domain: chim sdv

text:
Ben Sarra

Seifallah Hassine

Bassem Abid

Christine Jamoussi
email: christine.paul@insa-rennes.fr

Paul-Roth Odile

Hassine

Seifallah Abid

Bassem Jamoussi

Christine O Paul-Roth
email: christine.paul@univ-rennes1.fr

Bu Bu

New Highly Fluorescent Phthalocyanines Dendrimers with Fluorenyl-based Connectors vs Phenyl-based Connectors

Keywords:

published or not. The documents may come

Introduction

Nowadays, following the remarkable works of Vogtle, [START_REF] Buhleier | [END_REF] Tomalia, 2 Newkome 3 and Fréchet, 4 dendrimers form a wonderful class of molecules in the molecular world. In this respect, Fréchet and coworkers 4 have reported porphyrin systems with fluorene-containing oligoethertype dendrons as efficient one-and two-photon light-harvesting units and demonstrated that such an "antenna effect" was facilitated in dendritic architectures versus linear ones. More recently, related star-shaped porphyrins with fully conjugated oligofluorene arms have also been reported by Bo and co-workers and shown to behave as a remarkable light-harvesting systems. 5 In these assemblies, dendrons can work as efficient "light-harvesting antenna" in selected porphyrin-based dendrimers presenting molecular architectures recalling those collecting natural light in various photosystems. 6,7 These systems are foreseen as key building blocks which can be fine-tuned at will, by modification of the peripheral substituents and this for many recent applied developments. In this respect, impressive fundamental research based on porphyrins has been undertaken in fields related to material sciences and information treatment these last decades, 8,9 but also in fields related to health, such as photodynamic therapy (PDT) for instance. 10 Their use for PDT is particularly promising because the photosensitizers can be also fluorescent probes, allowing to perform curing and bioimaging at the same time in a so-called theranostic approach. 11,12 Fig. 1 Molecular structures of TPP-and TFP-cored porphyrin dendrimers with conjugated peripheral fluorenyl arms along with the reference compounds TFP and TFP-Bu.

Given that tetraphenylporphyrin (TPP) or related derivatives (TPP-C1 in Figure 1) are only modestly fluorescent in their free base form, most of the investigations in this field, relied on porphyrin conjugates featuring an expanded -manifold, in order to enhance among others their absorption and so their one-photon absorption (OPA) brightness ( x ФF).

Moreover, our group reported earlier, the synthesis of a simple porphyrin possessing four fluorenyl arms named tetrafluorenylporphyrin (TFP in Figure 1). 13 Surprisingly, TFP exhibited a remarkably high quantum yield (24%) compared to the reference TPP, demonstrating thereby the capacity of the fluorenyl units to enhance fluorescence quantum yields (ФF). Likewise, to TFP, n-butyl groups were added in position 9 on the terminal fluorene groups (TFP-Bu) to improve the overall solubility of the porphyrin TFP and the corresponding dendrimers. Then, we could recently show with various families of nonconjugated 14,15 or conjugated dendrimeric porphyrins, 16,17 that by appending fluorenylcontaining dendrons at the periphery of a central tetra-arylporphyrin core, fluorescent photosensitizers with significantly enlarged one-photon brightnesses could be obtained upon increasing the dendrimer generation G. 18 Furthermore, when fully unsaturated dendrons were used, a partial disruption of the manifold takes place at the meso positions in the most stable conformers. These twisted conformations adopted by the meso aryl groups allow the peripheral dendrons to behave as efficient light-harvesting antennae. 18 Their optical properties studies reveal that among the members of the different dendrimer families, the TFP-cored dendrimers are always the most efficient. 17,18 Recently, in order to improve further these fluorescent probes, we explored a new node and so replaced the classic 1,3,5-phenylene unit (C1; Figure 1) by a fluorenylbased unit (C2; Figure 1) in the dendrons. Thus, TFP-based dendrimer TFP-C2, the analogue of dendrimer TFP-C1 featuring these innovative connectors, was studied. 19 In generation one (G1) dendrimer TFP-C2, contrary to what is happening with classic connector C1, the 2alkynylfluorenyl units on C2 are no more connected to topologically orthogonal positions 20 and there is probably a better electronic communication between the various fluorenyl subunits. 18 The C2 fluorenyl connector, substituted in the position 9 by a double bond linked to two (2-ethynyl)fluorenyl groups, allows electronic conjugation between the four fluorenyl groups of the dendron. The large dendrons in TFP-C2, with rigid and entirely planar termini (except for the four butyl chains), adopt probably a propeller-shaped conformation around the central porphyrin core. 19 Motivated by further enhancing the efficiency of our systems and inspired by the phthalocyanine-cored dendrimers reported by Kimura 21,22 and others, [23][24][25][26][27][28][29][30][31][32] we recently wondered about the impact of replacing the central free-base meso-tetrafluorenylporphyrin (TFP-Bu) by zinc(II) phthalocyanine (ZnPc). Thus, we first synthesized the non-conjugated zinc(II) phthalocyanines series, decorated with fluorenyl arms connected by flexible ether linkers, 33 and then a conjugated zinc(II) phthalocyanine dendrimers series. 34 For this last one, we obtained successive generations of ZnPc-C1 type compounds (Fig. 2) and probed their photonic properties. 34 In details, we first synthesized the star shaped zinc(II) phthalocyanine (ZnPcFl in Figure 2), decorated with four fluorenyl arms, and then higher generations zinc(II) phthalocyanine dendrimers (generation 1 and 2), based on ZnPc-C1 model (Figure 2). 34 The idea behind this structural variation was to enhance the emission of these photosensitizers by using (i) a more luminescent central core than TFP, (ii) and the classic 1,3,5-phenylene node C1, for all these series. This goal was perfectly reached with this phthalocyanines series since all these compounds are more fluorescent than porphyrins dendrimers (with luminescence quantum yields around 29-37%). For these phthalocyanines, the comparison with the naked ZnPc complex (Fig. 2) also demonstrated the critical role of the peripheral fluorenyl-containing antenna on the optical properties. In this project, we will now combine the most efficient core and the dendron with the best connector C2. So, in the following, we will describe (i) synthesis of useful fluorenyl dendrons with C2 connector; (ii) synthesis of substituted ZnPc core; (iii) the synthesis and characterization of the targeted ZnPc-based dendrimer ZnPc-C2, featuring these units as components and last (iv) the study of the linear optical properties. Their optical properties as well as their energy transfer behavior will then be compared with parent phthalocyanine dendrimer ZnPc-C1 and discussed in the light of previous results. 17,33,34 Fig. 3 Molecular structures of zinc(II) phthalocyanines dendrimers with conjugated peripheral fluorenyl arms with different connectors Cn.

Results and discussion

Synthesis

To synthetically access the new dendrimer ZnPc-C2, two reverse Strategies A and B in three steps each, can be envisioned (Scheme 1). For Strategy A, i.e. (i) Synthesis of Zn(II) tetraiodophthalocyanine 4IZnPc, standing for ZnPc-cored precursor, (ii) Synthesis of the alkynyl-terminated dendron precursors A-D (1) and finally, (iii) Connection of Zn(II) phthalocyanine to the dendrons A-D (1) by Sonogashira coupling reactions. 35 For the second Strategy B, (i) Synthesis of the tetra-alkynyl Zn(II) phthalocyanine 4AZnPc, standing for ZnPc-cored precursor (ii) Synthesis of the bromo-dendron precursors Br-D (9) and finally, (iii) Connection of Zn(II) phthalocyanine to the dendrons Br-D (9) by Sonogashira coupling reactions. 35 Scheme 1. Two Retrosynthetic Strategies proposed to access to the phthalocyanine dendrimer ZnPc-C2.

To obtain new dendrimer ZnPc-C2, two reverse Strategies A and B will now be considered, we will first discuss the Strategy A : Conjugated Dendron 1. This Dendron was obtained from commercial fluorenone (2) in a few steps (Scheme 2) following two different approaches (i) the improved synthetic protocol described in this work and (ii) the synthetic protocol used previously in our group. 19 We will now describe in details the first approach (i).

(i) In the improved synthetic protocol, the 2-bromofluorenone 3 was obtained from the commercial fluorenone 2 using dibromide in water, then, we introduced a trimethylsilylacetylene (TMSA) group by Sonogashira reaction. 35 Compound 4 was reacted with carbon tetrabromide and triphenylphosphine offering the gem-dibromo derivative 5.

After, we insert two 9,9-dibuthyl-2-ethynyl-9H-fluorene antennae by using two equivalents of 6. This alkyne 6 was previously synthesized from commercial 2-bromo-9,9-dibutylfluorene as described recently. 16,17 The TMS protected dendron 7 was deprotected under basic condition (K2CO3) to give the terminal alkyne 1 with a global yield of 33% from intermediate 3 which is already higher than the yield obtained in the second approach (ii). This synthetic path is around three time more efficient than path (ii) In the synthetic protocol already reported. 19 Scheme 2. Syntheses of the conjugated dendron precursor A-D (1) following new approach (i) the improved synthetic protocol.

Desired dendron 1 and corresponding intermediates 3, 4, 5 and 7 were characterized by The connection of two extra fluorenyl antennae provided compound 7, and a little shift to lower field was again observed for H1 and H8. In fact, for non-symmetric compounds such as intermediate 7 or 9, a singlet at 9.15 ppm (H1) and doublet at 8.8 ppm (H8) are seen at low field (Fig. 4 and SI Fig. 3). This peculiar 1 H NMR signal can therefore be used as a convenient NMR marker to assess the presence of dendrons like 1 in final dendrimers (only if there is no overlap in this low field region). The aliphatic protons of n-butyl chains appear Synthesis of dendrimer (ZnPc-C2). The synthesis of Zn(II) tetraiodophthalocyanine (4IZnPc) is obtained following the method described by Torres. 36 The targeted dendrimer ZnPc-C2 was obtained by coupling prepared 4IZnPc with 6 equiv. of deprotected dendron 1, under Sonogashira conditions. 35 This dendrimer ZnPc-C2 was then obtained as a green solid in 65% yield (Scheme 3). This new dendrimer was characterized by NMR, elemental analysis and MALDI MS. In 1 H NMR spectrum (400 MHz, using THF-d8 as a solvent; see ESI Fig; 8), the large multiplets between 9.5-8 ppm are corresponding to the aromatic protons (Hα, Hα' and Hβ) of the phthalocyanine core, between 8 and 7 ppm, we observe large multiplets corresponding to the aromatic proton peaks, of the twelve fluorenyl units. The four large peaks in region of 2.3 to 0.3 ppm are corresponding to the protons of the sixteen butyl chains from the eight external fluorenyl groups.

