Hojjat Akhondi Asl

Pier Luigi Dragotti
email: p.dragotti@imperial.ac.uk

MULTICHANNEL SAMPLING OF TRANSLATED, ROTATED AND SCALED BILEVEL POLYGONS USING EXPONENTIAL SPLINES

, having only translations is not practical and one may want to look at the cases of more complicated geometric transformations, such as rotation and scaling. In this paper we present a sampling theorem for multichannel sampling of translated, rotated and scaled bilevel polygons using Radon projections and generalized exponential splines.

INTRODUCTION

Recently, it was shown [START_REF] Vetterli | Sampling Signals with Finite Rate of Innovation[END_REF][START_REF] Dragotti | Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon meets Strang-Fix[END_REF] that it is possible to sample and perfectly reconstruct some classes of non-bandlimited signals using suitable sampling kernels. Signals that can be reconstructed using this framework are called signals with Finite Rate of Innovation (FRI) as they can be completely defined by a finite number of parameters. Stream of weighted Dirac impulses and bilevel polygons are some examples of FRI signals.

There has been a recent interest in sampling FRI signals using exponential spline [START_REF] Unser | Cardinal Exponential Splines: Part I -Theory and Filtering Algorithms[END_REF] (E-spline) kernels. Dragotti et al. [START_REF] Dragotti | Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon meets Strang-Fix[END_REF] showed that E-splines can be used as the sampling kernel to sample and perfectly reconstruct 1-D FRI signals. Extensions to the multidimensional case were considered in [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF][START_REF] Asl | Single and Multichannel Sampling of Signals With Finite Rate of Innovation Using E-Splines[END_REF] where we proposed sampling theorems for a stream of 2-D Dirac impulses (based on the ACMP algorithm [START_REF] Vanpoucke | An Efficient Subspace Algorithm for 2-D Harmonic Retrieval[END_REF]) and bilevel polygons (based on Radon projections [START_REF] Herman | Image Reconstruction from Projections: The Fundamentals of Computerized Tomography[END_REF]). Apart from the sampling kernels used in [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF][START_REF] Asl | Single and Multichannel Sampling of Signals With Finite Rate of Innovation Using E-Splines[END_REF], the reconstruction algorithms are also different from the ones used in the conventional multidimensional sampling theories [START_REF] Shukla | Sampling Schemes for Multidimensional Signals with Finite Rate of Innovation[END_REF][START_REF] Maravic | Exact sampling results for some classes of parametric non-bandlimited 2-D signals[END_REF].

An advantage of E-spline sampling kernels over polynomial reproducing kernels such as B-splines is that, they can be employed in a fully symmetric multichannel sampling environment. By symmetric sampling, we mean that the sampling process can be evenly distributed between different acquisition devices. The inspiration and development of multichannel sampling of FRI signals is very recent and it has been looked at in [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF][START_REF] Seelamantula | A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction[END_REF][START_REF] Kusuma | Multichannel Sampling of Parametric Signals with a Successive Approximation Property[END_REF][START_REF] Baboulaz | Distributed Acquisition and Image Super-Resolution Based on Continuous Moments from Samples[END_REF].

In [START_REF] Seelamantula | A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction[END_REF] Seelamantula and Unser, by using simple RC filters, propose a simple acquisition and reconstruction method within the framework of multichannel sampling, where 1-D FRI signals such as an infinite stream of nonuniformly-spaced Dirac impulses and piecewise-constant signals can be sampled and perfectly reconstructed. In [START_REF] Kusuma | Multichannel Sampling of Parametric Signals with a Successive Approximation Property[END_REF] Kusuma and Goyal proposed new ways of sampling 1-D Dirac impulses using a bank of integrators or B-splines. Their proposed scheme is closely related to previously known cases [START_REF] Vetterli | Sampling Signals with Finite Rate of Innovation[END_REF][START_REF] Dragotti | Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon meets Strang-Fix[END_REF] but provides a successive approximation property, which could be useful for detecting undermodelling when the number of Dirac impulses are unknown. In [START_REF] Baboulaz | Distributed Acquisition and Image Super-Resolution Based on Continuous Moments from Samples[END_REF] Baboulaz and Dragotti use a multichannel sampling setup for sampling FRI signals and utilize that for image registration based on continuous moments and image super-resolution.

In [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF] we illustrate that symmetric multichannel sampling of bilevel polygons can be achieved with the geometric transformations being a 2-D translation between the different signals. In practice, this is usually not the case, and in this paper we want to look at the cases of more complicated geometric transformations, such as rotation and scaling. The paper is organised as follows: In Section II we will briefly discuss the sampling setup needed for sampling 2-D FRI signals (single channel) and based on that we describe our multichannel sampling setup. In Section III we present our algorithm for sampling and perfectly reconstructing translated, rotated and scaled bilevel polygons with the use of generalized E-splines and Radon projections. In Section IV we provide simulation results to support our proposed theory.

MULTICHANNEL SAMPLING SETUP

Before describing the multichannel sampling framework, let us first, for the sake of clarity, show how a general 2-D sampling setup (single channel) for FRI signals is represented. Figure 1 shows a general 2-D sampling setup for FRI signals where g(x, y) represents the input signal, ϕ(x, y) the sampling kernel, s j,k the samples and T x, T y are the sampling intervals. From the setup shown in Figure 1, the samples s j,k

s j,k = ∞ -∞ ∞ -∞ g(x, y) ϕ( x T x -j, y T y -k) dx dy (1)
where the kernel ϕ(x, y) is the time reversed version of the filter response h(x, y). ϕ(x, y) can easily be produced by the tensor product between ϕ(x) and ϕ(y), that is ϕ(x, y) = ϕ(x) ⊗ ϕ(y). As mentioned before, ϕ(x, y) is chosen to be an exponential reproducing kernel. The theory of exponential reproducing kernels is quite recent and is based on the notion of exponential splines (E-splines) [START_REF] Unser | Cardinal Exponential Splines: Part I -Theory and Filtering Algorithms[END_REF]. A function β α (x) with Fourier transform

β α (ω) = N n=0
1 -e αn-jω jω -α n is called E-spline of order N where α = (α 0 , α 1 , . . . , α N ) can be real or complex. The produced spline has a compact support and can reproduce any exponential in the subspace spanned by (e α0t , e α1t , . . . , e α N t ) which is obtained by successive convolutions of lower order E-splines ((N+1)-fold convolution). Exponential spline kernels can therefore reproduce, with their shifted versions, real or complex exponentials. That is, in 2-D form, any kernel satisfying:

j∈Z k∈Z c m,n j,k ϕ(x -j, y -k) = e αmx e βny (2)
is an E-spline for a proper choice of the coefficients c m,n j,k . Here, m = 0, 1, . . . , M , n = 0, 1, . . . , N , α m = α 0 + mλ 1 and β n = β 0 + nλ 2 . The values of (α 0 , β 0 ) and (λ 1 , λ 2 ) can be chosen arbitrarily, but too small or too large values could lead to unstable results for the reproduction of exponentials. E-splines are biorthogonal functions and the coefficients c m,n j,k can be found using the dual of β α (x). An important property of E-splines is that they are a generalized version of B-splines. This is because, if the α parameters are set to zero, then the produced spline would result in a B-spline, a polynomial reproducing spline. This property will be used to estimate the transformation parameters in Section III. The reader can refer to [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF][START_REF] Asl | Single and Multichannel Sampling of Signals With Finite Rate of Innovation Using E-Splines[END_REF] for sampling theories on single-channel sampling and perfect reconstruction of 2-D Dirac impulses and bilevel polygons using exponential splines.

We can now describe our multichannel sampling setup. A multichannel sampling system can be thought of multiple acquisition devices observing an input signal. In order to perfectly reconstruct the input signal using only one acquisition device, we normally require expensive acquisition devices with high sampling rates. By using a bank of acquisition devices (filters) and synchronizing the different channels exactly, we are able to reduce the number of samples needed from each device, resulting in a cheaper and more efficient sampling system. To model our multichannel system, consider a bank of E-spline filters to acquire FRI signals where each filter has access to a geometrically transformed version of the input signal. Figure 2 shows the described multichannel sampling scenario where the bank of filters ϕ 1 (x, y), ϕ 2 (x, y), . . . , ϕ N -1 (x, y) receive different versions of the input signal g 0 (x, y). Here, the geometric transformations (e.g. translation, rotation and scaling ) are denoted by T 1 , T 2 , . . . , T N -1 .

