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Design of species assemblages with contrasting species and functional diversitiesWe designed eight assemblages of native and perennial plants differing in terms of species richness (three levels), functional diversity of the traits involved in plant–arthropod interactions (two levels) and species identity (two sets of species). We combined these first two factors to define four categories of plant assemblages for further study:

Low functional diversity and medium species richness (14 species), LFMS;

High functional diversity and low species richness (9 species), HFLS;

High functional diversity and medium species richness (14 species), HFMS;

High functional diversity and high species richness (29 species), HFHS.

For each of these four categories, we designed two assemblages with different species identities, as described in the Supplementary information, resulting in eight plant assemblages in total. Functional characterization was based on a rough classification of plant species into functional groups (Supplementary Table S1), according to the mains traits involved in plant–species interactions easily accessible from databases: (1) flower resources, i.e. floral and extrafloral nectar or pollen, (2) accessibility of the resource, depending on flower shape, (3) availability of the resource, i.e. the flowering period and (4) flowering height.We generated the seed mixtures from commercial seeds, using ecotypes of local origin wherever possible (northern part of the Parisian basin, France). All applicable international, national, and institutional guidelines relevant for the use of plants were followed.Experimental designThe experiment was conducted between 2013 and 2017 in a 6.5-ha field at Grignon, France (N 48.837, E 1.956), on a deep loamy clay soil, in which soil depth decreased along a gradient from north to south. The field was divided in three blocks running from north to south to take this soil heterogeneity into account.Each assemblage was sown on a 6 × 44 m2 strip, with three replicates (Supplementary Fig. S2), with each assemblage represented once per block. A control treatment, sown with the same crop species as the rest of the field, was also included in the experimental design, resulting in nine experimental treatments in total. From the autumn of 2013 to the 2017 harvest, a winter barley–maize–faba bean–oilseed rape rotation was grown in the field. Crops were managed without insecticide treatment, but with a mean of 0.75 fungicide and 1.25 herbicide treatments per year. The observations were made in faba bean in 2016 and in oilseed rape in 2017.Botanical assessments and functional characterization of the plant communitiesBotanical assessments were conducted in April and June, in 2016 and 2017. In each treatment, the vegetation was assessed in 3 × 15 m2 plots at a position representative of the whole strip, generally in the center of the strip, to prevent edge effects. The percentage of the ground covered by each sown or spontaneously growing plant species was estimated by eye, by the same observer in each case. We noted the phenological development stage of each species in each treatment on an 11-point scale, to ensure an accurate assessment of flowering phenology. In the control plots (sown with the crop species only), we took into account the resources provided by weed species.The functional characterization of plant communities was based on the plant traits assumed to be involved in plant–parasitoid interactions6 (Supplementary Table S3). These traits were related to (1) the provision of trophic resources (presence of floral and extrafloral nectar, qualitative estimation of floral nectar), (2) the temporal availability of the resource (date of flowering onset and duration of flowering), (3) flower attractiveness (flower or inflorescence diameter, color, UV reflectance pattern), (4) nectar accessibility (flower opening diameter, corolla height, nectar depth and nectar tube diameter) and (5) the provision of physical habitats (leaf distribution, vegetative and flowering height). We measured most of these traits, particularly all those relating to flower morphology, phenology and nectar provision (see more detailed methods in the Supplementary information). Only a few were retrieved from previous publications and online databases: flower color and UV reflectance pattern, leaf distribution, vegetative and flower height.These traits were used (1) to determine the accessibility of nectar to each parasitoid (see below) and (2) to calculate the functional diversity of the plant assemblages. We calculated functional dispersion as the abundance-weighted mean distance of individual species from the centroid of all species in the trait space50 and Rao quadratic entropy51. Since these two parameters were highly correlated (Supplementary information), we considered only functional dispersion a measurement of functional diversity. The traits associated with the provision, availability and accessibility of nectar resources were measured for all the dicotyledonous species sown and for all spontaneous species occurring in the plant communities and flowering during parasitoid activity. Overall, considering the traits we measured and those retrieved