Pascale Marangé
email: pascale.marange@cran.uhp-nancy.fr

David Gouyon
email: david.gouyon@cran.uhp-nancy.fr

Jean-François Pétin
email: jean-francois.petin@cran.uhp-nancy.fr

Bernard Riera
email: bernard.riera@univ-reims.fr

Verification of functional constraints for safe product driven control

Keywords: Product driven control, Model Checking, Reconfigurable manufacturing system

This paper deals with dynamic reconfiguration of DES control within the context of manufacturing system to answer product variability or production resources availability. More precisely, it focuses on productdriven control (PDC) that embeds decisional and adaptation capabilities within the product. PDC can be defined in a static or dynamic way: in the first case, all switchable manufacturing trajectories are predefined and implemented in the product control while, in the second case, PDC can be seen as a non-deterministic and "on the fly" choice among control trajectories to fit with the manufacturing system availability and the product state. In this last case, PDC safety is ensured thanks to a filtering approach that enables to maintain PDC within a state space that satisfy functional and safety constraints whatever the control generated by the reconfiguration process is. This paper focuses on the definition and verification of a minimal set of constraints that ensure the sufficiency and the non blocking properties of the constraints. A case study illustrates the approach.

INTRODUCTION

The introduction of Information Technology in manufacturing systems gives manufacturers an opportunity to promote maketo-order business models and mass customisation of products [START_REF] Silveira | Mass customization: literature review and research directions[END_REF]. Facing this wide range of customer needs requires manufacturing control systems to have the ability to adapt itself (or to reconfigure itself) to variable demands in terms of product specifications or manufacturing system changes [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF].

As an answer to this industrial challenge, Product-Driven Control (PDC) consists in providing each product occurrence with information, decision and communication capabilities in order to make the product active in the scheduling and the execution of its manufacturing operations (McFarlane et al. 2003).

Control strategies embedded in the product can be defined in a static way including all possible trajectories [START_REF] Qiu | Extended structured adaptive supervisory control of shop-floor controls for an emanufacturing system[END_REF] or in a dynamic way to adapt "on the fly" control decisions to fit with the manufacturing system and the product state. In the first case, the estimated scheduling is defined before implementation; this definition can be very sensible against environment variation (failure, unpredictable events, unavailable resources, …). In the second case, we assume that control could be nondeterministic but limited to an ad-hoc choice between legal trajectories. Decision making is intrinsically a longer job, but the decision made is more robust against unpredictable events. This is compliant with our objective which is to facilitate the online reconfiguration of production. So, to ensure safety, it is necessary to verify that, whatever the "on the fly" control is, it is compliant with the functional characteristics of the product to be manufactured and with the process safety conditions. This verification can be done using a filtering approach (Marange et al. 2007) which enables the only decisions that satisfy a set of functional and safety constraints.

This paper aims at presenting a proved definition of the constraints which are necessary to execute such a safe product-driven control, and gives guidelines for their implementation. Section 2 introduces the formal foundations of PDC and an overview of existing design techniques. Section 3 deals with the design of PDC constraints and their verification using model checking. The proposed approach is illustrated in section 4 using a simplified case study. Conclusions and open issues for future research are discussed in section 5.

STATE OF THE ART

Product-driven control

From the process point of view, machine flexibility is the capability of machines to perform different operations. Taking into account functional redundancies between machines, routing flexibility is the ability of manufacturing a given set of part types using one or more routes through the machines [START_REF] Tsubone | A comparison between machine flexibility and routing flexibility[END_REF]. Therefore, product customization, machine and routing flexibility impact the manufacturing control so that its online dynamic reconfiguration should make it possible to fit any process rescheduling or any customized product definition.

According to [START_REF] Brennan | A Reconfigurable Concurrent Function Block Model and its implementation in Real-Time Java[END_REF], implementing a dynamic reconfiguration of control requires a configuration loop involving informational, decisional and operational activities for:

-monitoring [START_REF] Vogrig | Flexible manufacturing shop[END_REF], Zamai et al., 1998), diagnosis [START_REF] Toguyeni | Study of the diagnosability of automated production systems based on functional graphs[END_REF] or even prognosis in order to produce information about the control environment and to define when and where a reconfiguration is required, -decision-making to define the most appropriate control policy, -operational execution of the reconfigured control actions to manage switching from an obsolete control strategy to a new targeted configuration.

The main hypotheses of product-driven automation consist in providing the product with information, decision and communication capabilities in order to make the product active in the scheduling and the execution of its manufacturing operations. Products and resources are then interacting to perform manufacturing operations. Based on these conceptual guidelines, this paper focuses on the design of a product-driven distributed control system, shown in Fig. 1, which is based on the cooperation between:

-product control which controls the manufacturing routes according to a scheduled list of operations the product has to undergo; these controls are specific for each product occurrence in order to take into account their customization, -resource control which ensures correct execution of manufacturing operations and provide the product controllers with accurate reports.

Product-driven control engineering

The PDC definition is founded, on the one hand, on the modelling of the manufacturing system capabilities which describes the system topology and the manufacturing operations performed by each resource, and, on the other hand, on the modelling of product requirements in terms of the operations it has to undergo. Two different ways of thinking the design of PDC architecture can be considered.

The first one is based on the specification of a set of switchable control policies using a graph that represents all legal product routings and the functional redundancies between the machines (Berruet et al. 2000[START_REF] Toguyeni | Study of the diagnosability of automated production systems based on functional graphs[END_REF]. Generations of such a graph can rely on synthesis techniques within the framework of Supervisory Control Theory [START_REF] Qiu | Extended structured adaptive supervisory control of shop-floor controls for an emanufacturing system[END_REF][START_REF] Pétin | Supervisory synthesis for product-driven automation and its application to a flexible assembly cell[END_REF]. Then, operational PDC implements choices between the legal routes that results from the execution of a short path optimisation algorithm. This approach assumes that all possible manufacturing trajectories have been previously embedded in product-driven controllers and suffers from an exponential complexity in terms of number of control states, which naturally arises as the number of machines and product variability increase.

Second way of thinking consists in defining PDC as a non deterministic evolution within a state space guarded by a set of constraints. In other words, it means that the control decisions are not completely predefined but are postponed when a product ask for a transformation by selecting, even in a non-deterministic way, a control action compliant with the set of constraints.

Consequence is that no strong hypothesis on the reconfigured control properties can be assumed. Consequently, a filter has to be placed before the execution in order to dismiss the evolutions that do not comply with safety and functional constraints. This approach strongly depends on the constraints definition and more especially on their covering features. For the safety constraints, an approach has been proposed by (Marange, 2008) to specify a set of constraints for each plant elements and to verify, using model checking, that this set of constraints is preserved by any controller. This paper enriches this work by considering aspects related to product functional constraints. In this case, the constraints must be efficient enough to ensure the reachability of transformation control states according to given product features but they also must be permissive enough to ensure the existence of at least one manufacturing sequence (non-blocking constraints).

PROPOSED APPROACH

The proposed approach considers products and resources interacting in order to execute product manufacturing plans. To ensure safety and correctness of the execution, a set of constraints are designed and used as filtering conditions that maintain PDC reconfigured control in a legal state space. This section begins by giving an overview of the approach which illustrated with some models, then proposes a method to design and verify constraints sufficiency and non-blocking properties, and finally explains how these constrains can be implemented in a product driven control system.

Overview of the approach

In order to ensure that the functional manufacturing plan of the product is respected, a four steps approach is proposed (Fig. 2):

-functional constraints writing; -verification of constraints sufficiency. This consists in the verification that the minimal set of constraints ensuring the proper sequencing of operations, is included in the identified set of constraints;

-verification of constraints non-blocking to check that the constraints are not too restrictive, i.e. there is at least a way to achieve the product manufacturing plan; -implementation of the constraints which can be used "on line" to filter the only legal PDC actions.

Rules design

Init

Implementation

Final

Non blocking verification

Sufficency verification

Rules writing

Fig. 2: Activities of the proposed approach

To perform constraints verification, the following hypotheses are considered: -all plant evolutions are observable by the PLC, -functions sequence are considered only as logical constraints, and do not include time aspects, -the plant is considered without failure, -for the trajectories choice, the cost is not yet taken in account. In future works, choice criteria will integrate costs linked to resource performances or to transfert time between resources, -we considerer that the transfer resource is always available (as in the case of a conveyor).

Constraints design

During control execution, a function can be in several states: to be executed Fi te , in execution Fi ie , or executed Fi ex . The request for a function execution is noted Fi rq . To authorize the function execution, a filter using information contained in the product validates a set of constraints. These functional constraints, which can be defined as logic equations, are of two types: one is related to the product features and the other is related to the manufacturing resource capabilities.

Constraints writing

For each product, a set of constraints is defined to ensure that the good product is made. Each product is considered independently of each other, and execution conditions on other functions are defined for each function Fi:

-the functions that should have been executed before Fi, condition noted Fi before -the functions that cannot be executed at the same time than Fi, condition noted Fi during -the functions that cannot be executed after Fi, condition noted Fi after -the function that cannot be executed on the product, noted Fi prohibited Each condition can be extended according to the function states. For example, Fi before ex represents the condition Fi before with the parameters Fi ex .