Fig. 2. Multichannel sampling setup

In [START_REF] Baboulaz | Feature Extraction for Image Superresolution using Finite Rate of Innovation Principles[END_REF] Baboulaz considered the use of E-splines for sampling a stream of 1-D Dirac impulses in a multichannel sampling setup described in Figure 2. He showed that if two 1-D signals are just shifted version of the other, then by setting one parameter to be common between the exponents of the E-spline sampling kernels for the two signals, one can not only estimate the shifts between the two signals, but also can linearly relate the exponential moments of the two signals (the reader can refer to [START_REF] Baboulaz | Feature Extraction for Image Superresolution using Finite Rate of Innovation Principles[END_REF][START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF][START_REF] Asl | Single and Multichannel Sampling of Signals With Finite Rate of Innovation Using E-Splines[END_REF] for more detailed discussion). Because of the direct relationship between the exponential moments of the two signals, we can achieve perfect reconstruction of the reference signal with fewer exponential moments required. Since less moments are required from each signal, a lower order E-spline sampling kernel would be needed, which in turn less samples from each signal are required to achieve perfect reconstruction. This is because, from [START_REF] Dragotti | Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon meets Strang-Fix[END_REF] we know that a stream of Dirac impulses is uniquely determined from the samples if there are at most K Dirac impulses in an interval size of 2KLT where L is the support of the sampling kernel. Since the support of the sampling kernels is reduced in the multichannel case, we can achieve the same performance with a smaller sampling rate T .

ALGORITHM

Unfortunately we can not estimate the more complicated geometric transformations like the way it was done for the simple translation case in [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF] with exponential reproducing kernels. Also, even if we assume that the transformation parameters are known and given, we still can not use the sampling algorithm shown in [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF] for the multichannel framework. This is because introducing more complicated transforms such as rotation and/or scaling for example, would result in a non-linear relationship between the exponential moments of the different signals.

The first question we need to answer is that, assuming an oracle gives us the values of the transformation parameters, can we sample and perfectly reconstruct translated, rotated and scaled bilevel polygons in a symmetric multichannel framework? It is known that for an N-sided bilevel polygon, with N+1 projections, perfect reconstruction of the polygon can be achieved. That is points that have N+1 line intersections from the N+1 back-projections correspond to the N vertices of the polygon [START_REF] Maravic | Exact sampling results for some classes of parametric non-bandlimited 2-D signals[END_REF]. We also know that a Radon projection at an angle φ of a rotated image with respect to its reference image with an angle θ, is the same projection, but scaled and translated, on the reference image at the angle φ + θ. Therefore, if all the transformation parameters are known, and assuming that the rotation angle is not zero that is, θ = 0, then the N + 1 projections needed could be separated between the different channels, in order to sample and perfectly reconstruct the reference image in a symmetric manner.

The next question would be, how can we estimate the transformation parameters? We know that with the use of polynomial reproducing kernels, we can obtain the geometric moments of a signal, and geometric moments up to order 2 from two signals are enough to estimate translation, rotation and scaling parameters between the two signals. We also know that, as E-splines are a generalized version of B-splines [START_REF] Unser | Cardinal Exponential Splines: Part I -Theory and Filtering Algorithms[END_REF], we can reproduce a combination of polynomials and exponentials from E-splines. From the polynomials moments up to order 2, we can estimate all the transformation parameters.

RESULTS

As an example, in [START_REF] Asl | Single and Multichannel Sampling of Bilevel Polygons Using Exponential Splines[END_REF] we showed that to achieve perfect reconstruction for a 4-sided bilevel polygon, a 2-D E-spline order of 12 is required to produce 5 projections at the angles 0, 45, 90, tan -1 (2) and tan -1 ( 1 2 ). With 2-D E-spline order of 7 however we can produce 3 projections at the angles 0, 45, 90 on the reference signal, and a 2-D E-spline order of 7 on the second signal would give 3 projections for the reference signal at the angles θ, 45 + θ, 90 + θ where θ is the rotation parameter. Assuming θ is not zero, we would have enough projections to perfectly reconstruct the reference signal. Therefore an spline order of 7+2 = 9 (2 is needed for es-timating the transformation parameters) on each signal would give us enough projections to perfectly reconstruct the reference signal. An example for a 4-sided bilevel polygon with two acquisition devices is shown in Figure 3 where the reference signal, its translated, rotated and scaled version, their samples, the E-spline sampling kernel, and the reconstructed reference signal are all shown.

CONCLUSION

In this paper we showed that with the use of Radon projections and generalized E-splines, symmetric multichannel sampling of translated, rotated and scaled bilevel polygons can be achieved. For estimating the geometrical transformations, we showed that as E-splines are a generalized version of B-splines, we can reproduce combination of polynomials and exponentials from E-splines. Therefore from the polynomial moments up to order 2, we can estimate all the unknown transformation parameters. For symmetric multichannel sampling of geometrically transformed bilevel polygons, we illustrated that the N+1 Radon projections needed for perfect reconstruction of an N-sided bilevel polygon, can be separated between the different channels, assuming that the rotation parameter is not zero. Our sampling and reconstruction algorithm is based on noise-free communication between the transmitter and receiver which is rather not very practical. The future research of this work is to test the stability and performance of our method in the presence of noise.

Fig. 1 .

 1 Fig. 1. 2-D sampling setup

Fig. 3 .

 3 Fig. 3. Symmetric multichannel sampling of translated, rotated and scaled bilevel polygons using E-spline sampling kernels. (a) The reference signal in a frame data size of 256 × 256. (b) The translated ( x = -100, y = 150), rotated (θ = 35) and scaled (a = 1.1) version of the reference signal. (c) & (d) The 16 × 16 samples of both signals. (e) 2-D generalized E-spline of order 9 (f) The reconstructed vertices of the reference signal with 6 back-projections, the crosses are the actual vertices of the polygon. [Not to scale]


Michel Lafont
email: lafont@lyon.cemagref.fr

Anne Vivier

Sylvie Nogueira

Philippe Namour

Pascal Breil

Surface and hyporheic oligochaete assemblages in a French suburban stream

Keywords: Suburban watercourses, urban inputs, coarse sediments, hyporheic zone, Oligochaeta

The Chaudanne stream received urban inputs discharged through combined sewer overflows (CSOs). The water quality was not severely impaired, with pollution mainly of organic origin.

Oligochaete assemblages were studied in the coarse surface sediments and the hyporheic zone and sampled at 4 sites on 7 occasions during 2000 and 2001. The seasonal distribution of oligochaete assemblages was analyzed by a PCA, the oligochaete species being assigned to functional traits (FTrs). Site 1, located upstream of the CSOs, was characterized by FTrs 1 and 2 (species indicating permeability and those intolerant to water pollution). Below the CSOs, high densities of oligochaetes occurred in the benthic layer of sites 3 and 4, with a predominance of FTr3 (species with tolerance to water pollution). At site 4, FTr4 species (indicative of sludge conditions) constantly predominated in the hyporheic system, but predominated in the benthos only during low stream discharges associated with peaks in CSOs. FTr3 was related to amounts of the oxidized forms of nitrogen, high stream discharges and probably to groundwater upwellings and the sludge tolerant species group (FTr4) was associated with high NH 4 + contents. We are now testing the relevance and generalisation of this new approach.

Introduction

The assessment of the ecological impacts of combined sewer overflows (CSOs) has became a priority in urban aquatic systems [START_REF] Cyr | L'hydrologie urbaine : nouvelles problématiques, nouvelles approches de solutions[END_REF][START_REF] Paul | Streams in the urban landscape[END_REF][START_REF] Rogers | Use of physical, chemical, and biological indices to assess impacts of contaminants and physical habitat alteration in urban streams[END_REF]. The alteration of urban watercourses complicates prediction of the effects of CSOs, which are strongly related to rainfall patterns. In addition, the pollution originating from storm-water runoff is generally accompanied by other pollution sources, including permanent inputs and polluted overflows from impervious urban surfaces. These multiple sources of pollution are a common feature in urban aquatic areas, and are generally poorly known [START_REF] Faulkner | Problems of quality designation in diffusely polluted urban streams -the case of Pymme's Brook, north London[END_REF]. The recent EC Water Framework Directive [START_REF] Ue | et du Conseil du 23 octobre 2000[END_REF] emphasized the conservation or restoration of good ecological condition in all aquatic ecosystems, including those located in urbanized areas.

In this study, we tried to assess the ecological effects of a CSO on the Chaudanne stream, a suburban watercourse of Lyon's urban area (France). We focused on the surface coarse sediments and hyporheic system which largely predominates in the studied stream. Invertebrate assemblages were mainly composed of oligochaetes and crustaceans, and aquatic insect larvae were not abundant [START_REF] Bernoud | Réponse écologique d'un ruisseau périurbain aux rejets de temps de pluie. TFE Mastère « Eau Potable et Assainissement[END_REF]. This was related to the urbanization of the surrounding landscape which had altered the physical habitats. The preserved area located near the source of the stream was poor in aquatic insects, however it was naturally rich in oligochaetes and crustaceans [START_REF] Bernoud | Réponse écologique d'un ruisseau périurbain aux rejets de temps de pluie. TFE Mastère « Eau Potable et Assainissement[END_REF]. Consequently, we focused on benthic and hyporheic oligochaetes as i) they were the most abundant interstitial invertebrates in the study site and ii) the present study was supported by data sets considering the oligochaete assemblages in the surface coarse sediments and hyporheic system of polluted and unpolluted watercourses [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF][START_REF] Lafont | Essai de description biologique des interactions entre eau de surface et eau souterraine: application à l'évaluation de la vulnérabilité d'un aquifère à la pollution d'un fleuve[END_REF][START_REF] Lafont | Oligochaete worms as biological describers of the interaction between surface and groundwaters: a first synthesis[END_REF][START_REF] Lafont | Superficial and hyporheic oligochaete communities as describers of pollution and water exchanges in the River Moselle system (France)[END_REF]Lafont & Malard, 2001;[START_REF] Malard | A comparison of longitudinal patterns in hyporheic and benthic oligochaete assemblages in a glacial river[END_REF].

