Alexandre Dore

Mathieu Lihoreau
email: mathieu.lihoreau@univ-tlse3.fr

Jean Bailly

Yvon Billon

Jean- François Bompa

Dominique Henry

Laurianne Canario

Aubert Hervé

Automated detection of sow posture changes with millimeter-wave radars and deep learning

Keywords: animal welfare, lactating sow, radar sensor, convolutional neural network, behavioural classification

Automated behavioural analysis is a major challenge for precision farming.

• We developed automated detection of lactating sow postures with radars and deep learning.

• We identified five postures, including transitions risky for the piglets.

• Our method is accurate, fast and requires less memory than computer vision.

Introduction

An animal's behaviour can inform about its stress level (von Borel et al. 2007) and personality [START_REF] O'malley | Animal personality in the management and welfare of pigs[END_REF]. In the case of livestock, detailed behavioural are increasingly used to address key economic, ethical and societal issues related to animal health and welfare. In pig farming, for instance, sows are often confined in crates during the lactation period in order to limit their movements and slow down postural changes that can be dangerous for the piglets [START_REF] Edwards | Housing systems for farrowing and lactation[END_REF][START_REF] Edwards | Perinatal mortality in the pig: Environmental or physiological solutions?[END_REF]. However, these rearing conditions are not ethically acceptable anymore. Long-term detailed behavioural monitoring of sow activity has thus become essential to move towards freer housing conditions during the lactation period (e.g. [START_REF] Chidgey | Sow and piglet productivity and sow reproductive performance in farrowing pens with temporary crating or farrowing crates on a commercial New Zealand pig farm[END_REF]see Baxter et al. 2012 for a review). Ultimately, selecting sows that are calm, careful towards their piglets, and do not suffer from leg problems as future breeders would promote the use of more welfare-friendly systems.

The study of sow behaviour over extended periods of time is a fairly recent approach and technological solutions combining sensors and signal analyses for automated monitoring are being developed at a tremendous speed [START_REF] Fernandes | Image Analysis and Computer Vision Applications in Animal Sciences: An Overview[END_REF]. Two broad categories of approaches have been used. Invasive technologies include sensors attached to the animals, such as accelerometers that record the acceleration and orientation of the sow across time. These sensors are typically embedded in an ear tag [START_REF] Traulsen | Using acceleration data to automatically detect the onset of farrowing in sows[END_REF][START_REF] Oczak | Dynamics of sows' activity housed in farrowing pens with possibility of temporary crating might indicate the time when sows should be confined in a crate before the onset of farrowing[END_REF], a collar [START_REF] Cornou | Modelling and monitoring sows' activity types in farrowing house using acceleration data[END_REF], a harness [START_REF] Canario | Development and validation of an embedded tool to measure postural activity of lactating sows[END_REF], or fastened to one leg (Ringenbberg et al 2010). However, as piglets grow, they increasingly explore their environment and are likely to chew the device insistently, which may lead the sow to change posture and activity if the discomfort is significant.

Non-invasive technologies include remote sensors, such as infrared cells or video cameras. When positioned above a sow, infrared sensors enable the discrimination of lying, sitting and standing postures [START_REF] Mainau | Validation of an automatic system to detect position changes in puerperal sows[END_REF]. Cameras have been used to identify different postures when combined with machine or deep learning for data analysis [START_REF] Zheng | Automatic recognition of lactating sow postures from depth images by deep learning detector[END_REF].

Several image processing methods have proved effective in estimating the posture of sows kept in a crate [START_REF] Bonneau | Predicting sow postures from video images: Comparison of convolutional neural networks and segmentation combined with support vector machines under various training and testing setups[END_REF][START_REF] Nasirahmadi | Deep learning and machine vision approaches for posture detection of individual pigs[END_REF][START_REF] Okinda | Asphyxia occurrence detection in sows during the farrowing phase by inter-birth interval evaluation[END_REF]. For instance, convolutional neural networks have been used to estimate the posture of a sow with its litter in 4 an individual pen [START_REF] Nasirahmadi | Deep learning and machine vision approaches for posture detection of individual pigs[END_REF]. The rate of good classification for these methods is close to or above 90% for several classes of postures (e.g. sitting, standing, lying down). This suggest further development of algorithms for these non-invasive technologies can lead to the automatic monitoring of livestock behaviour at large scale in a near future. Pigs are good models to develop and crash test these approaches since sows are isolated from conspecifics during the lactation period. However, this seems out of reach with current computer vision approaches as the require large memories and computational power to be functional.

Here we introduce a non-invasive method for the automated detection of sow posture based on Frequency-Modulated Continuous-Wave (FMCW) millimeter-wave radars and illustrate its efficiency to identify postural changes of the sow that are risky for the piglets, when sows are maintained in crates. The ability of FMCW radars to monitor animal behaviour was recently demonstrated in insects (e.g. bees: [START_REF] Dore | 3D trajectories of multiple untagged flying insects from millimetre-wave beamscanning radar[END_REF] and mammals (e.g. sheep: Henry et al. 2019;[START_REF] Dore | A Non-Invasive Millimetre-Wave Radar Sensor for Automated Behavioural Tracking in Precision Farming-Application to Sheep Husbandry[END_REF]. The main advantage of radars is that data collection and processing is fast and requires less memory than computer vision (the memory used for each measure is 1Mb and 5Gb for one image without compression). [START_REF] Manteuffel | Parturition detection in sows as test case for measuring activity behaviour in farm animals by means of radar sensors[END_REF] used Doppler radars to analyse sow activity, but limited their investigation to the detection of movements, since this kind of radars only gives the speed of the sow across time. In our study, we first compared the efficiency of the radar tracking system to state of art video tracking. We then applied a Convolutional Neural Network (CNN) to the data in order to classify the postures and measure the quality of posture prediction.

Materials and Methods

Sows and ground-truth measurements

Measurements were made on ten lactating sows from the Large White breed, on the GenESI INRAE experimental farm of Le Magneraud (France; doi: 10.15454/1.5572415481185847E12).

Sows were studied up to two weeks after farrowing. Their behaviour was monitored with FMCW radars for a minimum of five hours. Video recordings were made in parallel to assess the reliability of the radar measurements. Postures were annotated manually from these recordings frame by frame every 100ms. The synchronisation between the radar and the video measurements was performed a posteriori by detecting manually the kneeling posture. This posture was chosen as reference because it was easily distinguished on the radar signal and was observed on all sows. We used five hours of annotated data per sow and considered five postures (Figure 1): standing; sitting; lying (i.e. ventrally); nursing (i.e. lying laterally with udder exposed), and kneeling.