To ensure the respect of these precedence conditions [START_REF] Allen | Maintaining knowledge about temporal intervals[END_REF] functional constraints are defined for each function Fi:

-0

rq beforeex Fi Fi ∧ = ) 0 =
ensures that prior functions needed before the execution of Fi have been executed, -ensures that the function included in Fi (

Fi

prohibited cannot be executed.

In addition to these precedence constraints, we have to verify that a given function (Fi rq ) is not requested when the product is present on a resource (noted pp j ) that does not provide this given function:

0 = ∧ rq j Fi pp .
Furthermore, the deactivation of function is forbidden before the end of its execution, what is represented by the constraint: 0

rq ex Fi Fi ↓ ∧ = .
The goal of these constraints is to ensure a correct manufacturing plan execution, but if they are not well defined, they can be too permissive or bring some blocking situations. So, once they are written, it is necessary to proceed to some verification.

Sufficiency and non-blocking property verification

Once product requirements given and resources capability built, the verification process helps the designer to identify and to formalise a set of necessary and sufficiency constraints. Verification of the constraints aims to ensure, on the one hand, that constraints are efficient enough to disable all the manufacturing plans which are incorrect, and on the other hand, that the constraints are not too restrictive, i.e. that it exists at least one possibility to manufacture the product. The verification of the sufficiency and non-blocking property is done on a system model. This model is defined in a modular way considering the execution environment, the control and function execution. In order to reduce the risk of state space explosion, the modelling tool which is used is UPPAAL timed automata (Alur & Drill 1994[START_REF] Behrmann | Toward an implementation of recovery procedures for flexible manufacturing systems supervision[END_REF].

Generic model of environment and resources

To verify that functional constraints are correctly defined, their sufficiency and non blocking properties are verified by model checking [START_REF] Schnoebelen | Vérification de logiciels: Techniques et outils du modelchecking[END_REF]). The system is then defined by models of the execution environment, tag reading and update, functions activation/deactivation control and functions execution, which are detailed below.

The model of the environment (Fig. 3) represents the cyclical evolution of the PLC, and will synchronize the evolution of the different models with synchronization messages. In a product point of view, the PLC cycle is defined as follows: PLC inputs reading, tag reading, functions evolution to identify which are the possible functions, application of the constraints to verify if properties are respected, functions execution and tag and PLC outputs update. Before a new cycle is started, a verification step is added to verify sufficiency and non-blocking.

Fig. 3: Model of the execution environment

When a product is present on a resource, information contained in the tag is read (Fig. 4a) to update functions state on each resource (requested, in execution …), then the control is executed, and finally the tag is updated (Fig. 4b) to trace the execution of functions. Reading and update can be done during each PLC cycle to ensure control consistency. As no assumption on the implemented control can be made, functions can be activated or deactivated during the period between the reception of messages function_evolution and constraint_application (Fig. 5).

a) Model of tag reading b) Model of tag update

Fig. 5: Generic model of function Fi activation/deactivation

Before functions execution, the function evolution phase tests functions activation/deactivation using the constraints set. For that, when the message constraint_application is received, the guard representing the constraint must be false; if not, the variable errori is updated to "true" (Fig. 6), and then forbid the function execution. Once functional constraints are defined, the constraints sufficiency has to be verified, to ensure that all the evolutions which do not bring a correct product will be filtered.

To verify constraints sufficiency, an observer, including an error state representing the paths that do not respect constraints, is designed for each constraint. If constraints are sufficient, then the property "regardless the way defined by the control, the error state is not reachable", is always true.

If it is simple to express the property to be checked, main difficulties remain in the definition of the observer that is prone to mistakes on the part of the expert (bad definition, forgetting elements ...) and in the risk of state explosion in model definition and in verification calculation. This fact justifies our observer modularity (i.e. one observer for each constraint).

Verification of constraints non blocking property

The last step of constraints design is to verify that they are not too restrictive to achieve the process plan. To verify the nonblocking control, the process plan is modelled with a finished product state. The verification of the non-blocking property of constraints consists then in finding at least one path reaching to the finished product state.

Control implementation

The set of specified and verified constraints can be implemented within a filtering supervisor that enable or disable the PDC actions according to the expected manufacturing of a product for any reconfigured control.

In this way, the control is implemented in resources, information on product state (functions executed, in execution …) and functional constraints are embedded in the product. The verification of constraints respect is made during control execution (Fig. 9):

-the resource detects product presence, -the resource read the tag on the product: information on product state and functional constraints, -the resource proposes a function to execute, -if the constraints are respected, the function is executed and the product is updated, -otherwise, the function execution is filtered and another function is proposed. This approach is interesting in the case of flexible or reconfigurable systems. As the control is not completely defined a priori, the execution of a function is not linked to a specific resource, thus some flexibility in the execution of the process plans is possible. However, the constraints do not ensure that the product will eventually be manufactured.

EXAMPLE: CONDITIONING SYSTEM

The considered conditioning system allows granules packaging, with or without label. It is composed of 4 partially redundant resources (R 1 to R 4 ) allowing 4 functions (Fig. 10): F 1 represents the bottle closing; F 2 represents the label collage, F 3 and F 4 represent the distribution of types A and B granules. These functions are completed by 4 transport functions. The variable ppi represents the product presence on the resource Ri.

From functions location on the resources, 8 resources constraints are defined:

-Resource (R 1 ) : and Table 1 describes the 10 various products that can be manufactured. According to the product type, a set of conditions is defined. For example, considering product P 9 , these conditions imply constraints on function execution (Table 2).

F 1 F 3 ∧ F 4 (1) F 2 (2) F 3 ∨ F 4 (3) F 2 Forbidden (4) Forbidden Forbidden F 3 ∅ F 4 ∨ F 1 (5) ∅ F 4 F 3 (6) F 3 (7) ∅
According to these conditions, 9 constraints are then defined:

-Condition 1: 0

) ( 4 3 1 = ∧ ∧ ex ex rq F F F -Condition 2: 0 ) ( 2 2 1 = ∨ ∧ ie rq rq F F F -Condition 3: 0 1 3 = ∧ ex rq F F and 0 1 4 = ∧ ex rq F F -Condition 4: 0 2 = rq F -Condition 5: 3 4 1 4 1 (( ) ( )) 0 rq rq rq ie ie F F F F F ∧ ∨ ∨ ∨ = -Condition 6: 0 ) ( 3 4 = ∧ ex rq F F -Condition 7: 4 3 3 ( ) rq rq ie F F F ∧ ∨ =0
In the first step of approach, the sufficiency of functional constraints is verified. The constraint 0 ) ( In the second step, a logical process plan (which does not specify executing resources) is defined to verify that at least a way exists to manufacture the product (Fig. 12). We define the following propriety:

( . _ E processplan produit fini) <> which is verified using UPPAAL.

CONCLUSION AND PERSPECTIVES

There is a growing interest in models, methods and tools that facilitate the D.E.S. reconfigurable control. This paper focuses on the safety issues of such reconfigurable system in the case of product-driven control. Main proposal consists in a filtering approach that enables to maintain PDC within a state space that satisfy functional (with regard to the product goals) and safety (with regards to the process operations) constraints without assuming any PDC properties (i.e. whatever the control generated by the reconfiguration process is). Presented refer to the constraints design and verification phase as shown on figure 2. Further work needs to be developed for implementation issues. Moreover, if the writing and verification of functional filter constraints has been illustrated on a simplified case-study, experiments on industrial-scale case-studies emphasize the effort that still must be employed to make the proposed engineering framework effective in practice. In future works, some hypotheses must be lifted. For example, temporal issues will be included in constraint definition, as the use of cost will be used during trajectory choice.

Fig. 1 :

 1 Fig. 1: Product-driven control architecture For implementation aspects, infotronics technology such as RFID tags embedded on the products enables individual identification of product occurrences that open a way towards the customization of control constraints for each product occurrence (McFarlane et al. 2003).

  executed at the same time that Fi, i.e. in a PLC cycle in which Fi is requested, functions included in Fi during , should not be already in execution or requested for activation, -ensures that the functions included in Fi 0 after rq ex Fi Fi ∧ = after cannot be executed after the Fi execution, -ensures that the functions included in Fi 0 = rq prohibited

Fig. 4 :

 4 Fig. 4: Generic models of tag reading and update

Fig. 6 :

 6 Fig. 6: Generic model of constraints Functions can be of two types: shape processing or transport function. Shape processing function (Fig. 7) is modelled by a 3 states automaton: {Not executed, In execution, Executed}. The automaton goes from Not executed to In execution when the activation is made (Fi rq =1), if a product is present on the resource (ppi=1) and if all constraints are met (errori=0). The function is executed when the time function_time passes. With transitions crossing, function state values are updated.

Fig. 7 :

 7 Fig. 7: Generic model of shape processing function (Fi) Transport function is represented with a 3 states automaton: {Not executed, Left from Start position, At End position}, transitions crossing is made according to time values (Fig. 8).

