Pauline Bellot

Sophie Marie Dupont

François Brischoux

Hélène Budzinski

Olivier Chastel

Clémentine Fritsch

Olivier Lourdais

Louise Prouteau

Steffi Rocchi

Frédéric Angelier

Bellot Pauline1

Brischoux Marie1

Budzinski François1

Chastel Hélène2

Fritsch Olivier1

Lourdais Clémentine3

Olivier1

Prouteau Louise1

Rocchi Steffi3

Angelier Frédéric1

Experimental Exposure to Tebuconazole Affects Metabolism and Body Condition in a Passerine Bird, the House Sparrow ( Passer domesticus )

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

INTRODUCTION

Whole-organism metabolism is a key physiological trait because it is involved in multiple biological processes (e.g., foraging, reproductive behavior; [START_REF] Biro | Do consistent individual differences in metabolic rate promote consistent individual differences in behavior?[END_REF][START_REF] Bryant | Energy expenditure in wild birds[END_REF][START_REF] Careau | Genetic correlation between resting metabolic rate and exploratory behaviour in deer mice (Peromyscus maniculatus)[END_REF][START_REF] Daan | Avian basal metabolic rates : Their association with body composition and energy expenditure in nature[END_REF][START_REF] Mcnab | The Physiological Ecology of Vertebrates : A View from Energetics[END_REF]. Whole-organism metabolic rates are measured as a function of the rate at which an organism oxidizes substrates to produce energy [START_REF] Careau | Energy metabolism and animal personality[END_REF]. Classically, they are determined by the sum of the energy cost of self-maintenance (resting metabolic rate [RMR]; [START_REF] Bryant | Energy expenditure in wild birds[END_REF][START_REF] Daan | Avian basal metabolic rates : Their association with body composition and energy expenditure in nature[END_REF][START_REF] Mcnab | The Physiological Ecology of Vertebrates : A View from Energetics[END_REF], and also the energy output that is available to the organism to perform additional daily or seasonal physiological and behavioral processes [START_REF] Biro | Do consistent individual differences in metabolic rate promote consistent individual differences in behavior?[END_REF]. Resting metabolic rate is defined as the metabolic rate of an adult animal at rest in its thermoneutral zone and in a postabsorptive state [START_REF] Hulbert | Basal metabolic rate : history, composition, regulation, and usefulness[END_REF]. Importantly, metabolic rates often show strong interindividual variations within species [START_REF] Burton | What causes intraspecific variation in resting metabolic rate and what are its ecological consequences[END_REF][START_REF] Konarzewski | Determinants of intra-specific variation in basal metabolic rate[END_REF], and this variability has previously been linked to different individual energetic strategies [START_REF] Biro | Do consistent individual differences in metabolic rate promote consistent individual differences in behavior?[END_REF][START_REF] Burton | What causes intraspecific variation in resting metabolic rate and what are its ecological consequences[END_REF][START_REF] Careau | Energy metabolism and animal personality[END_REF][START_REF] Nilsson | Metabolic consequences of hard work[END_REF][START_REF] Rønning | Is basal metabolic rate associated with recruit production and survival in free-living house sparrows?[END_REF].

In birds, metabolic rates are known to be dependent on many biotic and abiotic factors such as individual mass, age, hormones, and ambient temperature (e.g., [START_REF] Bouwhuis | Basal metabolic rate and the rate of senescence in the great tit[END_REF][START_REF] Broggi | Sources of variation in winter basal metabolic rate in the great tit[END_REF][START_REF] Burton | What causes intraspecific variation in resting metabolic rate and what are its ecological consequences[END_REF][START_REF] Chappell | The relationship of central and peripheral organ masses to aerobic performance variation in house sparrows[END_REF][START_REF] Chastel | Pre-breeding energy requirements : Thyroid hormone, metabolism and the timing of reproduction in house sparrows Passer domesticus[END_REF][START_REF] Dupont | Slowing down the metabolic engine: Impact of early-life corticosterone exposure on adult metabolism in house sparrows (Passer domesticus)[END_REF][START_REF] Konarzewski | Determinants of intra-specific variation in basal metabolic rate[END_REF][START_REF] Nzama | Seasonal variation in the metabolism-temperature relation of House Sparrows (Passer domesticus) in KwaZulu-Natal, South Africa[END_REF] and, importantly, metabolic rates can also be affected by exposure to environmental contaminants. For example, [START_REF] Verreault | Organohalogen contamination in breeding glaucous gulls from the Norwegian Arctic: Associations with basal metabolism and circulating thyroid hormones[END_REF] demonstrated that organohalogen contaminants could lead to a decrease in RMR in glaucous gulls.

Such contaminant-related alterations of metabolic rates may have detrimental impacts on fitness as a result of pathologies (e.g., [START_REF] Quagliariello | Metabolic syndrome, endocrine disruptors and prostate cancer associations: biochemical and pathophysiological evidences[END_REF] and/or a mismatch between energy availability and energy demands. In vertebrates, metabolism is under the control of the hypothalamus-pituitary-thyroid (HPT) axis and the resulting regulation of circulating thyroid hormones (TH) such as thyroxine (T4) and triiodothyronine (T3; [START_REF] Danforth | The role of thyroid hormones in the control of energy expenditure[END_REF][START_REF] Ortiga-Carvalho | Hypothalamus-pituitary-thyroid axis[END_REF]. For example, plasma concentrations of TH have been functionally related to RMR in humans and wild vertebrates [START_REF] Chastel | Pre-breeding energy requirements : Thyroid hormone, metabolism and the timing of reproduction in house sparrows Passer domesticus[END_REF][START_REF] Elliott | Thyroid hormones correlate with resting metabolic rate, not daily energy expenditure, in two charadriiform seabirds[END_REF][START_REF] Hulbert | Basal metabolic rate : history, composition, regulation, and usefulness[END_REF][START_REF] Kim | Thyroid hormone as a determinant of energy expenditure and the basal metabolic rate[END_REF][START_REF] Welcker | Thyroid hormones correlate with basal metabolic rate but not field metabolic rate in a wild bird species[END_REF]. In that context, the metabolic function of vertebrates is likely to be altered by pollutants which target the functioning of the HPT axis (i.e., endocrine disruptors, e.g., [START_REF] Ask | Per-and polyfluoroalkyl substances are positively associated with thyroid hormones in an arctic seabird[END_REF][START_REF] Jugan | Endocrine disruptors and thyroid hormone physiology[END_REF][START_REF] Li | Parental exposure to tebuconazole causes thyroid endocrine disruption in zebrafish and developmental toxicity in offspring[END_REF][START_REF] Sebastiano | High levels of fluoroalkyl substances and potential disruption of thyroid hormones in three gull species from SouthWestern France[END_REF][START_REF] Yu | Thyroid endocrine disruption in zebrafish larvae following exposure to hexaconazole and tebuconazole[END_REF].

Several studies have demonstrated that contaminants can alter the functioning of the HPT axis and the metabolism of vertebrates (e.g., [START_REF] Braham | The effects of DDT on energetics of the short-tailed shrew, Blarina brevicauda[END_REF], but most of these studies have focused on polychlorinated biphenyls [START_REF] French | Effects of pre-and postnatal polychlorinated biphenyl exposure on metabolic rate and thyroid hormones of white-footed mice[END_REF][START_REF] Smits | Thyroid hormone suppression and cell-mediated immunomodulation in American Kestrels (Falco sparverius) exposed to PCBs[END_REF][START_REF] Tori | Effects of polychlorinated biphenyls on the metabolic rates of mourning doves exposed to low ambient temperatures[END_REF][START_REF] Verreault | Organohalogen contamination in breeding glaucous gulls from the Norwegian Arctic: Associations with basal metabolism and circulating thyroid hormones[END_REF][START_REF] Voltura | Effects of dietary polychlorinated biphenyl exposure on energetics of white-footed mouse, Peromyscus leucopus[END_REF], organochlorine pesticides [START_REF] Blévin | Contaminants and energy expenditure in an Arctic seabird : Organochlorine pesticides and perfluoroalkyl substances are associated with metabolic rate in a contrasted manner[END_REF], polybrominated diphenyl ethers [START_REF] Allen | PBDE flame retardants, thyroid disease, and menopausal status in U.S. women[END_REF][START_REF] Sean | Dietary exposure to 2,2′,4,4′-tetrabromodiphenyl ether (pbde-47) alters thyroid status and thyroid hormone-regulated gene transcription in the pituitary and brain[END_REF], per-and polyfluoroalkyl compounds [START_REF] Ask | Per-and polyfluoroalkyl substances are positively associated with thyroid hormones in an arctic seabird[END_REF][START_REF] Blévin | Contaminants and energy expenditure in an Arctic seabird : Organochlorine pesticides and perfluoroalkyl substances are associated with metabolic rate in a contrasted manner[END_REF][START_REF] Sebastiano | High levels of fluoroalkyl substances and potential disruption of thyroid hormones in three gull species from SouthWestern France[END_REF], and neonicotinoids [START_REF] Zgirski | Early life neonicotinoid exposure results in proximal benefits and ultimate carryover effects[END_REF]. The potential impact of endocrine disruptors on metabolism remains neglected, especially regarding contaminants of emerging interest such as azoles. To comprehensively assess the potential actions of endocrine disruptors on the metabolism of organisms, it is essential to widen the panel of studied contaminants (including overlooked emerging, albeit widespread, molecules).

Among the known endocrine disruptors, many pesticides are attracting increasing attention because of their massive release in the environment [START_REF] Mahmood | Effects of Pesticides on Environment[END_REF].

