domain: spi sde sde.be

text:
Dimitri Justeau-Allaire
email: dimitri.justeau-allaire@cirad.fr

Ghislain Vieilledent

Nicolas Rinck

Philippe Vismara

Xavier Lorca

Philippe Birnbaum

Constrained optimization of landscape indices in conservation planning to support ecological restoration in New Caledonia

Keywords: Conservation planning, ecological restoration, connectivity, fragmentation, landscape indices, constraint programming, artificial intelligence, New Caledonia. 1

1. Curbing habitat loss, reducing fragmentation, and restoring connectivity are frequent concerns of conservation planning. In this respect, the incorporation of spatial constraints, fragmentation, and connectivity indices into optimization procedures is an important challenge for improving decision support.

2. Here we present a novel optimization approach developed to accurately represent a broad range of conservation planning questions with spatial constraints and landscape indices. Relying on constraint programming, a technique from artificial intelligence based on automatic reasoning, this approach provides both constraint satisfaction and optimality guarantees.

3. We applied this approach in a real case study to support managers of the "Côte Oubliée -'Woen Vùù -Pwa Pereeù" provincial park project, in the biodiversity hotspot of New Caledonia. Under budget, accessibility, and equitable allocation constraints, we identified restorable areas optimal for reducing forest fragmentation and improving interpatch structural connectivity, respectively measured with the effective mesh size and the integral index of connectivity.

4. Synthesis and applications. Our work contributes to more effective and policyrelevant conservation planning by providing a spatially-explicit and problem-focused optimization approach. By allowing an exact representation of spatial constraints and landscape indices, it can address new questions and ensure whether the solutions will be socio-economically feasible, through optimality and satisfiability guarantees. Our approach is generic and flexible, thus applicable to a wide range of conservation planning problems such as ecological restoration planning, reserve or corridor design.

Introduction

As the Earth has entered the Anthropocene, human impacts on the environment have led to the current global biodiversity crisis. Habitat loss and degradation due to land-use change are the leading causes of ecosystem collapse and biodiversity decline [START_REF] Haddad | Habitat fragmentation and its lasting impact on Earths ecosystems[END_REF].

Landscape configuration can also have profound impacts on ecological processes such as dispersal, gene flow, or fire resistance [START_REF] Taylor | Connectivity Is a Vital Element of Landscape Structure[END_REF][START_REF] Fahrig | Effects of Habitat Fragmentation on Biodiversity[END_REF]. These impacts are often assessed through habitat fragmentation metrics and inter-patch connectivity measures [START_REF] Uuemaa | Trends in the use of landscape spatial metrics as landscape indicators: A review[END_REF]. Fragmentation refers to the spatial patterns of habitat distribution [START_REF] Fahrig | Effects of Habitat Fragmentation on Biodiversity[END_REF] and inter-patch connectivity to the potential ability of species to migrate or disperse between habitat patches [START_REF] Taylor | Connectivity Is a Vital Element of Landscape Structure[END_REF].

Restoration and conservation planning can help to curb habitat loss and promote suitable landscape configurations, as well as helping to identify trade-offs between conservation targets and managers' objectives [START_REF] Rodrigues | Flexibility, efficiency, and accountability: Adapting reserve selection algorithms to more complex conservation problems[END_REF]Knight et al., 2008). Efficient decision support processes must rely on spatially-explicit, systematic, and reproducible approaches [START_REF] Pressey | Beyond opportunism: Key principles for systematic reserve selection[END_REF]. Over the last few decades, many such approaches have been devised, from geometric principles derived from biogeography theory [START_REF] Diamond | The island dilemma: Lessons of modern biogeographic studies for the design of natural reserves[END_REF] to the principle of complementarity in the representation of biodiversity features [START_REF] Vane-Wright | What to protect?-Systematics and the agony of choice[END_REF]. Systematic conservation planning (SCP) is now an active field of conservation biology. There is also a consensus on the mutual importance of spatial configuration and the representation of biodiversity features in the planning of conservation actions, to express managers' constraints as much as ecological requirements [START_REF] Margules | Systematic conservation planning[END_REF][START_REF] Williams | Spatial attributes and reserve design models: A review[END_REF].

Many optimization methods for SCP have been proposed, mostly relying on ad hoc heuristics, metaheuristics, or mixed-integer linear programs (MILP). Ad hoc heuristics are problem-specific local search algorithms either based on a forward (greedy) (e.g. Kirkpatrick, 2 1983;[START_REF] Nicholls | An upgraded reserve selection algorithm[END_REF] or backward (stingy) procedure (e.g. Zonation software, [START_REF] Moilanen | Zonation-Spatial conservation planning methods and software. version 4. user manual[END_REF]. In constructive heuristics (resp. destructive), solutions are obtained by iteratively adding (resp. removing) the planning unit which offers the highest gain (resp. loss) according to an objective function to maximize (resp. minimize). Metaheuristics are high-level and problem-independent stochastic search heuristics, such as simulated annealing (e.g. Marxan software, [START_REF] Ball | Marxan and Relatives: Software for Spatial Conservation Prioritization[END_REF] or tabu search (e.g. ConsNet software, [START_REF] Ciarleglio | ConsNet-A tabu search approach to the spatially coherent conservation area network design problem[END_REF]. The main advantage of heuristics is that they are often straightforward to understand and implement, but produce solutions of unknown quality relative to optimality. Finally, MILP is a constrained mathematical optimization approach where the objective function and the constraints are stated as linear equations, with some or all the variables being integers [START_REF] Billionnet | Mathematical optimization ideas for biodiversity conservation[END_REF][START_REF] Dilkina | Trade-offs and efficiencies in optimal budget-constrained multispecies corridor networks[END_REF]oppr R package, Hanson et al. 2019). Exact approaches such as MILP can require more time to generate solutions than heuristics, however, they offer guarantees relative to optimality and constraint satisfaction. Indeed, even though heuristics can reach constraint satisfaction for loosely constrained problems (e.g. species set covering problem, [START_REF] Revelle | Counterpart Models in Facility Location Science and Reserve Selection Science[END_REF], they can fail to provide this guarantee for highly constrained problems (e.g. [START_REF] Billionnet | Mathematical optimization ideas for biodiversity conservation[END_REF]. Constraint satisfaction problems on a finite domain are indeed in general NP-Complete [START_REF] Dechter | Constraint Processing[END_REF]. Although less widely used, dynamic programming approaches (e.g. [START_REF] Meir | Does conservation planning matter in a dynamic and uncertain world[END_REF] and Markov decision processes (e.g. [START_REF] Schapaugh | A simple method for dealing with large state spaces[END_REF] have also brought substantial advances in SCP but are limited to smaller problem sizes than the approaches described above.