Fig. 8 :

 8 Fig. 8: Generic model of transport function (Fi) 3.2.1.4. Verification of constraints sufficiency

Fig. 9 :

 9 Fig. 9: Interaction scenario with on line control verification

Fig. 10 :

 10 Fig. 10: Overview of the conditioning system

  Fig. 11: Sufficiency observer

Fig. 12 :

 12 Fig. 12: Process plan

Table 1 :

 1 Product types

	o
	o


Aline Tribollet

S Golubic

bioerosion of experimental carbonate substrates exposed for 3 years on the northen Great Barrier Reef, Australia

Keywords:

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

Introduction

Coral reefs are among the most complex and dynamic marine ecosystems. Healthy coral reefs are maintained by a balance between forces contributing to reef construction, primarily growth of corals and coralline algae, and reef destruction, essentially due to the agents of bioerosion [START_REF] Scoffin | Calcium carbonate budget of a fringing reef on the west coast of Barbados[END_REF][START_REF] Hutchings | Biological destruction of coral reefs[END_REF][START_REF] Glynn | Bioerosion and coral-reef growth: a dynamic balance[END_REF]. The existence of barrier reefs and atolls demonstrate the capacity of healthy coral reefs to maintain a positive net growth, which was historically able to keep up with rising sea levels. There is increased evidence that some coral reefs are presently loosing their integrity, and that the balance is shifting in favor of destructive forces [START_REF] Kiene | A model of bioerosion on the Great Barrier Reef[END_REF][START_REF] Glynn | Bioerosion and coral-reef growth: a dynamic balance[END_REF][START_REF] Pari | Bioerosion of experimental substrates on high islands and atoll lagoons (French Polynesia) after two years of exposure[END_REF][START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF]. Factors such as eutrophication [START_REF] Tomascik | Effects of eutrophication on reefbuilding corals. II. Structure of scleractinian coral communities on fringing reefs, Barbados, West Indies[END_REF]Szmant 2002), terrestrial runoff [START_REF] Rogers | Responses of coral reefs and reef organisms to sedimentation[END_REF][START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF], overfishing (Szmant 2002), rising pCO 2 [START_REF] Langdon | Effect of calcium carbonate saturation state on the calcification rate of an experimental coral reef[END_REF], and rising sea surface temperature [START_REF] Mumby | Unprecedented bleaching-induced mortality in Porites spp. At Rangiroa Atoll, French Polynesia[END_REF] are currently contributing to a rise of coral mortality and an accelerated degradation of coral reef structures [START_REF] Wilkinson | Status of coral reefs of the world[END_REF]. These conditions threaten the very survival of the reef ecosystem, as well as the coastal and insular human communities protected by the coral reefs (see [START_REF] Wilkinson | Status of coral reefs of the world[END_REF].

A large body of research concerned with the health and functioning of coral reef ecosystems concentrates on coral growth rates [START_REF] Barnes | Systematic variations in the depth of skeleton occupied by coral tissue in massive colonies of Porites from the Great Barrier Reef[END_REF][START_REF] Lough | Several centuries of variation in skeletal extension, density and calcification in massive Porites colonies from the Great Barrier Reef: a proxy for seawater temperature and a background of variability against which to identify unnatural change[END_REF]) and factors affecting coral growth including detrimental affects such as bleaching (Mumby et al. 1 2001), coral diseases [START_REF] Antonius | First protozoan coral-killer identified in the Indo-Pacific[END_REF][START_REF] Cervino | Yellow band and dark spot syndromes in Caribbean corals: distribution, rate of spread, cytology, and effects on abundance and division rate of zooxanthellae[END_REF]) and coelenterate predation (Pratchett 2001). Some of these effects are reversible, others are detrimental to corals and often measured in terms of coral mortality index [START_REF] Gomez | A review of the status of Philippine reefs[END_REF]). As a consequence, large areas of coral reefs become degraded with growing areas of dead coral rock and rubbles, leaving a reduced coverage of live corals [START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF]. Recently, [START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF] argued that coral growth rates (vertical extension) alone are poor indicators of coral reef health, especially for reefs threatened by eutrophication and sedimentation simultaneously. They suggested that reef health is best considered at the scale of whole reef growth and its carbonate budget (bioaccretionÀbioerosion).

Research on bioerosion and other destructive forces affecting coral reefs is equally important but has received less attention. Bioerosion is the main destructive force [START_REF] Scoffin | Calcium carbonate budget of a fringing reef on the west coast of Barbados[END_REF]) that modifies reef growth [START_REF] Stearn | Carbonate budget of a fringing reef, Barbados[END_REF], contributes to local sediment production [START_REF] Hutchings | Biological destruction of coral reefs[END_REF][START_REF] Conand | The carbonate budget of a fringing reef in La Reunion Island (Indian ocean): sea urchin and fish bioerosion and net calcification[END_REF], and thereby enhances biodiversity of the reef [START_REF] Hutchings | Biological destruction of coral reefs[END_REF][START_REF] Moran | Bioerosion and availability of shelter for benthic reef organisms[END_REF]. Bioerosion takes place in substrates under live coral [START_REF] Campion-Alsumard | Microbial endoliths in skeletons of live and dead corals: Porites lobata (Moorea, French Polynesia)[END_REF][START_REF] Risk | Bioerosion in Acropora across the continental shelf of the Great Barrier Reef[END_REF] and under live coralline algal crusts [START_REF] Tribollet | Bioerosion of the crustose coralline alga Hydrolithon onkodes by microborers in the coral reefs of Moorea, French Polynesia[END_REF], but it becomes intensified on dead substrates, that is, substrates not protected from biofouling by live tissues [START_REF] Hutchings | Biological destruction of coral reefs[END_REF][START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF]. As the rate of coral mortality increases, so does the area exposed to intensified bioerosion.

Bioerosion on coral reefs consists of the following interacting components: (1) microbioerosion by euendolithic [START_REF] Golubic | The lithobiontic ecological niche, with special reference to microorganisms[END_REF]) cyanobacteria, algae, and fungi, (2) grazing by gastropods, echinoids, and fish, and (3) macrobioerosion by sponges, worms, and bivalves. Each of these components of bioerosion is the subject of numerous studies that assessed the conditions in natural settings or by measuring bioerosion rates on experimentally exposed substrates, but only a few focussed on interrelations among all the three components simultaneously. For example, microboring rates were studied in sediment grains by [START_REF] Tudhope | Rate of dissolution of carbonate sediments by microboring organisms, Davies Reef, Australia[END_REF], in oyster shells by [START_REF] Che | Biodegradation of shells of the black pearl oyster, Pinctada margaritifera Var. Cumingii, by microborers and sponges of French Polynesia[END_REF], and in live and dead coralline algae by [START_REF] Tribollet | Bioerosion of the crustose coralline alga Hydrolithon onkodes by microborers in the coral reefs of Moorea, French Polynesia[END_REF]. Grazing rates were assessed by [START_REF] Bak | Patterns of echinoid bioerosion in two Pacific coral reef lagoons[END_REF] and [START_REF] Peyrot-Clausade | Sea urchin and fish on La Re´union and Moorea reefs[END_REF]. Macroboring rates under live corals were studied by [START_REF] Sammarco | Large-scale patterns in internal bioerosion of Porites: cross continental shelf trends on the Great Barrier Reef[END_REF], [START_REF] Risk | Bioerosion in Acropora across the continental shelf of the Great Barrier Reef[END_REF], [START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF], and [START_REF] Holmes | Bioerosion of live massive corals and branching coral rubble on Indonesian coral reefs[END_REF] in relation to eutrophication. The interaction between microbioerosion and grazing was studied by [START_REF] Schneider | Biokarst on limestone coasts, morphogenesis and sediment production[END_REF], between micro-and macrobioerosion by [START_REF] Zubia | Internal bioerosion of Acropora formosa in Re´union (Indian Ocean): microborer and macroborer activities[END_REF], and between macrobioerosion and grazing by [START_REF] Kiene | A model of bioerosion on the Great Barrier Reef[END_REF]Hutchings (1992, 1994), [START_REF] Reaka-Kudla | Experimental studies of rapid bioerosion of coral reefs in the Galapagos Islands[END_REF][START_REF] Pari | Bioerosion of experimental substrates on high islands and atoll lagoons (French Polynesia) after two years of exposure[END_REF].

Simultaneous assessment of all the three components of bioerosion was carried out at a local scale and for 1 year or 2 years exposure time, using Porites blocks by [START_REF] Chazottes | Bioerosion rates on coral reefs: interaction between macroborers, microborers and grazers (Moorea, French Polynesia)[END_REF]) in Moorea Island, French Polynesia (1995) and Reunion Island, Indian Ocean (2002). [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF] analyzed microbioerosion, grazing, and macrobioerosion for a year in the largescale setting of this study on the continental shelf of the northern Great Barrier Reef (GBR), Australia. These studies demonstrated the importance of the integration of all components of bioerosion in the quantification of total bioerosion rates. The present contribution evaluates the temporal progression in bioerosion rates and patterns at the same GBR sites over 3 years of exposure and provides data that will be useful for the estimation of whole reef carbonate budgets.