Experimental Setup

Two millimeter-wave FMCW radars (EasyRadar) manufactured by Silicon Radar (Franckfurt, Germany) were used. The radars were attached on a metal structure in the middle axis of the crate (Figure 1). One radar was placed above the sow's head (i.e.1.40m above ground). The other radar was located at the same height in the upper part of the sow's back, at a distance of 55cm from the first radar. Each radar transmitted a frequency-modulated electromagnetic signal (chirp) every 5ms with the carrier frequency of 122GHz, a modulation bandwidth B of 6.9GHz, and a transmitted power of 4mW. The radars were used as altimeters with the theoretical depth resolution d=c/(2B), where c=3e8m/s is the speed of light in vacuum. A resolution of 2.1cm was sufficient to estimate the posture of the sow. Radars were small enough (100 x 70mm 2 ) to be easily mounted above the crate without affecting the behaviour of the sows. A dielectric lens was mounted in front of each radar antenna to obtain a half-power beam width of 8°. In this way, the radars illuminated the sow, but not the top metallic bars of the crate.

Radar signal analysis and electromagnetic clutter mitigation

The raw data (radar signal) are available upon request to the corresponding author. To estimate the posture of the sows, we analysed the signal delivered by the two radars over time. We computed the beat frequency spectrum (i.e., echo level magnitude as a function of the distance) by applying a Fourier transform [START_REF] Stove | Linear FMCW radar techniques[END_REF] on the time signal. The result was a 2D raw data image of echo levels from which the posture of the sow could be estimated (Figure 2A). However, potential electromagnetic clutter, for instance due to the electromagnetic backscattering from the crate or from the piglets close to the sow, may alter the estimation accuracy of the posture. In order to mitigate this clutter, we used time-gating and spatial filtering.

First, we applied a mean filter on the data across the slow time axis (Figure 2B). The mean was 6 estimated over 1s, which corresponds to 20 consecutive radar measurements. Next, we applied Gabor filters to reduce the impact of uncorrelated data over time [START_REF] Feichtinger | Gabor analysis and algorithms: Theory and applications[END_REF]; see Figure 2C). Finally, we used an average filter (Figure 2D). The main advantage of using these filters is that they are simple to implement and suitable to real-time applications. In the final filtered 2D radar image (Figure 2D), some distinguishable behaviours of the sow could be detected at the distance of 1m, such as the transition to the standing posture around 1300s, 2700s and 3400s. These images obtained from two radars were used as input data for the posture classifier (see below).

Classification of sow postures using a Convolutional Neural Network analysis

To extract the postures of the sows, we used a CNN-based classifier. This approach has previously proved efficient for optical image classification [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF].

Here the number of convolution layers as well as the number of filters per layer were chosen to speed up the training step of the model. A total of 16 filters were used for the first convolutional layers and the number of filters was doubled after each reduction phase (as proposed in [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF]. An illustration of the different layers of the network, including phases of convolution, activation, batch normalisation, pooling, dense, and dropout, is given in The performance of the classifier in terms of the number of sow posture images that were correctly classified as well as the misclassified cases for each class was assessed with the confusion matrices. In the multi-class classification task, the evaluation metrics are computed based on these confusion matrices. We used three evaluation metrics to estimate the quality of the classifier: the specificity, the sensitivity and the accuracy [START_REF] Fawcett | An introduction to ROC analysis[END_REF]. The specificity (sp) indicates if the classifier gives negative results when the considered posture is not seen. The sensitivity (sb) indicates if the classifier gives positive results when the considered posture is seen. The accuracy (acc) indicates how often the classifier gives the true posture. Specificity, sensitivity and accuracy were calculated as follows:

ݏ ൌ ܶܰ ܶܰ ܲܨ , ܾݏ ൌ ܶܲ ܶܲ ܰܨ , ܽܿܿ ൌ ܶܰ ܶܲ ܶܰ ܶܲ ܲܨ ܰܨ
Where TP is the number of times that the estimated class corresponds to the true class, TN is the number of times the class is not predicted and corresponds to another class, FP is the number of times that the class is predicted, but does not correspond to the true class, and FN is the number of times that the class is not predicted and does correspond to the considered class.

Results

For a detailed analysis of the quantitative results, the ten individual classification architectures were compared in the form of confusion matrices (global matrix for the ten sows, and individual matrices for each sow) shown in Figure 4. All occurrences of true/predicted postures are reported in the matrices for the 5 detected postures. The probability of false detection for each posture is derived from these first results. The specificity and sensitivity values of postures computed from the confusion matrices are reported in Table 1. Highest specificity values were obtained for sitting (99.3%) and standing (99.8%). On average, all postures had an accuracy and a specificity higher than 92%. Sensitivity was higher than 90% for all postures except kneeling that was detected in less than 10% of the time. Nursing and lying were confused by 10% on average.

Kneeling had the lowest sensitivity (9.1%), but a high specificity (99.5%) and a high accuracy 8 (99.4%). Our method can thus detect four out of five postures with a high specificity, a high sensibility and a high accuracy.

The pie charts of the ground-truth measurements and estimated measurements of sow postures obtained from the validation datasets are shown in Figure 5. The relative time spent by each sow in each posture over a 2-hours period (corresponding to the validation dataset) was correctly estimated, with an error of less than 10% for all postures except kneeling. The difficulty in correctly estimating kneeling is likely due to the lack of sufficient radar data to analyse this posture with a convolutional neural network. Kneeling lasted only a few seconds (mean: 16s, standard deviation: 7s), which is considerably less than the other postures that lasted several minutes or hours (Table 2). In addition, the kneeling posture was much more sensitive than other postures to the measurement errors induced by the observer's annotation delay (i.e.

time needed to press a computer key to record the change in posture). Graphs of the probability of posture transitions indicate that the different sows lie down differently (Figure 7). In particular, two of them occasionally moved directly from standing to lying, without using the transient postures sitting and kneeling.

Discussion

Automated monitoring of behaviour in farm animals is a major challenge to improve animal welfare and breeding programs for genetic selection. In the case of pig farming, sow postural activity can be used as an indicator of health problems linked to increased piglet mortality. Here we introduced a new method for automated monitoring of postures and posture changes of sows kept in crate using the FMCW radars and a CNN classification. This solution is accurate, faster and requires little memory to store the data. It is thus applicable in real time. It also provides the advantages of not being affected by lightening condition (i.e. day and night analysis is never altered by the light at the level of the crate where the sow is measured) and non-invasive (i.e. do not alter sow behaviour in any way).

