Adriana C Mera

Yanko Moreno

Jean-Yves Pivan

Octavio Peña

Héctor D Mansilla
email: hmansill@udec.cl

Solvothermal synthesis of BiOI microspheres. Effect of the reaction time on the morphology and photocatalytic activity

Keywords: BiOI, caffeic acid, microspheres, photocatalyst, solvothermal synthesis, UV-

BiOI microspheres were synthesized by a solvothermal synthesis route from Bi(NO 3 ) 3 . 5H 2 O, using ethylene glycol in the presence of the ionic liquid 1-buthyl-3-methylimidazolium iodide.

The autoclave temperature was maintained constant at 120 °C and the reaction time was varied from 2 to 48 hours. The obtained materials were characterized by XRD, SEM, TEM, EDS, nitrogen adsorption, FTIR and DRS. In addition, the photocatalytic activity of synthesized BiOI was evaluated in the oxidation of caffeic acid under simulated solar irradiation. Samples obtained between 12 and 24 h of synthesis present microsphere shapes and higher photocatalytic activity. All materials exhibit higher activities than TiO2 Evonik P25 used as standard catalyst.

A c c e p t e d M a n u s c r i p t

Introduction

Selected metal oxides have been used for photocatalytic applications due to their low cost and high stability in aqueous solution [1,2].Among them, titanium dioxide and zinc oxide are the most mentioned in the literature for water and air purification testing [3][4][5]. Titania Evonik P25 presents strong oxidizing power, chemical and biological inertness, high stability to photocorrosion in the entire pH range and low cost. On the other hand, ZnO with high photocatalytic activity, photo-corrodes at alkaline pH [6]. However, the main drawback of both catalysts is associated to the large band gap (3.2 eV), which demand activation in the ultraviolet region of the spectra (λ <390 nm). This significantly limits the efficiency under sunlight, which accounts only for 3-5% below 390 nm wavelength. In addition, their high rates of electron-hole pairs recombination provoke a low efficiency in the photocatalytic process [7].Several researches have been done preparing new catalyst or modifying titania or ZnO in order to overcome these limitations [8][9][10][11]. The possibility to control structural features has become an interesting challenge in order to synthesize new materials with specific properties to be applied in environmental catalysis. For instance, hierarchical nanostructures based on bismuth oxyhalides (BiOX) have been proposed as new materials for photocatalysis due to their activity in the visible region of the spectra [12][13][14]. Structurally these materials present tetragonal systems (matlockite-like structure) with Bi 2 O 2 layers interleaved with two halogen atoms [15].

Particularly, bismuth oxyiodide (BiOI), presenting microsphere morphology, has provoked great interest in heterogeneous photocatalysis because it shows high photocatalytic activity under visible radiation and high degradation yields of a wide class of organic compounds, such as methylene blue, phenol, methyl orange, rhodamine B and sodium pentachlorophenate [16,17].

In addition, it has been reported that BiOI microspheres show higher photoactivity than titanium dioxide Evonik P-25 in the visible range [18][19][20].

The solvothermal synthesis has been described as the most suitable methodology for BiOI microspheres preparation. The solvothermal conditions, involving high temperature and pressure, modify the physicochemical behavior of the solvent, such as the dielectric constant. In A c c e p t e d M a n u s c r i p t 3 consequence, using this methodology it is possible to obtain compounds which under normal conditions of pressure and temperature, cannot be obtained [21].The aim of the present work is to synthesize BiOI under solvothermal conditions controlling the reaction time. The materials obtained were characterized and their photocatalytic activity measured on caffeic acid solutions. This compound was chosen as a representative phenol structure present in several agro industrial wastes such as winery wastewaters [22].

Experimental

Sample preparation

The synthesis of bismuth oxyiodide (BiOI) was performed using a solvothermal method. All reagents were of analytical grade (AR) and used as received. An ethylene glycol solution (20 mL, Acros, 99%), containing 1 mmol of the ionic liquid 1-buthyl-3-methylimidazolium iodide

[bmim]I (Sigma-Aldrich, 99.0%) was added slowly to 1 mmol of Bi(NO 3 ) 3 . 5H 2 O (Sigma-Aldrich, 99.9%) dissolved in ethylene glycol. The mixture was magnetically stirred at room temperature for 30 minutes and then transferred to a 25 mL Teflon-coated Parr ® steel autoclave.

The autoclave temperature was raised to 120 °C. Reactions were stopped at 2, 6, 12, 24, 30 and 48 h. Once each reaction was completed, the autoclave was cooled to room temperature. The products were separated by vacuum filtration and thoroughly washed using distilled water and absolute ethanol (Carlo Erba, 99.9%). Finally, the materials obtained were dried at 60 °C during 48 h in a forced air furnace.

Characterization

The crystalline structure of BiOI powder was studied by X-ray diffraction (XRD) performed in a Bruker D8 diffraction system with Cu Kα radiation (λ = 1.5406Å) in a 2-theta scan range of 10-80°. The surface morphology was determined by scanning electron microscopy (SEM) in a JEOL instrument operated at 20 kV and using a JSM-6400 computational system. Additionally, A c c e p t e d M a n u s c r i p t 4 transmission electron microscopy (TEM) using a JEOL JEM 1200 EX-II operated at 120 kV was recorded for synthesized samples. Energy dispersive X-ray spectroscopy (EDS) was performed with a JSM-6380 LV equipment operated at an accelerating voltage of 10 kV. The surface area of the materials was determined by adsorption-desorption isotherms using nitrogen at 77K and Brunauer-Emmett-Teller analysis (BET). The pore size distribution was determined though desorption isotherm applying the Barret-Joyner-Halenda method (BJH) and using TriStar II Micromeritics surface Area and Porosity analyzer. The FTIR spectra were obtained using a spectrometer IR Nicolet Nexus with Fourier transform. The diffuse reflectance spectrum (DRS) was obtained using a spectrophotometer Precisely Perkin Elmer Lambda 35 UV/Vis with integrating sphere.

Photocatalytic activity

The photocatalytic activity of synthesized materials was measured following the degradation of caffeic acid. Reactions were performed in the experimental set-up schematized in Figure 1. It consists of a 300 mL flask refrigerated by tap water. The lamp (Xe VIPHID 6000k, 12 W) was placed inside the reactor protected by a borosilicate closed cylinder. The lamp emission ranged between 380 and 900 nm with a spectrum similar to solar irradiation. Synthesized catalysts and TiO 2 Evonik P25 (25 mg each) were added to a caffeic acid solution (250 mL, 10 mg L -1 ) and magnetically stirred in dark during 20 min to reach the adsorption equilibrium. After that, the lamp was turned on and solution maintained under magnetic stirring. Samples were taken each 20 min and filtered on a nitrocellulose membrane (Millipore, 0.22 μm) for analysis. The remaining caffeic acid in solution was quantified measuring the absorption at 312 nm in a Shimadzu UV-1601 PC spectrophotometer and comparing it with a calibration curve done with a standard (Sigma Aldrich 97%). Mineralization of samples was determined by total organic carbon (TOC) analysis (Shimadzu TOC-V CPH/CPN).

A c c e p t e d

M a n u s c r i p t 5

Results and discussion

SEM and TEM analysis

In the reaction of bismuth nitrate and ionic liquid [bmim]I in the presence of ethylene glycol, hierarchical microspheres can be formed [23]. In this system, the ionic liquid plays two roles: first, is a source of iodide and second, it acts as a template agent [18]. Also, experiments using KI as iodide source were carried out. Since the shape of these materials were less spherical and present lower surface area and photocatalytic activities are not discussed here. In this work all the solvothermal synthesis of BiOI were conducted at the same temperature (120 ⁰C) varying only the reaction time (2, 6, 12, 24, 30 and 48 h). Figure 2 depicts the SEM images showing the morphology of the products obtained at different reaction times. It can be seen that structured microspheres are formed even at short periods of reaction (2 h) obtaining the most regular forms between 12-30 h (Figures2c-e). At higher reaction times (48 h) some disaggregation of the microspheres can be observed (Figure 2f). The average microspheres size obtained was approximately between 4-5 μm. The SEM images confirm that BiOI materials are constituted by spheres formed by irregular nanosheets connected between them and forming hierarchical microspheres. A verification of this can be observed in Figure 3a where the nanosheets are clearly shown. The composition of the material is confirmed by the EDS analysis shown in Figure 3b. Only bismuth, iodine and oxygen are evidenced in all the synthesized material. TEM images shown in Figure 4 verify the nanosheet structure of microspheres.

