Herbicides do not ensure for higher wheat yield, but eliminate rare plant species

Weed control is generally considered to be essential for crop production and herbicides have become the main method used for weed control in developed countries. However, concerns about harmful environmental consequences have led to strong pressure on farmers to reduce the use of herbicides. As food demand is forecast to increase by 50% over the next century, an in-depth quantitative analysis of crop yields, weeds and herbicides is required to balance economic and environmental issues. This study analysed the relationship between weeds, herbicides and winter wheat yields using data from 150 winter wheat fields in western France. A Bayesian hierarchical model was built to take account of farmers’ behaviour, including implicitly their perception of weeds and weed control practices, on the effectiveness of treatment. No relationship was detected between crop yields and herbicide use. Herbicides were found to be more effective at controlling rare plant species than abundant weed species. These results suggest that reducing the use of herbicides by up to 50% could maintain crop production, a result confirmed by previous studies, while encouraging weed biodiversity. Food security and biodiversity conservation may, therefore, be achieved simultaneously in intensive agriculture simply by reducing the use of herbicides.

critical expectation, although paradoxically, there is, at best, very little evidence to confirm such a relationship. Weeds may reduce the winter wheat yield by up to 23% on average worldwide, but actual loss due to weeds is less than 8% ( Table 1 in ref. 3) and the adverse effect of weeds on crop yields is best established on organic farms 23 . Furthermore, although many studies of the effects of herbicides on weed populations are available, most were conducted many years ago (review in ref. 24), as most herbicides and active ingredients came onto the market prior to the eighties 8 . Moreover, almost all these studies were conducted on single species and in experimental conditions 24,25 ; but see ref. 26). Therefore, the negative effect of weeds on crop yields has been modelled rather than tested empirically [27][28][29] .
Experimental and modelling studies usually ignore one further aspect: the farmers' decisions and practices 30,31 . Although the application rate is usually recommended by agrochemical firms, the effectiveness of herbicides depends on the application mode (i.e. timing, dose), environmental conditions (the relative humidity can increase herbicide efficacy), the choice of active ingredient, depending on the observed or expected weed species, and the agricultural techniques used in combination. There is strong evidence that farmers behave in different ways in response to strong weed pressure 32 , although this has not been accurately quantified (but see ref. 33,34). There may be differences in the appreciation of the risk encountered for a given level of weed abundance 31 , in the technique to be used to deal with the situation (typically, between tillage and use of herbicide) and in the herbicide treatment (type of active ingredient, frequency and dose 30 ). Although this has been studied for organic farming 23,30,31 , there is considerable uncertainty about the interaction between weed abundance in conventional fields, a farmer's behaviour and decisions and the effectiveness of weed control by the herbicides 35 .
This study used empirical data on weeds, herbicide practices and winter wheat yields from 150 fields belonging to 30 farmers, to determine whether the use of herbicides improved yields and/or decreased weed abundance. As no clear relationships between herbicide use and weeds nor between yields and weeds were detected using standard statistical models, we modelled these relationships taking into account implicitly the effects of farmers' behaviour and of environmental conditions on the effectiveness of weed management. Although farmers' behaviour is usually taken into account in decision support systems 31,33 and in mental models 30,32,36 using data obtained from surveys of farmers, for this study a hierarchical Bayesian framework was developed 37 which modelled farmers' behaviour (sensu lato) as a parameter influencing the latent variable, λ, of the expected number of weeds per unit area. This parameter quantifies the farmers' impact on the pairwise 'crop yield-herbicides-weeds' relationships. This method differed from the conventional statistical approach by assuming that a farmer's behaviour (denoted η R F and η A F for weed richness and abundance, respectively) affect the crop yield-herbicide relationship through his own perception of weeds and weed control management strategies (e.g. timing of treatment). To include more realistic conditions in the model, a framework was developed to take account of the adaptive management by a given farmer to deal with the specific conditions encountered in his fields, by allowing a nested effect of field within farmer (η R Ff and η A Ff for weed richness and abundance, respectively) and also taking account of the differential effectiveness of herbicide treatments depending on the weed species, η R Ffs (η A Ffs ). We then analysed the interactive effects of farmers's behaviour, for both η F (η A F ) and η Ff (η A Ff ), and the herbicide application rate on weeds, testing the hypothesis that herbicide treatment affected the abundance of weeds rather than species richness and targeted species (those thought to reduce the yields) rather than non-targeted species, using estimated values of η R Ffs (η A Ffs ).

