Floriane Larrasa
email: floriane.larras@inrae.fr

Sandrine Charlesa
email: sandrine.charles@univ-lyonl.fr

Arnaud Chaumota
email: arnaud.chaumot@inrae.fr

Céline Pelosia
email: celine.pelosi@inrae.fr

Morgane Le Gall5
email: morgane.le.gall@ifremer.fr

Laure Mamy6l
email: laure.mamy@inrae.fr

Rémy Beaudouin'
email: remy.beaudouin@ineris.fr

Moa Mosaics

Sam Sd

A critical review of effect modelling for ecological risk assessment of plant protection products

Keywords: Ecotoxicological m odels, ecological m odels, risk assessm ent, environm ent, ecotoxicity, m ulti-stressors, E

A wide diversity of plant protection products (PPP) is used for crop protection leading to the contamination of soil, water, and air, which can hâve ecotoxicological impacts on living organisms. It is inconceivable to study the effects of each compound on each species from each compartment, experimental studies being time consuming and cost prohibitive, and animal testing having to be avoided. Therefore, numerous models are developed to assess PPP ecotoxicological effects. Our objective was to provide an overview of the modelling approaches enabling the assessment of PPP effects (inc.luding biopesticides) on the biota. Six categories of models were inventoried: QSAR, DR and TKTD, population, multi-species, landscape, and mixture models. They were developed for various species (terrestrial and aquatic vertebrates and invertebrates, primary producers, micro-organisms) belonging to diverse environmental compartments, and address different goals (e.g., species sensitivity or PPP bioaccumulation assessment, ecosystem ser vices protection). Among them, mechanistic models are increasingly recognized by EFSA for P P P regulatory risk assessment but, to date, remain not considered in notified guidance documents. The strengths and limits of the reviewed models are discussed together with improvement avenues (multi-generational effects, multiple biotic and abiotic stressors. ..). This review also underlines a lack of model testing by rneans of fleld data and of sensitivity and uncertainty analyses. Accurate and robust modelling of PPP effects and other stressors on living organisms, from their application in the ffeld to their functional consé quences on the ecosystems at different scales of time and space, would help going towards a more sustainable management of the environment.

The European Plant Protection Product (PPP) Régulation (EC) No 1107/2009 (European Commission, 2009) requires the PPP ecotoxicological properties (among others) to be fully characterized before to be placed on the market. Active substances should only be included in PPP where it has been demonstrated that they are not expected to hâve any harmful effect on human or animal health or any unacceptable effects on the environment (European Commission, 2009). Breakdown products (from environmental dégradation or metabolic transformations) of substances hâve also to be identihed and evaluated [START_REF] Casalegno | Top-priority fragment QSAR approach in predicting pesticide aquatic toxicity[END_REF]European Commission, 2009). Considering the total number of PPP and the number of related breakdown products, such task is susceptible to lead to many ecotoxicological tests though animal testing has to be avoided. Thus, modelling approaches constitute an interesting support.

Models aim at delivering insights and possible solutions to real-world problems, but also at supporting regulators for risk assessment. Regarding PPP, they (i) allow the dérivation of critical effect concentrations and envi ronmental protective thresholds from animal and plant testing; (ii) could help to hll in data gap and thus save time, money, and reduce the number of animais used for experimental testing purposes [START_REF] Basant | Modeling the toxicity of Chemical pesticides in multiple test species using local and global qstr approaches[END_REF][START_REF] Casalegno | Top-priority fragment QSAR approach in predicting pesticide aquatic toxicity[END_REF]); (iii) improve mechanistic understanding. For régulation, decision makers hâve to select the most appropriate models for the problem at hand (extrapolation from experimental data, extrapolation to other species, higher level of biological organization, other environmental conditions...), and to get evidence that a model works, having démonstration that it is realistic while based on reliable data inputs and key assumptions. Consequently, there is a crucial need for a clear communication of models and of their context [START_REF] Grimm | Three Ques tions To Ask Before Using Model Outputs For Decision Support[END_REF]. To fulhll that need, EFS A has published several rec ommendations to support the development of models compatible with PPP régulation [START_REF] Efsa Ppr Panel | Scientihc Opinion On Good Modelling Practice In The Context Of Mechanistic Effect Models For Risk Assessment Of Plant Protection Products[END_REF].

In this context, the objective of this work was to review effect modelling approaches enabling ecological risk assessment of PPP (including biopesti cides) for organisms, biodiversity and ecosystem functions/services. The review starts with the présentation of the bibliometric methodology that led to the définition of the bibliographie corpus, and with the analysis of this corpus (Section 3). Then, the whole reviewed models, which belong to six main model categories (QSAR, DR and TKTD, population, multi-species, landscape, and mixture models) are presented (Section 4). In particular, sub-section 4.1 gives full details on each type of model including the main (standard or not) outputs they provide, while sub-section 4.2 further explains what are the main model usages. Section 5 points out the strengths and limits of the different model cat egories, including genericity and transversality, uncertainty quantification and reproducibility. In parallel with the corpus analysis, the Section 6 explores the recommendations in terms of usage of modelling approaches in the context of the European PPP régulation. Potential contributions and prospects of current and future modelling tools to Environmental Risk Assessment (ERA) are discussed (Section 7). ERA of PPP assesses the impact that the use of PPP has on non-target organisms, and on soil, water, and air (European Commis sion, 2009). ERA can be do ne as a prospective assessment for registration of substances before products enter the market, or as a rétrospective assessment for potentially harmful substances that are already in use [START_REF] Forbes | Species Sensitivity Distributions Revisited: A Critical Appraisal[END_REF]. Finally, the review ends with some perspectives to be considered to improve ecological risk assessment (ERA) to preserve biodiversity.

B ib liograp h ie corpus

Six main model categories were a priori dehned to structure the biblio graphie query: QSAR, DR and TKTD, population, multi-species, landscape, and mixture models (see Section 4):

• (Q )SA R category refers to the mathematical models to predict the ecotoxicity of compounds via statistical corrélation of molecular descriptors with the biological activity of interest.

