). Silicate, phosphate and total phosphorus showed higher Table 1. (A) Recorded mean and standard deviations (SD) of temperature (TEMP), conductivity (COND), dissolved oxygen (DO), pH and turbidity (TURB) in the flume and (B) measured values of suspended chlorophyll a (chl a), nitrate (NO 3 ), nitrite (NO 2 ), ammonium (NH 4 ), phosphate (PO 4 ), total phosphorus (total P) and silicate (Si) in the flume and the river. variations in the flume than in the river, and chlorophyll-a the reverse pattern. Mean chlorophyll-a was around 1.5 times higher in the experimental flume than in the river suggesting production by the epilithic biofilm. Nevertheless mean ammonia, phosphorus, silicate and total phosphorus were 1.7, 2.1, 2.5 and 1.8 times lesser in average in the experimental flume than in the river, suggesting consumption and adsorption in the flume by the epilithic biofilm.

(A) variable unit TEMP °C COND mS cm -1 DO mg L -1

Biomass of Epilithic and Drifting Biofilm

Epilithic biomass showed a colonisation phase followed by exponential growth to 487 mg chlorophyll-a, and 33 g AFDM m -2 after 65 and 71 incubation days respectively (Fig. 2A and2B). Both variables were significantly correlated (r 2 = 0.64; n = 12; P = 0.0018). The peak of biomass arrived at 9 weeks for AFDM and at 10 weeks for chlorophyll-a. In the 3 following weeks, biomass decreased to 356 mg chlorophyll a and 24 g AFDM m -2 . After 10 weeks, biomass followed an abrupt and statistically significant decline, with losses of 60% of AFDM and 80% of chlorophyll-a (Mann-Whitney P < 0.05). The inorganic content increased to 85% during the first 10 weeks and progressively decreased to 61% during the following weeks (Fig. 2C). Drifting particulate organic matter was first low, averaging 5% of biomass per day after 6 incubation weeks (Fig. 2D). Then, it exponentially increased to 233% during the 5 successive weeks, before decreasing to 67% in two weeks later.

Metabolism

GPP and R varied respectively between 3.8 and 9.6 and between 0.6 and 2.2 g O 2 m -2 d -1 . Biomass-specific GPP slightly decreased from 57 to 13 mg O 2 (mg chlorophyll-a) -1 d -1 until the day 71 coinciding with the first biomass increase and suddenly increased to 122 mg O 2 (mg chlorophyll-a) -1 d -1 coinciding with the biomass loss (Fig. 3A). Biomass-specific R exhibited the same pattern as biomass-specific GPP decreasing from 15.9 to 1.8 mg O 2 (mg chlorophyll-a) -1 d -1 and increasing to 28.2 mg O 2 (mg chlorophyll-a) -1 d -1 concomitantly with the biomass loss (Fig. 3B). Biomass accruals coincided with general decreases in biomass-specific net productivity, from 22.1 to 3.2 mg O 2 (mg chlorophyll-a) -1 d -1 between the days 22 and 71, and from 53.0 to 13.9 mg O 2 (mg chlorophyll-a) -1 d -1 between the days 92 and 106 (Fig. 3C). Between these drops, biomass-specific net productivity increased rapidly. Biofilm communities were dominated by autotrophic processes, with a mean GPP/R ratio of 5 (Fig. 3D). The highest ratios (between 6.7 and 8.1) coincided with periods of maximal biomass whereas the lowest ratio (2.5) occurred just before the biomass loss on 71 st day.