Results
Herbicide application rate did not affect weeds or crop yields. 108 species were found over the 150 fields with an average of 9.46 species per field (range 0-25). All but one species of the six most commonly found were annual dicotyledons, i.e. Polygonum aviculare L., Veronica persica Poir., Mercurialis annua L., Fallopia convolvulus L. and Galium aparine L., with the exception of Poa sp. (annual monocotyledon). We first attempted to determine a positive relationship between the crop yield and the herbicide application rates, expressed as the total application rate over the cultivation period, using linear mixed models (with field nested within farmer as a random effect). The relationship between the crop yield and the herbicide application rate was actually negative Weed abundance Ab_base Ab_farm Ab_field Ab_spec Table 1. Description of the Hierarchical Bayesian models. "Rich" and "Ab" indicate the models used with weed richness and estimated abundance, respectively. λ is the species richness (abundance) among fields and follows a Poisson distribution with mean μ. a is the scaling factor, b is the shape factor describing the concavity of the reduction curve, D is the herbicide application rate and η R . (η A .) is a parameter quantifying farmer's effect on the effectiveness of the treatment in his farm (η R F or η A F ) or in each of his field (η R Ff or η A Ff ). In the "Ab_spec" model, the effectiveness of the herbicides varies with species identity. Except for D, all parameters and latent variables were estimated from the observed data.
Scientific RepoRts | 6:30112 | DOI: 10.1038/srep30112 the result (ΔAIC <2 compared to the model without nitrogen input) and so nitrogen input was removed from the model. Furthermore, contrary to expectation, no significant relationships were observed between the herbicide application rate and either the weed frequency or the weed species richness (respectively No evidence was found for any relationship between weeds, herbicide application rates and crop yield. One reason could be that farmers adapt their treatment strategy in order to keep the weed risk below a given threshold and guarantee a minimum yield 33 . However, the very high variances found in all pairwise relationships ( Fig. 1) suggested testing an alternative scenario in which the variability in the farmer's behaviour was so high that it masked any possible relationship. Farmer's behaviour aggregates here what the farmer actually does (choice of active ingredients and number and timing of applications), interacting with the environmental conditions at the time of herbicide applications and the agricultural techniques used in combination with herbicides.
Farmers' behaviour affected the herbicide-weed relationship. Hierarchical Bayesian models were used to model the effect of herbicides on weed richness and abundance ( Fig. 2; Table 1) taking into account the variability in the farmer's behaviour. Such variability was introduced to model either a simple farmer effect (η R F and η A F ) assuming a similar effect across the five fields farmed by the farmer, or with variability between fields for a given farmer, which was modelled as a nested effect at field scale within a farm (η R Ff and η A Ff ) ( Table 1). The first set of models (Table 1) assumed that the effectiveness of herbicides did not vary with weed species (although all species abundances were modelled separately). The model fit was tuned by comparing weed richness or abundance as estimated by the model output with the observed values. The model with the nested effect at field scale within a farm (η Ff ) explained the variability in weed species richness much better (Rich_field: DIC = 31600; Fig. S3) than the model with only the farmer effect (η F ; Rich_farm DIC = 32590). This model also explained the weed species richness much better than the model without any farmer effect (Rich_base: DIC = 34200). Similar results were found for weed estimated abundance (Ab_field: DIC of the model with η A Ff = 7069, Ab_farm: DIC of the model with η A F = 6142 and Ab_base: DIC of the model without any effect = 5508; Fig. 3a). Estimated parameters are given in Table S3.