Fungicides are widely used pesticides that are increasingly employed in many crops, sometimes in very large quantities [START_REF] Zhang | Global pesticide use: Profile, trend, cost/benefit and more[END_REF]. Azoles compounds are currently the most used fungicides worldwide and they are applied to a wide range of crops, including vegetables, orchards, vineyards, field crops, and ornamental cultures [START_REF] Souders | Investigation into the sub-lethal effects of the triazole fungicide triticonazole in zebrafish (Danio rerio) embryos/larvae[END_REF]. This widespread and intensive production of azole compounds has led to environmental contamination of surface water [START_REF] Kahle | Azole fungicides: occurrence and fate in wastewater and surface waters[END_REF], soil [START_REF] Pelosi | Residues of currently used pesticides in soils and earthworms: A silent threat?[END_REF], and air [START_REF] Rokbani | Heterogeneous oxidation of two triazole pesticides (diniconazole and tebuconazole) by OH-radicals and ozone[END_REF]. As a result, residual contamination is also found in food (European Food Safety Authority, 2016), invertebrates, wild vertebrates, and humans [START_REF] Daniele | Development of a method for the simultaneous determination of multi-class pesticides in earthworms by liquid chromatography coupled to tandem electrospray mass spectrometry[END_REF][START_REF] Pelosi | Residues of currently used pesticides in soils and earthworms: A silent threat?[END_REF][START_REF] Polledri | Hair as a matrix to evaluate cumulative and aggregate exposure to pesticides in winegrowers[END_REF].

One concern with the release of azoles in the environment is their potential impact on nontarget species such as wild vertebrates (fish, birds, mammals, reptiles, or amphibians), mainly because azoles may affect multiple endocrine mechanisms [START_REF] Zarn | Azole fungicides affect mammalian steroidogenesis by inhibiting sterol 14 alpha-demethylase and aromatase[END_REF]. For example, recent studies have demonstrated that birds show a disruption of their physiology and a reduced breeding output when they are exposed to triazoles through their diet [START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF]Lopez-Antia et al., 2018, 2021). In addition, experimental studies in aquatic models have shown that triazoles can modify several physiological and behavioral components, such as glucose and protein regulation, mitochondrial function, endocrine mechanisms, and locomotor activity [START_REF] Cao | Developmental toxicity of the triazole fungicide cyproconazole in embryo-larval stages of zebrafish (Danio rerio)[END_REF][START_REF] Souders | Investigation into the sub-lethal effects of the triazole fungicide triticonazole in zebrafish (Danio rerio) embryos/larvae[END_REF][START_REF] Toni | Assessment of oxidative stress and metabolic changes in common carp (Cyprinus carpio) acutely exposed to different concentrations of the fungicide tebuconazole[END_REF].

Interestingly, few studies have shown that triazoles can affect the HPT axis and circulating TH levels in laboratory fish [START_REF] Li | Parental exposure to tebuconazole causes thyroid endocrine disruption in zebrafish and developmental toxicity in offspring[END_REF][START_REF] Yu | Thyroid endocrine disruption in zebrafish larvae following exposure to hexaconazole and tebuconazole[END_REF]. Despite these significant advances, the effects of low environmental concentrations of triazoles on physiological processes of wild terrestrial vertebrates is overall overlooked because most of the literature deals with acute ecotoxicity tests (e.g., median lethal dose; LC50) using aquatic vertebrate or invertebrate model species (such as zebrafish and earthworms; [START_REF] Andreu-Sánchez | Acute toxicity and bioconcentration of fungicide tebuconazole in zebrafish (Danio rerio)[END_REF][START_REF] Binev | Pathomorphological studies following experimental acute intoxication with the triazole fungicide triticonazole in pigs[END_REF][START_REF] Raby | Acute effects of binary mixtures of imidacloprid and tebuconazole on 4 freshwater invertebrates[END_REF][START_REF] Rico | Lethal and sub-lethal effects of five pesticides used in rice farming on the earthworm Eisenia fetida[END_REF][START_REF] Sancho | Short-term exposure to sublethal tebuconazole induces physiological impairment in male zebrafish (Danio rerio)[END_REF].

In the present study, we experimentally tested the impact of tebuconazole on metabolic rates and condition (body mass and body condition) in a wild bird species that inhabits agricultural environments, the house sparrow (Passer domesticus). Tebuconazole is currently one of the most used triazole in crops [START_REF] Berenzen | A comparison of predicted and measured levels of runoff-related pesticide concentrations in small lowland streams on a landscape level[END_REF][START_REF] Kahle | Azole fungicides: occurrence and fate in wastewater and surface waters[END_REF], and it is suspected to have detrimental effects on wild birds (e.g., [START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF][START_REF] Lopez-Antia | Birds feeding on tebuconazole treated seeds have reduced breeding output[END_REF]. Although several studies suggest that triazole compounds may interfere with metabolic rates, to our knowledge no study has experimentally tested the impact of tebuconazole on metabolic rates in wildlife. In the present study, we experimentally contaminated captive wild-caught house sparrows with tebuconazole and mimicked a realistic environmental exposition to tebuconazole. We then determined the impact of a chronic exposure to tebuconazole (~7 months) on the RMR (i.e., at 25 °C, which corresponds to thermoneutrality for house sparrows) and on the thermoregulatory metabolic rate (TMR; i.e., at 12 °C when sparrows have to spend additional energy to actively thermoregulate; [START_REF] Dupont | Slowing down the metabolic engine: Impact of early-life corticosterone exposure on adult metabolism in house sparrows (Passer domesticus)[END_REF] of sparrows. Metabolic rates were measured at these two temperatures to test if the potential effect of tebuconazole on metabolism may be exacerbated under energetically constraining conditions (i.e., at 12 °C). We also studied the effect of exposure to tebuconazole (exposed vs. control) on sparrow body mass and body condition (i.e., the mass corrected by the size of the birds) because these traits are tightly linked to energy balance, body reserves, and metabolic rates. In addition, we measured the overnight body mass loss of all individuals (see [START_REF] Dupont | Slowing down the metabolic engine: Impact of early-life corticosterone exposure on adult metabolism in house sparrows (Passer domesticus)[END_REF] as a measure of energy depletion during the overnight fast. Although no data are available regarding the impact of tebuconazole on metabolic rates in terrestrial vertebrates, we predicted that exposed sparrows would show reduced metabolic rates relative to controls because of the previously reported effect of triazoles on metabolic rates and TH levels in fish [START_REF] Cao | Developmental toxicity of the triazole fungicide cyproconazole in embryo-larval stages of zebrafish (Danio rerio)[END_REF][START_REF] Li | Parental exposure to tebuconazole causes thyroid endocrine disruption in zebrafish and developmental toxicity in offspring[END_REF][START_REF] Souders | Sub-lethal effects of the triazole fungicide propiconazole on zebrafish (Danio rerio) development, oxidative respiration, and larval locomotor activity[END_REF][START_REF] Yu | Thyroid endocrine disruption in zebrafish larvae following exposure to hexaconazole and tebuconazole[END_REF]. We also predicted that these effects of tebuconazole on metabolic rates may be exacerbated at lower temperature (TMR, 12 °C) compared to thermoneutrality (RMR, 25 °C) because altered metabolic rates may be more apparent when individuals are energetically constrained (i.e., thermoregulating). Finally, we predicted that exposed birds may also show higher body mass and body condition, and a reduced overnight body mass loss relative to controls if tebuconazole exposure is associated with reduced metabolic rates. Alternatively, tebuconazole could lead to a reduction in the body mass and body condition of individuals due to altered health status (e.g., reduced energy reserves).

MATERIAL AND METHODS

Study species and experimental design

The present study was conducted with captive wild-caught adult house sparrows. A total of 54 adult sparrows were used in this experiment (Nfemales = 31 and Nmales = 23). All sparrows were maintained in captivity in four similar outdoor aviaries (length 3 m, width 2 m, height 2 m). The birds were maintained in outdoor aviaries to keep them under natural seasonal temperature cycles. Each aviary was equipped with artificial shelter boxes (one box per bird).

The sparrows were fed ad libitum with a mixture of commercial seeds, millet on the stack, sand, and salt/minerals blocks. In all aviaries, water was dispensed through a drinking trough. Of the four aviaries, two of them formed the group of control individuals and the other two formed the group of individuals exposed to tebuconazole. Birds were split in the aviaries by treatment type and sex (Aviary 1: exposed females, N = 17; Aviary 2: control females, N = 14; Aviary 3: exposed males, N = 12; Aviary 4: control males, N = 11). This gives a total of 29 exposed and 25 control individuals. Over the total duration of the experiment, there was one death in each group (one in the control group and one in the exposed group). These individuals are not included in the numbers reported above. Sample sizes slightly differed between categories because a few of these wild-caught birds did not adjust to captivity and were released. Exposed individuals were treated with tebuconazole through their drinking water. Although other routes of exposure are classically used for farmland granivorous species (consumption of treated seeds; Lopez-Antia et al., 2016[START_REF] Zhang | Global pesticide use: Profile, trend, cost/benefit and more[END_REF], 2021), we chose a drinking water exposure to mimic an oral contamination potentially present in natura due to the presence of trace triazoles in surface water [START_REF] Kahle | Azole fungicides: occurrence and fate in wastewater and surface waters[END_REF]. In the two exposed aviaries, tebuconazole (CAS. No 107534-96-3, purity ≥98.0%; Sigma-Aldrich) was diluted with tap water using a precision balance (±0.0001 g) to reach a concentration of 550 µg L-1 . Considering that the average sparrow drinks the equivalent of 30% of its body weight per day (Bartholomew & Cade, 1963), a 25-g individual would consume approximately 4.1 µg of tebuconazole per day via drinking water.

