Tobias M Scheuermann

Paul Kotyczka

Christian Martens

Haithem Louati

Bernhard Maschke

Marie-Line Zanota

Isabelle Pitault

An Object-Oriented Library for Heat Transfer Modelling and Simulation in Open Cell Foams

Keywords: Port-Hamiltonian systems, metallic foam, cell method, distributed parameter systems, discrete modeling, geometric discretization, process systems, simulation

published or not. The documents may come

INTRODUCTION

Metallic foams are a type of material that is used in multiple ways for industrial purposes. Two classes of metallic foams are distinguished: closed and open cell foams. In closed cell foams, the fluid phase is encapsulated in closed cavities inside the foam. Open cell foams have connected porous cells so that the fluid can flow through the material. In this paper, we will concentrate on the latter. Due to their high surface to volume ratio, open cell metallic foams are used in catalytic reactors, see e. g. [START_REF] Frey | Open cell foam catalysts for co2 methanation: Presentation of coating procedures and in situ exothermicity reaction study by infrared thermography[END_REF]. In order to design and control the chemical processes in a reactor, numerical models of the thermodynamic behaviour are needed. Existing approaches use effective properties, e. g. from volume averaging over Cartesian unit cells [START_REF] Quintard | Two-medium treatment of heat transfer in porous media numerical results for effective properties[END_REF].

With the use of tomography, precise 3D voxel data of a given foam sample can be generated and topological as well as geometric data can be extracted using image processing software like iMorph [START_REF] Brun | Imorph: A 3d morphological tool to fully analyse all kind of cellular materials[END_REF]. We will show an approach to set up a numerical model for the heat transfer on open cell foams that is directly based on the possibly heterogeneous foam topology. Microscopic material parameters and the exact geometry complete the model in the discrete constitutive equations.

The separation of a (Dirac) interconnection structure to describe the structural exchange of power (or the time derivative of another appropriate potential) via pairs of conjugated port variables from material-dependent constitutive equations and energy storage, is at the heart of the Port-Hamiltonian (PH) framework, see e. g. [START_REF] Duindam | Modeling and Control of Complex Physical Systems[END_REF] for an overview. In [START_REF] Seslija | Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems[END_REF], and later for non-uniform boundary conditions in [START_REF] Kotyczka | Discrete port-hamiltonian formulation and numerical approximation for systems of two conservation laws[END_REF], the discrete modelling of conservation laws on dual chain complexes was presented. The preliminary work [START_REF] Scheuermann | Numerical approximation of heat transfer on heterogenous media[END_REF] illustrates the discrete modelling of heat transfer and exchange on open cell foams.

In this paper, we adopt this paradigm for the computerbased modelling and simulation of heat transfer on open cell foams. We present the necessary extensions for the classification of topological objects from the regular 2D case as presented in [START_REF] Kotyczka | Discrete port-hamiltonian formulation and numerical approximation for systems of two conservation laws[END_REF] to irregular 3D meshes in Section 2. The structured representation of the coupled heat equation on dual complexes is presented in Section 3, while we show how this model directly maps to the object oriented python code in Section 4. A numerical example is given in Section 5, and the paper closes with final remarks and an outlook in Section 6.

IMAGE PROCESSING

The input data for model generation and simulation is obtained from the image processing tool iMorph 1 . iMorph can extract the structure of the foam from 3D tomography pictures. A typical example is shown below. Fig. 1a shows the image of an open cell foam sample, while Fig. 1b displays the extracted solid graph. Besides the solid nodes (Fig. 2a) and struts (Fig. 2b), which are represented by the edges of the solid graph, iMorph identifies cells (Fig. 2c) in the fluid phase. These cells are connected by so-called "windows" (Fig. 2d).

DISCRETE HEAT EQUATION ON DUAL COMPLEXES

The modelling is based on the cell method, see [START_REF] Alotto | The Cell Method for Electrical Engineering and Multiphysics Problems[END_REF] for an introduction to this numerical scheme with references to the original works [START_REF] Tonti | A direct discrete formulation of field laws: the cell method[END_REF] and applications. The PH framework explicitly considers open systems, i. e. systems with boundary energy flow, see [START_REF] Seslija | Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems[END_REF] for the discrete modelling of conservation laws and van der Schaft and Maschke (2013) for PH systems on graphs. We follow the regular 2D approach described in [START_REF] Kotyczka | Discrete port-hamiltonian formulation and numerical approximation for systems of two conservation laws[END_REF]. The heterogeneous 3D case considered here requires some adaptations and additions, which are illustrated below.

Cells, Chains and Chain Complex

The topology and geometry of the foam is described in a structured way using j-dimensional cells, or in short "j-cells"2 , see [START_REF] Arnold | Mathematical Methods of Classical Mechanics[END_REF], Section 35.D or Flanders (1989), Section 5.5. A j-cell is a geometric object that consists of a convex polyhedron D ⊂ R j , a differentiable f : D → M on the n-dimensional manifold M and an orientation. A formal sum of j-cells is called j-chain.

The linear vector space of j-chains on a tessellation K is denoted C j (K, R). The boundary of each j-cell consists of a j -1-chain and is found by applying the boundary operator ∂ j . Applying the boundary operator twice to a jchain results in an empty set, which is the central property of a chain complex, see e. g. Jänich ( 2001), Section 7.6. The spaces of j-chains, j = n, . . . , 0, which, connected via the boundary operators, form an n-complex, can be represented in a sequence diagram:

C n (K, R) ∂n -→ C n-1 (K, R) ∂n-1 -→ . . . ∂1 -→ C 0 (K, R) (1)
In the following, we call a n-chain with the collection of all j-cells, j = 0...n, appearing in the sequence above, an ncomplex. The symbol ∂ will be used for both the boundary operator and its matrix representation, i. e. an incidence matrix. For our application, only the case with n = 3 is relevant, so we will restrict ourselves to this case.

Definition of the Primal 3-Complex

The primal 3-complex is initially given by the structure of the solid phase. Since an n-complex can be seen as a generalized directed graph, orientations have to be assigned to all j-cells. The nodes (0-cells) and edges (1-cells) of the primal 3-complex can be taken directly from the graph generated with iMorph. Faces (2-cells) correspond to the iMorph windows. The windows that enclose a fluid cell define a volume (3-cells).

The following classification of inner and border j-cells is necessary for the direct imposition of boundary conditions in the numerical model. Remark 1. On first sight it may seem, that some nodes in Fig. 3, especially at the corners, are missing. However, they were left out intentionally. Similar to the additional boundary edges in the 2D case in (Kotyczka and Maschke, 2017, Fig. 5), that have no nodes at the corner of the face, the volumes in the 3D case can also have corners without nodes. In 3D, there can even be kinks in the faces without having a "real" edge at that position. These kinks are drawn with dotted lines and lie inside a face and have therefore no effect on the result of the boundary operator applied to the face. Remark 2. The categorization differs from [START_REF] Kotyczka | Discrete port-hamiltonian formulation and numerical approximation for systems of two conservation laws[END_REF], because the physical variables are assigned to the geometric objects in another way. This is because the energy balance is evaluated on the dual volumes instead of the primal faces. Subsequently, the driving force is evaluated on the primal instead of the dual edges.

Construction of the Dual 3-Complex

The dual 3-complex is defined by construction. For better visibility, only one dual j-cell is drawn in Fig. 8. The same procedure is repeated for all other primal j-cells.

A barycentric dual is used, as in [START_REF] Alotto | The Cell Method for Electrical Engineering and Multiphysics Problems[END_REF]. This means, that the dual node is located at the barycentre of the primal volume (Fig. 8a). Accordingly, a dual edge intersects with its primal face at the barycentre of the face (Fig. 8b) and the dual face intersects with the primal edge also at the barycentre of the edge (Fig. 8c). The dual complex is completed with the dual volumes around the primal nodes (Fig. 8d).