Recent work has introduced several perspectives towards the integration of landscape spatial configuration in SCP optimization procedures. For instance, Marxan software uses a boundary length penalty in its objective function to influence the spatial configuration of the solutions. Additionally, Marxan Connect [START_REF] Daigle | Operationalizing ecological connectivity in spatial conservation planning with Marxan Connect[END_REF] provides many options to include structural or functional connectivity data in Marxan's input. Similarly, Zonation provides eight different methods to integrate connectivity in its prioritization process [START_REF] Moilanen | Zonation-Spatial conservation planning methods and software. version 4. user manual[END_REF]. In MILP approaches, several options are available to ensure spatial requirements, such as strictly guaranteeing the connectivity and compactness of delineated areas, or designing buffer zones [START_REF] Billionnet | Mathematical optimization ideas for biodiversity conservation[END_REF][START_REF] Wang | Optimal design of compact and connected nature reserves for multiple species: Reserve Networks for Multiple Species[END_REF]. Other approaches such as LQGraph [START_REF] Fuller | LQGraph: A software package for optimizing connectivity in conservation planning[END_REF] or Linkage Mapper (McRae et al., 2012) specifically aim to identify optimal corridors between core areas or existing protected areas. On the other hand, landscape ecologists have devised many indices to evaluate the level of fragmentation [START_REF] Mcgarigal | Landscape Pattern Metrics[END_REF] and connectivity [START_REF] Pascual-Hortal | Comparison and development of new graph-based landscape connectivity indices: Towards the priorization of habitat patches and corridors for conservation[END_REF][START_REF] Saura | A new habitat availability index to integrate connectivity in landscape conservation planning: Comparison with existing indices and application to a case study[END_REF]) within a landscape. Except [START_REF] Xue | Dynamic Optimization of Landscape Connectivity Embedding Spatial-Capture-Recapture Information[END_REF] and to the best of our knowledge, such connectivity and fragmentation indices were mainly used in scenario analysis contexts (e.g. [START_REF] Bodin | Ranking individual habitat patches as connectivity providers: Integrating network analysis and patch removal experiments[END_REF]. Integrating such indices into constrained optimization approaches is difficult due to their non-linearity and the curse of dimensionality. Nonetheless, it would improve the value of decision support by taking into account more powerful and ecologically relevant metrics in SCP.

Recently, we introduced a novel and generic SCP framework based on constraint programming [START_REF] Justeau-Allaire | Systematic Conservation Planning for Sustainable Land-use Policies: A Constrained Partitioning Approach to Reserve Selection and Design[END_REF], an exact constrained optimization technique based on automated reasoning. In this article, we have extended this framework with landscape indices and applied it in a current reforestation project in the "Côte Oubliée -'Woen Vùù -Pwa Pereeù" provincial park in the New Caledonia biodiversity hotspot. We worked in close collaboration with New Caledonian environmental managers to provide spatially-explicit decision support focused on reducing forest fragmentation and isolation, which are known to have adverse effects on tree communities in this region [START_REF] Ibanez | How does forest fragmentation affect tree communities? A critical case study in the biodiversity hotspot of New Caledonia[END_REF]. Under budget, land accessibility and equitable allocation constraints, we computed optimal solutions for two landscape indices: the effective mesh size (MESH; [START_REF] Jaeger | Landscape division, splitting index, and effective mesh size: New measures of landscape fragmentation[END_REF] and the integral index of connectivity (IIC; [START_REF] Pascual-Hortal | Comparison and development of new graph-based landscape connectivity indices: Towards the priorization of habitat patches and corridors for conservation[END_REF] applied to structural connectivity. MESH is a measure of landscape fragmentation which is based on the probability that two randomly chosen points are located in the same patch. Maximizing it in the context of reforestation favours fewer and larger forest patches. On the other hand, IIC is a graphbased inter-patch connectivity index based on a binary connection model. Its maximization in the context of reforestation favours restoring structural connectivity between large patches.

Our results demonstrated the flexibility of this approach and how its expressiveness (i.e. the breadth and variety of problems that it can represent and solve) facilitates the representation of the inherent diversity of real-world conservation problems, offering new perspectives for designing decision support tools in ecological restoration and more broadly in conservation planning (e.g. for reserve or corridor design).

Material and Methods

Case study: reforestation planning in the "Côte Oubliée -'Woen Vùù -Pwa Pereeù" provincial park, New Caledonia

New Caledonia is a tropical archipelago located in the South Pacific (see Figure 1.a). As the smallest biodiversity hotspot in the world, it hosts megadiverse marine and terrestrial ecosystems. Notably, New Caledonian flora is distinguished by one of the highest rates of endemism in the world -approximately 76% [START_REF] Myers | Biodiversity hotspots for conservation priorities[END_REF][START_REF] Morat | The taxonomic reference base Florical and characteristics of the native vascular flora of New Caledonia[END_REF], a high beta-diversity [START_REF] Ibanez | Structural and floristic diversity of mixed tropical rain forest in New Caledonia: New data from the New Caledonian Plant Inventory and Permanent Plot Network (NC-PIPPN)[END_REF], and the presence of relict taxa [START_REF] Grandcolas | New Caledonia: A very old Darwinian island?[END_REF][START_REF] Pillon | Time and tempo of diversification in the flora of New Caledonia[END_REF]. However, New Caledonian forests are under threat and the remaining forest is highly fragmented, as the result of anthropic activities such as bushfires, logging, urbanization, and nickel mining. New Caledonia is an overseas French collectivity which was first populated by the Kanak people. In this territory, the French Common Civil Code coexists with the Customary Civil Code, and institutions such as the Customary Senate provide a political framework to the Kanak people for promoting their culture, traditions, and environment. In this respect, customary authorities of the "Côte Oubliée 'Woen Vùù -Pwa Pereeù", a large area in the Southeast of the main island of New Caledonia, "Grande Terre" (see Fig- In this study, we focus on a reforestation project that must be planned by the SDDT.

One of its objectives is expected to be the zoning of two suitable areas for reforestation, one in each of the two customary districts of the Côte Oubliée, respectively Borendy and Unia, to involve both communities in the project. Since the Côte Oubliée is a low urbanized and mountainous area, most locations are difficult to access. Accordingly, to be accessible reforestation areas must be compact (within an enclosing circle whose maximum diameter is 1500 m) and close to existing tracks (at a maximal distance of 1000 m). In this study, we considered a realistic cost corresponding to 200 ha to reforest, equitably divided between Borendy and Unia (100 ha ± 10% in each district). Under these constraints, the aim was to optimize the potential contribution of the reforested areas to reduce forest fragmentation and improve forest structural connectivity in the provincial park.

Data

The Côte Oubliée is a poorly studied area, and we still have little knowledge about the dispersal of New Caledonian animal and plant forest species (see the last biological knowledge synthesis on the Côte Oubliée: [START_REF] Guillemot | Biodiversité et environnement dans la région de la Côte Oubliée « Woen Vùù » : état des connaissances et identification des intérêts écologiques[END_REF]. Although species occurrences are useful to guide planning, the region is insufficiently sampled to ensure an unbiased selection.

Species distribution models (SDMs) of tree species could also help to identify adequate reforestation areas. However, it would be necessary to have more occurrences in this region to obtain reliable predictions, due to the heterogeneity of tree community compositions which is still not well understood [START_REF] Pouteau | Disentangling the processes driving tree community assembly in a tropical biodiversity hotspot (New Caledonia)[END_REF]. In this respect, we adopted a forest-cover approach using remote sensing data (the dominant forest type in this area is dense rainforest). In this respect, we relied on a 2019 30 m binary forest-cover raster (cf. Figure 2.a), based on the historical analysis of temporal series from Landsat data (1982 to 2018) [START_REF] Vancutsem | monitoring of tropical moist forests dynamics[END_REF]. We focused on the extent of the Côte Oubliée Provincial Park (55.68 km height and 81.6 km width) and resampled the forest-cover raster to a resolution of 480 m (16×16 30 m cells) as a compromise between conservation planning and computational solving (480 m × 480 m ≈ 23 ha). We obtained a 116×170 raster map where each 480 m cell is characterized by a forest-cover proportion, according to the number of covered 30 m forest pixels. A 480 m cell was considered as degraded if its forest-cover proportion was smaller than 70% [START_REF] Fahrig | Rethinking patch size and isolation effects: The habitat amount hypothesis[END_REF][START_REF] Vieilledent | Combining global tree cover loss data with historical national forest cover maps to look at six decades of deforestation and forest fragmentation in Madagascar[END_REF]. As reforestation must occur in the provincial park, we retained the cells within the boundaries of the provincial park to which we included parts of forest patches extending outside the park to avoid the boundary problem [START_REF] Moser | Modification of the effective mesh size for measuring landscape fragmentation to solve the boundary problem[END_REF]. The resulting raster map contained 3629 forest cells and 2715 nonforest cells, as illustrated in Figure 2.b. Consequently, we quantified the area to be reforested in each 480 m cell as the area needed to reach a forest-cover proportion of 70% (cf. Figure

Mathematical formulation

Base problem: variables and managers' constraints

To each cell of the input raster grid we associate a planning unit (PU) that can be selected for reforestation, these are the decision variables of our base model. Let S be the set of PUs in the study area, we define the following subsets of S according to the data: U, the set of accessible PUs located in the Unia district; B, the set of accessible PUs located in the Borendy district; F ≥70% , the set of PUs with forest-cover proportion ≥ 70%; F <70% , the set of PUs with forest-cover proportion < 70%.