• D ose-R esponse (D R ) and ToxicoK inetics-ToxicoD ynam ic (TK TD ) category refers to static dose-response models (DR) and dynamic TK and TKTD models. • Population category refers to the population dynamic models, including ail degree of detail and disaggregation (stock, matrix, life cycle, individualbased models...). • M ulti-species category refers to the models considering several species, namely species sensitivity distribution (SSD) and food-chain models assuming they include both food-web models (with only trophic relationships) and community models (also considering other kinds of inter-species interac tions). In case, food-chain models account for the dynamics of abiotic factors they can also be classihed as "ecosystem models". • Landscape category refers to the models considering the landscape struc ture (e.g., spatial and temporal variability) to predict the exposure of organisms to a Chemical compound, the associated toxicity or the population effects in non-target species.

• The category of m ixtures refers to the models used to analyse the interac tion of several Chemicals; these models can also be used to assess the effects of combined stressors (e.g. PPP and ecological factors).

M e th o d o lo g y

Scientihc articles and international proceedings screening was conducted with the Web of Science (WoS), the world's leading scientihc citation search and analytical information platform (Clarivate Web of Science © Copyright Clarivate 2020). The final paper collection from WoS was achieved in December 2020, then manually completed over time until April 2021 from complementary bibliographie databases, such as PubMed [START_REF] Mcentyre | The ncbi handbook[END_REF], Google Scholar [START_REF] Lopez-Cozar | Google scholar as a data source for research assessment[END_REF], Scopus [START_REF] Baas | Scopus as a curated, high-quality bibliometric data source for academie research in quantitative science studies[END_REF], publi cations within authors' own databases, even grey literature (e.g., regulatory documents). This paper collection covers the period 2000-2020 chosen as contiguous with the existence of the WoS itself.

On a general point of view, the bibliographie query was performed according to the following steps:

• Définition of a hrst query over the limited period 2018-2020 (see Section 3.2).

• First analysis on the basis of titles and abstracts of papers to identify points of improvement of the query. • Update of the query by adding and removing some terms.

• Running the final query over the period 2000-2017, over 2018-2020 again, and combination of both periods. • Final analysis of the results with Orbit Intellixir bibliometric software (Copyright © Questel 2021, ail rights reserved).

Besides the query terms, we limited our paper collection to only include research and review papers written in English, as well as scientihc articles published in peer-reviewed journals. The paper collection, any reference being duplicated, was imported into Intellixir and analyzed to quantify, for example, the scientihc production per year, country, organization, and annual évolution of publication rates. Collaboration networks between countries, public insti tutions and/or private companies, as well as the main research concepts, were graphically represented using the most relevant formats available in Intellixir. In particular, papers were analyzed to point out the main trends in research related to the use of models in ERA for PPP, as well as to highlight their strengths and limitations, leading to the identiheation of future key topics for research. Some papers were manually added or removed from the hnal collection before performing the analysis. The Supplementary Information (SI) is avail able at https://doi.org/10.5281/zenodo.5775038 [START_REF] Larras | A critical review of modelling approaches for environmental risk assessment due to pesticides -Supplementary Informa tion[END_REF], where the full list of keywords is provided, as well as both source hles with ail référ encés and their DOI in . csv format: the list of references in the initial corpus, CONTENTS and the list of additional references. Reasons for which some papers were added are the following:

• Some scientific research areas were missing although corresponding keywords were in the final query, such as sensitivity analysis, uncertainty, calibration, validation and prédiction. So, some papers were added accordingly. • Very recently published papers, not published yet (such as papers in bioRxiv for example), were also added by hand. • Some general methodological references were clearly missing as they do not specihcally concerned PPP. • Ail references focused on human health risk assessment were removed as we exclusively focused on ERA.

D e ta ils on th e b ib liograp h ie qu ery

The bibliographie query was composed of seven items, each of them encompassed within three global items and associated with a sub-query ( Running the first bibliographie query over the limited period 2018-2020 led to 380 references. This short list was quickly analysed from titles and abstracts to improve the different items and their associated sub-queries. Of these 380 references, only 130 were kept (35%).

The updated sub-queries we obtained were run over the period 2000-2017, then again on the period 2018-2020. The combination of both hnally provided the final paper collection we in-depth analysed. This collection was composed of a total of 1259 papers. From this total, relevant papers for the review were checked one-by-one hnally leading to a paper collection of 376 references (~ 30%) that were analysed by Intellixir.

S im p le b ib lio m e tr ic m ea su rem en ts

As fîrst results, we provide here simple bibliometric measurements giving a factual description of the paper collection (n = 376).

The time course of the selected référencés (Figure 1) clearly shows an increase in work integrating modelling tools over the last twenty years, together with a strong inequality between contributing countries. The countries with the highest number of contributions in our bibliographie corpus could be explained by the nationality of the main producing and R&D companies [START_REF] Basic | Pesticides: a model th at's costing us dearly[END_REF], which are in the main contributing institutions (see below), and/or by the leading countries in natural sciences research (Nature Index, 2020). Looking at the main research topics, that is words found in titles and abstracts, as automatically extracted by Intellixir, makes emerge the main keywords. The three main keywords are Model (in 98.5% of the papers), P estic id e (69.0%), and Exposure(66.4%). Aquatic (31.3%) is the first living environment found (10tft position) and the first PPP usages found are In se c tic id e (24.8%) and Herbicide(19.6%).