After having detailed successful Strategy A, to obtain new dendrimer ZnPc-C2, we will now rapidly consider reverse Strategy B, we can notice that this last path was used earlier to obtain similar generation G1 dendrimer TFP-C2 19 based on a porphyrin core rather than on a phthalocyanine acceptor Bromo Dendron 9. This synthesis has already been described above, in Strategy A, as an intermediate in (ii) the synthetic protocol already reported, 19 and obtained in three steps from 2-bromofluorenone 3 (scheme 2).

Phthalocyanine-based dendrimer ZnPc-C2. For this second Strategy B, the synthesis of the tetra-alkynyl Zn(II) phthalocyanine 4AZnPc (see Scheme 2), standing for ZnPc-cored precursor, is necessary. This tetra-alkynyl phthalocyanine 4AZnPc was obtained in two steps as a green solid, in 50% yield (Scheme 4). First by coupling 4IZnPc with 6 equiv. of ethynyltrimethylsilane (TMSA), under Sonogashira conditions, 35 to obtain protected 4TMSZnPc (yield 75 %). Then, the TMS protection groups were removed by treatment with tetra-n-butyl ammonium fluoride (TBAF) in THF, so 4AZnPc containing four terminal alkynyl groups was obtained with a yield of 67 % as described by Torres. 36 Finally, the connection of dendrons 9 to central Zn(II) phthalocyanine 4AZnPc core was tried several times, by Sonogashira coupling reactions, in different conditions. Unfortunately, we could only obtain dark polymers, probably produced by the homo-coupling of the tetra-alkynyl phthalocyanine 4AZnPc. As previously stated, this Strategy B was followed earlier to obtain the porphyrin based dendrimer TFP-C2, but in this case the rigid fluorenyl node is further from the central core, so there is less steric hindrance and the Sonogashira coupling is more favorable although the reported coupling efficiency is only around 20%. 19 Scheme 4. Try to obtain new dendrimer ZnPc-C2, by reverse Strategy B.

These phthalocyanine precursors were characterized by [START_REF] Buhleier | [END_REF] H NMR (400 MHz) using THF-d8 as solvent (SI Fig. 4). For 4TMSAZnPc and deprotected form (4AZnPc), the large peaks at low field (between 9.2-8 ppm) are corresponding to the twelve aromatic protons of the phthalocyanine core (Hα, Hα' and Hβ). For phthalocyanine 4TMSAZnPc, the singlet at 0.62 ppm is corresponding to the protons of the four TMS groups, and by reaction with TBAF, this peak disappeared and a new singlet at 4.07 ppm arises, attributed to the four alkynyl protons of deprotected phthalocyanine 4AZnPc. To conclude, we succeed by following Strategy A, with 4IZnPc as an acceptor and alkyne dendron 1 as a donor, rather than following reversed Strategy B, using tetra alkynyl 4AZnPc with bromo-dendron 9.

Photophysical properties

Absorption and emission spectra in solution

The normalized UV-visible (abs) and emission (em) spectra of the new dendrimer ZnPc-C2

using bare zinc phthalocyanine ZnPc as reference, were measured in THF solution at room temperature (Figures 5 and6) and compared to those of the known compounds ZnPcFl, 34 and ZnPc-C1, 19 decorated with four and eight fluorenyl units, respectively (see Fig. 2). The former phthalocyanine ZnPc-C1, used classical connector C1, whereas for new dendrimer ZnPc-C2, fluorenyl connector C2 is used with a zinc phthalocyanine ZnPc core, for the first time. The UV/Vis absorption spectra of all these phthalocyanines were recorded between 250 and 800 nm (Figure 5). The new dendrimer ZnPc-C2 features the characteristic absorption bands of phthalocyanines already seen on the spectra of ZnPc, 34,[START_REF] Edwards | Vapor Absorption Spectra and Stability: Phthalocyanines[END_REF] which are: (i) the Q-bands, corresponding to main absorption bands, detected in the visible range between 650 and 750 nm, and resulting from π-π* transitions from the HOMO to the LUMO and LUMO+1 with a vibronic sub-band around 630 nm; (ii) the Soret band, corresponding to a

-ZnPc -ZnPcFl -ZnPc-C1 -ZnPc-C2
wide band between 300 and 500 nm and resulting from π-π* transitions from deeper lying MOs to the LUMO and LUMO+1, and finally, (iii) the N band, a less intense and narrower band centered around 280-300 nm. The latter still corresponds to a set of more energetic π-π* transitions within the phthalocyanine core. 34 These last two absorption bands can not be detected for ZnPcFl, ZnPc-C1 and ZnPc-C2 because they are overlapped by another intense absorption band, absent in ZnPc, which grows in intensity when progressing from ZnPcFl to ZnPc-C1 and then to ZnPc-C2 (Figure 5) i.e. roughly with the increasing size of the conjugated π-manifold within the arms when going from four to eight and finally twelve fluorenyl units, respectively. This broad band, going from 250 nm to 500 nm, which becomes more important than the Q-band for the two dendrimers (ZnPc-C1 and ZnPc-C2), can be confidently attributed to dendron-centered π-π* transitions. 13,34 This extra absorption, around 300-400 nm, largely fluorenyl-based, is absent for the bare reference ZnPc. For new dendrimer ZnPc-C2, this extra absorption is even larger and more red-shifted (going to 450-500 nm) and more intense, to what had been previously observed with ZnPc-C1. 34 Moreover, when this fluorenyl-based absorption is compared to these previously observed around 300 nm with phthalocyanines presenting non-conjugated dendrons, such as reported earlier by our group 33 a bathochromic shift is stated for it in ZnPcFl, ZnPc-C1 and ZnPc-C2. This shift reflects at least in part the better π-conjugation existing between the peripheral arms and core in these compounds.

On the other hand, a bathochromic shift is experienced by the main Q-band following roughly the same order. Thus, this maximum shifts towards the red, from 671 to 706 nm, along the order: ZnPc < ZnPc-C1 < ZnPcFl ≈ ZnPc-C2. The star-shaped phthalocyanine

ZnPcFl presenting roughly the similar Q-band (706 nm) as corresponding dendrimer ZnPc-C2. Again, this shift reflects the importance of the π -manifold present on the peripheral dendrons, conjugating with the central core. Figure 6a shows the emission spectra of dendrimers ZnPcFl, ZnPc-C1 and ZnPc-C2

in THF, as well as that of ZnPc used as bare reference. After excitation at 606 nm i.e. in the Q vibronic sub-band, a strong red emission between 650 and 850 nm, characteristic of the phthalocyanine core, is observed. As for one-photon absorption, these dendrimers present a red-shifted emission relative to that of ZnPc. Without surprise, the wavelength ordering between the dendrimers follows that previously observed in absorption for the Q-band: ZnPc < ZnPc-C1 < ZnPcFl ≈ ZnPc-C2. Then, to probe the efficiency of the energy transfer process (ET) between the peripheral dendrons, as energy donors D and the central phthalocyanine, as energy acceptor A, we have excited the dendrimers in their specific π-π* band, at about 300 nm (Figure 6b). By doing so, we observed no residual emission of the dendrons in the 350-450 nm range, 19,33,34 but only the characteristic emission band from the phthalocyanine core (between 650 and 850 nm) which proves an efficient ET process. As previously done with phthalocyanines ZnPcFl and ZnPc-C1, 33,34 the fluorescence quantum yields (ФF) were determined by comparison with ZnPc in a toluene/pyridine mixture (99:1). Compared to this standard ZnPc (ФF = 26%), all quantum yields found for these compounds are higher than this value (Table 1). We noticed earlier that among the dendrimer series, based on ZnPc core with connector C1, there is a regular increase in their fluorescence quantum yield with increasing generations (29% < 32% < 36%), suggesting that the increase of the π -manifold on the peripheral dendrons favors the non-radiative deactivation of the phthalocyanine core. 34 In this work, when generation G1 dendrimers with different connectors C1 and C2, meaning reported ZnPc-C1 and new ZnPc-C2, are compared, a better quantum yield (35%) is found for ZnPc-C2, possibly in line with better conjugation for C2.

When compared to the fluorescence quantum yield of zinc complexes previously investigated by our group (29-37%), 33,34 these quantum yields cover an almost similar range of values, but only the yield found for the largest compound ZnPc-C2 compares to that previously obtained (37%), which was the most luminescent compound among our complete series. 33,34 The efficiency of ET between the dendrons D and the phthalocyanine A, was also tested by exciting the dendrons at about 300 nm (Figure 6b) and, as observed before, only the phthalocyanine emission band (between 650 -850 nm), with similar fluorescence quantum yields to that is seen when the compounds are excited in their Q-bands. This reveals again that for compound ZnPc-C2, the energy absorbed by the four large dendrons is almost quantitatively transferred to the central core, with an optimal process (ФEnT ~ 100%). are no longer connected to orthogonal positions 19,20 and therefore there is a better electronic communication between the three fluorenyl subunits of the dendron. In consequences, their absorption bands are strongly red shifted and enlarged compared to that of bare ZnPc. In fact, these large dendrons in ZnPc-C2, with rigid and entirely planar termini (except for the four butyl chains), adopt probably a propeller-shaped conformation around the central ZnPc core.

Conclusions

During these investigations, we observed again that rigid and conjugated fluorenyl-based connector C2 leads to higher performances than the 1,3,5-phenylene spacer C1 as observed earlier with central porphyrin core. 19 This original connector ameliorates the electronic communication within the dendrimeric branches without affecting the fluorescence performances. For this reason, this connector should now be used in the future when designing dendrimers of higher generation based on phthalocyanines.

Experimental Section

General

Unless otherwise stated, all solvents used in reactions were distilled using common purification protocols, [START_REF] Perrin | Purification of Laboratory Chemicals[END_REF] except DMF and i Pr2NH which were dried on molecular sieves (3 Å).

