Bassam Nohra
email: bassam@nohra.net

Laure Candy
email: laure.candy@ensiacet.fr

Jean-François Blanco
email: jeanfrancois.blanco@ensiacet.fr

Yann Raoul
email: yann.raoul@oleon.com

Zéphirin Mouloungui
email: zephirin.mouloungui@ensiacet.fr

Synthesis of High-Molecular-Weight Multifunctional Glycerol Polyhydroxyurethanes PHUs

Keywords: polyhydroxyurethanes, glycerol carbonate acrylate, dimethyl carbonate, Aza-Michael, aminolysis, type-AB polymerization

Glycerol carbonate acrylate is a 5-membered cyclic carbonate synthesized from glycerol that is used as a chemical coupling agent and has proven highly suitable for use in the synthesis of multifunctional polyhydroxyurethanes (PHUs). The multifunctionality of the structure of PHUs is determined by the density of the carbon-amine groups generated by the Aza-Michael reaction and that of the urethane groups and adjacent primary and secondary hydroxyl groups generated by aminolysis. Glycerol carbonate acrylate is polymerized with polyfunctional mono-, di-, tri, and tetra-amines, by type-AB polyaddition, either in bulk or in solution, through stepwise or one-pot reaction strategies in the absence of added catalysts. These approaches result in the generation of linear, interchain, and crosslinked structures, through the polyaddition of linear and branched amines to the ethylene and cyclic carbonate sites of glycerol carbonate acrylate. The resulting collection of organic molecules gives rise to polyethylene amino ester PHUs with a high molar mass, exceeding 20,000 g•mol -1 , with uniform dispersity.

Introduction

In 2011, Keul et al. [START_REF] He | Synthesis, characterization, and application of a bifunctional coupler containing a five-and a six-membered ring carbonate[END_REF] introduced the concept of using bifunctional coupling agents in the development of multifunctional polymers. Unsaturated functional cyclic carbonate monomers had long been used in the development of polar and reactive polymers [START_REF] Kihara | Synthesis and reaction of polymethacrylate bearing cyclic carbonate moieties in the side chain[END_REF][START_REF] Webster | Synthesis and applications of cyclic carbonate functional polymers in thermostteing coatings[END_REF]. These monomers have a 5-membered cyclic carbonate structure which contributes to their high dielectric constant, density, viscosity, and boiling point [START_REF] Ding | Liquid-solid phase diagrams of binary carbonates for lithium batteries[END_REF]. The CO 2 sequestration at the cyclocarbonate group confers polarity and reactivity to the monomers and polymers which contain these groups. Among unsaturated functional cyclic carbonate monomers, it has been widely demonstrated that acrylate or methacrylate monomers can be easily polymerized to generate high-molar mass thermosetting polymers [START_REF] Kihara | Synthesis and reaction of polymethacrylate bearing cyclic carbonate moieties in the side chain[END_REF][START_REF] Webster | Synthesis and applications of cyclic carbonate functional polymers in thermostteing coatings[END_REF][START_REF] Camara | Free radical polymerization study of glycerin carbonate methacrylate for the synthesis of cyclic carbonate functionalized polymers[END_REF]. These polymers react with amines via their cyclic carbonate groups, thereby generating the necessary flexibility and hardness without the need to use isocyanate, which is both hazardous and toxic [START_REF] Kihara | Synthesis and reaction of polymethacrylate bearing cyclic carbonate moieties in the side chain[END_REF][START_REF] Webster | Synthesis and applications of cyclic carbonate functional polymers in thermostteing coatings[END_REF][START_REF] Camara | Free radical polymerization study of glycerin carbonate methacrylate for the synthesis of cyclic carbonate functionalized polymers[END_REF][START_REF] Besse | Synthesis and applications of unsaturated cyclocarbonates[END_REF][START_REF] Lamarzelle | Activated lipidic cyclic carbonates for non-isocyanate polyurethane synthesis[END_REF].

This sequential approach, based on the synthesis of cyclic carbonate monomers by CO 2 fixation, generating dangling cyclic carbonate groups, followed by the generation of polar polymers with hydroxyurethane groups but without isocyanates, has undergone radical changes both in academic research and in applications for the production of organic coatings [START_REF] Kihara | Synthesis and reaction of polymethacrylate bearing cyclic carbonate moieties in the side chain[END_REF][START_REF] Webster | Synthesis and applications of cyclic carbonate functional polymers in thermostteing coatings[END_REF][START_REF] Besse | Synthesis and applications of unsaturated cyclocarbonates[END_REF][START_REF] Lamarzelle | Activated lipidic cyclic carbonates for non-isocyanate polyurethane synthesis[END_REF][START_REF] Mouloungui | Manufacture of Glycerol-Based Polyhydroxyurethanes[END_REF]. However, monomer synthesis is still based on 2,3-epoxypropyl chemistry. This molecule is obtained from petroleum [START_REF] Kihara | Synthesis and reaction of polymethacrylate bearing cyclic carbonate moieties in the side chain[END_REF][START_REF] Benyahya | Synthesis of glycerin carbonated-based intermediates using thiol-ene chemistry and isocyanate free polyhydroxyurethanes therefrom[END_REF][START_REF] Nohra | From Petrochemical Polyurethanes to Biobased Polyhydroxyurethanes[END_REF] and the carbon footprint of synthesis therefore remains high due to the synthesis of polyacrylates and polymethacrylates, with the risk of generating non-biodegradable organic hydrocarbon polymers [START_REF] Santerre | Biodegradation evaluation of polyether and polyester-urethanes with oxidative and hydrolytic enzymes[END_REF][START_REF] Dupret | Biodegradation of poly(ester-urethane)s by a pure strain of microorganisms[END_REF].

Since 1998, we have been developing procedures for preparing cyclic carbonate chemical coupling agents from glycerol, for the synthesis of multifunctional glycerol monomers, oligomers, and polymers [START_REF] Claude | Process for the Preparation of Glycerol Carbonate[END_REF][START_REF] Vieville | Synthesis of glycerol carbonate by direct carbonatation of glycerol in supercritical CO 2 in the presence of zeolites and ion exchange resins[END_REF][START_REF] Yoo | Catalytic carbonylation of glycerin by urea in the presence of zinc mesoporous system for the synthesis of glycerol carbonate[END_REF][START_REF] Dinh | Polyol Polycarbonates, Organic Compositions Containing Them, a Method for Obtaining these Organic Compositions and a Process for Extraction of Polyol Polycarbonates and Their Applications[END_REF][START_REF] Leising | Manufacture of Carbonate Oligomers of α/α t -Alkoxylated Glycerol Cyclo-Carbonate[END_REF][START_REF] Mouloungui | Process for Acyl Glycerol Oligomer Synthesis[END_REF][START_REF] Mouloungui | Acyl Glycerol Oligomers[END_REF]. The monomer at the heart of these chemical processes is glycerol carbonate [START_REF] Claude | Process for the Preparation of Glycerol Carbonate[END_REF][START_REF] Vieville | Synthesis of glycerol carbonate by direct carbonatation of glycerol in supercritical CO 2 in the presence of zeolites and ion exchange resins[END_REF][START_REF] Yoo | Catalytic carbonylation of glycerin by urea in the presence of zinc mesoporous system for the synthesis of glycerol carbonate[END_REF][START_REF] Sonnati | Glycerol carbonate as a versatile building block for tomorrow: Synthesis, reactivity, properties and applications[END_REF]. This glycerol-based chemical coupling agent was identified in 2004 in France [START_REF] Mouloungui | Chevreul Conference: Unusual ways of synthesis of oleophilic compounds, beginning from solid vegetable substrates (oleaginous seeds), liquids (glycerol and vegetable oil derivatives) for the chemical industry[END_REF]. The US Department of Energy Report entitled Top Value-Added Chemicals from Biomass identified glycerol as one of 12 key renewable building-block chemicals with great promise in terms of versatility and sustainability [START_REF] Werpy | Top Value Chemicals from Biomass[END_REF]. In 2013, we identified glycerol carbonate acrylate (GCA) as a cyclic carbonate of glycerol suitable for use in the development of multifunctional polyhydroxyurethanes (PHUs) [START_REF] Nohra | From Petrochemical Polyurethanes to Biobased Polyhydroxyurethanes[END_REF]. We showed that the mixing of GCA and monoalkylamines resulted in two reactions: an Aza-Michael reaction and an aminolysis reaction [START_REF] Nohra | Aza-Michael versus aminolysis reactions of glycerol carbonate acrylate[END_REF]. The Aza-Michael reaction adds an amine at the ethylene site of GCA. This condensation reaction creates carbon-nitrogen bonds. The nitrogen of the primary amine then forms new secondary and tertiary intermolecular bonds. This increases the density of the carbon-nitrogen bonds and of ethylene and carboxyester sites on GCA. During this condensation, the cyclic carbonate core of the molecule remains closed. We have shown that the condensation of the monoalkylamine begins preferentially at the ethylene site. An aminolysis reaction then occurs between the amine and cyclocarbonate sites. This reaction generates two urethane groups and two adjacent primary and secondary hydroxyl groups.

In this study, we investigated the potential of GCA for use as a cyclic carbonate based chemical coupling agent in the production of multifunctional high-molar mass PHUs. The Aza-Michael reaction generates functional linear and branched mono, di-, tri-, and tetra-amines and increases the density of nitrogen-carbon bonds. The aminolysis reaction increases the density of urethane and hydroxyl units. Linear, interchain, and crosslinked structures result from this increase in urethane unit density and from increases in the densities of adjacent primary and secondary hydroxyl groups, and ethylene and carboxyester groups, favoring the formation of multifunctional PHUs.