Discrete PH Respresentation

For a structured discrete model of the heat transfer on the foam, we start with the well-known heat equation with distributed parameters on a single phase,

x ∈ Ω ⊂ R 3 , t ∈ R + 0 , c Ṫ (x, t) = λ∆T (x, t).
(2) T (x, t) denotes the temperature, the heat capacity c and the thermal conductivity λ are assumed to be constant. We rewrite (2) in port-Hamiltonian form (neglecting for the moment the boundary conditions) using the inner energy density u(x, t) as state and T (x, t) as co-state/effort 3 , u

f = 0 -div -grad 0 T φ . (3)
φ(x, t) and f (x, t) denote the vectors of heat flux and the temperature gradient as the thermodynamic driving force.

The model is completed with the constitutive laws

φ = λf u = cT. (4)
The discrete model is found by integrating the equations over the appropriate j-chains of the dual and the primal complex, respectively, as indicated in Table 3 with superscript s or f referring to the solid or the fluid phase.

3 Which is the conjugate quantity w. r. t. the artificial potential

Ω 1 c u 2 (x, t)dx.
Û s k = - l∈I(k) Φs k,l -Φsf k (5a) ∂ ∂t Û f k = - l∈I(k) Φf k,l + Φsf k . ( 5b
)
The heat flow Φsf k represents the heat transfer between both phases. The temperature differences along a strut (index k, 1 and 2 refer to the start and end node) for both phase, as well as between both phases are

F s k = -(T s k,2 -T s k,1 ), F f k = -(T f k,2 -T f k,1 ) (6a)
F sf k = T s k -T f k .
(6b) Finally, the discrete approximations of the constitutive equations ( 4) for both phases, together with the heat transfer model between both phases are

Φs k = λA s k F s k |r k,2 -r k,1 | , Φf k = λA f k F f k |r k,2 -r k,1 | (7a) Φsf k = αA sf k F sf k (7b) Û s k = V s k c s T s k , Û f k = V f k c f T f k .
(7c) The discrete geometry parameters (note that ( 5) and ( 6) contain only topological information) are given in Table 2.

A s/f k Solid / fluid part of the area of f k A sf k Contact area of the phases in v k V s/f k Solid / fluid part of the volume of v k
To obtain a numerical model of the heat transfer in the complete foam, we collect the whole set of variables Ûk , F k , T k and Φk in the vectors Ûi/b , F i/b , T i/b and Φi/b , which represent inner / border co-chains as algebraically dual objects to the j-chains of the primal and the dual complex 4 . The result is the following system of equations, where d3

ii/bi = -(d 1 ii/bi ) T and d 1 ii/ib denote the co-incidence matrices (i. e. the transposed boundary matrices) between 4 For a given j -1-co-chain c j-1 , which contains the integral values of a quantity over j -1-chains, the duality pairing, see [START_REF] Seslija | Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems[END_REF],

c j-1 , ∂ j c j = d j c j-1 , c j (8)
defines the co-boundary operator d j . The sequence of spaces of cochains and co-boundary operators defines a co-chain complex

C 0 (K, R) d 1 -→ C 1 (K, R) d 2 -→ . . . d n -→ C n (K, R). (9)
faces and volumes on the dual complex and nodes and edges on the primal complex, respectively 5 .

       Us i Uf i F s i F f i F sf i        =       0 0 (-d 1 ii ) T 0 I 0 0 0 (-d 1 ii ) T -I d 1 ii 0 0 0 0 0 d 1 ii 0 0 0 -I I 0 0 0              T s i T f i Φs i Φf i Φsf i        +       0 0 (-d 1 ib ) T 0 0 0 0 (-d 1 ib ) T d 1 ib 0 0 0 0 d 1 ib 0 0 0 0 0 0           T s b T f b Φs b Φf b     (10)
The subscripts i and b denote the locations (in the interior or at the boundary) of the j-chains, on which the discrete quantities are defined as presented in the previous subsections. Note that the skew-symmetry of the first matrix mimics the formal skew-adjointness of the matrix operator in (3).

The model is again completed by the constitutive laws

Ûs/f = C s/f T s/f (11a) Φs/f = Λ s/f F s/f (11b) with the diagonal matrices C s/f = diag(V s/f k c s/f ) (12a) Λ s/f = diag λA s/f k |r k,2 -r k,1 | (12b) 4. IMPLEMENTATION
For the implementation of the 3-complexes and their jcells, we chose an objected oriented approach using the programming language Python. The goal of this implementation is to represent the relations between j-cells in the code. The general structure of the core classes is shown as a UML diagram in Fig. 9. For better treatment of jcells with reverse orientation, the implementation includes some more classes than shown, but they follow the same architecture.

To avoid redundancy, the classes of all j-cells inherit from a Cell class where common properties like numbering or labeling are implemented. Node, Edge, Face and Volumes classes must be instantiated from top to bottom, since every class needs an aggregation of its predecessor. This approach relates to the application of the co-boundary operator as in (9).

All objects of j-cells are collected in an instance of the PrimalComplex class, where the classification is implemented and the incidence matrices are calculated. The DualComplex automatically generates all dual j-cells.

NUMERICAL EXAMPLE

The presented approach is applied to a grid based on Kelvin cells as shown in Fig. 10, which has 848 degrees 5 For the relations of co-incidence matrices between the dual complexes, see [START_REF] Kotyczka | Discrete port-hamiltonian formulation and numerical approximation for systems of two conservation laws[END_REF] of freedom (DOFs). For better replicability, the grid is constructed, so that we can test the numerical method without depending on user settings in iMorph or the need to compensate possibly occuring defaults in the iMorph result. On the top and bottom boundary, a DBC is applied (Fig. 11a). The other boundaries have a NBC (Fig. 11b), in our case the heat transfer is set to 0, meaning it is perfectly isolated at theses boundaries. The material parameters used in the simulation are given in Table 3. Fig. 12 shows the transient behaviour of the temperature on 4 selected nodes. T 0 is the constant temperature at the bottom boundary, while T 3 is increased at the top. T 1 and T 2 are the temperatures of two nodes at different heights close to the front boundary.

For comparison, a Finite Element (FE) simulation with 18 081 DOFs was performed with a surrogate parameter for the diffusivity a eff = λ eff ρ eff c eff using FEniCS [START_REF] Alnaes | The fenics project version 1.5[END_REF]. The results are shown with markers and the superscript c. The perfect matching of both our simulation based on the structured model with the surrogate FE simulation is due to two facts: (a) the surrogate diffusivity has been determined by curve fitting and (b) did we only consider the "harmless" case of pure heat conduction without the consideration of convective transport.

CONCLUSION AND OUTLOOK

We showed a structured approach to obtain a numerical model of heat transfer through metallic open cell foams, in which the separation of topology (expressed in terms of co-incidence matrices) on the one side and geometry and material parameters (constitutive equations) on the other side mimics the PH structure of the local PDE model. The model allows to identify macroscopic foam parameters, and can be used for design optimization and (after possible model reduction) for control.

The model structure directly maps to the objects and dependencies of the object oriented python library, which can read topology and geometry data over an interface to the iMorph image processing software. We presented the simulation of a realistic foam model and its comparison to a FE simulation with surrogate effective parameters.

At the moment, we work in several directions: (a) the simulation of real foam data and comparison with the experimental data obtained at LGPC Lyon, (b) the integration of convection in the model and (c) improving robustness of our model generation with respect to artefacts like not fully connected graphs from image processing.

  This work was supported by Deutsche Forschungsgemeinschaft (project number 317092854) and Agence Nationale de la Recherche (ID ANR-16-CE92-0028), project DFG-ANR INFIDHEM.

Fig. 1 .

 1 Fig. 1. Metallic open cell foam (Kelvin cells)

Fig. 2 .