(1) Let R u ⊆ F <70% and R b ⊆ F <70% be the sets of PUs to reforest respectively in Unia and Borendy, that is sets of PUs available for restoration. The sets R u , R b , F ≥70% , and F <70% \ (R u ∪ R b ) must form a partition of S, and R u ∪ R b ∪ F ≥70% corresponds to the potential forest-cover resulting from reforestation. To each of these sets is associated a grid graph.

For a given set, each PU in the set is a node and two nodes are connected if and only if the corresponding PUs are adjacent according to the four-connected neighbourhood definition in the regular square grid. We now introduce the following constraints:

Constraint 1 (CONNECTED). Let R ⊆ S be a region, CONNECTED(R) holds if and only if the region R is connected according to its associated graph.

Constraint 2 (RESTORABLE). Let R ⊆ S be a region, a an integer variable, and p ∈ [0, 1]. RESTORABLE(R, a, p) holds if and only if each PU in R can be restored to a forest-cover proportion of p by reforesting at least a ha. In any solution satisfying this constraint, the value of a thus corresponds to the minimum area to restore to reach a forest-cover proportion of p. Formally, let v p x be the minimum area to reforest to restore the PU x to p, then:

RESTORABLE(R, a, p) ⇔ a = x∈R v p x .
Constraint 3 (RADIUS). Let R ⊆ S be a region and ρ a real variable. RADIUS(R, ρ) holds if and only if the radius of the smallest enclosing circle containing R equals ρ (in meters).

Given two regions R u ⊆ S and R b ⊆ S, the budget, accessibility, and equitable allocation requirements are satisfied if and only if all the following constraints are satisfied:

R u ⊆ U ∩ F <70% ∧ R b ⊆ B ∩ F <70% ; (2) CONNECTED(R u ) ∧ CONNECTED(R b ); (3)
a u ∈ 0.5 • A max ± 10% ∧ RESTORABLE(R u , a u , 70%); (4) a b ∈ 0.5 • A max ± 10% ∧ RESTORABLE(R b , a b , 70%); (5)
a u + a b ≤ A max ; (6)
a max ∈ [0, +∞] ∧ RESTORABLE(R u ∪ R b , a max , 100%); (7)
a max ≥ A max ; (8)
ρ u ∈ [0, P max ] ∧ RADIUS(R u , ρ u ); (9)
ρ b ∈ [0, P max ] ∧ RADIUS(R b , ρ b ). (10)
With A max the total area to reforest (200 ha) and P max the maximum radius of the smallest circle enclosing reforested areas (1500 m). Constraint (2) ensures that the reforested regions are located in accessible and degraded areas respectively in Unia and Borendy. Constraint

(3) ensures that each reforested region is connected. Constraints (4) and ( 5) ensure that the budget is equitably allocated between Unia and Borendy, with a u and a b two integer variables representing the minimum areas to restore respectively in Unia and Borendy. Constraint (6)

ensures that the minimum area to restore in Unia and Borendy together does not exceed A max .

Constraint (7) ensures that the integer variable a max equals the total area that can be reforested in Unia and Borendy together. Constraint (8) ensures that the totality of the budget can be invested in the selected areas. Finally, Constraints ( 9) and ( 10) ensure that each selected region is compact.

Constrained optimization of fragmentation indices

From the base problem described in the previous section, we defined two optimization problems, respectively associated with the maximization of MESH and IIC. We computed the value of each index in the current landscape, then we found every optimal solution and retained the index optimal value, the improvement brought by the optimal value compared to the current one, the number of optimal solutions, and the solving times for reaching the optimal value and then enumerate all optimal solutions. In the following, we denote the set of patches of a region R by P (R). These patches are directly derived from the raster representation of the landscape by extracting the connected components of the grid graph associated with the raster grid, as illustrated in Figure 3. when the investigated region is divided into equally sized patches such that the probability that two randomly chosen points are in the same patch remains the same [START_REF] Jaeger | Landscape division, splitting index, and effective mesh size: New measures of landscape fragmentation[END_REF]. For a region R, it is given by:

MESH(R) = 1 A L k∈P (R) A 2 k . (11)
With A k the area of patch k, and A L the total landscape area. The constrained optimization of MESH associated with our case study is given by: maximize

(Ru,R b )⊆S 2 MESH(R u ∪ R b ∪ F ≥70% ); subject to: (2) ∧ (3) ∧ (4) ∧ (5) ∧ (6) ∧ (7) ∧ (8) ∧ (9) ∧ (10). ( 12
)
Maximization of IIC. IIC is a graph-based inter-patch connectivity index introduced by Pascual-Hortal and [START_REF] Pascual-Hortal | Comparison and development of new graph-based landscape connectivity indices: Towards the priorization of habitat patches and corridors for conservation[END_REF]. It focuses on groups of patches (components) that are structurally or functionally connected and evaluates their sizes distribution along with the topological complexity of these components (i.e. the potential ability to move from one patch to another within a component). It ranges from 0 (no habitat in the landscape) to 1 (all the landscape is occupied by habitat). For a region R, it is given by:

IIC(R) = 1 A 2 L k∈P (R) l∈P (R) A k • A l 1 + d kl . ( 13
)
Where A k is the area of the patch k, A L the total landscape area and d kl the topological distance (i.e. shortest path length) between k and l in the landscape graph. Due to the lack of knowledge on species dispersal in the Côte Oubliée area, we used IIC as a structural connectivity index. To determine whether two forest patches are structurally connected, which is required to calculate IIC (see [START_REF] Pascual-Hortal | Comparison and development of new graph-based landscape connectivity indices: Towards the priorization of habitat patches and corridors for conservation[END_REF], we used the smallest possible edge-to-edge distance threshold of at most one non-forest cell. This distance threshold can be represented by the two-wide-four-connected neighbourhood [START_REF] Justeau-Allaire | Systematic Conservation Planning for Sustainable Land-use Policies: A Constrained Partitioning Approach to Reserve Selection and Design[END_REF].