Bacterial Composition

Bacterial community composition (BCC) was studied using DGGE on three gels. Irrespective of the gel, dendrograms based on Jaccard similarity index of DGGE banding patterns discriminated between two groups of samples that shared respectively 35, 32 and 40% of the detected bands (Fig. 4). These differences were statistically significant (Monte Carlo test, 10000 permutations, P < 0.01). Nevertheless groups varied slightly between gels. In every gel, the first group included the 6 samples collected during the first 65 days (first biomass accrual phase), the second group samples collected from the 85 th incubation day (samples after biomass loss). Dates between days 43 and 80 were either located in the first group (gel 3), either in the second group (gel 1) or in both groups (gel 2). Number of bands was similar for each cluster in all gels, with 27-40, 26-33 and 29-36 OTUs (Operational ) is reported on each graph (circle). Taxonomic Units) being present per sample in the first group and 28-36, 24-35 and 22-30 OTUs per sample in the second group. The mean band richness was lower in gels 2 (S = 29) and 3 (S = 30) than in the gel 1 (S = 35).

Algal Composition

Species richness was relatively low, varying from 9 to 21 taxa (Fig. 5). The algal community was dominated by diatoms, which represented 97 to 100% of the total abundance. Two taxa strongly dominated the algal community: Fragilaria capucina DESMAZIERE var. vaucheriae (KÜTZ) LANGE-BERTALOT represented 28 to 85% and Encyonema minutum HILSE ex. RABENHORST represented 2 to 47% of the total community. Apart from these two species, only 4 species reached abundances higher than 5% at least once: Achanthidium minutissimum KÜTZ., Fragilaria crotonensis KITTON and Nitzschia fonticola GRUN., and Diatoma ehrenbergii KÜTZ.. The last sample was quite different from others: with the lowest diversity, it was largely dominated by Fragilaria capucina (85%) and by Diatoma erhenbergii, which did not exceed 5% in other samples. No substantial changes in algal composition and species richness were observed during the main biomass loss

Discussion

A 15 week experiment using a laboratory flume was designed to check variations of epilithic biofilm structure and function under constant flow (mean current velocity (± SD) of 0.225 (±0.002) m s -1 ). Flow can be considered constant at the studied scale even if biofilm development could alter the local physical environment including flow conditions [START_REF] Battin | Contributions of microbial biofilms to ecosystem processes in stream mesocosms[END_REF]. For that matter, another part of the present study dealing with such biofilm-flow interactions showed that friction velocity (u*) and equivalent roughness length (ks), two parameters describing the local flow near the bed, evolved with biomass accretion (GRABA et al. in press). Driven by the pluvial-nival flow regime (hydrologic regime characterised by rain supply year-around in addition to spring snowmelt) of the River Garonne, a nutrientenriched river according to [START_REF] Dodds | Suggested classification of stream trophic state: distributions of temperate stream types by chlorophyll, total nitrogen[END_REF], water quality experienced natural changes. The main limitation of the experimental device was observed analysing algal and bacterial diversity. Diatoms dominated the assemblage consistently with the typical benthic algal composition of the River Garonne [START_REF] Eulin | Epilithic diatom communities during the colonization of artificial substrates in the River Garonne (France). Comparison with the natural communities[END_REF]. Algal species richness however was 5 times lower than natural community richness at the same period in the River Garonne. Despite cautions taken in the present experiment by (i) the introduction of a large pool of biofilm origins during the seeding phase and (ii) the 10 μm pore-size filtering designed to ensure seeding by algal propagules, poor algal diversity was observed. It could be inherent to partially re-circulating and filtering system that did not ensure continuous enrichment but is more likely to be due to flume characteristics (e.g., low substratum heterogeneity, constant light intensity and flow regime) that reduced environmental variability. Consistently, band richness of DGGE profiles was slightly lower than those previously obtained for natural assemblages in the same river [START_REF] Lyautey | Bacterial diversity of epilithic biofilm assemblages of an anthropised river section, assessed by DGGE analysis of a 16S rDNA fragment[END_REF][START_REF] Lyautey | Bacterial community succession in natural river biofilm assemblages[END_REF]. The studied biofilm should be considered as a simplified assemblage selected by the selected experimental settings.