Comparatively, the LD50 of tebuconazole reported in the Northern Bobwhite was 1988 mg kg-1 (Pesticide Properties Database, 2022). In the two control aviaries, control individuals had access to regular tap drinking water without tebuconazole. The concentration of tebuconazole in the drinking water of the control and exposed groups was analyzed to confirm an exposure concentration of 550 µg L-1 in the exposed individuals and tebuconazole-free water for the control individuals (by liquid chromatography tandem mass spectrometry [LC-MS/MS]; Qualyse Laboratory). Water was changed every week for both control (tap water) and exposed sparrows (tap water with tebuconazole). Exposure to tebuconazole began on 6 November 2019 until 29 June 2020, immediately after the metabolic rates measurements (see below). We specifically decided to expose individuals during several months to the exposed or control treatments to test the impact of a prolonged exposure to tebuconazole on metabolic rates ("exposed sparrows" vs. "control sparrows"). Accordingly, in vineyards, the period of spraying of pesticides occurs from the beginning of March to the end of August (~6 months). After 7 months, four exposed and four control sparrows were captured and bled to obtain plasma to measure their degree of contamination by tebuconazole. Plasma levels of azoles were determined using LC-MS/MS methodology at the LPTC-EPOC (L'équipe de Physico et Toxico Chimie de l'environnement -Environnements et Paléoenvironnements Océaniques et Continentaux) laboratory [START_REF] Zgirski | Early life neonicotinoid exposure results in proximal benefits and ultimate carryover effects[END_REF]. Briefly, 25 µl of sparrow plasma was weighed to which 30 µl of Isotope-Labelled Internal Standards (ILISs) solution was gravimetrically added.

A chicken quality control plasma was used. Then, a precipitation solvent (acetonitrile) was added to the mixture to obtain a total volume of 150 µl. After extraction and centrifugation of the samples, the supernatant was transferred to an injection vial prefilled with 1050 µl of Milli-Q water. Each extract was then injected into the analytical system composed of a Poroshell 120 SB C18 guard column (Agilent) used as on-line SPE cartridge. Target compound separation was achieved on a Poroshell Phenyl-Hexyl column (Agilent). The quantification of azoles was performed by using a 6490 Triple Quad mass spectrometer (Agilent) in positive electrospray mode in dynamic multiple reactions monitoring. Two high-resolution transitions were chosen for the analyte: one for quantification and the second for confirmation. Finally, we checked the analytical sequence with quality controls, and we used internal standard ILIS to calculate the concentration. Injection and handling blanks were used to confirm the accuracy of the quantification. The limit of quantification of tebuconazole was 25 pg g-1 of plasma (see [START_REF] Zgirski | Early life neonicotinoid exposure results in proximal benefits and ultimate carryover effects[END_REF] for more details on the methodology). To have enough plasma to assay tebuconazole and reduce the amount of blood that was drawn from each bird, samples from the four exposed sparrows and the four control sparrows, respectively, had to be pooled. The concentration of tebuconazole in the pooled plasma of exposed sparrows was 59.7 pg g-1 , which is similar to the concentrations that are found in the plasma of birds living in conventional agroecosystems (in June/July 2019, 34 individuals were caught in the Cognac vineyard area, France, mean ± SD: 70.7 ± 84.9, range 26.0 [min], 222.2 [max]). Tebuconazole was not detected in the plasma pool of control sparrows.

Metabolism measurements

In the present study, the main variables of interest were TMR and RMR. During the treatment period, the birds were kept in outdoor aviaries and were subject to the natural climatic cycle before being transferred to temperature-controlled respirometry chambers. Metabolic rate was measured by multi-channel continuous flow through respirometry (RM8 Multiplexer; Sable Systems International) following previously described protocols [START_REF] Dupont | Slowing down the metabolic engine: Impact of early-life corticosterone exposure on adult metabolism in house sparrows (Passer domesticus)[END_REF].

Metabolic rates were measured for each individual at two ambient temperatures (Ta), (i) in colder thermal conditions, Ta = 12 °C (TMR), and (ii) in the thermoneutral zone for this species, Ta = 25 °C (RMR) using a temperature-controlled climatic chamber (±1 °C; Cryosystem, airconditioned system Carel Master Cella). The multichannel open-circuit respirometer includes seven test chambers and an empty chamber considered as a control (3000 ml). This system enabled the metabolic rates of seven individuals to be analyzed simultaneously. The outside air was supplied at a constant flow rate (∼450 ml min-1 ) to each chamber via an air pump (Bioblock Scientific 551) and a mass flow controller (FlowBar-8; Sable Systems). To obtain the target humidity of the supply air, ambient air was first saturated by bubbling it through two serially connected, heated water columns and then though an empty column, all within a temperature-controlled chamber (400 DG; LMS) set at 4 °C. Sequential samples were taken from the air expelled from each chamber via a gas flow switch (RM-Multiplexer; Sable Systems). Then the expelled air was passed through a hygrometer (RH 300; Sable Systems) and the water was extracted using Drierite. Finally, dried air samples were sent to a CO2 analyzer (CA10A; Sable Systems) and then to an O2 analyzer (FC10A; Sable Systems).

Measurements of TMR and RMR were carried out over a period from 3 June 2020 to 28 June 2020. The two measurements were carried out over two experimental sessions per individual, each 10 days apart. For these measurements, the order of passage of the birds was randomly chosen. Each bird was randomly assigned to a specific temperature of measurement for the first session (TMR at 12 °C or RMR at 25 °C) and was then assigned to the other temperature of measurement for the second session so that all birds were tested at both temperatures (TMR and RMR). The effects of the session did not significantly affect metabolic rates (linear module

[LM], F(0.08) = 0.776). On the day of the measurement, at 18:00 hours, food was removed from the aviaries so that the individuals could fast before the TMR and RMR measurements.

At 20:00 hours, the sparrows were weighed with an electronic scale (initial mass), their tarsus was measured with a caliper (±0.01 mm) to assess body size, and the birds were placed in the dark glass chamber. The Ta of the climatic chambers was set at 12 °C or 25 °C depending on the session of measurement (TMR or RMR). The metabolic rates were measured six times per sparrow per session for 10 h. These measurements were averaged for each individual to give an average TMR and RMR. The oxygen level was calculated following [START_REF] Dupont | Slowing down the metabolic engine: Impact of early-life corticosterone exposure on adult metabolism in house sparrows (Passer domesticus)[END_REF]. The next morning (at 6:00 AM), the sparrows were removed from the metabolic analysis boxes and weighed (final mass) before being released in their aviary of origin. The TMR and RMR were corrected by the mass of each individual (ml h-1 g-1 ).

Individual body mass and body condition index

The initial body mass (before the metabolism measurement) and the final body mass (after the metabolism measurement) were used to assess the effect of the treatment on the body condition of the sparrows. The tarsus of each individual was also measured with a caliper (±0.01 mm) before the metabolism measurement. The body condition index (BCI) was calculated from the extraction of residuals from the linear regression of individual body mass as a function of tarsus length (LM, F(1,214) = 165.5, p ≤ 0.001).

Statistical analysis

All the statistical analyses were carried out on Rstudio (R Ver 4.0.3) with the packages lm4, lmerTest, AICcmodavg, car, MuMIn, and ggplot2. To test the effect of the experimental treatment on metabolic rates (TMR 12 °C and RMR 25 °C) and body condition of the sparrows, linear mixed-effect models (LMMs) were applied. Our variables of interest (dependent variables) were metabolic rates (TMR and RMR) and body condition. Both TMR and RMR were measured for all individuals, and they were statistically analysed together by including the temperature of metabolic measurements variable (TMR 12 °C, RMR 25 °C). We checked that all models met the assumptions of normality and homoscedasticity of residuals. First, an LMM with three fixed-effect variables (sex, temperature of metabolic measurements [TMR 12 °C or RMR 25 °C], treatment [control or exposed]) and their interactions were carried out to test the effect of treatment on the metabolic rates of sparrows (TMR and RMR). Individual identity was added as a random effect in the models because each metabolic measurement was performed twice (for TMR 12 °C and RMR 25 °C). The models were selected using the corrected Akaike information criterion selection (AICc) method. After selection of the best model, specific comparisons were conducted by using contrast procedures to better describe the differences that were found between different groups of birds. Second, an LMM with four fixed effects (sex, temperature of metabolic measurements [TMR 12 °C or RMR 25 °C]), treatment [control or exposed], time of mass measurements [initial or final], and their interactions) were carried out to test the effect of tebuconazole on BCI and the body mass of individuals. Individual identity was added as a random effect in the models because the mass of individuals was measured twice (initial and final body mass) for each session (TMR 12 °C and RMR 25 °C).

Model selection was done as stated above, using the AICc selection method. After LMM, specific comparisons were conducted by using contrast procedures to better describe the differences that were found between different groups of birds. Because the results on body mass and body condition were very similar (same significant and nonsignificant terms), we only present the results on body condition in the results section. Indeed, body mass and body condition were highly correlated (Pearson correlation, r = 0.75, t(1,214) = 16.64, p ≤ 0.001). The results on body mass are presented as an annex (see Supporting Information).