Materials and methods

Area of study

Six sites were selected near either end of a 200-km-long inshore-offshore profile of the northern Great Barrier Reef (GBR; Fig. 1). These sites include two inshore reefs: Snapper Island and Low Isles, and four reefs located near the edge of the continental shelf: Lizard Island, Harrier Reef, Ribbon Reef N°3, and Osprey Reef, which are considered here as offshore reefs (described in [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF]. The inshore reefs on the GBR, such as at Snapper Island and Low Isles, are surrounded by nutrient-enriched turbid waters [START_REF] Johnson | Sedimentary framework of mainland fringing reef development, Cape Tribulation area[END_REF][START_REF] Bell | Status of eutrophication in the Great Barrier Reef lagoon[END_REF][START_REF] Furnas | Biological and chemical oceanographic features of the Cairns-cooktown region relevant to Crown-of-Thorns starfish outbreaks. Review for the Crown of Thorns Starfish Research Committee[END_REF]. The waters at Lizard Island are much less influenced by the land [START_REF] Ikeda | Biological, chemical and physical observations in inshore waters of the Great Barrier Reef, North Queensland 1975-1978[END_REF][START_REF] Wolanski | Physical oceanography processes of the Great Barrier Reef[END_REF][START_REF] Furnas | Biological and chemical oceanographic features of the Cairns-cooktown region relevant to Crown-of-Thorns starfish outbreaks. Review for the Crown of Thorns Starfish Research Committee[END_REF]). Harrier Reef and Ribbon Reef N°3 on the barrier reef and Osprey Reef in the Coral Sea, are surrounded by clear and oligotrophic waters [START_REF] Bell | Status of eutrophication in the Great Barrier Reef lagoon[END_REF].

Sampling design and sample treatment

Forty-eight experimental blocks (8 cm•8c m •5 cm) were cut from the interior of live heads of the massive coral Porites sp. using a band saw. The live heads were collected at Snapper Island and Lizard Island in shallow waters. Massive Porites was used because the genus is abundant on the GBR, and skeleton of dead Porites is a natural habitat for microbial endoliths. Extrapolations from rates of erosion measured for one specific substrate such as massive Porites to coral reefs as a whole have limitations as it has been shown that rates vary largely between substrates [START_REF] Risk | Bioerosion in Acropora across the continental shelf of the Great Barrier Reef[END_REF][START_REF] Che | Biodegradation of shells of the black pearl oyster, Pinctada margaritifera Var. Cumingii, by microborers and sponges of French Polynesia[END_REF][START_REF] Holmes | Bioerosion of live massive corals and branching coral rubble on Indonesian coral reefs[END_REF][START_REF] Tribollet | Bioerosion of the crustose coralline alga Hydrolithon onkodes by microborers in the coral reefs of Moorea, French Polynesia[END_REF][START_REF] Scho¨nberg | Substrate effects on the bioeroding desmosponge Cliona orientalis. 1. Bioerosion rates[END_REF]. However, Porites skeletons have been used in other bioerosion studies [START_REF] Kiene | A model of bioerosion on the Great Barrier Reef[END_REF]Hutchings 1992, 1994;[START_REF] Chazottes | Bioerosion rates on coral reefs: interaction between macroborers, microborers and grazers (Moorea, French Polynesia)[END_REF][START_REF] Chazottes | The effects of eutrophication-related alterations to coral reef communities on agents and rates of bioerosion (Reunion Island, Indian Ocean)[END_REF], thus allowing for comparison of the results. The blocks showing evidence of previous bioerosion were discarded. Each block was soaked in fresh water and then dried and its initial dimensions were measured. The density of Porites heads from which blocks were cut was also measured (see [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF]. Eight randomly chosen experimental blocks were attached to 1-m•1-m steel grid. Two such grids were mounted on dead coral substrates in September 1996 at each of the selected sites (habitats described in [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF], at a distance of 3-5 m to each other and at a depth of 7-10 m. Two blocks per grid were randomly collected in September 1997 and 1999, thus after 1 year and 3 years of exposure.

The collected blocks were preserved in a buffered 7% solution of formaldehyde in seawater and later cut in half with a band saw. One half was used to determine macroboring organisms, while the other half was cut in four 7-mm-thick slices (see [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF]. Three slices per block were used for quantification of the rates of bioerosion and bioaccretion; each slice allowing one measure of bioerosion and bioaccretion (the slice with anchoring bolt was discarded). No attempt was made to separate biological erosion processes from associated but negligible physical loss of weakened structures (ex: saltation).

The quantification of microbioerosion was approached in two ways. SEM images of the exposed surface of the block were evaluated by Visilog 5.1 (Noesis Co.) to obtain the surface removed by microborers. The depth of microboring penetration was measured from petrographic thin section cut perpendicular to the exposed block surface to obtain the volume of carbonate removed by microborers (see [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF]. Grazing, macroboring, and bioaccretion rates were measured using NIH-image software (http://rsb.info.nih.gov/nih-image/) and Adobe Photoshop 5.0. These methods were introduced in the present paper and the earlier published data were recalculated according to improved imagery. Microand macroboring rates were quantified here as ''residual'' on the basis of the block volume that remained after grazing (for definition, see [START_REF] Chazottes | Bioerosion rates on coral reefs: interaction between macroborers, microborers and grazers (Moorea, French Polynesia)[END_REF]. The participating macroboring organisms were identified by groups on the basis of shapes and sizes of their excavations (Fig. 2). The relative proportion of each group (sponges, worms, and bivalves) was evaluated separately on the basis of the projected surface area of their boreholes and expressed as percent values. The projected bioeroded surface area (or the projected surface area covered by encrusting calcareous algae) on each vertical slice was measured by NIH image analysis and the volume of eroded (or added) carbonate was calculated from the measured thickness of each slice.

The amounts of carbonate removal were calculated from the initially obtained density values for each block. Bioaccretion values were obtained using a density of 1.26 g cm À3 for calcareous algae [START_REF] Laubier | Le corallige`ne des Albe`res[END_REF]. Microboring, grazing, macroboring, and bioerosion rates were expressed in percent of CaCO 3 removed per block. All values were extrapolated from the experimental blocks and expressed as kg of removed or added CaCO 3 per m 2 of total exposed surface area of block (exposed surface of the six sides) and per year (kg m À2 year À1 ). The cumulative rates were also quantified (kg per m 2 of exposed surface area of block after 1 year and 3 years of exposure). Bioerosion or total bioerosion rates were calculated for each block as the sum of microbioerosion, grazing, and macrobioerosion. The role played by each agent in bioerosion was also expressed in percentage. Net bioerosion rates were determined from bioerosion minus bioaccretion.

Statistical analyses

Data sets were tested for normality and homoscedasticity using frequency histograms and Cochran's test [START_REF] Sachs | Applied statistics. A handbook of techniques[END_REF]. All bioerosion and bioaccretion analyses were transformed by log(x + 0.01) prior to analysis for purposes of normalization [START_REF] Dagnelie | The´orie et me´thodes statistiques. Applications agronomiques. In: Ducolot J (ed) The´orie et me´thodes statistiques[END_REF]. A series of three-way nested analyses of variance (ANOVA) with equal or unequal sample size was carried out to investigate the variation of microbioerosion, grazing, macrobioerosion, bioaccretion, and net bioerosion data: among blocks of a grid, among grids within a site, and among sites [START_REF] Sokal | Biometry. WH Freeman[END_REF]. A series of two-way ANOVA tests (cross-classification) was employed to investigate the effects of site and length of exposure on the different rates of bioerosion. After each ANOVA, multiple comparisons of means according to the SNK test [START_REF] Sokal | Biometry. WH Freeman[END_REF] were used to identify which sites were significantly different from each other. In both sets of ANOVA tests, the mean and standard error of rates of microboring (n=40), grazing (n=3), macroboring (n=3), bioaccretion (n=3), and net bioerosion (n=3) were used for each block. A series of Spearman's tests (a=0. 05 Scherrer 1984) was also conducted to correlate all measured variables after 1 year and 3 years of exposure. The statistics were carried out using the software packages Super Anova 1.11(1991) and Statview 5.0 (1998).

Results

The rates of bioerosion of exposed blocks were measured separately for the main biological agents: micro- borers (euendolithic cyanobacteria, algae, and fungi), grazers (mainly scarid fish), and macroborers (sponges, polychaete and sipunculid worms, and bivalves). Rates of bioaccretion were measured only for encrusting coralline algae. Data are presented for 1 year and 3 years of exposure, comparing six sites on a coast-to-offshore profile across the GBR, Australia. The three-way nested ANOVAs followed by SNK tests revealed that microbioerosion, grazing, and total bioerosion varied significantly among sites. This distinction was not expressed for macrobioerosion during the first year of exposure, but became established after 3 years. No significant differences within sites were shown for any of the measured bioerosion rates, although differences among blocks within a grid were significant, indicating a patchy distribution of the erosional impacts at the block level (Table 1).