η R F (η A F ) and η R Ff (η A Ff ) are surrogates for the effectiveness of treatment and vary between 0 and 1, a value of 1 being the effectiveness expected if weed control were complete. There was a strong farmer identity effect on the effectiveness of the weed control treatment (Fig. 3b): the farmers' effect appeared to depend on the field (see variation of η A Ff over the five fields farmed by each farmer in Fig. 3d), as already shown based on surveys of farmers 32,34 . This suggests that farmers either adapted their management at field level, or possibly that the effectiveness differed between fields because of exogenous factors (e.g. meteorological conditions are known to affect the effectiveness of herbicides 38 ). Herbicide management options varied for 19 farmers out of the 30 (63.3%) in our dataset suggesting that farmers changed their management practices to some extent depending on the field. Only one third of the 30 farmers applied exactly the same herbicide treatment to each of their five fields and so the differences between fields is likely to have been due to the effectiveness of the treatment rather than the herbicide used. Furthermore, there was only weak and non-significant correlation between η R Ff (η A Ff ) and the farmers' weeding strategies, described by the diversity and date of introduction of products applied as well as the number of tank-mixed commercial herbicides (SM, Fig. S5 and Table S5).
Most η R Ff values in the weed richness model were close to 0 with a maximum of 0.65 (Fig. 3b), indicating significant discrepancies between the expected effect of the herbicide treatment at a given strength and the effect observed on weed richness. The asymmetric distribution (Fig. 3b) of η R Ff suggested that most herbicide treatments had almost no effect and that, for almost all the farmers, the treatment did not reduce either weed richness or weed abundance, i.e. η A Ff was close to 0, in at least one of their fields (Fig. 3d). 64.5% of η R Ff estimates for the richness model and 60% of η A Ff estimates for the abundance model were below 0.2 (Fig. S3C). In addition, η R Ff estimates for the richness model (Rich_field) were generally lower than η A Ff estimates for the abundance model (Ab_field, Fig. 3c), suggesting that herbicides tended to be generally more efficient at controlling total weed richness than weed estimated abundance.
Herbicides were effective for controlling rare species but did not control abundant species. To give more realistic conditions and models, we then relaxed the assumption of identical effect of herbicides on weed species, and assumed that the effectiveness of herbicide varied with species identity, i.e. η A Ffs estimates the effectiveness of herbicide treatment on a given weed species in each field for each farmer (model Ab_spec in Table 1). Determining the probability of weed species survival in relation to the amount of herbicide applied, and depending on the relative weed abundance, showed that herbicides were very effective at suppressing rare weeds (i.e. the less abundant species in absence of herbicides) but less effective at suppressing the most abundant weeds (Figs 4a and S5). In a small number of cases, herbicides reduced the survival of abundant species (upper part of Fig. 4a) but only when high doses were applied (i.e., upper 90% quartile). The survival probability profiles of the most abundant species differed from species with lower abundance, again indicating that herbicide was not a primary factor in controlling the most abundant weed species (top part of Fig. 4a). Herbicides also failed to control four of the most noxious weed species identified by farmers in the study site (see methods section, and ref. 39). Although herbicides failed to control abundant, targeted noxious weeds, we tested whether fields where treatment was the most effective had the highest wheat yields. This was not the case, since there was no relationship between the effectiveness of herbicide treatment (η R Ff ) and wheat yield (Fig. 4b). . It was assumed that, when no herbicide was applied, species richness among fields followed a Poisson distribution with mean μ. Herbicides reduced the species richness to an observed species richness λ (the number of species that survived treatment). The reduction was a function of three parameters: a was the scaling factor, b was the shape factor describing the concavity of the reduction curve and D effective was the effectiveness of the herbicide depending on D and η R Ff. D was the observed herbicide application rate and η R Ff was a parameter quantifying farmer's effect on the effectiveness of the treatment in each of his field. Except for D, all parameters and latent variables were estimated from the observed data.

Discussion
The main purpose of this study was to determine whether decreasing the amount of herbicide used would significantly reduce yield owing to an increase in weed richness and/or abundance, as has frequently been suggested 20 ; see review in ref. 21. However, using a dataset of 150 fields, there was no correlation between weed richness or frequency and winter wheat yields. Furthermore, no correlation was found to indicate that the herbicide application rate had an effect on weeds or on yield. Taking account of the possible role of farmers and environmental conditions in the effectiveness of treatment, the results suggested that many treatments were ineffective (Fig. 3c), probably accounting for the lack of effects. Even where treatment was effective, however, there was no correlation between the effectiveness of treatment and yield (Fig. 4b). Even though herbicide application rates had no effect on weed estimated abundance, including targeted species, or on yield, the results suggested that the only tangible effect of herbicides was on less abundant weed species, which were not targeted by farmers. The validity and robustness of this approach is discussed below. The findings are compared with available literature and some consequences of the study with regard to pesticide use and biodiversity management in farmlands are described.