RESULTS

TMR and RMR

As expected, there was a very strong and significant effect of temperature on the metabolic rates of sparrows (Table 1 and Figure 1). Specifically, TMR (12 °C) was significantly higher than RMR (25 °C; contrast: t(1,52) = 22.11, p < 0.001). We found a significant "Temperature × Treatment" interaction on metabolism (Table 1 andFigure 1), showing that the influence of the experimental treatment on metabolism differed significantly depending on the temperature of the metabolic measurements (i.e., 12 °C vs. 25 °C). Indeed, at 12 °C the TMR of the exposed group was not significantly different from the control group (contrast: t(1,90.6) = -0.40, p = 0.694; Figure 1A). However, at 25 °C, the RMR of exposed individuals was significantly lower than that of controls (contrast: t(1,90.6) = 2.00, p = 0.049; Figure 1B). Sex did not significantly influence the metabolism of individuals (t(1,52) = 1.11, p = 0.298). Moreover, all the interactions related to sex were nonsignificant (all p-value > 0.207), suggesting that sex did not influence the TMR and RMR of the control and exposed sparrows (Table 1).

TABLE 1: Effects of temperature of metabolic measurements (thermoregulatory metabolic rate 12 °C or resting metabolic rate 25 °C), treatment (control or exposed to tebuconazole), and their interaction on the metabolism of individuals (rate of oxygen consumption, VO2, ml h-1 g-1 ).

The identity of the individuals was added as a random factor. A linear mixed-effects model was used. Significant terms are indicated with the following codes: ***

FIGURE 1: Rate of oxygen consumption (VO2, ml h-1 g-1 ) according to the temperature of the metabolic measurement: at 12 °C (A, thermoregulatory metabolic rate [TMR]) and at 25 °C (B, resting metabolic rate [RMR]) as a function of treatment (control or exposed to tebuconazole).

The gray and purple colors represent the metabolic values of control and exposed individuals, respectively. Resting metabolic rate was significantly lower in exposed sparrows compared to control sparrows, whereas TMR did not differ statistically between exposed and control sparrows. Means ± SE are presented. The different letters indicate significant differences between treatments (controls or exposed to tebuconazole).

Response variable

Explanatory

Body condition index

Control and exposed sparrows did not differ in initial body size (i.e., tarsus length before the metabolism measurement, LM, F(1, 52) = 0.05, p = 0.830). As expected, the initial BCI of the sparrows was higher than their final BCI, because the explanatory variable "Time" was highly significant (Table 2), showing that all birds lost weight overnight (Figure 2). Importantly, there was no significant effect of the "Treatment × Time", "Sex × Time", or "Sex × Time ×

Treatment" interactions on BCI (Table 2), demonstrating that the overnight weight loss did not differ between sexes or between exposed and control sparrow. Sex did not significantly influence the BCI of individuals (Table 2) although there was an effect of the "Treatment" on BCI (Table 2) with an overall higher BCI for exposed birds relative to control ones (contrast:

t(1,50) = -2.40, p = 0.020). Interestingly, the "Temperature × Sex," "Temperature ×

Treatment", and "Temperature × Treatment × Sex" interactions had significant effects on BCI (Table 2), demonstrating that the influence of the experimental treatment on BCI significantly differs depending on the temperature of metabolic measurements (i.e., TMR 12 °C vs. RMR 25 °C) and the sex of the individual (Figure 2). Specifically, exposed females had a higher BCI than control females at 25 °C (contrast: t(1,60.2) = -3.03, p = 0.004; Figure 2B), but not at 12 °C (contrast: t(1,60.2) = -0.62, p = 0.540; Figure 2A). In males, this effect was not significant at both 25 °C (contrast: t(1,60.2) = -1.50, p = 0.140; Figure 2D) and 12 °C (contrast: t(1,60.2)

= -1.42, p = 0.162; Figure 2C) despite a trend toward a higher BCI in exposed males relative to controls (Figure 2C,D).

DISCUSSION

In the present study, we showed for the first time in wild bird species that long-term exposure to a widely used azole (tebuconazole) can significantly reduce the RMR (i.e., measured at thermoneutrality, 25 °C) of exposed individuals although their TMR (i.e., 12 °C) was not affected by the experimental treatment. In addition, exposed individuals had a higher body mass and BCI than controls, although overnight body mass loss did not differ between the two groups.

Metabolic rates

Our study demonstrates for the first time that the use of tebuconazole can alter metabolic rates and may have a detrimental impact on birds. Overall, tebuconazole exposure was associated with a significant decrease in RMR (25 °C). Consistent with our results, previous studies have shown that exposure to propiconazole and cyproconazole in zebrafish embryos caused up to a 50% decrease in RMR, as well as an overall alteration in mitochondrial bioenergetics [START_REF] Cao | Developmental toxicity of the triazole fungicide cyproconazole in embryo-larval stages of zebrafish (Danio rerio)[END_REF][START_REF] Souders | Sub-lethal effects of the triazole fungicide propiconazole on zebrafish (Danio rerio) development, oxidative respiration, and larval locomotor activity[END_REF]. Similarly, [START_REF] Teng | Metabolomics and transcriptomics reveal the toxicity of difenoconazole to the early life stages of zebrafish (Danio rerio)[END_REF] and [START_REF] Perez-Rodriguez | Tebuconazole reduces basal oxidative respiration and promotes anxiolytic responses and hypoactivity in early-staged zebrafish (Danio rerio)[END_REF] found that difenoconazole and tebuconazole, respectively, had similar effects in developing zebrafish. In the present study, we demonstrated for the first time that environmental concentrations of tebuconazole can have qualitatively similar effects in nonaquatic vertebrates (i.e., adult wild birds). This shows that different azole fungicides are able to alter, and more specifically to reduce, metabolic rates in birds, probably through a modification of mitochondrial processes [START_REF] Cao | Developmental toxicity of the triazole fungicide cyproconazole in embryo-larval stages of zebrafish (Danio rerio)[END_REF][START_REF] Souders | Sub-lethal effects of the triazole fungicide propiconazole on zebrafish (Danio rerio) development, oxidative respiration, and larval locomotor activity[END_REF]. However, and interestingly, [START_REF] Souders | Investigation into the sub-lethal effects of the triazole fungicide triticonazole in zebrafish (Danio rerio) embryos/larvae[END_REF] did not report any effect of triticonazole on the metabolic rates of zebrafish embryos, even after increasing the maximum test concentration (from 100 to 250 µM) and extending the exposure time (from 24 to 48 h). Therefore, the mode of action of azole compounds on metabolic rates may be specific to the compound, the duration of exposure or the stage of development. Importantly, we used much lower tebuconazole concentration in our study relative to previous studies (e.g., [START_REF] Andreu-Sánchez | Acute toxicity and bioconcentration of fungicide tebuconazole in zebrafish (Danio rerio)[END_REF][START_REF] Raby | Acute effects of binary mixtures of imidacloprid and tebuconazole on 4 freshwater invertebrates[END_REF][START_REF] Toni | Assessment of oxidative stress and metabolic changes in common carp (Cyprinus carpio) acutely exposed to different concentrations of the fungicide tebuconazole[END_REF]. Nonetheless, based on preliminary field data (see Methods), our concentrations gave plasma tebuconazole levels similar to those found in wild birds living in agroecosystems.

Despite the use of these lower, but environmental, concentrations, we found a significant impact of tebuconazole exposure on the RMR of sparrows. This suggests that environmental fungicide applications are sufficient to cause metabolic disruption in nontarget bird species, such as those living in agroecosystems. As a result, our study demonstrates that the use of tebuconazole can alter a key physiological trait and may have a detrimental impact on wild birds.

Contrary to our prediction, the impact of tebuconazole exposure on metabolic rates was not exacerbated when the birds had to thermoregulate (i.e., for the TMR measurement at 12 °C).

Indeed, we did not detect any impact of tebuconazole on this metabolic measurement (TMR).

We predicted that tebuconazole would have a stronger impact on TMR because mitochondrial activity is increased when individuals have to thermoregulate (i.e., 12 °C in our study; [START_REF] Mozo | Thermoregulation: what role for UCPs in mammals and birds?[END_REF] and previous studies have suggested that azole compounds could alter the functioning of mitochondria [START_REF] Souders | Sub-lethal effects of the triazole fungicide propiconazole on zebrafish (Danio rerio) development, oxidative respiration, and larval locomotor activity[END_REF]. However, it is likely that the energetic costs of thermoregulation vary dramatically between individuals depending on their insulation properties (feather density and quality, fat content, etc.). This interindividual variability could have masked a potential effect of tebuconazole on TMR. In addition, it is also possible that the impact of tebuconazole on metabolic rates is reduced when the activity of the cellular machinery is important, as is the case at 12 °C (TMR) relative to 25 °C (RMR). To better understand how tebuconazole can affect metabolic rates of wild birds, it appears now crucial to study the impact of environmental concentrations of tebuconazole on the mitochondrial functioning and bioenergetics of terrestrial birds. It would also be relevant to study the effect of tebuconazole on metabolic rates along a wide range of ambient temperature to better understand if the impact of tebuconazole on metabolism may be exacerbated at more challenging temperatures. One of the potential targets of tebuconazole responsible for the alteration of RMR in exposed individuals could be the HPT axis. Indeed, in vertebrates metabolism is under the control of this neuroendocrine pathway. Therefore, the impact of azoles on RMR could be related to a potential disruption of this axis [START_REF] Liu | Effects of prochloraz or propylthiouracil on the cross-talk between the HPG, HPA, and HPT axes in Zebrafish[END_REF][START_REF] Yu | Thyroid endocrine disruption in zebrafish larvae following exposure to hexaconazole and tebuconazole[END_REF]. Specifically, it has been shown that the thyroid hormones are key drivers of tissue oxygen consumption and metabolic activity in endotherms [START_REF] Bobek | Age-related changes in oxygen consumption and plasma thyroid hormone concentration in the young chicken[END_REF][START_REF] Danforth | The role of thyroid hormones in the control of energy expenditure[END_REF][START_REF] Freake | Thermogenesis and Thyroid Function[END_REF][START_REF] Hulbert | Thyroid hormones and their effects : A new perspective[END_REF]. Moreover, T3 levels are positively associated with RMR in multiple bird species [START_REF] Elliott | Thyroid hormones correlate with resting metabolic rate, not daily energy expenditure, in two charadriiform seabirds[END_REF][START_REF] Welcker | Thyroid hormones correlate with basal metabolic rate but not field metabolic rate in a wild bird species[END_REF][START_REF] Zheng | Geographic variation in basal thermogenesis in little buntings : Relationship to cellular thermogenesis and thyroid hormone concentrations[END_REF], including house sparrows [START_REF] Chastel | Pre-breeding energy requirements : Thyroid hormone, metabolism and the timing of reproduction in house sparrows Passer domesticus[END_REF]. Several studies have shown that triazoles are potential endocrine disruptors of the HPT axis in model species and exposure to tebuconazole has been associated