Adsorption-desorption analysis

The pore size distribution was determined by the Barret-Joyner-Halenda (BJH) method. The BJH isotherm shown in Figure 5 describes the N 2 adsorption-desorption profiles of the synthesized materials. All the samples exhibit irreversible type IV adsorption isotherms with an H3 hysteresis loop confirming the mesopore structure [24]. All samples exhibited a narrow pore size distribution at around 20 nm, as shown in Figure 5 (inset). Table 1 shows the average values of textural properties of the synthesized materials obtained at different reaction times. It can be seen that the BET surface and pore diameter are uniform. There is no evident correlation between the reaction time and the textural properties. In the Table 1 it can be observed that the only change in the textural features is the BET surface area, increasing between 12 and 24 h. Considering that the temperature and pressure of the reaction system remain constant, changing only the reaction time, it is possible that at times below 12 hours the A c c e p t e d M a n u s c r i p t 6 microspheres are being formed, reaching the maximum growth between 12-24 h. At longer periods of reaction the material could suffer sinterization, reducing the BET surface area.

X-ray diffraction

The crystal phase of synthesized bismuth oxyiodides was unambiguously determined through X-ray diffraction on polycrystalline samples. Figure 6 shows the peaks of the synthesized compounds. These phases correspond to the tetragonal system, which is in agreement with JCPDS card 01-073-2026 for BiOI. It should be noted that the first pick, around 7-9°, corresponds to the plane (001). The shift can be explained because when the reaction was carried out at short reaction time the crystals phases are not well defined.

No impurity peaks or presence of other phases were observed. The average size of crystallites can be estimated using the Scherrer formula (Eq. 1) [25].

B B K D   cos  (1)
Where λ is the wavelength of X-ray radiation (λ = 0,15406 nm, for copper), K is the Scherrer's constant (K=0.94),  is the Bragg angle, β is the half width of the peak. The average crystal size is given in Table 1 staying quite constant, around 8.1 nm, for reaction times between 6 to 30 h.

FT-IR Analysis

The composition of BiOI was confirmed through infrared spectra. Figure 7 shows the FTIR spectra of the materials obtained at different reaction times. Signals around 3600 and 1600 cm -1 correspond to O-H symmetrical stretching and scissoring, respectively, due to adsorbed water.

Peaks at 512 cm -1 and 778 cm -1 are attributed to stretching vibrations of Bi-O. Finally, the signals between 500 cm -1 to 1554 cm -1 are associated to the stretching vibration of the tetragonal crystal links BiOI [26,27]. It is also confirmed the absence of residualethylene glycol and ionic liquid.

Optical properties

The band gap of the material is a decisive attribute that modulates the activity of the semiconductor in the visible region of the sunlight [28]. The optical properties of the synthesized materials were studied using diffuse reflectance spectroscopy (DRS) in the UV-Vis range. Figure 8 depicts the DRS curves of the BiOI obtained at 12 h and 24 h of preparation, from which the band gap were determined. The optical borders of the materials were 590 nm and 578 nm for BiOI after 12 h and 24 h reaction, respectively. The Eg of the materials were calculated by the Tauc representation, using the equation 2, where α represents the absorption coefficient, h is the Planck constant,  is the radiation frequency, Eg the band gap, and n is related to the indirect transition (n=4for BiOI) [29,30].

α (h) = A (h -Eg) n/2
(2)

The inset of Figure 8 allows the determination of the band gap directly from extrapolation in the Tauc plot. The values found are 1.95 and 1.98 for materials prepared at 12 and 24 h in autoclave, respectively. Table 2 reports the values of optical borders and band gap obtained for all the synthesized BiOI, ranging between 1.95 and 2.05, which are similar to those reported in literature [31][32][33].

Photocatalytic activity

The photocatalytic activity of the synthesized materials was evaluated using caffeic acid as a target molecule. This substrate was chosen because is a well known antioxidant present in the effluents coming from the winery industry. The reaction was conducted under UV-visible radiation and the degradation profiles compared to the catalyst Evonik P25 (former Degussa P25). Reactions were carried out in aqueous suspension during 60 min. The TOC course can be explained considering the formation of long term intermediates refractory to oxidation. Recently, Augugliaro et al. report the oxidation of phenolic compounds containing carboxylic acid group using TiO 2 [34]. They found phenolic intermediates, dicarboxilic and carboxylic acids. Also in homogeneous system (photo-Fenton reaction) the intermediates identified were phenolic compounds and anhydrides formed by condensation reactions [35]. All of these compounds are known as difficult to be oxidized. Figure 10 shows the caffeic acid profiles including the blanks. Photolysis alone does not provoke the decomposition of the caffeic acid (less than 10 % in one hour). In this Figure it can be observed that the materials synthesized by solvothermal procedure present higher catalytic activity than Evonik P25, usually considered as the most active photocatalyst in the UV-Vis region [36][37][38].

Since that titania and BiOI have similar surface area (52 and 54 m 2 g -1 , respectively) their photocatalytic activities can be compared. It is important to indicate the use of wavelengths over 380 nm for titania is not the best condition for comparison, however our goal is to find the better synthesis conditions for new materials that can be activated exclusively with solar light. The synthesized catalyst provokes degradation extent over 80 % in one hour and the commercial reference P25 does not surpass 55 % in the same period of time. Table 3 gives the degradation extent after 1 h irradiation and initial constant rates of all the prepared catalysts. It can be concluded that all of them reach higher activities than Evonik P25 being higher than those prepared in autoclave with reaction times below 24 h. Apparently higher times in the autoclave provoke some disaggregation of the structure decreasing the activity. The initial rates of caffeic acid oxidation, calculated using the equation (3), are shown in Table 3 [39]. The initial rates of the materials obtained between to12 and 24 hours presents the highest activity.

(

A c c e p t e d M a n u s c r i p t 9

Recycling of the BiOI microspheres

Consecutive runs of caffeic acid photocatalysis with the Xe lamp using the same catalyst produce the curves presented in Figure 11, where reproducible experiments can be observed.

After two consecutive runs using the same catalyst carefully washed the catalytic activity of the BiOI decay slightly in around 10 %. The decrease of the catalytic activity can be explained by the mass loss and disaggregation of the sponge structure. The SEM and EDS images recorded after two reaction cycles show that no significant changes occurred in the morphology of the microspheres (not shown). In addition, FTIR spectra and XRD of samples used in two consecutive runs show no significant changes compared to the unused material. This issue is strongly relevant because the potential use of these materials depends on their stability during long periods of time.

Conclusions

In summary, it was possible to obtain hierarchical BiOI microspheres using the solvothermal route with short periods of reaction times. Among the materials synthesized the best results in catalytic activity correspond to materials prepared between 12 and 24 h of reaction in autoclave.

All the materials prepared present higher activity than EVONIK P25 under UV-Vis illumination.

Figure 9

 9 depicts the curves of UV-Vis spectra of caffeic acid (10 ppm) and their evolution during the photocatalytic process using the catalyst prepared at 12 hour of autoclave. The most pronounced degradation occurs during the first 20 min of irradiation. After 60 min irradiation the changes are lessA c c e p t e d M a n u s c r i p t 8 significant. The mineralization, measured as total organic carbon, reaches around 50 % using the same catalyst (data not shown). After 1 h the TOC removal remains almost unchanged.

A c c e p t e d M a n u s c r i p t

Figure 1 .

 1 Figure 1. Experimental setup used during the photocatalytic tests

Figure A c c e p t e d M a n u s c r i p t

  Figure

FIGURE 2 Figure 2 .

 22 FIGURE 2

Figure3. a )

 a Figure3. a) Expanded SEM image of the BiO microspheres of synthesized for 24 h. b) EDS of BiOI microspheres synthesized for 24 h.

FIGURE 4

 4 FIGURE 4

Figure 4 .

 4 Figure 4.TEM images of BiOI microspheres synthesized for a) 2h b) 6h c) 12h d) 24h e) 30h f) 48h.

FIGURE 5 Figure 5 .

 55 FIGURE 5

A c c e p t e d M a n u s c r i p t FIGURE 7

 7 FIGURE 7

Figure7.

  Figure7. IR Spectra a) Ethylene glycol, b) ionic liquid [bmim], c) BiOI Microspheres synthesized for 12 h with [bmim].