 2 Fig. 2. Structures in open cell foams defined by iMorph

  Fig. 4. Primal nodes

  Fig. 5. Primal edges Inner faces: Faces belonging to windows that are entirely inside the domain, are called inner faces f i ∈ F i .

  Fig. 6. Primal faces

Fig. 8 .

 8 Fig. 8. Primal and associated dual cells

Fig. 9 .

 9 Fig. 9. Simplified UML diagram

Fig. 10 .

 10 Fig. 10. Geometry of the example foam

Fig. 12 .

 12 Fig. 12. Transient beaviour of the foam

Table 1 .

 1 j-chains and associated quantities

	j-chain	(Integral) physical quantity
	Primal node n k Primal edge e k	s/f k Temperature T Driving force (temperature difference) F k s/f
	Dual face fk Dual volume vk	Heat flow rate Energy Û s/f k	Φs/f k
	If k is the index for a dual control volume, and the set I(k)
	contains the indices of the boundary faces, the discrete
	energy balance on such a control volume can be written
	for both the solid and the fluid phase as
	∂
	∂t

Table 2 .

 2 Geometry parameters

	Parameter Definition
	r k	Position vector of node n k

  [START_REF] Seslija | Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems[END_REF].

	Cell		DualCell
	Node	1..*	DualNode	1..*
	2		2
	2..*		2..*
	Edge	1..*	DualEdge	1..*
	3..*		3..*
	2..*		2..*
	Face	1..*	DualFace	1..*
	4..*		4..*
	1..2		1..2
	Volume	1..*	DualVolume	1..*
		1		1
	PrimalComplex	DualComplex

Table 3 .

 3 Material parameters

	Dimensions	l × w × h	40 × 40 × 40 mm
	Mass		m	16.463 g
	Density of aluminium		ρ s	2.7 × 10 -3	g mm 3
	Density of air		ρ f	1.204 × 10 -6	g mm 3
	Heat capacity of Al		c s	0.897	J g K
	Heat capacity of air		c f	1.005	J g K
	Thermal conductivity of Al	λ s	0.2	W mm K
	Thermal conductivity of air	λ f	2.6 × 10 -5	W mm K
	Heat transfer coefficient		α	1.0 × 10 -4	W mm 2 K
	Surrogate thermal diffusivity a eff	1.85	mm 2 s

The term "cell" is used in two contexts, that should not be confused with each other: It is used in iMorph to describe a cavity in the foam or a j-dimensional geometric object. Therefore, the latter is always denoted as j-cell.

ACKNOWLEDGEMENTS

The authors cordially thank Jerôme Vicente from University Aix-Marseille for the help with iMorph and in particular for implementing modifications in the new iMorph version that allow us to directly access all necessary objects and parameters.


Frédéric Marin
email: frederic.marin@u-bourgogne.fr

Virginie Morin

Frédéric Knap

Nathalie Guichard

Benjamin Marie

Gilles Luquet

Peter Westbroek

Davorin Medakovic

Fred Knap

Caspartin: thermal stability and occurrence in mollusk calcified tissues

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

INTRODUCTION

Among mollusks, the biomineralization of the shell is regulated by a mixture of glycoproteins and polysaccharides, collectively named the shell matrix. This amalgamate is secreted by the calcifying mantle epithelium. It interacts with the mineral ions, to form calcium carbonate biominerals, calcite or aragonite. The matrix remains closely associated with the formed minerals. It can be retrieved by dissolving the mineral phase with a weak acid or with a calcium-chelating agent like EDTA. It is then usually analyzed by classical fractionation techniques, mostly electrophoresis or chromatography. One drawback of these approaches is that they are tedious and time-consuming, and that they do not allow the comparison of numerous matrices at the same time.

One way to overcome this difficulty is to use immunological techniques. Antibodies constitute indeed powerful tools in biomineralization research [START_REF] Muyzer | Immunology and organic geochemistry[END_REF]. They have been successfully employed for serotaxonomical studies [START_REF] Muyzer | Immunological approaches in geological research[END_REF][START_REF] Curry | Immunological responses from brachiopod skeletal macromolecules; a new technique for assessing taxonomic relationship using shells[END_REF] and for detecting macromolecules from fossil shells [START_REF] Muyzer | Immunological approaches in geological research[END_REF][START_REF] Collins | Macromolecules in brachiopod shells: characterization and diagenesis[END_REF] Typically, an antibody recognizes specifically a short portion of the target-antigen, for proteins, 4 to 10 amino acids. An antibody allows large-scale comparisons against several matrices, and, because the immunological recognition is sensitive, the technique does not require large quantities of antigens.

In the present case, a polyclonal antibody was obtained from caspartin, a shell protein extracted from the outer prismatic layer of the bivalve Pinna nobilis [START_REF] Marin | Caspartin and calprismin, two proteins of the shell calcitic prisms of the Mediterranean fan mussel Pinna nobilis[END_REF]. Caspartin is an Asp-rich protein, migrating at 17 kDa of apparent molecular weight. It is not glycosylated, weakly bind calcium, and is able to polymerize. It is located around and within the prisms. Its complete primary structure has not been elucidated yet. In the present study, the anticaspartin antibody is used for two purposes: -To check the thermal stability of caspartin.

-To investigate the presence of caspartin, or immunologically related proteins, in the calcified tissues of several mollusks.

MATERIALS AND METHODS

Shell material preparation

Shells of juvenile specimens of the mediterranean fan mussel Pinna nobilis were provided by CERAM (Centre d'Etude des Ressources Animales Marines, Prof. N. Vicente, Marseille, France). Only the prismatic calcitic shell layer was used for the study. Prismatic shell fragments were scrupulously cleaned. Isolated calcitic prisms were obtained after a long treatment with dilute sodium hypochlorite, as described in a previous study [START_REF] Marin | Large-scale fractionation of molluscan shell matrix[END_REF].

Protein purification and polyclonal antibody production

The sieved cleaned powder of calcitic prisms was decalcified with dilute acetic acid, and the acetic acid-soluble matrix was treated as previously described [START_REF] Marin | Molluscan shell matrix characterization by preparative SDS-PAGE[END_REF]. Caspartin, an Asp-rich 17-kDa protein, was obtained by preparative SDS-PAGE [START_REF] Marin | Large-scale fractionation of molluscan shell matrix[END_REF]. Polyclonal antibodies against caspartin were raised in a white rabbit, according to a standard immunization procedure [START_REF] Marin | Molluscan shell matrix characterization by preparative SDS-PAGE[END_REF]. The specificity of the antiserum was checked on Western-blots [START_REF] Towbin | Electrophoretic transfer of proteins from polyacrylamide gels to nitrocellulose sheets: procedures and some applications[END_REF].

Thermal stability of caspartin

The thermal stability of caspartin was measured as follows: prism preparation (1 g) were heated at 100°C in a drying oven, for different durations, from 1 to 11 days. The preparations were crushed, dissolved in cold dilute acetic acid (10% vol/vol) overnight then centrifuged (3900 g) for separating the insoluble matrix from the soluble fraction containing caspartin. The volumes of the soluble matrices were reduced by ultrafiltration (10 kDa cutoff membrane), then dialyzed against water. All the matrices were freeze-dried, before being analyzed on SDS-PAGE (15% acrylamide). The gels were stained with silver or 'Western-blotted' on PVFD membranes (Immobilon), which were subsequently incubated with the anti-caspartin antiserum (for technical details, see [START_REF] Marin | Caspartin and calprismin, two proteins of the shell calcitic prisms of the Mediterranean fan mussel Pinna nobilis[END_REF].

Occurrence of caspartin or caspartin-related peptides in several shell matrices

The presence of peptides, which are immuno-reactive with the anti-caspartin antibody, was checked as follows: NaOCl-cleaned shells of several mollusks including bivalves, and outgroups like gastropods and cephalopods, were crushed, and 300 mg of sieved powder of each species were dissolved overnight with EDTA (6 ml, 20% vol/vol). The solutions were centrifuged (3900 rpm, 15 min.), and the supernatants were tested against the anti-caspartin antibody, by conventional ELISA and by dot-blot. For each antigen, serial dilutions were performed. Each sample was tested twice with each technique. We took care to exclude from the analysis samples which cross-reacted with the preserum, or with the secondary antibody.