Results

Reaction Schemes for the Synthesis of Glycerol Amino Ethylene Ester PHUs

Stepwise type-AB polymerization to provide a linear glycerol amino ethylene ester PHUs can be achieved by two strategies (Figure 1): a stepwise reaction strategy and a one-pot reaction strategy. In the stepwise strategy (steps 1 and 2), the first step is the formation of a bicyclic carbonate compound through the stoichiometric Aza-Michael addition of diamine groups to the glycerol carbonate acrylate (step 1). The addition of a second mole of diamine to the cyclic groups leads to the production of glycerol amino ethylene esters PHUs (step 2). The second strategy (pathway 2), based on a one-pot reaction, involves the addition of larger quantities of diamine than of GCA, and leads to the formation of glycerol amino ethylene ester PHUs.

We initially investigated the effects of certain experimental parameters, by studying the selfreaction of GCA at a temperature of 90 • C under mechanical stirring. No degradation or polymerization of GCA was observed.

Stepwise Strategy for the Synthesis of Glycerol Amino Ethylene Ester PHUs

We studied the Aza-Michael addition of a diamine (HMDA) to GCA double bond (pathway 1). We used two moles of GCA per mole of diamine and we obtained a highly viscous solution of bicyclic carbonates with a complete consumption of acrylate functions. Given the reactivity of GCA, this first step inevitably led to the formation of small amounts of polymer in the reaction medium, also increasing its viscosity. Polyaddition, to generate the PHU polymer, was then initiated by adding a second mole of diamine per mole of bicyclic carbonate. This reaction had a very low conversion rate (about 32%) and led to the production of a hydroxyurethane oligomer. The poor miscibility of the bicyclic carbonates/diamine (or triamine) system determined the conversion rate of the reactants. The stepwise strategy, even if it is selective, is responsible for a lack of reactivity for the GCA bifunctional coupling agent.

One-Pot Strategy for the Synthesis of Glycerol Amino Ethylene Ester PHUs

Glycerol amino ethylene ester PHUs were preferentially synthesized via pathway 2. Several preliminary studies by polyaddition were performed without solvent and at a temperature of 90 • C. We then varied several parameters: the nature of the amine, the reaction temperature, the molar ratio of GCA to amine, and reaction in the presence or absence of solvent. All these parameters would be expected to influence the characteristics of the polymers formed. We will focus here, in particular, on the impact of these parameters on the molar mass of the polymer and its dispersity index.

Effect of the Nature of the Amine

We reacted two moles of GCA with two moles of diamine (or three moles of GCA with two moles of triamine), without solvent, at a temperature of 90 • C. By using different types of amines (chain length, functional groups, order), we were able to obtain various glycerol amino ethylene ester PHUs (Table 1). We noted clear differences in number-average and mass-average molar mass between the various polymers synthesized. The values obtained were markedly higher than published data. The conversion rate was affected by the nature of the amine used. The glycerol carbonate conversion rate was below 100% in all cases, indicating that cyclic carbonate residues remained present in the medium. Proton NMR and infrared spectroscopy also demonstrated the presence of these residues in the mixture. However, these studies also showed that all the double bonds of GCA were consumed. The use of a secondary diamine precluded PHUs formation, resulting in a conversion rate of 0%. Indeed, characterization of the mixture showed a complete absence of cyclic carbonate consumption, consistent with the low reactivity, in Aza-Michael reactions without solvent, of secondary amines not functionalized by cyclic carbonate moieties. Moreover, the steric hindrance and reactivity of the amine may be important parameters in the polyaddition of diamines to GCA [START_REF] Webster | Synthesis and applications of cyclic carbonate functional polymers in thermostteing coatings[END_REF][START_REF] Clements | Reactive Applications of Cyclic Alkylene Carbonates[END_REF]. The reaction of GCA with a secondary amine resulted in the formation of 100% bicyclic carbonates when dimethyl carbonate (DMC) was used as the solvent [START_REF] Nohra | Aza-Michael versus aminolysis reactions of glycerol carbonate acrylate[END_REF].

These syntheses generated linear glycerol amino ethylene ester PHUs from GCA and a linear diamine. Molar mass decreased with the length of the aliphatic chain. Branched linear polymers were also obtained in reactions using an amine with primary and secondary amine functions (trial 4). Finally, glycerol aminoester PHUs in the form of a star (or network) were obtained with high-functionality amines, such as triamines (trial 5).

Effect of the Temperature

We performed the type-AB polyaddition reaction at three different temperatures: 60, 90, and 120 • C. At 60 • C, the conversion rate was only 40% with HMDA (Table 2). The resulting polymer had a low mean number-average molar mass, at 8500 g•mol -1 . Infrared spectroscopy and proton NMR studies showed that residual double bonds were present. The acrylate groups of the GCA were therefore incompletely consumed. Increasing the reaction temperature to 90 • C increased the conversion rate to 75% and resulted in the generation of a glycerol amino ethylene ester PHUs with a mean molar mass of 23,300 g•mol -1 . Increasing the reaction temperature to 120 • C had little effect on the conversion rate and the polymer obtained had a mean molar mass of 25,400 g•mol -1 . Conversion rate and molar mass followed similar patterns between 60 • C and 120 • C (Figure 2). However, the dispersity index (D) drifted away from one between 60 • C and 90 • C. Synthesis at 120 • C led to the production of a molecule with a molar mass similar to that at 90 • C, but with a better D. These features suggest that a more uniform polymer was produced, consistent with the D obtained by anionic polymerization pathways [START_REF] Champetier | Introduction à la Chimie Macromoléculaire[END_REF]. Benyahya et al. [START_REF] Benyahya | Optimization of the synthesis of polyhydroxyurethanes using dynamic rheometry[END_REF] obtained a polymer with a number-average molar mass of 20,000 g•mol -1 , but with a less favorable D of 2.5, in a reaction using a linear diamine as dodecadecyldiamine.

We have shown that the Aza-Michael reaction is the fastest step in our sequential polymerization approach. The concentration of the amine would, therefore, be expected to have only a small effect on reaction kinetics. We thus consider the reaction to be a pseudo-order 1 reaction, rather than a second-order reaction [START_REF] Ochiai | Kinetic and computational studies on aminolysis of bicyclic carbonates bearing alicyclic structure giving alicyclic hydroxyurethanes[END_REF]. The kinetics of the reaction depends principally on the concentration of GCA. The rate of the reaction can thus be written:

v = kapp × C t
After integration, the change in GCA concentration can be expressed as follows:

(1)

t GCA t0 GCA = e -(kapp ×t) (2)
Taking the conversion rate into account, after 2 h of reaction, the energy of activation for this kinetic system can be defined using the Arrhenius expression, as follows:

ln kapp = ln A -( Ea ) × 1 ( 3
)
where R is the perfect gas constant, T is the temperature in K, and A is the frequency factor.

Based on measured conversion rates (Table 2), for reactions at 60 • C, 90 • C, and 120 • C, we obtain an activation energy of 22 kJ•mol -1 . This value is consistent with published results. Tomita et al. [START_REF] Tomita | Polyaddition Behavior of bis(Five-and Six-Membered Cyclic Carbonate)s with Diamine[END_REF] showed that the activation energy for a five-membered bicyclic carbonate was 24.9 kJ•mol -1 .

Effect of the Solvent

We chose to work with dimethyl carbonate (DMC), which has good solvation and environmental acceptance properties [START_REF] Ding | Liquid-solid phase diagrams of binary carbonates for lithium batteries[END_REF][START_REF] Tundo | The Chemistry of Dimethyl Carbonate[END_REF]. DMC is a polar non cyclic carbonate solvent with interesting characteristics. It can thin our viscous media by breaking intermolecular and intramolecular hydrogen bonds of intermediates oligomers and final polymers thanks to his high dielectric constant (ε = 3.087), low density (1.0636 at 25 • C), and low viscosity (0.589 cP at 25 • C). Its low boiling point of 90.5 • C at 760 mmHg is an advantage being easy recovered in substantially pure conditions after being processed.

C /C

The use of DMC increased the conversion rate from 75% to 100%, regardless of the diamine used (Table 3). This increase in conversion rate was accompanied by an increase in the mean number-average molar mass and a slight decrease of the D. The uniformity of the polymer thus appeared to increase with conversion rate. The use of DMC results in a particularly high concentration of reaction centers and, thus, to high conversion rates. It also helps to control the viscosity of the mixture and to regulate the reactional thermal phenomena. The resulting polymers displayed elasticity if generated with the branched polyamine TETA.

Both GCA and diamines are soluble in DMC. The medium gradually becomes heterogeneous as the polymer forms. The polymer precipitates and the DMC could therefore, be recovered by filtration at the end of the reaction. It is, therefore, possible to recycle both the solvent and the residual amine. This synthesis is sufficiently robust to be carried out in a stirred batch reactor, and it could also be scaled up. It would also be possible to transfer the process from a stirred batch reactor to a clean continuous process in which the reaction and separation sequences are coupled to DMC recycling (Figure 3).

Effect of the GCA/Amine Molar Ratio

The effect of the GCA/amine molar ratio was evaluated for polymerization reactions in the presence and absence of DMC (Table 4). Without DMC, increasing the amount of amine (trials 2 and 11) resulted in a small increase in molar mass and a slight increase in conversion rate. This is probably due to the limited miscibility of the diamine in the medium. The medium becomes increasingly viscous towards the end of the reaction. These rheological properties were used by Benyahya et al. [START_REF] Benyahya | Optimization of the synthesis of polyhydroxyurethanes using dynamic rheometry[END_REF] who studied the optimization of PHU synthesis, using a dynamic rheometer to determine the best operating conditions as a function of changes in the rheological characteristics of PHU synthesis media. If there are too few amine groups (trial 12), with a GCA/amine molar ratio of 2/1, polymerization leads to the production of low-molar mass glycerol amino ethylene ester PHUs with a low rate of conversion. Typically, 80% conversion of GCA double bonds by the Aza-Michael addition of diamine to alkene sites is observed, resulting in the generation of bicyclic carbonates. These molecules then react with the diamine, with a conversion rate of 20%. A deficiency of diamine in the medium and the very different reactivity of the two GCA groups affect the conversion rate and the characteristics of the polymer. In the high-temperature reaction conditions used, the reaction medium is a viscous liquid. This liquid forms a rigid transparent gel on cooling.