A c c e p t e d M a n u s c r i p t

FIGURE 8 Figure8.

 8 FIGURE 8

FIGURE 9 Figure9.

 9 FIGURE 9

A c c e p t e d M a n u s c r i p t FIGURE 10

 10 FIGURE 10

Figure10.

  Figure10. Degradation profiles of caffeic acid in the presence of BiOI synthesized for 12 h, Evonik TiO 2 P25 and direct photolysis.

A c c e p t e d M a n u s c r i p t

Figure 11 .

 11 Figure 11. Recycling of microspheres synthesized for 12 h.

Table 1 .

 1 Textural features for different reaction times at 120 ºC

	Table
	Time (h)	BET(m 2 /g) Pore diameter (nm)	Crystal size(nm)
	2	48	19,0	3,9
	6	47	21,4	8,1
	12	54	19,0	8,1
	24	58	18,6	8,1
	30	44	23,4	8,1
	48	42	24,6	4,0
	TiO 2 P-25	52	6,9	-

Table 2 .

 2 Optical features of synthesized BiOI materials at 120 ºC

	Time (h)	Optical borders (nm)	Eg (eV)
	2	570	2,00
	6	580	2,05
	12	590	1,95
	24	578	1,98
	30	582	2,00
	48	585	2,05
	TiO 2 P-25	-	3,20

Table 3 .

 3 Photocatalytic activity of synthesized BiOI at 120 ºC expressed as degradation percent after 1 hour illumination with Uv-Vis light and initial rate

	Time (h)	Degradation (%)	Initial rate (mg L -1 min -1 )
	2	81,2	0,0260
	6	83,0	0,0264
	12	85,5	0,0273
	24	84,7	0,0268
	30	76,8	0,0241
	48	76,2	0,0211
	TiO 2 P-25	53,0	0,0095

Acknowledgements

This work has been developed under financial support of National Founds for Science and Technology (Fondecyt, grant 1130502), National Commission of Science and Tecnology (Conicyt/Anillo PIA (ACT-130) and Conicyt/FONDAP/15110019) Projects. Additionally authors thank REDOC.CTA Project UCO 1202. ACM thanks to CONICYT for doctoral fellowship (63105856) and Convention de Mobilité doctorale (Institut Français N° 18/CUS/2012)

A c c e p t e d M a n u s c r i p t


Nicola Gallai
email: gallai@supagro.inra.fr

Jean-Michel Salles

Josef Settele

Bernard E Vaissière

Economic valuation of the vulnerability of world agriculture confronted to pollinator decline

Keywords: pollination, valuation, vulnerability, agriculture, ecosystem service, crop

There is mounting evidence of pollinator decline all over the world and consequences in many agricultural areas could be significant. We assessed these consequences by measuring 1) the contribution of insect pollination to the world agricultural output economic value, and 2) the vulnerability of world agriculture in the face of pollinator decline. We used a bioeconomic approach, which integrated the production dependence ratio on pollinators, for the 100 crops used directly for human food worldwide as listed by FAO. The total economic value of pollination worldwide amounted to €153 billion, which represented 9.5% of the value of the world agricultural production used for human food in 2005. In terms of welfare, the consumer surplus loss was estimated between €190 and €310 billion based upon average price elasticities of -1.5 to -0.8, respectively. Vegetables and fruits were the leading crop categories in value of insect pollination with about €50 billion each, followed by edible oil crops, stimulants, nuts and spices. The production value of a ton of the crop categories that do not depend on insect pollination averaged €151 while that of those that are pollinatordependent averaged €761. The vulnerability ratio was calculated for each crop category at the regional and world scales as the ratio between the economic value of pollination and the current total crop value. This ratio varied considerably among crop categories and there was a positive correlation between the rate of vulnerability to pollinators decline of a crop category and its value per production unit. Looking at the capacity to nourish the world population after pollinator loss, the production of 3 crop categories -namely fruits, vegetables, and stimulants-will clearly be below the current consumption level at the world scale and even more so for certain regions like Europe. Yet, although our valuation clearly demonstrates the economic importance of insect pollinators, it cannot be considered as a scenario since it does not take into account the strategic responses of the markets.

Introduction

The production of 84% of crop species cultivated in Europe depends directly on insect pollinators, especially bees [START_REF] Williams | The dependence of crop production within the European Union on pollination by honey bees[END_REF]. And [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF] found that 87 crops, that is 70% of the 124 main crops used directly for human consumption in the world, are dependent on pollinators. Insect pollination is both an ecosystem service and a production practice used extensively by farmers all over the world for crop production. It is an ecosystem service in that wild pollinators, in particular wild bees, contribute significantly to the pollination of a large array of crops [START_REF] Kremen | Crop pollination from native bees at risk from agricultural intensification[END_REF][START_REF] Morandin | Wild bee abundance and seed production in conventional, organic, and genetically modified canola[END_REF][START_REF] Greenleaf | Wild bees enhance honey bees' pollination of hybrid sunflower[END_REF][START_REF] Winfree | Native bees provide insurance against ongoing honey bee losses[END_REF][START_REF] Winfree | Wild bee pollinators provide the majority of crop visitation across land-use gradients in New Jersey and Pennsylvania, USA[END_REF]. And it is also a management tool in that honeybees, bumblebees and a few other bee species are purchased or rented by farmers in many countries to supplement the local pollinator fauna [START_REF] Mcgregor | Insect pollination of cultivated crop plants[END_REF][START_REF] Olmstead | Bee pollination and productivity growth: the case of alfalfa[END_REF][START_REF] Robinson | The value of honey bees as pollinators of U.S. crops: Part II[END_REF][START_REF] Free | Insect pollination of crops[END_REF][START_REF] Dag | Using bumblebees to improve almond pollination by the honeybee[END_REF]. Thus the economic benefit of insect pollination is clear for farmers and the market of colony rental is now well developed and organized for honey bees in the United States of America [START_REF] Sumner | Bee-conomics and the leap in pollination fees[END_REF] and Europe [START_REF] Carreck | The movement of honey bee colonies for crop pollination and honey production by beekeepers in Great Britain[END_REF] as well as for bumble bees all over the world [START_REF] Velthuis | A century of advances in bumblebee domestication and the economic and environmental aspects of its commercialization for pollination[END_REF]. This practice also suggests that there is already not enough wild pollinators to insure adequate pollination of all crops throughout the year in these countries. Yet the abundance and diversity of wild bees as well as the abundance of honeybees are now declining and some species are clearly at risk [START_REF] Biesmeijer | Parallel declines in pollinators and insect-pollinated plants in Britain and the Netherlands[END_REF]National Research Council, 2007;Oldroyd, 2007;[START_REF] Stokstad | The case of the empty hives[END_REF]. The current decline of insect pollinator populations emphasizes the need to better assess the potential loss in terms of economic value that may result from this trend and the possible ultimate disappearance of pollinators, and to estimate the level of vulnerability of the world agriculture to insect pollinators.

Two main ways have been used to date to assess the monetary value of pollinators.

The first one consists in simply assessing the total value of insect-pollinated crops. This approach has been used at a national scale in the USA [START_REF] Martin | The use of bees for crop pollination[END_REF][START_REF] Levin | Value of bee pollination to United State agriculture[END_REF][START_REF] Metcalf | The Value of insects to humans, In : Destructive and Useful Insects: Their Habits and Control[END_REF] as well as on a world scale [START_REF] Costanza | The Value of the world's ecosystem services[END_REF][START_REF] Pimentel | Economic and environmental benefits of biodiversity[END_REF]. Since the production of most crops is only partially reduced in the absence of insect pollinators, a second more refined approach to improve the previous estimate has been to introduce a dependence ratio that takes into account the real impact of insect pollinators on crop production. This dependence ratio enables the calculation of the production loss in case of a complete disappearance of pollinators, and the economic value of insect pollination service is assimilated with the corresponding loss of crop value. Thus the monetary assessment is directly related to reported values of the dependence of crop production on the level of insect pollination and, in this paper, it will be called a bioeconomic approach. This type of assessment has also been done at national and larger scales (France - [START_REF] Borneck | Evaluation de l'incidence économique de l'entomofaune pollinisatrice en agriculture[END_REF]Hungary -Benedek, 1983;Switzerland -Fluri & Frick, 2005; United Kingdom - [START_REF] Carreck | The economic value of bees in the UK[END_REF]USA -Robinson et al., 1989[START_REF] Morse | The value of honey bees as pollinators of U.S. crops in[END_REF][START_REF] Losey | The economic value of ecological services provided by insects[END_REF]12-member-states European Community -Borneck & Merle, 1989).