RESULTS

Production of a polyclonal antibody against caspartin

Large-scale extraction of caspartin from the prism soluble matrix yielded few mg of this protein. One mg of the freeze-dried protein was used for the production of polyclonal antibodies. The working dilutions of the first, second and third bleeding antisera are respectively 1:2000, 1:3000 and 1/10000. The specificity of the different antisera is tested by Western blots (Fig. 1, right) on the whole acetic acid-soluble matrix. We observe that the antiserum (2 nd bleeding) reacts against caspartin but does not cross-react with any other component of the prism matrix. Note that this antiserum cross-reacts with a 17 kDa band of the acetic acid-soluble matrix of the nacre of Pinna nobilis. This suggests that caspartin is also present in the nacre matrix, but in much lesser amount (data not shown). This antiserum may be used for subsequent studies.

The results of the stability experiments at 100°C are shown on Fig. 2. Both the silver stained gel and the Western blot suggest that caspartin is stable at 100°C. We do not record a significant decrease of the reactivity, which would indicate a degradation of caspartin. Nor we observe that caspartin smears towards low molecular weight compounds. On the contrary, the patterns observed after 192 h (8 days) or after 264 h (11 days) are not significantly different from those obtained at T0 or after 12 hours heating.

Occurrence of caspartin -or immunologically related proteins-in calcified tissues

The results of the dot blot experiments and of the ELISA are shown in Table 1. In addition, for the bivalve class, we also indicate for each species the mineralogy (calcite or aragonite or both) and the shell microstructures, as defined by Taylor and coworkers (1969;[START_REF] Taylor | The shell structure and mineralogy of the Bivalvia. II. Lucinacea -Clavagellacea. Conclusions[END_REF]. The immunological signals obtained with the different species are not correlated to the mollusk phylogeny. Some genera which are phylogenetically distant from Pinna nobilis, like the outgroup Haliotis, give a strong cross-reactivity with the anti-caspartin antibody. On the other hand, some closely related genera, like Pteria, give a moderate cross-reactivity. Within the bivalve class, the immunological pattern is not correlated to the shell microstructures. For example, the two representatives of the paleoheterodont bivalves, which exhibit a nacro prismatic shell, do not cross-react at all, while the three representatives of the pectinoids, characterized by shell foliated microstructures, give a strong cross-reactivity.

In few cases (Pinctada radiata, Mercenaria mercenaria, Trochus maculatus, Crepidula fornicata), discrepancies are observed between the two techniques. These discrepancies are not explained yet, but may relate to technical limitations: for ELISA, the lack of binding of immunoreactive peptides on the microplate polymer; for dot blot, the removal of peptides, which pass through the nitrocellulose membrane during the vacuum transfer. We are also fully aware that the analysis may be biased. In particular, only the EDTA-soluble fraction is taken into account. Furthermore, the two tests are only qualitative, because the amount of dissolved matrix may vary in a broad range from sample to sample. At last, the target epitopes of our antibody are not identified yet.

DISCUSSION

The stability of shell proteins is still a debated question since the late fifties. Precursor works of [START_REF] Abelson | Organic constituents of fossils[END_REF], [START_REF] Vallentyne | Pyrolysis of amino acids in Pleistocene Mercenaria mercenaria shells[END_REF], [START_REF] Hare | Laboratory simulation of amino acid diagenesis in fossils[END_REF], [START_REF] Wyckoff | The Biochemistry of Animal Fossils[END_REF], [START_REF] Akiyama | Thermal alteration experiments of scallop shells in relation to the diagenetic change of fossil proteins[END_REF] showed that the amino acids that constitute the shell matrices exhibit a different diagenetic stability. One drawback of these fundamental works was to consider diagenesis at the amino acid level, on bulk matrix, and not at the macromolecular level. Because no shell proteins were identified at that time, it was not possible to check their respective stability, for detecting putative differential degradation patterns. In the present case, we are able to follow a single protein, caspartin. Our experiment at 100°C shows that caspartin is rather stable at this temperature. Other experiments performed at higher temperatures (120°C, 200°C, not shown) indicate that the rate of degradation is dramatically increased. This suggests that there may be a threshold in the thermal stability of caspartin. These results have to be compared with those of [START_REF] Muyzer | Immunology and organic geochemistry[END_REF] on the soluble matrix of Mercenaria mercenaria. et al. (1969; 1973). All the one-letter abbreviations are explained above.

The apparent stability of caspartin at 100°C is intriguing. Caspartin is an intracrystalline Asp-rich protein [START_REF] Marin | Caspartin and calprismin, two proteins of the shell calcitic prisms of the Mediterranean fan mussel Pinna nobilis[END_REF]. In thermal degradation experiments performed in aqueous solutions, aspartic acid is rather unstable [START_REF] Vallentyne | Biogeochemistry of organic matter, II. Thermal reaction kinetics and transformation products of amino compounds[END_REF], and peptidic bonds involving aspartic acid residues are the most easily broken [START_REF] Partridge | Preferential release of aspartic acid during hydrolysis of proteins[END_REF]. The discrepancies between these theoretical data and our experiment suggest that caspartin is stabilized by the mineral phase or by other macromolecules of the matrix. Clearly, this idea needs to be tested further.

The second aspect of our study concerns the occurrence of caspartin-like proteins in the shell of several mollusks. The pattern obtained is neither correlated with the mollusk phylogeny, nor with the shell microstructures. In a paper published some years ago [START_REF] Marin | Evolution: disjunct degeneration of immunological determinants[END_REF], we obtained similar conclusions with an antiserum raised against a whole soluble matrix. The present data suggest that caspartin cannot be used for serotaxonomy, and that it is not a marker of shell microstructure. This work will be refined in two manners: first, for the samples, which give the highest cross-reactivity with the anti-caspartin antibody, we will identify on Western blots, the cross-reacting bands, in order to obtain N-terminal sequences. In parallel, when the full primary structure of caspartin is known, we will develop monoclonal antibodies against selected domains of caspartin. These antibodies will be screened again against several molluscan matrices. Since most of the known shell proteins are composed of functional modules arranged in tandem, the microstructures may be determined by a number of key-modules. Another alternative possibility is that shell microstructures emerge at supra-molecular level, from complex spatial rearrangements of the matrix proteins. If true, this hypothesis has major implications on our ability to produce in vitro biomimetic materials with complex microstructures.

Figure 1 .

 1 Figure1. Elaboration of a polyclonal antibody elicited against caspartin, a soluble shell protein purified from the calcitic prismatic layer of the bivalve Pinna nobilis. For further details, see[START_REF] Marin | Caspartin and calprismin, two proteins of the shell calcitic prisms of the Mediterranean fan mussel Pinna nobilis[END_REF].

Figure 2 .

 2 Figure 2. Thermal stability of caspartin, checked on silver stained gel (top) and on Western blot (bottom). As both gels suggest, caspartin is rather stable when heated at 100°C for several days.Each lane = 30 to 40 µg acetic acid-soluble matrix.

  Presence of caspartin -or immunological related proteins -in the EDTA-soluble extracts of several shells. The reactivities are measured by ELISA and by dot blot. Significance of the reactivity signs. For ELISA: 0: OD < 0.15; +: 0.15 < OD < 0.25; ++: 0.25 < OD < 0.5; +++: OD > 0.5; OD = optical density at 405 nm. For dot-blot: 0: no cross-reactivity; +: weak cross-reactivity; ++: cross-reactivity; +++: strong cross-reactivity. For the bivalves, the mineralogy and microstructures are indicated, according to Taylor

ACKNOWLEDGMENTS

This paper is a contribution to an ACI ("Aide Concertée Incitative" JC3049) awarded to F. MARIN by the French "Ministère Délégué à la Recherches et aux Nouvelles Technologies". An additional support is provided by EGIDE via a "Programme d'Action Intégrée" with Croatia (PAI Cogito 09084XG).