Two examples illustrating the construction of the landscape graph from a raster representation are provided in Figure 4 and Figure 5. The constrained optimization of IIC associated with our case study is given by: maximize

(Ru,R b )⊆S 2 IIC(R u ∪ R b ∪ F ≥70% );

Solving method: The constraint-based systematic conservation planning framework

To solve this problem, we used the constraint-based systematic conservation planning (SCP) framework briefly presented in the introduction [START_REF] Justeau-Allaire | Systematic Conservation Planning for Sustainable Land-use Policies: A Constrained Partitioning Approach to Reserve Selection and Design[END_REF] Choco (Prud'homme et al., 2017), and its source code is available on GitHub1 . Most of the constraints needed by the case study were already available in the framework. We, however, extended it with the RADIUS constraint, implemented with a linear-time filtering algorithm based on the best-known algorithm for the smallest enclosing circle problem [START_REF] Welzl | Smallest enclosing disks (balls and ellipsoids)[END_REF], the MESH constraint, and the IIC constraint, implemented with a two-stage algorithm which first constructs the landscape graph from the raster representation and then computes all-pairs shortest paths by performing a breadth-first search from each node of the landscape graph.

We ran all optimization problems described in the previous section on a Linux server (Intel Xeon E5-2620 CPU 2.40GHz × 12, 64GB RAM). The case study source code is available on GitHub2 and we packaged an executable command-line jar to reproduce the single-region version of the problem (installation and usage instruction are available on the GitHub page).

Box 1: Constraint programming in a nutshell

Constraint programming (CP) is a declarative paradigm for modelling and solving constraint satisfaction and constrained optimization problems. In this context, declarative means that the modelling of a problem is decoupled from its solving process, which allows the primary focus to be on what must be solved rather than describing how to solve it. CP is a subfield of artificial intelligence which relies on automated reasoning, constraint propagation and search heuristics. As an exact approach, CP can provide constraint satisfaction and optimality guarantees, as well as enumerating every solution of a problem. In CP, the modeller represents a problem by declaring variables whose possible values belong to a specified finite domain, by stating constraints (mainly logical relations between variables), and eventually by defining an objective function to minimize or maximize. A solution to the problem is an instantiation of every variable such that every constraint is satisfied. As opposed to mixed-integer linear programming, constraints can be non-linear and variables of several types (e.g. integer, real, set, graph). A CP solver then handles the solving process relying on an automated reasoning method alternating a constraint propagation algorithm (deduction process on values within domains that does not lead to any solution) and a backtracking search algorithm.

In a nutshell, more than satisfiability, each constraint embeds a filtering algorithm able to detect inconsistent values in variables domains. At each step of the backtracking search algorithm, the solver calls the constraint propagation algorithm that repeatedly applies these algorithms until a fixpoint is reached. When it is proven that a part of the search tree contains no solution, the solver rolls back to a previous state and explores another part of the search tree: this is backtracking. Note that most CP solvers are also able to handle Pareto multi-objective optimization. Interested readers can go further by reading the Handbook of Constraint Programming [START_REF] Rossi | Handbook of Constraint Programming[END_REF].

Results

We summarized the results of the constrained optimization of MESH and IIC in Table 1 and mapped optimal solutions in Figures 6 and7. First, the solver found the optimal value for MESH in about 30 minutes and quickly enumerated all optimal solutions. Conversely, enumerate all optimal solutions. Moreover, although several optimal solutions were found, for a given index they were all located in the same zone and reconnected the same patches. 1: Results characteristics: for each index, its value in the current landscape, its optimal value, the improvement after optimization, the number of optimal solutions and solving times. MESH: effective mesh size, IIC: integral index of connectivity. MESH did not assume any possible link between physically disconnected forest patches, thus highlighted areas favouring the physical connection of large patches together. In Borendy, it connected medium-sized patches into a large patch. In Unia, it merged two small patches with a large patch. On the other hand, IIC assumed possible links between physically disconnected but close patches, thus did not consider the medium-sized patch in Borendy as disconnected and favoured merging several small patches to reduce the topological complexity of the forest component. In Unia, it reconnected the southernmost forest component with the main forest component of the provincial park.

These results contributed to decision support by providing two scenarios that are optimal according to their respective index. In this regard, they provided a spatially-explicit and problem-focused baseline for discussions between stakeholders of the project, as well as specific areas presenting particular landscape-scale properties, thus potential candidates to prospection for local-scale assessments. Such results, along with the proposed methods, were well received and considered useful by the stakeholders of the "Côte Oubliée -'Woen Vùù -Pwa Pereeù". Most importantly, they were enthusiastic to see that the solver guarantees that every constraint will be satisfied by the solutions and that it will inform the user when no solution exists that satisfies all the constraints.

On the use of landscape indices in systematic conservation planning

These results illustrated the potential for integrating more complex and ecologically meaningful landscape indices into conservation planning to reduce fragmentation and improve connectivity. Fragmentation is known to have adverse effects on forest tree communities in New Caledonia [START_REF] Ibanez | How does forest fragmentation affect tree communities? A critical case study in the biodiversity hotspot of New Caledonia[END_REF] and there is strong evidence on the importance of structural connectivity for facilitating species dispersal, persistence, and gene flow between communities [START_REF] Taylor | Connectivity Is a Vital Element of Landscape Structure[END_REF]. Optimizing such indices in systematic conservation planning (SCP) is thus useful to inform on the potential benefits of conservation actions on landscape fragmentation and connectivity. Being able to take into account the benefits of conservation projects over several indices is also an important step for providing holistic management recommendations. The main advantage of constrained optimization over prioritization and scenario analysis approaches is that the solutions are produced considering every possible combination of planning units satisfying user-defined constraints. This characteristic assures decisions makers that no feasible or better (according to an optimization objective) opportunity has been missed.

Advantages of the constraint-based approach for systematic conservation planning

Our constraint-based SCP framework demonstrated its ability to address and solve real-world SCP problems with satisfiability and optimality guarantees. By emphasizing a spatiallyexplicit and problem-focused approach, it presents several strengths. First, its expressiveness (i.e. the breadth and variety of problems that it can represent and solve) allows an accurate representation of the various constraints that stakeholders need to take into account for implementing conservation actions. Combined with a satisfiability guarantee, we can ensure that the proposed solutions will satisfy every managers' constraint and thus be socio-economically feasible, which is a requirement for policy-relevant conservation science [START_REF] Game | Policy Relevant Conservation Science[END_REF][START_REF] Williams | The past and future role of conservation science in saving biodiversity[END_REF]. Moreover, the flexibility of our approach makes it relevant to a wide range of conservation planning questions, as constraints and objectives can be seamlessly modified, added, or removed from the model without affecting the solving process. For instance, it can help to design optimal corridors, protected areas, fire-protected zones, or even provide insight for maintaining and restoring connectivity for migratory species. Note that although our use case was focused on forest cover, our constraint-based approach is also suited to include several biodiversity features and can handle multiple management zones.

We believe that, besides being a useful methodological tool, such an approach can contribute to narrowing the "research-implementation gap" (Knight et al., 2008). With a modelling tool expressive enough to represent accurately conservation scientists' aims along with managers' constraints, it becomes possible to design conservation actions that are realistic for managers, as well as offering an integrative and evidence-based tool for scientists.

Current limitations and perspectives for systematic conservation planning

A lot of effort is still required to invest in development to provide a wide-audience software package, as our framework in its current state still requires knowledge of constraint programming (CP) to be used correctly. Moreover, as CP is an exact optimization approach, computation of optimal solutions can take time for large problems, and it is difficult to predict this time as it depends on the problem's structure (e.g. problem size, number and nature of the constraints). In its current implementation, we can, however, assert that exercises involving 50000 planning units (which is Marxan's limit in most cases; [START_REF] Ardron | Marxan good practices handbook[END_REF] would likely exceed the memory capacity of a standard desktop computer or not complete within a feasible amount of time. Another limitation directly relates to the regular square grid representation, which involves a trade-off between the spatial resolution and the sophistication of the model. In our case study, this spatial resolution limited the distance threshold needed to compute IIC to at least 480 m, which can be too large for some species. A promising perspective to overcome this limitation would consist of using an irregular grid representation to locally increase the spatial resolution without increasing the number of planning units.