It was necessary, in this preliminary work, to assess the relevance of the information value of oligochaetes, in particular to see if gradients of alterations might be evident in a relatively unimpaired situation such as the Chaudanne stream. In addition, the choice of a suburban site was dictated 1) by the fact that catchment management is easier to control than in urban watercourses; 2) that the imperviousness of the urbanized surrounding landscape is not constant; and 3) that relatively preserved areas can still be found. If alteration gradients could be illustrated by oligochaete worms in a situation of intermediate disturbance, the generalization to similar or more altered situations should be possible in the future.

Study site

The Chaudanne stream is a tributary of the Yzeron river [START_REF] Bernoud | Réponse écologique d'un ruisseau périurbain aux rejets de temps de pluie. TFE Mastère « Eau Potable et Assainissement[END_REF]. The Yzeron river enters the Rhône river at Oullins, a city located in the southwestern area of the Lyon's urban area. The length of the Chaudanne stream is 2743 m and it flows southeast, from 443 m elevation to its entry into the river Yzeron at 306 m (average gradient = 5 %). The basin area is 2.83 km 2 . Its head water is located in a rural area (2.22 km 2 ). The length of the studied reach is about 2.5 km. Four sites were studied (Fig. 1). Site 1 is located near the spring, uninfluenced by agricultural, road or urban inflows.

It is therefore considered as a reference site. Site 2 receives the first polluted input, from the drainage ditch of a factory. Site 3 is located 150 m below the main polluted input (Combined Sewer Overflow CSO of the "Pont de la Barge"). Site 4 is 500 m downstream of the CSO and receives a third input from the car park of a commercial zone (Nogueira, 2001, Fig. 1). The imperviousness of the surrounding urbanized landscape of sites 2, 3 and 4 does not exceed 15% [START_REF] Bernoud | Réponse écologique d'un ruisseau périurbain aux rejets de temps de pluie. TFE Mastère « Eau Potable et Assainissement[END_REF]. The stream bed is composed of stones, gravel and sand. The current velocity of surface waters is about 30 cm.s -1 in the riffles where the biological and chemical samples were collected. The surface water velocity decreases to less than 10 cm.s -1 during low stream discharges (August, October 2000). The temperature of surface waters varies from 6.5°C in winter (February 2000) to 18°C in summer (August 2000). The temperature of hyporheic waters (-20 to -30 cm depth) varies from 6.4°C in winter to 17°C in summer. The pH and conductivity are similar in surface and hyporheic waters and, respectively, vary from 6.5 to 8.3 and from 170 µS.cm -1 (site 1) to 532 µS.cm -1 (site 4) (Namour, unpublished data).Daily stream discharge measurements were available from a gauge located at site 2.

Material and methods

Benthic and hyporheic oligochaetes were sampled at the four sites on seven occasions (April, June, August, October andDecember 2000, February andApril 2001). Benthic sediments were collected using a Surber-type net (400 cm 2 aperture; net mesh-size: 0.160 mm). In the hyporheic system, 10 litres of material (sediments and interstitial water) were pumped from a depth of 20 to 30 cm using a Bou-Rouch pump [START_REF] Bou | Un nouveau champ de recherches sur la faune aquatique souterraine[END_REF]. At each site, three replicates were collected (a sample each 10 m). The three benthic replicates were pooled at each occasion. The three hyporheic replicates were kept separate. Samples were preserved in the field with 4% formaldehyde. In the laboratory, the mineral particles (stones, gravel, sand) of benthic and hyporheic samples were separated from the organic fractions (organic fragments and invertebrates) by decanting, and the organic fractions were washed through a 0.160 mm sieve. The residue from the sieving of each sample was poured into a gridded sub-sampling box. 100 oligochaete specimens were sorted by hand under a binocular microscope, if necessary from sub-samples taken randomly with a pipette from the squares of the sub-sampling box. Worm specimens were mounted on slides in a mixture of lactic acid and glycerin (50% glycerin, 50% lactic acid), covered by a cover-glass, and identified to species when possible under a microscope. Stream discharge was very low during August 2000, allowing benthic sampling of sites 2 and 3 only, the others being dry. The hyporheic sediments of the control site (Site 1) were sometimes clogged by silt, and the hyporheic system was dry during August 2000 at Site 4.

Hyporheic samples with total oligochaete densities in the 3 replicates less than 10 specimens were not retained, as the relative abundances of oligochaete species were mainly considered in the statistical analyses. To allow a comparison with pooled benthic collections, the data of the hyporheic replicates were pooled together, each pooled sample being characterized by the mean values (calculated from the 3 replicates) of the biological variables. Consequently, 18 hyporheic and 26 benthic samples were retained for analyses. The surface replicates were pooled in the field to allow a comparison with previous data sets. Conversely, the hyporheic replicates were kept separately and pooled only in the multivariate analysis. The data of each hyporheic replicate remain available and will be considered in other papers.

Data analysis

The seasonal distribution patterns of oligochaete assemblages at the 4 sites were analysed by a standardized Principal Component Analysis (PCA, software: ADE-4, [START_REF] Thioulouse | ADE-4: a multivariate analysis and graphical display software[END_REF]). The benthic system (26 samples) was separated from the hyporheic system (18 samples). The oligochaetes were gathered into 4 ecological groups (Table 1), called "functional traits" (FTrs, [START_REF] Lafont | Etat écologique d'un ruisseau péri-urbain soumis à des rejets de temps de pluie ; premiers résultats et perspectives[END_REF].

The FTrs were derived from the ecological knowledge of indicator oligochaete species that reveals the ecological functioning of the functional units "coarse surface sediments" and "hyporheic system" (FU3 & 4, Lafont 2001). Two other variables were considered: the total number of oligochaete species and the densities per sample, Log 10 (n + 1) transformed for normality (NOSP and EFBO, respectively).

These two last variables enabled incorporation of the species whose ecological preferences are not known or not considered as ecologically distinct.

The PCA reduces the number of input variables, and was here expected to describe meaningful ecological gradients and spatio-temporal patterns of benthic and hyporheic assemblages. Because relationships among variables could be slightly different between the hyporheic and the benthic systems and as the sampling devices were different, we performed a PCA for each system.

Results

A total of 46 taxa was found in the surface sediments and hyporheic system. The immature Tubificidae (with and without hair setae) and Lumbriculidae were not counted as individual taxa because adults of them were present. The unidentified Enchytraeidae accounted for 10 taxa. A notable record was Rhyacodrilus ardierae, which was first discovered near the spring of the river Ardières, in a headwater reach similar in size to the Chaudanne stream. It is considered a pollution-intolerant species [START_REF] Lafont | Description de Rhyacodrilus ardierae n. sp. (Oligochaeta, Tubificidae) récoltée dans l'Ardières (affluent de la Saône, France)[END_REF].

Distribution patterns of oligochaete assemblages

For the benthic samples (Fig. 2A), the axis F1 (53.6 % of the total variance) of a PCA of oligochaete assemblages separated species-rich samples, dominated by the species considered as indicators of hydrological exchanges between surface and ground water (AED species) and by pollution-intolerant ones (NSPO, FTr1, FTr2), that typically reflected the assemblage features of site 1, from assemblages characteristic of sites 2, 3 and 4 (Fig. 2B). These were characterized by high densities of oligochaetes (EFBO) and a predominance of pollution-tolerant species (FTr3). The second axis F2 (26.8 %) discriminated the samples rich in Tubificidae (FTr4) (site 2 October 2000, site 3, August and October 2000, site 4 June and October 2000). In the surface sediments, the factor F1 of the PCA was considered as characterizing organically polluted waters. The factor F2 characterized another type of pollution, with a predominance of Tubificidae worms indicating the presence of sludge in the sediment interstices. The reference site (1) was clearly separated from the remaining sites by an increasing dominance of FTr3+4 species, indicating a downstream pollution gradient, although the site located just below the combined sewer overflow (3) was apparently no more impaired than the site immediately above the outflow (2).

In the hyporheic zone (Fig. 3A), axis F1 accounted for 44.4 % of the total variance. It illustrated the difference between the global predominance of the Tubificidae (FTr4) at site 4 (Fig. 3B), from an association of AED and pollution-intolerant species (FTr1 & 2), particularly at sites 1 and 3. Axis F2 (24.5 % of the total variance) was mainly correlated with the absolute densities of oligochaetes (EFBO), and characterized the sites 3 (December 2000) and 4 (June and October 2000).