Combining the DMC effect with a stepwise addition of the diamine led to a complete reaction of the GCA alkene groups and a more than 90% conversion rate for bicyclic carbonates. It consisted in restoring the amount of amine present to equilibrium levels to obtain higher conversion rates.

The aliphatic diamine contains two primary amine sites and two secondary amine sites, all able to react in Aza-Michael reactions [START_REF] Nohra | Aza-Michael versus aminolysis reactions of glycerol carbonate acrylate[END_REF]. We tried to react each of these sites with GCA to generate additional cyclic moieties, thereby making it possible to increase the molar mass of the polymer. The addition of 4 moles of GCA per mole of amine lead to the formation of 4 cyclic carbonate groups as the GCA alkene group conversion was complete. The consecutive addition of 2 moles of amine lead to conversion rates of 90% for cyclic carbonates, corresponding to the opening of four cyclic carbonate groups. This strategy was also successfully applied to TAEA which has three primary amine groups.

Characterization of Glycerol Amino Ethylene Ester PHUs

We characterized the glycerol amino ethylene ester PHUs, by determining the quantitative composition of the mixtures obtained. The products were analyzed by infrared spectroscopy to detect ester functions (1737 cm -1 ) and urethane functions (1705 cm -1 ). The FTIR spectrum of a low-molar mass glycerol amino ethylene ester PHUs, with incomplete consumption of the bicyclic carbonates (polymer in gel form, trial 12) is shown in Figure 4. The alkene band at 1640 cm -1 disappeared after the Aza-Michael addition of diamine to GCA, and the cyclic carbonate band at 1795 cm -1 disappeared after the complete opening of the GCA molecule by the addition of multiple diamine or triamine molecules to form glycerol amino ethylene ester PHUs (Figure 5).

The attribution of the 13 C-NMR signals is based on data obtained for glycerol amino ethylene ester PHUs with cyclic carbonate conversion rates close to 100% (Figure 6). The characteristic bands can be attributed to the carbons of the ester at 173 ppm and those of urethane at 158.94 and 158.57 ppm.

The lack of resonance at 156-157 ppm confirms that the cyclic carbonate groups had opened completely to form glycerol amino ethylene ester PHUs. Furthermore, the alkyl chain carbons located at polymer chain centers (obtained by adding diamine to GCA) were found not to be identical to those at the ends of the alkyl chain (after the opening of cyclic carbonates by a diamine or triamine). Carbon a t displays greater deshielding than carbon a. By integrating carbon zgig 13 C-NMR signals (Figure 7), it is possible to calculate the OH I area/OH II area ratio of the glycerol amino ethylene ester PHU formed [START_REF] Nohra | Aminolysis Reaction of Glycerol Carbonate in Organic and Hydroorganic Medium[END_REF]. We calculated this ratio by comparing the integrals for characteristic groups. We integrated carbon NMR signals during zgig acquisition and obtained a 25/75 ratio perfectly consistent with published data [START_REF] Steblyanko | Addition of Five-Membered Cyclic Carbonate with Amine and Its Application to Polymer Synthesis[END_REF].

Discussion

Glycerol carbonate acrylate is a bifunctional coupling agent that allows moving from CHO to CHON structures by reacting both the ethylene and cyclic carbonates sites of GCA by Michael Addition and condensation reaction with amines, respectively. The CHON structures combine ester, secondary and/or tertiary amine, primary and secondary hydroxyls, and urethane functions spaced with disubstituted ethylene units. These original PHUs could only be obtained by the polymerization of the specific glycerilic cyclic carbonate GCA.

We have developed two different approaches for obtaining high-molar mass glycerol amino ethylene ester PHUs from GCA by a stepwise reaction strategy and a one-pot reaction strategy, without any catalysts. The reaction can be monitored by FTIR spectroscopy to follow the conversion of alkene and cyclic carbonate groups and the formation of urethane and hydroxyl groups. The ratio of primary to secondary hydroxyl groups in the polymer can be determined by 13 C-NMR.

With the stepwise strategy, we have demonstrated that the step 1 (Michael reaction) produces cyclic carbonates structures spaced with secondary or tertiary amines in their aliphatic chain. Due to the high reactivity of amines for the alkene sites of the acrylate, the Aza-Michael addition of amines to GCA results in the synthesis of glycerol amino ethylene ester cyclic carbonates. These bicyclic carbonates molecules are weakly reactive when adding additional amines [START_REF] Nohra | Aza-Michael versus aminolysis reactions of glycerol carbonate acrylate[END_REF]. The rate constant for Aza-Michael addition is well above that for the opening of the cyclic carbonate ring. The presence of Van der Walls bonds of N-H type competes to create in situ structured networks and are responsible for the increase in viscosity in the reactional medium. The networks are so cohesive that the consecutive insertion of amines on the cyclic carbonates moieties is limited leading to a weak opening of the cycles; the limited formation of C, H, O, N structures; and the production of low molar mass PHUs.

The one-pot strategy favors the almost simultaneous occurrence of Michael addition and condensation to produce high molar mass CHON structures. The differences in the molar masses were highlighted by the study of experimental parameters. We initially studied the bulk type AB polymerization reaction in experiments in which we varied the nature of the amine. The type of amine and the GCA/amine ratio affected the average molar mass and morphology of the polymer generated. Temperature also affected the polymerization reaction and the rate of conversion for cyclic carbonates. This conversion rate increased substantially between 60 • C and 90 • C, with no further change at 120 • C. The increasing viscosity of the mixture at higher temperatures limited reactivity.

The polycondensation is favored by varying the GCA/Amine ratio and by adding DMC as solvent. The addition of DMC resulted in polymers with a higher molar mass and a good dispersity index. This last point also opened perspectives for using DMC to allow improving the stepwise strategy. DMC acts as a diluent co-component likely to break the Van der Walls bonds and to activate the reactivity of the amine sites and their condensation with cyclic carbonates sites. Moreover, a chemical synergistic effect activating the reactive species in the medium was developed by the joint presence of DMC and intermediate glycerilic cyclic carbonates generated in situ. These bicyclic carbonate intermediates have useful polar, conductive, and activating properties. They promote autocatalytic reactions through the in situ activation of amine and cyclic carbonate sites, facilitating in particular the aminolysis in the absence of added catalysts. These activating properties are the driving force behind this new AB-type polymerization pathway for the generation of glycerol amino ethylene ester PHUs.

Our method of choice was the one-pot reaction with DMC as compatibilizer as it presented the advantages of being a clean, inexpensive, and efficient process. All of the GCA and amine atoms enter the PHUs atomic composition promoting the atom economy and an environmental efficiency [START_REF] Sheldon | Atom efficiency and catalysis in organic synthesis[END_REF]. No catalyst was used and no residual byproducts or co-reagents were detected in the final media. DMC also presents the advantage of being recovered and recyclable at the end of the reaction, especially since it is not contaminated with catalysts.

With the one-pot strategy, high molar masses ranging from 25,000 to 55,000 g•mol -1 were obtained with equivalent dispersity indexes, representative of identical hydrocarbon skeletons, typical of the -CH 2 -CH 2 -ethylenic spacer. Our synthesis pathways generated polymers in the form of gels, foams, and resins. These rigid, flexible, or elastic products have many possible applications. This type-AB polymerization can be used to generate oligoprecursors for bulk, solution, or photochemical polymerization. Various non-toxic biodegradable reactive groups are available for the production of tailor-made copolymers with specific properties for particular applications compatible with the environment.

Experimental Section

Materials

Glycerol carbonate (Huntsman, Port Neches, TX, USA, 99.5%), acryloyl chloride (Sigma Aldrich, Saint Quentin Fallavier, France, 97%), Ethylenediamine (EDA, Sigma Aldrich, 99%), hexamethylenediamine (HMDA, Sigma Aldrich, 98%), N,N t -diethylethylenediamine (DEEDA, Sigma Aldrich, 99%), triethylenetetramine (TETA, Sigma Aldrich, >97%), tris (2-aminoethyl)amine (TAEA, Sigma Aldrich, 96%), Dimethyl carbonate (DMC, Sigma Aldrich, 97%), were used as received.

Synthesis

Synthesis of Glycerol Carbonate Acrylate (GCA)

GCA was synthesized from glycerol carbonate and acryloyl chloride and characterized as previously described [START_REF] Werpy | Top Value Chemicals from Biomass[END_REF].

Two-Step Synthesis of Glycerol Amino Ethylene Ester PHUs

Step 1: 0.116 mole (20 g) of GCA was placed in a 100 mL reactor equipped with a 500 rpm mechanical stirring and heated to 90 • C. 0.058 mole of amine (chosen between EDA, HMDA, DEEDA, TETA, TAEA) was slowly added. The reaction was carried out for 1 h at 90 • C and the progress of the reaction was followed by FTIR.

Step 2: 0.058 mole of amine was added, under stirring, to the preceding reaction medium and the reaction was continued for 2 h at the same temperature. 4.2.3. One-Pot Synthesis of Glycerol Amino Ethylene Ester PHUs 0.116 mole (20 g) of GCA was placed in a 100 mL reactor equipped with a 500 rpm mechanical stirring and heated to 90 • C. 0.116 mole of amine (chosen between EDA, HMDA, DEEDA, TETA, TAEA) was slowly added. For reactions using solvent, 40 mL of DMC were added to GCA before heating. The reaction was carried out for 2 h at 90 • C and the progress of the reaction was followed by FTIR.