Isabelle Gounand
email: isabelle.gounand@eawag.ch

Eric Harvey
email: eheric.harvey@eawag.ch

Pravin Ganesanandamoorthy
email: pravin.ganesanandamoorthy@eawag.ch

Florian Altermatt
email: florian.altermatt@eawag.ch

Subsidies mediate interactions between communities across space

published or not. The documents may come

2

Abstract

Most spatial ecology focuses on how species dispersal affects community dynamics and coexistence. Ecosystems, however, are also commonly connected by flows of resources. We experimentally tested how neighbouring communities indirectly influence each other in absence of dispersal, via resource exchanges. Using two-patch microcosm meta-ecosystems, we manipulated community composition and dynamics, by varying separately species key functional traits (autotroph versus heterotroph species and size of consumer species) and trophic structure of aquatic communities (species growing alone, or in presence of competitors or predators). We then analysed the effects of species functional traits and trophic structure on communities connected through spatial subsidies in the absence of actual dispersal. Both functional traits and trophic structure strongly affected dynamics across neighbouring communities. Heterotroph communities connected to autotroph neighbours developed better than with heterotroph neighbours, such that coexistence of competitors was determined by the functional traits of the neighbouring community. Densities in autotroph communities were also strikingly higher when receiving subsidies from heterotroph communities compared to their own subsidies when grown in isolated ecosystems. In contrast, communities connected to predator-dominated ecosystems collapsed, without any direct contact with the predators.

Our results demonstrate that because community composition and structure modify the distribution of biomass within a community, they may also affect communities connected through subsidies through quantitative and qualitative changes of detritus flows. This stresses that ecosystem management should account for such interdependencies mediated by spatial subsidies, given that local community alterations cascade across

Introduction

Spatial flows between ecosystems are ubiquitous in nature. Research on spatial ecology and meta-community dynamics demonstrated the fundamental role of dispersal for species coexistence and biodiversity at local and regional scales [START_REF] Mouquet | Coexistence in Metacommunities: The Regional Similarity Hypothesis[END_REF][START_REF] Leibold | The metacommunity concept: a framework for multi-scale community ecology[END_REF][START_REF] Holyoak | Metacommunities: spatial dynamics and ecological communities[END_REF][START_REF] Seymour | Dendritic network structure and dispersal affect temporal dynamics of diversity and species persistence[END_REF]. In parallel, ecosystem ecology and ecosystem-level studies have shown that spatial flows of resources are also fundamental drivers of community dynamics [START_REF] Polis | Toward an integration of landscape and food web ecology: the dynamics of spatially subsidized food webs[END_REF], 2004[START_REF] Harvey | Spatially cascading effect of perturbations in experimental meta-ecosystems[END_REF]. In natural ecosystems, many communities have a net heterotrophic functioning and productivity relies on subsidies coming from neighbouring ecosystems.

For instance benthic marine-or freshwater-systems rely on detritus inputs sinking from pelagic waters [START_REF] Fitzgerald | An algal carbon budget for pelagic-benthic coupling in Lake Michigan[END_REF]Gardner 1993, Schindler and[START_REF] Schindler | Habitat coupling in lake ecosystems[END_REF], and at aquatic-terrestrial boundaries, ecosystems experience strong bi-directional resourceexchanges, with riverine vegetation subsidizing river or lake communities with deadorganic matter [START_REF] Hall | Organic Matter Flow in Stream Food Webs With Reduced Detrital Resource Base[END_REF][START_REF] Cole | Carbon in catchments: Connecting terrestrial carbon losses with aquatic metabolism[END_REF][START_REF] Richardson | Resource subsidies across the land-freshwater interface and responses in recipient communities[END_REF], while riparian systems benefit from nitrogen-rich inputs of emergent aquatic insects [START_REF] Baxter | Tangled webs: Reciprocal flows of invertebrate prey link streams and riparian zones[END_REF][START_REF] Gratton | Flux of aquatic insect productivity to land: Comparison of lentic and lotic ecosystems[END_REF][START_REF] Dreyer | Quantifying aquatic insect deposition from lake to land[END_REF], or fish carcasses [START_REF] Hocking | Salmon species, density and watershed size predict magnitude of marine enrichment in riparian food webs[END_REF]. The quantification of these resource spatial flows (thereafter called subsidies), and the recognition of their importance for local community dynamics by meta-community ecology, eventually led to a formal integration of community and ecosystem perspectives on spatial flows within the meta-ecosystem framework, accounting for both organism dispersal and resource exchanges between ecosystems [START_REF] Loreau | Meta-ecosystems: a theoretical framework for a spatial ecosystem ecology[END_REF], Massol et al. 2011, Massol et al. in review).

Previous studies on allochthonous subsidies generally investigated subsidy effects on recipient communities from a donor-controlled perspective, thus without consideration of the reciprocal effects on both connected ecosystems (e.g. [START_REF] Cole | Differential support of lake food webs by three types of terrestrial organic carbon[END_REF]. Reframed into a spatial perspective, however, subsidies could be considered as a vector of indirect interactions between community dynamics, with donor community dynamics modulating the quantity and quality of exported resources. Both composition (species traits) and structure (trophic interactions) of communities control the quantity and quality of detritus locally produced, and potentially exported to other ecosystems as subsidies. On the one hand, the population dynamics and life cycles of the species composing a community determine the amount of detritus produced locally (e.g. subsidy pulses triggered by 17-year emergence cycles of cicadas reported by [START_REF] Menninger | Periodical cicada detritus impacts stream ecosystem metabolism[END_REF]). On the other hand, species functional traits determine detritus quality via their stoichiometry [START_REF] Sitters | Spatial stoichiometry: cross-ecosystem material flows and their impact on recipient ecosystems and organisms[END_REF]. Indeed, key species functional traits such as autotrophy translate into carbon-nutrient ratios biased toward high values due to their carbon-fixing photosynthesis activities, compared to the content of heterotrophic species (see [START_REF] Sterner | Nutrient Stoichiometry in Aquatic Ecosystems[END_REF]Elser 2002, Sterner 2009 for cross-taxon comparisons). Through a direct effect on the stoichiometric balance and the degradability of building block molecules, community composition modulates not only detritus composition, but also the rate at which detritus is made available as a new resource for subsidized communities [START_REF] Enriquez | Patterns in decomposition rates among photosynthetic organisms: the importance of detritus C:N:P content[END_REF][START_REF] Scott | Foliage litter quality and annual net N mineralization: comparison across North American forest sites[END_REF][START_REF] Allison | A trait-based approach for modelling microbial litter decomposition[END_REF], such as plant litter composition driving decomposition rates in forest and stream ecosystems worldwide [START_REF] Cornwell | Plant species traits are the predominant control on litter decomposition rates within biomes worldwide[END_REF][START_REF] García-Palacios | The importance of litter traits and decomposers for litter decomposition: a comparison of aquatic and terrestrial ecosystems within and across biomes[END_REF].

Community structure and the strength of species interactions within a community should also affect the quantity and quality of detritus by modulating the biomass 6 distribution across trophic levels [START_REF] Shurin | All wet or dried up? Real differences between aquatic and terrestrial food webs[END_REF]. Empirical studies, for instance, showed that in a wide range of ecosystems, changes in one trophic level induce trophic cascades over an entire food web, which leads to drastic changes in biomass distributions [START_REF] Schmitz | Trophic Cascades in Terrestrial Systems: A Review of the Effects of Carnivore Removals on Plants[END_REF][START_REF] Carpenter | Trophic cascades, nutrients, and lake productivity: Wholelake experiments[END_REF][START_REF] Jackson | Historical overfishing and the recent collapse of coastal ecosystems[END_REF][START_REF] Frank | Trophic cascades in a formerly cod-dominated ecosystem[END_REF]. Beyond the traditional focus on species loss and local productivity change, the spatial consequences for subsidy-connected ecosystems of these structural changes and the subsequent modified detritus production have still to be investigated.