The F1-F2 plane discriminated site 1 from all the others. This site was frequently clogged by mineral particles and no oligochaetes were collected. But when silt was absent or reduced, the assemblages of the hyporheic zone were dominated by AED (FTr1) and pollution-intolerant species (FTr2).

Correlations with chemical features.

In the benthic system, the distribution pattern of oligochaetes on the F1-F2 plane was associated with an increasing gradient of nitrates (Fig. 2B), particularly from below the CSO (sites 3 and 4). Site 1 had good chemical quality compared to the 3 other ones, except for phosphorus. But the high standard deviation of phosphorus concentrations at the other sites reflected the phosphorus (and ammonium) peaks, characteristic of CSOs in urbanized environments [START_REF] Paul | Streams in the urban landscape[END_REF][START_REF] Walsh | Effects of urbanization on streams of the Melbourne region, Victoria, Australia. I. Benthic macroinvertebrate communities[END_REF]). In the hyporheic system (Fig. 3B), site 1 exhibited relatively high values of NH 4 + and PO 4 3-, probably related to mineral clogging at this site. The chemical alteration was marked at site 4 when considering ammonium salt contents (1.44 mg.L -1 , Fig. 3B), but not at the first site below the CSO (site 3). The nitrate contents also declined at site 4, implying reducing conditions, in contrast to sites 2 and 3, where high nitrate contents indicated oxidized situations.

Relations between stream discharge and assemblage features

The sludge effect, characterized by pollution-tolerant Tubificidae and Lumbricillus spp., was observed in the benthic system at all sites (Fig. 4) when the stream bed discharges were very low with high CSO peaks (August and October 2000), but was least pronounced at the reference site (site 1). The sludge effect was also strongly pronounced at site 4 during June, when stream discharges were falling. These results suggested that rainfall led to overflows from the surrounding environment and brought sediments into the stream, even at the reference site, and that the purification capacity of the stream decreased (low discharges). The sludge effect (FTr4) remained most pronounced at the sites below the sources of pollution (2, 3 and 4). When stream discharges increased (> 14 L.s -1 ), the sludge effect was much less marked in the benthic layer, but it remained strong in the hyporheic layer of site 4 (Fig. 4).

Discusssion

The species richness of the Chaudanne stream was high (46 taxa), probably because we considered both the surface and subsurface layers. The reference site (site 1) was predominated by pollution-intolerant species, which also are AED species, together with a greater species richness. We found similar ecological traits in a glacial unpolluted river (river Roseg, Lafont & Malard, 2001;[START_REF] Malard | A comparison of longitudinal patterns in hyporheic and benthic oligochaete assemblages in a glacial river[END_REF], where the surface and hyporheic habitats were colonized by pollution-intolerant AED species, particularly where upwellings of groundwater occurred. Site 3, located just below the main CSO, exhibited a distribution of epigean oligochaete assemblages similar to that of the site 2 above the CSO. In the hyporheic layer, the distribution of oligochaetes typified a rehabilitated situation compared to site 2 (Fig. 3B), with a predominance of pollution-intolerant AED species. This suggests that the effect of the CSO is not detrimental just below its inputs, and that benthic and hyporheic systems at site 3 were preserved by ground water upwellings. The high stream discharges had also a beneficial effect, probably by taking away the polluted sludge of the CSOs. Site 4 was the most vulnerable to a sludge effect, particularly in the hyporheic system, that might be attributed to an attenuation of the slope of the stream and the predominance of downwellings of polluted surface waters. These last observations emphasize the fact that the hyporheic system can accumulate nutrients and polluted inputs [START_REF] Hynes | Groundwater and stream ecology[END_REF][START_REF] Jones | Streams and ground waters[END_REF] and retain residues of past and present pollution [START_REF] Danielopol | Groundwater fauna associated with riverine aquifers[END_REF][START_REF] Giere | Meiobenthology. The microscopic fauna in aquatic sediments[END_REF][START_REF] Lafont | Superficial and hyporheic oligochaete communities as describers of pollution and water exchanges in the River Moselle system (France)[END_REF].

The alteration of chemical quality is seen below the CSO, but with relatively low concentrations of solutes. The mean ammonia salt contents reached 1.44 mg.L -1 at site 4. These contents are considered indicative of a "fair" quality in urban ecosystems [START_REF] Faulkner | Problems of quality designation in diffusely polluted urban streams -the case of Pymme's Brook, north London[END_REF]). An increase in phosphorus and nitrogen loads was observed between site 2 (just above the CSO) and site 3 just below the CSO, but did not reach alarming values. The hyporheic zone of site 1 exhibited relatively high values of ammonia salts and phosphorus contents, potentially related to the clogging of interstices by mineral particles. This conflicts with the good biological quality of the site. We assume that the comparison between solute concentrations and oligochaetes will be better understood by considering the fluxes of solutes, rather than their instantaneous concentrations. Probably, nitrogen and phosphorus exhibited relatively high contents in the hyporheic zone at site 1 because they were not intensely assimilated by living organisms, which were scarce or absent.

The temperatures of surface and hyporheic waters are important factors, particularly for deriving patterns of downwelling surface water and upwelling ground water [START_REF] Evans | Hyporheic temperature patterns within riffles[END_REF].

However, temperature was not considered an important factor because temperature ranges did not reach extreme values in Chaudanne stream. Temperature, as well as other important factors like oxygen and organic matter [START_REF] Strayer | Oxygen, organic matter, and sediment granulometry as controls on hyporheic animal communities[END_REF], will be considered in future studies,

The FTrs illustrated clear-cut gradients of oligochaete distribution in a situation not still severely polluted and where organic pollution predominated. The FTrs were empirically defined from literature data and our own experience and appear an attempt that by-passes regional and spatial heterogeneities and defines the functionalities of the studied habitats [START_REF] Lafont | Etat écologique d'un ruisseau péri-urbain soumis à des rejets de temps de pluie ; premiers résultats et perspectives[END_REF]. We are conscious that this approach is debatable. FTtr1 (permeability) seems relevant and supported by literature. FTr4 (sludge effect) is also relevant and supported by field experience on polluted coarsegrained habitats in running waters. The FTr2 (intolerance to water pollution) and FTr3 (tolerance to water pollution) are questionable. Moreover, the tolerance/intolerance to pollution of a given species is also strongly related to the habitat where it has been collected [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF].

The great majority of pollution studies regarding oligochaete communities considered fine sediments (see [START_REF] Chapman | Utility and relevance of aquatic oligochaetes in Ecological Risk Assessment[END_REF] and not coarse sediments or hyporheic systems. Nais communis is more tolerant of organic pollution in coarse than in fine sediments [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF]. The pollutiontolerant species of fine sediment-dwelling Tubificidae are collected in coarse sediments only when polluted sludge is trapped within the interstices [START_REF] Brinkhurst | Observation on the recovery of a British river from gross organic pollution[END_REF][START_REF] Datry | Video-logging for examining biogenic structures in deep heterogeneous subsurface sediments[END_REF]. Without polluted sludge, these species are not collected, even if the interstitial water is polluted. The ecological preferences of oligochaete species are also dependant upon the salinity of waters [START_REF] Leland | Benthic invertebrate distributions in the San Joaquin River, California, in relation to physical and chemical factors[END_REF], habitat heterogeneity [START_REF] Carter | Inter-annual changes in the benthic community structure of riffles and pools in reaches of contrasting gradient[END_REF] and time [START_REF] Verdonschot | Micro-distribution of oligochaetes in a soft-bottomed lowland stream (Elsbeek; The Netherlands)[END_REF]. But the hyporheic system is less sensitive to physical disturbances like floods than the benthic system, and its consideration in the ecological studies of watercourses has been recommended [START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF][START_REF] Boulton | Imperilled subsurface waters in Australia: Biodiversity, threatening processes and conservation[END_REF][START_REF] Hynes | Groundwater and stream ecology[END_REF][START_REF] Lafont | A conceptual approach to the biomonitoring of freshwater : the Ecological Ambience System[END_REF][START_REF] Petts | A perspective on the abiotic processes sustaining the ecological integrity of running waters[END_REF]. The evaluation of the tolerance/intolerance to pollution of oligochaete species is probably more reliable in the hyporheic layer. Indeed, in the hyporheic layer, the species stay in more direct and constant exposition to pollutants than in the superficial zone, where flow regimes are prevailing factors [START_REF] Bunn | Basic principles and ecological consequences of altered flow regimes for aquatic biodiversity[END_REF] and reduce the probability of species exposure to pollutants.

Another issue is that several species occupy 2 FTrs while others occupy only one (e. g. C.

atrata is characteristic of FTrs 1 & 2, the Tubificidae of FTr4). This means that the value of C. atrata is 0 to FTr4, and that the value of Tubificidae is 0 to FTr1 & 2, etc. This is an empiric simplification that needs several improvements. For example, Chaetogaster diastrophus is a common and abundant species in the Chaudanne stream, but it is above all a species which is tolerant to organic enrichment, but intolerant to severe organic pollution or toxic substances [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF]. It did not fit any of the 4

FTrs considered here, but other FTrs will be investigated, and we are conscious that the functioning of coarse and hyporheic sediments cannot be described by only 4 FTrs.