Irrespective of a limited pool of algal species (dominated by diatoms), autotrophic energy fixation prevailed in the community metabolism during the whole experiment as proved by the GPP/R values always held higher than 1. The reduction or the increase in light penetration as the mat develops or recedes explained that biomass-specific GPP decreased when biomass increased and clearly increased during the recovery phase [START_REF] Riber | Boundary-layer and internal diffusion effects on phosphorus fluxes in lake periphyton[END_REF][START_REF] Stevenson | Effects of algal density and current on ion transport through periphyton communities[END_REF]. The general pattern of biomass observed in the flume was similar to patterns observed in situ and in accordance with the benthic theoretical curve described in [START_REF] Biggs | Patterns in benthic algae of streams[END_REF]. One 10-week accrual phase and one consecutive 2 week loss phase were observed before to recovery at an intermediate level during 2 weeks. The AFDM peak and time taken to reach this peak were comparable to values measured in the River Garonne [START_REF] Boulêtreau | Assessing the importance of a self-generated detachment process in river biofilm models[END_REF]. In the course of the loss phase, a drop of 80% was observed in epilithic chlorophyll-a. The concomitant increase in drifting material proved that this drop was partly due to biofilm removal.

Whether the algal pool could maintain the production constant asks the question of the role of the reduced algal diversity on the primary production of the assemblage. This question fits in with the new challenge in functional ecology to describe how biodiversity dynamics, ecosystem processes and abiotic factors interact [START_REF] Loreau | Biodiversity and ecosystem functioning: current knowledge and future challenges[END_REF]. The competitive exclusion principle applied to ecosystem function implies that resources would be used more efficiently when more species coexist [START_REF] Hardin | The competitive exclusion principle[END_REF]. In our experiment, a poorly diversified assemblage proved however to support a phototrophic biofilm development comparable to those of natural assemblages in the river. It can be hypothesized that stable conditions of light and flow could have favoured adapted taxa that supported biofilm growth. Conversely, exhibiting low resistance, the selected assemblage was not fitted when the disturbance occurred.

No evidence of macrofauna (specimens in samples, bioturbation prints or adult emergence in the flume) was observed. If grazing cannot be completely excluded by microfauna such as protozoans it does not totally explain the observed disturbance. Note that reduced grazing pressure that resulted from scarce macrograzer evenness could also have contributed to poor algal and bacterial diversity that is discussed above. Nevertheless, two parameters, temperature and suspended matter, exhibited relevant variations: temperature underwent a seasonal trend to warming and punctual suspended matter pulses coincided with flood events in the River Garonne. By considering [START_REF] Boulêtreau | Assessing the importance of a self-generated detachment process in river biofilm models[END_REF], the concomitance of the biomass peak and high temperature conditions could be favourable to the assumption of autogenic sloughing. But GPP/R was higher than 2 during the whole experiment and biomass-specific GPP was particularly low just before biomass loss, limiting intensive oxygen bubble production and discrediting a photosynthetic origin of autogenic sloughing. As for heterotrophic degradation, [START_REF] Lyautey | Bacterial community succession in natural river biofilm assemblages[END_REF] have shown that architectural changes were accompanied by changes in the BCC, fitting with a conceptual model proposing a shift from N-autotrophy to N-heterotrophy when epilithic biomass reaches a threshold [START_REF] Teissier | Detailing biogeochemical N budgets in riverine epilithic biofilms[END_REF]. In the present study, BCC clearly changed between before and after biomass loss but biomass-specific R exhibited the weakest values at this time. No marked metabolism shift to from phototrophic to heterotrophic activity could support any putative autogenic sloughing.