The crop yield losses resulting from a reduction in pesticide use is generally quantified without taking account of the effect of farmers' decisions (e.g. ref. 40). Our study used Bayesian Hierarchical Models with a latent variable which models the farmer's behaviour (including, e.g., application mode, choice of active ingredient, cropping systems, farmer' belief and perception) interacting with environmental conditions. Bayesian and Markov hierarchical models with hidden state variables to allow for human behaviour have commonly been used 41 for decision models 42 and for policy-making because they can realistically predict human behaviour 43 or easily accommodate underlying environmental attitudes 44 . In this study, the modelling approach relied on several strong assumptions. Firstly, it was assumed that weed species were randomly distributed in a given area, with a Poisson distribution. This assumption was used to estimate the average number of species to be expected in a field where herbicide had been applied and compare this estimated value with the observed value. There is some evidence that weed species are distributed randomly in farmland areas or at least that random assemblage of weeds (sensu neutral model 45 ) cannot be disregarded. For instance, in the same study site 46 found that weed communities in organic farms were best explained by mass effect metacommunity models, and ref. 47, also in the same study site, found that weed functional diversity differed very little from random assemblage, in particular in winter wheat. We also assumed that the abundance of each species also had a Poisson distribution, although this is a much more conventional, less controversial assumption 48,49 , and was a good predictor of its cover. Indeed farmers could respond to cover, and not to abundance which could also explained the lack of relationship between herbicides and weed estimated abundance. Secondly, the effect of the herbicide application rate on weed richness (abundance) was expressed using a non-linear function. We made this assumption in the model structure to ensure that the estimated value of weed richness (abundance) decreased with decreasing herbicide application rates and remained positive (or null). A reduction factor (Fig. 2c) was used to describe how farmers' management decisions affected the effectiveness of herbicides, i.e. it was assumed that herbicides were not fully effective with a difference between the observed richness (or abundance) and the expected richness (or abundance) for perfect effectiveness of the herbicide treatment. Thirdly, the herbicide application rate was described using two different indicators, the total dose of herbicides and the TFI, which describe complementary aspects of weed control treatments. The results were similar for either indicator (details are given in SM). Investigating the weed-crop yield relationship over several years would allow quantifying the effect of climate on weeds a well as crop biomass production, and the output of their interactive relationship. In addition, this study considered only conventional farming. Despite it is the most common farming system in developed countries, it would be of great interest to include alternative farming systems such as organic farming in this analysis to explore the effect of mechanical weeding on the weed-crop yield relationship (e.g., organic farming and Agri-Environmental Schemes in ref. 9, which used the same data set for France). This obviously requires further analyses carried out in different areas, for different farming systems and over several years. Despite repeated claims that weed density lowers yields (e.g. review in ref. 24), the evidence is less conclusive than usually claimed 51 . In an extensive review 24 established that at least 30 species of weeds reduce wheat yield to varying degrees (ranging from a few % up to 75%) and at a highly variable threshold of number of seeds or plants/m 2 . However, extremely few studies have investigated this effect at community level (none in ref. 24 for instance) 52 studied the long-term effects of applying full and half doses of herbicide on 10 fields: compared to a control, full and half doses increased the proportion of difficult-to-control weed species significantly in half of the sites, while crop yields were actually higher in some sites when using half doses. Many other studies have demonstrated that doses can be reduced by 50% or even more compared to the recommended dose without detectable loss of yield 52,53 , increase in weeds 54 or both (review in ref. 21). Indeed, without crop being present, weed control was at least 70% effective in 50% of the studies, even when the herbicide application rate was only 20% of the recommended rate, whereas in conjunction with crop cultivation, no detectable effect was found with up to 50% reduction in herbicide use compared to the recommended doses 21 . Furthermore, using experimental data from the literature 55 found that wheat has the highest competitive ability among 26 crops against weeds. Consequently, weed competition may have little effect on winter wheat (certainly lower than on other crop species), which questions the use of large amounts of herbicide in winter wheat cropping systems.