Overall the tight link between community composition and dynamics, and local detritus production triggers an indirect connection between communities connected by subsidy exchanges: the recipient community fed by subsidies becomes indirectly linked to the donor community dynamics through the qualitative and quantitative characteristics of the exported resources. Such subsidy linkages between ecosystems imply that local community composition and structure may matter for the functioning of neighbouring communities even in the absence of species' dispersal. This hypothesis has fundamental implications for the functioning of connected ecosystems and for their response to anthropogenic pressure, since it postulates the spatial spread of local perturbations. Any event that would modify local community composition and dynamics, such as biological invasions, is susceptible to pass on neighbouring community dynamics through subsidy disruption even if species dispersal cannot occur (e.g. [START_REF] Baxter | Fish Invasion Restructures Stream and Forest Food Webs By[END_REF]).

Here we propose a test of such indirect "neighbour effects" with experimental microcosm meta-ecosystems. We used aquatic microbial communities consisting of bacteria feeding on organic resources, various autotroph and bacterivorous protists, and a top predator. The microcosms were mimicking a wide range of natural ecosystems, from heterotrophic, such as in stream or benthic waters, to autotrophic, such as forests or pelagic phytoplankton-based ecosystems, and from resource to predator dominated.

We built two-patch meta-ecosystems connecting ecosystems only by spatial subsidies (spatial flows of detritus and inorganic resources, and no organisms dispersing). In one ecosystem we manipulated species traits (autotroph versus heterotroph species and consumer body size), while in the other ecosystem we manipulated community structure by adding a competitor or a predator (see Fig. 1). We followed temporal changes in community dynamics (i.e., species density and biomass) in each ecosystem, and then compared the dynamics between connected and isolated ecosystems to test if communities with different structure and composition could affect each other only through subsidy exchanges. Specifically we asked whether autotroph versus heterotroph community dynamics could have differential impacts on neighbours, and whether the addition of a species inducing novel trophic interactions (e.g. competition or predation) could affect neighbour dynamics in the absence of organism dispersal.

Methods

Experimental design

To test the indirect influence of community composition on one another via crossecosystem subsidies, we performed a two-patch meta-ecosystem experiment with protists growing in microcosm ecosystems solely connected by subsidies (spatial flows of detritus). We varied species traits in Ecosystem 1 and trophic structure in Ecosystem 2 according to a factorial design (Fig. 1). In Ecosystem 1 we grew one of these three species with contrasting traits alone (monocultures): the autotroph flagellate Euglena gracilis (∼35 µm), a large bacterivorous ciliate (Paramecium aurelia, ∼96 µm), or a small bacterivorous ciliate (Tetrahymena pyriformis, ∼30 µm). In Ecosystem 2, our focal species, Colpidium striatum, a small bacterivorous ciliate (∼45 µm) was grown alone, or either with Paramecium aurelia as a competitor, or was submitted to predation by the generalist filter feeding waterflea Daphnia magna (∼0.5 to 2 mm). Treatments are hereafter called "Autotroph", "Large heterotroph" and "Small heterotroph" in Ecosystem 1 and "Focal Species" (FS), "FS+Competitor", "FS+Predator" in Ecosystem 2. We connected Ecosystem 1 and Ecosystem 2 only by subsidy exchanges (detritus, including inorganic resources present in the growing medium), and prohibited any type of species dispersal. We had a five-fold replication of the nine meta-ecosystem types (all possible combinations of Ecosystems 1 and 2), as well as the control ecosystems without diffusion, resulting in an experiment consisting of 45 independent 2-patch metaecosystems and 30 isolated 1-patch ecosystems (120 microcosms).

Experiment setup

Ecosystems were assembled in microcosms of 250 mL Schott bottles filled with 100 mL culture medium. All organisms (bacteria, protists, and waterfleas) used in the experiment were grown in pre-autoclaved protist pellet suspension filtered through Whatman filters (0.31 g protist pellets 1 L -1 tap water; Protist pellets from Carolina Biological Supply, Burlington NC, USA). Microcosms were assembled with 75 ml protist medium, 5 mL of bacterial culture (Serratia fonticola, Bacillus subtilis and Brevibacillus brevis; added one day prior to protist addition), and completed with 20 mL of protist culture at carrying capacity (10 mL per species in the competition treatment). For the predation treatment, we added four equal-sized juvenile Daphnia magna to each microcosm. More details on protist culture and experimental procedures are found in [START_REF] Altermatt | Big answers from small worlds: A user's guide for protist microcosms as a model system in ecology and evolution[END_REF].

Microcosms were randomized within the 5 replicate blocks, and the experiment took place at 20 °C and constant lighting. We replaced all Daphnia that died within the first six days due to initial conditions (i.e., insufficient oxygen-levels in the freshly autoclaved medium).

Diffusion

Ecosystem 1 and 2 were connected by bi-weekly reciprocal subsidy exchanges.

These spatial flow events consisted in sampling 30 mL from each ecosystem, microwaving these samples for 100 seconds, until they reached a full boil, to turn all living biomass into detritus, and then adding it into the respective connected ecosystem after a cooling period of two hours at ambient temperature (20 °C). This diffusion 10 method mimics detritus flows associated with recurrent perturbation-induced mortality.

Isolated controls were also submitted to the same perturbations, but the microwaved samples were added back in the microcosm of origin to isolate the diffusion effects from perturbation-induced mortality.

Samplings and measurements

In parallel, we tracked changes in community dynamics in each microcosm during one month. We measured population densities every Tuesday and Friday (i.e., twice a week), leaving as much time as possible for protist growth after each diffusion event (occurring on Wednesdays and Saturdays). At each measurement point we took two 0.5 mL samples per microcosm, one to measure protist density by video analysis, the other to measure bacterial dynamics by flow cytometry. The volumes sampled were considered sufficiently small to not affect local dynamics [START_REF] Altermatt | Interactive effects of disturbance and dispersal directionality on species richness and composition in metacommunities[END_REF]) and thus did not need to be replaced by fresh medium. We recorded one 5 s-video per sample following a standardized video procedure [START_REF] Pennekamp | BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes[END_REF]Schtickzelle 2013, Altermatt et al. 2015). From each video we extracted densities of moving individuals along with morphometric and movement information, such as cell size and speed. This was achieved using the R-package bemovi [START_REF] Pennekamp | BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes[END_REF] coupled to the image analysis free-ware ImageJ (ImageJ, National Institute of Health, USA). The additional traits measured served to discriminate species identity in mixtures (competition treatment), provided as inputs to trait distance analysis with the svm algorithm (e1071 Rpackage [START_REF] Meyer | Misc Functions of the Department of Statistics (e1071)[END_REF], and to calculate bio-areas as a proxy for biomass. Since automated particle detection relies on movement, the method systematically underestimated densities of Euglena gracilis, which is much less mobile than the other species. Therefore, we complemented density estimates of this species with visual counts from the videos. To exclude false positives, we also performed a visual check of all videos where a protist species had less than 3 individuals per frame. We counted Daphnia individuals visually. Finally, we measured the total abundance of the 3-species bacterial community on a flow cytometer (BD Accuri TM C6 cell counter) on SYBR green fixed samples (dilution x1000), following a standard protocol [START_REF] Altermatt | Big answers from small worlds: A user's guide for protist microcosms as a model system in ecology and evolution[END_REF].