Microboring rates

Microbial endolith community became fully established after 1 year of exposure and did not change qualitatively after 3 years. The dominant microborers, responsible for carbonate removal from the exposed surfaces of the block were the chlorophyte Ostreobium quekettii and the cyanobacteria Plectonema terebrans and Mastigocoleus testarum. Euendolithic fungi were also abundant. A SNK test showed that microbioerosion was lower at the inshore sites than at the offshore sites. At Snapper Island, 0.58±0.02% of CaCO 3 was removed from the experimental blocks by microborers. Extrapolated from the block surfaces, this was equivalent to about 0.13±0.005 kg CaCO 3 m À2 year À1 . The highest rate of microboring was found at the oceanic site, Osprey Reef, with 5.26±0.19% of carbonate 2). The general increase of microboring rates from the coast toward the Coral sea remained expressed after 3 years of exposure (Fig. 3), with the lowest values for Snapper Island, with 0.23±0.006 kg CaCO 3 m À2 removed after 3 years (corresponding to a rate of 0.08 kg CaCO 3 m À2 year À1 ) and the highest values for Harrier Reef (1.42±0.065 or 0.47 kg m À2 year À1 ) and Osprey Reef (1.29±0.059 or 0.43 kg m À2 year À1 ). The latter two sites were pooled by the SNK test, as were data for Lizard Island and Ribbon Reef N°3 (see Table 2).

Grazing rates

Only teeth marks of scarid fish were observed on the outer surface of blocks, indicating that they were probably the primary grazers of exposed blocks. The SNK test showed two groups of sites and an increase of grazing from the coast to the ocean (Fig. 3). Snapper Island and Low Isles, the two inshore sites, exhibited the lowest mean grazing rate of 0.007±0.001 kg m À2 year À1 . The four offshore sites showed higher rates ranging between 0.32±0.04 at Lizard Island and 0.77±0.22 kg m À2 year À1 at Ribbon Reef N°3 (Table 2). The mean grazing rate for the offshore group was 0.53±0.13 kg m À2 year À1 (2.9±0.72% of CaCO 3 removed per block).

After 3 years of exposure, the trend of increasing grazing pressure from the inshore to the offshore sites was enhanced. The SNK test now grouped the data into three groups of sites (Fig. 3). The lowest rates still characterized the inshore sites, Snapper Island and Low Isles, averaging 0.25±0.064 kg m À2 for the 3 years or 0.08 kg CaCO 3 m À2 year À1 (1.38±0.36% of CaCO 3 removed per block in 3 years), whereas the highest rates were recorded for Ribbon Reef N°3 and Osprey Reef of 4.80±0.89 kg m À2 on the average or 1.6 kg m À2 year À1 (27.10±5.03% of CaCO 3 removed per block in 3 years). Lizard Island and Harrier Reef formed an intermediate group with an average rate of 1.30±0.16 kg m À2 or 0.43 kg m À2 year À1 (Fig. 3, Table 2).

Macroboring rates

After 1 year of exposure, macrobioerosion was mainly due to worms (sipunculids and polychaetes) and a few juvenile bivalve molluscs. Only at Snapper Island, macrobioerosion resulted from worms, bivalves, and sponges (Table 3). The three-way nested ANOVA showed no significant differences among sites (Table 1). Rates of macroboring varied between 0.01±0.003 kg m À2 year À1 at Low Isles and 0.13±0.014 kg m À2 year À1 at Snapper Island (Fig. 3; Table 2). The mean macroboring rate for the six sites was 0.05±0.023 kg m À2 year À1 , derived from 0.26±0.11% of CaCO 3 removed per block.

After 3 years of exposure, the same groups of macroboring organisms were present. The boring sponges increased in frequency and in area of occupancy. The contribution of boring bivalves increased, because of their abundance and individual size increase (Fig. 2, Table 3). Significant differences among sites were highlighted by the three-way nested ANOVA (Table 1). The SNK test showed two groups of sites (Fig. 3). One group of sites comprised of Snapper Island, Low Isles, and Harrier Reef which exhibited the highest mean rate of macroboring of 0.83±0.214 kg m À2 after 3 years of exposure or 0.28 kg CaCO 3 m À2 year À1 (4.87±1.26% of CaCO 3 removed per block after 3 years) with the participation of all groups of macroborers (Table 3). The other group included Lizard Island, Ribbon Reef N°3, and Osprey Reef with a mean rate of macroboring of 0.23±0.101 kg m À2 or 0.08 kg m À2 year À1 (1.56±0.61% of CaCO 3 removed per block after 3 years). In the latter group of sites, worms played a major role in macrobioerosion process (Table 3).

Bioaccretion rates

In this study, bioaccretion was due entirely to encrusting coralline algae, which showed low rates of colonization and accretion on the experimental blocks. The three-way nested ANOVA did not reveal any significant differences Fig. 3 Histogram presenting spatial and temporal variability of cumulative rates of microboring, grazing, macroboring, and total bioerosion of dead coral blocks exposed for 1 year and 3 years at six sites from the northern coast of Queensland to the Coral Sea. Mean rates are expressed in kg of CaCO 3 removed per m 2 of exposed surface area of block after one (clear grey) and 3 years of exposure (dark grey). The whisker represents the standard error of rates of bioaccretion among sites (P>0.2). After 1 year of exposure, rates were close to zero in all sites, averaging 0.03 kg m À2 year À1 . The rates averaged 0.14±0.04 kg m À2 after 3 years.

Bioerosion rates (microbioerosion + grazing + macrobioerosion)

After 1 year of exposure, total bioerosion was mainly due to microborers (their contribution ranging between 61% and 91%, Fig. 4a), except at Snapper Island and at Ribbon Reef N°3. At the inshore site, Snapper Island, macroborers eroded as much material as did microborers. At Ribbon Reef N°3, grazers were the dominant agents (67%) followed by microborers (31%). The SNK test revealed three groups of sites. The two inshore sites exhibited the lowest rates of bioerosion averaging 0.21±0.021 kg m À2 year À1 or 0.87±0.09% of CaCO 3 removed per block (Fig. 3, Table 2). The highest rate was found at the oceanic site Osprey Reef (2.17±0.21 kg m À2 year À1 or 8.23±0.94% of CaCO 3 removed per block). The remaining group (Lizard Island, Harrier Reef, and Ribbon Reef N°3) showed intermediate rates (Table 2).

After 3 years of exposure, the main agents of bioerosion were macroborers (>57%) at the two inshore sites. At the four offshore sites, grazers were the principal agents of erosion (43-84%) in synergy with microborers (15-39%; Fig. 4b). The SNK test regrouped the sites as follows: Lizard Island was pooled with the two inshore sites, averaging 1.81±0.16 kg m À2 after 3 years of exposure or 0.60 kg CaCO 3 m À2 year À1 (9.36±0.81% of CaCO 3 removed per block after 3 years, Table 2). Osprey Reef and Ribbon Reef N°3 were pooled and showed the highest rates (average 6.07±0.62 kg m À2 or 2.02 kg m À2 year À1 or 32.28±3.52% of CaCO 3 removed per block). The remaining Harrier Reef presented an intermediate rate (3.60±0.28 kg m À2 or 1.30 kg m À2 year À1 ).

Tests of the duration of exposure versus sites (twoway ANOVAs) showed significant differences between bioerosion rates measured after 1 year and 3 years of exposure, significant differences among the sites (as shown above) and significant interaction between those factors (Table 4). The SNK tests showed that the various annual rates of bioerosion (microboring, grazing, macroboring, and total bioerosion) increased over time at all sites except for microbioerosion at Osprey Reef, where it remained practically constant. The increase for total bioerosion rates was not proportional, but varied from site to site by factors from 2 to 11.

The rates of microboring and grazing were positively correlated over time, whereas the rates of microboring and macroboring were independent (Table 5). The rates of macroboring and grazing appeared to be independent after 1 year, but were negatively correlated after 3 years (Table 5). After 1 year, bioaccretion was positively correlated with grazing and microbioerosion, but no correlation was expressed after 3 years. There was no correlation between bioaccretion and macrobioerosion.

Grazing loss was negatively correlated with the skeletal density of experimental substrates. There was no correlation between skeletal density and micro-or macrobioerosion, although the initial density of the exposed Porites coral skeleton varied significantly between coral heads (between 1.15 g cm À3 and 1.73 g cm À3 ; P=0.0002; [START_REF] Tribollet | Large-scale spatial variability in bioerosion of experimental coral substrates on the Great Barrier Reef (Australia): importance of microbrers[END_REF]; but not between sites (P>0.05).

Discussion

Record of bioerosion rates over time

Bioerosion under live and growing corals and crustose algae is quantitatively and often qualitatively different from bioerosion on dead carbonate substrates (Le [START_REF] Campion-Alsumard | Microbial endoliths in skeletons of live and dead corals: Porites lobata (Moorea, French Polynesia)[END_REF][START_REF] Risk | Bioerosion in Acropora across the continental shelf of the Great Barrier Reef[END_REF][START_REF] Tribollet | Bioerosion of the crustose coralline alga Hydrolithon onkodes by microborers in the coral reefs of Moorea, French Polynesia[END_REF]. Quantification of rates and progression of bioerosion on experimentally exposed blocks of cleaned coral skeletons is designed to provide a close approximation of processes occurring on dead corals and coral rubbles. The significance of these processes increases as the areas covered by healthy growing corals decreases on degrading reefs. The measured annual rates of bioerosion calculated after 3 years of exposure were significantly and disproportionally higher than those recorded after the first year. The reasons may vary for different organisms and organism groups involved in bioerosion.