Compounds were purified by chromatography on silica gel using different mixtures of eluents as specified. [START_REF] Buhleier | [END_REF] H and 13 C NMR spectra were recorded on BRUKER Ascend 400 and 500 at 298 K. The chemical shifts (in ppm) are referenced to internal tetramethylsilane. High-resolution mass spectra were recorded on different spectrometers: a Bruker MicrOTOF-Q II, a Thermo Fisher Scientific Q-Exactive in ESI positive mode and a Bruker Ultraflex III MALDI Spectrometer at CRMPO (centre regional de mesures physiques de l'Ouest) in Rennes.

Reagents were purchased from commercial suppliers and used as received. Compounds 2ethynyl-9,9-dibutyl-fluorene (6), 16,17 was synthesized as described earlier. The zinc tetraiodophthalocyanine complex I4ZnPc, the protected 4TMSAZnPc intermediate and the zinc tetraalkynyl-phthalocyanine complex 4AZnPc were obtained as previously described in the literature by Torres. 36

Synthesis

(i) Improved synthetic protocol 2-((trimethylsilyl)ethynyl)-9H-fluoren-9-one (4). To a mixture of 2-bromo-fluoren-9-one 3 (8 g, 30.9 mmol, 1 equiv), Pd(PPh3)2Cl2 (1.08 g, 1.54 mmol, 5% equiv) and CuI (0.29 mg, 1.54 mmol, 5% equiv) were successively added THF (60 mL), Et3N (60 mL) and ethynyltrimethylsilane (8.54 mL, 61.7 mmol, 2 equiv) under argon atmosphere. The system was degassed by freeze-pump-thaw twice and heated for 24 h at 80 o C. The reaction mixture was poured into saturated NH4Cl and extracted with DCM, the combined organic layers were dried with MgSO4. Volatiles were evaporated and the residue was further purified by silica chromatography using heptane as eluent to give title compound 4 as a yellow solid (6.0 g, 70%). ((9-(1,5-bis(9,9-dibutyl-9H-fluoren-2-yl)penta-1,4-diyn-3-ylidene)-9H-fluoren-2yl)ethynyl) trimethylsilane (7). In a Schlenk tube, to a mixture of ((9-(dibromomethylene)-9H-fluoren-2-yl)ethynyl)trimethylsilane 5 (0.5 g, 1.15 mmol, 1 equiv), 9,9-dibutyl-2-ethynyl-9H-fluorene 6 (1.0 g, 3.47 mmol, 3 equiv), Pd(PPh3)2Cl2 (4.9 mg, 0.007 mmol, 0.6% equiv)

and CuI (1.32 mg, 0.007 mmol, 0.6% equiv) were successively added DMF (14 mL), i Pr2NH (14 mL) and under argon. The system was degassed by freeze-pump-thaw twice and heated for 2 days at 95 o C. After evaporation of volatiles, the residue was further purified by chromatography (heptane), and intermediate 7 was obtained as an orange powder (0.7 g, 69%). (94 mg, 0.68 mmol, 3 equiv). The mixture was stirred overnight at room temperature. After being evaporated, residue was further purified by chromatography using heptane/CH2Cl2 (4:1) as an eluent system, getting desired Dendron A-D (1) as an orange powder (150 mg; 82% yield). [START_REF] Buhleier | [END_REF] H NMR (400 MHz, CDCl3): δ = 9.17 Phthalocyanine dendrimer ZnPc-C2 (1). In a Schlenk tube, to a mixture of zinc tetraiodophthalocyanine complex 4IZnPc (10 mg, 0.97 mmol, 1 equiv), Dendron 1 (47 mg, 5.9 mmol, 6 equiv), Pd(PPh3)2Cl2 (4.2 mg, 6x10 -3 mmol, 6% equiv) and CuI (1.14 mg, 6x10 -3 mmol, 6% equiv) were added THF (4 mL) and NEt3 (4 mL) under argon. Then, the system was degassed by freeze-pump-thaw twice and stirred overnight at room temperature. After being evaporated, the suspension was poured into cold methanol. The dark green precipitate was then filtered off and washed with hot methanol. The crude product was purified by column chromatography on silica gel using heptane/THF (9:1) as eluent. Desired compound

Fig. 2

 2 Fig. 2 Molecular structures of zinc(II) phthalocyanines dendrimers ZnPc previously synthesized with conjugated peripheral fluorenyl arms along with the reference compounds ZnPc and ZnPcFl and intermediates (4TMSAZnPc and 4AZnPc).

1 H

 1 NMR in CDCl3 (as shown in SI Fig.S3band for intermediate 8 and dendron 9 see SI Fig.1, 2 and 3a). We can observe that by exchanging the bromine, present in 2-bromofluorenone 3, by a TMS group, a new peak appears around 0.26 ppm for the three methyl groups for compound 4 (still present for 5 and 7). Then fluorenone 4 is transformed to 5 by exchanging oxygen for CBr2, and the presence of these two bromo atoms causes a large shift to low field from 7.6 to 8.5 ppm for the very close protons H1 and H8.

Scheme 3 .

 3 Scheme 3. Syntheses of the new conjugated dendrimer ZnPc-C2, by Strategy A.

Fig. 5 .

 5 Fig. 5. The UV-visible absorption spectra of the series ZnPcFl, ZnPc-C1 and ZnPc-C2 and ZnPc used as a reference in THF.

Fig. 6 .

 6 Fig. 6. a) Normalized emission spectra of the series ZnPcFl, ZnPc-C1 and ZnPc-C2 and ZnPc used as a reference in THF, after excitation at 606 nm; b) Normalized emission spectra of these phthalocyanines under similar conditions after excitation at the arm (300 nm).

  To summarize, in this work we investigate the impact of the structural change of the central core of dendrimers, going from porphyrin to phthalocyanine, in relation with the impact resulting from the changes in dendron connectors. A new conjugated dendrimer ZnPc-C2 has been synthesized and characterized. For this dendrimer the peripheral fluorenyl units are linked to the central ZnPc core by original fluorene-based connectors C2 instead of the more classic 1,3,5-phenylene C1 previously used in related compounds. Comparison of absorption, emission and ET studies of these dendrimers ZnPc-C1 and ZnPc-C2 are discussed here. In contrary to what is happening with classic connector C1, the 2-alkynylfluorenyl units on C2

Dendron A-D: 2 , 2 '

 22 -(3-(2-ethynyl-9H-fluoren-9-ylidene)penta-1,4-diyne-1,5diyl)bis(9,9-dibutyl-9H-fluorene) (1). Intermediate 7 (200 mg, 0.23 mmol,1 equiv) was added into a mixture of CH2Cl2 (18 mL), MeOH (6 mL), THF (6 mL), together with K2CO3

  (s, 1H), 8.86 (d, J = 7.5 Hz, 1H), 7.91 -7.65 (m, 10H), 7.59 (d, J = 7.8 Hz, 1H), 7.48 -7.32 (m, 8H), 3.22 (s, 1H), 2.08 (dq, J = 10.7, 5.4 Hz, 8H, CH2-Bu), 1.23 -1.07 (m, J = 7.2 Hz, 8H, CH2-Bu), 0.81 -0.55 (m, 20H, CH2 & CH3-Bu). 13 C NMR (100 MHz, CDCl3): δ = 151.

Table 1 .

 1 Photophysical data of generation G1 dendrimers ZnPc-C1, ZnPc-C2 and bare ZnPc used as a reference, and ZnPcFl in THF at R.T.

		abs (arm)	abs (Pc)	max	em
	Compound			(M -1 cm -1 )		F a 
		(nm)	(nm)	at Q max	(nm)
	ZnPc	-	343, 602, 666	234000 671, 741	0.26
	ZnPcFl	338	628, 697	398000 706, 781	0.29
	ZnPc-C1	329, 346	624, 692	393000 701, 774	0.32
	ZnPc-C2	305, 380	699	272000 706, 781	0.35

a quantum yield determined relative to (py)ZnPc in toluene / pyridine 99:1 (F = 0.30, J. Chem. Phys., 1971, 55, 4131), upon excitation at 606 nm.

  [START_REF] Buhleier | [END_REF] H NMR (400 MHz, CDCl3) δ = 9.14 (d, J = 1.3 Hz, 1H), 8.94 -8.84 (m, 1H), 7.90 (dd, J = 8.0, 1.4 Hz, 1H), 7.83 -7.73 (m, 8H), 7.70 (d, J = 7.8 Hz, 1H), 7.61 -7.56 (m, 1H), 7.47 -7.36 (m, 8H), 2.16 -1.98 (m, 8H), 1.15 (m, 8H), 0.72 (q, J = 7.3 Hz, 20H), 0.37 (s, 9H).13 C NMR (101 MHz, CDCl3) δ = 151.3, 151.2, 151.1, 143.8, 142.5, 140.4, 140.3, 140.1, 139.6, 138.1, 137.6, 132.9, 130.9, 130.9, 129.5, 129.4, 127.9, 127.1, 127.0, 126.5, 126.4, 125.6, 123.0, 122.0, 120.9, 120.3, 120.1, 120.1, 119.9, 119.5, 106.1, 102.7, 100.1, 99.7, 94.1, 89.5, 89.3, 55.3, 55.2, 54.9, 40.3, 40.2, 31.9, 29.0, 29.1, 26.00, 23.1, 22.8, 14.2, 13.9, 0.3.

  3, 151.2, 151.1, 143.5, 142.6, 142.5, 140.4, 140.3, 139.5, 138.1, 137.6, 133.0, 131.2, 130.9, 129.5, 129.5, 128.0, 127.9, 127.1, 127.0, 126.4, 126.1, 125.6, 123.0, 120.9, 120.8, 120.3, 120.1, 119.9, 119.5, 102.9, 100.0, 99.8, 89.3, 89.2, 84.6, 55.3, 55.3, 40.3, 40.2, 29.8, 26.0, 23.2, 23.1, 14.2, 13.9. HRMS-ESI (m/z): for C62H58: m/z = 802.456 [M] +. (calcd: 802.4533). Anal. Calcd. (%) for C62H58: C, 92.72; H, 7.28.

	Found: C, 92.25; H, 7.57.

Acknowledgments

The authors acknowledge "the Ministère de l'Enseignement Supérieur et de la Recherche Scientifique de Tunisie" for PhD funding (SBH). This project was supported by the departmental committees CD35 and CD85 of the "Ligue contre le Cancer du Grand-Ouest". We also thank Olivier MONGIN and Nicolas RICHY for their help with optical measurements and discussions.