Figure 2 below describes the main collaborations between host institutions of ail co-authors who contributed to each paper. These main collaborations are dehned as at least one reference authored by each institution plus at least four co-publications between institution pairs. The ten main contributing institutions (accounting for multiple affiliations) represent 42% of the total contributing ones, among which the top-hve is composée! of SYNGENTA JEALOTTS GROUP (6.8%), UNIV WAGENINGEN IMARES (NL, 6.6%), BAYER (DE, 3.9%) and CNRS (FR, 3.9%). Ail affiliations of the first authors hâve been taken into account, and for example, ALTERRA WAGENINGEN and UNIV WAGENINGEN IMARES are used for a same author in 90% of the articles. N tbHfl î > K A

.4 A d van ced b ib lio m etric m ea su rem en ts

In order to refine the previous bibliometric description, we went further into the analysis of the main concepts appearing within the paper collection. Figure 3 shows ail words appearing at least 35 finies within the référencés. We notice that some words form well identihed groups, four in total, distinguished by different colors and corresponding to the semantic proximity of words. The Model group is strongly related to the P estic id e group of words, while relationships with more general ternis, such as Environment r is k assessment (left side of Figure 3), are tinier. Nevertheless, single word Risk and pair Risk assessment are within the big P estic id e group, the Risk word appearing almost at the same frequency than the P estic id e word (267 versus 223 occur rences). It is particularly interesting to note that the Regulatory word belong to the Model group. Corning back to the time course of the référencés, and refhhng the anal ysis by model types, leads to Figure 4. To this aim, ail the models used in each paper was noted, and thus, a same article could be counted in different model categories. It is worth noting that models diversify over time, with an increase in the use of TKTD models, especially since 2018, the year at which the Scientihc Opinion on the state-of-the-art of TKTD models was published by EFSA (EFSA PPR Panel, 2018a). We also notice that mixture models are widely used ail along the period 2000-2020 with a regular increase for almost 15 years. Regarding (Q)SAR models, if used a few in the past, there is an upsurge in PPP référencés involving these models since 2017. The bibliometric évolution of the use of population models within our corpus focused on PPP literature is interesting to analyse further, as it can be compared to the gen eral évolution of population modelling practices in applied ecology. We used as a référencé the review of [START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF], who gathered a corpus of 450 population models used for risk assessment in ecology, including conser vation science studies. The rate of publication related to the use of population models for PPP ERA lias experienced a strong growth since 2010 (1.5 arti cles per year over the period 2000-2010, 4 per year over 2011-2015 and 9 per year over 2016-2020). This dynamic is spécifie to the held of PPP ERA, as we do not observe the same inflation in the corpus of [START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF]: 50% increase in the rate of publications in 2011-2014 compared to 2004-2010, while PPP studies exerted a 100% increase on the similar periods. We can also note a recent amplification of population modelling applications to PPP impacts in pollinators, 30% of the population studies since 2017, against 10% before this date in our corpus. The dynamics recorded from 2010 onwards cor rélâtes with the structuring of a community of European and North American researchers, both academie and industrial, on ecological modeling for regulatory Chemical risk assessments (LEMTOX workshop 2007[START_REF] Forbes | Ecological models in support of regulatory risk assessments of pesticides: developing a strategy for the future[END_REF], TJS-EPA Risk Assessment Forum Technical Workshop on Population-Level ERA 2008, Roskilde Workshop on Integrating Population Modeling into ERA 2009, MODELINK workshop 2012-2013, 7th Framework European Program CREAM 2009-2013, SETAC interest group on Effect Modeling). For instance, the European CREAM project (https://cream-itn.eu/) was responsible for a strong increase in papers on TKTD and population models in PPP effect modelling in this period. The agrochemical industry has invested heavily in this dynamics, signing nearly 40% of the publications on PPP population models since 2011, whereas before this date it was practically absent from the authorship (less than 10%). This rising interest of PPP ERA community in population models is explained by the fact that the protection goal in revised PPP regis tration procedures for most species is either the population or the community [START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF][START_REF] Dohmen | Population-level effects and recovery of aquatic invertebrates after multiple applications of an insecticide[END_REF]EFSA Scientihc Committee, 2016). Moreover, the use of higher Tier risk assessment, which aims at inte grating fine ecological realism, allows overcoming the conservatism inhérent in risk assessment based on the application of safety factors to lower Tier assess ment outputs [START_REF] Maund | Probabilistic risk assessment of cotton pyrethroids: V. combining landscape-level exposures and ecotoxicological effects data to characterize risks[END_REF][START_REF] Dalkvist | Population-level impacts of pesticide-induced chronic effects on individuals dépend more on ecology than toxicology[END_REF][START_REF] Brain | Risk assessment considérations with regard to the potential impacts of pesticides on endangered species[END_REF]. In this context, population and landscape models are mobilized particularly to assess (i) the relative importance of PPP toxic stress compared with natural stochastic fluctuations [START_REF] Topping | Modeling the influence of temporal and spatial factors on the assessment of impacts of pesticides on skylarks[END_REF], (ii) the influence of biological and environmental factors conditioning population state and sensitivity to PPP [START_REF] Dalkvist | Population-level impacts of pesticide-induced chronic effects on individuals dépend more on ecology than toxicology[END_REF][START_REF] Forbes | Assessing pesticide risks to threatened and endangered species using population models: Findings and recommendations from a croplife america science forum[END_REF][START_REF] Thorbek | Using Beehave to explore pesticide protection goals for European honeybee (Apis melifera L.) worker losses at different forage qualifies[END_REF][START_REF] Schmolke | Honey bee colony-level exposure and effects in realistic landscapes: An application of beehave sim ulating clothianidin residues in corn pollen[END_REF][START_REF] Abi-Akar | Simulating honey bee large-scale colony feeding studies using the beehave model-part ii: analysis of overwintering outcomes[END_REF], especially possible compensatory effects due to the interplay between PPP démographie effects and the natural density control of populations [START_REF] Wang | Population models in pesticide risk assessment: Lessons for assessing population-level effects, recovery, and alternative exposure scénarios from modeling a small mammal[END_REF][START_REF] Mintram | Assessing population impacts of toxicant-induced disruption of breeding behaviours using an individual-based model for the three-spined stickleback[END_REF], (iii) the ability to recovery related to démographie resumption after short term exposure or recolonization processes from refuge areas that could make PPP impacts ecologically acceptable at larger time or spatial scales [START_REF] Galic | Simulating population recovery of an aquatic isopod: Effects of timing of stress and landscape structure[END_REF][START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF]Focks et al., 2014;[START_REF] Dohmen | Population-level effects and recovery of aquatic invertebrates after multiple applications of an insecticide[END_REF]. We crossed the analysis of categories of biological group with the model types (Figure 5). Articles were classified following t.hese different groups of taxa: micro-organisms (e.g. single spccics bactcria from water or soil media), aquatic microbial connnunities (e.g. biofilm), aquatic primary producers (microalgae and macrophytes), aquatic invertebrates, various aquatic groups (studies gathering more tlian one aquatic biological group, such as food-web studies), teleost fish, airiphibians. reptiles, terrestrial invertebrates (including bees), terrestrial primary producers, marmiials and birds. A large majority of papers conccrncd aquatic invertebrates (29.5%), ail categories of models having been employed. At the second and third positions, with close number of occurrences, are terrestrial invertebrates (17.3%) and fish (13.3%). In addition to the previous cross-analysis on biological group categories, Figure 6 provides an overview of the level of biological organization at which the models were built, sub-divided by the type of living environment where the studied species in the papers referred to. As expected, almost half of the papers deal with the individual level (19.5%), followed by a quarter of the papers at the population level (25.8%). Community level models are less numerous (11.2%). A rather important part of the papers (10.9%)) do not refer to a spécifie level of biological organization. Several reasons may explain this fact: for example no model was employed; landscape or ecosystem was concerned as a whole (so that. several levels may be concerned); or several levels were concerned without one more important than the others (so that they could not be classified into one spécifie category). Combining this information with the living environment of the studied organisms provides information rather redundant with those extracted from Figure 5. Indeed, whatever the model category or almost, freshwater species hâve been the most studied, then the terrestrial ones. equivalently followed by t.he other types of species living envi ronment. Saltwater species arc less represented bccausc saltwater coesystems are not considered in the European régulation. Based on our literature review, we identified six categories of models that fulfill ail or a part of the above requirements. They are described below.