This first general survey was a feasibility study. We now plan to conduct multidisciplinary research on the Chaudanne stream, including studies of crustaceans and hydraulics modeling. This research is expected to improve our present knowledge about the value of oligochaete species and present or future FTrs as functional descriptors [START_REF] Lafont | A conceptual approach to the biomonitoring of freshwater : the Ecological Ambience System[END_REF][START_REF] Ruysschaert | Assessment of the hyporheic fluxes in a headwater stream exposed to combined sewer overflows[END_REF].

Table 1. Functional traits (FTrs) of the surface and hyporheic sediments.

Functional traits FTrs Oligochaete species characterizing each FTr

FTr1: Percentages of oligochaete species which indicate active hydrologic exchanges between surface and ground water (AED species) [START_REF] Gaschignard | Impact d'une crue sur les invertébrés benthiques d'un bras mort du Rhône[END_REF][START_REF] Juget | Oligochaeta of the epigean and underground fauna of the alluvial plain of the French upper Rhône (biotypological try)[END_REF][START_REF] Juget | Oligochaeta (incl. Aphanoneura) des eaux souterraines continentales[END_REF][START_REF] Juget | Theoretical habitat templets, species traits, and species richness: aquatic oligochaetes in the Upper Rhône River and its floodplain[END_REF][START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF][START_REF] Lafont | Essai de description biologique des interactions entre eau de surface et eau souterraine: application à l'évaluation de la vulnérabilité d'un aquifère à la pollution d'un fleuve[END_REF][START_REF] Lafont | Oligochaete worms as biological describers of the interaction between surface and groundwaters: a first synthesis[END_REF][START_REF] Lafont | Superficial and hyporheic oligochaete communities as describers of pollution and water exchanges in the River Moselle system (France)[END_REF] Trichodrilus [START_REF] Brinkhurst | Observation on the recovery of a British river from gross organic pollution[END_REF][START_REF] Datry | Video-logging for examining biogenic structures in deep heterogeneous subsurface sediments[END_REF][START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF][START_REF] Lafont | Superficial and hyporheic oligochaete communities as describers of pollution and water exchanges in the River Moselle system (France)[END_REF]. FTr1, FTr2: functional traits permeability and intolerance to water pollution; FTr3, FTr4: functional traits tolerance to water pollution and sludge effect; the chemical variables are expressed as mg.L -1 ; the standard deviations are put in brackets; NH4: ammonium salts; NO3: nitrates; PO4: orthophosphates.

Immatures of

Lafont et al. Table 1

Figure 4

Comparison between the stream discharge (unbroken lines), the CSOs' peaks and the sludge effect

  Tubificidae with and without hair setae, Tubifex ignotus, T. tubifex, Limnodrilus hoffmeisteri, Bothrioneurum sp, Lumbricillus spp. (in bacterial sewage-treatment beds, Solbé, 1975) Other species (less than 5% of oligochaete assemblages in the Chaudanne stream, except Chaetogaster diastrophus & Nais communis) are represented by the species richness and the absolute abundances of oligochaete assemblages per sample.

Figure captions Figure 1

 1 Figure captions

Figure 2

 2 Figure 2

Figure 3

 3 Figure 3

(

  FTr4), at the 4 stations of the stream Chaudanne; vertical arrows: dates of biological samples; stream discharge and CSOs' peaks are expressed as m 3 .s -1 ; ?: undetermined data.Lafont et al. Fig.3

Acknowledgements

We warmly thank Andrew Boulton, an anonymous reviewer and Adrian Pinder for their comments that enabled us to significantly improve our manuscript and the English language. We thank Christophe Lafont for his help in the field and the laboratory. This work was funded by the Observatoire de Terrain en Hydrologie Urbaine (OTHU), the Lyon's Urban Community, and the EU project URBEM (Urban River Basin Enhancement Methods, 5 th PCRD).


Michel Lafont
email: lafont@lyon.cemagref.fr

Anne Vivier

Oligochaete assemblages in the hyporheic

Keywords: Running waters, coarse sediments, hyporheic zone, Oligochaeta

Oligochaete assemblages in the hyporheic zone and coarse surface sediments: their importance for understanding of ecological functioning of watercourses M. Lafont, A.

Introduction

This paper does not represent an exhaustive survey of research contributions and as such is very incomplete regarding the study of surface coarse and hyporheic sediments for the watercourse functioning evaluation. We tried to underline what should be reasonably attainable when dealing with the ecology of oligochaete assemblages living in coarse surface sediments and the hyproheic zone, and their importance for understanding of ecological functioning of watercourses.

The hyporheic zone may be defined as the saturated interstitial areas beneath the stream bed and into the stream banks that contain some proportion of channel water [START_REF] Gibert | Surface water/groundwater ecotones[END_REF][START_REF] Vervier | A perspective on the permeability of the surface freshwater-groundwater interface[END_REF][START_REF] White | Perspectives on defining and delineating hyporheic zones[END_REF]. Underestimated for a long time, its relations with surface waters and its importance for understanding the ecology of river corridors is now well recognized [START_REF] Hynes | Groundwater and stream ecology[END_REF][START_REF] Bencala | A perspective on stream-catchment connections[END_REF][START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF][START_REF] Bretschko | Bed sediments, groundwater and stream limnology[END_REF][START_REF] Brunke | The ecological significance of exchange processes between rivers and groundwater[END_REF][START_REF] Danielopol | Ecological investigations on the alluvial sediments of the Danube in the Vienna area -a phreatobiological project[END_REF][START_REF] Danielopol | Groundwater fauna associated with riverine aquifers[END_REF][START_REF] Gibert | Surface water/groundwater ecotones[END_REF][START_REF] Hancock | Human impacts on the stream-groundwater exchange zone[END_REF][START_REF] Jones | Streams and Ground Waters[END_REF][START_REF] Malard | A landscape perspective of surfacesubsurface hydrological exchanges in river corridors[END_REF][START_REF] Malard | Longitudinal pattern of invertebrates in the hyporheic zone of a glacial river[END_REF][START_REF] Triska | Influence of exchange flow between the channel and hyporheic zone on NO 3 production in a small mountain stream[END_REF][START_REF] Valett | Perspectives on the hyporheic zone: integrating hydrology and biology. Introduction[END_REF]. [START_REF] Ward | The four-dimensional nature of lotic ecosystems[END_REF] pointed out the four dimensional (length, width, depth, time) structure of lotic ecosystems. [START_REF] Fellows | Whole-stream metabolism in two montane streams: Contribution of the hyporheic zone[END_REF] demonstrated that 40 to 93% of the whole stream respiration occurred in the hyporheic zone. These authors also demonstrated that important ecological processes can occur in the shallow but hydrologically dynamic hyporheic zone.

The bottom of watercourses formed in coarse-grained sediments is related to the hyporheic system and is the prime habitat where water exchanges between surface and subsurface occur. Coarse sediments generally predominate in the majority of freshwater ecosystems in France, excluding the deep zones of lakes, reservoirs, some back waters and aquatic habitats in the wetlands, but including the littoral zone of many lakes, including Lake Geneva. For example, the deep zones of the river Rhône are composed of coarse sand and gravel at 8m depth downstream of the urban area of Lyon, although the width of the river is about 200 m [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF]. Even in the slow-flowing river Saône, at Site Auxonne (150 metres width, current velocity less than 0.1 m.s -1 .), the fine-grained sediments are restricted to the bank areas where coarse sediments also predominate. The deep zone (-4 metres) is composed of gravel and coarse sand (Lafont, 1989 and unpublished data).

The benthic habitats of running waters formed by coarse sediment and the hyporheic habitats display a high permeability. The efficiency of permeable sediments in the degradation of organic matter was for a long time recognized [START_REF] Bou | Conséquences écologiques de l'extraction des alluvions récentes dans le cours moyen du Tarn[END_REF][START_REF] Solbe | Annelida[END_REF][START_REF] Solbe | The effects of temperature on the performance of experimental percolating filters with and without mixed macro-invertebrate populations[END_REF][START_REF] Williams | The effect of Psychoda alternata (Say.) (Diptera) and Lumbricillus rivalis (Levinsen) (Enchytraeidae) on the efficiency of sewage treatment in percolating filters[END_REF]) and used for purification processes in waste-water treatment plants (Bruce et al., 1983, cited by Datry et al., 2003). Their study in natural watercourses presents a challenging task for present and future researches. Research is now focusing on this domain and numerous recent papers have underlined the strong physicochemical and biological connections between surface and groundwater, and their importance for the ecological study of lotic ecosystems [START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF][START_REF] Boulton | Imperilled subsurface waters in Australia: Biodiversity, threatening processes and conservation[END_REF][START_REF] Hancock | Human impacts on the stream-groundwater exchange zone[END_REF]. To date biological studies were mostly devoted to metabolic and microbial activities (see [START_REF] Jones | Streams and Ground Waters[END_REF][START_REF] Griebler | Groundwater Ecology, European Communities[END_REF], or to crustacean assemblages (see [START_REF] Griebler | Groundwater Ecology, European Communities[END_REF]. The oligochaete assemblages received much less attention and research on that subject progressed more slowly than the biogeochemical and hyodrological studies [START_REF] Stanley | Surface-subsurface interactions: past, present, and future[END_REF], with generally a disconnection between the consideration of surface and subsurface zones [START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF].