Kleinpeter Cirad

Vigne Mathieu

Cirad

Vivien Kleinpeter
email: vivien.kleinpeter@cirad.fr

Keywords: substance flow analysis (SFA), nitrogen, regional metabolism, circularity, efficiency, Reunion Island

published or not. The documents may come

Assessing the roles of crops and livestock in nutrient circularity and use efficiency in the agri-food-waste system: a set of indicators applied to an isolated tropical island

Assessing the roles of crops and livestock in nutrient circularity and use efficiency in the agri-food-waste system: A set of indicators applied to an isolated tropical island

Vivien Kleinpeter, Manon Alvanitakis, Mathieu Vigne, Tom Wassenaar,

Danny Lo Seen, Jonathan Vayssières

To cite this version:

Vivien Kleinpeter, Manon Alvanitakis, Mathieu Vigne, Tom Wassenaar, Danny Lo Seen, et al.. Assessing the roles of crops and livestock in nutrient circularity and use efficiency in the agri-food-waste system: A set of indicators applied to an isolated tropical island. Resources, Conservation and Recycling, 2023, 188, pp.106663. 10.1016/j.resconrec.2022.106663. hal-03814913

Introduction

Agri-food systems (AFS) provide multiple services to human societies: human food (and more generally food security), animal feed, bioenergy (bio-fuel, dung), animal traction for transport, leisure, cultural activities, ornamental plants, construction materials and clothing [START_REF] Willemen | Space for people, plants, and livestock? Quantifying interactions among multiple landscape functions in a Dutch rural region[END_REF][START_REF] Huang | Comparative review of multifunctionality and ecosystem services in sustainable agriculture[END_REF]FAO, 2021). However, AFS can also have negative environmental impacts resulting from the alteration of nutrient cycles. Inputs to agri-food systems require the extraction of limited resources, particularly phosphorus (P) from mines [START_REF] Liu | A high-resolution assessment on global nitrogen flows in cropland[END_REF] and non-renewable fossil energy [START_REF] Service | New recipe produces ammonia from air, water, and sunlight[END_REF]. The use of non-renewable fossil energy also results in greenhouse gas (GHG) emissions (CO2), which contribute to climate change [START_REF] Crippa | Food systems are responsible for a third of global anthropogenic GHG emissions[END_REF]. AFS are also responsible for large releases of reactive nitrogen (N) into the atmosphere, leading to N cascade effects [START_REF] Gruber | An Earth-system perspective of the global nitrogen cycle[END_REF]) (i) increasing GHG emissions (N2O) and (ii) increasing atmospheric deposition (NOx and NH3) thereby affecting the productivity, functioning and composition of natural and cultivated ecosystems, the eutrophication of terrestrial and aquatic systems (NO3-), and global acidification. Nutrients that leave the AFS through runoff and leaching may also contribute to eutrophication [START_REF] Carpenter | Nonpoint Pollution of Surface Waters with Phosphorus and Nitrogen[END_REF]. Today, the interference of human activities in N and P cycles is considered to have gone beyond planetary boundaries, i.e. beyond the safe operating space for human society to maintain the resilience of the Earth's system [START_REF] Rockström | A safe operating space for humanity[END_REF][START_REF] Steffen | Planetary boundaries: Guiding human development on a changing planet[END_REF].

Reducing the negative impacts of AFS on these nutrient cycles requires reducing the nutrient use efficiency gap of the system itself, i.e.

the gap between the current and achievable system nutrient use efficiency [START_REF] Cui | Closing the N-Use Efficiency Gap to Achieve Food and Environmental Security[END_REF]. It is with this goal in mind that van der Wiel et al. ( 2020) extended the limits of AFS to all nutrient managing activities and coined the "agro-food-waste" system, the latter being of composed of five interconnected sub-systems: crop (food) production, animal production, food and feed processing, consumption, and waste management. Based on the same reflexion, here we refer to an "agri-food-waste" system (AFWS) which combines (i) the concepts of an agri-food system (FAO, 2021) (including both food and non-food agricultural production), (ii) current connected activities in terms of material flows containing nutrients (e.g. waste management, energy production) and (iii) potential other connectable waste management activities.

By focusing on the local environmental impacts of an AFWS, without seeking to change local economic activities or human dietary habits (i.e. structural changes), the nutrient use efficiency gap of the system could be reduced by two means (i) increasing circularity between sub-systems and (ii) increasing the internal (i.e. processes) efficiency of sub-systems. These two concepts of circularity and process efficiency has not yet been considered as two separate parts of a systemic AFWS efficiency approach but are often used separately to assess or evaluate AF(W)Ss and/or their sub-systems [START_REF] Zhang | Managing nitrogen for sustainable development[END_REF][START_REF] Van Der Wiel | Restoring nutrient circularity: A review of nutrient stock and flow analyses of local agro-food-waste systems[END_REF].

In particular, circularity reflects how nutrient cycles are closed (i.e. flows circulating among the sub-systems rather than leaving the system). The immediate action that can be taken to further close the cycles, without structural changes, is recycling unused secondary products (wastes and by-products) between different sub-systems (e.g. rather than putting them in landfills or discharging them into the environment). Process efficiency reflects how the different sub-systems limit the sources of inefficiency related to their processes themselves (e.g. losses into the atmosphere). Actions that can be taken without structural changes are (i) adjusting inputs to real needs (e.g. for livestock production: adjusting feed intake to needs) and (ii) reducing losses into the atmosphere and to the sub-soil and surface water (e.g. for crop production: burying fertiliser, in-soil incorporation of manure during spreading, sustainable soil quality management).

It is important to distinguish between these two aspects (circularity and process efficiency) when assessing the roles of sub-systems in the efficiency of an AFWS as they represent two means to improve its efficiency, and thus enable a systemic multi-level understanding.

The sub-systems we chose to focus on are crops and livestock as they play critical roles in the environmental impact of AF(W)S [START_REF] Thévenot | Accounting for farm diversity in Life Cycle Assessment studies -the case of poultry production in a tropical island[END_REF][START_REF] Lassaletta | Food and feed trade as a driver in the global nitrogen cycle: 50-year trends[END_REF][START_REF] Zanten | Defining a land boundary for sustainable livestock consumption[END_REF][START_REF] Crippa | Food systems are responsible for a third of global anthropogenic GHG emissions[END_REF]. We chose to assess crops and livestock separately as they are two specific types of biophysical processes. Crop production depends on plant growth processes that differ from those involved in animal production, which depend on animal demographic and growth processes.

Among AFWS, crop and livestock production can play a negative role as they are known for their limited process efficiency [START_REF] Vayssières | Managing nutrient cycles in crop and livestock systems with green technologies[END_REF] and are sometimes responsible for unused secondary products [START_REF] Hasler | Life cycle assessment (LCA) of different fertilizer product types[END_REF]FAO, 2018;[START_REF] Walling | Greenhouse gas emissions from inorganic and organic fertilizer production and use: A review of emission factors and their variability[END_REF]. Crop production causes N losses into the atmosphere when fertiliser is spread. Croplands are also the scene of many losses to the sub-soil and to surface water due to nutrient leaching and runoff. Losses could be due to over-fertilisation, but could also depend on the quality and structure of the soil. Livestock production leads to losses into the atmosphere from both manure storage and management. Livestock manure is also sometimes misused, i.e. is spread in areas where plant needs are already covered, simply to get rid of the manure. Some manure management also consists of N denitrification thereby intentionally breaking the N cycle. Livestock feeding is also often not adjusted to the animals' real needs, resulting in more nutrients in the manure, thereby increasing the openness of the nutrient cycles.

Crop and livestock production can also play a positive role in AFWS through process efficiency and circularity. Crops are the preferred target for organic wastes, as recycling to other activities mostly requires higher levels of technology [START_REF] Harder | Recycling nutrients contained in human excreta to agriculture: Pathways, processes, and products[END_REF]. Livestock enables the recycling of secondary products that would otherwise remain unused, especially crop residues, weeds and spontaneous fodder [START_REF] Oosting | Farmed animal production in tropical circular food systems[END_REF][START_REF] Van Zanten | The role of farm animals in a circular food system[END_REF]. Livestock manure can supply organic matter for crop production, with beneficial effects on soil fertility [START_REF] Leinweber | Management effects on forms of phosphorus in soil and leaching losses[END_REF]. In many places, these practices contribute to crop-livestock integration, i.e. a combination of farming practices that favours circularity and efficiency within AFWS [START_REF] Herrero | Smart Investments in Sustainable Food Production: Revisiting Mixed Crop-Livestock Systems[END_REF][START_REF] Stark | Crop-livestock integration, from single practice to global functioning in the tropics: Case studies in Guadeloupe[END_REF].

The specific isolated roles of crop and livestock production in the nutrient use efficiency of AFWS have thus already been identified.

However, their systemic role has not yet been characterised (i) in relation to all other sub-systems that comprise the AFWS and (ii) by distinguishing circularity and process efficiency as two separate parts of the nutrient use efficiency of the AFWS.

The purpose of this paper is to propose a method with quantitative indicators to characterise the role of crops and livestock in the nutrient use efficiency of an AWFS, in terms of nutrient process efficiency and circularity between sub-systems. The proposed method is illustrated in an isolated insular context, tropical Reunion Island, and with nitrogen metabolism.

The Reunion Island AFWS is a case study of interest because, on one hand, the AFWS is based on intensive production systems and large imports of inputs, while on the other hand, the proximity of economic activities facilitates the recycling of secondary products. Also, as

Reunion Island is a well delimited region, existing databases already contain most of the necessary flow data. We chose to focus on nitrogen metabolism to illustrate one application of the method because it is intended to be applicable to all nutrients and nitrogen included losses into the atmosphere whereas phosphorus and potassium do not. Furthermore, nitrogen is a key nutrient for life and an important limiting factor in both crop and livestock production.

We assessed the current role of crop and livestock production in nutrient use efficiency in the AFWS by re-examining the use efficiency, process efficiency, and circularity concepts. These concepts needed legitimate clarification for our method. For example circularity is sometimes used as an objective (van der [START_REF] Van Der Wiel | Restoring nutrient circularity: A review of nutrient stock and flow analyses of local agro-food-waste systems[END_REF] and sometimes a means [START_REF] Tseng | Pathways and barriers to circularity in food systems[END_REF]. Nutrient use efficiency sometimes only refers to process efficiency [START_REF] Ma | Modeling Nutrient Flows in the Food Chain of China[END_REF] but is sometimes defined as a circularity indicator [START_REF] Papangelou | Assessing agro-food system circularity using nutrient flows and budgets[END_REF]. The set of indicators proposed in this paper is not specific to the crop and livestock production sub-systems, it is meant to be used to assess the role of any AFWS sub-system.