Unfortunately, these studies have used a wide range of dependence ratios for the same crops (Table 1). Indeed, these ratios were estimated based largely on personal communications and interpretation of review material, such as [START_REF] Mcgregor | Insect pollination of cultivated crop plants[END_REF] and [START_REF] Free | Insect pollination of crops[END_REF], which do not provide dependence ratios. None of the bioeconomic studies to date have evaluated the impact of insect pollinators at the world scale, nor did they make a geographical analysis of the impact of pollinators in terms of the possible vulnerability of agriculture or examined the potential impact of pollinator loss on production compared with the consumption structure.

Our first objective was to quantify the economic loss that could result from the total disappearance of insect pollinators on world agricultural output and we based our calculations on the dependence ratios recently published for the crops used directly for human food [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF]. Due to the many crop species and the heterogeneity of the structure of the agricultural production, the vulnerability to pollinator decline is likely to vary widely among the different continents and regions. Our second objective was therefore to provide a measure of the vulnerability of the regional and world agriculture when confronted to the decline, or even the total disappearance, of insect pollinators. Finally our third objective was to compare the production and consumption of insect-pollinated crop categories at the regional and world scale in the face of pollinator loss in order to draw some insight on potential local shortages and impacts on trade. Our calculations were based on the assumption of a total pollinator loss, but our results can be extended to any level of pollinator decline as there is empirical evidence that the yield of entomophilous crops -that is crops that are pollinated by insects solely or in a dominant way -responds linearly to pollinator density [START_REF] Dedej | Honey bee (Hymenoptera: Apidae) pollination of rabbiteye blueberry Vaccinium ashei var. 'Climax' is pollinator density-dependent[END_REF][START_REF] Steffan-Dewenter | Seed set of male-sterile an male-fertile oilseed rape (Brassica napus) in relation to pollinator density[END_REF][START_REF] Clement | Flies (Diptera: Muscidae: Calliphoridae) are efficient pollinators of Allium ampeloprasum L. (Alliaceae) in field cages[END_REF].

1 Methods

Principles

Among the main crops that contribute to human food, some, such as most cereals, do not depend on insects for their pollination, while others can be highly or totally dependent on insect pollination, such as many fruits, vegetables and stimulant crops [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF].

Our study is based on the hypothesis that the economic impact of pollinators on agricultural output is measurable through the use of dependence ratios quantifying the impact of a lack of insect pollinators on crop production value. This decrease in the production value could result from a reduction in yield as well as in quality [START_REF] Free | Insect pollination of crops[END_REF]. Unfortunately, this impact on production value is unknown for most crops as what is usually reported is solely the degree of dependence of the production on insect pollinators [START_REF] Borneck | Evaluation de l'incidence économique de l'entomofaune pollinisatrice en agriculture[END_REF][START_REF] Robinson | The value of honey bees as pollinators of U.S. crops: Part II[END_REF][START_REF] Southwick | Estimating the economic value of honey-bees (Hymenoptera, Apidae) as agricultural pollinators in the United-States[END_REF][START_REF] Morse | The value of honey bees as pollinators of U.S. crops in[END_REF][START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF]. It is this dependence ratio that we used again in our study to calculate the economic impact of pollinators and the vulnerability of the agricultural output at various scales.

Because of the lack of substitution among agricultural produce, the economic impact and the vulnerability of the agricultural output is not enough to assess the full value of insect pollinators as, indeed, one ton of rice is not an appropriate substitute for one ton of coffee or of cantaloupe. Thus, in addition to looking at individual crops, we examined the vulnerability to pollinator decline of the FAO crop categories to which each crop belonged based upon the assumption that crops within a category could be considered as potential appropriate substitute for one another while this would not be the case for crops in different categories.

We used the following 10 categories based on FAO: cereals, edible oilseed crops, fruits, nuts, pulses, roots and tubers, spices, stimulant crops, sugar crops, vegetables.

Indicators and formulae

We used a bioeconomic approach to calculate the economic value of the impact of pollinator loss as well as the overall vulnerability of the agricultural output to such a loss. The variables used for each crop i, where i ∈ [1;I], in each world region x, where x ∈ [1;X], were the quantity produced (Q ix ), the quantity consumed (C ix ), the dependence ratio of the crop i on insect pollinators (D i ) and the price of crop i per unit produced in region x (P ix ). We used the price of each crop in each of the 5 regions of the world (sensu FAO; see supplementary material -Appendix 1) because, despite the growing interdependence of agricultural markets, producer prices for the same crop may vary widely from one region to another and therefore cannot be appropriately summarized by a single average world price. Indeed, we found that neither the FAO database nor that of any other world organization provided these prices on a worldwide basis for all our study crops. The total economic value of insect pollination (IPEV) was then calculated as follows:

IPEV = € P ix × Q ix × D i ( ) x=1 X ∑ i=1 I ∑ [1]
Following [START_REF] White | Natural Hazards: Local, National and Global[END_REF], a precise definition of vulnerability was given by [START_REF] Turner | A framework for vulnerability analysis in sustainability science[END_REF] and used by [START_REF] Schröter | Assessing vulnerabilities to the effects of global change: An eight step approach[END_REF] to assess the vulnerability of Europe faced with global change. Vulnerability is a function of three elements: exposure, sensitivity and adaptive capacity. In this context, we used the ratio of the economic value of insect pollination to the economic value of the crop (EV) to calculate a level of vulnerability since it provides a measure of the potential relative production loss attributable solely to the lack of insect pollination. The ratio of vulnerability (RV) for the world output used for human food was thus calculated as follow:

RV = € IPEV EV = € P ix × Q ix × D i ( ) x=1 X ∑ i=1 I ∑ P ix × Q ix ( ) x=1 X ∑ i=1 I ∑ (%) [2]
So defined, the agricultural vulnerability to pollinator decline depends upon crop dependence to pollinators, and farmers' capacity to adapt to pollinator decline. We used part of the overall matrix to calculate the vulnerability of a crop, of a crop category, and of the agricultural industry in a given region when faced with pollinator decline.

To compare production with consumption per region and per crop category, we calculated the 2005 relative overproduction as:

€ Q ix -C ix ( ) x=1 X ∑ i=1 I ∑ C ix ( ) x=1 X ∑ i=1 I ∑ [3]
The corresponding matrix after total pollinator loss was:

€ Q ix (1-D i ) -C ix ( ) x=1 X ∑ i=1 I ∑ C ix ( ) x=1 X ∑ i=1 I ∑ [4]

Data collection

The geographical scale of our study was the world based upon the 2005 data from the FAO database (http://www.fao.org) and thus restricted to the 162 countries that are members of this international organization. Following FAO definitions, we gathered these countries into 5 main regions (Africa, Asia & Oceania, Europe, North America and Caribbean, South and Central America), and, within each region, into sub-regions (see supplementary data -Appendix 1).

We limited the scope of our study to the direct crops and commodity crops used directly for human food as reported by FAO (see supplementary data -Appendix 2). Direct crops are those listed individually with their production by the FAO while a commodity is an aggregation of different crops for which the production figures are pooled together and most are reported as Not Elsewhere Classified. Commodity production figures are based on a questionnaire that countries fill out to include important crops for the world market that are not listed individually by the FAO. We included the commodity crops in the study because they represent a significant part of the agricultural world output.

For Q ix and C ix, we used the 2005 FAO production and consumption data, respectively (http://www.fao.org). For P ix , we needed the mean 2005 producer price per unit weight for each crop or commodity and each region as we opted to take into account regional specialization, geographical context, and socio-economic factors. We chose this approach because producer prices vary with many factors such as crop management, climate, varieties and market in such a way that a regional approach should provide more accurate price estimates than a worldwide approach. To fit complex geographical patterns as well as to be able to concentrate on large producing regions without having to go to the level of individual countries for which many price data are not available either, we used the five main world regions defined previously (see supplementary data -Appendix 1). Major world field crops, like most cereals and sugar crops, are produced on a large scale and have a large-enough commercial value to be traded on financial markets. For these crops, we used the "free on price was not available in either of these two large databases, as well as for all the commodities, we used the average producer price listed on the FAOSTAT website for the period 1991-2002 for the most important producing country of each world region. We used this method to reduce the effect of year-to-year price variation as well as the biases on prices that might take place in small producing countries. Furthermore, when a country or a world region largely exceeded its expected share of world production for a given crop based on its sole size, we considered it to be specialized in this crop. For example, Asia produced 90% of the rice, so we assumed that the world demand for rice, and thus its world price, would be influenced by the Asian supply. In this example, we took the producer price of Asia rice and applied it on a worldwide basis. In all cases, we used the local currency and the exchange rate of the years of the data collected to calculate the prices and production values in 2005 euros.