Characterization

Fourier Transform Infrared Spectroscopy

Fourier transform infrared (FTIR) spectra were achieved by transmission on a PerkinElmer Spectrum 65 spectrometer (PerkinElmer SAS, Courtaboeuf, France).

Nuclear Magnetic Resonance (NMR) Spectroscopy

1 H and 13 C nuclear magnetic resonance (NMR) spectra were achieved on a Bruker Advance ® 300 MHz instrument (Bruker Biospin S.A.S., Wissembourg, France) using tetramethylsilane (TMS) as an internal standard and equipped with QNP probe ( 1 H, 19 F, 31 P, 13 C). The proportions of secondary and primary OH groups were determined at 293.2 K, with zgig 13 C pulse program. The delay time D1 is greater than or equal to 30 s in order to permit the full relaxation of all nuclei concerned in the assay.

Size Exclusion Chromatography (SEC)

SEC was used to determine molecular masses and dispersity indexes of the polymer samples. Analyses were achieved on a system equipped with a P580 Pump (Dionex, Voisins-le-Bretonneux, France),an ASI-100 Automated sample Injector (Dionex, France), and a 350 RI detector (Varian, Les Ullis, France). Two PL Aquagel-OH30 (8 µm × 300 mm × 7.5 mm) columns in series were used at a 0.8 mL•min -1 flow rate with water as eluent 30 • C. The molar masses were calculated with respect to polysaccharide standards (Polymer Laboratories Mp = 180 g•mol -1 to Mp = 3.8 × 10 5 g•mol -1 ).

Figure 1 .

 1 Figure 1. Synthesis of a glycerol amino ethylene ester PHUs (R = C 2 H 4 , C 6 H 12 , C 6 H 15 N 2 ).

Figure 2 .

 2 Figure 2. One-pot strategy; impact of the temperature on molar mass, dispersity index, and conversion rate for HMDA addition on GCA; ( ) Log Mw, () D, ( ) T GCC .

Figure 3 .

 3 Figure 3. Batch process scheme for the synthesis of high-molecular-weight glycerol amino ethylene ester PHUs.

Figure 4 .

 4 Figure 4. Infrared spectrum of a glycerol amino ethylene ester PHU gel (trial 12).

Figure 5 .

 5 Figure 5. Infrared spectrum of a glycerol amino ethylene ester PHU resin (trial 9).

Figure 6 .

 6 Figure 6. Representation and nomenclature for a glycerol amino ethylene ester PHUs for 13 C-NMR (dept135) in D 2 O.

Figure 7 .

 7 Figure 7. zgig 13 C-NMR spectrum for a glycerol amino ester ethylene PHUs in D 2 O.

Table 1 .

 1 One-pot strategy; Influence of the amine on the synthesis of glycerol amino ethylene ester PHUs. T = 90 • C, duration = 2 h. Mass-average molecular mass (Mw) determined by SEC; c Dispersity index (Mw/Mn); d Visual appearance of the polymers obtained; e Conversion rate (%) of cyclic carbonates determined by 1 H-NMR.

	Trial	Amine	M n	a	M w b	D c	Aspect d	T GCC (%) e
	1	EDA	35,600	52,400	1.43	Foam	69
	2	HMDA	23,300	28,700	1.23	Rigid resin	75
	3	DEEDA	-		-	-	No polymerization	0
	4	TETA	32,800	44,000	1.34	Rigid resin	79
	5	TAEA	42,200	53,400	1.26	Solid granules	83

a Number-average molar mass (Mn) determined by SEC; b

Table 2 .

 2 One-pot strategy; influence of the temperature on the synthesis of glycerol amino ethylene ester PHUs. Duration = 2 h.

	Trial	Amine	T ( • C)	Mn a	M w b	D c	T GCC (%) d
	6	HMDA	60	8500	10,200	1.11	40
	7	HMDA	90	23,300	28,700	1.23	75
	8	HMDA	120	25,400	30,200	1.18	82
	a Number-average molar mass (Mn) determined by SEC; b Mass-average molar mass (Mw) determined by SEC;
	c Dispersity index (Mw/Mn); d Conversion rate (%) of cyclic carbonates determined by 1 H-NMR.

Table 3 .

 3 One-pot strategy; influence of DMC solvent on the synthesis of amino ethylene ester PHUs. T = 90 • C, duration = 2 h. Number-average molar mass (Mn) determined by SEC; b Mass-average molar mass (Mw) determined by SEC; c Dispersity index (Mw/Mn); d Visual appearance of the polymers obtained; e Conversion rate (%) of cyclic carbonates determined by 1 H-NMR.

	Trial Amine Solvent	Mn a	M w	b	D c	Aspect d	T GCC (%) e
	2	HMDA	/	23,300	28,700	1.23	Rigid resin	75
	4	TETA	/	32,800	44,000	1.34	Rigid resin	79
	9	HMDA	DMC	27,300	31,400	1.15	Rigid resin	95
	10	TETA	DMC	42,800	54,000	1.26	Elastic	96

a

Table 4 .

 4 Influence of the GCA/amine molar ratio on the synthesis of amino ethylene ester PHUs. T = 90 • C, duration = 2 h.

	Trial	GCA/Amine a	Amine Solvent	Mn b	Mw c	D d	Aspect e	T GCC (%) f	T GCA (%) g
	2	1/2	HMDA	/	23,300	28,700	1.23	Rigid resin	75	100
	11	1/3	HMDA	/	25,200	29,000	1.15	Rigid resin	79	100
	12	2/1	HMDA	DMC	5600	7000	1.23	Rigid gel	20	80

a GCA/amine ratio of the reagents; b Number-average molar mass (Mn) determined by SEC; c Mass-average molar mass (Mw) determined by SEC; d Dispersity index (Mw/Mn); e Visual appearance of the polymers obtained; f Conversion rate (%) for cyclic carbonates determined by 1 H-NMR; g Conversion rate (%) for ethylenic group of GCA determined by 1 H-NMR.

Acknowledgments: This work was supported by ADEME (Angers, France) and ONIDOL (Paris, France). Author Contributions: Z.M. and L.C. conceived and designed the experiments; B.N. performed the experiments; B.N. and J-F.B. analyzed the data; J-F.B. and Y.R. contributed reagents/materials/analysis tools/end-uses applications; Z.M. and L.C. wrote the paper.

Conflicts of Interest:

The authors declare no conflict of interest.


Daniel S Karp

Rebecca Chaplin-Kramer

Timothy D Meehan

Emily A Martin

Fabrice Declerck

Heather Grab

Claudio Gratton

Lauren Hunt

Ashley E Larsen

Alejandra Martínez-Salinas

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Megan E O'rourke

Adrien Rusch

Katja Poveda

Mattias Jonsson

Jay A Rosenheim

Nancy A Schellhorn

Teja Tscharntke

Stephen D Wratten

Wei Zhang

Aaron L Iverson

Lynn S Adler

Matthias Albrecht

Audrey Alignier

Gina M Angelella

Muhammad Zubair Anjum

Jacques Avelino

Péter Batáry

Johannes M Baveco

Felix J J A Bianchi

Klaus Birkhofer

Eric W Bohnenblust Aa

Riccardo Bommarco

Michael J Brewer Bb

Berta Caballero-López Cc

Yves Carrière Dd

Luísa G Carvalheiro Ee

Luis Cayuela Ff

Mary Centrella

Aleksandar Cetkovi

Dominic Gg

Henri Charles

Ariane Hh

Alejandro C Chabert Ii

Aldo Costamagna Jj

Mora De La

Joop Kk

De Kraker

Nicolas Desneux

Eva Diehl

Tim Diekötter

Carsten F Dormann Pp

James O Eckberg Qq

Martin H Entling Rr

Daniela Fiedler

Pierre Franck

F J Frank Van Veen

Thomas Frank

Vesna Gagic

Michael P D Garratt Ww

Awraris Getachew

David J Gonthier Yy

Peter B Goodell Zz

Ignazio Graziosi

Russell L Groves

Geoff M Gurr Bbb

Zachary Hajian-Forooshani

George E Heimpel Ddd

John D Herrmann

Anders S Huseth Eee

Diego J Inclán Fff

Phirun Iv hhh Adam J Ingrao Ggg

Katja Jacot

Gregg A Johnson Qq

Laura Jones

Marina Kaiser Gg

Joe M Kaser Ddd

Tamar Keasar Iii

Tania N Kim Jjj

Miriam Kishinevsky

Douglas A Landis Ggg

Blas Lavandero Lll

Claire Lavigne Tt

Anne Le Ralec

Debissa Lemessa Nnn

Deborah K Letourneau Ooo

Heidi Liere

Yanhui Lu Ppp

Yael Lubin Qqq

Tim Luttermoser

Bea Maas

Kevi Mace Sss

Filipe Madeira

Viktoria Mader Nn

Anne Marie Cortesero

Lorenzo Marini Vvv

Eliana Martinez

Holly M Martinson Xxx

Philippe Menozzi

Matthew G E Mitchell Zzz

Tadashi Miyashita Aaaa

Gonzalo A R Molina Bbbb

Marco A Molina-Montenegro

Matthew E O'