Comparison with existing methods

Our radar-based tracking system provides several advantages over other existing methods. For instance, the radars are more accurate and less invasive than accelerometers [START_REF] Ringgenberg | Validation of accelerometers to automatically record sow postures and stepping behaviour[END_REF][START_REF] Canario | Development and validation of an embedded tool to measure postural activity of lactating sows[END_REF]. Although the detection sensitivity with the two approaches were similar for the three postures lying, nursing and standing, the radar data gave an estimation of the sitting posture with a much higher sensitivity than accelerometers (90% with radars, 37% with accelerometers). In addition, detecting other postures such as the sitting is meaningful for the analysis of sow behaviour related to piglet crushing, because it is included in the calculation of sow postural changes that are risky for the piglets [START_REF] Melisová | Sow postural changes, responsiveness to piglet screams, and their impact on piglet mortality in pens and crates[END_REF]. Presumably, lying down through the transient postures sitting and kneeling indicates that sows are cautious towards their piglets when lying down.

We also found that the radar data processing is much faster and requires less memory than video processing for comparable results [START_REF] Leonard | Development and application of an image acquisition system for characterizing sow behaviors in farrowing stalls[END_REF][START_REF] Bonneau | Predicting sow postures from video images: Comparison of convolutional neural networks and segmentation combined with support vector machines under various training and testing setups[END_REF]. For example, [START_REF] Zheng | Automatic recognition of lactating sow postures from depth images by deep learning detector[END_REF] obtained similar results on the same five postures with a Kinect camera and a deep learning analysis on sows kept in individual pen, i.e., with more possibility to move. Using the same experimental design as ours, Bonneau et al ( 2021) achieved 98% sensitivity for four postures with a conventional 2D camera. Therefore, the main advantage of our approach lies in the processing of radar signal which is faster and requires less memory than that of video signal. Indeed, the processing by successive filtering is fast enough for a real-time application and this procedure is easily parallelisable. Using an Intel Core i7 processor with 4 threads makes it possible to process 12000 radar measurements per second. For a single measurement with two radars, only 800 bits are required, compared with several millions (3Mbits) for a standard definition camera. In our study the total data size of the five hours of measurements on ten sows presented was 2Go, which is compatible with the use of radars at large scale for farming applications. Additionally, by default and contrary to video image analysis, our analysis is independent of light conditions. This may be particularly relevant for future applications such as monitoring farrowing, which preferably takes place outside the working hours of the care takers, and therefore when the rooms are not lit [START_REF] Canario | Genetic trends in maternal and neonatal behaviors and their association with perinatal survival in French Large White swine[END_REF].

New possible analyses

Beyond being non-invasive, accurate and fast, the radar approach could be used to monitor sow 10 carefulness when lying down [START_REF] Pokorná | Carefulness and flexibility of lying down behaviour in sows during 24h post-partum in relation to piglet position[END_REF]. In the past, posture changes were rarely characterised by considering the passage through transient postures, i.e., kneeling and sitting (but see [START_REF] Pokorná | Carefulness and flexibility of lying down behaviour in sows during 24h post-partum in relation to piglet position[END_REF][START_REF] Wischner | Prelying behaviour patterns in confined sows and their effects on crushing of piglets[END_REF] and if so, have involved small groups of animals.

Automated monitoring with radars in a farrowing crate enables such accurate recording of whether the sow lies down carefully. This feature can be linked to piglet crushing events.

Our data also indicate it is possible to detect piglets with radars. Prior to this study, preliminary measurements were performed in which the sow's postures were estimated and the standard deviation was calculated over 20min, while the sow remained in a given posture. The standard deviation obtained was of 2.5cm for the nursing posture which is slightly higher than the theoretical depth resolution. However, the electromagnetic clutter may alter the measurement accuracy in some situations. For example, part of the metal bars of the crate that are visible to the radar may generate undesirable electromagnetic backscattering and result in false detections in the CNN analyses. This negative effect can be limited by precise positioning of the radars, so that the radar main beam does not intercept the metallic bars. False detections may also occur when piglets are close to the sow, or when they ride on its back. Figure 6 illustrates this phenomenon with two 2D radar images recorded simultaneously above (a) the head and (b) the back of a sow. The posture estimated from the radar processing (indicated as red cross)

sometimes varies abruptly, due to the presence of piglets in the area of interest, i.e., on the back of the sow (e.g. around 600s, 800s and 1100s). Detection of the piglets at the udder is therefore presumably possible. The radars can be effective in monitoring additional behavioural aspects of the sow-piglets relationship that are of importance for piglet survival.

Conclusions and perspectives

Our study demonstrates the applicability and efficiency of FMCW radars to monitor postures and postural changes of crated sows. This approach holds considerable promises for future applications since minor developments are possible to improve the system. For instance, adding radars will enable to detect new postures and consolidate the estimation of the current ones. Our method was applied to detect the postural activity of the sow from the estimation of the height of its head and its back. Consequently, it could not detect lateral movements of the sow and if the sow was lying on the right or left side. This estimation would be possible by adding a third radar on the side of the sow for detecting lateral movements and consequently, for estimating the orientation of the sow in the crate and whether she is nursing the piglets or not. Moreover, the kneeling posture was not correctly estimated for any sow. This posture is interesting to capture, as it reflects a cautious approach of the sow to lie down, compared with sows that slide along the bars from the standing posture [START_REF] Pokorná | Carefulness and flexibility of lying down behaviour in sows during 24h post-partum in relation to piglet position[END_REF]. Sliding is a less suitable way to lie down for sows as it induces some piglet crushing [START_REF] Fraser | Behavioural perspectives on piglet survival[END_REF][START_REF] Damm | Lying down and rolling behaviour in sows in relation to piglet crushing[END_REF]. The kneeling posture lasts only a few seconds, and its estimation is sensitive to potential annotation errors due to human delay between observation and pressing a computer key. However, from the monitoring of more sows and fixing the radar on the crate rather than a metallic structure above, it should be possible to improve the reliability of the measurement and the accuracy of the posture estimator.

Using different types of radars can also improve piglet detection. With our method, the detection of piglets on the floor is difficult because they rarely enter the radars field of view and are small compared to the sow. The radar beam width was too small to allow detecting piglets.

One solution to this problem would be to use two 2D radars instead of the current device, and position one on each side of the sow. In this way, the detection should work even if the sow hides the piglets from one of the radars beam. Access to such data on the presence of piglets around the sow would benefit the characterisation of sow carefulness to lie down [START_REF] Pokorná | Carefulness and flexibility of lying down behaviour in sows during 24h post-partum in relation to piglet position[END_REF][START_REF] Wischner | Prelying behaviour patterns in confined sows and their effects on crushing of piglets[END_REF]. Adjusting radar characteristics can also increase detection distances. Until now, results were obtained in indoor environment where the sow cannot move.