We calculated the dependence ratios D i based upon the five levels of the extensive recent review of [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF] see supplementary data -Appendix 2). Starting with the complete set of direct and commodity crops used for human food, we selected the ones for which we had production and price data. For the individual crops among the 11 commodities, neither the production nor the producer price was available and the crops that composed each of these commodities were not all dependent on insect pollination at a similar level for their production. Consequently we could not calculate the economic value of pollinators for these commodity crops and they were not considered further. For the direct crops, we focused on those reviewed in Appendices 1 and 2 of [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF] for which we calculated the average dependence ratio based on the reported range of dependence to animal-mediated pollination in this work (See supplementary data -Appendix 2).

Results

We found 89 direct crops and 11 commodities used for human food (100 lines in Appendix 2). Among these, 46 direct crops in 7 categories are dependent on insect pollinators for their production and pollinators are essential for 6 of these crops. The contribution of insect pollinators is also reported as great for 13 direct crops, modest for 13 and little for 14 (Appendix 2). It is noteworthy that within each crop category, there was considerable variation among the crops as to their level of dependence on pollinators.

The 2005 world production value for crops used for human food was €1618 trillion, and the total value of the 46 insect-pollinated direct crops was €625 billion, that is 39% of the world production value (Table 2 and supplementary data in Appendix 3). The economic value of insect pollination was €153 billion (Table 2). The most pollinator-dependent crop categories ranked by decreasing economic value of insect pollination were vegetables, fruits, and edible oil crops (Table 2). It is noteworthy that the production value of a ton of the crop categories that do not depend on insect pollination -namely cereals, sugar crops, and roots & tubers -averaged 151 € while that of those that are pollinator-dependent averaged 761 €, or five times more, and these values were significantly different (t = 4.851; n = 3 and 7, respectively; P = 0.0013; t test on the Log-transformed values to have similar variance among the two groups).

The rate of vulnerability of the world agricultural production used for human food in the face of total pollinator loss was 9.5% (Table 2). This overall value may seem small, but it does not reveal the large range of values among the different crop categories. The stimulant crops with a total production value of only €19 billion had the highest vulnerability ratio (39%). And vegetables, the category with the highest crop production value (€418 billion)

still had a vulnerability ratio of 12%. Interestingly, there was a positive correlation between the rate of vulnerability of a crop category to pollinators and its value per production unit (r = 0.729, n = 10, P = 0.017).

Looking at the economic vulnerability ratios of the different crop categories among the regions of the world indicates that, in each region, there is a category that is highly vulnerable to pollinator loss with vulnerability ratios ranging from 22% to 94% (Table 4).

Interestingly, nuts were the most vulnerable crop category over the largest area (7 subregions), followed by fruits and stimulant crops (5 sub-regions each). Furthermore, because some regions are specialized in the production of some pollinator-dependent crop category, the vulnerability of the world production for these categories is much higher than the overall worldwide value indicated on Table 3. For example, East Asia produced nearly 52% of the world vegetables with a vulnerability ratio of 15% while the worldwide value was 12%

(Tables 2 and4). Also North and South Americas produced 36% of the edible oil crops with a vulnerability ratio greater than 22%, while the worldwide value was 16% (Tables 2 and4).

And West Africa, South East Asia and North America together produced 36% of the nuts in the world with a vulnerability ratio ≥ 44% in all three regions. The situation appeared particularly critical for stimulant crops as West Africa produced 56% of the world production with a vulnerability ratio of 90% (Table 4). This region produced a lot of coffee and/or cocoa, both of which are dependent of insect pollinators for their production, and the consequences of a total pollinator loss on these crops could be considerable not only for the revenues that West Africa derives from these crops, but also on a global scale for the world production and resulting price structure of these stimulants.

On a global scale, the difference between production and consumption in 2005 was positive for all crop categories that are pollinator-dependent1 . Looking at these same differences after total pollinator loss, the overall world food supply would not be in jeopardy, but the production drop would create a deficit in three crop categories including fruits and vegetables, two pollinator-dependent categories with a high economic value and low ability for storage from one year to the next (Table 5). Looking at these three categories for which the overall production would no longer meet consumption patterns after total pollinator loss, we examined their change in availability in each geographical region. The deficit resulting from the loss of pollinators appears important in many region and crop category combinations, and it could have some serious consequences in two types of situations. First, in some regions where production was clearly exceeding consumption, the loss of pollinators would result in a deficit such that production would no longer be able to meet consumption. This is the case for fruits in North Africa as well as in Central, East and South Asia (

Discussion

We found a value of about €153 billion as an assessment of the economic value of insect pollination for the world agriculture in 2005. This is the direct result of the calculations based on equation [1] using the dependence ratios towards pollinators given by a recent review [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF] and the production value of the most important crops directly used for human food. It measures the part of the gross value of the world food production attributable to insect pollination and can therefore be considered as a conservative assessment of the gross value of the insect pollination service. Indeed, in an early valuation of the service provided by bees on US agriculture, [START_REF] Martin | The use of bees for crop pollination[END_REF] stated that the value of beef and dairy products that result from the seed production of forage legumes such as alfalfa accounts for about 80% of the economic value of insect pollinators. At the world scale, such a high value is most unlikely, at least because forage legume are not as important worldwide as in the USA. But this statement nevertheless underlines the fact that the indirect impact of pollinator decline on forage production, though quite difficult to assess, may not be anecdotal. Similarly, our assessment did not take into account the value of pollinators for the seed production necessary to grow the vegetative parts of many species which are consumed by humans (such as many vegetables; see Appendix 1 in [START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF], and our supplementary data -Appendix 2), nor the seed production for ornamental flowers and other uses not devoted to human food such as biofuels. Soybean and other pollinator-dependent edible oil crops contribute to the supply of biofuels, but current relative prices limit their use and biofuels are mainly produced from non-pollinator dependent crops such as sugar cane and corn [START_REF] Schubert | Can biofuels finally take center stage ?[END_REF]; Appendix 2).

In the literature, we found only two studies giving an economic valuation of the pollination service at the world scale [START_REF] Costanza | The Value of the world's ecosystem services[END_REF][START_REF] Pimentel | Economic and environmental benefits of biodiversity[END_REF]). Yet the comparison of our results with those of these two studies is difficult because their methods are so different. Costanza et al. used the findings of [START_REF] Levin | Value of bee pollination to United State agriculture[END_REF] to determine a lower limit of the value of insect pollination service of US$140 million, corresponding to the value of honey and beeswax in 1980, and an upper limit of US$18.9 billion, which was the value of 1980 U.S crops that they considered dependent on insect pollinators (fruits, nuts, vegetables, seeds, fibers, cattle, calve and liquid milk production). Conservatively and without further justification, they chose a value of US$2 billion from this interval and assumed that the U.S. Even after appropriate corrections, the 2005 estimated values from these two studies (€20 billion and €40 billion for [START_REF] Costanza | The Value of the world's ecosystem services[END_REF]Pimentel et al., 1997, respectively) remain considerably smaller than our result (€153 billion; Table 2). Such a difference raises many questions. Since these authors give little explanations on their methods, we might assume that they have integrated in their calculations some more sophisticated -though unformulated -considerations, especially in relation to the behavior of economic actors that will adapt to a pollinator-free context.

These €153 billion stand for about 9.5% of the world value of the crops used directly for human food. This ratio of vulnerability can be interpreted as an indicator of the value of pollination service relatively to the other factors that contribute to agricultural production worldwide. The value of the vulnerability ratio is of course contingent upon the relative prices of crops and, especially, the prices of pollinator-dependent crops relative those which are not 2 .

It must be clearly stated that this economic valuation is not a scenario assessment, since all economic agents can change their behavior in order to adapt to a pollinator decline.