Neal Dddd

Itai Opatovsky Eeee

Sebaastian Ortiz-Martinez

Michael Nash

Örjan Östman Gggg

Annie Ouin

Damie Pak

Daniel Paredes

Soroush Parsa

Hazel Parry

Ricardo Perez-Alvarez

David J Perovi

Julie A Bbb

Sandrine Peterson Ddd

Petit

Stacy M Philpott Ooo

Manuel Plantegenest

Milan Ple Cas Gg

Therese Pluess

Xavier Pons

Simon G Potts Ww

Richard F Pywell Nnnn

David W Ragsdale Oooo

Tatyana A Rand Pppp

Lucie Raymond

Benoît Ricci Llll

Chris Sargent

Jean-Pierre Sarthou

Julia Saulais

Jessica Schäckermann

Nickp Schmidt Dddd

Gudrun Schneider

Christof Schüepp

Frances S Sivakoff Ssss

Henrik G Smith Tttt

Kaitlin Stack

Whitney Uuuu

Sonja Stutz

Zsofia Szendrei

Mayura B Takada Wwww

Hisatomo Taki Xxxx

Giovanni Tamburini

Linda J Thomson Yyyy

Yann Tricault Zzzz

Noelline Tsafack Aaaaa

Matthias Tschumi

Muriel Valantin-Morison

Mai Van

Trinh Ccccc

Wopke Van Der Werf Ddddd

Kerri T Vierling Eeeee

Ben P Werling Fffff

Jennifer B Wickens Ww

Victoria J Wickens Ww

Ben A Woodcock Nnnn

Kris Wyckhuys

Haijun Xiao Iiiii

Mika Yasuda

Akira Yoshioka

Yi Zou

M Kaiser

Y Lu

Y Lubin

M E O'neal

S Petit

M Ple

Y Z Performed

Crop pests and predators exhibit inconsistent responses to surrounding landscape composition

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

The idea that noncrop habitat enhances pest control and represents a win-win opportunity to conserve biodiversity and bolster yields has emerged as an agroecological paradigm. However, while noncrop habitat in landscapes surrounding farms sometimes benefits pest predators, natural enemy responses remain heterogeneous across studies and effects on pests are inconclusive. The observed heterogeneity in species responses to noncrop habitat may be biological in origin or could result from variation in how habitat and biocontrol are measured. Here, we use a pest-control database encompassing 132 studies and 6,759 sites worldwide to model natural enemy and pest abundances, predation rates, and crop damage as a function of landscape composition. Our results showed that although landscape composition explained significant variation within studies, pest and enemy abundances, predation rates, crop damage, and yields each exhibited different responses across studies, sometimes increasing and sometimes decreasing in landscapes with more noncrop habitat but overall showing no consistent trend. Thus, models that used landscape-composition variables to predict pest-control dynamics demonstrated little potential to explain variation across studies, though prediction did improve when comparing studies with similar crop and landscape features. Overall, our work shows that surrounding noncrop habitat does not consistently improve pest management, meaning habitat conservation may bolster production in some systems and depress yields in others. Future efforts to develop tools that inform farmers when habitat conservation truly represents a win-win would benefit from increased understanding of how landscape effects are modulated by local farm management and the biology of pests and their enemies.

services to farmers, and (ii) determine to what extent landscape information alone can be used to model and predict variation in pest control across systems.

First, we compiled an extensive pest-control database composed of 18,094 total observations of pest and enemy abundance, enemy activity (predation rates), crop damage, and yields across 6,759 sites in 31 countries (Fig. 1). We then used a modelaveraging approach to explore to what extent surrounding forest, grassland, scrubland, annual crops, and perennial crops (i.e., landscape composition), at multiple spatial scales, could explain spatial patterns in the pest-control variables recorded in each study. From prior observations [START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF][START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF], we predicted that landscapes with more noncrop habitat would generally increase enemy abundance and activity (pest predation) but that pest abundance, damage, and crop yield would exhibit significant variation in how they respond to noncrop habitat across studies. Nevertheless, we predicted that landscape models would be able to explain variation in independent datasets, provided that the independent dataset and the dataset from which the landscape model was constructed shared geographic, crop, and/or landscape features.

Results

Pest-Control Models. We constructed separate models (n = 359) that explored how surrounding landscape composition affected each unique pest-control variable reported in each study (hereafter referred to as unique "pest-control responses"). We report a summary of the 359 pest-control responses, focal crops, target pests, and sample sizes (Dataset S1) and include the entire biological control database (Dataset S2). Pest-control responses were made up of censuses of dominant pests, all pests, and dominant enemies (n = 76, 27, and 78 responses, respectively), exclosure and sentinel pest experiments that measured enemy activity (n = 23 and 68, respectively), crop-damage surveys that measured pest activity (n = 34), and crop-yield data (n = 53). Though 31 countries were represented, there was a strong temperate bias, with 39% of the 132 studies from Europe, 23% from North America, 14% from Central and South America, 12% from Asia, 8% from Australia and New Zealand, and 4% from Africa. Similarly, though the database encompassed many distinct crops (n = 41 crops, 38 species), the vast majority of sites were in annual (90%) versus perennial (10%) agriculture.

Overall, we found that there was significant variation among studies in the effects of different landscape variables on pestcontrol responses. Contrary to our first prediction, we observed no consistent effects of "natural" landscape variables (forest, grassland, scrubland; aggregate natural habitat category) or "agricultural" landscape variables (perennial crops, annual crops; aggregate crop category) on enemy and pest abundance and activity. That is, χ 2 tests indicated that surrounding noncrop habitat and cropland affected pest-control variables positively and negatively in a roughly equivalent number of models (all P > 0.05; Fig. 2). Effects of natural landscape variables were often even inconsistent within studies. For example, in the majority of enemy-abundance models, enemies responded positively to one natural land-use type (e.g., forest) but negatively to another (e.g., grassland). Restricting our focus to only the most predictive land-use variable present in each model did not change these conclusions. We still found that most pest-control variables responded positively and negatively to landscape variables in a roughly equivalent number of models (SI Appendix, Fig. S1; all P > 0.05). An exception was crop yields, which tended to decline with surrounding natural land uses more often than not (χ 2 = 9.8, P < 0.01). Similarly, no single spatial scale tended to be most predictive, though more pest-abundance and enemy-activity (cage experiments) responses were best predicted by models that placed greater weight on areas closer to sampling sites (SI Appendix, Fig. S2). benefits for crop pollinators [START_REF] Kennedy | A global quantitative synthesis of local and landscape effects on wild bee pollinators in agroecosystems[END_REF], surrounding noncrop habitat is also generally thought to benefit predators and parasitoids and thereby enhance biological control of crop pests. Indeed, both qualitative (e.g., refs. 2 and 3) and quantitative (e.g., refs. 4 and 5) syntheses have concluded that, on average, enemy abundance, diversity, and activity (pest consumption) increase in landscapes with more noncrop habitat. The benefits of noncrop habitat are likely multifaceted: Just as for pollinators [START_REF] Kennedy | A global quantitative synthesis of local and landscape effects on wild bee pollinators in agroecosystems[END_REF], noncrop habitat can provide enemies with supplemental food resources, nesting locations, and/or overwintering sites [START_REF] Bianchi | Sustainable pest regulation in agricultural landscapes: A review on landscape composition, biodiversity and natural pest control[END_REF][START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF][START_REF] Gurr | Habitat management to suppress pest populations: Progress and prospects[END_REF]. However, the assumption that more noncrop habitat in farming landscapes universally increases biocontrol belies significant variation among studies in how enemies respond to landscape composition (i.e., the relative proportions of crop and noncrop land-use types in the landscapes surrounding farm fields) [START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF][START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF]. Moreover, the effect of landscape composition on pests themselves remains inconclusive, as many crop pests also benefit from nearby noncrop habitat [START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF][START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF]. As a result, programs focused on improving the conservation value of farming landscapes could, in some cases, precipitate increased yield losses to crop pests [START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF].

The great variation among studies in pest and enemy responses, coupled with a research bias for studies in temperate systems, has also precluded our ability to use relationships derived in prior quantitative syntheses to model pest control globally. As a result, despite presumed significant contributions to agricultural production-estimated at approximately US$4.5 billion/y in avoided crop damage in the United States alone (8)-and repeated recognition in ecosystem-service frameworks [START_REF]Millennium Ecosystem Assessment (2005) Ecosystems & Human Well-Being: Synthesis[END_REF][START_REF]TEEB for agriculture and food interim report[END_REF], natural biological control is rarely taken into account in landscape-level planning and environmental decision making. Existing decisionsupport tools and models focus on pest-control dynamics as a function of on-farm activities [START_REF] Kean | The population consequences of natural enemy enhancement, and implications for conservation biological control[END_REF][START_REF] Zhang | Incorporating natural enemies in an economic threshold for dynamically optimal pest management[END_REF]. The few landscape-level models that do exist and could inform decision making require a thorough understanding of the life histories of target pests and their natural enemies (e.g., attack rates, growth rates, etc.) [START_REF] Bianchi | Changes in agricultural land use can explain population decline in a ladybeetle species in the Czech Republic: Evidence from a process-based spatially explicit model[END_REF][START_REF] Bianchi | Spatial variability in ecosystem services: Simple rules for predator-mediated pest suppression[END_REF][START_REF] Jonsson | Ecological production functions for biological control services in agricultural landscapes[END_REF]. At present, such models can be applied only by experts in very data-rich environments and may not be generally applicable.