Nevertheless, we have shown that there is good potential for formulating and solving SCP problems using CP. There is a continued debate on the importance of optimality in SCP methods, which mainly contrasts local search approaches with MILP [START_REF] Underhill | Optimal and suboptimal reserve selection algorithms[END_REF][START_REF] Pressey | Optimality in reserve selection algorithms: When does it matter and how much?[END_REF][START_REF] Rodrigues | Optimisation in reserve selection procedures-why not?[END_REF][START_REF] Hanson | Optimality in prioritizing conservation projects[END_REF]. However, optimality should not be the only consideration. We even argue that expressiveness is a prerequisite to optimality [START_REF] Rodrigues | Flexibility, efficiency, and accountability: Adapting reserve selection algorithms to more complex conservation problems[END_REF][START_REF] Moilanen | Two paths to a suboptimal solution -once more about optimality in reserve selection[END_REF]. To conclude, recent years have seen substantial advances in artificial intelligence. We believe that, as illustrated by this study, such advances are providing new opportunities for formulating and solving conservation planning problems.

  ure 1.b), established a moratorium on nickel mining activity between 2014 and 2016. They called for cessation on any road, mining or infrastructure project, in response to the erosion of many areas, due to bushfires and mining activity. This moratorium was renewed for ten years (from 2018 to 2028) and led to the creation in April 2019 of the "Côte Oubliée 'Woen Vùù -Pwa Pereeù" Provincial Park by the South Province of New Caledonia. With 93000 ha of terrestrial and 27000 ha of marine protected area, the provincial park blocked 102 mining concessions, includes three existing natural reserves and is adjacent to four existing natural reserves (see Figure 1.c). It now remains for the managers of the South Province's Sustainable Development Department for the Territories (SDDT) to establish the management plan of the park, with a strong emphasis on reducing forest fragmentation.

Figure 1 :

 1 Figure 1: (a) Location of New Caledonia. (b) Location of the "Côte Oubliée" area. (c) Map of the "Côte Oubliée -Woen Vùù -Pwa Pereeù" provincial park, with included and adjacent existing natural reserves.

  2.d). Finally, we identified accessible areas for reforestation as a 1000 m buffer around tracks using the tracks vector data provided by the SDDT, classified according to the two customary districts covered by the provincial park, Borendy and Unia (see Figure2.c).

Figure 2 :

 2 Figure 2: Input data maps. (a) 2019 30 m binary forest map produced from Landsat historical data analysis. (b) Upscaled 480 m binary forest map. A 480 m cell was considered as forest if its forest-cover proportion at 30 m was at least 70%. (c) 480 m accessible areas (1000 m buffer around tracks) map, classified by customary districts. (d) 480 m restorable area map, that is the non-forest area for each cell.

Figure 3 :

 3 Figure 3: Raster representation of the landscape (left) and the associated grid graph (right).In this example, there are three connected components, thus three patches.

Figure 4 :

 4 Figure 4: Illustration of the two-wide-four-connected neighbourhood distance threshold used to construct the landscape graph needed to compute IIC. The left patch intersects with the two-wide-four-connected neighbourhood of the black pixel located in the right patch. The patches are thus considered structurally connected.

Figure 5 :

 5 Figure 5: Construction of the forest landscape graph from a raster-based representation, using the two-wide-four-connected neighbourhood distance threshold.

Figure 6 :

 6 Figure 6: Mapping of a solution maximizing the effective mesh size (MESH).

Figure 7 :

 7 Figure 7: Mapping of a solution maximizing the integral index of connectivity (IIC).

  . As this framework relies on constraint programming (CP), we have provided a quick description of this technique's fundamental principles in Box 1. In this constraint-based SCP framework, any problem states as follows: given a tessellated geographical space S, find a partitioning of S

into n regions {R 0 , ..., R n-1 } satisfying a set of constraints C, available from a constraint catalogue. The CP model associated with this formulation relies on three representations of the space: integer variables (one for each PU), set variables (one for each region), and graph variables (one for each region), and each user constraint applies to the most relevant space representation. This formulation allows the modelling of regions' expected properties through constraints. This framework was implemented upon the java open-source CP solver

https://github.com/dimitri-justeau/choco-reserve

https://github.com/dimitri-justeau/cote-oubliee-choco-reserve-code

Acknowledgements

This work was funded by the CIRAD (French Agricultural Research Centre for International Development) and the IAC (New Caledonian Instute of Agronomy). We are grateful to the South Province, AMAP, LIRMM and IMT Mines Albi for providing a stimulating work environment. We are also grateful to everyone who contributed to this work indirectly, through technical help, discussions and exchanges, among them Emmanuel Coutures, Thomas Ibanez, Robin Pouteau, the Choco team, the AMAP team in New Caledonia, the RELIQUES project members, and Dimitri Justeau-Allaire's PhD committee members.

Finally, we are grateful to three anonymous reviewers who helped to greatly improve the manuscript.

Data availability statement

Data available via the Dryad Digital Repository https://doi.org/10.5061/dryad.p8cz8w9nw (Justeau-Allaire et al., 2020b). Source code available via the Zenodo Digital Repository https://doi.org/10.5281/zenodo.4202715 (Justeau-Allaire et al., 2020a) or via the GitHub Digital Repository https://github.com/dimitri-justeau/cote-oubliee-choco-reserve-code.

Authors' contributions

G.V., N.R., and D.J. collected and prepared the data. P.B., N.R., G.V., and D.J. conceived the ideas and the methodology. X.L., P.V., and D.J. modelled the problem, designed the algorithms, and produced the source code. P.B., G.V., X.L., and D.J. analysed the results. D.J. led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.


Raluca Nastase

Jean-Michel Tatibouët

Elodie Fourré
email: elodie.fourre@univ-poitiers.fr

Depolymerization of inulin in the highly reactive gas phase of a non thermal plasma at atmospheric pressure

Keywords: inulin, dielectric barrier discharge (DBD), FT-IR, depolymerization, fructose

The interest of fructose production arises from its sweetening character used in application such as food and pharmaceutic industries. Fructose formation is achieved by the short treatment of inulin by non thermal plasma at atmospheric pressure, under air, using a dielectric barrier discharge (DBD) configuration. Promising results were observed as a total conversion of inulin was achieved within 10 mins of treatment (18 kV, 2 kHz), without the addition of solvent, nor catalyst and at room temperature. Additionally to fructose (32 %), fructooligosaccharides of higher degrees of polymerization were produced. The mechanism underlying the depolymerization process appears to start with the oxidation of inulin followed by the cleavage of the -glycosidic bond and eventually ring opening of the monomer.