These changes will have some costs, namely opportunity costs. But one can assume that producers will make efficient trade-offs between the costs of changing crop species, or varieties, or production technologies -namely pollination techniques -and the losses resulting from keeping less profitable practices 3 . 21 2 It must be mentioned that crops vary in the manner in which their prices behave. Tropical fruits and spices also suffer from price volatility, which produce losses or windfall gains. There are high price regimes and low price regimes as in the case of coffee and spices (also bee-pollinated crops) coinciding with crop failures in major producing countries such as Brazil (for coffee) and Guatemala (for cardamom). This might implicitly mean high elasticity of demand in high price regimes and low elasticity in low price regimes. 3 For orchard crops that are perennial in nature, elasticity of adaptation measures such as shifting to other crops is low. Supply elasticity for perennial crops tends to be low as compared to demand elasticity. As a result, the It appears difficult to gauge the real significance of a vulnerability of about 10% on the agricultural industry. In some cases, a small variation may induce large consequences, especially through the impact it might have on the financial equilibrium of farms. The transmission of the price change can have variable effects within the food supply chain (Wu, 2004;[START_REF] Tang | Multi-agent and market based dynamic optimisation and its extensions to distributed supply chain procurement planning problems[END_REF] and the capacity of the food supply chain operators to adapt to new situations and limit the consequences, either through technical change or because of the existence of market power, is poorly known [START_REF] Hassan | Price Linkage and Transmission between Shippers and Retailers in the French Fresh Vegetable Channel[END_REF].

Furthermore, the decline of pollinators will certainly be heterogeneous among different regions of the world due to differences in land and crop management as well as the abundance and diversity of wild and managed bees. For example, in a reverse scenario [START_REF] Roubik | Do competing honey bees matter? Dynamics and abundance of native bees before and after honey bee invasion[END_REF] found that the arrival of Africanized honey bees in South and Central America resulted in much higher population densities of bees, and this translated into increased coffee production [START_REF] Roubik | Tropical agriculture: The value of bees to the coffee harvest[END_REF]. On a smaller scale, landscape management is also likely to affect pollinator density [START_REF] Kremen | Crop pollination from native bees at risk from agricultural intensification[END_REF][START_REF] Klein | Importance of pollinators in changing landscapes for world crops[END_REF].

A first step towards a better understanding of the meaning of a 10% vulnerability ratio could consist in introducing an economic measure of this vulnerability in terms of consumer surplus. [START_REF] Southwick | Estimating the economic value of honey-bees (Hymenoptera, Apidae) as agricultural pollinators in the United-States[END_REF] estimated the economic value of honeybees as agricultural pollinators in the USA based upon a measure of the surplus gain resulting from their pollination service. They considered a price reaction to quantity limitation related to the dependence ratio that leads to the following expression of the consumer monetary surplus gain for each crop:

Gain = € Q 1 (P 1 -P 0 ) + P(Q) -P 0 [ ] Q 1 Q 0 ∫ dQ [5]
22 opportunity costs of taking up new crops would likely be very high.

where P 0 and Q 0 are the price and quantity with honeybee pollination, the price P was estimated as a function of the quantity Q and the income of American households from temporal series, P 1 and Q 1 are the price and quantity without honeybee pollination.

Our assessment is based upon the calculation of the loss in terms of agricultural production for each crop i, that is P i0 (Q i0 -Q i1 ) (see Figure 1). This result must be transformed into economic surplus loss for consumers to obtain an assessment of the social cost of pollinator decline. Since there are no appropriate data to find econometrically for each crop at the world scale the price elasticities, assumptions must be made on the shape and value of P(Q). A simple idea is to assume that for all crops the price elasticities (E) are constant. Inverse demand functions can then easily be expressed and consumer surplus variations analytically calculated.

The choice of a constant elasticity price is acceptable for most crops as long as the price range remains in the neighborhood of current prices. The neighborhood wideness is variable with the crop and its economic status as primary good or luxury good. It is probably unacceptable when the ratio of dependence is very high, since the price should then rise considerably (e.g. for the 6 crops with a dependence ratio of 95%, which means that for a price elasticity value of -1, the price following total pollinator loss would be multiplied by 20).

Given a constant elasticity price, the mathematical representation of the demand function comes from the definition of the price-elasticity E = € δQ Q δP P , which leads to € P(Q) -EQP'(Q) = 0 and, assuming E ≠ 0, gives the inverse demand function:

€ P(Q) = P 0 Q Q 0       1 E [6]
We will also assume, following [START_REF] Southwick | Estimating the economic value of honey-bees (Hymenoptera, Apidae) as agricultural pollinators in the United-States[END_REF], that the long-term supply curve is perfectly elastic, which means that farmers can switch from one crop to another without increasing production cost and without constraint of arable land availability.

It means that there is no producer surplus variation and then the consumer surplus variation is actually the social surplus variation.

We used the large matrix that was built to measure the economic value of insect pollination (Appendices 2 and 3) to calculate what would be the consumer surplus loss according to several price elasticity values. For each value, we applied our hypotheses to each crop with its specific dependence ratio to pollinators.

The choice of a unique value for E may seem like an oversimplification. But choosing different values of E for each crop in each region would be equally arbitrary since these values could not be determined from appropriate econometric data. Some crops, like cereals, are generally associated with low price elasticities, usually estimated to be |E| < 0.5 in the literature. Other crops, such as fruits, appear to have higher price-elasticities, |E| > 1 and possibly much more in some cases [START_REF] Southwick | Estimating the economic value of honey-bees (Hymenoptera, Apidae) as agricultural pollinators in the United-States[END_REF].

The choice of the unique value of E for all crops must take into account the relative importance of crops with high and low elasticities, which are used to calculate the total consumer surplus loss. Fruits, vegetables, nuts, edible oil crops, stimulant crops, and spices are the most pollinator-dependent crop categories and they are also those that will make the largest part of the total loss. Yet they are also those that appear most likely to have the highest elasticities. So the overall appropriate figure for E is likely to be in the neighborhood of -1.

Furthermore, a distinction must be made between short-term and long-term elasticities, the latter being traditionally higher (|E| > 1). Since we consider a hypothetical situation of total pollinator loss, long-term elasticities appear more appropriate.

We have to assess now what will happen to the food production and markets after insect pollinators decline to a complete loss. The first consequence is a loss in production from Q 0 to Q 0 (1-D) for a similar production effort (i.e. without change in the total production costs). If a smaller production is obtained for the same total cost, we can assume that the unitary production cost will grow from P 0 to P 0 /(1-D) = P 1 . We will then consider that P i1 is the new price of the crop i on the market of our pollinator-free economy. At this price, the effective demand will be Q i (P i1 ) = Q i1 . This assumption allowed us to calculate the consequent surplus loss (CSloss ; Figure 1) according to the value of E.

€

CSloss i = Q i1 P i1 -P i0 ( ) + P i (Q i ) -P i0 [ ] Q i1 Q i 0 ∫ dQ [7]
For the value E = -1, it comes from [6] that P(Q) = P 0 .Q 0 /Q, and Q 1 (P 1 -P 0 ) = P 0 (Q 0 -Q 1 ). The consumer surplus loss is then:

€ CSloss = P(Q) [ ] Q 1 Q 0 ∫ dQ = P 0 Q 0 Q Q 0 Q 1 ∫ δQ = P 0 Q 0 .Log Q 1 Q 0 [8]
where P 1 and Q 1 are the price and quantity without insect pollination, P 0 and Q 0 are the price and quantity with insect pollination. If we apply this expression to a quantity reduction related to a total pollinator loss for a crop with a ratio of dependence D, Q 1 = Q 0 (1-D) and it comes:

€ CSloss = P 0 .Q 0 .Log(1 -D)
. This value is easy to calculate using the matrix of prices and quantities in Appendices 2 and 3. Applying this formula to all crops used directly for human food on a worldwide basis gives a total loss of consumer surplus of about €260 billion for 2005.

For any price-elasticity E ≠ -1, it comes:

€ CSloss = P 0 Q 0 1 + E 1 1 -D       1+ E -1         . [9]
This value can be calculated for any value of E using the database of all crops in each world region (Appendices 2 and 3):

€ P ix 0 Q ix 0 1+ E 1 1-D i       1+E -1         x=1 X ∑ i=1 I ∑ .
[10]

For E = -0.8, we find €310 billions; and for E = -1.5, about €191 billion (see Table 7).