Because there is no established standard for measuring either pest control or landscape composition, it is possible that the diverse responses of pests and enemies to surrounding landscape composition result from researchers measuring pests, enemies, their interactions, and the landscapes they inhabit in different ways. Alternatively, the heterogeneity in species responses could be real, resulting from shifting interactions between different species of pests and enemies with varying traits in different landscapes. Here we standardize, reanalyze, and quantitatively synthesize published and unpublished studies to (i) assess the role of surrounding noncrop habitat in providing pest-control Significance Decades of research have fostered the now-prevalent assumption that noncrop habitat facilitates better pest suppression by providing shelter and food resources to the predators and parasitoids of crop pests. Based on our analysis of the largest pest-control database of its kind, noncrop habitat surrounding farm fields does affect multiple dimensions of pest control, but the actual responses of pests and enemies are highly variable across geographies and cropping systems. Because noncrop habitat often does not enhance biological control, more information about local farming contexts is needed before habitat conservation can be recommended as a viable pest-suppression strategy. Consequently, when pest control does not benefit from noncrop vegetation, farms will need to be carefully comanaged for competing conservation and production objectives. Model Performance. Despite observed heterogeneity, we did find that landscape composition explained variation in pest-control responses within studies (average R 2 0.14 to 0.20; Fig. 3 and SI Appendix, Table S1). The average correlation across individual studies between observed data and model predictions was significantly larger than 0, and ranged from 0.37 (all enemies) to 0.45 (sentinel pest experiments). With respect to individual datasets, correlations between model predictions and observed data were significant and positive ∼50% of the time (SI Appendix, Table S1). Interestingly, model performance varied across biogeographic realms (SI Appendix, Fig. S3). Models tended to explain more variation in pest variables (pest abundance and damage) when studies were located in the Palearctic (42% of responses; χ 2 = 5.6, P = 0.02) and, to a lesser extent, in the Nearctic (28% of responses; χ 2 = 3.0, P = 0.08) compared with other areas. While landscape relationships with natural enemy variables (enemy abundance and activity) did not vary geo-graphically (all P > 0.05), more variation in yield data was explained in the Nearctic than in other areas (χ 2 = 4.4, P = 0.04).

To actually assess our models' predictive power, we examined how well observations in each dataset correlated with predictions generated from the full suite of models from the other (independent) datasets. As hypothesized, field observations did not correlate with average predictions across all independent models (Fig. 4 and SI Appendix, Table S2). That is, correlations between average model predictions and field observations were not statistically distinguishable from 0, which was not surprising given such high observed variation among studies in the directionality of landscape-composition responses.

Using Model Subsets to Improve Predictive Power. To improve predictive power, we used a full-factorial sensitivity analysis (Methods) to explore multiple scenarios of filtering and applying subsets of models to field observations, rather than using the Abundance (n=181)

Activity (n=125) Yield (n=53)
31 countries 132 studies 6759 sites Fig. 1. Map of study locations. We collected pest-control data from 132 studies across 6,759 sites and 31 countries. Pest-control data included abundances of dominant pests, all pests, and natural enemies (black dots; 181 responses), pest and predator activity data from crop-damage surveys, sentinel pest experiments, and exclosure experiments (cyan dots; 125 responses), and yield data (red dots; 53 responses). Fig. 2. Landscape effects on pest-control variables. After selecting the most predictive model for each pest-control response (N = 367) and redefining landcover variables as natural (forest, grassland, and scrubland; green bars) versus crop (annual and perennial; orange bars), we tallied the number of pest-control responses for which models had either positive (solid), negative (diagonal hashed), or mixed (horizontal) estimates of the effect of each landscape predictor. Panels represent the seven pest-control variables, including abundance (A) and activity (B and C) of natural enemies; abundance (D and E) and activity (F) of pests; and crop yields (G). χ 2 tests indicated that pest-control response variables showed heterogeneous patterns of association with the extent of surrounding natural habitat and cropland-with roughly equivalent numbers of pest-control responses having models with positive and negative effects (all P > 0.05).

geographically. For example, models from Nearctic and Palearctic realms generally explained more variation in pest abundance and activity than models from other areas. This difference may from latitudinal variation in data quality. Fewer regional land-use maps exist in data-poor tropical areas, and informal inspection of the global land-use map suggested that land-cover classifications were often inaccurate in tropical landscapes. C ro p Y ie ld s Fig. 4. Testing landscape models. (Top) Correlating average predictions across all possible landscape models (Methods) against independent field observations resulted in low predictive power. Each gray circle is the observed correlation for one dataset (set of field observations); filled circles are significant correlations (P < 0.05). Black circles are average correlations across all tested datasets; lines are confidence intervals. (Bottom) More selective application of models to independent field observations caused correlations to be on average positive for all pest-control variables except pest damage and crop yields (asterisks indicate P < 0.05). Specifically, this panel demonstrates that predictive power was higher when a more selective subset of models was applied to the independent field observations, subject to several of the following constraints: (i) Field observations and the data from which models were constructed (model data) shared the same crop; (ii) the same land-cover variables were present in model data and field observations; (iii) landscape values in field observations were within the range of landscape values in the model data; and (iv) models explained significant variation in their own data (r > 0.25). Dominant pests, pest damage, and crop yields were subject to constraints (i) and (ii); all pests to (i), (ii), and (iii); sentinel experiments to (i), (ii), and (iv); and all enemies and cage experiments to (i), (ii), (iii), and (iv).

average predictions generated from all landscape models (SI Appendix, Table S3). While this approach suggested several model-selection methods that improved predictive power, correlations between model predictions and field observations remained low. For example, correlations between field observations and average model predictions tended to be higher when we only used models constructed from studies that focused on the same crop as the field observations. Prediction was also enhanced when we only included models that shared the same land-cover variables as those present around the field observations or, even more stringently, when land-cover variable values associated with the field observations were within the range of values present in the model data (i.e., the landscape-composition gradients matched). By strategically selecting models from studies that better matched the field observations, we could increase correlations between average model predictions and observed pestabundance, enemy-abundance, and enemy-activity data such that correlations were, on average, positive across all field observations (Fig. 4, Bottom and SI Appendix,Table S2). Critically, however, model predictions rarely explained significant variation among individual pest-control responses: In ∼12 and ∼5% of responses, correlations between field observations and model predictions were significantly positive and negative, respectively. Explorations of other strategies for improving predictive power yielded mixed results (SI Appendix, Table S3). Only using models from studies in the same biogeographic realm as the field observations marginally improved predictive power for pestdamage responses but reduced predictive power for all other pest-control variables. When models and field observations shared the same biome, predictive power significantly increased for some variables (e.g., enemy activity measured in cage experiments) but decreased for others (e.g., enemy activity measured in sentinel experiments, crop yield). Similarly, predictive power sometimes increased (e.g., all pests, crop yield) and sometimes decreased (e.g., dominant pests, all enemies, sentinel experiments, cage experiments) when we only used models from studies that were located within 500 km of field observations.

Discussion

Despite heterogeneity in environmental conditions, farm management, and species assemblages, we found that every dimension of pest control, from enemy abundance to crop yields, tended to show some associations with the surrounding landscape composition. Our work thus confirms prior observations that habitat composition of the broader farmscape can modulate on-farm pest control (2-4). Interestingly, explanatory power varied Fourth, discordance with prior findings may be attributable to additional sources of variability tested in the original studies but not addressed by this analysis. Indeed, landscape composition by itself explained on average only 14 to 20% of the variation in pest-control variables, leaving substantial variation unaccountedfor after correlating model predictions with field observations. Landscape-composition effects could easily be present but masked by variation in local farm-management factors or local climate variables that published studies usually treat as covariates. Indeed, crop diversification, insectary plantings, and insecticide treatments all influence pest control and, in some cases, can modify landscape effects [START_REF] Jonsson | Agricultural intensification drives landscape-context effects on host-parasitoid interactions in agroecosystems[END_REF][START_REF] Letourneau | Does plant diversity benefit agroecosystems? A synthetic review[END_REF][START_REF] Chaplin-Kramer | Pest control experiments show benefits of complexity at landscape and local scales[END_REF].

Finally, different pest and enemy species often respond differently to landscape variables [START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF]. Because most of the variables we modeled were not species-specific (e.g., abundance of all possible pests), differences in the species that were modeled versus the species present in the tested datasets likely lessened the accuracy of our predictions. Indeed, while many natural enemies need noncrop habitats to complete their life cycles [START_REF] Gurr | Habitat management to suppress pest populations: Progress and prospects[END_REF], some enemies are more dependent on cropland than they are on noncrop vegetation [START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF]. Moreover, if pests increase in simple landscapes, then enemies may increase too, as they start to exploit this burgeoning resource.

A Path Forward. If we hope to move toward more sustainable land and pest management, decision makers need to be informed about tradeoffs among multiple ecosystem services of their landuse decisions. For example, a variety of stakeholders interested in agricultural development are concerned with the consequences of habitat loss that accompany land-use change, including governments [START_REF] Mitchell | The Monteregie connection: Linking landscapes, biodiversity, and ecosystem services to improve decision making[END_REF][START_REF] Ouyang | Improvements in ecosystem services from investments in natural capital[END_REF], multilateral development banks [START_REF] Mandle | Entry points for considering ecosystem services within infrastructure planning: How to integrate conservation with development in order to aid them both[END_REF], and corporations [START_REF] Nepstad | More food, more forests, fewer emissions, better livelihoods: Linking REDD+, sustainable supply chains and domestic policy in Brazil, Indonesia and Colombia[END_REF]. These actors have typically been focusing on impacts of agriculture on biodiversity, carbon storage, and water, but agricultural expansion or intensification also has massive implications for ecosystem services to agriculture, like pest suppression [START_REF] Chaplin-Kramer | Spatial patterns of agricultural expansion determine impacts on biodiversity and carbon storage[END_REF][START_REF] Meehan | Agricultural landscape simplification and insecticide use in the midwestern United States[END_REF]. High cross-system variability impeded this initial attempt to develop simple landscape models that could deliver accurate pestcontrol predictions, but has also opened the door to new avenues of exploration. We suggest three promising paths forward that leverage our newly created, open-access pest-control database.