Analyses

We characterized the indirect effects of neighbouring communities on each other through subsidy flows using log response-ratios of protist densities at each time point, for the different neighbour treatments (either species traits or trophic structure) in the connected ecosystem, with 95% confidence intervals (CI). The responses were tested relative to controls without diffusion, such that CIs not comprising zero reveal significant effects of diffusion, while none overlapping CIs between neighbour treatments reveal a significant neighbour effect. We tested the effects of trophic structure on neighbour community dynamics by comparing the density of species in Ecosystem 1 (each monoculture) when connected to different communities driven by specific interactions in Ecosystem 2 (i.e. FS, FS+Competitor, FS+Predator). Conversely, we tested the effects of functional traits on neighbour community dynamics by comparing the density of our focal species, Colpidium striatum, in Ecosystem 2 when connected to different species population with specific functional traits in Ecosystem 1 (i.e. Autotroph, Large heterotroph, Small heterotroph). We studied the potential interaction with time by 12 running generalized linear models (GLM) on log response-ratios with species traits or trophic interaction in the connected ecosystem and time as explanatory variables. We used Gaussian distributions as link functions to avoid overestimation of positive effects due to the ratio [START_REF] Berlow | Quantifying variation in the strengths of species interactions[END_REF]. The effect of species traits in Ecosystem 1 on competitive outcome in Ecosystem 2 was also tested with a GLM on the density of Colpidium relative to Paramecium (using the relative proportion), with species traits in the connected ecosystem and time as explanatory variables. For each GLM, the level of significance and the effect size of each factor, and their interactions, were assessed using a standard F test (Type II analysis of deviance). For each significant term of interest we ran post-hoc pairwise comparisons (with Tukey adjusted p-values) to evaluate specific contrast among variables. When time was not significantly affecting the terms of interest we performed the post-hoc analysis on simplified GLM sub-models (without the effect of time) in order to avoid unnecessary inflations of time II error [START_REF] Nakagawa | A farewell to Bonferroni: The problems of low statistical power and publication bias[END_REF]).

Lastly, because neighbour effects can originate from changes in both subsidy quantity and quality, we examined approximated biomass (bio-areas) at the different trophic levels (bacteria, protist, predator) according to community characteristics (species traits or trophic structure) to bring an element of interpretation, assuming that the different trophic levels produce different qualities of detritus. For bacteria we took a constant mean individual area of 1 µm², assuming no significant change of size over the experiment (bio area = 1 µm² * cell counts). For protists, we measured mean individual's area directly from the video analysis, and extrapolated it to the total population [START_REF] Pennekamp | BEMOVI, software for extracting behavior and morphology from videos, illustrated with analyses of microbes[END_REF]. Bio-area of Daphnia was estimated visually based on four size classes. To test protist and bacteria bio-area differences among communities along time we ran four different GLM with either species traits (Ecosystem 1) or trophic structure (Ecosystem 2) and time as explanatory variables. We studied residual distributions to select the most appropriate link function (Gamma or Gaussian). All analyses were conducted with R 3.1.2 (R Development Core team, 2014), using the 'car' package [START_REF] Fox | An {R} Companion to Applied Regression[END_REF] for type II analysis of deviance, and the 'lsmeans' package for post hoc pairwise comparisons [START_REF] Lenth | lsmeans: Least-squares means[END_REF]. 16 (Fig. 5, right side), and almost all biomass was concentrated at the predator level (99.97% of the estimated bio-area at the end of the experiment). Protist and bacteria biomasses did not differ between FS and FS+Competitor communities, but were significantly lower in the FS+Predator community (adjusted p-value <0.0001 for every pairwise comparison; see Supplementary material Appendix 5 Tables A5). Interestingly, positive neighbour effects of the autotroph species on neighbour ecosystems occurred despite the fact that autotroph protist biomass was generally lower or did not differ from other neighbours (Fig. 5a, left side), but were associated with significantly higher bacterial biomass (Fig. 5b, left side, see Supplementary material Appendix 5 Tables A5 for all multiple comparisons).

Discussion

Community ecology usually assumes that species dispersal and local interaction dynamics are the main processes driving regional biodiversity and species coexistence [START_REF] Leibold | The metacommunity concept: a framework for multi-scale community ecology[END_REF][START_REF] Holyoak | Metacommunities: spatial dynamics and ecological communities[END_REF]. With our experiment, we show that exchange of subsidies among ecosystems also shapes community dynamics by mediating indirect interactions between communities. By integrating resource dynamics in metacommunities, the meta-ecosystem concept offers an operational framework to envision spatial feedbacks between resource and community dynamics at a large spatial scale [START_REF] Loreau | Meta-ecosystems: a theoretical framework for a spatial ecosystem ecology[END_REF]. Here, we demonstrate in experimental meta-ecosystems that the integration of feedbacks between community dynamics and spatial subsidies is needed to understand ecosystem dynamics, and are essential to forecast the spatial spread of local perturbations.

Our experiment reveals three striking subsidy-mediated effects among communities solely connected by detritus spatial flows. First, autotroph communities positively affected densities in the connected communities, such that the persistence of our focal species in the presence of a competitor was tributary to these autotroph subsidies. Second, population densities in the autotroph community heavily depended on subsidies from heterotroph communities. Third, by contrast to these positive effects, local predation negatively affected connected communities, even though the predator was not allowed to disperse, but was only indirectly affecting them through the alteration of subsidy flows. These three effects demonstrate that local community composition and structure can strongly affect community dynamics in neighbouring ecosystems, even in the absence of dispersal.

18

We explain the observed effects in terms of subsidy changes in quantity and quality. The specific functioning of autotroph, heterotroph, and predation-pressured communities impacted subsidies in contrasting ways. Photosynthetic activity by autotrophs introduced new resources in the system otherwise closed, by fixing atmospheric carbon, stored as carbohydrates (labile forms of carbon) or dissolved in the medium by release activity [START_REF] Baines | The production of dissolved organic matter by phytoplankton and its importance to bacteria: Patterns across marine and freshwater systems[END_REF][START_REF] Biersmith | Carbohydrates in phytoplankton and freshly produced dissolved organic matter[END_REF][START_REF] Guenet | Priming effect: bridging the gap between terrestrial and aquatic ecology[END_REF]. The greater bacteria densities in autotroph compared to heterotroph communities likely profited from the exploitation of photosynthesis-derived dissolved carbon [START_REF] Børsheim | Photosynthetic algal production, accumulation and release of phytoplankton storage carbohydrates and bacterial production in a gradient in daily nutrient supply[END_REF]. In addition, the small size of bacteria and their higher surface/volume ratio may have enhanced recycling rates due to a greater proportion of dead material exposed to decomposition [START_REF] Berg | Decomposition of root litter and some factors regulating the process: Long-term root litter decomposition in a scots pine forest[END_REF]. Overall, even if not directly measured, subsidies flowing from autotroph communities were undoubtedly more abundant and more readily available than the ones flowing from heterotroph communities. These rich subsidies subsequently triggered a bottom-up effect in the neighbouring community resulting in higher densities of bacterivorous consumers.

Interestingly in the reverse direction also, subsidies from heterotroph communities positively impacted autotroph community dynamics. This result stresses that neighbour effects may not only happen via changes in subsidy abundance but also through alterations to detritus stoichiometric balance. While not directly measured, the generally greater ratio of nitrogen to carbon in heterotroph organisms [START_REF] Elser | Nutritional constraints in terrestrial and freshwater food webs[END_REF][START_REF] Sterner | Nutrient Stoichiometry in Aquatic Ecosystems[END_REF]) is a straightforward explanation for the higher densities of autotroph communities when exchanging detritus with heterotroph communities compared to isolated controls, along with likely ammonium release activity of the bacterivorous protists [START_REF] Probyn | Ammonium regeneration by microplankton in an upwelling environment[END_REF].