Cleaned and newly exposed substrates appear to require an initial time of conditioning, including surface coating by microbial biofilms followed by a succession of epilithic and endolithic microorganisms [START_REF] Hutchings | Biological destruction of coral reefs[END_REF]. The time required for stabilization of the microbioeroding community is probably shorter than that for R coefficient of correlation, P Greenhouse-Geisser corrected probability, s means that the test was significant grazers and macroborers, which is evident from the comparison of microbioerosion data after 1 year and 3 years of exposure. Grazing patterns show a positive correlation with microbioerosion, because grazing is largely dependent on epilithic and endolithic algal biomass and their growth rates for food [START_REF] Bruggemann | Foraging by the stoplight parrotfish Sparisoma viride. I. Food selection in different, socially determined habitats[END_REF]. Conversely, development of microborers depends on grazers as those reduce: (a) the settlement and growth of epilithic organisms, which compete with endoliths for space [START_REF] Golubic | Carbonate dissolution[END_REF]) and (b) the shading of endoliths habitat, thus enhancing the growth of phototrophic microborers (Scheinder and Torunski 1983).

The assemblage of macroborers within the block showed a delay in development over a 3-year period. After 1 year of exposure, macroborers were represented mostly by worms at all sites, and the macrobioerosion rates were too low to show any significant trends. After 3 years of exposure, macroborers included larger organisms with longer developmental cycles (e.g. boring sponges and bivalves), indicating that the settlement started with small propagules and the surviving individuals increased multifold in size, enlarging their boreholes in the process. The requirement for several years of exposure before the evaluation of macroborer's contribution to bioerosion has been discussed by several authors [START_REF] Kiene | A model of bioerosion on the Great Barrier Reef[END_REF]Hutchings 1992, 1994;[START_REF] Pari | Bioerosion of experimental substrates on high islands and atoll lagoons (French Polynesia) after two years of exposure[END_REF][START_REF] Chazottes | The effects of eutrophication-related alterations to coral reef communities on agents and rates of bioerosion (Reunion Island, Indian Ocean)[END_REF]. In our study, larger macroborers were particularly numerous at inshore sites where the grazing pressure was the lowest. The same pattern was repeated at Harrier Reef among the offshore sites, where the higher frequency of endolithic bivalves was coincident with lower grazing pressure. Intense grazing pressure at the offshore sites corresponded generally with a dominance of worms. The inverse relation between grazing pressure and diversification of macrobioeroding community has been documented at a local scale by [START_REF] Sammarco | Effects of grazing and damselfish territoriality on internal bioerosion on dead corals: indirect effects[END_REF] and [START_REF] Kiene | Bioerosion experiments at Lizard Island, Great Barrier Reef[END_REF]. [START_REF] Kiene | A model of bioerosion on the Great Barrier Reef[END_REF], in his study of the GBR, described a similar situation as ''immature reef'', as opposed to a ''mature'' reef where sponges and bivalves were the principal agents of macrobioerosion, grazing pressure was limited and encrustation well developed. Thus, the community of macroborers requires the longest time to become established on experimental blocks.

Bioerosion patterns across the northern Great Barrier Reef

The rates of bioerosion in the present contribution were compared along a 200-km-long inshore-offshore profile on the northern GBR. Microbioerosion rates increase significantly with the distance from the coast. Grazing rates followed the same pattern as a dependent parameter (Fig. 3). In contrast, the macrobioerosion showed the opposite trend of a significant decrease in rates with increased distance from the shore. Total bioerosion followed the trend of microbioerosion and grazing, showing that microborers and grazers were the main agents of bioerosion on the studied profile.

Lower rates of settlement by microbial euendoliths and microbioerosion at the inshore sites, may have been caused by the observed sediment entrapment in the epilithic algal turf and by the resulting light limitation. On the offshore sites, microboring communities were established more rapidly (e.g. the rates at Osprey did not change between the first and the third year of exposure). The inshore-offshore distinction becomes evident after 1 year, and this trend is enhanced after 3 years of exposure. Our rates were 3-to 25-fold higher than those found by [START_REF] Chazottes | The effects of eutrophication-related alterations to coral reef communities on agents and rates of bioerosion (Reunion Island, Indian Ocean)[END_REF] at La Reunion after 1 year of exposure (0.04 to 0.07 kg m À2 year À1 ). In fact, the data on microbioerosion are difficult to compare without considering grazing pressure. In [START_REF] Chazottes | The effects of eutrophication-related alterations to coral reef communities on agents and rates of bioerosion (Reunion Island, Indian Ocean)[END_REF] study, the grazers were mostly echinoids, while they were fish at our sites. Echinoids are the most efficient grazers [START_REF] Bak | Patterns of echinoid bioerosion in two Pacific coral reef lagoons[END_REF][START_REF] Reaka-Kudla | Experimental studies of rapid bioerosion of coral reefs in the Galapagos Islands[END_REF] and thus the measurable microboring activity, that is, the ''residual'' microbioerosion is lower in experimental blocks grazed by echinoids [START_REF] Chazottes | The effects of eutrophication-related alterations to coral reef communities on agents and rates of bioerosion (Reunion Island, Indian Ocean)[END_REF] than in blocks grazed by fish (the present study).

Low rates of grazing on inshore sites may have been caused by food preferences of grazers, as well as by the smaller average size of fish prevalent in coastal waters. [START_REF] Russ | Distribution and abundance of herbivorous grazing fishes in the Central Great Barrier Reef. I. Levels of variability across the entire continental shelf[END_REF] and [START_REF] Bellwood | A functional analysis of grazing in parrotfishes (family Scaridae): the ecological implications[END_REF] showed that scarid fishes are smaller and less abundant at the inshore sites than on the outer barrier reef and in the Coral Sea. After 3 years of exposure, grazing rates were still lower at inshore sites than at offshore sites, following the pattern of microbioerosion. [START_REF] Pari | Bioerosion of experimental substrates on high islands and atoll lagoons (French Polynesia) after two years of exposure[END_REF] and [START_REF] Peyrot-Clausade | Bioerosion in the carbonate budget of two Indo-Pacific reefs: La Reunion Island (Indian ocean) and Moorea (Pacific ocean)[END_REF] found important rates of grazing on near-shore sites affected by eutrophication on Tahiti barrier reef, due to the abundance of echinoid grazers. However, the number of echinoids at our sites was negligible (personal observation). [START_REF] Sammarco | The Great Barrier Reef vs. the Caribbean: comparisons of grazers, coral recruitment patterns and reef recovery[END_REF] showed that the density of echinoids on the GBR is very low (1 m À2 ) and that their erosive activity can be neglected. This explains why our grazing rates were generally 2-to more than 30-fold lower than those attributable to echinoids as found by [START_REF] Chazottes | Bioerosion rates on coral reefs: interaction between macroborers, microborers and grazers (Moorea, French Polynesia)[END_REF] at la Reunion Island (1.63-3.52 kg m À2 year À1 ), [START_REF] Reaka-Kudla | Experimental studies of rapid bioerosion of coral reefs in the Galapagos Islands[END_REF] in Galapagos (22.8 kg m À2 year À1 ) and [START_REF] Peyrot-Clausade | Bioerosion in the carbonate budget of two Indo-Pacific reefs: La Reunion Island (Indian ocean) and Moorea (Pacific ocean)[END_REF] at Moorea, French Polynesia (1.74 kg m À2 year À1 ). On our profile, intermediate grazing rates found at Lizard Island were probably due to the presence of damselfish (personal observation). [START_REF] Sammarco | Effects of grazing and damselfish territoriality on internal bioerosion on dead corals: indirect effects[END_REF] demonstrated that grazing pressure by scarid fish is reduced in the presence of territorial damselfish, which protect their turf. In the case of the Ribbon Reef N°3, the microbioerosion appears to become limited by intensive grazing pressure as shown by an inverse relation between the values for microbioerosion and grazing (Fig. 3). Fish grazing was negatively correlated with the initial coral skeleton density of each block but no correlation was shown between skeletal density and micro-or macroboring rates. It is possible that differences in block density accounted for inter-block variability of grazing. Moreover, the differences between results from the offshore sites, especially the Ribbon and Harrier reefs (both outer barrier reefs), indicate that other factors may be at work in controlling grazing rates.