with alteration of T3 levels and with numerous dysregulations of the genes involved in the HPT axis [START_REF] Li | Parental exposure to tebuconazole causes thyroid endocrine disruption in zebrafish and developmental toxicity in offspring[END_REF][START_REF] Yu | Thyroid endocrine disruption in zebrafish larvae following exposure to hexaconazole and tebuconazole[END_REF]. Therefore, the reduction of RMR in exposed individuals could result from an endocrine disruption of the HPT axis and more specifically from a reduction of T3 levels in exposed individuals. To our knowledge, the impact of environmental concentrations of tebuconazole or azole compounds on T3 levels has never been examined in wild terrestrial vertebrates. In addition, tebuconazole may also indirectly affect RMR through its impact on other mechanisms of actions that are tightly connected to metabolism (e.g., oxidative stress, blood biochemistry, immunity; Lopez-Antia et al., 2018). Future studies should now examine the response of the HPT axis, and T3 levels, to environmental concentrations of tebuconazole to better understand how this fungicide can alter metabolic rates.

Body mass and body condition

As predicted, the body mass and BCI of exposed individuals were significantly higher than those of controls. However, body mass was measured only after several months of exposure to tebuconazole, and we must therefore remain cautious regarding this result. Additional experiments examining the long-term impact of exposure to tebuconazole on body condition are necessary to confirm the results from our study. This effect was surprisingly dependent on the temperature of measurement. Despite this intriguing temperature-dependent effect, this result is in line with the lower RMR of exposed birds because metabolic rates are positively correlated with energy mobilization and the depletion of body reserves in vertebrates [START_REF] Nagy | Energetics of free-ranging mammals, reptiles, and birds[END_REF][START_REF] Peters | The Ecological Implications of Body Size[END_REF], including the house sparrow [START_REF] Dupont | Slowing down the metabolic engine: Impact of early-life corticosterone exposure on adult metabolism in house sparrows (Passer domesticus)[END_REF]. Although our results were only apparent at one temperature and in females only, they suggest that environmental concentrations of tebuconazole can have a strong impact on energy regulation in wild birds, as previously suggested by [START_REF] Lopez-Antia | Birds feeding on tebuconazole treated seeds have reduced breeding output[END_REF]. Interestingly, we further found that tebuconazole had a significant impact on the body condition of females, and a similar (but not significant) trend was observed in males. This suggests that females may be more sensitive to the impact of environmental concentrations of tebuconazole on energy regulation.

At the proximate level, such a sex-dependent effect may be explained by sexual differences in the metabolic and endocrine pathways that are disrupted by tebuconazole. Indeed, azole compounds such as tebuconazole are known to readily interfere with cytochrome P450 enzymes, which are involved in the synthesis and regulation of sexual steroid hormones such as oestradiol [START_REF] Taxvig | Endocrinedisrupting activities in vivo of the fungicides tebuconazole and epoxiconazole[END_REF][START_REF] Vinggaard | Screening of selected pesticides for inhibition of CYP19 aromatase activity in vitro[END_REF][START_REF] Yang | Effects of tebuconazole on cytochrome P450 enzymes, oxidative stress, and endocrine disruption in male rats[END_REF][START_REF] Zarn | Azole fungicides affect mammalian steroidogenesis by inhibiting sterol 14 alpha-demethylase and aromatase[END_REF][START_REF] Zhang | Inhibition of cytochromes P450 by antifungal imidazole derivatives[END_REF]. Importantly, oestradiol is known to affect energy regulation, fat deposition, and body condition in vertebrates, including humans [START_REF] Brown | Central effects of estradiol in the regulation of food intake, body weight, and adiposity[END_REF]. Dysregulation of oestradiol levels by chronic exposure to tebuconazole could explain the higher body condition of exposed females. Supporting this hypothesis, Lopez-Antia et al. (2021) found that tebuconazole can reduce circulating cholesterol levels in red-legged partridges (Alectoris rufa)

and cholesterol is a precursor of sexual hormones [START_REF] Brown | Central effects of estradiol in the regulation of food intake, body weight, and adiposity[END_REF]. This effect was also found with exposure to another azole on the same species (Lopez-Antia et al., 2018). In addition, Fernández-Vizcaíno et al. ( 2020) even found that exposure to tebuconazole was associated with reduced oestradiol levels in the same species.

Surprisingly, and despite these effects of tebuconazole on blood biochemistry [START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF][START_REF] Lopez-Antia | Birds feeding on tebuconazole treated seeds have reduced breeding output[END_REF], these studies did not report a significant impact of tebuconazole on body mass or body condition in red-legged partridges [START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF][START_REF] Lopez-Antia | Birds feeding on tebuconazole treated seeds have reduced breeding output[END_REF]. Similarly, a previous study did not find any effect of another triazole compound on the body condition of the same species (difenoconazole; Lopez- et al., 2013). However, and importantly, the impact of tebuconazole on body condition has to our knowledge never been tested in other bird species. Red-legged partridge and house sparrows have different body size, body mass, fat reserves, and mass-specific metabolic rates.

Antia

These differences are associated with different fasting capacities [START_REF] Rodríguez | The effects of fasting and refeeding on biochemical parameters in the red-legged partridge (Alectoris rufa)[END_REF] that could explain this discrepancy between studies. In addition, most of these previous studies have exposed individuals to tebuconazole during short periods (i.e., less than a month), although the impact of tebuconazole on body condition could appear progressively and become apparent after several weeks or months of exposure. Although exposure to plant protection products is multifactorial and chronic, the duration of exposure in our experiment is probably in the upper range of what can be found in agroecosystems. Thus, it is possible that the effects of tebuconazole varied over the time of exposure, particularly if the birds up regulated their detoxification system. Therefore, it would be relevant in future studies to test how metabolism and body condition change during chronic exposure to triazole.

Despite a strong effect of tebuconazole on RMR, overnight body mass loss surprisingly did not differ between exposed and control sparrows. However, we would expect overnight body mass loss to be reduced in exposed sparrows because of their lower RMR. Such a counterintuitive result may be explained by different body composition, such as fat content, between exposed and control sparrows. Indeed, lipid catabolism is associated with a much higher energetic yield (energy produced per gram of tissue) than protein catabolism in birds [START_REF] Jenni | Fuel supply and metabolic constraints in migrating birds[END_REF] and consequently with a lower body mass loss. Body composition was not available in our study, but other experimental studies reported that exposure to tebuconazole or other triazoles can affect circulating blood metabolites, such as triglycerides and cholesterol, in the red-legged partridge [START_REF] Lopez-Antia | Experimental exposure of red-legged partridges (Alectoris rufa) to seeds coated with imidacloprid, thiram and difenoconazole[END_REF], 2021;[START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF] suggesting a strong impact on energy regulation and metabolic pathways in terrestrial birds.

In addition to potential dysregulation of lipid metabolism, tebuconazole could also affect the body mass of sparrows by modifying feeding behaviour (e.g., hyperphagia). In our study, we did not measure the feeding behavior of exposed and control sparrows. This potential effect of tebuconazole on feeding behavior could be mediated by changes in the hypothalamic-pituitaryadrenal (HPA) axis. Indeed, this endocrine axis plays a key role in the control of appetite in vertebrates [START_REF] Grün | Endocrine disrupters as obesogens[END_REF][START_REF] Suzuki | The role of gut hormones and the hypothalamus in appetite regulation[END_REF], including birds [START_REF] Astheimer | Interactions of corticosterone with feeding, activity and metabolism in passerine birds[END_REF]. Such an effect could also be mediated by the disruption of other endocrine axes, such as the hypothalamic-pituitary-gonads (HPG) axis. Indeed, tebuconazole is known to affect steroidogenesis in nontarget species by interfering with aromatase (CYP19), which is responsible for the conversion of androgens to estrogens [START_REF] Poulsen | Tebuconazole disrupts steroidogenesis in Xenopus laevis[END_REF][START_REF] Saxena | Modelling inhibition of avian aromatase by azole SAR and QSAR in[END_REF]. This may cause a dysregulation of estrogen levels (such as oestradiol), and estrogens are known to have an inhibitory action on food intake [START_REF] Asarian | Modulation of appetite by gonadal steroid hormones[END_REF][START_REF] Butera | Estradiol and the control of food intake[END_REF][START_REF] Hirschberg | Sex hormones, appetite and eating behaviour in women[END_REF]. Accordingly, some studies have experimentally demonstrated that estrogen deficiency via aromatase elimination causes obesity in mice (e.g., [START_REF] Misso | Cellular and molecular characterization of the adipose phenotype of the aromatase-deficient mouse[END_REF][START_REF] Takeda | Progressive development of insulin resistance phenotype in male mice with complete aromatase (CYP19) deficiency[END_REF]. [START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF] found that exposure to tebuconazole is associated with reduced oestradiol levels in the red-legged partridge, suggesting that a disruption of steroid hormone homeostasis could affect feeding behavior and explain why exposed individuals had a higher BCI/mass than controls. However, Lopez-Antia et al. ( 2021) also reported that exposure to tebuconazole did not have any significant effect on feeding behavior in the same species, suggesting that increased body condition in exposed sparrows may be mainly explained by the impact of tebuconazole on metabolic rates and energy expenditure. Further studies are now necessary to better understand how tebuconazole affects the condition of sparrows and to test whether these effects are mediated by the disruption of several endocrine axes (HPA, HPG, HPT).