Overall, in our autotroph-heterotroph coupled ecosystems, heterotroph subsidies likely relaxed autotroph nitrogen limitation, while autotroph subsidies fuelled heterotroph growth with abundant labile carbon. Ecosystem couplings resulting in such resource spatial complementarity are common between freshwater and riparian systems, with riparian ecosystems exchanging abundant leaf litter against nitrogen-rich aquatic insects [START_REF] Baxter | Tangled webs: Reciprocal flows of invertebrate prey link streams and riparian zones[END_REF][START_REF] Bartels | Reciprocal subsidies between freshwater and terrestrial ecosystems structure consumer resource dynamics[END_REF], and thus highlight the general significance of our findings.

By contrast, subsidies from communities with predators had negative effects on neighbour community dynamics. We used a generalist predator species, capable of consuming almost all protists and bacteria. Consequently, most of the biomass in these ecosystems was concentrated at the highest trophic level, in the chitinous exoskeleton of Daphnia. The molecular robustness of chitin as well as the low proportion of organic material exposed to decomposition of larger organisms likely slowed down the recycling process of predator detritus compared to other detritus [START_REF] Berg | Decomposition of root litter and some factors regulating the process: Long-term root litter decomposition in a scots pine forest[END_REF][START_REF] Hamre | Enzyme processivity changes with the extent of recalcitrant polysaccharide degradation[END_REF].

The delay between slow recycling process and community dynamics triggered a spatial cascade, leading to the accumulation of subsidies into recalcitrant form and to the progressive starvation of neighbouring communities. It is noteworthy that in our closed meta-ecosystems and in the absence of autotrophic species, the amount of subsidy transferred is always the same (30% of total volume), therefore ruling out any local collapse of subsidy to explain the negative effect of the predation. Therefore, the observed indirect negative impact of predation on neighbour density likely comes from a lower quality of subsidies. Beyond the specific effect of this particular predator, this result stresses that changes in biomass distribution within a community may affect 20 neighbours by modifying subsidy characteristics.

Overall, our experiment shows general mechanisms by which natural communities can indirectly but strongly influence each other's functioning, via the abundance, stoichiometry and decomposability of detritus locally produced and subsidizing other ecosystems. Measuring directly the stoichiometric changes in subsidies produced by contrasted communities could be a natural extension of this experiment to investigate these mechanisms further. We demonstrate that, next to species dispersal (for example tested by [START_REF] Staddon | Connectivity, non-random extinction and ecosystem function in experimental metacommunities[END_REF]), spatial dynamics of detritus are essential by themselves to understand the fundamental functioning of connected ecosystems, as well as their response to perturbations. The importance of subsidies is often studied only from the recipient ecosystem's local perspective (see [START_REF] Marcarelli | Quantity and quality: unifying food web and ecosystem perspectives on the role of resource subsidies in freshwaters[END_REF][START_REF] Sitters | Spatial stoichiometry: cross-ecosystem material flows and their impact on recipient ecosystems and organisms[END_REF] for reviews), and ecosystem managers usually consider the threat of direct alterations to resource flows (e.g. nutrient pollution), but rarely threats potentially induced by alterations of community structure or composition in connected ecosystems (but see the crash of forest spider communities, induced by prey-subsidy disruption following the invasion of a stream by an exotic fish in [START_REF] Baxter | Fish Invasion Restructures Stream and Forest Food Webs By[END_REF]. Our results suggest that any kind of perturbation (e.g. land-use change, overharvesting) can have wider repercussions in space than those observed on local communities because of subsidy disruption (e.g. cascades across aquatic-terrestrial boundaries: [START_REF] Greig | Warming, eutrophication, and predator loss amplify subsidies between aquatic and terrestrial ecosystems[END_REF][START_REF] Fey | Recognizing cross-ecosystem responses to changing temperatures: soil warming impacts pelagic food webs[END_REF][START_REF] Schulz | Review on environmental alterations propagating from aquatic to terrestrial ecosystems[END_REF]. The extent to which local perturbations spatially cascade to other communities will depend on the strength of the subsidy coupling between ecosystems, an essential piece of information on which more research is needed. Our findings call for the adoption of a spatial perspective in ecosystem management and restoration ecology that integrates fine-tuned knowledge of 398 resource spatial exchanges between ecosystems. 32 Supplementary material (available online as Appendix oik-03922 at <www.oikosjournal.org/readers/appendix/oik-03922>). Appendix 1 Data available from the Dryad Digital Repository: <http:// dx.doi.org/10.5061/dryad.93hd6 >

Figure 1 .

 1 Figure 1. The experimental design consists of two-patch meta-ecosystems linked by

Figure 2 .Figure 3 .Figure 4 .Figure 5 .

 2345 Figure 2. Effect of the species traits in Ecosystem 1 on the density of focal species in

space onto other ecosystems even if species dispersal is completely absent.

Acknowledgements

We thank the EMERGe research group, Tom Battin and Anita Narwani for discussions, Björn C. Rall for a previous review of our manuscript, Esther Keller and Elvira Mächler for technical support and Esther Keller and Piet Spaak for providing the Daphnia magna.

Funding

This work was supported by the Swiss National Science Foundation Grant PP00P3_150698, University of Zurich and Eawag.

Results

Subsidy-mediated effects on population density

Both local community functional traits (autotrophy versus heterotrophy) and trophic structure induced strong significant effects on connected communities via subsidy exchanges and in the absence of dispersal (see Supplementary material Appendix 1 Table A1 andAppendix 2 Table A2). At the end of the experiment, population densities of our focal species in Ecosystem 2 were significantly higher when connected to autotroph compared to heterotroph communities (F2,60 = 39.40, p<0.0001 in Focal Species and FS+Competitor treatments (see Supplementary material Appendix 1 Table A1, and Appendix 5 Table A5 for post-hoc multiple comparisons) or compared to isolated communities (Fig. 2, panels a and b). The only exception was in the FS+Predator treatment where predation resulted in the extinction of the focal species irrespective of functional traits in the connected community (Fig. 2c). Predators drove protist to extinction and concentrated all the biomass in their body, which cascaded on detritus quality and negatively affected population density in subsidy-connected communities in Ecosystem 1 compared to the focal species grown alone (FS) (Fig. 3, p<0.0001 for the factor "trophic structure" on each community; see Supplementary material Appendix 1 Table A2 for the GLM and Appendix 5 Tables A5 for post-hoc multiple comparisons). Moreover, the benefit (or not) of being a connected versus an isolated community depended on species functional traits. Some species were relatively insensitive to spatial subsidies when connected to FS or FS+Competitor communities (e.g. Large heterotroph, Fig. 3b). In contrast, the autotroph did always far better when connected to heterotroph communities, regardless of the trophic structure, compared to isolated autotroph communities, which received only their own autotroph detritus (Fig. 3a: confidence intervals above the zero line). At last, consumer size (Large versus Small heterotroph) did not impact significantly species density in the connected ecosystem.

Subsidy-mediated effect on competition

While trophic structure in one ecosystem significantly impacted community dynamics in the connected ecosystem, the reverse was also true: we found that the competition outcome (in Ecosystem 2) strongly depended on species functional traits in the connected ecosystem (Fig. 4,F3,144 = 8.56,p<0.0001; see Supplementary material Appendix 3 Tables A3 for full results of the GLM). At the end of the experiment, coexistence between the two competitors (Colpidium and Paramecium) was only observed in the meta-ecosystems with the autotroph as a neighbour (Fig. 4a). In the presence of heterotrophic neighbours, we systematically observed competitive exclusion of our focal species (Colpidium) by its competitor (Fig. 4b-d, with an exception in one isolated replicate ecosystem), while it persisted over the course of the experiment when connected to the autotroph community (Fig. 4a).

Changes in biomass distribution

We observed that the biomass distribution among trophic compartments (bacteria / protists / predator) varies among community types, as inferred from bio-areas (Fig. 5; Supplementary material Appendix 4 Tables A4). In the ecosystems where the predator was present, both bacteria and protist biomass decreased dramatically within a few days