Interstitial oligochaete assemblages and watercourse functioning

Overview

Oligochaete assemblages are well-known as common inhabitants of surface sediments and hyporheic zone, and they are also significant colonizers of groundwater, especially in deep karstic zones [START_REF] Malard | Groundwater contamination and ecological monitoring in a mediterranenan karst ecosystem in southern France[END_REF]. The consideration of a batch of 93 species demonstrated that at least 62 species were collected both in surface and groundwater [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF]. Moreover, the oligochaete assemblages may occur at all depths, from the surface to the deep hyporheos (Weigelhofer & Waringer, 2003). In addition, it is less mentioned that the surface coarse sediments shelter the richest assemblages of oligochaetes [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF]. Oligochaetes firmly keep their historical status of "sludge worms", giving the impression that they are only an accessory fauna in coarse sediments, whilst the Arthropods are the main faunal elements. Moreover, the use of unsuitable filtration methods, for example 0.500 mm mesh-size which is commonly used in macrobenthos studies, leads to a significant underestimation of oligochaete densities [START_REF] Nalepa | Screen mesh size affects estimates of macro-and meio-benthos abundance and biomass in the Great Lakes[END_REF] and the loss of about 50% of the species [START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF]. The species richness of small oligochaetes is greater, and this is particularly true in the interstices of the surface coarse sediments and hyporheic system, which generally shelter the smallest species. For example, in the Family Tubificidae, Branchiura sowerbyi, Tubifex tubifex or Limnodrilus spp. are giant species compared to members of the Rhyacodrilinae. Even Nais elinguis may be a giant compared to Rhyacodrilus falciformis, small Phallodrilinae, or species of the genus Cernosvitoviella.

The hyporheic oligochaetes have been less studied than other assemblages (e.g. crustaceans), with the exception of pioneer contributions like those of [START_REF] Botea | Contributii la studiul răspîndirii olgochetelor limicole din R.P.R[END_REF], [START_REF] Ladle | Studies on the biology of oligochaetes from the phreatic water of an exposed gravel bed[END_REF], [START_REF] Ferrarese | Ricerche sulla fauna interstiziale iporreica dell'Adige in relazione allo stato di inquinamento del Fiume[END_REF], [START_REF] Bird | Distribution, life cycle and population dynamics of the aquatic enchytraeid Propappus volki (Oligochaeta) in an English chalkstream[END_REF], Schwank (1982aSchwank ( , 1982b)), [START_REF] Dole | Le domaine aquatique souterrain de la plaine alluviale du Rhône à l'est de Lyon. I: diversité hydrologique and biocénotique de trois stations représentatives de la dynamique fluviale[END_REF], [START_REF] Gaschignard | Impact d'une crue sur les invertébrés benthiques d'un bras mort du Rhône[END_REF][START_REF] Dumnicka | Naididae (Oligochaeta) from subterranean waters of West Indian islands. Distribution, taxonomic remarks and description of a new species[END_REF], [START_REF] Juget | Aquatic oligochaeta of the Rhône-Alpes area: current research priorities[END_REF][START_REF] Juget | Oligochaeta of the epigean and underground fauna of the alluvial plain of the French upper Rhône (biotypological try)[END_REF][START_REF] Juget | Contribution to the study of Rhyacodrilinae (Tubificidae, Oligochaeta), with the description of two new stygobiont species from the alluvial plain of the French Upper Rhône, Rhyacodrilus amphigenus, sp. n. and Rhizodriloides phreaticola, g. n., sp. n[END_REF], [START_REF] Juget | Oligochaeta (incl. Aphanoneura) des eaux souterraines continentales[END_REF][START_REF] Strayer | Aquatic Microannelids (Oligochaeta and Aphanoneura) of undergroundwaters of Southeastern New-York[END_REF].

The lack of studies involving both invertebrate communities and hydrologic measurements has been pointed out [START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF], but this is not surprising because multidisciplinary researches are generally more difficult to organize. However, multidisciplinary studies put to the light more interesting findings than the sole consideration of biology or hydrology [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF][START_REF] Valett | Perspectives on the hyporheic zone: integrating hydrology and biology. Introduction[END_REF].

Examples from case studies

River Rhône at Grand Gravier site: definition of AED species

A first example is given by the comparison between oligochaete species and hydrologic measurements at a suburban polluted site (the "Grand Gravier") of the River Rhône downstream of the suburban area of Lyon [START_REF] Lafont | Essai de description biologique des interactions entre eau de surface et eau souterraine: application à l'évaluation de la vulnérabilité d'un aquifère à la pollution d'un fleuve[END_REF]. The hydrodynamic parameters were measured at a site about 500 metres long. Within this site, two stations of 50 metres each were selected and the filtration velocity of water through the sediments was assessed by piezometric measurements (2 transects per station). Station 1 (transects T1 and T2, Table 1) was characterized by a significant lower filtration velocity than Station 2 (T3 and T4). At both stations, oligochaeta were sampled in surface coarse sediments by means of a Surber net and a metallic corer driven into the substrate by a hammer (depth of the samples: 0 to 100 mm). A mesh-size of 0.160 mm was retained for the sediment filtration. The identification of oligochaetes was conducted to the level of species and informed us about several exciting features: 1) although a polluted site, the species richness was relatively high (33 species);

2) the biological quality of Station 2 (greater filtration velocity) was significantly better than that of Station 1, and this was related to a decrease of the percentages of pollution-tolerant Tubificidae;

3) at Station 2, a significant increase in the percentages of Gianius riparius (Phallodrilus riparius), Stylodrilus spp., Pristina and Pristinella spp., Marionina argentea, Spirosperma velutinus and Cernosvitoviella atrata was observed. These species were already known as groundwater dwellers and their significant abundances in surface sediments related to upwellings of groundwater (Botea, 1962;Gashignard, 1984;[START_REF] Juget | Aquatic oligochaeta of the Rhône-Alpes area: current research priorities[END_REF][START_REF] Juget | Oligochaeta of the epigean and underground fauna of the alluvial plain of the French upper Rhône (biotypological try)[END_REF][START_REF] Juget | Contribution to the study of Rhyacodrilinae (Tubificidae, Oligochaeta), with the description of two new stygobiont species from the alluvial plain of the French Upper Rhône, Rhyacodrilus amphigenus, sp. n. and Rhizodriloides phreaticola, g. n., sp. n[END_REF][START_REF] Juget | Oligochaeta (incl. Aphanoneura) des eaux souterraines continentales[END_REF][START_REF] Lafont | Contribution à la gestion des eaux continentales: utilisation des oligochètes comme descripteurs de l'état biologique et du degré de pollution des eaux et des sédiments[END_REF].

A second field investigation was performed in the same site at three different depths (-1.5, -4 and -8 metres, Table 1). Biological samples ware taken using the same Surber type net operated by divers and the mean filtration velocities were available at these stations [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF]. A significant increase in percentages of groundwater dwellers (Stylodrilus spp., S. velutinus, Rhyacodrilus sp., Pristinella osborni) was observed at 4 m depth, where the filtration velocities through the sediments were greater (mean filtration velocity: 6.3 m day -1 ). Conversely, the pollutiontolerant species did not significantly decline. More surprising was the increase of the percentages of Psammoryctides barbatus at -4 m, probably in relation to the predominance of coarse sand (Lafont et al., 1992). The results were more complex than expected, but suggested that the relations between filtration velocities and the percentages of groundwater-dwelling oligochaetes followed a linear pattern.

After these two field studies, the groundwater-dwelling oligochaetes were considered as Active Exchange Describers between surface and subsurface (AED species, [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF], because 1) they were primarily groundwater dwellers and; 2) they predominated in the surface layers where filtration velocities through hyporheic sediments were greater. A list of Active Exchange Describers (AED) was proposed [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF] and is constantly improved (Table 2).

River Roseg

In the glacial river Roseg (Switzerland), the upwellings of groundwater were measured by chemical analyses of the SiO 2 contents. [START_REF] Malard | Shifting dominance of subcatchment water sources and flow paths in a glacial floodplain (Val Roseg, Switzerland)[END_REF] showed that silica was an effective tracer of groundwater input to the river. Benthic oligochaetes were sampled with a Hess-sampler (sampling area: 0.043 m 2 ). Hyporheic oligochaetes were collected by driving a mobile pipe to a depth of 30 cm below the streambed [START_REF] Malard | A comparison of longitudinal patterns in hyporheic and benthic oligochaete assemblages in a glacial river[END_REF]. Ten litres of interstitial water were extracted using a Bou-Rouch pump [START_REF] Bou | Un nouveau champ de recherches sur la faune aquatique souterraine[END_REF]. The benthic and hyporheic samples were filtered through a 0.100 mm mesh size. The hyporheic oligochaete assemblages exhibited significant species richness and abundances only at stations where upwellings of groundwater occurred (Lafont & Malard, 2001).