First, future efforts could increase model complexity, incorporating landscape configuration and diversity predictors as well as indicators of local farming practices. A key consideration will be choosing variables for which sufficient data exist to model pest control in data-poor environments. Fortunately, some global, wall-to-wall datasets that could be used to characterize local farming practices already exist and others are being developed. For example, the International Institute for Applied Systems Analysis has created a global crop field size dataset [START_REF] Fritz | Mapping global cropland and field size[END_REF], and EarthStat maintains a global crop-composition dataset [START_REF] Monfreda | Farming the planet: Geographic distribution of crop areas, yields, physiological types, and net primary production in the year 2000[END_REF] that can be used to construct crop-diversity indices.

Second, models could be made more dynamic to account for temporal changes in predator and pest relationships. Many studies in our database resurveyed pests, enemies, and their interactions multiple times and averaged them throughout the growing season. Indeed, few published studies have reported relationships between landscapes and insects at multiple time intervals, despite evidence that these relationships can change both between years and during the growing season [START_REF] Plecas | Landscape composition and configuration influence cereal aphid-parasitoid-hyperparasitoid interactions and biological control differentially across years[END_REF]. As noted above, aggregate measures of pest or enemy abundance may mask important effects on pest growth or densities at harvest [START_REF] Chaplin-Kramer | Detecting pest control services across spatial and temporal scales[END_REF].

Third, including trait data as species-level covariates in pestcontrol models could help identify groups of species that react similarly to landscape variables. Traits have been used to explain variation in tropical bird community responses to land-use intensification worldwide [START_REF] Newbold | Ecological traits affect the response of tropical forest bird species to land-use intensity[END_REF], and similar approaches may help make sense of the context dependence of these results based on Though landscape-composition variables often explained variation in pest-control responses within studies, we observed substantial variation among studies in how pests, enemies, predation rates, crop damage, and yields responded to different landscape variables. Specifically, we did not observe a consistent increase or decrease in response to surrounding noncrop habitat in any variable. Although increased biological control can cause pests to decline in landscapes with more noncrop habitat, pests too can benefit from noncrop habitat [START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF]. This variability also pertained to enemies, despite meta-analyses showing that enemy abundance [START_REF] Bianchi | Sustainable pest regulation in agricultural landscapes: A review on landscape composition, biodiversity and natural pest control[END_REF][START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF] and activity (5) increase in landscapes with more noncrop habitat. Key to this finding is acknowledging that meta-analyses take the effect sizes reported by individual studies (often including interactions with other variables and other idiosyncrasies in analysis), not in the standardized, uniform way presented here that isolates the effect of noncrop habitat. These results contrast prior pollinator studies, which tend to report more consistently positive effects of noncrop habitat [START_REF] Kennedy | A global quantitative synthesis of local and landscape effects on wild bee pollinators in agroecosystems[END_REF][START_REF] Ricketts | Landscape effects on crop pollination services: Are there general patterns?[END_REF]. One explanation for this difference may be that the greater diversity of organisms involved in pest control (e.g., birds, bats, spiders, beetles, flies, etc.) may underlie their more diverse landscape responses. Even more importantly, complex, tritrophic interactions between enemies, pests, and crops may make for more context-specific dynamics than in comparatively simpler pollinator-plant systems.

Sources of Variation. Ultimately, such context dependence in pest and enemy responses to landscape composition made it difficult to generalize effects of land use-change decisions on pest control. While we did identify some strategies that could marginally increase predictive power (e.g., by only applying models to datasets focused on the same crop), models were still only able to predict very limited amounts of variation in pest-control variables when applied to independent datasets. Surprisingly, predictive power did not even increase when we only used models that were built from studies near to (<500 km), in the same biome as, or in the same biogeographic realm as field observations. Below, we detail five possible explanations for the remarkable variation that we observed in landscape responses; the first two focus on potential problems with underlying datasets, and the latter three focus on unaccounted-for sources of variation that could be addressed in future analyses.

First, discordance between our findings and the broader pestcontrol literature (4) may reflect underlying publication biases. Prior reported trends may lack reproducibility because authors are incentivized to continue interrogating their data and conducting new experiments until they find significant results [START_REF]Estimating the reproducibility of psychological science[END_REF]. We do not find this explanation particularly likely, however, because prior meta-analyses do report significant cross-study variation in pest responses [START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF].

Second, our broad quantitative synthesis may have missed key temporal dynamics that may influence landscape effects but are rarely measured in pest-control studies. Specifically, if predator and pest abundances fluctuate and respond to each other in an oscillatory system [START_REF] Levins | Effects of density dependence, feedback, and environmental sensitivity on correlations among predators, prey, and plant resources: Models and practical implications[END_REF], then snapshot estimates of species abundances or interactions may not reflect the longer-term impact of surrounding landscape composition. For example, one study found that, near natural habitats, syrphid fly larvae suppress week-to-week population growth of aphids, contributing to lower densities at harvest, but aggregating data into annual average abundances masked landscape effects [START_REF] Chaplin-Kramer | Detecting pest control services across spatial and temporal scales[END_REF].

Third, pests and enemies may respond more strongly to aspects of the surrounding landscape that we did not measure, such as landscape configuration (i.e., the spatial arrangement of surrounding land-use types) or diversity (i.e., the number of surrounding land-use types present) [START_REF] Tscharntke | When natural habitat fails to enhance biological pest control--Five hypotheses[END_REF][START_REF] Perovic | Effect of landscape composition and arrangement on biological control agents in a simplified agricultural system: A costdistance approach[END_REF][START_REF] Martin | Scale-dependent effects of landscape composition and configuration on natural enemy diversity, crop herbivory, and yields[END_REF]. Still, our approach of analyzing the proportional area of different land-use types represents the most common landscape metric used in pestcontrol studies [START_REF] Chaplin-Kramer | A meta-analysis of crop pest and natural enemy response to landscape complexity[END_REF][START_REF] Perovic | Effect of landscape composition and arrangement on biological control agents in a simplified agricultural system: A costdistance approach[END_REF].

types of field observations. First, some researchers reported data from experiments in which pests were collected, placed in chambers, and monitored to quantify the fraction of emerging parasitoids. Second, in sentinel pest experiments, researchers placed pests in crop fields and returned later to measure the fraction that had been parasitized or consumed (e.g., ref. [START_REF] Karp | Farming practices for food safety threaten pest-control services to fresh produce[END_REF]. Third, researchers used field exclosures to exclude natural enemies and quantify differences in pest abundances and/or crop damage between plants with and without natural enemies (e.g., ref. [START_REF] Rusch | Agricultural landscape simplification reduces natural pest control: A quantitative synthesis[END_REF]. Activity data were accompanied by information on the date, duration, type, and number of infield experiments. Crop yield data were also collected if available. Data on total crop quantity or quality were supplemented with information regarding crop species, measure type (fruit weight, biomass/area, etc.), and crop quality (marketable versus total yield). Before analysis, all pest-control data were standardized to increase comparability across diverse data types (see SI Appendix for more details).

Landscape Composition. To quantify surrounding landscape composition, we used a hierarchical approach to acquire land-cover maps that encompassed all areas within 2 km of each study site (SI Appendix). Specifically, we asked authors to submit high-resolution land-use maps of their study regions when available; otherwise, we used either regional maps or, as a last resort, a 30-m global land-cover product [START_REF] Jun | Open access to Earth land-cover map[END_REF]. Land-cover maps were classified into seven categories: (i) forest and tree plantations, (ii) grassland, (iii) scrubland, (iv) annual cropland, (v) perennial cropland, (vi) urban areas, and (vii) other. We then used a distance-weighting function (with multiple spatial scales) to quantify landscape composition around each study site and value each landscape sector as a function of distance to the study site [START_REF] Jonsson | Ecological production functions for biological control services in agricultural landscapes[END_REF][START_REF] Karp | Farming practices for food safety threaten pest-control services to fresh produce[END_REF] (SI Appendix).

Model Averaging. We modeled pest-control data as a function of landscapecomposition variables, creating separate models for each pest-control response (i.e., each unique pest-control variable measured in each study). Because landscape variables were often highly collinear within studies, we first iteratively excluded individual landscape variables until variance inflation factors (VIFs) were less than 2.5, dropping the landscape variable with the highest VIF first [START_REF] Zuur | Mixed Effects Models and Extensions in Ecology with R[END_REF]. Subsequent reanalysis that included all variables, regardless of collinearity, did not indicate any systemically higher predictive power. We then used a modelaveraging procedure in which the full suite of all possible landscape models (i.e., every combination of landscape predictors) was used to quantify effects of each landscape-composition variable on the pest-control responses (MuMIn package in R). Specifically, nonshrinkage variance estimates were obtained for each fixed effect, where only models that included a given fixed effect contributed to its ultimate predicted value. For each pest-control response variable, all landscape variables associated with one spatial scale were included as fixed effects. Different spatial scales were analyzed separately. Along with landscape variables, we also included sampling method, study year, and crop type as fixed effects. For datasets in which crop yields were measured at multiple times throughout the growing season, we also included "elapsed time since planting" as an additional fixed effect. In all cases, "farm identity" was included as a random effect when multiple sampling sites were situated on the same farm.

Pest-control variables were often log-, square root-, or fourth roottransformed to abide by model assumptions (normality and homoscedasticity). Transformations did not resolve normality and heteroscedasticity concerns in 47 and 63 of 367 analyses, respectively. Subsequent sensitivity analyses indicated that excluding those models did not affect any of our conclusions or systematically improve our ability to predict variation in pestcontrol responses in independent datasets (see below). Therefore, these models were retained.