Introduction

Within the variety of existing biopolymers, inulin represents a renewable and abundant raw material, valuable for different application domains such as food industry, biofuel production and pharmaceutics. [1,2] Inulin acetylation leads to carbohydrate esters used in the textile, plastic industries and in pharmaceutics as drug carriers. [3][4][5] Inulin is a polymeric chain of  (1-

2) fructosyl fructose units ended by a glucose monomer with a polymerization degree (DP) up to 60. It can be extracted from the roots or rhizomes of chicory, dahlia, Jerusalem artichoke and yacon. Inulin is particularly used for the production of fructose and fructose syrup [ [1], 2, 6- [8]] which is a very valuable substitute to sucrose due to its high sweetening property. [[8]]

Currently, the main fructose production process relies on starch enzymatic hydrolysis which requires the use of amylase, amyloglucosidase and glucose isomerase to form glucose, fructose (45%) and oligosaccharides. The procedure is rather complex and costly, especially the fructose extraction step from the resulting fructose syrup. An alternative procedure which involves the direct enzymatic hydrolysis of inulin, via the action of inulinase, [[9], [11]] is an efficient way to produce fructose (95% yield). We have recently reported that the treatment of cellulose by dielectric barrier discharge (DBD) plasma improved its reactivity towards hydrolysis. [12] Non thermal atmospheric plasma (NTAP) is now recognized as an unconventional media proposing an alternative solution for gas, chemicals or matter activation. NTAP can be found in a diversity of industrial applications such as surface functionalization, etching or thin film deposition, biomedical applications, in vivo treatment, volatile organic compound elimination and more recently biopolymer deconstruction. [13][14][15] One of the reasons of its popularity comes from its ability to generate valuable compounds with low environmental impact while being flexible and energy efficient. NTAP can be generated from diverse electrical sources and adopt various forms depending on the reactor geometry and electrical signal used (DC, AC or pulsed voltage). They are categorized in sections such as corona discharges, dielectric barrier discharges (DBD), gliding arc discharges, plasma needle, plasma jets and micro hollow cathode discharges. Within this variety of non thermal plasma discharges, DBD plasmas have the advantages to be easily generated in various reactor geometries without the risk of electric arc formation since at least one electrode is isolated by a dielectric material. The high voltage applied between electrodes generates an intense electric field which leads to the formation of highly energetic electrons able to induce excited species in the gas phase from non-elastic collisions between electrons and molecules of the gas phase. The energy of electrons is then directly transferred to gas phase species without heating of the rest of the gas phase. These excited species can react with other molecules of the gas phase and/or with a material to induce reactions only feasible at high temperature while the main temperature remains low.

Following our previous work on cellulose deconstruction [12,16] we have studied the use of non-thermal plasma at atmospheric pressure to transform inulin biopolymer into fructose, glucose and fructo-oligosaccharides with low degrees of polymerization (DP).

Experimental Section

DBD plasma reactor and DBD plasma reactor and pulsed high voltage generator

The DBD plasma reactor is represented schematically in Figure 1. A dielectric barrier discharge plasma was generated between two copper electrodes separated from each other by two dielectrics. One electrode was a copper film of size 50 mm x 50 mm (Advanced Tape) fixed on a quartz dielectric plate (2 mm thick). The other electrode was a copper grid (50 mm

x 50 mm x 1 mm) covered by a thin glass plate (1 mm thick) used to avoid the direct contact of the grid with the polymer. The gap between the two dielectrics was 1mm. The reactor case was airtight, allowing the control of the gas flow and its chemical composition. (

) 1
Figure 2: Input power as a function of applied voltage at constant frequency of 2 kHz and under air flow at 50 mL min -1 .

Material and conditions

The material tested consisted of inulin (Figure 3) from chicory (procured from Sigma-Aldrich). The experiments were carried out using 50 mg of inulin powder placed on the quartz dielectric plate in the center of the plasma reactor. The system was kept at atmospheric pressure under dry air flow (50 mL min -1 ) at room temperature (without heating of the reactor). In order to determine the optimal parameters for inulin conversion and fructose yields, the electrical parameters (frequency, 1-2.5 kHz and voltage, 16-21 kV) and the treatment time (1-32 mins) were modified. Gas chemical composition was also studied in order to identify the species responsible for the inulin depolymerization and the underlying pathways of the reaction. The effects of these parameters were evaluated in terms of inulin conversion, products formation (especially fructose) and their relative amount according to the surface area of the size exclusion chromatography (SEC) peaks.

Characterization

Following the plasma treatment, the samples were dissolved in water and further analyzed by SEC, using a HPLC Shimadzu LC-20AT pump, a Sugar KS-802 column (8 mm ID * 300 mm Length) and a Shimadzu RID-10A detector, using ultra-pure water as mobile phase (1 mL min -1 ). All the samples were prepared following the same procedure prior to their analysis consisting in dissolving 0.8 mg of inulin in 1 ml of ultra-pure water. The yields of fructose were calculated from the calibration curve of fructose and fructose peak areas after plasma.

The other results are indicated in terms of area distribution (AD in %) calculated as it follows Routine Infrared spectra were collected for the solid samples before and after plasma treatment on a Perkin Elmer FT-IR (Spectrum One) operating at wavenumber in the range 4000-650 cm -1 . The spectra after normalization allowed us to monitor possible functionalization and/or stabilization of species on the surface of the sample.

Results and Discussion

Optimization of process parameters

The effects of the input voltage, frequency, treatment time, temperature in the reactor and gas chemical nature of the plasma were studied.

Regarding the voltage influence (Figure 4) and for a treatment time of 5 min, a minimum voltage (17 kV) was required to initiate the conversion of inulin. As the voltage increased, inulin was converted into fructose, DP2 and DP3 compounds, with a small amount of glucose.

Fructose content reached a maximum (≈15 %) between 18 and 19 kV, while glucose and compounds of DP≥2 increased with increasing voltage. Additionally, the powder was colourless up to 19 kV and turned light yellow over 20 kV, suggesting a partial degradation of fructose and glucose. At a fixed voltage of 18 kV, the frequency rise led to similar results as those obtained by increasing voltage: inulin was deconstructed into fructose, glucose and low DP compounds (Figure 5b).

From the comparison of area distributions, a slight reaction occurs at 1000 Hz and only a small amount of fructose (0.3% yield) is detected (Figure 5b). Fructose peak area reached a maximum formation at 2000 Hz which corresponds to a yield of 15 % (Figure 5a). Higher frequency (2500 Hz) leads to a complete inulin conversion and a decrease of fructose yield whereas glucose and DP≥2 products continue to increase. The effect of the signal frequency follows a similar trend to the input voltage and is consistent with an effect due to the increase of input power. For the higher input power (P>14W) fructose was not detected while the inulin powder turned to mild brown indicating a possible degradation of inulin and small oligosaccharides to coke and levulinic acid or furanic derivatives [17] . An increase of the temperature (up to 100°C) of the reactor was observed at voltages over 19 kV and 2.5 kHz. At a constant input power (18 kV, 2 kHz) the inulin transformation as a function of time has

shown that the maximum fructose yield was obtained after 9 minutes of reaction and is consistent with the total conversion of inulin (Figure 6). Simultaneously with the fructose formation, DP2, DP3 compounds and glucose were observed. From 9 min, DP2 peak area includes the glucose peak area since the two peaks overlapped on the chromatogram.

An increase of the temperature (up to 70°C at 18 kV and 2 kHz) of the reactor was also observed as a function of the plasma treatment time. To determine the role of the temperature in the depolymerization process, the reactor was kept at 35°C by cooling the air flow circulating through the reactor.

Inulin conversion was followed as a function of time (Figure 7) in standard conditions (18 kV, 2 kHz, 50 ml min -1 ). The same trend as for experiments without temperature control was observed but with a slower conversion rate. The total inulin transformation was achieved for reaction time higher than 32 min instead of 9 min and with a higher fructose yield (32% instead of 21%). This behavior strongly suggests that the reaction is not directly induced by the impact of energetic electrons generated by the plasma. It would proceed through excited species generated from the electronic collisions with the gas phase molecules (in addition to a minimum temperature gradient).