The radar detects the back of the sow at all times. The use of radar with sows free of movements can be more challenging. Then, it should be possible to detect the sow by using a single 3D radar with a larger beam width, including position and posture simultaneously. To do so, the radar should be placed centrally on the ceiling above the pen to cover the entire pen with the radar beam.

Finally, adding data would also make it possible to define a single classifier to estimate the posture for all sows and develop more detailed behavioural analyses [START_REF] Bonneau | Predicting sow postures from video images: Comparison of convolutional neural networks and segmentation combined with support vector machines under various training and testing setups[END_REF].

So far, the relevance of radars to detect sows that are injured (e.g. excessive time spent lying) or that are not careful towards their piglets (e.g. fast transition from standing to lying) has not been studied. Data recorded for longer periods on animals contrasted on these aspects could be 12 collected with the radar technology. All these improvements are easily reachable, which strongly suggests that automated fine recording with radars will help to analyse the relationship between sow postural changes and risk of piglet crushing. Importantly, radar tracking has limited constraints on the size and shape of animals [START_REF] Henry | Automated monitoring of livestock behavior using frequency-modulated continuous-wave radars[END_REF][START_REF] Dore | 3D trajectories of multiple untagged flying insects from millimetre-wave beamscanning radar[END_REF][START_REF] Dore | A Non-Invasive Millimetre-Wave Radar Sensor for Automated Behavioural Tracking in Precision Farming-Application to Sheep Husbandry[END_REF], thus offering ample possibilities for tracking a wide range of animals in various environments in applied and fundamental ethology research. between the 5 postures for the 10 sows (A-J) over a 5 hours period. Labels A-J correspond to the same sows as in Table 1.

Figures

ng he

Tables

Table 1 -Specificity, sensitivity and accuracy of each of the 5 postures for the 10 sows obtained from individual CNNs. Labels A-J correspond to the same sows as in Figure 7.

Figure 3 .

 3 Figure 3.CNN models were applied individually on each sow, since radar to ground distances were adjusted to the body size of each sow. To build a model, data from each sow was separated into two subsets containing respectively the first 60% and the last 40% of each posture data. The first subset was used for the training of the CNN. The second subset was used to estimate the quality of the predictions by checking that the results on the training dataset were not due to overfitting.During the training phase, we used 32 annotated data between two adaptations of the neural network weights. The CNN weights were adjusted following the method described by[START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] which used a stochastic gradient descent and momentum estimation to optimise the neural network weights. The cost function was the standard function used by[START_REF] Murphy | Machine learning: A probabilistic perspective[END_REF] for multi-class classification. This function computes the minimal cross entropy for each output class. During the initial training, the five postures of interest were considered (Figure1). After the training phase, each CNN was tested on the validation dataset.

Figure 1 - 18 Figure 3 -

 1183 Figure 1 -Images of sow postures as recorded by the video camera: A) nursing (lying laterally with udder exposed), B) lying (ventrally), C) kneeling, D) sitting, E) standing. F) Two FMCW radars were positioned above the sow to monitor head and back elevation. Radar beams are highlighted in green.

Figure 6 -

 6 Figure 6 -Two-dimensional images of the two radars illuminating (a) the head and (b) the back of a sow when piglets are riding on its back. Red crosses represent the computed first local maxima for each slow time bin. The presence of piglets on the sow back can be observed at various times. A threshold for the distance estimation can be used (around 0.6m for the two radars) to determine if the sow is lying or standing.

Table 2 -

 2 Tme spent in each of the 5 postures by the 10 sows over the 5 hours period. 480

	sensitivity

Acknowledgements

We thank the staff of the GenESI INRAE experimental farm for their practical help and care of the animals.

Funding

The Authors thank the Region Occitanie Council (France) for financial support through the SIDIPAR project. While writing, ML, DH and HA received funding from the French National Research Agency (ANR) to ML and HA (ANR-19-CE37-0024-3DNaviBee). AD and ML were also supported by a European Research Council (ERC) Consolidator grant to ML (GA101002644 -Bee-Move).

Competing interest

The authors have no competing interest.


Amélie Cabirol

Tamara Gómez-Moracho

Coline Monchanin

Mathieu Cristian Pasquaretta

Mathieu Lihoreau
email: mathieu.lihoreau@univ-tlse3.fr.

Considering variance in pollinator responses to

Keywords: Apis cerana, Apis mellifera, Bombus impatiens, Bombus terrestris, cognition, inter-individual variability, pesticides, pollinators

Introduction

Human activities have led to a dramatic increase in the extinction rates of animal species [START_REF] Barnosky | Has the Earth 's sixth mass extinction already arrived ?[END_REF][START_REF] Dirzo | Defaunation in the Anthropocene[END_REF][START_REF] Wagner | Insect declines in the anthropocene[END_REF]. Associated stressors have partly been identified and act synergistically [START_REF] Brook | Synergies among extinction drivers under global change[END_REF][START_REF] Dirzo | Defaunation in the Anthropocene[END_REF][START_REF] Sánchez-Bayo | Worldwide decline of the entomofauna: A review of its drivers[END_REF][START_REF] Siviter | Agrochemicals interact synergistically to increase bee mortality[END_REF]. These include habitat loss, pollutions, and the introduction of invasive species. These factors add up to the ones naturally encountered by animals in their environment, such as the presence of predators, pathogens, and parasites. Given the raising number of species threatened with extinction [START_REF] Barnosky | Has the Earth 's sixth mass extinction already arrived ?[END_REF][START_REF] Sánchez-Bayo | Worldwide decline of the entomofauna: A review of its drivers[END_REF], it has become urgent to understand how animal populations can cope with human-induced stressors in order to orient policies towards an efficient regulation of activities affecting the biodiversity.