To determine whether pest-control variables exhibited consistent responses to landscape composition, we first reclassified landscape variables into natural habitat variables (forest, grassland, or scrubland) and crop variables (annual or perennial crops). Then, because three models (one for each spatial scale) were constructed for each dataset, in this and every subsequent analysis we restricted our focus to the one spatial scale in which landscape predictors explained the most variation. Next, we tallied the number of models in which natural habitat variables or crop variables were predicted to have consistently positive, consistently negative, or mixed effects on each pest-control variable. For example, if pest abundance increased with surrounding forest cover but decreased with grassland cover, then we categorized pest abundance as exhibiting mixed responses to surrounding natural habitat. In another analysis, we isolated the land-use variable with the highest-ranked importance for each model. We then tallied the number of models for which important natural habitat variables or crop variables increased or decreased pest-control metrics. In both cases, we used χ 2 tests to assess whether each pest-control variable increased or decreased in response to surrounding natural habitat or cropland. life history, mobility, habitat preference, and other characteristics [START_REF] Segoli | Should increasing the field size of monocultural crops be expected to exacerbate pest damage?[END_REF]. For example, specialist pests that depend on crop resources are likely to exhibit more negative associations with surrounding noncrop vegetation than generalist pests [START_REF] Root | Organization of a plant-arthropod association in simple and diverse habitats: The fauna of collards (Brassica oleracea)[END_REF]. Such trait-driven models may be especially important when using future predictive models to identify tradeoffs, for example, exploring when surrounding noncrop habitat would depress one pest's abundance but likely benefit another. An alternative approach to increasing predictive power would be redefining landuse types into more functionally relevant classifications that are tailored to specific pests and/or enemies [START_REF] Fahrig | Functional landscape heterogeneity and animal biodiversity in agricultural landscapes[END_REF]. For example, with sufficient natural history information, landscapes could theoretically be classified into species-specific foraging, nesting, roosting, and unused sites.

Conclusions

By compiling and systematically analyzing the largest pestcontrol database of its kind to date, we have demonstrated that landscape composition alone can explain variation in the abundance and activity of natural enemies and crop pests. Critically, however, we found remarkable variability in how pests and enemies respond to different landscape metrics, preventing the prediction of pest-control responses by simple empirical models constructed from independent datasets. Ultimately, these results suggest that natural habitat conservation cannot be considered a panacea. While habitat conservation is known to enhance pest control in many cropping systems globally (4), there are also areas where conservation may bolster biodiversity-even of natural enemies-but still reduce crop production by simultaneously enhancing pests. Our study thus highlights the need to examine multiple services (e.g., pest control, pollination, soil conservation) and disservices when designing or assessing policies such as Europe's agrienvironment schemes, which incentivize habitat creation in farmland [START_REF] Holland | Semi-natural habitats support biological control, pollination and soil conservation in Europe. A review[END_REF].

Looking forward, generalizable decision-support tools for pest control are needed to help farmers understand when habitat conservation represents a true win-win and when conservation activities will need to be carefully comanaged to reduce the risk of damaging pest outbreaks. Future efforts to develop such models could recognize and account for system-specific variability by incorporating local management factors, temporal variation, and life-history variation among species into predictive models. To this end, we envision the supporting pest-control data that we have assembled to be a living database. Through ongoing efforts to address species traits, compile data on local management practices, and develop infrastructure to continue adding new studies that focus on different crops and geographies, the reach of our approach will continue extending to novel contexts, increasing predictive power and offering remarkable opportunities to answer critical questions about the ecology of pest control.

Methods

Database Compilation. We formed a working group of 19 pest-control experts and practitioners to compile a database of spatial pest-control observations. First, we developed a list of potential data contributors, leveraging past syntheses (2-5), literature searches, and our professional networks. Potential contributors were contacted and asked to complete a data-entry form. Studies were included if pest-control observations were obtained across at least five distinct sampling locations (mean 50 sites), all within crop fields and across a gradient of surrounding landscape composition. Authors were required to report the following information for each sampling site: spatial coordinates, crop type, farm name, and study year. For predator, parasitoid, and pest-abundance data, we also requested information on species taxonomy, sampling dates, sampling methods (pan trap, pitfall trap, sweep net, etc.), and the number and duration of censuses. We also required each author to identify each animal as a dominant (economically important) pest, secondary pest, predator, or parasitoid.

Pest activity was measured as the fraction or amount of each crop consumed, infested, or damaged. Predator activity was measured through three Analysis of Model Fit. We calculated Pearson correlation coefficients and R 2 values between model predictions and observed data to assess model fit, as these metrics are directly comparable across models. We then used t tests to determine whether the average Pearson correlation coefficient (across all datasets) differed from 0. We also tested whether models explained more variation in pest-control responses in certain regions. To do so, we implemented linear mixed models that predicted correlation coefficients from a variable identifying the biogeographic realm of the study. We used likelihood ratio tests to compare models with and without the biogeographic realm predictor.

Prediction Analysis. To quantify our models' predictive power, we correlated the observed pest-control variable values in each of the 367 pest-control responses ("field observations," hereafter) with the average of all predictions generated across our many landscape models, using the following procedure. First, we selected which landscape models to use. Models built from datasets ("model data," hereafter) that shared >25% of their study sites with the field observations were excluded so that models and field observations could be considered totally independent. We also excluded models when model data had more finely resolved land-cover classes than independent field observations. Models constructed from one pest-control variable could be applied to observations of a different pest-control variable, provided that they were either both enemy variables or pest variables. Yield models were always applied to only yield data.

Once a set of candidate models was obtained for each set of independent field observations, we used the model-averaged estimates of the effects of each landscape variable to predict pest-control variable values. Predictions from each model were scaled by subtracting the mean value and dividing by the SD, and then averaged across all models. Finally, we calculated the Pearson correlation between the field observations and the multimodel-averaged predictions. Again, we used t tests to determine whether the average Pearson correlation coefficient (across all tested datasets) differed from 0.

We also conducted a sensitivity analysis to determine if there were strategies for filtering and applying subsets of models to independent field observations so as to increase predictive power. We repeated the above model-testing procedure but after choosing to only include models derived from studies that (i) focused on the same crop as the independent field observations, (ii) were in a same biome [START_REF] Olson | Terrestrial ecoregions of the world: A new map of life on Earth[END_REF], (iii) were in the same biogeographic realm, (iv) were located <500 km away from the field observa-tions, and (v) had the same landscape variable values as the values present in the field observations. Specifically, we tried only including models constructed from studies in regions with the same land-use classes as the field observations and, even more stringently, experimented with only including models when landscape variable values associated with field observations were within the range of the variable values in the model data (i.e., the landscape gradients matched). The sensitivity analysis was conducted in a full-factorial manner, whereby every combination of the five inclusion procedures was analyzed independently. Finally, independent from the full-factorial sensitivity analysis, we also experimented with excluding models that did not explain any variation in their own datasets (Pearson's r between model predictions and observations was <0.25). For each scenario and for each tested dataset, we calculated the Pearson correlation coefficients between model predictions and testing data.

We then used linear mixed models to evaluate whether each model restriction procedure improved or diminished overall predictive power across the independent field observations. Specifically, for each class of pest-control variable, mixed models were used to relate the Pearson correlation coefficients (response) to a series of fixed effects that indicated whether each exclusion procedure outlined above had taken place (e.g., exclude models that were focused on a different crop, in a different biome, etc.). Because the same field observation datasets appeared in each exclusion scenario, "field observation dataset name" was included as a random effect. We also included a random effect of "unique scenario combination" to identify all of the studies that were subject to the same set of exclusion procedures (e.g., exclude models that were focused on a different crop but allow models to be in different biogeographic realms and biomes). Then, we used likelihood ratio tests to compare the full mixed model with models in which we iteratively removed each fixed effect (indicator variables of each exclusion procedure).

Fig. 3 .

 3 Fig. 3. Explanatory power of landscape pest-control models. After selecting the most predictive spatial scale (Methods), model predictions were correlated with observed data. Gray dots are both Pearson correlations between model predictions and observed data and R 2 values (square of Pearson's r). Filled circles and empty circles indicate significant (P < 0.05) and nonsignificant correlations, respectively. Black dots indicate the mean correlation across all datasets between observed and predicted values. Black lines correspond to 95% confidence intervals.

Scientific and Industrial Research Organisation (CSIRO), Brisbane, QLD 4001, Australia; p Agroecology, University of Goettingen, 37077 Goettingen, Germany; q

ACKNOWLEDGMENTS. We thank the many growers, field assistants, pestcontrol advisors, funders, agricultural experiment stations, and researchers who provided access to study sites, technical expertise, labor, and other types of investment underlying the studies in our database. This work was supported through the National Socio-Environmental Synthesis Center (SESYNC)-National Science Foundation Award DBI-1052875 for the project "Evidence and Decision-Support Tools for Controlling Agricultural Pests with Conservation Interventions" organized by D.S.K. and R.C.-K. a Department of Wildlife, Fish, and Conservation Biology, University of California, Davis, CA 95616; b Natural Capital Project, Woods Institute for the Environment, Stanford University, Stanford, CA 94618; c National Audubon Society, Boulder, CO 80305; d Department of Animal Ecology and Tropical Biology, Biocenter, University of Würzburg, 97074 Würzburg, Germany; e Biodiversity and Ecosystem Services, Bioversity International, 34397 Montpellier, France; f Department of Entomology, Cornell University, Ithaca, NY 14853; g Department of Entomology, University of Wisconsin, Madison, WI 53706; h Department of Entomology, University of Maryland, College Park, MD 20742; i Bren School of Environmental Science & Management, University of California, Santa Barbara, CA 93106-5131; j Tropical Agricultural Research and Higher Education Center (CATIE), Turrialba, Costa Rica 30501; k Department of Horticulture, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061; l Institut National de la Recherche Agronomique (INRA), UMR 1065 SAVE, ISVV, Université de Bordeaux, Bordeaux Sciences Agro, F-33883 Villenave d'Ornon, France; m Department of Ecology, Swedish University of Agricultural Sciences, SE-75007 Uppsala, Sweden; n Department of Entomology and Nematology, University of California, Davis, CA 95616; o Commonwealth