(Q )SA R m odels

The knowledge about systematic relationships between the structure and activities of the Chemicals dates back to the prime infancy of the modem pharmacology and toxicology [START_REF] Devillers | A general QSAR model for predicting the acute toxicity of pesticides to Lepomis macrochirus[END_REF]. Since the pioneering work of Corwin Hansch in the 60's, the development and utilisation of structure-activity rela tionships hâve become increasingly more important over the past years for industrial and regulatory applications [START_REF] Mombelli | The computational prédiction of toxicological effects in regulatory contexts: current use and future potential of (q) sar tools[END_REF]. In particular, a large number of models hâve been developed recently for the PPP: 38 papers from 2000 and 2020, including 28 on the last flve years, in our bibliographie corpus. Currcnf structure -activity relationship usage in PPP safety assessment can be divided into rule based expert Systems ;SAR models) and statistical Systems ('Q)SAR models). The notation (Q)SAR includes both types of models.

Expert Systems (SAR) use rule-based methods to qualitatively predict spé cifie endpoints by matching identified molecular (sub) structures or fragments of the compound to similar structures (known as structural alcrts) with known adverse effect s (e.ff., liver toxicity. skin irritation, mutagenicity) [START_REF] Herrmann | Q)Sar tools for the prédiction of mutagenic properties: Are they ready for application in pesticide régulation?[END_REF].

Statistical Systems ((Q)SAR Systems) use mathematical models to predict the toxicity of compounds via statistical corrélation of molecular descriptors with the biological activity of interest. (Q)SAR model is composed by t.hree CONTENTS éléments: (i) data on the biological properties to be predicted, (ii) data on molecular descriptors which translate Chemical structures into numbers, and (iii) a modelling algorithm that is able to identify the relationship between molecular descriptors and biological activity. The basic assumption of these models is that similar Chemicals (biological, Chemical, and/or physical prop erties) induce similar effects (from a qualitative and quantitative point of view) in living beings [START_REF] Lo Piparo | Qsar models for daphnia magna toxicity prédiction of benzoxazinone allelochemicals and their transformation products[END_REF]. Some authors had therefore proposed spécifie sub-names for (Q)SAR models to stress these différences, e.g., Quantitative Structure -Property Relationship (QSPR) models [START_REF] Basant | Modeling the toxicity of Chemical pesticides in multiple test species using local and global qstr approaches[END_REF], Quantitative Structure -Toxicity Relationship (QSTR) models [START_REF] Lo Piparo | Qsar models for daphnia magna toxicity prédiction of benzoxazinone allelochemicals and their transformation products[END_REF], Quantitative Activity -Activity Relationship (QAAR) models [START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF] or Quantitative Structure -Activity -Activity Relationship (QSAAR) models [START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF].

(Q)SAR models could also be classihed according to a trade-off between their accuracy and genericity. Depending on the intended purpose and on the underlying data set of the model, (Q)SAR models are used to predict the properties of con-generic compounds (local (Q)SAR) or of more diverse compounds (global (Q)SAR) [START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF][START_REF] Herrmann | Q)Sar tools for the prédiction of mutagenic properties: Are they ready for application in pesticide régulation?[END_REF][START_REF] Jia | Norm Index-Based QSAR Model for Acute Toxicity of Pesticides Toward Rainbow Trout[END_REF]. These authors proposed that depending on the respective requirements of sensitivity (correct positive) and specihcity (correct négative), appropriate models (global/local), accounting for the Chemical space of query structures, hâve to be selected. Basant et al. (2015a) proposed a figure clearly describing the (Q)SAR mod elling procedure (Figure 7). This procedure follows the OECD principles for (Q)SAR models (OECD, 2014). These hve principles were proposed to facilitate the considération of a (Q)SAR model for regulatory purposes (explained in Mombelli and Ringeissen 2009):

1. a dehned endpoint. 2. an unambiguous algorithm. 3. a dehned domain of applicability (AD). 4. appropriate measures of goodness-of-ht, robustness and predictivity. 5. a mechanistic interprétation, if possible.