To illustrate how the method can also be used to assess the potential role of crops and livestock, i.e. to characterise the changes in the indicators depending on improvement actions, we chose to use an improvement scenario. The most relevant scenario for Reunion Island was the recycling of unused secondary products (i.e. the circularity part) as it represents ongoing multi-stakeholder dynamics in Reunion

Island [START_REF] Vigne | Une agronomie clinique et territoriale pour accompagner la transition vers une économie circulaire autour de l'agriculture : mise à l'épreuve et enseignements du projet GABiR à La Réunion[END_REF]. The scenario also offers an opportunity to identify the links between recycling actions and both circularity indicators and AFWS efficiency indicators.

In this paper, we do not consider structural changes, rather, as the first step in our reflection, we consider the actions needed to increase circularity and process efficiency in a defined economic structure. These actions (see figure 1) are logistic, organisational and technical, and should result in fewer sources of inefficiency and less imports. Implementing these actions in the short term is more realistic than implementing structural changes (e.g. changes in land use, changes in herd size). These actions apply in particular in the context of isolated islands, which raises particular questions due to the economic and environmental costs of long-distance imports. Disregarding structural changes particularly implies not accounting for a change in atmospheric inputs and local production, and in exports of primary products (types and/or quantities). Disregarding structural changes drove our choice of the groups of indicators (figure 1), in particular to define system efficiency as an objective. Importing more food instead of producing locally, or exporting more, would for example 'artificially' increase the system efficiency, but on the other hand, would externalise environmental impacts. Disregarding structural changes also drove our choice of the system, as considering structural changes could expand potential connectable activities beyond waste management.

Method

The method is based on 1) nutrient flow analysis of the AFWS, 2) selection and calculation of indicators using a detailed typology of flows, and 3) analysis of an improvement scenario based on recycling.

Nutrient flow analysis of the agri-food waste system

The AFWS consists of inputs of nutrients to plants (fertiliser), animals (feed, bedding) and humans (food) as well as upstream and downstream flows, including flows entering the system from the world market and from the atmosphere, and flows leaving the system to enter the world market, the atmosphere, the sub-soil and surface water, and landfills. The coherence of this system is based on the fact that activities undertaken inside the system are interconnected by the use or supply (or potential use or supply) of the same materials that comprise the flows of the system. The definition of the system is thus specific to the region: a type of material can be considered as potentially usable in the system in some contexts while it can be considered as not available in other contexts.

The system we studied (nitrogen flows) was quantified using nine sub-systems (table 1). The flow quantification is done over a year. The sub-systems other than crops and livestock were chosen according to their activity sector. We chose not to allocate waste management to several sub-systems based on the origin of the inputs in order to obtain a global understanding of this sector, in particular in terms of total quantity of secondary products received and supplied by the crop and livestock sub-systems. Data were collected from 2017 to 2021 either at the source through interviews (e.g. provided by the firms), or calculated based on the literature (e.g. regional studies and databases). Further details are provided in supplementary material (SM1).

Table 1: typology of AFWS sub-systems

Sub-system Description

Crops

Cropland production, which includes grassland and non-food products (e.g. flowers). Losses into the atmosphere that occur while both synthetic and organic fertiliser are being spread (including direct manure deposition by animals grazing on pasture), are allocated to this sub-system.

Livestock

Animal production (e.g. meat, milk, manure), management of the manure in stables and during manure storage. Forestry and wood processing Production and processing of wood intended for the system. Fisheries Fish production and fishing Processing and distribution of plant and animal inputs Processing and distribution of fertiliser (all imported in this group), livestock bedding (all imported in this group), livestock and pet feed. Processing and distribution of agri-food products Processing and distribution of imported food and agricultural primary products (food and nonfood)

Human living activities

Food consumption, production of urban plants (kitchen gardens, gardens and green spaces), consumption of pet feed.

Energy production

Energy production (electricity, heat, biofuel), which includes combustion and anaerobic digestion.

Waste management

Management of livestock manure off-farm (composting, drying, denitrification), treatment of animal carcasses and dead animals (shredding, incineration), processing of waste from the wood sector, wastewater treatment (denitrification), treatment of solid industrial and urban waste (shredding, composting).

Indicators

Many indicators have already been used to assess circularity and efficiency at regional level [START_REF] Corona | Towards sustainable development through the circular economy-A review and critical assessment on current circularity metrics[END_REF][START_REF] Parchomenko | Measuring the circular economy -A Multiple Correspondence Analysis of 63 metrics[END_REF]). Here we focus on complementary indicators to reveal the role played by crops and livestock in the nutrient use efficiency of an AFWS. Three groups of indicators (blue boxes in figure 1) were chosen to characterise (i) AFWS efficiency (see 2.2.1), (ii) process efficiency (see 2.2.2) and (iii) circularity between sub-systems (see 2.2.3). The indicators were defined and calculated based on a typology of 15 flows (table 2). 'Product' is used here as a generic term to refer to handled material. The production of primary products is the purpose of the activities. Secondary products are other products, i.e. wastes and by-products. Inefficiency refers here to nutrient use and not to the purpose of the process. Indeed, some processes are designed to intentionally lose nutrients, e.g. denitrification in wastewater treatment plants. The sources of inefficiency were divided in two parts, those due to the processes and those due to non-recycling (table 2). Unused secondary products (placed in landfills or discharged into the environment) were considered as inefficient due to nonrecycling. Variations in stock (i.e. storage in soils and population growth), losses into the atmosphere and losses to the sub-soil and surface water were considered as sources of process inefficiency. The stock variations correspond to the difference between the initial and the final state of the stock for a one year period.

A key point is that the nutrient use efficiency was calculated in two different ways. To assess the efficiency of the system, nutrient use efficiency was calculated for the used output products (i.e. primary products and used secondary products). In other words, considering both process inefficiency and non-recycling inefficiency as sources of inefficiency. To assess the efficiency of the sub-systems (i.e.

processes), nutrient use efficiency was calculated for the total output products (i.e. primary products, used secondary products and unused secondary products). In others words, not including the non-recycling of unused secondary products as a source of inefficiency, which made it possible to isolate the assessment of the inefficiency due to processes. The assessment of the inefficiency due to nonrecycling is itself isolated in the circularity group of indicators, where unused secondary products are sources of inefficiency. *Favourable trends are hypotheses concerning the recycling-based improvement scenario (see 2.3.).

Indicators to assess AFWS efficiency

Nutrient use efficiency has already been used as an indicator at both system and sub-system levels [START_REF] Grillot | Agent-based modelling as a time machine to assess nutrient cycling reorganization during past agrarian transitions in West Africa[END_REF][START_REF] Zhang | Managing nitrogen for sustainable development[END_REF]. Nutrient use efficiency assesses the efficiency of the use of nutrient to produce output products. It generally focuses on the production of primary products. However, in the context of nutrients flows in an AFWS, secondary products are sometimes inevitable (e.g. manure, human excrement) and we consequently consider them to be fully-fledged products. We thus defined an explicit nutrient use efficiency for the used output products (NUE-UP, equation 1) as the conversion of the total inputs (inputtot) into used output products (outputUP), i.e. to both primary products (outputPP) and used secondary products (outputUSP). The total inputs include product inputs and atmospheric inputs (i.e. atmospheric deposition and symbiotic fixation). Inefficiency includes all sources of inefficiency (SItot): due to processes and due to non-recycling (see table 2, flow n°8 to 15).

˗ 1 ˗ ˗ (eq. 1)
In order to inform the two parts of the NUE-UP regarding primary and the secondary products, we set a primary product nutrient use efficiency (NUE-UPPP, equation 2) and a secondary product nutrient use efficiency (NUE-UPSP). NUE-UPPP assesses the conversion of the total inputs (inputtot) into primary output products (outputPP). NUE-UPSP assesses the conversion of total inputs (inputtot) into used output secondary products (outputUSP).

˗ 1 (eq. 2)

˗ 1 (eq. 3)

In order inform the nature of the sources of inefficiency, the total sources of inefficiency (SItot) were divided into two parts: those due to non-recycling (SINR) (see table 2, n°8 and9) and those due to the processes (SIPr) (see table 2, n°10 to 15). The SINR rate (equation 4) and SIPr rate (equation 5) are the shares of respectively, non-recycling inefficiency (SINR), and process inefficiency (SIPr) of the total sources of inefficiency.

! "# 1 $ ! (eq. 4) $ ! % & ' % & 1 ! (eq. 5)
Even though this group of indicators was set to assess the AFWS efficiency, they were also calculated at sub-system level. Indeed, at subsystem level, it is also informative to have the total sources of inefficiency and to distinguish whether they are due to the processes or to non-recycling.

Indicators to assess process efficiency

To assess nutrient use efficiency at the sub-system level by considering only inefficiency due to the processes themselves (i.e. excluding the non-recycling of unused secondary products in the inefficiency), we chose to set a nutrient use efficiency for the total output products (NUE-TP, equation 6). NUE-TP thus assesses the conversion of the total inputs (inputtot) into total output products (outputTP), i.e.

into both primary products (outputPP) and total (used and unused) secondary products (outputSP). It should be noted that the total output products (outputTP) is not the same as the total outputs (outputtot), the latter being the sum of the total output products (outputTP) and the process inefficiency (SIPr). Overall, for the system and for each sub-system, the total input (inputtot) is equal to the sum of the total outputs (outputtot) and the stock variation.

˗(

)

1 * ˗( ˗( (eq. 6)
In order to inform the two parts of the NUE-TP regarding the primary and the secondary products (like for the NUE-UP), we set a primary product nutrient use efficiency (NUE-TPPP, equation 7) and a secondary product nutrient use efficiency (NUE-TPSP, equation 8). As all primary products are used products, NUE-TPPP does not differ from NUE-UPPP. NUE-TPSP assesses the conversion of the total inputs (inputtot) into total secondary output products (outputSP).