CONCLUSION

Taken together, our results showed physiological effects of tebuconazole on house sparrows, including a significant decrease in RMR (e.g., 25 °C) and a significantly higher mass and BCI in exposed individuals. These first results on terrestrial vertebrates show the importance of evaluating the potential risks associated with chronic exposure to tebuconazole in agroecosystems, including for humans. It now seems relevant to investigate what the underlying effects of a decrease in RMR might be on the fitness of the species (reproduction and survival) and more broadly in vertebrates. Indeed, a reduction in RMR could result in a decrease in the energy devoted to self-maintenance and lead to an alteration in the ability of individuals to reproduce and survive [START_REF] Blévin | Exposure to oxychlordane is associated with shorter telomeres in arctic breeding kittiwakes[END_REF][START_REF] Burton | What causes intraspecific variation in resting metabolic rate and what are its ecological consequences[END_REF][START_REF] Goutte | Survival rate and breeding outputs in a high Arctic seabird exposed to legacy persistent organic pollutants and mercury[END_REF]. Recent studies have demonstrated impaired reproductive performance in red-legged partridges following exposure to triazole compounds [START_REF] Fernández-Vizcaíno | Multi-level analysis of exposure to triazole fungicides through treated seed ingestion in the red-legged partridge[END_REF]Lopez-Antia et al., 2018, 2021). Thus, these first results involving the effect of triazole compounds on vertebrates living in agroecosystems stimulate further studies to fill the existing gaps on the toxicity of these phytosanitary products widely used throughout the world.

TABLE 2 : Effects of temperature of metabolic measurements (12 °C or 25 °C), time of measurement (initial: before measuring metabolism or final: after measuring metabolism), treatment (control or exposed to tebuconazole), sex (female or male), and their interaction on the body condition index according to linear mixed-effects modelling.

 2

	Response variable	Explanatory variables	NumDF DenDF F-value	p-value
	Body Condition Index	Temperature	1	157	0.65	0.421
		Time	1	157	180.32	<0.001 ***
		Treatment	1	50	5.78	0.020 *
		Sex	1	50	<0.01	0.958
		Temperature x Treatment	1	157	7.51	0.007 **
		Temperature x Sex	1	157	5.12	0.025 *
		Treatment x Sex	1	50	<0.01	0.924
		Temperature x Treatment x Sex 1	157	6.43	0.012 *

The identity of the individuals was added as a random factor. Significant terms are indicated with the following codes: ***

Supporting Information

The Supporting information is available on the Wiley Online Library at https://doi.org/10.1002/ etc.5446. Acknowledgment-We thank E. Beaugeard, E. Daniaud, A. Dupoué, S. Hope, B.

Mohring, and P. Pardon for their help during the present study. The platform PLATINE (https:// www.u-bordeaux.fr/Recherche/Plateformes/Sciences-de-lenvironnement/Plateforme-dechimie-analytique-organiqueenvironnementale-PLATINE) of the University of Bordeaux and UMR EPOC is acknowledged for technical and analytical support. The present study has been funded by the Agence Nationale de la Recherche (ANR project VITIBIRD ANR-20-CE34-0008 to F. Angelier), the Région Nouvelle-Aquitaine (MULTISTRESS project to O. Chastel), the Agence nationale de sécurité sanitaire de l'alimentation, de l'environnement et du travail (ANSES project BiodiTox #2019/1/031 to F. Brischoux), the Centre National de la Recherche Scientifique, and MITI-PEPSAN (mission for transversal and interdisciplinary initiatives to C.

Fritsch).

Conflict of Interest

The


Hossein Mohammadi

Rodolphe Le Riche

Eric Touboul

Making EGO and CMA-ES complementary for global optimization

Keywords: Black-box global optimization, CMA-ES, EGO, Optimization of expensive functions

The global optimization of expensive-to-calculate continuous functions is of great practical importance in engineering. Among the proposed algorithms for solving such problems, Efficient Global Optimization (EGO) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are regarded as two state-of-the-art unconstrained continuous optimization algorithms. Their underlying principles and their performances are different, yet complementary: EGO fills the design space in an order controlled by a conditional Gaussian process while CMA-ES learns and samples multi-normal laws in the space of design variables. In this paper, a new algorithm, called EGO-CMA, is proposed which combines the EGO and the CMA-ES algorithms. In EGO-CMA, the EGO search is interrupted early and followed by a CMA-ES search whose starting point, initial step size and covariance matrix are calculated from the already sampled points and the associated conditional Gaussian process. EGO-CMA improves the performance of both EGO and CMA in our 2 to 10 dimensional experiments.

Introduction

Continuous numerical optimization problems are at the core of many applications in science and engineering. It often happens that the underlying function is not only expensive to evaluate but also mathematically multimodal.

One approach to deal with expensive and multimodal optimization problems is to use surrogate models or metamodels. The idea of employing surrogate models for optimization of costly functions, with a focus on Gaussian Processes, has been reviewed in [START_REF] Donald | A taxonomy of global optimization methods based on response surfaces[END_REF]. The deterministic Efficient Global Optimization (EGO) algorithm [START_REF] Jones | Efficient global optimization of expensive black-box functions[END_REF], which relies on a kriging model (i.e., conditional Gaussian Process), has become a standard for continuous global optimization in less than twenty dimensions when the number of function evaluations is inferior to 1000 [START_REF] Roustant | DiceOptim: Two R packages for the analysis of computer experiments by kriging-based metamodeling and optimization[END_REF].

Another popular algorithm in continuous global optimization is the stochastic Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [START_REF] Hansen | Completely derandomized selfadaptation in evolution strategies[END_REF]. CMA-ES is interpreted as a robust local search method in [START_REF] Hansen | Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation[END_REF]. Its robustness is attributed to invariance properties with respect to objective function scaling and coordinate system rotations. This algorithm was consistently found to be highly performing on the Black-Box Optimization Benchmarking (BBOB) framework for low, moderate, and highly multimodal functions for problems dimensions between 5 and 40 [START_REF] Hansen | Comparing results of 31 algorithms from the black-box optimization benchmarking bbob-2009[END_REF] if it is coupled with a restart mechanism. In [START_REF] Auger | A restart cma evolution strategy with increasing population size[END_REF][START_REF] Hansen | Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed[END_REF], restart strategies are proposed to prevent premature convergence of CMA-ES to a local minimum.

Much research on global optimization of costly functions has already involved augmenting Evolution Strategies (ES) with metamodels [START_REF] Yaochu | Surrogate-Assisted Evolutionary Computation: Recent Advances and Future Challenges[END_REF]. The general idea is to replace some evaluations of the true objective function with metamodel estimates and trigger true evaluations through an error rate measure. Let us focus here on the Covariance Matrix Adaptation (CMA) variant of evolution strategies. In [START_REF] Kern | Local metamodels for optimization using evolution strategies[END_REF], CMA-ES has been coupled with a local regression metamodel, making the lmm-CMA algorithm, where the metamodel allows savings in the ranking of the candidate solutions. References [START_REF] Loshchilov | Intensive Surrogate Model Exploitation in Self-adaptive Surrogate-assisted CMA-ES (saACM-ES)[END_REF][START_REF] Loshchilov | Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy[END_REF] present the s* ACM-ES (surrogate Assisted Covariance Matrix adaptation Evolution Strategy), an algorithm with a ranking support vector machine as metamodel and where the number of iterations (generations) done with the metamodel depend on its error rate.

Kriging has sometimes been the metamodel added to the evolution strategies. The motivation for using kriging is the availability of a prediction uncertainty. In the work of [START_REF] Ulmer | Evolution strategies assisted by gaussian processes with improved pre-selection criterion[END_REF], a pre-selection of the most promising points is done based on a kriging model, which enables sampling more solutions and makes the search more efficient. Two criteria are investigated as performance measures, the (mean) objective function prediction and the probability of improvement over the best observed point. Note that this probability of improvement can be defined thanks to the kriging uncertainty. In [START_REF] Bueche | Accelerating evolutionary algorithms with gaussian process fitness function models[END_REF], kriging serves as a local metamodel and various performances are measured by different compromises between search intensification around the current best solution and exploration. In [START_REF] Kruisselbrink | A robust optimization approach using Kriging metamodels for robustness approximation in the CMA-ES[END_REF], a local kriging enables dealing with noisy objective functions by easing the estimation of the objective function expectation.

The optimization algorithm introduced in this paper differs from previous contributions in the fact that the EGO and CMA-ES search principles are invoked one after each other without iterations. The motivation is that EGO is efficient in the early design of experiments stage of the optimization, while CMA-ES is a converging search process.