Macroboring activity showed significant differences among sites only after 3 years. The trend along the studied GBR transect is opposite from microboring and grazing rates. Macrobioerosion showed significantly higher rates at the inshore sites and decreased toward the ocean sites. This trend is consistent with the trend observed at the central GBR by [START_REF] Sammarco | Large-scale patterns in internal bioerosion of Porites: cross continental shelf trends on the Great Barrier Reef[END_REF] and [START_REF] Risk | Bioerosion in Acropora across the continental shelf of the Great Barrier Reef[END_REF]. These authors suggested that macrobioerosion increases with rising eutrophication. This is consistent with macrobioerosion values at our inshore sites, which were surrounded by nutrient-enriched waters. In both studies, sponges and bivalves were dominant at inshore sites, consistent with the presence of high terrigenous inputs and low grazing pressure. In general, turbid and nutrient-enriched coastal waters provide important food supply for macroboring suspension-feeding organisms [START_REF] Rose | Increase in Clinoa delitrix infestation of Montastrea cavernosa heads on an originally polluted portion of the Grand Cayman fringing reef[END_REF][START_REF] Hallock | The role of nutrient availability in bioerosion: consequences to carbonate buildups[END_REF][START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF][START_REF] Holmes | Bioerosion of live massive corals and branching coral rubble on Indonesian coral reefs[END_REF]. Rates obtained in this study were similar to those found in similar experimental substrates by [START_REF] Chazottes | Bioerosion rates on coral reefs: interaction between macroborers, microborers and grazers (Moorea, French Polynesia)[END_REF] and [START_REF] Pari | Bioerosion of experimental substrates on high islands and atoll lagoons (French Polynesia) after two years of exposure[END_REF] in French Polynesia. They are also comparable with rates found by [START_REF] Reaka-Kudla | Experimental studies of rapid bioerosion of coral reefs in the Galapagos Islands[END_REF] on Galapagos reefs, when expressed as percent of CaCO 3 removed per block. The rates of macroboring erosion measured after 3 years of exposure were similar to those measured after more than 4 years of exposure recorded by [START_REF] Kiene | A model of bioerosion on the Great Barrier Reef[END_REF]Hutchings (1992, 1994)

at Lizard

Island. This suggests that rates of macrobioerosion reach a stabilized level after more than 3 years of exposure.

In calculating total bioerosion, we have identified three major components: microbioerosion, grazing, and macrobioerosion. These activities on coral reefs are balanced by the processes of bioaccretion. At the level of exposed experimental blocks, the accretionary process was mainly the result of the growth of crustose rhodophytes. The development of rhodophyte crusts modified the rates of microbioerosion by providing local protection from grazing, but also shading. However, this had no effect on macrobioerosion. The same result was found at la Re´union by [START_REF] Chazottes | The effects of eutrophication-related alterations to coral reef communities on agents and rates of bioerosion (Reunion Island, Indian Ocean)[END_REF]. The total carbonate added by the crust was negligible when compared with the total rate of bioerosion, so that net bioerosion can be considered roughly equivalent to total bioerosion as recorded. The total bioerosion at the block scale increased with the distance from the coast, mainly due to the fact that microbioerosion and grazing were the major processes of bioerosion at the four offshore sites. Macrobioerosion was the principal process only at the two inshore sites. In this study, the 3 years of exposure showed disproportional increase in rates of microbioerosion and especially of grazing and macrobioerosion. This provided an image more closely corresponding to conditions on degraded parts of the reefs, and stresses the importance of long-term settings.

Nevertheless, the general inshore-offshore trends were evident after both 1 year (Tribollet et al. 2002, present study) and 3 years of exposure.

Thus, bioerosion in total appeared more important in ''pristine reefs'' as represented by offshore reefs (especially Osprey Reef) than in nutrient-enriched turbid reefs as represented by inshore reefs. We cannot conclude, however, that offshore reefs were more degraded than the inshore reefs, as we only quantified bioerosion at the scale of experimental blocks of massive Porites. Our results showed also that the pattern of macrobioerosion does not necessarily coincide with the pattern of bioerosion in total. From these results, we can extrapolate as to the bioerosion rates on previously degraded portions of the reef, devoid of actively growing and accreting corals. These results complement the studies of the accreting coral-covered portions of the reef. [START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF] claimed the usefulness of coral growth rates as a measure of health of coral reefs. They studied reefal net carbonate production in polluted versus unpolluted reefs in south Sulawesi and Indonesia, estimating simultaneously live coral cover, coral growth and calcification, skeleton density, as well as macrobioerosion in live corals. Their study revealed that coral growth rates on polluted reefs were not different from those on unpolluted reefs. They also noted that net reef erosion occurred in polluted reefs when live coral cover was low and macrobioerosion intensity high. However, their study did not include microbioerosion and grazing, and did not extend beyond actively growing coral cover. The contrast between constructive and destructive activities in coral reefs would have been more obvious if (1) total bioerosion rather than macrobioerosion alone was considered, and (2) bioerosion in both live and dead corals was quantified. Thus, the model of net carbonate production in polluted versus unpolluted reefs proposed by [START_REF] Edinger | Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?[END_REF], does not include a complete picture of processes in the reef and therefore has to be considered with caution. We suggest, therefore, that the estimates of the state of health of coral reefs and models of reef carbonate cycles, include an evaluation of healthy and growing, as well as damaged, portions of the reef and consider total bioerosion that includes microborers, grazers, and macroborers.

Comparative evaluation of three different components of bioerosion over a large-scale setting connecting different environmental conditions illustrated several salient and distinctive features of each. Microbial bioerosion when acting alone (at the initial stage of bioerosion) is a light-limited and thus, self-stabilizing process which becomes progressive only in the presence of grazing [START_REF] Schneider | Biokarst on limestone coasts, morphogenesis and sediment production[END_REF][START_REF] Chazottes | Bioerosion rates on coral reefs: interaction between macroborers, microborers and grazers (Moorea, French Polynesia)[END_REF]. The interdependence between microbioerosion and grazing explains the close correlation between the measured values and their patterns across the northern GBR shelf: grazing mitigates the shading effect of epilithic layers, permitting microbial penetration deeper into the rock. With continuing grazing, the zone of microbial endoliths and the amount of carbonate they remove, moves like a front through the substrate. Thus their activity measured at any time during the exposure experiment represents a net or ''residual'' microbioerosion, whereas the gross microbial bioerosion includes the part that has been turned over through the grazers. Such interdependence or synergy does not exist between micro-and macroborers, the latter being mostly filterfeeders, which respond more directly to the trophic state of the waters surrounding the reef. Intensive grazing does however, have a selective impact on macroboring organisms by limiting their settlement and early development. Grazers may inflict significant damage on populations of endolithic worms, but affect insignificantly adult endolithic sponges and bivalves. An interesting observation refers to the role of crustose rhodophytes. As they expand over new surfaces, as observed on the oceanic sites of the transect, rhodophyte crusts cover but do not displace the established microbial endoliths. They do, however, introduce additional shading and an added protection from grazing, which also limits the progression of microbial boring and further destruction of the substrate. All these complex interactions highlight the importance of studying simultaneously the different agents of bioerosion to estimate carbonate loss rates under various environmental conditions and through time. This is essential in order to understand the impact of the increasing rate of coral mortality on the reef as a whole, and to better evaluate reefs' health and carbonate cycles.

Fig. 1

 1 Fig. 1 Study sites in the northern GBR (Australia). From the northern coast of Queensland to the Coral Sea: inshore sites-Snapper Island and Low Isles; mid-shelf site-Lizard Island; outer barrier sites-Harrier Reef and Ribbon Reef N°3; oceanic site-Osprey Reef. The last four sites were considered in this study as offshore reefs as opposed to the inshore reefs

Fig. 2

 2 Fig. 2 Scanned slices of dead coral blocks exposed for 1 year (a) and 3 years (b, c, d) to colonization. The arrow at the bottom in the left corner of each picture indicates the block orientation to the water surface. a. Block from Ribbon Reef N°3 exhibiting worm boreholes (short arrow) and encrusting calcareous algae (long arrow). b. Block from Harrier Reef (outer barrier reef) showing traces of boring worm (narrow white arrows) and sponges (large white arrow). Sponge traces were attributed to Cliona sp.. The black arrow indicates an encrusting calcareous alga. c. Block from Ribbon Reef N°3 (outer barrier reef) exhibiting traces of boring worms (narrow arrow) and bivalves (wide arrows). The dotted lines show the initial dimensions of the block. d. Block from Low Isles (inshore reef) exhibiting traces of boring worm (narrow arrow) and sponges (wide arrows). Sponge traces were attributed to Aka sp.. The scale bar is 1 cm

Fig. 4

 4 Fig. 4 Relative contribution (%) of microborers, grazers, and macroborers to bioerosion of dead coral blocks at six sites from the northern coast of Queensland to the Coral Sea, after 1 year (a) and 3 years (b) of exposure

Table 1

 1 Three-way nested ANOVA of log(x + 0.01) transformed rates of microboring, macroboring, grazing, total bioerosion, and bioaccretion after 1 and 3 years of exposure at six sites from the northern coast of Queensland to the Coral Sea 35±0.05 kg CaCO 3 m À2 year À1 . Intermediate rates were found at Low Isles (0.16±0.013), Ribbon Reef N°3 (0.36±0.014), Lizard Island (0.70±0.055), and Harrier Reef (0.75±0.032; Table2). The SNK test pooled data from Lizard Island and Harrier Reef (see Table