The computation of internai and external validation metrics (on the species included in the training set or on other species) and the définition of the domain of applicability appear as important steps, as proposed by the OECD principles. The domain of applicability is dehned as "the physico-chemical, structural, or biological space, knowledge or information on which the training set of the model has been developed, and for which it is applicable to make prédictions for new compounds [...]. Ideally, the (Q)SAR should only be used to make prédictions within that domain by interpolation not extrapolation" [START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF][START_REF] Eriksson | Methods for reliability and uncertainty assessment and for applicability évaluations of classihcation-and regression-based qsars[END_REF]. It is important to note that the Figure 7 does not explicitly include the "data curation" step (included in OECD principle 1, "a dehned endpoint") described as essential by other authors: data curation contribut.es to define unambiguously an endpoint. {e.g., identical exposure t.ime for SCso) [START_REF] Khan | QSAR modeling of Daphnia magna and hsh toxicities of biocides using 2d descriptors[END_REF][START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF]. Indccd, the (Q)SAR modcls can only bc as rcliable as the experimental data that are used for their calibration, and therefore, the standardisation procedures to obtain each data and to curatc the data set of compounds should be considered with care [START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF].

As reported by [START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF], there are several easily accessible databases that can be used to develop (Q)SAR rnodels (e.g., ACToR, Bind-ingDB, CCRIS...). In the bibliographie corpus analysed, other databases were frequently used to develop (Q)SAR: EISA's Chemical hazards database "Open-FoodTox", US-EPA ECOTOXicology knowledge-base (ECOTOX), Pesticide Properties DataBase (PPDB), OECD (Q)SAR toolbox, Office of Pesticide Programs (OPP), Pesticides Ecotoxicity Database (produced by the Interna tional Center for Pesticides and Health Risk Prévention), AMBI'I' (developed by Cefic-LRI, current version 2.0 at https://apps.ideaconsult.net/data/ui), and BBA (Biologische Bundesanstalt, -Fédéral Biological Research Center for Agriculture and Forestry).

Nevert.heless, ideallv, databases for model calibration should be developed in a single laboratory and by means of a single protocol to enhance the signal to noise ratio. However, these conditions are not met in most of the (Q)SAR models that are developed today, and much less in t.hose developed from databases in which the information is deposited by numerous contributors [START_REF] Khan | QSAR modeling of Daphnia magna and hsh toxicities of biocides using 2d descriptors[END_REF][START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF]. Consequently, (Q)SAR modellers should always subject to curation the systematic and random errors présent in ail databases by spécial and well-established protocols and tools [START_REF] Khan | QSAR modeling of Daphnia magna and hsh toxicities of biocides using 2d descriptors[END_REF][START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF].

A large diversity of Chemical descriptors (experimental measurements or theoretical molecular descriptors) is used to develop (Q)SAR models spécifie to the PPP. The most common descriptor is the octanol-water partition coef ficient Kow [START_REF] Devillers | A general QSAR model for predicting the acute toxicity of pesticides to Lepomis macrochirus[END_REF]. However, the rapidly falling price of computing power has stimulated the use of more sophisticated statistical methods for increasing the domain of application of the (Q)SAR models [START_REF] Devillers | A general QSAR model for predicting the acute toxicity of pesticides to Lepomis macrochirus[END_REF]. Hence, the spatial dimension of the Chemical descriptors (one, two, three or four dimensions) hâve been used to distinguish different (Q)SAR models on the descriptor basis. In the literature, over 6000 descriptors hâve been proposed and the number is still growing [START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF]. Considering the large number of calculated descriptors, it was necessary to use approaches of variable réduction, which consists in the sélection of a subset of variables able to preserve the essential information contained in the whole data set but eliminating redundancy [START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF][START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF]. Hence, severe sélection steps using a range of methods were applied to reduce the number of descriptors. Classically, ail highly correlated descriptors (pairwise corrélation coefficient above 0.9) and those with low variance (s2 < 0.3) or the semi-constant descriptors (more than 80% of the data with the same value) were excluded [START_REF] Venko | Classification models for identifying substances exhibiting acute contact toxicity in honeybees (Apis mellifera)[END_REF]Yang et al., 2020). To this goal, after centring and scaling the descriptors, [START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF] used the following methods: Decision Trees (DT), k-nearest neighbours (k-NN), Multiple Linear Régression (MLR), Partial Least Squares (PLS) régression (based on Genetic algorithm), and Random Forest (RF). Additionally, the Norm index concept was proposed by [START_REF] Jia | Norm Index-Based QSAR Model for Acute Toxicity of Pesticides Toward Rainbow Trout[END_REF], and a sériés of normed descriptors based on molecular structure were dehned and used to develop (Q)SAR mod els with satisfactory prédiction results for the aquatic acute toxicity of various PPP [START_REF] Jia | Qsar model for predicting the toxicity of organic compounds to fathead minnow[END_REF][START_REF] Jia | Norm Index-Based QSAR Model for Acute Toxicity of Pesticides Toward Rainbow Trout[END_REF]. (Q)SAR models for PPP could also be based on descriptors computed by other in silico methods, using a combination of hngerprint, structure-based pharmacophore approaches, homology modelling, molecular-docking and molecular dynamics simulation [START_REF] Chaudhuri | Exposure to spectracide@ causes behavioral déficits in drosophila melanogaster: Insights from locomotor analysis and molecular modeling[END_REF][START_REF] Marimuthu | In silico approaches to evaluate the molecular properties of organophosphate compounds to inhibit acetylcholinesterase activity in housefly[END_REF].