Though a more refined analysis remains to be done, it is possible to suggest some changes that are likely to take place in the behavior of producers, agro food supply chains, and consumers, if the decline in insect pollination services is further confirmed. Farmers would at least to some extent switch from pollinator-dependent crops to less dependent species or, when available, varieties. But a first reaction would probably be in many cases, as it is widely done for fruit production in the USA, to try to improve insect pollination through the management of selected species and the development of artificial pollination techniques.

For the rare pollinator-dependent crops with low price elasticity (|E| < 1; i.e. apples with E = -0.59, [START_REF] Southwick | Estimating the economic value of honey-bees (Hymenoptera, Apidae) as agricultural pollinators in the United-States[END_REF] the farmers' income will increase when yields decrease since prices will rise faster ('King effect'). This effect should nevertheless be limited by competition among farmers and resulting production enhancing investment.

Following the agro food supply chains, it can be assumed that optimization tuning will aim at reducing the impact of pollinator decline onto consumers, through substitution both in the nature of the good and the processing formula. Finally, consumers would modify their choices according to the relative prices of food items and, in the case of strong change; the food budget might compete with other parts of the consumption patterns 4 .

The potential loss in some food production may not have measurable consequences in economic terms only, as it might also have serious consequences on human health. In 21 4 The emergence of organic foods and widespread concerns about GM foods has reduced elasticity of substitution for health foods (organic and non GM traditional foods) despite health foods carrying higher prices. Finally, the loss in output of conventional pollinated crops due to inadequate pollination forms a deadweight loss, net loss to producer and consumers and hence to society.

particular, the decrease of fruit and vegetable availability could impact the health of consumers worldwide. The World Health Organisation (WHO) has set a lower limit of 400 grams per capita and per day for fruit and vegetable consumption (WHO Report, 1990). [START_REF] Naska | Fruit and vegetable availability among ten European countries: how does it compare with the 'five-a-day' recommendation?[END_REF] studied fruit and vegetable consumption among ten European countries and found that more than 50% of the households were below this recommendation. In the case of a total disappearance of pollinators, this situation is very likely to worsen.

Conclusions

The aim of our work was to assess the vulnerability of the food production worldwide faced to the decline of insect pollinators. Non-food agricultural production, cattle raising, and natural vegetation will also be impacted but are not studied in this paper. Using a bioeconomic approach, we calculated a world value for the contribution of pollinators to the production of crops used directly for human food of €153 billion, which is about 9.5% of the total value of the production of human food worldwide.

Since this first result was obtained through multiples sums, we extracted partial results such as the most vulnerable crop categories (stimulant crops, nuts and fruits) or the categories that stood for the largest part of the economic vulnerability (fruits, edible oil crops, vegetables). Related to their agricultural orientations, some regions appeared more vulnerable like Middle East Asia (15%), Central Asia (14%), East Asia (12%) and non European Union countries (12%). At the global scale, the vulnerability of the Northern countries appeared higher than the southern ones, which suggests that the decline of insect pollinators might have heavy consequences for the North-South agro-food trade. To complete these data, we calculated the capacity to nourrish world population after pollinator loss and found that the production of 3 crop categories will be clearly below the current consumption at the world scale and even more so for certain regions like Europe.

Although we created a complete database of prices and production quantities for each crop in each region of the world and we used a very recent review to get the dependence ratio of each crop on insect pollination, the uncertainties are probably large but difficult to assess, especially since ecological responses to pollinator decline on large scales remain poorly known (National Research Council, 2007). More specifically, there is an ongoing debate on the existence of a "pollinator paradox" meaning that though crops depend on pollinators, the overall crop yield may not necessarily be as dependent because farmers will take into account pollinator decline in their production management and strategies [START_REF] Ghazoul | Recognizing the complexities of ecosystem management and the ecosystem service concept[END_REF].

Despite these uncertainties, we discussed these results in terms of consumer surplus loss, which is a more appropriate indicator of the economic valuation of these vulnerabilities.

Since it was not possible to rely on econometrically estimated price elasticities for each crop in each region, our calculations relied on the assumption of an average sensitivity of prices to quantity shortage. Stating that the most vulnerable crops appear to be more sensitive to price variation, the more realistic elasticity parameter is likely to be |E| > 1. Furthermore, since we considered the evolution over the long term, we can make the optimistic assumption that farmers would adapt without significant cost, and the social surplus losses would be in the range of €310-191 billions for elasticity parameters ranging from -0.8 down to -1.5.

Although our results demonstrate the economic importance of insect pollinators, it cannot be considered as a scenario since it does not take into account the strategic response of the market. Producers might have several levels of response strategies in interaction with the intermediate demands of the food supply chain. Moreover, the response of consumers faced to dramatic changes of relative prices would probably be more elaborate than the simple priceelasticity can summarize. Short and long term reaction for each crop and in each region would probably be quite different and should be studied specifically in further work.

World Health Organization, 1990. Diet, Nutrition and the Prevention of Chronic diseases.

Technical Report Series no. 797. Geneva: WHO.

Wu S.D., 2004. Supply chain intermediation: A bargaining theoretical framework. In D.

Simchi-Levi, S.D. Wu and Z.M. Shen (Eds.), Handbook of Quantitative Supply Chain Analysis. Kluwer Academic Publishers, 67-115.

Tables and figures

Table 1 -Heterogeneity of the production dependence ratios reported for some selected crops in regards to insect pollination (extrema are underlined).

Table 2 -Economic impact of insect pollination on the main categories of the world agricultural production used directly for human food and ranked by their rate of vulnerability to pollinator loss. Table 5 -Effect of pollinator loss on the capacity to provide food at the world scale for the pollinator-dependent crop categories.

Table 6 -Regional effect of pollinator loss on the capacity to meet consumption before and after (in bold) total pollinator loss for the three crop categories for which the overall 2005 balance was negative following pollinator loss.

Q 0 Q 0 (1-D) = Q 1a € CSloss i = Q i1 P i1 -P i0 ( ) + P i (Q i ) -P i0 [ ] Q i1 Q i 0 ∫ dQ i € Pollinator value i = P i0 (Q i0 D i ) Q 1b Q 1c

  figure of US$ 8 billion for the crops used for human foods only, the economic value of insect

Figure 1 -

 1 Figure 1 -Estimates of the consumer surplus loss for different values of price elasticity

Table 6

 6 given crop category and could therefore be severely impacted by the drop of production following pollinator loss. This is the case for example with fruits in the European Union where consumption exceeded production by 20% in 2005 and this deficit would double following total pollinator loss in Europe. Other examples include fruits in West Africa and North America, vegetables in Central Africa, Oceania, the European Union and North America, and stimulant crops in the European Union and North America.

	and Middle East Asia, and South America, and (ii) for stimulant crops in South Africa. A
	second type of situation where pollinator loss could have serious consequences arises for
	regions which are already barely meeting their consumption patterns or which are net
	23

).

A case in point is East Asia where fruit production exceeded consumption by 19% in 2005 and where total pollinator loss would result in a deficit with consumption exceeding production by 26%, which is considerable since this region produces nearly 20% of the world fruit output. Other examples of a similar situation of consumption exceeding production as a consequence of pollinator loss are found (i) for vegetables in North and South Africa, East

Table 3 -

 3 Geographical distribution of crop production value, economic impact of pollinators and vulnerability ratio among the 16 regions of the world defined following FAO (http://faostat.fao.org).

Table 4 -

 4 Economic vulnerability ratio (in bold) and 2005 production figures in 10 6 metric tons (in italics) for the pollinator-dependent crop categories among the 16 regions of the world defined following FAO (http://faostat.fao.org). X% highest value of the economic vulnerability ratio for the sub-region.

Table 7 -

 7 Consumer surplus loss at the world scale for 2005 in relation with price elasticity Figure 1 -Estimates of the consumer surplus loss for different values of price elasticity

Table 1 -

 1 Heterogeneity of the dependence ratios reported for the production of some selected crops in regards to insect pollination (extrema are underlined).