Many of these stressors do not kill animals, but nevertheless significantly impact their fitness through inaccurate behaviour or reduced reproduction [START_REF] Klein | Why bees are so vulnerable to environmental stressors[END_REF]. Measuring these sublethal effects of stressors on populations is difficult because of the technical challenge of monitoring large numbers of animals and tease apart the many confounding factors linked to field conditions. Most studies have thus focused on the effects of stressors on individual animals using controlled laboratory setups to measure single phenotypic traits, such as cognition or reproduction [START_REF] Badyaev | Stress-induced variation in evolution: From behavioural plasticity to genetic assimilation[END_REF]). Yet, the relevance of such risk assessment methods compared to field population-level studies has been questioned as mismatching conclusions often emerged from the two approaches [START_REF] Thompson | The relevance of sublethal effects in honey bee testing for pesticide risk assessment[END_REF][START_REF] Henry | Reconciling laboratory and field assessments of neonicotinoid toxicity to honeybees[END_REF]. Even though stressors may affect individual phenotypic traits in the lab, life in a natural, sensory, and socially enriched environment can buffer or amplify these effects [START_REF] Wright | Enriched environment prevents chronic stressinduced spatial learning and memory deficits[END_REF][START_REF] Henry | Reconciling laboratory and field assessments of neonicotinoid toxicity to honeybees[END_REF][START_REF] Lambert | Natural-enriched environments lead to enhanced environmental engagement and altered neurobiological resilience[END_REF][START_REF] Cabirol | Experience during early adulthood shapes the learning capacities and the number of synaptic boutons in the mushroom bodies of honey bees (Apis mellifera)[END_REF].

Studies investigating the impact of stressors on phenotypic traits often report shifts in their means at the population level. Agrochemicals, for instance, were shown to reduce food consumption and delay migration in songbirds [START_REF] Eng | A neonicotinoid insecticide reduces fueling and delays migration in songbirds[END_REF], to alter endocrine functions in amphibians and fish [START_REF] Mann | Amphibians and agricultural chemicals : Review of the risks in a complex environment[END_REF][START_REF] Besson | Anthropogenic stressors impact fish sensory development and survival via thyroid disruption[END_REF], and to reduce learning performance in bees [START_REF] Siviter | Quantifying the impact of pesticides on learning and memory in bees[END_REF]. We therefore argue that studying how stressors affect the variance of these traits will provide important complementary information about the severity of stressors on animal populations and may reconcile results obtained in the lab and in the field.

It is well recognized that animals exhibit variability in behavioural and physiological responses to stressors [START_REF] Ebner | Individual differences in stress susceptibility and stress inhibitory mechanisms[END_REF][START_REF] Mazza | Coping with style: individual differences in responses to environmental variation[END_REF]. Some individuals may better cope with particular stressors than others. Thus understanding how this variance in stress-response is affected at the population level is crucial for risk assessment [START_REF] Nakagawa | Meta-analysis of variation: Ecological and evolutionary applications and beyond[END_REF]. If the variance is low in the population following stressor exposure, all individuals may suffer the consequences associated with the altered phenotype. On the contrary, if the variance remains high in the population, even though the mean is affected, some individuals may still exhibit an adaptive phenotype. In some cases, stressors may even increase phenotypic variance, a phenomenon suggested to promote the evolutionary diversification of species [START_REF] Badyaev | Stress-induced variation in evolution: From behavioural plasticity to genetic assimilation[END_REF]. Stressors act as agents of selection and stressinduced variation should therefore be considered when assessing the resilience of a population to a particular stressor [START_REF] Hoffmann | Heritable variation and evolution under favourable and unfavourable conditions[END_REF].

Here we highlight the importance of studying the phenotypic variance in animal populations exposed to stressors. To support this claim, we analysed the effect of stressors on the mean and variance of cognitive performances in bees. We focused on honey bees (Apis) and bumblebees (Bombus), as they are arguably the most studied pollinators. They are also known to be affected by multiple natural and human-induced stressors, and in particular pesticides [START_REF] Potts | Global pollinator declines: trends, impacts and drivers[END_REF][START_REF] Goulson | Bee declines driven by combined Stress from parasites, pesticides, and lack of flowers[END_REF]. Honey bees and bumblebees live in colonies with a division of labour and are therefore characterized by an important level of inter-individual behavioural and cognitive variability [START_REF] Jeanson | Interindividual variability in social insectsproximate causes and ultimate consequences[END_REF]. Foragers, in particular, have evolved a rich cognitive repertoire enabling them to locate and recognise plant resources, handle them, and navigate back to their hive to unload food for the colony [START_REF] Chittka | Bee cognition[END_REF]. One of the most reported sublethal effect of stressors on bees is the decrease in their cognitive performance (learning and memory), which has been associated with a decreased foraging success and colony survival [START_REF] Klein | Why bees are so vulnerable to environmental stressors[END_REF]. A recent meta-analysis confirmed that exposure to neonicotinoid pesticides at field-realistic doses, either in acute or chronic exposure, consistently alter the mean olfactory learning and memory performance of bees [START_REF] Siviter | Quantifying the impact of pesticides on learning and memory in bees[END_REF]. However, the impact of stressor intensity (dose and duration) on the variance of the learning performance was not analysed. We therefore explored these effects by analysing the raw datasets from 24 studies that assessed bee cognition applying olfactory and visual learning protocols in either an appetitive or aversive context. Although a decreased cognitive performance was expected in stressed bees, we predicted that the effect of stressors on the variance would depend on the stressor intensity, which would help estimate the hazardous nature of a given stressor.

Materials and methods

Search and selection of datasets

The search for scientific publications falling within the scope of our research question was performed in July 2020 using the PubMed database. The keywords used for the search were ("Stressor" OR "Pesticide" OR "Parasite") AND ("Cognition" OR "Learning") AND ("Pollinators" OR "Bees"). A total of 71 studies were found, of which 22 met our inclusion criteria. Two datasets belonging to the authors of this study were also included as they filled the inclusion criteria. These studies measured the impact of stressors on the cognitive performance of bees. A summary of the studies is given a Table 1.

Cognitive tasks. We focused on cognitive data from bees exposed to stressors during their adult life, as bees treated as larvae might be more sensitive to stressors (i.e. pesticides; [START_REF] Siviter | Quantifying the impact of pesticides on learning and memory in bees[END_REF] Thus, this kind of data was not considered in our analyses (see [START_REF] Smith | Insecticide exposure during brood or early-adult development reduces brain growth and impairs adult learning in bumblebees[END_REF][START_REF] Tan | A neonicotinoid impairs olfactory learning in Asian honey bees (Apis cerana) exposed as larvae or as adults[END_REF]. Briefly, in all these studies, cognitive performance was assessed using associative learning paradigms testing the ability of bees to associate an olfactory or/and a visual stimulus with an appetitive or aversive reinforcement [START_REF] Giurfa | Behavioral and neural analysis of associative learning in the honeybee: a taste from the magic well[END_REF].