Nearly all the collected species belonged to AED indicator taxa (Table 2), with the exception of Nais communis, a superficial species suspected to have developed morphological and physiological adaptations to subterranean life (Lafont & Malard, 2001). The benthic oligochaetes followed quite similar distribution patterns at stations where significant upwellings of groundwater occurred [START_REF] Malard | A comparison of longitudinal patterns in hyporheic and benthic oligochaete assemblages in a glacial river[END_REF]. The same predominant species were collected both in the surface and hyproheic sediments. The main difference was that the composition, abundance and distribution of oligochaete communities were more stable over time in the hyporheic system than in the benthic system.

River Moselle

In the river Moselle (France), the situation of surface water downwelling areas was also investigated, and we started from the hypothesis that they might be indicated by the invasion of subsurface areas by surface-dwelling oligochaete species. The oligochaete communities were collected at 5 stations both in surface and hyporheic sediments in June, August and October 1992 [START_REF] Lafont | Superficial and hyporheic oligochaete communities as indicators of pollution and water exchange in the River Moselle, France[END_REF]. Benthic oligochaetes were sampled with a Surber net sampler (sampling area: 0.04 m 2 ). Hyporheic oligochaetes were collected by driving a mobile pipe to a depth of 30 cm below the streambed, and ten litres of interstitial water were extracted using a Bou-Rouch pump [START_REF] Bou | Un nouveau champ de recherches sur la faune aquatique souterraine[END_REF]. The benthic and hyporheic samples were filtered through a 0.160 mm mesh size. The hydrologic measurements were restricted to the annual hydrographs of the river (1992). The use of a Factorial Correspondence Analysis (FCA) on the relative abundances of oligochaete species, collected in benthic and hyporheic samples, allowed to identify the three species groups which explained the first plane of the FCA (F1-F2= 37% of the total inertia). Group 1 included two superficial Naididae species, Nais barbata and Nais bretscheri. Group 2 was characterized by the predominance of superficial Tubificidae taxa, which are well-known for their pollution-tolerance (Limnodrilus hoffmeisteri and immature worms without hair setae). Group 3 comprised the Active Exchange Describers (AED) (P. volki, Pristina longiseta, P. aequiseta foreli and P. jenkinae). The seasonal evolution of oligochaete assemblages at Station 1 (the less polluted situation, no water pumping) showed that, both in surface sediments and the hyporheic system, the assemblages changed from being a superficial Naididae population (Group 1) in June, to a population of AED species (Group 3) in August and October (Fig. 1). At Station 4, the most polluted situation (paper-mill industry) with intensive groundwater pumping, surface sediments and the hyporheic system were predominantly colonized by taxa of Group 2 (pollution-tolerant genus Limnodrilus, Fig. 2). The dynamics of hydrological functioning, illustrated by the hydrographs, were consistent with the distribution of oligochaete assemblages at Station 1. The hyporheic system was invaded by surface species at the end of high surface water discharges (June, previous predominance of surface water downwellings). On the contrary, both surface sediments and the hyporheic system were invaded by AED species when low riverbed discharges occurred (August to October), suggesting that the river was predominantly fed by upwellings of groundwater. At Station 4, the predominance of the superficial and pollution-tolerant genus Limnodrilus, both in superficial sediments and the hyporheic system, was considered as the consequence of intensive pumping, the groundwater table being constantly low and downwellings of polluted surface water constantly predominating either during high or low riverbed discharges.

River Rhône at Chasse-sur-Rhône site

At Chasse-sur-Rhône, a polluted site of the river Rhône (downstream of the urban area of Lyon), the goal was to assess the vulnerability of a water-pumping area for drinking water supply [START_REF] Durbec | Etude de la vulnérabilité à la pollution du champ captant de Chasse-sur-Rhône (38)[END_REF]. The oligochaete samples were collected both in surface and hyporheic sediments in October 1992, under low river discharge conditions. The sampling methodology was strictly similar to the one used for studying the river Moselle. The 5 studied stations in the river were facing five pumping wells (P1 to P5) located into the banks. The percentages of pollution-tolerant species of Tubificidae were higher in the hyporheic zone than in the surface sediments at Stations P1 and P4, equal at P2 and P3 and lesser at P5 (Fig. 3). The biological features suggested: a) the predominance of downwellings of surface water at the whole site and the vulnerability of the groundwater resource to surface pollution, with Station P3 being the most vulnerable, and; b) the storage of pollution in the hyporheic system of P1 and P4, due to former downwellings. One sampling season was considered, however the biological results were in accordance with those of the hydrological study [START_REF] Durbec | Etude de la vulnérabilité à la pollution du champ captant de Chasse-sur-Rhône (38)[END_REF], except for P2, where the hydrological study did not mention the vulnerability to pollution.

Case of an urbanized site (Rhône basin)

At the Crépieux-Charmy site (urban area of Lyon), an alluvial zone of about 375 hectares was delineated for the protection of the groundwater resource devoted to drinking water supply. The oligochaete and crustacean assemblages were sampled on three occasions (June and November 1993, July 1994) in the coarse surface and hyporheic sediments at 12 stations of the river Rhône, the Miribel and the Jonage canals. The sampling methodology was the same as the one used for studying the river Moselle and Chasse-sur-Rhône site. The surface waters were only slightly polluted as the area is upstream of the industrial activities [START_REF] Camus | Etude de la vulnérabilité à la pollution du champ captant de Crépieux-Charmy (69)[END_REF]. The oligochaete species richness accounted for at least 59 species, with rare species like Trichodrilus intermedius. When considering the 13 species only found at the Grand Gravier [START_REF] Lafont | Essai de description biologique des interactions entre eau de surface et eau souterraine: application à l'évaluation de la vulnérabilité d'un aquifère à la pollution d'un fleuve[END_REF][START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF] and three others only found at Chasse-sur-Rhône [START_REF] Durbec | Etude de la vulnérabilité à la pollution du champ captant de Chasse-sur-Rhône (38)[END_REF], the coarse and hyporheic sediments of these three urbanized sites (Crépieux-Charmy, Gand-Gravier, Chasse-sur-Rhône) sheltered at least 75 species. The examination of the percentages of superficial species in the hyporheic layer and of the AED species in the surface sediments enabled a map to be drawn of the hydrologic exchange zones (Fig. 4). These results were in accordance with the global view of hydrologic evaluation, with the predominance of upwelling processes during low surface water discharges (July 1994, Fig. 4). The Crépieux-Charmy site gives an illustration of how to exploit oligochaete assemblages in integrated functional studies, although further refinements are expected (e.g. comparison of invertebrate assemblage patterns with hydrological modelling). This study also demonstrated the importance of surface coarse and hyporheic sediments for the protection of oligochaete biodiversity.

Discussion, conclusion

Very similar distribution patterns of surface and hyporheic oligochaete assemblages were obtained from different watercourses -the Moselle, the Rhône and the glacial river Roseg. Nine of the 16 oligochaete taxa collected from the river Roseg [START_REF] Malard | A comparison of longitudinal patterns in hyporheic and benthic oligochaete assemblages in a glacial river[END_REF] were found in the Crépieux-Charmy and Grand Gravier areas. The 6 Active Exchange Describers (AED) of the river Roseg were all collected in the river Rhône (Table 2). The main difference is that the number of AED species is greater in the Rhône than in the Roseg, in relation to a less harsh environment.

The pollution-tolerant species found in the hyporheic zone of the river Moselle are the same as those that dwell in polluted surface sediments [START_REF] Lafont | Superficial and hyporheic oligochaete communities as indicators of pollution and water exchange in the River Moselle, France[END_REF]. The same applies to karstic areas [START_REF] Malard | Groundwater contamination and ecological monitoring in a mediterranenan karst ecosystem in southern France[END_REF]. The great interest when considering oligochaete assemblages lies in their simultaneous values as water exchange and pollution indicators, which are related to their ability to colonize both surface and groundwater habitats. The studies of the river Moselle and river Rhône at the Chasse-surRhône site led us to the view that the hyporheic system keeps the "memory" of past and present pollutions in stony streams and rivers [START_REF] Lafont | Superficial and hyporheic oligochaete communities as indicators of pollution and water exchange in the River Moselle, France[END_REF]. This concept was strengthened by results obtained from the study of the ecological incidence of intermittent pollutions (combined sewer overflows CSOs) at four stations of a suburban stream (stream Chaudanne, Lafont et al., accepted).