Since the introduction of herbicides (in the 50s 8 ), weeds have become a secondary problem for farmers and were no longer considered a decisive factor in the design of farming systems 34 . For decades, herbicides allowed farmers to hope for totally weed-free fields. Nowadays, maximum weed control has been shown to be unnecessary, even to achieve high yields or income 53,55,56 . Besides providing new evidence, this study suggested that herbicide use did not increase yields and affected rare species (i.e. species at low abundance in absence of herbicide application) rather than common weed species and non-targeted species rather than noxious species. The analysis focused solely on wheat, which is the most important crop in the world (in terms of area cultivated), and weeds are the most important pest group in wheat production worldwide 3 . We believe, therefore, that the results suggest that a reappraisal of how herbicides affect yields of major crops is needed.
If reducing herbicides by more than 50% would increase biodiversity and reduce contamination of water and risk to health, with an undetectable effect on yield, it would further increase farmer's income (i.e. lower costs for farmers for equivalent crop yields). Despite these clear advantages, farmers are reluctant to reduce herbicide use: for instance, integrated pest management (IPM) has long been promoted by experts 22,57 for economic and environmental reasons but is still seldom used. It has been suggested that farmers continue to use herbicides despite their effects on environmental sustainability, as well as farmers' health, because of their awareness of the delayed risks of lower weed control, with increasing seedbank density 32 . Alternatively, farmers' use of herbicides may be rooted in a market system that encourages the adoption of biophysically unsustainable techniques 11 : these may lower current costs and boost yields in the short term but eventually lower yields and raise production costs in the longer term 58 . Agricultural practices tend to continue to apply such systems once they have been adopted even though they are unsustainable 58,59 . All the possible explanations of our results call for mid-term (>4 to 6 years) experimental studies that explicitly incorporate the farmer's behaviour (weeding practices, perceptions, attitudes to weeds) thus requiring interdisciplinary research (socio-economic, agricultural and ecology sciences). These experiments could be implemented in different countries where wheat is an important crop.
To ensure food security while conserving biodiversity in intensive agriculture, government policies have often targeted a combination of changes in herbicide use with increased diversification in crop rotations, as well as the use of IPM or organic farming 13,22 . We argue here that it is perhaps far easier merely to reduce the use of herbicides.

Materials and Methods
Study area and sampling design. In Table S1. For each farm, five winter wheat fields were selected in consultation with the farmer, with no a priori selection. The fields were distributed throughout the study site (Fig. S1). All fields sampled from different farms were at least 1 km apart.

Survey of farmers and herbicide treatments. Information about crop yields and farming practices
(pesticide and fertilizer use, ploughing and mechanical weed control system) and general information about the farm (number of crops, proportion of land covered by AES, field size) was collected by means of a questionnaire sent out to all participating farmers. The response was 98% representing 30 farms. Herbicide use was described by the name and the concentration of each of the active ingredient and the day or week of application. Herbicides were further classified as monocotyledon specific, dicotyledon specific or broad spectrum. Crop yields were not available for 3 of the 30 farms.
Weed surveys. Botanical surveys were carried out once during the flowering to milk-ripening stage of winter wheat, in spring/summer 2007 10 . For each of the 150 fields, surveys were carried out in ten quadrats (4 m 2 ) at 10 m intervals in line from the border of the field toward the centre, perpendicular to the tracks made by farm machinery within the field. The first quadrat was 20 meters from the edge of the field. For each quadrat, weed species were recorded as either present or absent, irrespective of the number of individual plants, giving a list of species present in each quadrat.