A brief introduction to EGO and CMA-ES

Efficient Global Optimization (EGO)

EGO algorithm which first proposed in [START_REF] Jones | Efficient global optimization of expensive black-box functions[END_REF] is a method for using conditional Gaussian Processes (GP) to find the unconstrained minimum of a continuous multi-dimensional function. EGO iteratively creates a design of experiments aimed at finding the lower point of a function. At each iteration, one point is added to the existing design points such that a global optimization oriented infill sampling criterion is maximized. There are different types of infill sampling criteria, see [START_REF] Brochu | A tutorial on bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning[END_REF], but the expected improvement (EI) criterion is particularly popular. Because it does not have any arbitrary parameters to tune in order to set a compromise between search intensification and exploration. In the following the mathematical background of this algorithm is given.

Kriging model which is used in the EGO algorithm has been founded on the theory of Gaussian processes. A GP defines a distribution over functions. Formally, a GP indexed by D is a collection of random variables Y (x); x ∈ D ⊆ R d such that for any n ∈ N and any x 1 , ..., x n ∈ D, Y (x 1 ), ..., Y (x n ) follows a multivariate Gaussian distribution. A GP is parameterized by a mean function, µ(.), and a covariance function, or kernel, K(., .) [START_REF] Edward Rasmussen | Gaussian Processes for Machine Learning[END_REF].

The choice of kernel plays a key role in the obtained kriging model. The practice is that a parametric family of kernels is selected (e.g., Matérn, polynomial, exponential) and then the unknown parameters are estimated based on the observed values. For example, a squared exponential kernel is expressed as

cov Y (x i ), Y (x j ) = K Y (x i ), Y (x j ) = σ 2 d k=1 exp - | x i k -x j k | 2 2θ 2 k , (1)
in which σ 2 is a scale parameter known as process variance. The parameter θ k is called characteristic length-scales and determine the correlation length. These parameters are usually estimated by ML or cross-validation. Interested readers are referred to [START_REF] Edward Rasmussen | Gaussian Processes for Machine Learning[END_REF] for more about kernels. Now suppose that kernel K(., .) and its associated centered (µ(.) = 0) GP are given. The matrix of design points X = x 1 , ..., x n denotes the locations where the samples are taken with the response values y = y 1 , ..., y n . To take into account this information, one can extract the posterior distribution of the underlying GP (Y (x)) x∈D . The posterior mean and variance of the conditional GP are given by [START_REF] Edward Rasmussen | Gaussian Processes for Machine Learning[END_REF]:

m(x) = c(x) C -1 y , (2)
v(x) = σ 2 -c(x) C -1 c(x) , (3)
where c(x) = K(x, x 1 ), ..., K(x, x n ) is the vector of covariances between a new point x and the n already observed sample points. The n × n matrix C is a covariance matrix between the data points and its elements are defined as

C i,j = K x i , x j .
A point is expected to improve the objective function if its predicted value is better than the current best point or the uncertainty in its prediction is such that the possibility of producing a better solution is high. Let y min be the minimum sampled value of the true function we have observed yet. The improvement over the current y min can be defied as

I(x) = max{0, y min -Y (x)}. ( 4
)
Then, EI is computed as follows:

EI(x) = (y min -m(x))Φ y min -m(x) s(x) + s(x)φ y min -m(x) s(x) if s(x) > 0 0 if s(x) = 0, (5)
where s(x) = v(x), φ(.) and Φ(.) are the probability density function (pdf) and the cumulative distribution function (cdf) of the standard normal distribution respectively. At each iteration of EGO, the EI criterion is maximized and the optimal solution is added to the current design points. Then, the function value is evaluated at the optimal solution. The new function value is added to y and the parameters of kriging model are re-estimated.

The EI function is highly multimodal. Hence, the optimization is usually performed using stochastic optimization algorithms. For example, in the Scilab KRISP toolbox [need reference], the maximization of the EI is done by CMA-ES algorithm. Using such stochastic algorithms makes EGO stochastic as well. But if the EI maximization is done deterministically, EGO is a deterministic global optimization algorithm, as opposed to CMA-ES.

Covariance Matrix Adaptation Evolution Strategy (CMA-ES)

First introduced by Hansen, Ostermeier, and Gawelczyk [START_REF] Hansen | On the adaptation of arbitrary normal mutation distributions in evolution strategies: The generating set adaptation[END_REF], CMA-ES is considered as the state-of-the-art algorithm for numerical black-box optimization if sufficient budget is afforded. CMA-ES is an iterative stochastic optimization algorithm where at each iteration, a population of search points are generated according to a multivariate normal law. Let m (g) be the mean vector of the multivariate normal distribution in generation g. The ith individual denoted by x (g+1) i is generated through:

x (g+1) i = N m (g) , σ (g) 2 C (g) = m (g) + σ (g) N 0, C (g) , i = 1, ..., λ, (6)
where σ (g) ∈ R + is called mutation step size and C (g) ∈ R d×d is a covariance matrix. The former controls the step length and the later governs the shape of the distribution ellipsoid. It should be noted that the initialized covariance matrix is the identity matrix; C (0) = I. After generating λ individuals, they are evaluated and ranked according to the objective (fitness) function. Then µ best of them are selected. We denote the ith best search point by x i:λ . This selection that is only based on the fitness ranking makes CMA-ES invariant with respect to any monotonous transformation of the objective function. In general, λ and µ are determined as follows:

λ = 4 + 3 ln(d) , (7)
µ = λ 2 . ( 8
)
How to update the mean, the covariance matrix and the step size for the next generation, i.e., m (g+1) , C (g+1) , and σ (g+1) has critical influence on the algorithm performance. The mean of the next generation is obtained from

m (g+1) = µ i=1 ω i x (g+1) i:λ = m (g) + σ (g) µ i=1 ω i y i:λ , (9)
where

y i:λ = x (g+1) i:λ -m (g) σ (g)
and ω i denotes the weight. This update moves the mean vector towards the best solutions. Note that the weights in Equation ( 9) are strictly positive and normalized:

µ i=1 ω i = 1, ω 1 ω 2 ... ω µ > 0, ( 10
)
and their default values can be found in [START_REF] Hansen | The CMA Evolution Strategy: A Tutorial[END_REF].

The update of the step size and the covariance matrix uses the notion of "evolution path". The evolution path contains the correlation between consecutive steps and stores information of the previous updates. We refer to [START_REF] Hansen | Completely derandomized selfadaptation in evolution strategies[END_REF] for more information in this regard. We end up this section by giving a summary of CMA-ES algorithm.

1. Initialize the distribution parameters: m (0) , C (0) , σ (0) . 2. Set parameters λ and µ to their default values.

While stopping criterion not met:

(a) Generate new population sampled from multivariate normal distribution:

x (g+1) i = N m (g) , σ (g) 2 C (g) = m (g) + σ (g) N 0, C (g) , i = 1, ..., λ.
(b) Update the mean value m (g+1) , the step size σ (g+1) and the covariance matrix C (g+1) .

3 Comparing EGO and CMA-ES

(x i ) 2
[-5.12, 5.12]

Ackley f (x) = -a exp -b 1 d d i=1 x 2 i -exp 1 d d i=1 cos (cx i ) [-32.768, 32.768] + a -exp(1), a = 20, b = 0.2, c = 2π Rastrigin f (x) = 10d + d i=1
x 2 i -10 cos(2πx i ) [-5.12, 5.12]

Michalewicz f (x) = - d i=1 sin(x i ) sin 2a ix 2 i π , a = 10 [0, π]
except Michalewicz, are located at (2.5, ..., 2.5) 1×d . The total number of calls to the objective function or budget is 70 × d.

The initial design points of EGO are determined by Latin Hypercube Sample (LHS). The number of these points is three times the problem dimension. We repeat EGO three times on each function defined in R d . However, the number of repetition for CMA-ES is 10 to reduce randomness of the algorithm.

For running EGO and CMA-ES, the R packages DiceOptim and cmaes have been used, respectively. Figure 1 illustrates one run of EGO and CMA-ES on Sphere function in dimension 5. The solid line represents the function value of the points obtained by the optimization algorithm and the dashed-dotted line shows the best observed function value thus far. In the figure, EGO has an early improvement (Figure 1a) while CMA-ES converges to the minimum as the number of calls to the objective function increases (Figure 1b).

The analysis of EGO and CMA-ES

To compare EGO and CMA-ES the median of the best function values obtained by each algorithm is calculated. In addition, we consider three different starting points for CMA-ES. The results of this comparison in dimension 5 are illustrated in Figure 2. For the sake of brevity, the performance of EGO and CMA-ES in dimensions 2 and 10 is not shown here. But the results are close to Figure 2.

The analysis of the figures reveals that EGO algorithm is quick at the beginning and then slow down after some iterations. Moreover, it dos not converge to the global optimum. On the other side, CMA-ES shows a monotone improvement and tends to converge the global minimum if it does not stall in local minima.

To shed more light on the search principles of EGO and CMA-ES a visual example is used here. Figure 3 depicts the search points obtained during the optimization of Ackley function by each algorithm. What is clear from the figure is that EGO is an space-filling algorithm. It tries to find the global minimum by filling the holes in the search space, Figure 3a. However, the search points in CMA-ES algorithm tend to converge the optimum, Figure 3b.