Olfactory learning was tested in 9 out of the 24 studies. These studies used olfactory learning protocols with appetitive conditioning of the extension of the proboscis of bees (PER; 17 studies) or aversive conditioning of the sting extension (SER; 2 studies). Either response was conditioned by presenting bees a conditioned stimulus (an odour) paired with an unconditioned stimulus (a reward of sucrose solution or an electric shock), for 3-15 trials in appetitive assays and 5-6 trials in aversive assays. Trainings included absolute learning (the odour is reinforced) and differential learning (an odour is reinforced, the other is not). Visual learning was tested in 5 out of 24 the studies. These studies used visual learning protocols with appetitive conditioning in a Y-maze (1 study) or on artificial flowers (1 study), or aversive conditioning with electric shocks (1 study). One of these studies applied a multimodal appetitive conditioning combining both odour and colour cues to be learnt by bees in an array of artificial flowers [START_REF] Muth | Modality-specific impairment of learning by a neonicotinoid pesticide[END_REF]. Here again bees were tested for differential learning.

The last study included a test of social recognition when placed with a conspecific [START_REF] Shepherd | Increased aggression and reduced aversive learning in honey bees exposed to extremely low frequency electromagnetic fields[END_REF].

Stressors.

The stressor type covered different pesticides, parasites, predator odours, alarm pheromones, and heavy metal pollutants. Studies performed with pesticides whose median lethal dose (LD50; i.e. dose that kills 50% of the population) could not be identified in the literature were excluded from our final selection.

Exposure duration.

In all these studies, stressors were applied before the cognitive tests, except in two studies in which it was used as the CS during conditioning (i.e. petrol exhaust [START_REF] Leonard | Petrol exhaust pollution impairs honey bee learning and memory[END_REF], alarm and predator pheromones [START_REF] Wang | Honey bees modulate their olfactory learning in the presence of hornet predators and alarm component[END_REF]). We categorised the duration of exposure using the common dichotomy between acute and chronic treatments. An acute treatment was characterized by a single administration of the pesticide to each individual bee. When bees were exposed to the pesticide more than once, either as a substance present in their environment or as a food directly offered to each individual, the exposure type was considered chronic.

Bee genus. The bee species studied in the selected publications were the honey bees Apis cerana and Apis mellifera, and the bumblebees Bombus impatiens and Bombus terrestris. These species were not selected purposefully, but rather emerged from the refinement obtained with other inclusion criteria. All but three raw datasets were available online with the published material. Those three datasets were kindly provided by their authors. The list of the 24 selected studies is available in Table 1. The raw data are provided in Dataset S1.

Dataset organisation and normalisation of variables

The raw data were downloaded and saved as .csv files. A new dataset (Dataset S1) was created, which combined information on the species, the cognitive task studied, the type of stressor, the type of exposure (acute/chronic), and, in the case of pesticide studies, the dose (µg/bee) or concentration (ppb). Within each study, data were grouped in different categories according to homogeneous experimental methodologies (i.e. 38 categories).

To allow comparison across studies, a z-score was calculated for each individual on its cognitive performance by applying the function 'scale' in R (package {base}) which uses the mean and the standard deviation of the sample to scale each element. Within each study, the function 'scale' was applied on the cognitive performance of bees belonging to the same category of bee species, cognitive task, stressor type and exposure type. When learning performance was measured as a binary response (e.g. success vs. failure) across multiple trials, the raw data was first used to calculate a learning score for each individual corresponding to the number of successful trials. Such a calculation was required because the variance in binary variables can be mathematically predicted from the mean and sample size and does not reflect biological variance (Supplementary Fig. S1). For pesticide studies, the dose (acute exposure) and concentration (chronic exposure) were normalized using the LD50.

Individual z-scores were used to calculate the mean and the variance of the z-scores for each control and stressed group. We thereafter refer to these variables as the "mean" and the "variance" of the cognitive performance. Each study may contain multiple control and stressed groups depending on the number of experiments performed and the number of stressors used. The final sample sizes are therefore larger than the number of studies and are displayed on the figures.

Data analyses

All analyses were conducted in R Studio v.1.2.5033 (RStudio Team 2015). Linear mixedeffects models (LMMs; package {lme4}; [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF] were used to investigate the impact of stressors on the mean and the variance of the cognitive performance. The group (control vs. stressed), the type of stressor, the species or the type of tasks were defined as independent variables. The experiment's identifier was set as random factor.

Similar models were used to assess the impact of pesticides on the mean and variance of the cognitive performance. In the subset of pesticide studies (15 studies),

Pearson correlation tests were also performed to assess the relationship between the mean and the variance of the cognitive performance within control and stressed groups. LMMs were conducted to study the influence of the pesticide dose (log-transformed) on individual zscores, with the experiment's identifier set as random factor.

Results

All stressors reduced the cognitive mean but not the variance

We first explored the overall effects of stress on the cognitive mean and variance of bees across the 24 studies. As expected from previous studies, the mean cognitive performance was severely impacted by exposure to stressors (Fig. 1A). Overall, stressed bees exhibited a significantly lower mean cognitive performance than control bees (LMMs; group effect: F 1,90 > 15, P < 0.001 for all models) irrespective of the type of stressor they were exposed to (group*stressor effect: F 4,90 = 0.92, P = 0.454; Fig. 1A), the bee genus (group*genus effect:

F 1,94 = 1.23, P = 0.271; Fig. 1C) and the type of cognitive task (group*task effect: F 3,93 = 0.84, P = 0.477; Fig. 1E).

The effects of stressors on cognitive variance were less pronounced and more heterogeneous (Fig. 1B). Variance did not differ significantly between control and stressed bees (LMMs; group effect: F 4,122 < 4.12, P > 0.05 for all models). We found no effect of the bee genus (group*genus effect: F 1,128 = 0.65, P = 0.421; Fig. 1D) nor of the type of cognitive task (group*task effect: F 3,120 = 0.75, P = 0.533; Fig. 1F). There was a significant interaction between exposure to stressor and the type of stressor, indicating a heterogeneous effect of stressors on the variance of the cognitive performance (group*stressor effect: F 4,122 = 3.44, P = 0.011; Fig. 1B). While variance decreased in stressed bees exposed to pesticides, it tended to increase in stressed bees exposed to other stressor types, compared to their respective control group. Thus exposure to stressors globally reduced the cognitive performances of bees, with mixed effects on variance depending on stressor type.

Chronic exposure to pesticides reduced cognitive mean and variance

To investigate whether stressor intensity plays a role in the differential effects of stressors observed on the variance of the cognitive performance of bees, we focused our analyses on the 15 pesticide studies of our dataset (Table 1). Pesticide studies were the most abundant in the literature and present the advantage that a normalization of stressor intensity across drugs was possible using LD50s (amount of substance necessary to kill 50% of individuals in the population) and durations of exposure (acute or chronic).