Statistical analysis of the relationships between crop yield-herbicides and crop yieldweeds. The relationship between crop yield and herbicides was analysed using a linear mixed model (LMM) with the farmer as random effect and with and without nitrogen input as a co-variable. Two indicators were used for the amount of herbicide applied: the total application rate and the treatment frequency index (SM Materials and Methods). LMM were analysed with a type III analysis of variance with Satterthwaite approximation for degrees of freedom. A model selection procedure based on Akaïke Criterion (AIC 60 ) was performed to determine the effect of nitrogen input. The same procedure was applied to analyse the relationships between crop yield and weed richness (abundance). All analyses were performed using the R "LmerTest package" 60,61 Modelling farmers' behaviour in the herbicide-weed relationships-Herbicide-Weed species richness model. In order to account for the high variability in the herbicide-weed richness relationship (LMM described above) 62 , hierarchical Bayesian models were used (Fig. 2c). It was assumed that the number of weed species in a given area, i.e. species richness, followed a Poisson distribution with mean μ when no treatment was applied. It was also assumed that herbicide treatment reduced the mean number of species and, therefore, λ, the species richness expected in a given area when a treatment was applied, was modelled as a Poisson distribution of mean μ/(1 + aD) b where D is the amount of herbicide applied, a is a scale factor and b is a shape factor describing the concavity of the reduction after the application of the herbicide. The non-linear function of D allows the species richness to tend to zero as D becomes large, and to equal μ when no herbicide is applied (D = 0). A second model took account of farmers' behaviour on the effectiveness of chemical weed control. A parameter η R F was used to describe the effectiveness of the treatment as a function of the farmer, λ being modelled as a Poisson distribution with mean μ/(1 + aη R F D) b . All fields of a given farm, F, shared a common farmer effect, η R F . A third model included the farmer effect at field scale with a factor η R Ff for field f belonging to a farm F as η R Ff = η R F η R f . The best of the three models (without η R F , with η R F and with η R Ff ) was selected based on the deviance information criterion (DIC) which is a hierarchical modelling generalization of the AIC 63 .
Herbicide-Weed abundance model. No relationship was observed between herbicide use and abundance using LMM. Consequently, hierarchical models similar to those for the herbicide-weed species richness were built but, at the last step the species abundance was estimated using the presence-absence data (see details in Estimating weed abundance). The initial model assumed that herbicides had a similar effect on all weed species in the field and two models were built: one considered the same effect of the farmer's decision in all his fields λ s = μ s /(1 + aη A F D) b and the other modelled the effect of the farmer's behaviour at field scale λ s = μ s /(1 + aη A Ff D) b . In both models, λ s was the average number of plants of a given weed species s in a given area. The second step was to build a more realistic model, λ s = μ s /(1 + a s η A Ffs D) bs , which considered that the effect of the herbicide depended on the weed species s.
Estimating weed species abundance and survival rate. The weed abundance at field scale was estimated by assuming that weed abundance follows a Poisson distribution and that the probability of finding at least one plant in an area W(4000 m 2 ) was: 1 − exp(μ s W/(1 + aη A F D) b ) (see SI Materials and Methods for further details). We measured the survival of a species as the probability to observed one individual in W. For a species s with abundance intensity λ s , its survival rate was therefore e −Wλs under the assumption of Poisson distribution of the individuals of this species.
Estimating the model parameters. The Bayesian posterior distributions for each of the model parameters, including uncertainty due to variability in the data and the uncertainty of prior information, were approximated using Monte Carlo-Markov chain (MCMC) methods with prior information for the parameters (μ, a, b and η R F /η R Ff /η R Ffs (η A F /η A Ff /η A Ffs )). The following priors were used: a Gaussian distribution N(0, 10) for log(μ), log(a) and log(b), so that a, b and μ follow log-Gaussian distributions, ensuring that μ, a and b were strictly positive and a non-informative uniform distribution U(0, 1) for η R F (η A F ), η R Ff (η A Ff ) and η R Ffs (η A Ffs ). 20,000 iterations were run with three independent chains in the MCMC procedure. For each chain, the first 10,000 iterations were discarded. After this "burn-in" period, inferences were derived from a sample of 20,000 iterations. Modelling was performed using Winbugs 63 under R with the BRugs package 64 . Both the convergence of MCMC chains using Gelman-Rubin convergence statistic 65 and the performance of the estimate (ESM Fig. S5A,B) were assessed 66 .