To investigate the characteristics of the two algorithms in higher dimensions, we use a criterion called discrepancy. This criterion measures how far a given distribution of points deviates from a perfectly one [START_REF] Dupuy | DiceDesign and DiceEval: two R packages for design and analysis of computer experiments[END_REF]. Let |S| denotes the number of points in a set S. The discrepancy of the design matrix X is defined by [START_REF] Dalbey | Fast generation of space-filling latin hypercube sample designs[END_REF]:

D(X) = |X ∩ c d | n -V ol c d , (11)
where . represents an appropriate norm over all d dimensional rectangular subsets c d of the unit hypercube [0, 1] d . A small value of D(X) means that the design point X is close to a uniform design.

If EGO and CMA-ES are compared based on the discrepancy criterion, the discrepancy of search points in EGO is less than CMA-ES. The reason is that while EGO tends to fill the search space, CMA-ES tries to converge to the minimum. As an example, the discrepancy of the two algorithm has been calculated on Ackley function in dimensions 5 which is 0.002 for EGO and 0.12 for CMA-ES.

EGO-CMA algorithm

EGO-CMA algorithm makes benefit of both EGO and CMA-ES. The logic which is used in this algorithm is that the search space is first explored by EGO and then CMA-ES is used to converge the optimum. So in the EGO-CMA a switch take place from EGO to CMA-ES. We recall that EGO shows a quick improvement at the beginning but slows down after some budget. One reasonable stopping criterion could be the occurrence of a long plateau, with respect to the total budget, in the diagram of EGO performance. Then the best point obtained by EGO, x best , is selected and CMA-ES starts from this point. In our implementation, EGO stopped if there is no improvement after 0.15 × budget calls to the objective function.

At each iteration of EGO algorithm a kriging model is fitted to the design points. In EGO-CMA we try to make use of the fitted kriging model as an approximation of the true function. In fact, EGO-CMA is started from x best with a "good" covariance matrix and a "good" step size calculated from the points already sampled and the fitted kriging model. What is a "good" covariance matrix and step size is discussed below.

Assume that we are given a convex-quadratic objective function f

H (x) = 1 2
x Hx, where the Hessian matrix is positive definite. The optimal covariance matrix in Evolution Strategies (ESs) is a covariance matrix whose lines of the equiprobable mutation steps are aligned with the level sets of the objective function [START_REF] Rudolph | On correlated mutations in evolution strategies[END_REF]. And this is the case when the covariance matrix of a search distribution is proportional to the inverse of H.

The Hessian matrix H can be decomposed into:

H = BD 2 B , (12)
where B is an orthogonal matrix, B B = BB = I. Columns of B are orthonormal basis of eigenvectors. D is a diagonal matrix with square roots of eigenvalues of H as diagonal elements. Substituting the Hessian matrix by BD 2 B and defining variable t as t = DB x, the objective function becomes f H (t) = 1 2 t t. According to Equation ( 6), any search point has normal distribution. In the space of variable t, search points have the following normal distribution

t (g+1) i = DB N m (g) , σ 2 C (g) = (13)
DB m (g) + σ (g) N 0, DB C (g) BD , i = 1, ..., λ .

The covariance matrix of the above distribution is the identity matrix times the step size σ (g) if and only if C (g) = BD -2 B which is the inverse of H. In other words, when the covariance matrix is proportional to the inverse of Hessian matrix, CMA-ES can be seen as locally optimizing a Spherical function.

In CMA-ES, the parameter step size σ aims at achieving fast convergence to the global optimum. If R = x * -m (g) denotes the distance between the global minimum x * and the mean vector m (g) , then the most expected value of σ achieving this goal can be calculated from

x (g+1) i -m (g) = σ (g) N 0, C (g) ⇒ σ * (g) = R N 0, C (g) . ( 14
)
The initial mean vector and covariance matrix of CMA-ES in the EGO-CMA algorithm are m (0) = x best and C 0 = H -1 . To ease the calculation of σ * (g) in Equation ( 14), we prefer to work in the space of the variable t. In this space, the initial mean vector is DB x best and the distance R is equivalent to R = DB (x * -x best ) . Moreover, the random variable

t (g+1) i -DB x best σ (g) has standard normal distribution. Since N (0, I) ∼ N √ d -0.5, 0.5 , (15)
a "good" initial step size is the one that fulfills

σ * (0) = R √ d -0.5 . ( 16
)
To obtain σ * (0) we need to calculate the distance R. We propose a creative approach to approximate R using Taylor expansion. The second order Taylor expansion of the objective function at point x best is:

f (x) f (x best ) + f (x best ) (x -x best ) + 1 2 (x -x best )H(x best )(x -x best ).( 17
)
Minimization of Equation ( 17) gives an approximation of x * by which we can calculate R as follows:

R = x * -x best = -H -1 (x best ) f (x best ) . (18)
If the last kriging model used for approximating true function is not convex, the Hessian matrix is not positive semidefinite. When it happens, we force the Hessian matrix to be positive semidefinite. Considering the eigenvalue decomposition in [START_REF] Yaochu | Surrogate-Assisted Evolutionary Computation: Recent Advances and Future Challenges[END_REF], we substitute the negative eigenvalues by 10 -6 . However, this might increase the condition number of the Hessian matrix which is the ratio of the largest to the smallest eigenvalue. To improve the condition number, we add a positive value, δ, to the elements on the main diagonal of the Hessian matrix. δ which increases increases all the eigenvalues by δ can be calculated from

δ = CLλ min -λ max 1 -CL , (19)
where CL stands for condition number limit and λ min and λ max indicate the smallest and largest eigenvalue of the Hessian matrix. Based on our experiments we suggest to set the condition number limit CL equal to 10 3 . To sum up, a summary of EGO-CMA algorithm is provided below.

1. Start an EGO with the initial design of experiments determined by LHS.

2. When there is no further improvement after 0.15 × budget objective function evaluations, stop EGO.

3. Select the point with the smallest function value and set it as x best .

4. Compute the Hessian matrix H at x best using the last kriging model of the EGO algorithm.

5. Set m (0) = x best , C (0) = H -1 and compute σ * (0) from ( 16).

6. Start CMA-ES with the default values in the previous step. Stop when the budget is exhausted.

Simulation Results

The performance of EGO-CMA is tested here with the default parameter setting explained in Section 4. Each run of EGO-CMA is repeated 5 times on each function and then the results are compared with EGO and CMA-ES. We again recall that each curve is the median of the repetitions. Also, we only consider the CMA-ES with the starting point that leads to superior performance. The results of this comparison in dimension 5 and 10 are illustrated in Figures 4 and5, respectively. The results show that EGO-CMA outperforms CMA-ES in all functions and also EGO except the Rastrigin function in dimension 5. In this case, EGO-CMA switches to CMA-ES before EGO detects the global minimum location. Note that when budget is greater than 250, EGO improves the objective function value.

In the case of the Sphere function, EGO can roughly detect the location of global minimum quickly which allows EGO-CMA to further increase the accuracy. The accuracy of EGO-CMA is about 10 -8 and 10 -5 for the Sphere function in dimension 5 and 10, respectively.

Conclusions

This paper presents a new algorithm, called EGO-CMA, for unconstrained continuous black-box optimization. EGO-CMA combines the strengths of EGO and CMA-ES: while EGO is a space-filling strategy, CMA-ES is a robust local search.

In the proposed algorithm, search space is first explored by EGO and then a switch to CMA-ES take place. CMA-ES is started from the point with the smallest function value obtained by EGO. Moreover, the initial covariance matrix and the step size of CMA-ES are calculated from the design points already sampled and the kriging model of the EGO algorithm. Therefore, The cooperation between the two algorithms goes beyond a plain succession as the Gaussian process learned by EGO allows improving the initialization of key parameters of CMA-ES. The results of our 2 to 10 dimensional experiments show that EGO-CMA outperforms EGO and CMA-ES for the same budget.

Figure 1 :

 1 Figure 1: The performance of EGO and CMA-ES on the Sphere function in dimension 5. The x-axis is the number of calls to the objective function and the y-axis is the logarithmic value of the function. The solid line shows the history of the function values observed during optimization and the dash-dotted line represents the best ever observed function value.

Figure 2 :

 2 Figure 2: The performance of EGO and CMA-ES on four test functions in dimension 5.

Figure 3 :

 3 Figure 3: A 2D illustration of the difference between EGO (3a) and CMA-ES (3b). The test function is Ackley. The bullets are the points generated by the optimization algorithms. The diamonds in the leftmost picture are the initial DoE for EGO. The asterisk in the rightmost picture shows the starting point of CMA-ES.

Figure 4 :

 4 Figure 4: The comparison of EGO, CMA-ES and EGO-CMA on four test functions in dimension 5.

Figure 5 :

 5 Figure 5: The comparison of EGO, CMA-ES and EGO-CMA on four test functions in dimension 10.

Table 1 :

 1 We have employed four analytical test functions: Sphere, Ackley, Rastrigin, and Michalewicz. These functions are defined in Table1. The Sphere function is unimodel, separable and differentiable. This function is used to observe the pure convergence speed of the algorithms. The Ackley function has many local minima with a large hole at the center which is the location of the global minimum. The Rastrigin function is highly multimodal, but locations of the minima are regularly distributed. The Michalewicz function is a multimodal function with d! local minima. The parameter a exists in the Michalewicz function defines the steepness of the valleys and ridges; a larger a leads to a more difficult search.The search space of the functions have been rescaled to [-5, 5] d . d = 2, 5, 10 is the search space dimensionalities. The global optimum of the functions, Test functions

	Name	Function

3.1 Test functions and experimental setup

Acknowledgement

The authors would like to acknowledge support by the French national research agency (ANR) within the Modèles Numérique project "NumBBO-Analysis, Improvement and Evaluation of Numerical Blackbox Optimizers".