In order to bring further understanding of the depolymerization process by plasma, the effect of gas composition was studied by varying the N2/O2 ratio in standard conditions (19 kV, 2 kHz, 7 mins of plasma treatment). As shown in Figure 8a, the increase of the oxygen content led to a more efficient depolymerization. When the voltage was kept constant at 19 kV, the ratio of gases influenced only slightly the deposited power (Figure 8b) and the trends of the inulin samples chromatograms remained similar, with nearly or total deconstruction of inulin and the formation of fructose, glucose and fructooligosaccharides of DP ≥ 2. At the lowest oxygen content in the gas phase (20 %), inulin was partially deconstructed and a fraction of fructose was also degraded into HMF. At the two other ratios, 50 % and 80 % O2, depolymerization of inulin was complete without HMF formation. In pure gases like helium or nitrogen, no reaction occurs (Figure 9), although a nitrate concentration below 25 mg dm -3 was measured in case of pure N2 plasma. An imperceptible depolymerization into fructose and DP2 is obtained in pure oxygen. No pH modification was observed in all cases. . The infrared spectra showed no changes in the inulin structure under pure helium or nitrogen.

Only a slight oxidation band at 1730 cm -1 was observed under pure oxygen (Figure 10).

In addition to HLPC analysis, MALDI-TOF spectrum (Figure 11) confirmed that depolymerization of inulin led to the formation of DP2, DP3 and DP4 molecules. It is not possible to identify whether the DP2 molecule is inulobiose or sucrose, nor if the DP3 are composed exclusively of 3 fructose units or 1 glucose and 2 fructose units (also valid for higher DPs molecules). The pH measurement after dissolution of the treated samples (N2/O2 plasma) in water shows a decrease of the pH from 6 to 3.5 by increasing the treatment time from 1 to 7 minutes which remains constant for higher treatment time. This behavior could be due to the formation of nitric acid from reaction of nitrous oxides (formed in air by the plasma) and water [18] or by the formation of carboxylic acids from inulin or oxidation products.

The concentration of NO3 -was measured with Quantofix ® nitrate/nitrite strips (Table 1). The hypothesis of inulin depolymerization by nitric acid was suggested. Moreover, the presence of HMF under high nitrogen concentration showed that fructose dehydration to HMF could be related to the presence of high concentration of nitric acid (Table 1).

In order to verify this hypothesis, a series of experiments was performed using a He/O2 gas mixture in the same experimental conditions. Results are shown in Figure 12 and similarities with N2/O2 gas mixtures experiments are observed in terms of inulin depolymerization into fructose and small fructooligosaccharides. DP2 formation depends on the He ratio in the gas phase, 80 and 90 %, which also corresponds to the highest powers. As the helium content (and thus power) decreases, DP2 band area decreases. Additionally, inulin depolymerization is not complete under helium/oxygen. The pH measurements of the samples treated by plasma under He/O2 gas mixture present the same variation than with N2/O2 gas mixture. HPLC revealed also the presence of formic acid as inulin degradation product over 7 min treatment. In addition to formic acid, carboxylic acid molecules derived from inulin oxidation could be responsible of the pH decrease. From all these observations, oxygen activation by N2 or He excited species appears to be necessary to trigger the depolymerization. The formation of oxygen active species such as radicals  OH or metastable O2 -, O * depends on the oxygen/helium or oxygen/nitrogen ratio. It is known in the literature as penning effect: oxygen acts as a quenching gas and helium or nitrogen transfer their energy via collisions to ionize oxygen [19][20][21] . The formation of nitric acid under N2 / O2 plasma discharge would not only explain the complete conversion of inulin (which remains incomplete under He / O2) but also the degradation into HMF under high nitrogen content (80 %N2 / 20 %O2). The increase of temperature, from excited species relaxation, would also take part in the depolymerization process as it forms an energy reservoir [START_REF] Rios | AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition[END_REF] altering the plasma discharge.

It is suggested here that the concentration of active oxygenated species generated from the plasma discharge, such as oxygen radicals or metastable oxygen, increases with the oxygen content in the gas phase. Based on previous studies [START_REF] Duan | [END_REF] the depolymerization was achieved by reaction with active oxygen (ROS) /nitrogen (RNS) species. The slight increase of the reactor's temperature would lead to the release of water molecules from highly hygroscopic inulin and would enhance the formation of H2O2 [START_REF] Duan | [END_REF]24] .

From H2O2, OH and oxygen radicals would be formed following [25] :

According to different authors [25,26] , the high reactivity of OH radicals and singlet oxygen is responsible of the depolymerization process. OH can abstract hydrogen atoms from every C-H positions on the fructose ring, resulting in carbon radicals which will lead to the breakdown of the β-glycosidic bonds between the fructose units. Additionally, it was suggested that carboxylic acids of polysaccharides act as active catalyst center for the depolymerization process [27] .

Ex situ infrared investigation of air plasma treated inulin

The IR spectra of raw inulin is shown in Figure 13. It shows well defined and narrow peaks that are arising from the ordered structure of inulin, mainly composed of monomeric units of fructose. The main bands [27][28][START_REF] Tipson | Infrared spectroscopy of carbohydrate[END_REF][START_REF] Ibrahim | [END_REF] are referred in Table 2. The broad band (maximum at 3341 cm -1 ) is related to OH stretching vibration of polymeric intermolecular hydroxyl groups. The bands at 2936 cm -1 and 2890 cm -1 were attributed to asymmetric and symmetrical stretching vibrations of CH2, respectively and the band at 1330 cm -1 to CH2 bending. At 1645 cm -1 , OH bending vibration band is related to adsorbed water, inulin being highly hygroscopic. Below 1500 cm -1 , in the fingerprint region, a multitude of bands, some with weak intensities, are detected. A small band corresponding to the CH2 symmetric bending mode of the hydroxymethyl functions is observed at 1430 cm -1 .

Following closely, lower bands at 1380 and 1332 cm -1 are identified as bending modes of OCH, CCH, CH2 for the former and CCH, COH for the latter. At 1240, 1220 and 1196 cm -1 , bands representative of CCH, COH and OCH bending modes are detected. They are closely followed by more prominent bands at 1160, 1130, 1025, 985, 832, 874 and 817 cm -1 corresponding to the stretching vibrations of CO, CC and complex bending modes of pyranose ring vibrations (CCC, CCO, CO and CC). Upon the plasma treatment, various modifications of the spectra were observed as a function of treatment time.

In the high region, 4000-2500 cm -1 , slight changes were observed on the normalized spectra, consisting of an increase of the OH band intensity up to 5 mins that shifted from 3295 to 3353 cm -1 ,(60 cm -1 shift). The decrease of DP leads to an increase of the OH vibrational bands from fructose. As a matter of fact, dimeric OH bands can be found in the 3550-3450 cm -1 region while those from polymers are in the region 3400-3225 cm -1 . Similarly, the CH2 stretching bands followed the same trend, without shift. Above 7 mins of plasma treatment, a decrease of the band intensity indicates a loss of OH and CH2 groups due to the dehydration of fructose into HMF.

In the 2500-1100 cm -1 region, a new band was detected at 1730 cm -1 and was attributed to the formation of aldehydes or ketones from the oxidation of C6H2OH groups. A large shift and narrowing of the 1635 cm -1 band to 1664 cm -1 was observed. It appears that the bending vibration of H2O disappeared as a function of time while a band characteristic of bending of OH from -D fructose emerged between 5-7 mins. Another hypothesis is the formation of an amide, whose characteristic bands is at 1660 cm -1 (C=O stretching). Additional band at 1522 and 1402 cm -1 would confirm the presence of amides with N-H bending and C-N stretching, respectively.

C-OH hydroxymethyl character at 1430 cm -1 and 1380 cm -1 (bending modes of OCH, CH2, CCH) was slowly hindered by the increase of the band at 1402 cm -1 and 1450 cm -1 , the latter mostly corresponding to C-O stretching from carboxylic acid or carboxylate ions.