˗( ˗ ˗( × , rate (eq. 7)

˗( % & "# ˗( × , rate (eq. 8)
In order to inform the nature of the output products, we set the primary output product rate (OPPP rate, equation 9) and the secondary output product rate (OPSP rate, equation 10). OPPP rate is the share of the primary output products (outputPP) of the total output products (outputTP). The OPSP rate is the share of the secondary output products (outputSP) of the total output products (outputTP). In particular, it shows if the processes mainly (or only) produce primary or secondary products.

, !

) 1 , rate (eq. 9)

, !

) 1 , rate (eq. 10)

Indicators used to assess circularity between sub-systems

Cycling and recycling indexes

The cycling index is already widely used in the literature as an indicator to assess nutrient circularity at the system level and between subsystems with a delimited system boundary [START_REF] Alvarez | Whole-farm nitrogen cycling and intensification of crop-livestock systems in the highlands of Madagascar: An application of network analysis[END_REF]. Specifically, this index shows how the nutrients circulate inside the system rather than entering or leaving the system. We set the cycling index (C index, equation 11) as the proportion of total internal flows between sub-systems (IF) among the total flows (TF).

1 234!5 6 76 (eq. 11)

However, in our conceptual framework, the C index could not reach 100% as we assume no structural changes (i.e. the same exported primary products and same atmospheric inputs). To inform the maximum C index in this context, we set a theoretical maximum C index (Cmax index, equation 12). The maximum internal flows between sub-systems (IFmax) would be the sum of the current internal flows between sub-systems (IF) and the current unused secondary products (SINR) flows. The total flows would then be the sum of the maximum internal flows between sub-systems (IFmax), the minimum sources of inefficiency (SImin), the minimum import of products (IMPORTmin), the unchanged current export of products (EXPORT) and the unchanged atmospheric inputs (ATMOin). SImin is the minimum quantity of the total sources of inefficiency attainable when the quantity of internal flows is maximum. IMPORTmin is the minimum quantity of imported products attainable when the quantity of internal flow is maximum. If the atmospheric inputs (ATMOin) are lower than the export of products (EXPORT), SImin would be null. The minimum import of products (IMPORTmin) would be the difference between export of products (EXPORT) and atmospheric inputs (ATMOin). If the atmospheric inputs (ATMOin) are higher than the export of products (EXPORT), SImin would be the difference between the atmospheric inputs (ATMOin) and the export of products (EXPORT). The minimum imports of products (IMPORTmin) would be null.

18 5 234!5 6 9:; 6 9:; 9:; < = 7 9>? @A = 7 B7<= >?

(eq. 12)

where:

IFmax = IF + SINR If ATMOin < EXPORT then SImin = 0 and IMPORTmin = EXPORT -ATMOin If ATMOin > EXPORT then SImin = ATMOin -EXPORT and IMPORTmin = 0
In order to assess the quantity of secondary products that are part of the internal recycling routes among the total flows of secondary products, we set a recycling index (R index, equation 13). The R index is the share of locally used secondary products, i.e. the internal flows of secondary products between sub-systems (SPFint), among the total flows of secondary products (SPFtot).

C 234!5 6 >?

6

(eq. 13)

Origins and destinations of the recycling routes

To assess whether a sub-system is a receiver and/or a supplier of secondary products from the perspective of the system, we defined two indicators to show the origins and destination of the recycling routes (i.e. flows of internal used secondary products within the system).

The recycling destination rate (Rdest rate, equation 14) is the proportion of internal secondary products flows going to a sub-system (SPFint to the sub-system) of the total internal flows of secondary products (SPFint). The recycling origin rate (Rorig rate, equation 15) is the proportion of internal secondary product flows coming from the sub-system (SPFint from the sub-system) of the total internal flows of secondary products (SPFint).

C DEF !

6 >? GE F H˗FIF EJ 6 >?

(eq. 14)

C $ K ! 6 >? L$ J GE F H˗FIF EJ 6 >?

(eq. 15)

Recycling of the outputs and inputs of the sub-systems

In order to assess whether secondary products are recycled at the sub-system level or not, we set an output recycling rate (Rout rate, equation 16) as the proportion of the output of used secondary products (outputUSP) of the total output of secondary products (outputSP).

C ! (eq. 16)

To assess to what extent a sub-system uses secondary products among its inputs, we set the input recycling rate (Rin rate, equation 17) as the proportion of inputs of secondary products (inputSP) of the total inputs (inputtot). Due to the presence of favourable atmospheric inputs, the Rin rate had no favourable trend in certain sub-systems (in particular crop production). We thus set as a complementary indicator, an input products recycling rate (PRin rate, equation 18) as the proportion of inputs of secondary products (inputSP) of the total input products (inputP). The calculation of the share of inputs according to type is widely reported in the literature on crop production [START_REF] Lassaletta | Nitrogen use in the global food system: past trends and future trajectories of agronomic performance, pollution, trade, and dietary demand[END_REF][START_REF] Van Der Wiel | Restoring nutrient circularity in a nutrient-saturated area in Germany requires systemic change[END_REF].

C ! (eq. 17)

C ! (eq. 18)

Exploring recycling-based improvement scenarios

The proposed scenario is an illustration of one among other possible actions (figure 1) that may increase AFWS efficiency. The action affects one of the two means, i.e. increasing the circularity between sub-systems.

Scenario

Today, stakeholders in Reunion Island are willing to move towards a "zero biowaste" agenda (MTES, 2018) ), and are proposing actions aimed at recycling all unused secondary products. To explore (i) what gain these actions would represent relative to the nutrient use efficiency of the total system and (ii) what role crops and livestock could play, we chose to test a scenario comprising recycling of the unused secondary products through crops and livestock.

Exploratory steps

i) We considered the hypothesis that the nitrogen present in the unused secondary products could theoretically replace the nitrogen in imported products used for crop or livestock production (fertilisers, growing medium, feed and animal bedding). The unused secondary products were characterised according to their potential use for crop and/or livestock production. To give an obvious example, sewage sludge cannot be used as animal feed.

ii) The amounts of mobilizable N were then compared to the N contained in imported products used for the same purpose. For example, 10 tons of nitrogen newly recycled to fertilise crops would replace 10 tons of nitrogen imported as fertiliser. Note that a substitution rate higher than 100% means that all unused secondary products could not be recycled. For example, if the N in imported fertiliser were lower that the N in the newly mobilizable fertiliser (which was not the case in this study).

iii) Finally, nitrogen flows of unused secondary products are reoriented and the corresponding quantity in imported products is reduced.

Hypothesis concerning modifications in the AFWS nutrient metabolism

In addition to no structural changes in the system, potential modifications of AFWS nutrient metabolism that may occur in the scenario are related to other working hypotheses:

• in our conceptual framework, the imported products intended for crops and livestock first go to the sub-system of the processing and distribution of plant and animal inputs before going to the crop and livestock sub-systems,

• no process inefficiency of the substituted nitrogen occurs in the feed processing and distribution sub-system,

• emission factors remain unchanged, i.e. losses into the atmosphere during manure spreading on the land, leaching and runoff,

• unused secondary products could be used directly without passing through other sub-systems (e.g. waste management),

• the scenario would thus result in a decrease in local primary products equal to the reduction of imported products.

Case study

Reunion Island is a French island located in the Indian Ocean. Like other tropical islands, Reunion Island has a high human population (342 inhabitants/km 2 ), and which is increasing by +0.5% per year, thereby fuelling two conflicting dynamics: increasing need for food and decreasing availability of croplands due to urban sprawl [START_REF] Insee | Insee Flash La Réunion[END_REF]. Under the pressure of both resources and limited land, in the past, Reunion Island made the decision to import human food and at the same time, to establish high-input crop and livestock production systems that rely on imports of synthetic fertilisers and raw materials for animal feed. Croplands (41 940 ha) are mostly export-oriented:

54% is used to grow sugarcane almost entirely for export of sugar, 29% is grassland (grazing and production of hay and grass silage), intended for the local livestock production, and 13% is dedicated to fruit and vegetable production, mainly destined for the local market (DAAF La Réunion, 2020). Local production covers 40% of the local demand for meat, 100% of the demand for eggs, and 70% of the demand for fruit and vegetables. The context of Reunion Island with a small export to import ratio is also found in other isolated islands [START_REF] Bahers | Vulnérabilité métabolique et potentialités des milieux insulaires[END_REF][START_REF] Singh | Sociometabolic risk and tipping points on islands[END_REF]. It should be noted that nutrient cycles in Reunion Island have some specificities due to the prevailing humid tropical conditions [START_REF] Vayssières | Managing nutrient cycles in crop and livestock systems with green technologies[END_REF]. More nitrogen losses into the atmosphere are likely to occur due to high temperatures and more run-off caused by more intense rainfall events. and stock variations (4.b) according to the sub-system (see table 1). For the island, share of the inefficiency according to the sub-system (4.c): regarding total inefficiency (SItot), process inefficiency (SIPr) and non-recycling inefficiency (SINR).

Results

2a. Detailed diagram of the AFWS nitrogen flows, including internal flows between sub-systems 2b. Synthetic "black-box" diagram of the AFWS with aggregated nitrogen flows

The AFWS in Reunion Island

This section provides an overview of the nitrogen use efficiency at the level of the AFWS. A distinction is made between its two parts:

process efficiency and circularity.

AFWS use efficiency

Annual inputs into the AFWS in Reunion Island represent about 17 000 tons of nitrogen (tN) (figure 1). The N inputs consisted of products imported from the world market (96%), symbiotic fixation (3%) and atmospheric deposition (2%) and imports from the ocean provided by local fisheries (0.3%) (figures 3.a. and 4.a.). Most of the imports from the world market were intended for human consumption (5 500 tN), or animal feed (5 000 tN), and for fertilisation (5 000 tN). The nutrient use efficiency in Reunion Island was 0.7% (NUE-UP table 3).

About 100 tN were exported annually. Exported products were only primary products: mainly sugar cane and some fruit and vegetables.

Process efficiency and circularity

Total AFWS inefficiency was mainly due to process inefficiency (86%) rather than to non-recycling of secondary products (14%) (SIPr rate and SINR rate table 3).

Within process inefficiency, we mainly found unintentional atmospheric emissions (39%, e.g. when spreading fertiliser on land), stock variations in the soil (28%), and secondary products in landfills (12%, e.g. urban biowastes) (figure 3.c). Among the sources of nonrecycling inefficiency, we found unused secondary products in landfills represented 83% and unused secondary products discharged into the environment represented 17% (figure 3.e.). These non-recycled flows represented 13% of the total flows of secondary products, meaning 87% of the flows of secondary products are recycled (R index table 3).