The pollution indicators Tubifex tubifex and Lumbricillus rivalis predominated, from April 2000 to April 2001, in the hyporheic system at Station 4, located 500 m downstream of the CSOs, indicating that the hyporheic interstices became soaked with polluted sludge. This situation was related to high ammonium salt contents in the hyporheic waters and suggested that downwellings of polluted waters predominated. Moreover, T. tubifex and L. rivalis significantly occurred in the coarse surface sediments at Station 4 only when the CSOs were high and stream discharges very low (August to the beginning of October 2000). These results emphasized the general view that coarse surface sediments are more exposed to the variations of surface hydraulic conditions and more unstable than the hyporheic system [START_REF] Giere | Meiobenthology. The microscopic fauna in aquatic sediments[END_REF], a situation also illustrated by the study of the river Roseg [START_REF] Malard | Groundwater contamination and ecological monitoring in a mediterranenan karst ecosystem in southern France[END_REF]. In consequence, the benthic sediments give incomplete diagnoses of pollution effects.

The concept of the vulnerability of groundwater to a surface pollution was previously proposed [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF][START_REF] Lafont | Superficial and hyporheic oligochaete communities as indicators of pollution and water exchange in the River Moselle, France[END_REF]. However, this was a simplistic view as the hyporheic zone may also contaminate the surface sediments, a feature which is well-documented regarding nutrients [START_REF] Holmes | The importance of ground water to stream ecosystem function[END_REF] -that probably exists in the rivers Moselle and Rhône. Moreover, the surface sediments are not always permanently saturated and can become exposed during low water discharges, or removed during floods. Conversely, the hyporheic system is generally permanently saturated, even when the surface stream-bed has dried up, and it remains intact during floods, particularly in the deeper layers [START_REF] Mcelravy | Distribution and seasonal occurrence of the hyporheic fauna in a northern California stream[END_REF]. Because of this, the hyporheic zone may accumulate more pollutants. In conclusion, for fundamental or applied studies, the sole consideration of the surface sediments gives us incomplete information [START_REF] Danielopol | Groundwater fauna associated with riverine aquifers[END_REF][START_REF] Ferrarese | Ricerche sulla fauna interstiziale iporreica dell'Adige in relazione allo stato di inquinamento del Fiume[END_REF][START_REF] Hynes | Groundwater and stream ecology[END_REF][START_REF] Rouch | L'origine de la faune aquatique souterraine, entre le paradigme du refuge et le modèle de la colonisation active[END_REF][START_REF] Ward | Distribution patterns of interstitial freshwater meiofauna over a range of spatial scales, with emphasis on alluvial river-aquifer systems[END_REF]. In the case of pollution studies, it is a serious gap which might lead to a biased view about the state of ecological degradation. Furthermore, as the self-purification capacities of a river are strongly related to the hydric exchanges between surface and subsurface [START_REF] Hancock | Human impacts on the stream-groundwater exchange zone[END_REF], the biological assessment of downwellings (predominance of superficial species in the hyporheic zone) and upwellings (predominance of AED species in the surface sediments) would be very useful in the functional studies of watercourses where coarse sediments predominate.

Unfortunately, most biomonitoring schemes focus on the surface habitats and neglect the hyporheic system. In France, the IBGN index (invertebrate index, [START_REF] Afnor | Détermination de l'indice biologique global normalisé (IBGN)[END_REF], the diatom index IBD [START_REF] Afnor | Détermination de l'Indice biologique Diatomées (IBD)[END_REF] and the oligochaete index IOBS [START_REF] Afnor | Détermination de l'indice oligochètes de bioindication des sédiments (IOBS)[END_REF] only refer to the surface habitats. The biomonitoring of hyporheic zones remains disconnected from that of the benthic system, except some valuable recent proposals [START_REF] Boulton | River ecosystem health down under: assessing ecological conditions in riverine groundwater zones in Australia[END_REF][START_REF] Boulton | Imperilled subsurface waters in Australia: Biodiversity, threatening processes and conservation[END_REF]. This situation is not satisfactory because of the close connections between surface and groundwater.

The value of oligochaetes as pollution indicators is well-recognized, as well as their strong relations with organic matter which is for example attested by their role in wastewater treatments [START_REF] Bou | Conséquences écologiques de l'extraction des alluvions récentes dans le cours moyen du Tarn[END_REF]Bruce et al., 1983, cited by Datry et al., 2003). Oligochaete metabolic activity in coarse sediments and the hyporheic zone is well less known. This is an important ecological trait which has not been studied enough, but is in the course of being developed in field [START_REF] Datry | Dynamics and adaptive responses of invertebrates to suboxia in contaminated sediments of a stormwater infiltration basin[END_REF] and experimental case studies (Mermillot-Blandin et al., 2003).

The value of oligochaete assemblages as indicators of pollution, metabolic activities and water exchange is shared with other biocenoses. However the attractive characteristic of oligochaetes is that they might enable biologists to simultaneously assess the effects of pollution, dynamics of water exchanges and metabolic activities. Conversely, oligochaetes are not universal indicators and other taxocenoses must be considered to supplement and refine the diagnoses. The simultaneous use of crustacean and oligochaete communities at the Crépieux-Charmy site (Fig. 4) is a good example of an integrated ecological diagnosis. If the ecological value of oligochaetes in surface coarse sediments and the hyporheic system was until now underestimated, it is also important not to overestimate their importance.

The present and relevant classifications of groundwater organisms (stygoxene, stygophile and stygobite organisms) [START_REF] Claret | A functional classification of interstitial invertebrates: supplementing measures of biodiversity using species traits and habitat affinities[END_REF] were historically based on the examination of crustacean assemblages or aquatic insect larvae. However, oligochaete species do not easily fit into these classifications and new proposals must be made. The hyporheic zone is generally considered as an ecotone and a refuge during floods or drought [START_REF] Griebler | Groundwater Ecology, European Communities[END_REF]. Regarding oligochaete communities, the hyporheic zone might be above all a reservoir of species, and probably the main route for the dissemination of species (Lafont & Malard, 2001). These observations are consistent with the concepts of Brestsko (1991) and Naiman et al. (1988, cited by Brestchko 1991).

As a conclusion, it is suggested that the study of coarse surface sediments and hyporheic systems is indispensable to understand the ecological functioning of watercourses. The fine sediments must be considered in biomonitoring studies (Lafont et al., 2001), but in watercourses where the coarse sediments predominate, the interest of fine sediments for the understanding of river functions declines when their percentage cover of the river bed is reduced [START_REF] Lafont | A conceptual approach to the biomonitoring of freshwater : the Ecological Ambience System[END_REF]. Our present research focuses now on the study of surface coarse sediments and the hyporheic system, with special reference to the comparison between the distributions of invertebrate assemblages, the modelling of hydrological exchanges and the geomorphological background. [START_REF] Lafont | Essai de description biologique des interactions entre eau de surface et eau souterraine: application à l'évaluation de la vulnérabilité d'un aquifère à la pollution d'un fleuve[END_REF]; [START_REF] Lafont | Oligochaete worms as biological describers of the interactions between surface and groundwater: a first synthesis[END_REF].

- ------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------

- Station 1 Station 2 Deep zone --------------------------------------------------------------------------------------------------------------------------- Transects T1 T2 T3

21

Table 2. List of Active Exchange Describers (AED); from [START_REF] Juget | Theoretical habitat templets, species traits, and species richness: aquatic Oligochaetes in the Upper Rhône River and its floodplain[END_REF]; Lafont (unpublished data); Lafont et al. (1992 and accepted); [START_REF] Sambugar | Groundwater oligochaetes from Southern-Europe. Tubificidae with marine phyletic affinities: new data with description of a new species, review and consideration on their origin[END_REF]; **: mentioned in the surface and hyporheic sediments of the glacial river Roseg [START_REF] Malard | A comparison of longitudinal patterns in hyporheic and benthic oligochaete assemblages in a glacial river[END_REF].

Hydrologically validated AED

Spirosperma velutinus,

all

Figure 4

The Crépieux-Charmy site ; the ways of the water exchanges between surface and subsurface were mapped in July 1994 by the examination of crustacean (C) and oligochaete (O) assemblages.

Figure captions Figure 1 :

 captions1 Figure captions

Figure 2 :

 2 Figure 2:

Figure 3

 3 Figure 3

Table 1 .

 1 Structure of oligochaete assemblages at four transects at the Grand Gravier site (River Rhône); (1): pollution-tolerant Tubificidae, excluding Spirosperma velutinus and Psammoryctides barbatus; AED: Active Exchange Describers (Pristina and Pristinella spp., Cernosvitoviella sp., Stylodrilus sp., S. velutinus, Rhyacodrilus sp.); from

Acknowledgements

We thank D. Danielopol for his kind proposal of commenting on our manuscript, also F. Malard for his help before the Nine International Symposium on Oligochaete Biology. We are gratefully indebted to the two anonymous reviewers for their comments that enabled us to significantly improve the manuscript. This work was partly funded by the European Project URBEM (Urban Water Enhancement Methods).