Globally, and in the PPP bibliographie corpus, the most common techniques for establishing (Q)SAR models are based on regression-based approaches, and the methods of MLR [START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF]Yang et al., 2020;Yang et al., 2020) and PLS [START_REF] Jackson | Use of Quan titative Structural Analysis To Predict Fish Bioconcentration Factors for Pesticides[END_REF][START_REF] Khan | QSAR modeling of Daphnia magna and hsh toxicities of biocides using 2d descriptors[END_REF][START_REF] Marimuthu | In silico approaches to evaluate the molecular properties of organophosphate compounds to inhibit acetylcholinesterase activity in housefly[END_REF] are classical approaches to régression problems in (Q)SAR models. In PPP (Q)SAR, genetic algorithms are often used to ht MLR [START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF]Yang et al., 2020;Yang et al., 2020) or PLS models [START_REF] Jackson | Use of Quan titative Structural Analysis To Predict Fish Bioconcentration Factors for Pesticides[END_REF][START_REF] Khan | QSAR modeling of Daphnia magna and hsh toxicities of biocides using 2d descriptors[END_REF]. For these techniques, a postulate is made that only linear relationships exist between the variables involved in the modelling process while it is generally not true [START_REF] Devillers | A general QSAR model for predict ing the acute toxicity of pesticides to Oncorhynchus mykiss[END_REF]. The Artificial Neural Networks (ANN) hâve shown their usefulness for deriving complex structure-activity relationships possibly non-linear [START_REF] Devillers | A general QSAR model for predict ing the acute toxicity of pesticides to Oncorhynchus mykiss[END_REF][START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF]. Several different neural networks were used to develop (Q)SAR models for PPP: Multilayer perceptron (MLP) (Dev illers and Flatin, 2000;[START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF], Counter-propagation ANN [START_REF] Drgan | Robust modelling of acute toxicity towards fathead minnow (pimephales promelas) using counter-propagation artihcial neural networks and genetic algorithm[END_REF][START_REF] Venko | Classification models for identifying substances exhibiting acute contact toxicity in honeybees (Apis mellifera)[END_REF], and GMDH neural networks [START_REF] Lo Piparo | Qsar models for daphnia magna toxicity prédiction of benzoxazinone allelochemicals and their transformation products[END_REF]. Diverse methods of linear classifications were also used in the field of PPP ecotoxicity. [START_REF] Mazzatorta | QSAR in ecotoxicity: An overview of modem classification techniques[END_REF] provided an overview of the classification techniques and conclude that no general rule exists to define the best approach to a spécifie classification problem. Recent research in Machine Learning and Statistics resulted in several efficient approaches to perform a linear or a non-linear classification: Support-Vector Machines (SVM) (Maz zatorta et al., 2006), quantile support vector machine régression (QSVMR) [START_REF] Villain | Quantile régression model for a diverse set of Chemicals: Application to acute toxicity for green algae[END_REF], DT and RF (Basant et al., 2015b[START_REF] Basant | Modeling the toxicity of Chemical pesticides in multiple test species using local and global qstr approaches[END_REF][START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF] In our literature analysis on (Q)SAR for PPP, a large majority of the (Q)SAR models were developed to predict the acute toxicity on aquatic animais: mainly fish and crustaceans (55% of the (Q)SAR models reviewed; Table 3). Insects (i.e., 100% of the terrestrial invertebrates) represent the third group of non-target species for which (Q)SAR models hâve been devel oped (half of them concerns honeybees). Despite the extent of the harmful effects of PPP on bees, studies specifically devoted to (Q)SAR models for the prédiction of PPP toxicity on this pollinator (six articles from 2000 to 2020) remain rather limited [START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF] T a b le 3 P ercen tag e of (Q )S A R m odels by ta x a (39 p a p ers were analysed; one p a p e r can be counted for different biological m odels).

Although the majority of the (Q)SAR models were developed for aquatic species, these models are available for a broad range of Chemicals but predict toxicity to only a few standard test organisms and do not address the broader range of taxa within aquatic communities [START_REF] Raimondo | Application of Interspecies Corréla tion Estimation (Ice) models and QSAR in estimating species sensitivity to pesticides[END_REF]. Bas ant et al. (2016) hâve proposed that, for a comprehensive safety évaluation of Chemicals by means of (Q)SAR models development, toxicity data in multiple test species of different trophic levels and complexities are needed. Therefore, if new ecotoxicological data are produced, (Q)SAR models with a single species toxicity analysis could replace and/or be enhanced by multi-species models [START_REF] Basant | Modeling the toxicity of Chemical pesticides in multiple test species using local and global qstr approaches[END_REF][START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF].

As noted by other authors on (Q)SAR non-specific of the PPP toxicity and confirmed by our analysis of (Q)SAR for PPP, there are few applicable (Q)SAR models for algal toxicity due to the lack of a consistent data set with experimental algal test results and because of the variability of the results [START_REF] Villain | Quantile régression model for a diverse set of Chemicals: Application to acute toxicity for green algae[END_REF][START_REF] Douziech | Reliable and représentative in silico prédictions of freshwater ecotoxicological hazardous concentrations[END_REF].

D R and T K T D m odels

In total, 58 papers were selected to embrace various types of dose-response (DR) and toxicokinetic-toxicodynamic (TKTD) models. DR models are less represented (18.9%) compared to TKTD models (72.4%, see Table 4 for details). DR and TKTD models make the link between Chemical concentra tions to which living organisms are exposed to and the potential effects on their life-history traits (survival, growth rates, reproduction features). The main différence between DR and TKTD approaches is that time is taken into account or not. On an ERA point of view, only DR models are used today at Tier-1 assessment in support of the daily work of regulators (see Section 6). Nevertheless, in order to better address risks of time-variable exposures, a situation that often occurs with PPP, the Tier-2 assessment may be rehned by the use of TKTD models (EFSA PPR Panel, 2013) (namely to conduct a Tier-2C assessment). In addition, based on a recent Scientihc Opinion on the state of the art of TKTD effect models for regulatory risk assessment of PPP for aquatic organisms (EFSA PPR Panel, 2018a), EFSA emphasized the added-value of TKTD models for the Tier-2C assessment, even considering the General Unihed Threshold models of Survival (namely, GUTS models, [START_REF] Jager | General Unihed Threshold Model Of Survival-A Toxicokinetic-Toxicodynamic Framework For Ecotoxicology[END_REF]; [START_REF] Jager | Modelling Survival Under Chemical Stress. A Comprehensive Guide To The GUTS Framework[END_REF]) as ready-to-use for ERA in their two reduced versions (GUTS-RED models), when analysing standard toxicity test data for survival (see Section 6). A full application case study of GUTS models for ERA at Tier-2C has been published by [START_REF] Brock | Application of General Unihed Threshold Models of Survival Models for Regulatory Aquatic Pesticide Risk Assessment Illustrated with An Example for the Insecticide Chlorpyrifos[END_REF].