Considering total flows, the circularity of the current Reunion Island AFWS was assessed at 52% of internal flows between sub-systems (i.e. flows between sub-systems represent 52% of the total flows of the system studied) (C index table 3). Also, with no changes in atmospheric inputs and in the production of primary products, we could set a theoretical maximum C index at 95% (Cmax index table 3).

Crops and livestock within the AFWS

Analysis of the share of the sub-systems in the nutrient use efficiency of the system (the objective)

The sources of inefficiency originating from crops and livestock explained 51% (42% from crops and 9% from livestock, respectively) of the total sources of inefficiency of the AFWS (figure 4.c.). Crops and livestock were not responsible for non-recycling inefficiency (figure 3.a. and 4.c.). The main sources of non-recycling inefficiency were waste management (43%) and human living activities (38%). Crops and livestock were responsible for respectively 49% and 10% of the sources of process inefficiency of the AFWS (figure 4.c.). The second main source of process inefficiency after crops was waste management (31%).

Analysis of the efficiency of sub-system processes (one of the two means to reach the objective).

Crop process efficiency was 37% (NUE-TP table 3). The main crop productions were primary products, which accounted for 95% of total production (OPPP rate, table 3), the great majority represented by N in fodder and sugar cane. The secondary crop products were crop residues and spontaneous fodder used as animal feed. Crop process inefficiency was mainly due to the accumulation of surplus nitrogen in soils, i.e. stock variation in soils (54.6%), and unintentional losses into the atmosphere from the soil and while spreading fertilisers (33.6%) (figure 3.c.). The remaining 11.8% were represented by on-soil leaching and runoff. Crop process efficiency was the second lowest process efficiency after the waste management, which had an NUE-TP of 36%.

Livestock process efficiency was 81% (NUE-TP table 3). The main output products were secondary products, i.e. manure (81% of total production) (OPSP rate, table 3). Livestock process inefficiency was only due to unintentional atmospheric nitrogen emissions from the manure in the stables and during storage (figure 3.d. and 3.e.). It should be noted that 4% of waste management inputs originated from livestock, in the form of off-farm manure management (i.e. composting and denitrification processes). The process efficiency of this offfarm manure management was 72% (NUE-TP, table 3).

Analysis of circularity between sub-systems (one of the two means of reaching the objective).

Recycling destinations

Among the total local recycling routes in the AFWS (i.e. internal secondary product flows), respectively 41% and 1.8% went to the crop and the livestock sub-systems (Rdest rate Recycling routes also reached livestock through the feed industry, as local secondary products represented 3% of the feed industry input flows, e.g. molasses (Rin rate table 3).

Recycling origins

Of the total local recycling routes in the AFWS, respectively 1% and 31% originated from crops and livestock (Rorig rate table 3). Livestock played the second highest recycling supplier role after waste management, which had a Rorig rate of 32%. At the sub-system level, 100%

of the secondary products produced by crops and livestock were recycled (Rout rate table 3). The sub-system with the lowest recycling rate of secondary production was waste management, which had a Rout rate of 59%.

Improvement of the AFWS use efficiency through recycling

This part presents the results of the recycling-based improvement scenario. Unused secondary products represented about 2000 tN per year. The majority of these products were sewage and sewage sludge (41%), urban biowaste (34%) and industrial biowaste (18%). Their current destinations were landfills (83%) and sub-soil and surface water (17%). Unused secondary products consisted of food industry processing residues, food distribution losses, household food waste (including uneaten food), ashes and animal tissues from slaughterhouse waste management, sewage sludge and urban green waste. Technically, these products could be used as crop fertiliser.

They were not usable or meant to be used for livestock production. They represented 63% of N inputs from total crop primary products.

According to the hypothesis concerning direct substitution of primary products by these non-recycled secondary products, the proportion of secondary products among crop inputs would increase from 58% to 80% (Rin rate table 3). The share of the secondary products among crop input products would increase from 63% to 86% (PRin rate table 3). The share of primary products among the crop inputs would decrease from 38% (figure 4.a) to 13% (data not shown).

At the AFWS level, the efficiency of the island AFWS would increase from 0.7% to 0.8% (NUE-UP table 3), i.e. representing an increase of +14%. The cycling index would increase from 52% to 56% (C index table 3), i.e. representing an increase of +8%. Imports would be reduced by -15%. It should be noted that self-sufficiency in human food would not change.

Discussion

Roles of crops and livestock in AFWS nitrogen use efficiency

Current role of crops and livestock

Their roles in Reunion Island

The recycling receiver role of crops in Reunion Island does not seem surprising as 63% of the secondary products used by activities other than waste management are or originate from manure and sewage plant sludge, which are directly (or indirectly after energy production) only recyclable on the land. The context in Reunion Island appears to be special, with a high proportion of nitrogen from secondary products among N inputs to crops (i.e. 58%, 38% for manure alone), whereas at the scale of the world, for example, Lassaletta et al.

(2016) found 33% of secondary products that only consisted of manure. This suggests that crops in Reunion Island play a specific role in recycling secondary products originating from other activities than livestock (waste management, food-feed industries and energy production). It should be noted that land use is oriented towards the production of sugar, which contains almost no nitrogen. Nitrogen from sugarcane is thus almost entirely found downstream in secondary products. The part going to livestock (i.e. molasses) is very small compared to the part transferred to croplands.

For grasslands alone, N inputs correspond to 73% of manure, 25% of synthetic fertiliser and 2% of atmospheric inputs. For other croplands, N inputs correspond to 52% of secondary products (26% for manure alone), 38% of synthetic fertiliser and 10% of atmospheric inputs, whereas at the global scale, [START_REF] Lassaletta | Nitrogen use in the global food system: past trends and future trajectories of agronomic performance, pollution, trade, and dietary demand[END_REF] found respectively, 16% (manure only), 59.5% of synthetic fertiliser and 24.5% of atmospheric inputs.

In regions with a much higher ratio of crop to livestock production, the recycling receiver role of crops was found to be less important.

For regions in France with an "intensive cropping system" Le Noë et al. ( 2017) found 69% of synthetic fertiliser, 17% of atmospheric inputs, 13% of manure and 1% of urban sludge, whereas in regions with an "intensive specialised livestock system", the same authors found 39% of synthetic fertiliser, 13% of atmospheric inputs, 47% of manure and 1% of urban sludge. Livestock-versus crop-dominated agricultural regions can thus offer opportunities to create circularity between sub-systems and reduce dependency on imported synthetic fertiliser, however in these regions, lower process efficiency values were also often found for crops [START_REF] Le Noë | How the structure of agro-food systems shapes nitrogen, phosphorus, and carbon fluxes: The generalized representation of agro-food system applied at the regional scale in France[END_REF][START_REF] Svanbäck | Reducing agricultural nutrient surpluses in a large catchment -Links to livestock density[END_REF][START_REF] Swaney | Nitrogen use efficiency and crop production: Patterns of regional variation in the United States, 1987-2012[END_REF].

Only a few studies used a comparable systemic scope of the AFWS and included waste management, the food-feed industry and/or energy production in their nitrogen flow analysis. For the Flanders and Wallonia regions of Belgium [START_REF] Papangelou | Assessing agro-food system circularity using nutrient flows and budgets[END_REF] found that respectively, 3% and 2% of the crop N inputs came from secondary products other than manure, while van der [START_REF] Van Der Wiel | Restoring nutrient circularity in a nutrient-saturated area in Germany requires systemic change[END_REF] found 8% for the German state of North Rhine-Westphalia.

The N use efficiency of crops we found (NUE-TP, 37%), is close to the mean found by [START_REF] Zhang | Managing nitrogen for sustainable development[END_REF] for India (30%), other Asian countries (41%) and the world (42%), and by [START_REF] Ma | Nitrogen and phosphorus use efficiencies and losses in the food chain in China at regional scales in 1980 and 2005. Science of The Total Environment, Climate Change and Macronutrient Cycling along the Atmospheric, Terrestrial, Freshwater and Estuarine Continuum -A Special Issue dedicated to Professor Colin Neal[END_REF] for China (35%).

The recycling supplier role of livestock in Reunion Island is not surprising as livestock raising is the activity which consumes the largest amount of nitrogen (as indicated by the size of the livestock box in figure 2), and knowing that it mainly produces N in secondary products rather than in primary products (OPSP rate, 81%). Livestock's very low recycling receiver role is also not surprising in a region where few crop residues and industrial secondary products are meant to be used by livestock. Concerning the primary product N use efficiency of livestock (NUE-TPPP, 16%), [START_REF] Billen | A biogeochemical view of the global agro-food system: Nitrogen flows associated with protein production, consumption and trade[END_REF] reported a similar result at the scale of North America (17%) and Europe (16%).

Concerning the share of crops and livestock among the total sources of inefficiency for N (51% in our study), [START_REF] Firmansyah | Assessment of nitrogen and phosphorus flows in agricultural and urban systems in a small island under limited data availability[END_REF] found 68% for the "urban-agricultural system" of the tropical island of St. Eustatius. These authors also found a system efficiency (NUE-UP) of 0.9%, which is close to that of our study (0.7%).

Different roles depending on the conceptual framework

A change in the conceptual framework could result in different perspectives regarding the importance of the role played by crops and livestock.

First, activities are sometimes allocated to sub-systems differently, in particular grasslands, which are often considered as a sub-system of the livestock sector (Gerber and FAO, 2013). In our results, grasslands (i) received manure and (ii) are the scene of losses through leaching and runoff. In this case, allocating grassland to livestock activities would (i) reduce the efficiency of the livestock process and (ii) reduce its recycling supplier role. The indicators would also reveal a reduced receiver role for crops as 57% of the manure goes to grasslands.