Both acute and chronic treatments reduced the mean cognitive performance of bees (Fig. 2; LMM; acute: F 1,34 = 5.89, estimates±standard error: -0.232±0.095, P = 0.021; chronic:

F 1,20 = 28.69, -0.465±0.083, P < 0.001). They also tended to reduce the cognitive variance within populations, although to different extent. Cognitive variance of stressed bees was significantly lower than that of control bees in the chronic treatments (Fig. 2B; F 1,20 = 10.34, estimates: -0.317±0.107, P < 0.01) but not in the acute treatments (Fig. 2A; F 1,47 = 0.40, estimates: -0.005±0.078, P = 0.532). However, we found a positive correlation between the mean cognitive performance and its variance in both stressed groups (acute: r = 0.437, P < 0.01; chronic: r = 0.657, P < 0.005), but not in control groups (acute: r = 0.057, P = 0.868; chronic: r = 0.072, P = 0.833). This shows pesticides tended to reduce both mean and variance in the two treatments, but this effect was more pronounced for chronic exposure.

High pesticide doses reduced cognitive mean and variance

To further explore whether the effect on mean and variance differed with stress magnitude, we analysed different doses and durations of pesticide exposure. A dose-dependent effect on cognitive performance was found for both acute and chronic exposure (Fig. 3). Cognitive performances (Individual z-scores) significantly decreased with increasing doses of exposure (LMM; Fig. 3A, acute: estimates = -0.144±0.018, P < 0.001, Fig. 3B; chronic: estimates = -0.121±0.020, p < 0.001). Interestingly, both mean and variance decreased with increasing pesticide doses for acute and chronic exposures (Figs 3C-D). This means most bees in the population tested seemed to show a decreased cognitive performance following a treatment with high pesticide doses, irrespective of exposure duration.

Discussion

Many environmental stressors affect the behaviour and cognition of animals [START_REF] Killen | Environmental stressors alter relationships between physiology and behaviour[END_REF][START_REF] Klein | Why bees are so vulnerable to environmental stressors[END_REF][START_REF] Siviter | Quantifying the impact of pesticides on learning and memory in bees[END_REF][START_REF] Siviter | Agrochemicals interact synergistically to increase bee mortality[END_REF]. While studies reporting such sublethal effects have typically focused on mean phenotypic traits, all individuals in a population are not similarly affected by stressors, and the resulting phenotypic variance may be critical for stress resilience. Here we tested this hypothesis by analysing raw datasets of 24 bee studies. We showed different effects on the cognitive mean and variance of insects exposed to stressors, depending on stress level and exposure mode, thus validating the importance of examining variance in addition to mean phenotypic traits in ecotoxicological studies.

Focusing on pesticide revealed the mean cognitive performance of bees was altered by both chronic and acute exposures. This result is consistent with a previous meta-analysis [START_REF] Siviter | Quantifying the impact of pesticides on learning and memory in bees[END_REF]. However, the variance in cognitive performance of bees was only decreased after a chronic exposure. This means some bees were able to better cope than others with short pesticide exposure, but not to repeated stress. This is, to our knowledge, the first study showing a differential effect of acute and chronic exposures to a stressor on learning performance in an animal. Such variance in response to stress might be due to homeostatic physiological processes that can counteract the effect of an acute exposure to the drug, which is only present in the body for a short duration [START_REF] Cohen | Pesticide-mediated homeostatic modulation in arthropods[END_REF]. Indeed most pesticides act on the nervous system of bees whose plasticity to maintain homeostasis is well-known [START_REF] Turrigiano | Hebb and homeostasis in neuronal plasticity[END_REF][START_REF] Cabirol | The neurophysiological bases of the impact of neonicotinoid pesticides on the behaviour of honey bees[END_REF]. For instance, neurons can compensate a change in the balance between brain excitation and inhibition by modulating the efficacy of specific synapses [START_REF] Pozo | Unraveling mechanisms of homeostatic synaptic plasticity[END_REF]. As neonicotinoids activate the excitatory cholinergic neurotransmission pathway, one might expect the brain to counteract this increased excitation [START_REF] Cabirol | The neurophysiological bases of the impact of neonicotinoid pesticides on the behaviour of honey bees[END_REF]. However, the lasting presence of toxic compounds in the bodies during a chronic exposure seems to complicate the process of resilience to this stressor for most individuals.

Interestingly, for both acute and chronic pesticide exposure, the mean cognitive performance and its variance decreased with increasing doses of toxic compounds. The positive correlation between the mean and the variance is consistent with this finding: the more a stressor affects the mean, the more it affects the variance. This advocates for the use of low pesticide concentrations in the field. Reducing use to doses having sublethal effects on pest insects would still protect crops when pest density is low and thereby would be less damaging to non-target insects [START_REF] Colin | Pesticide dosing must be guided by ecological principles[END_REF].

Altogether, our results thus suggest that an acute exposure to low pesticide doses is the least damaging for bee populations. Indeed, despite the reduced mean cognitive performance, an unaltered variance of the learning performance following pesticide exposure means that some individuals may have maintained sufficient cognitive abilities to support efficient foraging [START_REF] Klein | Why bees are so vulnerable to environmental stressors[END_REF]. Cognitive and behavioural variance is thought to be particularly important for populations resilience after environmental changes [START_REF] Jandt | Behavioural syndromes and social insects: personality at multiple levels[END_REF] as it augments the probability that some individuals display adapted behaviour to the new environmental conditions. In group-living species, such as social insects, the high diversity of behavioural phenotypes within colonies is known to improve the efficiency of collective decision-making and the ability of groups to find optimal solutions to changing conditions [START_REF] Burns | Diversity of speed-accuracy strategies benefits social insects[END_REF][START_REF] Michelena | Personality and collective decision-making in foraging herbivores[END_REF].

In nature, bees often encounter pesticides over long time periods especially when colonies are located near treated crops and in the hive due to the residues present in the honey and wax [START_REF] Godfray | A restatement of the natural science evidence base concerning neonicotinoid insecticides and insect pollinators[END_REF][START_REF] Godfray | A restatement of recent advances in the natural science evidence base concerning neonicotinoid insecticides and insect pollinators[END_REF][START_REF] Tsvetkov | Chronic exposure to neonicotinoids reduces honey bee health near corn crops[END_REF]. The consequences of such a chronic exposure to pesticides are often not a priority in risk assessment procedures.

Policy regulations in the European Union and in the US regarding the commercialization of new plant protection products (PPPs) ask for acute toxicity assays on bees and other nontarget animals before asking for chronic toxicity assays (EPPO, 1992, 2010; U.S.

Environmental Protection Agency and Code of Federal Regulations (CFR), 2010). Only when acute toxicity is significant would a chronic toxicity assay be performed. Although the European Food Safety Authority recommends the inclusion of chronic exposure assays earlier in the risk assessment procedure, such assays are not yet mandatory (EFSA, 2013).