Abrasion by suspended material can result in epilithon scouring [START_REF] Horner | Responses of periphyton to changes in current velocity, suspended sediment and phosphorus concentration[END_REF][START_REF] Uehlinger | Spatial and temporal vairability of the periphyton biomass in a prealpine river (Necker, Switzerland)[END_REF][START_REF] Biggs | Patterns in benthic algae of streams[END_REF]. Abrasion impact is expected to be still more effective with sand and coarse silt-sized particles than with clay and fine silt-sized particles. Abrasion impact is most effective at the top of substrates where mean flow structures were numerically demonstrated to be more energetic (e.g., [START_REF] Coceal | Mean flow and turbulence statistics over groups of urban-like cubical obstacles[END_REF]. If sand and coarse siltsized particles represented 64% of the SM composition, biomass removal was gradual and mainly impacted the base of substrates. The gradual increase of the biofilm inorganic content (coinciding with the turbidity peak) suggested silt deposition to be responsible for biomass loss too. Silt particles are demonstrated to be transported thanks to mechanisms such as siltation, rolling, sliding and subsequently be trapped into biofilm matrix and on mucilaginous surfaces of diatoms stalks [START_REF] Hoagland | -Colonization and community structure of two periphyton assemblages, with emphasis on the diatoms (Bacillariophyceae)[END_REF][START_REF] Graham | Siltation of stone-surface periphyton in rivers by clay-sized particles from low concentrations in suspension[END_REF]. The mucilage produced by organisms offers many potential binding sites for a variety of colloidal, organic and inorganic elements [START_REF] Flemming | Sorption sites in biofilms[END_REF]. The biofilm response to the major turbidity pulse was delayed as would be expected if small particles were adsorbed and incorporated into the biofilm matrix, thus making sloughing easier, especially if oxygen bubbles are incorporated. Flocs and aggregates are demonstrated to form on the surfaces of bubbles that subsequently collapse [START_REF] Wotton | Do benthic biologists pay enough attention to aggregates formed in the water column of streams and rivers[END_REF]. Fine sediment suspension and deposition were demonstrated to prevent attachment of algal cells to the substrate and to affect production by reducing light penetration (e.g., VAN NIEUWENHUYSE and LA PIERRE, 1986;[START_REF] Davies-Colley | Effects of clay discharge on streams: 1. optical properties and epilithon[END_REF][START_REF] Wood | Biological effects of fine sediments in the lotic environment[END_REF] and by reducing nutrient availability due to adsorption/desorption on inorganic particles and weakest diffusion.

The impacts of fluid and solid forces on epilithic communities during flood disturbances are always mixed in natural conditions. The present experimental design that keeps current velocity constant with natural changes in suspended matter concentration allows to quantify and understand the isolated natural impact of suspended material on changes in epilithic community structure and function. For lack of control in the present study, suspended matter can only be suspected to have affected the biofilm pattern because a turbidity event occurred concomitantly with biomass loss. Validating the hypothesis of siltation impact would require experimenting on the micrometer scale by using tools such as confocal microscopes and micro sensors to consider biofilm local shading of primary producers and/or local chemical limitations. This original data set provides a weekly characterization of structural and functional changes in epilithon biomass. It is a good candidate to improve modelling by implementing new processes (e.g., solid impact on detachment).

Figure 2 .

 2 Figure2. Temporal changes of epilithic biomass (mean ± standard error) in (A) mg of chlorophyll-a per square meter (n = 4), (B) g of ash-free dry matter (AFDM) per square meter (n = 6), (C) inorganic content (%) and (D) of drift AFDM biomass in % of epilithic AFDM. Temporal changes in turbidity (NTU) are reported on each graph (solid line).

Figure 3 .

 3 Figure 3. Temporal metabolism changes (black square) in (A) biomass-specific GPP (mg O 2 (mg chlorophyll-a) -1 d -1 ), (B) biomass-specific R (mg O 2

Figure 4 .Figure 5 .

 45 Figure 4. UPGMA Jaccard distance dendrograms (left column) generated from the DGGE profiles of the bacterial community (right column) present in epilithic biofilm samples collected between days 22 and 120. Richness is given for each sample at the bottom of each band.

Acknowledgements

STÉPHANIE BOULÊTREAU was supported by FEDER (Fonds Européens de Développement Regional). This work was supported by the national research project ACI -FNS «ECCO Ecosphère Continentale : processus et modélisation». We wish to thanks C. MUR and D. DALGER for water chemistry analysis and A. BEER, S. FONT and G. DHOYLE for flume equipment and maintenance.