Second, our conceptual framework targets the AFWS NUE-UP at the level of a region. Life cycle thinking is a possible complementary approach to the analysis of nutrient flows, with the aim of increasing the NUE-UP at supply chain level. In yet another approach, Harder et al. ( 2021) suggest including "external sub-system components" in the analysis. In line with this approach, Koppelmäki et al. ( 2021) also suggest considering "nested circularity" in which "nutrient, biomass and energy cycles are connected and closed across multiple spatial scales". In our study, using a life cycle thinking approach would increase the recycling receiver role of livestock. This is because (i) some primary products in the system are manufactured upstream using local secondary products (3% of inputs to the feed industry), and (ii) some imported products destined for livestock are secondary products (e.g. soybean meal as a component of feed). Considering all the upstream and downstream livestock flows, the quantity of sources of inefficiency would be further increased. Locally it would consist of losses into the atmosphere originating from manure management (e.g. composting) and spreading on local land. Outside the system, it would include all sources of inefficiency due to the production of imported feed and bedding. In our study, no secondary products originating from livestock raising are exported. In the case of Reunion Island, a life cycle thinking approach would not change the role of crops. Nearly all the imported crops inputs are primary products and originate from imports of synthetic fertiliser.

Uncertainties

Although the focus of the paper is on the conceptual framework for defining indicators, we should be aware of the uncertainties associated with their calculation. Each variable used in the calculation of an indicator comes with its own level of uncertainty. The uncertainty of each indicator thus results from the aggregation of the uncertainties of the variables associated with it. In our study, the input and output product flows were quantified using data from local databases and surveys, with limited uncertainties. However, uncertainties are higher for the respective share of the different sources of process inefficiency (atmospheric emissions, storage in soils, run-off and leaching) as they are determined through emission factors established under tropical conditions similar to those of Reunion Island but mostly not locally measured and known to be strongly influenced by a range of locally varying conditions. Thus, the indicators calculated with the input and output product flows can be considered as reliable information, which is the case for all indicators presented in table 3 (eq. 1 to 18). The least reliable information is the share of the different components of the process inefficiency presented in figure 3.b, 3.c and 3.d. The latter uncertainties could be decreased by producing and using locally measured emission factors taking into account the diversity of practices and pedo-climatic conditions met [START_REF] Rosenstock | Toward a protocol for quantifying the greenhouse gas balance and identifying mitigation options in smallholder farming systems[END_REF].

Potential roles of crops and livestock

Circularity

The scenario we studied consisted of recycling unused secondary products in crop and livestock production. It revealed a specific role for cropland as a potential destination. However, it also showed that the limiting factor for recycling to land is land availability. Indeed, if the N in unused secondary products had been twice as high, it would be impossible to recycle all the N, as it would have been more than the amount of N synthetic fertiliser imported. For livestock, the limiting factor was the type of secondary product to be recycled, i.e. some secondary products cannot be used as feed, either directly or after being mixed with other secondary products that cannot be used as feed. However, solutions such as the collection at source of leftover food should be considered [START_REF] Pinotti | Recycling food leftovers in feed as opportunity to increase the sustainability of livestock production[END_REF].

Process efficiency

Process efficiency is another means to increase AFWS efficiency. Levers differ according to the type of activity. For crops and livestock sub-systems, we need to increase the primary product nutrient use efficiency (NUE-TPPP), in particular by better adjusting inputs to

needs. An increase of the secondary product nutrient use efficiency (NUE-TPSP) would increase circularity but not necessarily AFWS efficiency. For waste management, we need to increase the secondary nutrient use efficiency (NUE-TPSP) as inputs and outputs are only secondary products.

Complementarity of efficiency and circularity concepts and corresponding indicators

A relevant conceptual framework and indicators for studying the metabolism of other substances

Our study focused on nitrogen metabolism but the indicators can be used for phosphorus (P) and potassium (K) in addition to nitrogen.

The conceptual framework could also be used to study the energy and carbon use efficiency of the AFWS [START_REF] Vigne | Flux d'énergie dans des systèmes d'élevage laitiers contrastés: Elaboration d'indicateurs et analyse de la diversité inter et intra-territoire[END_REF]. This would be advantageous as we know it is useful to consider N, P and K nutrients together (van der [START_REF] Van Der Wiel | Restoring nutrient circularity: A review of nutrient stock and flow analyses of local agro-food-waste systems[END_REF]. In particular, we are aware that these results are strongly influenced by the typical losses of N into the atmosphere. In the case of P, for example, process inefficiency would only consist in stock variation, leaching and runoff.

However, for both nutrients and carbon, it is important to note that a positive stock variation could be a beneficial 'inefficiency'. For example, we do not necessarily aim to prevent population growth. Also, increasing carbon stocks helps mitigate climate change [START_REF] Paustian | Climate-smart soils[END_REF][START_REF] Minasny | Soil carbon 4 per mille[END_REF]. Conversely, a negative stock variation of nutrients in soils could challenge the sustainability of the system, as nutrients would possibly run out. This highlights the fact that AFWS nutrient use efficiency indicators will, in many decisionmaking contexts, inform a multi-criteria analysis that includes additional indicators. The problem of GHG emissions is particularly important, knowing that more recycling would probably decrease international transport but require more local transport, thereby rendering the GHG balance uncertain.

Different indicators to distinguish means and objective

The case of Reunion Island illustrates the need to avoid considering efficiency at AFWS level alone. A more comprehensive understanding of the sources of inefficiencies is obtained by adding two other groups of indicators: the efficiency considering the total output products (i.e. to assess process efficiency) and circularity between sub-systems (including the origins and destinations of nutrient flows for each sub-system).

These two supplementary groups of indicators need to be analysed together. Firstly, because increasing process efficiency and circularity individually does not necessarily increase AFWS efficiency. Secondly, because no relational trend can be established between process efficiency and circularity. For example, in our illustration using the AFWS of Reunion Island, livestock process efficiency could be improved by better adjusting inputs to real needs at herd level. This could result in less nitrogen in the manure and hence less losses into the atmosphere from stabling and manure storage. These reduced losses mean increased efficiency at the process level. It would also mean increased efficiency at the AFWS level. However, at the system level, local circularity would be reduced, as fewer secondary products would be circulating.

Different indicators to distinguish different levers

In addition to assessing the current and potential role of crops and livestock, the distinction between circularity, process efficiency, and system efficiency was also useful to characterise the AFWS nutrient metabolism. It allowed us to distinguish the part of the system inefficiency that is due to the non-recycling of unused secondary products and that due to the processes. In Reunion Island, for nitrogen, we found that the system inefficiency is more due to process inefficiency than to non-recycling of secondary products. From a practical point of view, this makes it possible to determine whether the cause of the inefficiency is due to "intra-activity" individual practices or to "inter-activity" organisational factors (e.g. logistics). It suggests that in Reunion Island actions should focus on increasing process efficiency (e.g. by limiting nitrogen losses into the atmosphere) in order to increase system efficiency.

Conclusion

Considering (i) system efficiency, (ii) process efficiency and (iii) circularity indicators together made it possible to characterise the roles played by crops and livestock in the nutrient use efficiency of an agri-food-waste system (AFWS). The indicators are complementary and this paper suggests that they should be used together to provide the comprehensive understanding required for sound policy guidance.

The system efficiency group of indicators allowed us to assess the objective at regional level. The process efficiency group of indicators allowed us to assess the roles linked to the processes themselves. The circularity group of indicators allowed us to assess the roles linked to circularity between sub-systems. The paper also suggests that process efficiency and circularity should not be seen as objectives but as two means for improved nutrient use efficiency at the AFWS level.

In the AFWS of Reunion Island, our results point to a recycling receiver role for crops and a recycling supplier role for livestock. We also found higher process efficiency for livestock than crops. The recycling-based scenario we explored revealed a potential role of crops in improving AFWS efficiency, in particular by substituting imported synthetic fertilisers with secondary products that are currently not used. However, although not explored here, other options involving process efficiency and/or structural changes (e.g. changes in land use, or changes in human dietary habits), may even have more impact on AFWS efficiency.

This conceptual framework was tested in an isolated island territory. Other contexts should now be considered, for example studying AFWS with contrasted crop or livestock orientations and/or contrasted proportions of secondary products originating from waste management and the food-feed industry.

Figure 1 :Table 2 :

 12 Figure 1: Actions, means, objective and their corresponding indicators. The objective refers to the assessment of a system when tending to have the least negative environmental impacts resulting from changes in the nutrient cycles. We assume a system with no structural changes.

Figure 2 :

 2 Figure 2: Nitrogen flows (in tons N/year) in the agri-food-waste system (AFWS) of Reunion Island. The size of the arrows is proportional to the importance of N flows and the size of the sub-system boxes is proportional to the total N inputs of the sub-systems. FW = forestry and wood processing. EP = energy production. ∆S = stock variations. pop. = population.

Figure 3 :

 3 Figure 3: For Reunion Island, crop and livestock levels, share of inputs (inputtot) (3.a), outputs (outputtot) and stock variation (3.b), total inefficiency (SItot) (3.c), process inefficiency (SIPr) (3.d) and non-recycling inefficiency (SINR) (3.e) according to the type of flow (see numbers in table 2). Quantitively, for each level, the inputs (3.a) are equal to the outputs and the stock variations (3.b). Quantitatively, for each level, total inefficiency (3.c) is equal to the sum of process inefficiency (3.d) and non-recycling inefficiency (3.e).

Figure 4 :

 4 Figure 4: For Reunion Island, crop and livestock levels, share of the input (intputtot) origins (4.a) and the destination of outputs (outputtot)

Table 3 :

 3 Indicators of nitrogen use efficiency considering the used output products, nitrogen use efficiency considering the total output products and nitrogen circularity between sub-systemsValues in brackets represent the potential if the recycling-based scenario were applied (see2.3 )

	System

  table 3). Crops played the second highest recycling receiver role after waste management, which

had a Rdest rate of 44%. At the sub-system level, local secondary products represented 58% of the crop input flows (Rin rate table 3).

Primary products (almost entirely imported synthetic fertiliser) and atmospheric inputs accounted for respectively 34% and 8% of the crop input flows (figure 4.a). Considering only input products (i.e. not including atmospheric inputs), local secondary products accounted for 63% of crop input flows (PRin rate table 3). Local secondary products represented 4% of livestock input flows (Rin rate table 3).

exported used secondary products -8 losses of unused secondary products -landfill 9 losses of unused secondary products -discharged into the environment 10 losses into the atmosphere -intentionally -11 losses into the atmosphere -unintentionally -12 losses to sub-soils and surface water -intentionally -13 losses to sub-soils and surface water -unintentionally -Variations in stock within sub-systems 14 variation in stock -storage in soils -15 variation in stock -population growth -