The effects of PPPs that will be encountered chronically in the field might therefore be underestimated. Note that the fact similar results were obtained in Bombus and Apis confirms honey bees are overall suitable surrogates for non-Apis species in regulatory risk assessments of pesticide toxicity [START_REF] Arena | A meta-analysis comparing the sensitivity of bees to pesticides[END_REF][START_REF] Heard | Comparative toxicity of pesticides and environmental contaminants in bees : Are honey bees a useful proxy for wild bee species ?[END_REF][START_REF] Thompson | Are honeybees suitable surrogates for use in pesticide risk assessment for non-Apis bees?[END_REF], as currently considered by the European commission (EPPO 2010).

This is true at least when exploring general trends. But these results must then be complemented on non-Apis bee species that may vary in their sensitivity to pesticides [START_REF] Arena | A meta-analysis comparing the sensitivity of bees to pesticides[END_REF].

Overall, our study revealed a differential effect of chronic and acute exposures to pesticides as well as an important influence of the stressor intensity on the proportion of individuals that might be impacted. Focusing on variance helped identify acute stress conditions bees may be able to cope with, which could not be done by looking at the mean only. Interestingly all types of stressors did not similarly influence bee cognition. While the mean was severely impacted by all stressors, variance seemed to increase in some nonpesticide stressors. This positive effect could be triggered by the relatively small sample sizes found for some stressors (N ≤ 5 for the control groups used to assess the effect of parasites, pollution, and co-exposures). But if it is confirmed, this means stress can favour the diversification of cognitive abilities [START_REF] Badyaev | Stress-induced variation in evolution: From behavioural plasticity to genetic assimilation[END_REF], an observation already made in rodents where low intensity stressors can have beneficial effects on the cognitive performance [START_REF] Hurtubise | Effects of stress on behavioral flexibility in rodents[END_REF]. These intriguing effects of stress on cognitive traits demonstrate the importance of considering phenotypic variance in future analyses of the impact of environmental stressors on animals. We hope such approach can be generalised to assess more thoroughly the hazardous nature of the stressors and identify the modes of exposure that might be less damaging for wild populations. Future investigations should also consider the possible interaction between agrochemicals, which have synergistic effects on bee mortality, but antagonistic effects on behaviour when looking at the mean only [START_REF] Siviter | Agrochemicals interact synergistically to increase bee mortality[END_REF]. Ultimately the results of such studies should lead to explicit guidelines for farmers on the safe use of these toxic substances.

Authors' contribution

Figure 1 .

 1 Figure 1. Stressors decrease the mean cognitive performance of bees, but not the variance. Violin plots showing the mean (left) and the variance (right) of the cognitive performance for control (black) and stressed (red) bees are displayed according to: A-B) the type of stressors; C-D) the bee genus; E-F) the type of cognitive tasks. White triangles represent the mean. Sample sizes are displayed above the violins. P-values from LMM are displayed for group effect only and are in bold when significant.

Figure 2 .

 2 Figure 2. Pesticide exposure duration affects the variance of the cognitive performance. The mean and the variance of the cognitive performance are plotted for

Figure 3 .

 3 Figure 3. Effect of the pesticide dose on cognitive performance. Individual z-scores are plotted relative to the normalized pesticide dose (logarithm of %LD50) for A) acute exposure (N = 2,141 bees) and B) chronic exposure (N = 1,026 bees). Estimate trends are displayed in solid blue lines. Plots showing the mean cognitive performance relative to the normalized pesticide dose (logarithm of %LD50) and coloured according to variance for C) acute (N = 13 controls, N = 36 stressed) and D) chronic exposure (N = 11 controls, N = 11 stressed).

Table 1 : Summary of the 24 studies used.

 1

	Stressor	Genus	Exposure type	Reference
	Pesticide	Apis	Acute	(Ludicke and Nieh, 2020)
	Pesticide	Apis	Acute	(Hesselbach and Scheiner, 2018)
	Pesticide	Apis	Acute	(Urlacher et al., 2016)
	Pesticide	Apis	Acute,	(Tan et al., 2015)
	Pesticide	Apis	Chronic	(Mustard et al., 2020)
	Pesticide	Apis	Chronic	(Tan et al., 2017)
	Pesticide	Apis, Bombus	Acute	(Siviter et al., 2019)
	Pesticide	Bombus	Acute	(Muth et al., 2019)
	Pesticide	Bombus	Acute, chronic	(Stanley, Smith and Raine, 2015)
	Pesticide	Bombus	Chronic	(Smith et al., 2020)
	Pesticide	Bombus	Chronic	(Lämsä et al., 2018)

AC, CP and ML designed the study. AC, TGM and CM collected the data. TGM processed the data and prepared dataset. CM, TGM and CP analysed the data. AC wrote the first draft of the manuscript. All authors substantially contributed to revisions.

Acknowledgements

We thank Jacques Gautrais for discussions about mean and variance correlations, and Dara Stanley and Ken Tan for providing raw data of their studies.

Data availability statement

Raw data are available in Dataset S1 (.xlsx file). The data supporting the results will be archived in Dryad Digital Repository upon publication of the manuscript.

Fundings

AC has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 892574. CM was funded by a PhD fellowship from the French Ministry of Higher Education, Research and Innovation and from Macquarie University. TGM and ML were supported by a grant of the European Regional Development Found FEDER (MP0021763 -ECONECT), and by an ERC Consolidator grant (GA101002644 -BEE-MOVE) to ML.

Conflict of Interest

The authors declare no competing interests.

Supplementary materials 547

Supplementary figure S1. Analysis of variance in studies with binary data. (A) Impact of a pesticide and parasite on bumblebees' learning performance measured with a classical conditioning of the proboscis extension response (PER) (from [START_REF] Piiroinen | Chronic neonicotinoid pesticide exposure and parasite stress differentially affects learning in honeybees and bumblebees[END_REF]. The percentage of individuals that extended the proboscis in response to the conditioned stimulus (i.e percentage of learners) is plotted across 10 successive learning trials. (B) Matrix representing the impact of a stressor on the variance in learning performance. For an equal sample size in the control and treatment groups, the impact of the treatment on variance can be calculated using the mean of each group. An increased (orange) or decreased variance (blue) can be predicted.

Piiroinen, Saija, Cristina Botías, Elizabeth Nicholls, and Dave [START_REF] Piiroinen | Chronic neonicotinoid pesticide exposure and parasite stress differentially affects learning in honeybees and bumblebees[END_REF]