	Crop species	Common name	Borneck & Bricout, 1984 Robinson et	Southwick &	Morse &	Klein et al., 2007
					al., 1989	Southwick,	Calderone,
						1992	2000
			Min Max	Mean				Min	Max Mean
	FRUITS
	Fragaria x ananassa	Strawberry	0.100 0.200	0.150	0.4	0.30	0.2	0.1	0.4	0.25
	Malus domestica	Apple	0.100 0.200	0.150	1.0	0.80	1.0	0.4	0.9	0.65
	Vitis vinifera	Grape	0.001 0.010	0.006	0.1	0.15	0.1	0.0	0.0	0.00
	NUTS
	Amygdalus communis	Almond	0.100 0.200	0.150	1.0	0.90	1.0	0.4	0.9	0.65
	VEGETABLES
	Cucumis melo	Melon (incl. cantaloupe)	0.100 0.200	0.150	0.8	0.70	0.9	0.9	1.0	0.95
	Mean			0.120	0.66	0.57	0.64			0.50

Table 2 -

 2 Economic impact of insect pollination of the world agricultural production used directly for human food and listed by the main categories ranked by their rate of vulnerability to pollinator loss; the economic value of insect pollination was calculated following[1].

	Crop category	Average value of a production unit	Total production economic value (EV)	Insect pollination (IPEV) economic value	Rate of vulnerability (IPEV/EV)
		€ per metric ton	10 9 €	10 9 €	%
	Stimulant crops	1225	19	7.0	39.0
	Nuts	1269	13	4.2	31.0
	Fruits	452	219	50.6	23.1
	Edible oil crops	385	240	39.0	16.3
	Vegetables	468	418	50.9	12.2
	Pulse	515	24	1.0	4.3
	Spices	1003	7	0.2	2.7
	Cereals	139	312	0.0	0.0
	Sugar crops	177	268	0.0	0.0
	Roots & tubers	137	98	0.0	0.0
	All categories pooled together		1 618	152.9	9.5

Table 3 -

 3 Geographical distribution of crop production value, economic impact of pollinators and vulnerability ratio among the 16 sub-regions of the world defined following FAO (http://faostat.fao.org); the economic value of insect pollination was calculated following [1]; subregions with high vulnerability ratios (≥ 10%) are in bold.

	Geographical region and sub-region	Total production economic value (EV)	Insect pollination economic value (IPEV)	Rate of vulnerability for the region (IPEV/EV)
		10 9 €	10 9 €	%
	AFRICA
	Central Africa	10.1	0.7
	East Africa	19.6	0.9
	North Africa	39.7	4.2
	South Africa	19.2	1.1
	West Africa	48.9	5.0
	ASIA
	Central Asia	11.8	1.7
	East Asia	418.4	51.5
	Middle East Asia	63.5	9.3
	Oceania	18.8	1.3
	South Asia	219.4	14.0
	South East Asia	167.9	11.6
	EUROPE
	European Union (25 members)	148.9	14.2
	Non EU25	67.8	7.8
	NORTH AMERICA
	Bermuda, Canada & USA	125.7	14.4
	SOUTH & CENTRAL AMERICA
	Central America & Caribbean	51.1	3.5
	South America	187.7	11.6

Table 4 -

 4 Economic vulnerability ratio (in bold) and 2005 production figures in 10 6 metric tons (in italics) for the pollinator-dependent crop categories among the 16 sub-regions of the world defined following FAO (http://faostat.fao.org). X% highest value of the economic vulnerability ratio for the sub-region.

	Geographical region and sub-region	Edible oil crops	Fruits Nuts Pulse Spices	Stimulant crops	Vegetables
	AFRICA
	Central Africa	8% 4.37	4% 5.71 0.04 0.12 0.05 0% 1% 5%	69% 0.28	10% 2.58
	East Africa	18% 2.08	4% 22% 10% 3% 6.39 0.18 1.70 0.18	17% 1.05	4% 6.85
	North Africa	13% 3.86	16% 58% 15% 4% 15.73 0.24 1.04 0.14	-0	13% 30.45
	South Africa	17% 2.74	15% 45% 0% 25% 7.95 0.08 0.41 0.06	16% 0.16	8% 4.11
	West Africa	9% 23.81	11% 46% 2% 10.88 1.03 0.00 0.25 3%	90% 2.53	5% 17.47
	ASIA
	Central Asia	25% 4.00	41% 35% 4% 2.16 0.03 0.06 0.00 4%	-0	14% 8.59
	East Asia	17% 62.76	36% 16% 10% 3% 94.71 1.70 5.64 0.76	2% 1.08	15% 462.56
	Middle East Asia	18% 5.27	24% 18% 3% 32.97 1.55 2.98 0.23 1%	3% 0.28	18% 49.57
	Oceania	24% 3.69	28% 33% 6% 5.08 0.05 2.14 0.01 1%	94% 0.01	8% 2.86
	South Asia	19% 44.41	23% 23% 0% 56.09 1.00 13.24 3.79 2%	11% 1.51	7% 92.93
	South East Asia	11% 186.07	13% 44% 3% 44.32 1.39 2.22 0.87 2%	38% 2.74	7% 30.90
	EUROPE
	European Union (25 members)	8% 31.94	30% 48% 5% 60.05 0.82 5.49 0.13 1%	-0	7% 65.35
	Non EU25	24% 17.81	51% 4% 1% 13.31 0.28 2.83 0.12 3%	0% 0.02	12% 35.08
	NORTH AMERICA
	Bermuda, Canada & USA	23% 110.74	24% 46% 3% 27.62 1.31 6.56 0.04 0%	-0	8% 39.74
	SOUTH & CENTRAL AMERICA
	Central America & Caribbean	14% 5.73	10% 1% 5% 29.86 0.21 1.12 0.16 2%	29% 1.21	12% 19.49
	South America	22% 113.38	9% 25% 9% 71.44 0.30 0.45 0.28 3%	30% 4.55	8% 25.17
	TOTAL	622.66	484.27 10.21 46.00 7.07	15.42	893.70

Table 5 -

 5 Effect of pollinator loss on the capacity to provide food at the world scale for the pollinator-dependent crop categories. The differences between 2005 production and consumption figures are expressed in relative terms as % of the 2005 consumption figures following FAO (http://faostat.fao.org).

		Relative production	Relative production
	Crop categories	surplus before	surplus after pollinator
		pollinator loss	loss
		___________% of consumption___________
	Stimulant crops	18	-24
	Fruits	12	-12
	Vegetables	19	-6
	Spices	11	8
	Nuts	29	16
	Edible oil crops	75	40
	Pulses	60	54

Table 6 -

 6 Regional effect of pollinator loss on the capacity to meet consumption before and after (in bold) total pollinator loss for the three crop categories for which the 2005 overall balance was negative following pollinator loss. The differences between 2005 production and consumption figures are expressed in relative terms as % of the 2005 consumption figures following FAO (http://faostat.fao.org).

	Geographical region (FAO classification)	Fruits		Stimulant crops	Vegetables
		______________% of consumption______________
	AFRICA
	Central Africa	22	16	633	102	-4	-16
	East Africa	-51	-54	369	297	9
	North Africa	15	-4	-100	-100	16	-13
	South Africa	56	29	10	-5	2	-11
	West Africa	-22	-28	2982	169	21
	ASIA
	Central Asia	31	-22	-100	-100	40
	East Asia	1	-26	-30	-30	28	-4
	Middle East Asia	31	2	-43	-43	31	-12
	Oceania	60	21	-93	-100	-4	-22
	South Asia	20	-3	23	45	9
	South East Asia	30	20	289	140	15
	EUROPE
	European Union (25 members)	-20	-40	-100	-100	-3	-16
	Non EU25	-30	-61	-98	-98	-2	-23
	NORTH AMERICA
	Bermuda. Canada & USA	-30	-46	-100	-100	-3	-16
	SOUTH & CENTRAL
	AMERICA
	Central America & Caribbean	54	35	183	99	63
	South America	83	65	176	103	17	-4

Table 7 -

 7 Consumer surplus loss at the world scale for 2005 in relation with price elasticity

	Price elasticity	Consumer surplus
	parameter	loss (10 9 €)

This global statement is not in contradiction with the fact that, according with the World Health Organization (WHO) some 3.7 billion people were malnourished in

or, following the Food and Agricultural Organization (FAO) estimates, 850 million, as FAO recorded only the people that are protein/calories malnourished, rather than nutrient deficient.

Acknowledgements

This research was funded by the EC within the FP6 Integrated Project "ALARM" (Assessing LArge scale environmental Risks for biodiversity with tested Methods; GOCE-CT-2003-506675; http://www.alarmproject.net; Settele et al., 2005). The authors thank Joshua Bishop, Jean-Marie Boisson, Gabriel Carré, Charles Figuières, Ghislain Géniaux, Mabel Tidball and three anonymous referees for valuable comments on an early version of this text.