In addition to GUTS models already recommended as they are to handle survival data, others TKTD models allow considering sublethal effects such as growth for plants, or both reproduction and growth for ectotherms with DEBtox models. Note that DEB stands for Dynamic Energy Budget with 'tox' extension referring to additional stress functions that can be applied on some DEB parameters to account for different modes of action of potentially toxic Chemical substances [START_REF] Jager | Revisiting Simplihed Debtox Models For Analysing Ecotoxicity Data[END_REF]. Among plant models, the Lemna model is also considered ready to be used in ERA [START_REF] Schmitt | Mechanistic TK/TDmodel simulating the effect of growth inhibitors on Lemna populations[END_REF]EFSA Scien tihc Committee, 2018). Regarding DEBtox models, EFSA only considers their current state limited to research applications, mainly because they still lack enough documented and evaluated case studies (EFSA Scientihc Committee, 2018). An explanation may corne from the diversity of DEB models themselves for which a unifying framework seems dihicult to establish regarding the diversity of biological species htness they are able to describe (Add-my Pet,

2021).

It is worth to note that TKTD models, even if recommended today at Tier-2C assessment (EFSA PPR Panel, 2013), could also be used at Tier-1 assessment (Charles et al., 2021). Indeed, TKTD models translate the Chemi cal exposure (even if time-variable) into expected effects on the life-history traits of living organisms. TKTD models explicitly describe the Chemical dynamic within organisms and the related damages (namely the TK part) together with the dynamic of the effects (namely the TD part). In doing so, TKTD models allow to connect the external exposure concentration dynamics to the prédiction of effects over time. Consequently, TKTD models allow to calculate any x% effect at any time t, thus providing ECXyt or LCXyt (Baudrot and [START_REF] Baudrot | Recommendations To Address Uncertainties In Environmental Risk Assessment Using Toxicokinetics-Toxicodynamics Models[END_REF], in particular ECso or LC^o values at final time as requested for ERA at Tier-1.

Focusing only on the toxicokinetics, we face with a wide diversity of mod els that are ail compartment hrst-order kinetic models. These so-called TK models either consider an organism as a whole, thus written with only one compartment (Charles et al., 2021;[START_REF] Ratier | New Perspectives On The Calculation Of Bioaccumulation Metrics For Active Substances In Living Organisms[END_REF][START_REF] Rubach | Toxicokinetic Variation In 15 Freshwater Arthropod Species Exposed To The Insecticide Chlorpyrifos[END_REF], or consider several compartments that may represent internai entities such as the digestive System or a set of organs, or even dehning compartments as organs or physiological fluids to hnely decipher Chemical fluxes between compartments (see [START_REF] Grech | Toxicokinetic Models and Related Tools In Environmental Risk Assessment Of Chemicals[END_REF] for a review). These latest category of rehned TK models are called Physiologically-Based TK (PBTK) models. They are équivalent to physiologically-based pharmaco-kinetic (PBPK) models in their writing, the way they are rather called when vertebrate or mammal species are concerned [START_REF] Berntssen | Do Background Levels Of The Pesticide Pirimiphosmethyl In Plant-Based Aquafeeds Affect Food Safety Of Farmed Atlantic Salmon? Food Additives and Contaminants -Part A Chemistry[END_REF][START_REF] Li | Multi-compartmental toxicokinetic modeling of fipronil in tilapia: Accumulation, biotransformation and élimi nation[END_REF][START_REF] Maclachlan | Influence of physiological status on residues of lipophilie xenobiotics in livestock[END_REF][START_REF] Maclachlan | Physiologically based pharmacokinetic (Pbpk) model for residues of lipophilie pesticides in poultry. Food Additives and Con taminants Part A-Chemistry Analysis Control Expo sure[END_REF][START_REF] Mavroudis | Development and validation of a physiology based model for the prédiction of pharmacokinetics/toxicokinetics in rabbits[END_REF]. Except work by [START_REF] Weijs | Applica tion of Bayesian Population Physiologically Based Pharmacokinetic (Pbpk) Modeling and Markov Chain Monte Carlo Simulations to Pesticide Kinetics Studies in Protected Marine Mammals: Ddt, Dde, and Ddd in Harbor Porpoises[END_REF] who implemented a Bayesian approach to infer their model parameters, PBPK models are mainly used to perform simulations, parameters being valued from the scientihc literature. These simulations typically serve to extrapolate between species or from mammals species towards humans. It is worth noting that [START_REF] Berntssen | Do Background Levels Of The Pesticide Pirimiphosmethyl In Plant-Based Aquafeeds Affect Food Safety Of Farmed Atlantic Salmon? Food Additives and Contaminants -Part A Chemistry[END_REF] proposed to account for the seasonal fluctua tions in their PBTK model. Today, only few PBTK models are developed for ecotoxicological purpose (42 models published until 2019 as reviewed in [START_REF] Grech | Toxicokinetic Models and Related Tools In Environmental Risk Assessment Of Chemicals[END_REF][START_REF] Gestin | One and Multi-Compartments Toxico-Kinetic Modeling To Understand Metals ' Organotropism and Fate In Gammarus Fossarum[END_REF], and, to our knowledge, very few PBTK models exist for PPP [START_REF] Abbas | A physiologically based pharmacokinetic and pharmacodynamie model for paraoxon in rainbow trout[END_REF][START_REF] Pery | A physiologically based toxicokinetic model for the zebrahsh danio rerio[END_REF][START_REF] Mit | Modeling Acétylcholine Esterase Inhibition Resulting From Exposure To A Mixture Of Atrazine and Chlorpyrifos Using A Physiologically-Based Kinetic Model In Fish[END_REF][START_REF] Grech | Generic physiologically-based toxi cokinetic modelling for hsh: Intégration of environmental factors and species variability[END_REF].