from databases, the trait matrix was complete for more than 95% of the species, accounting for 99.6% of total plant cover.Assessment of the levels of parasitism on five herbivorous pests of faba bean and oilseed rapeIn the adjacent crop, 5 and 20 m from the wildflower strip, we measured the level of parasitism in one herbivorous pest of faba bean (2016) and four herbivorous pests of oilseed rape (2017). We chose a distance close to the strip (5 m) to prevent confounding effects with the other adjacent strips, knowing that their effect is the strongest in the first few meters from the strip52. A further distance was also chosen (20 m) to determine whether the strips promoted biological control at field level, while taking into account the spatial constraint of the distance between strips (50 m between opposing strips).All the protocols are detailed in the Supplementary information. Parasitism was assessed in Bruchus rufimanus larvae after the visual examination of faba bean seeds after harvest. For oilseed rape, we collected and reared Ceutorhynchus pallidactylus and Psylliodes chrysocephala larvae until the adult stage or parasitoid emergence. In Brassicogethes aeneus larvae, parasitism was assessed by observing the eggs of Tersilochus heterocerus in the host larvae in oilseed rape flowers. Finally, after oilseed rape harvest, we retrieved cocoons of Dasineura brassicae from the soil, which we dissected, recording the number of cocoons occupied by parasitoids.Measurement of parasitoid traitsWe carried out morphological measurements on parasitoids (Supplementary Table S4), to determine their degree of access to the nectar provided by plants, as a function of the size of their mouthparts and head, which limit corolla penetration, using an approach analogous to that of van Rijn and Wäckers16. Parasitoid individuals, preserved in 70% ethanol, were obtained (1) from our rearing experiments (for Bruchus rufimanus, Psylliodes chrysocephala and Ceutorhynchus pallidactylus), (2) from the dissection of cocoons for Dasineura brassicae or (3) by field sampling in the flower strips with a sweep net in April 2017 to collect Tersilochus heterocerus, parasitoids of Brassicogethes aeneus identified with53. For each parasitoid species or morphospecies, we measured, on at least 10 individuals, proboscis length, proboscis width (at mid-length)54 and the maximum dorsal head width, including the eyes. Observations were carried out under a binocular microscope (Leica M80, 60 ×) linked to a video camera (Moticam 10, Motic), and measurements were made with ImageJ v1.50i digital image analysis software (National Institute of Health, Bethesda, http://imagej.nih.gov/ij).Nectar resources for parasitoidsWe estimated the amount of nectar provided by the plants by summing, for each flower strip corresponding to a treatment, the percent cover of plants providing available and accessible nectar, as assessed in vegetation surveys. Separate estimates were obtained for each parasitoid species or morphospecies.Plant species producing floral or extrafloral nectar were first selected on the basis of the observations detailed in the botanical assessment section. Nectar was considered to be available when it was produced during the period of parasitoid activity (Supplementary Table S4), by selecting species at the flowering stage or producing extrafloral nectar based on the phenological observations carried out during the botanical assessments. Nectar accessibility depended on morphological matching between plants and insects. Extrafloral nectar, which is not enclosed in a perianth, but produced on bracts or stipules, was considered to be accessible. We determined the accessibility of floral nectar with a mechanistic trait-based approach (Supplementary Information), by adapting the geometric model proposed by van Rijn and Wäckers16. A decision tree was built (Fig. 2) to take into account the three constraints limiting nectar accessibility: (1) ability of the insect to penetrate the flower, which is dependent on head size and flower opening, (2) ability to reach the nectar, which depends on proboscis length, nectar depth and corolla height, and (3) proboscis width and nectar tube diameter in the presence of nectar.Statistical analysesWe investigated the effects of the different plant assemblages on the rates of parasitism for the five herbivorous species, at 5 and 20 m from the flower strip, considered separately as individual response variables. We first tested the effect of each assemblage (nine treatments as factors) on parasitism rates. We used generalized linear mixed models in the lme package55, with a binomial error distribution. The models included plot (n = 9 flower strips × 3 replicates = 27), strip (1–3) or block (1–3) as a random effect. All models were run three times with each random effect variable, and the model giving the lowest AIC was retained. Strips consistently yielded the lowest AIC. This factor was therefore introduced as a random effect variable for all statistical analyses. The significance of the fixed effects was evaluated by type II analyses of deviance with Wald chi-squared tests from the Anova function from the car package56. If a significant effect (p value  More

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