	Source of variation	df	MS	F	P
	Microbioerosion after 1 year of exposure
	Site	5	25.69	13.13	0.004**
	Grid (site)	6	1.96	1.56	0.24NS
	Block (site, grid)	12	1.26	64.02	0.0001***
	Residual	976	0.02
	Microbioerosion after 3 years of exposure
	Site	5	11	4.70	0.043*
	Grid (site)	6	2.44	1.05	0.44NS
	Block (site, grid)	12	2.32	225	0.0001***
	Residual	936	0.01
	Macrobioerosion after 1 year of exposure
	Site	5	0.83	2.97	0.11NS
	Grid (site)	6	0.28	1.20	0.37NS
	Block (site, grid)	12	0.23	8.70	0.0001***
	Residual	42	0.03
	Macrobioerosion after 3 years of exposure
	Site	5	1.32	5.07	0.04*
	Grid (site)	6	0.26	0.54	0.77NS
	Block (site, grid)	12	0.49	7.32	0.0001***
	Residual	48	0.07
	Grazing after 1 year of exposure
	Site	5	5.42	38.50	0.0002**
	Grid (site)	6	0.14	0.87	0.54NS
	Block (site, grid)	12	0.16	2.36	0.02*
	Residual	42	0.07
	Grazing after 3 years of exposure
	Site	5	0.91	9.38	0.01**
	Grid (site)	6	0.10	1.59	0.23NS
	Block (site, grid)	12	0.06	6.22	0.0001***
	Residual	48	0.01
	Total bioerosion after 1 year of exposure
	Site	5	30	23.46	0.0007***
	Grid (site)	6	1.27	0.68	0.67NS
	Block (site, grid)	12	1.86	172.1	0.0001***
	Residual	42	0.01
	Total bioerosion after 3 years of exposure
	Site	5	2.93	6.43	0.02*
	Grid (site)	6	0.46	0.54	0.77NS
	Block (site, grid)	12	0.83	2.96	0.004**
	Residual	48	0.28

df degree of freedom, MS mean square, F Fisher's index, P Greenhouse-Geisser corrected probability, NS = P>0.05, *P<0.05, **P<0.01, ***P<0.001 removed, that is, 1.

Table 2

 2 Amount of calcium carbonate removed by the boring micro-flora, grazers, macroborers, and all agents, from exposed surfaces of coral blocks (kg m À2 ) after 1 year and 3 years of exposure at six sites from the northern coast of Queensland to the Coral Sea

	Sites	Microbioerosion	Grazing		Macrobioerosion	Total bioerosion
		1 year	3 years	1 year	3 years	1 year	3 years	1 year	3 years
	Snapper Island 0.15±0.006 0.23±0.006 0.004±0.001 0.31±0.061	0.13±0.014 0.74±0.147 0.27±0.04 1.30±0.13
		(0.56±0.020) (0.94±0.023) (0.02±0.003) (1.70±0.318)	(0.53±0.078) (4.67±1.152) (1.06±0.15) (7.37±1.05)
	Low Isles	0.16±0.006 0.54±0.017 0.01±0.003 0.19±0.066	0.01±0.003 1.16±0.318 0.18±0.02 1.89±0.32
		(0.61±0.022) (2.22±0.074) (0)	(1.07±0.378)	(0.06±0.023) (6.40±1.721) (0.74±0.10) (9.72±1.69)
	Lizard Island 0.71±0.055 0.89±0.023 0.32±0.040 0.97±0.081	0.11±0.003 0.37±0.162 1.09±0.13 2.26±0.26
		(2.77±0.115) (3.54±0.100) (0.02±0.003) (5.41±0.482)	(0.57±0.217) (2.03±0.883) (4.72±0.47) (11±1.34)
	Harrier Reef	0.76±0.032 1.42±0.065 0.36±0.075 1.64±0.156	0.02±0.003 0.59±0.084 1.22±0.14 3.60±0.28
		(2.68±0.097) (5.34±0.266) (0.02±0.006) (8.58±0.987)	(0.11±0.017) (3.11±0.462) (4.70±0.35) (17.58±1.82)
	Ribbon Reef-3 0.38±0.014 0.96±0.040 0.77±0.222 5.39±1.085	0.04±0.009 0.12±0.029 1.23±0.29 6.40±0.99
		(1.49±0.057) (3.81±0.155) (0.05±0.014) (30.65 ±6.155) (0.23±0.046) (0.69±0.170) (5.80±1.12) (34.90±5.90)
		1.40±0.049 1.29±0.059 0.68±0.087 4.23±0.638	0.03±0.009 0.21±0.052 2.19±0.21 5.74±0.80
	Osprey Reef	(5.

26±0.186) 5.12±0.243) (0.05±0.006) (23.50±3.580) (0.18±0.061) (1.16±0.292) (8.23±0.94) (29.66±3.98)

The percentage of the bioeroded volume of block is presented in parenthesis. Means and standard errors are presented for each site (n=160 for microbioerosion, and n=12 for grazing, macrobioerosion and total bioerosion)

Table 3

 3 Proportional contribution (%) of the different groups of boring macro-organisms (sponges, worms, mollusc bivalves) to macrobioerosion at six sites from the northern coast of Queensland to the Coral Sea and after 1 year and 3 years of exposure

	Sites	Sponges		Worms		Bivalves
		1 year	3 years	1 year	3 years	1 year	3 years
	Snapper Island	22.24±11.64	22.09±10.02	34.52±9.90	33.20±9.32	43.56±10.64	44.71±9.15
	Low Isles	0	49.20±13.11	81.60±9.24	30.80±11.15	18.43±9.24	20.02±9.83
	Lizard Island	0	20.07±9.51	100	74.80±10.10	0	5.10±3.06
	Harrier Reef	0	2.28±2.28	94.50±5.48	87.68±7.11	5.48±5.49	10.04±7.04
	Ribbon Reef-3	0	29.40±0.08	100	28.70±9.09	0	41.85±9.06
	Osprey Reef	0	18±9.88	92.04±5.83	69.06±11.50	8±5.83	12.90±8.77
	Means and standard errors are presented for each site (n=12)

Table 4

 4 Two-way ANOVA of log(x + 0.01) transformed rates of microboring, grazing, macroboring, and total bioerosion of coral blocks after 1 year and 3 years of exposure at six sites from the northern coast of Queensland to the Coral Sea MS Mean Square, F Fisher's index, P Greenhouse-Geisser corrected probability, *P<0.01, **P<0.001

	Source of variation	df	MS	F	P
	Microboring rates
	Time of exposure	1	29.88	597	0.0001**
	Sites	5	33.33	666	0.0001**
	Time of exposure • site	5	3.28	65.62	0.0001**
	Residual	1948	0.05
	Grazing rates
	Time of exposure	1	33.83	226.97	0.0001**
	Sites	5	14.7	98.65	0.0001**
	Time of exposure • site	5	1.03	6.93	0.0001**
	Residual	127	0.15
	Macroboring rates
	Time of exposure	1	24.63	191.73	0.0001**
	Sites	5	1.04	8.08	0.0001**
	Time of exposure • site	5	1.15	8.95	0.0001**
	Residual	125	0.13
	Bioerosion rates
	Time of exposure	1	3.45	196.54	0.0001**
	Sites	5	0.64	36.34	0.0001**
	Time of exposure • site	5	0.06	3.65	0.004*
	Residual	125	0.02
	df degree of freedom,

Table 5

 5 Spearman's tests (R) of all paired sets bioerosion measures of coral blocks at six sites (pooled) from the northern coast of Queensland to the Coral Sea after 1 year and 3 years of exposure

	Sets of variable in pairs	1 year	3 years
	Microbioerosion -grazing	0.72 (P=0.0005)S	0.61 (P=0.004)S
	Microbioerosion -macrobioerosion	À 0.25 (P=0.23)	À0.12 (P=0.57)
	Macrobioerosion -grazing	À0.10 (P=0.45)	À0.41 (P=0.05)S
	Microbioerosion -bioaccretion	0.58 (P = 0.006)S	À0.03 (P=0.89)
	Grazing -bioaccretion	0.63 (P=0.002)S	À0.32 (P=0.13)
	Macrobioerosion -bioaccretion	À0.15 (P=0.10)	0.17 (P=0.08)
	Microbioerosion -coral skeleton density	À0.23 (P=0.26)	À0.02 (P=0.91)
	Grazing -coral skeleton density	À0.68 (P=0.004)S	À0.51 (P=0.014)S
	Macrobioerosion -coral skeleton density	0.10 (P=0.64)	0.33 (P=0.11)

Acknowledgements

This study was made possible by grants from the French-Australian Cooperation in Marine Sciences and the French Program PNRCO about coral reefs, and by GBRMPA for allowing us to collect coral. We would like to thank M. Peyrot-Clausade, P. Hutchings and A.J. Underwood for having made this study possible and for their help. We also thank the following companies and persons for their assistance in the field or providing logistical support: Undersea Explorer company and its crew at Port Douglas, L. Vail and A. Hoggett of Lizard Island Marine Station, K. Atwood of the Australian Museum, Sydney, C. Marschal and C. Bezac of the Marine Station d'Endoume, Marseille. We thank also C. Langdon and Columbia University of the city of New York, E. Hochberg, J. Le Campion and T. Le Campion for their technical support, help and reviews.