Modification of the 1330 cm -1 band that increases in intensity and disappears at the expense of a small band at 1340 cm -1 is observed. This shift could be due to the progressive depolymerization of inulin into fructose, whose band at 1340 cm -1 reflects the bending vibrations of OCH and CCH of -D fructose.

Small protuberances at 1271 cm -1 and 1242 cm -1 disappeared up to 7 mins and a 1275 cm -1 small but wide band emerged from 9 mins and could be related to C-O stretch of carboxylic acids or N-H stretch of amide.

A loss of the bridging C-O-C character is also observed at 1130 cm -1 from 1 to 5 mins.

An increase and widening of the band is observed at 1196 cm -1 , corresponding to OCH and CCH bending vibrations bands of fructose, glucose and fructooligosaccharides of higher DP.

In addition to inulin stretching ring vibration CCH and COH, CH and OH bending vibrations of D-glucose are observed in this region.

In the 1100-600 region, noticeable changes are observed as a function of the plasma treatment time. Especially at 7 mins, where a loss, shift or emergence of bands at 1075 cm -1 (gain), 1030 cm -1 (loss), 986 cm -1 (loss), 978 cm -1 (gain), 934 cm -1 shifts to 921 cm -1 , 874 cm - 1 (loss) and 855 cm -1 (emergence) were observed.

The total loss from 1 to 7 mins of 986 cm -1 , 934 cm -1 and 874 cm - Appearance from 7 mins of 986 cm -1 to 978 cm -1 (C-O, CCO fructose), shift of 934 cm -1 to 921 cm -1 (C-O, CCH + ring fructose) confirms the loss of the polymeric structure to monomer characteristics. The 889 cm -1 shoulder and 874 cm -1 shift to 855 cm -1 could be related to glucose and fructose ring vibration, COH and CCH.

From 2 mins, a band at 778 cm -1 emerged and slowly shifted to 770 cm -1 corresponding to CCO and CCH bending of D-fructose, the shift to 770 cm -1 is probably due to addition of CCO and CCH bending vibrations of D-glucose.

Based on this exhaustive list of band assignments, conclusions can be drawn regarding inulin depolymerization reaction. The changes in the high region 4000-2500 cm -1 refers to the deconstruction of inulin into fructose and further decomposition into HMF at longer treatment times. In the mid region 2500-1100 cm -1 , the various modifications concern the oxidation of OH vibration band most probably on C6H2OH into aldehyde, ketone and further carboxylic acid with increased treatment duration. Though the hypothesis of oxide formation is the most reliable, it should be kept in mind that the interpretation could also imply different bands of NH, CN bending and stretching vibrations, thus the presence of amide. The formation of -D fructose is supported by different bands related to OCH, CCH, OH vibrations and loss of the COC bridge oxygen, which is a characteristic band of polymers. Glucose formation also detected in the mid and low region, below 1100 cm -1 .

Conclusion

Depolymerization of inulin into fructose (32 % yield) was successfully achieved by non thermal plasma at atmospheric pressure. The distributions of inulin, fructose, glucose and DP≥2 fructooligosaccharides were dependent on the plasma discharge electrical characteristics and reactive species involved in the gas phase. It was suggested that ROS and RNS play a key role in the depolymerization process, via OH radicals or nitric acid attack.

Oxidized inulin could also act as a catalyst center for its deconstruction. Infrared analysis revealed the oxidation of inulin into carboxylic acid, aldehyde or ketone, followed by the breakage of glycosidic bond and ring opening. The presence of amides was also suggested, providing evidence that RNS are involved in the process. A way to improve the fructose yield would consist in developing a reactor with a controlled cooling system. However, small fructo-oligosaccharides can also be considered for applications, such as food industry.

Figure 1 :

 1 Figure 1: Experimental set-up.

Figure 3 :

 3 Figure 3: schematic representation of inulin polymer.

( 2 )

 2 Where AC is the peak measured area for each compound and AT the total area of detected compounds. Trends of compounds formation or conversion are comparable but, due to the lack of response coefficient of most of the reaction products, it is not possible to give a quantitative analysis of results.The distribution of the DP (degrees of polymerization) present in the samples succeeding plasma treatment were determined by MALDI-TOF (Matrix Assisted Laser Desorption Ionization-Time Of Flight) recorded on a Bruker AutoFlex III apparatus after dilution of the samples in a matrix of 2,5-dihydroxybenzoic acid (DHB) prior to analysis. The irradiation of the crystalline mixture gives rise to the desorption of ions characteristic of the sample which are then analysed by mass spectrometry according to their mass-to-charge ratio, m/z.

Figure 4 :

 4 Figure 4: a) fructose yield and b) area distribution of inulin conversion and reaction products

Figure 5 :

 5 Figure 5: a) fructose yield and b) Area distribution of inulin and reaction products as a

Figure 6 :

 6 Figure 6: a) fructose yield and b) area distribution of inulin and reaction products as a

Figure 7 :

 7 Figure 7: a) fructose yield and b) area distribution of inulin and reaction products as a

Figure 8 :

 8 Figure 8: a) Size Exclusion Chromatograph of plasma treated inulin samples for different

Figure 9 :

 9 Figure 9: Size Exclusion Chromatograph of plasma treated inulin samples under pure gases

Figure 10 :

 10 Figure 10: Infrared spectra of inulin samples after plasma treatment in different pure gases.

Figure 11 :

 11 Figure 11: MALDI-TOF analysis of the plasma treated inulin sample at 19 kV, 2 kHz and 7

Figure 12 :

 12 Figure 12: a) Size Exclusion Chromatograph of plasma treated inulin samples under various

Figure 13 :

 13 Figure 13: FT-IR spectra of the inulin sample from 1 to 12 minutes of plasma treatment

  1 bands which are relevant to C-O-C bridge oxygen, C-O from furanose and pyranose rings vibrations indicates not only a depolymerization by cleavage of the -1,2 bond but also an opening of the ring at the C-O position.

Table 1 :

 1 NO3 -concentration as a function of gas ratio at a voltage of 19 kV, frequency of 2 kHz and flow rate of 50 ml dm-3 .

	N2 : O2 ratio	NO3 -concentration
		(x, mg dm -3 )
	80 : 20	x > 500
	50 : 50	250 < x < 500
	20 : 80	50 < x < 100

Table 2 .

 2 Major infrared bands of raw inulin.

	Range (cm -1 ) group vibration	remarks
	3680-3000	O-H	stretching	Intermolecular	bonded	OH
				(polymeric)
	2936	C-H	Asymmetric stretching	>CH2 methylene
	2890	C-H	symmetric stretching	>CH2 methylene
	1645	O-H	bending	From adsorbed water
	1430	C-OH Symmetrical stretching hydroxymethyl
	1332	COH	bending	Intermolecular bonded OH
		CCH	bending	>CH2 methylene
	1240	C-O	stretching
		CCH	bending
		COH	bending
	1220	COH	bending
		CCH
	1196	OCH	bending
		CCH
	1160	C-O-C	CO + CC	Pyranose ring vibrations
		CCC	CCC
	1130	C-O-C bending	Bridge oxygen
	1025	C-O-C CO
			CC
	985	C-O	CO	Valent stretching vibrations of C-O-C
		CCO	CCO	groups and ring vibrational modes
	934	C-O	CO + CCH + as (ring)
		CCH
	874		CC + CCH + CH	Methylene acetal and ring vibration
	817	C-H	Bending (wagging)	-pyranose ring vibration