Population m odels

Aiming at an ecologically-relevant assessment of PPP hazard for ecosystems, the scaling-up of toxicological effects usually assessed at the organisai level now benefits from the development of population models. Mechanistic population models can also be employed to analyse démographie responses in experimental model ecosystems or in the held. They hâve long been developed in species conservation science as tools for projecting the viability of populations and the long-term outcomes of management actions or biological resource exploitation [START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF]. These models are increasingly recognized as important tools in PPP risk assessment [START_REF] Forbes | Ecological models in support of regulatory risk assessments of pesticides: developing a strategy for the future[END_REF][START_REF] Stark | Demography and modeling to improve pesticide risk assess ment of endangered species[END_REF][START_REF] Forbes | Assessing pesticide risks to threatened and endangered species using population models: Findings and recommendations from a croplife america science forum[END_REF][START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF]Schmolke et al., 2017Schmolke et al., , 2018)). We identihed 87 papers related to population models and PPP . This includes 55 case studies spécifie to the impacts of PPP on non-target species: 25% in aquatic invertebrates -with only 2 marine studies [START_REF] Lindsay | Impacts of stage-specihc acute pesticide exposure on predicted population structure of the soft-shell clam, mya arenaria[END_REF][START_REF] Thursby | Coupling toxicokinetictoxicodynamic and population models for assessing aquatic ecological risks to time-varying pesticide exposures[END_REF] -, 25% in terrestrial invertebrates (two thirds of which on pollinators), 30% in vertebrates (half in mammals and one third in birds), and 20% of the studies in primary producers (algae and plants equally).

Using the classification established in previous reviews of population model implémentation in ERA [START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF][START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF], three main categories of models can be identihed regarding the way in which they describe populations: unstructured, structured and Agent-Based Models (ABMs). In unstructured population models (e.g., scalar models, ordinary differential équation... ), a unique state variable (population size or total biomass) is considered. The population is viewed as a random mixture of individuals, particularly with respect to their exposure and sensitivity to the contaminant. Unstructured models represent only 15% of PPP population modeling case studies in our corpus, with a strong bias towards taxonomie groups: they concern the totality of the studies on unicellular algae and half of the plant population studies (e.g., [START_REF] Weber | Combination of a higher-tier flow-through System and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspicatus and Pseudokirchneriella subcapitata[END_REF][START_REF] Schmitt | Mechanistic TK/TDmodel simulating the effect of growth inhibitors on Lemna populations[END_REF]Hommen et al. 2016) against less than 5% of the animal studies (only one study in rodents, [START_REF] Wang | Démographie uncertainty in ecological risk assessments[END_REF]one in birds, Millot et al. 2015). Structured models (matrix models, Leslie, Lefkovitch, metapopulation models, differential équation Systems, compartment models...) take into account a structure within populations (e.g., âge classes, sex, developmental stages, spatial distri bution) to model their response to toxic stress based on the alterations of life history traits under PPP exposure. A very underdeveloped option in this category is compartment models relative to the healthy, contaminated or affected status of individuals (very used in epidemiology) with only one example of a bee colony model exposed to a neonicotinoid insecticide [START_REF] Bryden | Chronic sublethal stress causes bee colony failure[END_REF]. Structured models represent one third of the case studies identihed in our cor pus, covering a large taxonomie spectrum: aquatic invertebrates, terrestrial invertebrates, birds, hsh and plants. ABMs (50% of the 55 case studies), often also called Individual Based Models (IBMs) in the case of population models, cover ail taxa as well. ABMs hâve been proposed for a wide variety of ecosystem organization scales, ranging from social relationships within pollinator hives [START_REF] Crall | Social buffering of pesticides in bumblebees: Agent-based modeling of the effects of colony size and neonicotinoid exposure on behavior within nests[END_REF], or population dynamics of earthworms in contam inated soil columns [START_REF] Johnston | Earthworm distribution and abundance predicted by a process-based model[END_REF][START_REF] Forbes | Mechanistic effect modeling of earthworms in the context of pesticide risk assessment: synthesis of the foresee workshop[END_REF], up to the occupancy of river networks by aquatic invertebrate populations at the watershed scale (Focks et al., 2014). This demonstrates the high generic value of the population modeling framework to studying the unintended effects of PPP in ecosystems. In ABMs, each individual is represented and can differ from ail other individuals, depending on biological or state attributes or location. This formalism explains that the sub-individual effects of PPP (behavior modifi cation, food limitation... ) or other abiotic influences and biotic interactions (compétition, prédation...) are directly integrated in ABMs (e.g., [START_REF] Topping | Modeling the influence of temporal and spatial factors on the assessment of impacts of pesticides on skylarks[END_REF]. For structured and unstructured models, sub-individual effects and environmental influences are treated by means of external "submodels" (e.g., [START_REF] Lopes | Ecotoxicology and population dynamics: Using debtox models in a leslie modeling approach[END_REF][START_REF] Topping | Risk assessment of uk skylark populations using life-history and individual-based landscape models[END_REF]) that link them to the modification of life history traits (e.g., survival, growth, fecundity) or directly to population criteria (e.g., carrying capacity) (see [START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF], for the review of methodological aspects).

The population endpoints supplied by these models can be of different natures. Under certain stability assumptions of environmental condition régime during population exposure scénarios (constancy, periodicity, even stochasticity), the unstructured and structured models can be analytically studied to provide démographie indicators (population growth rate, equilibrium densities, stable structure, perturbation analysis... ), which guarantee robustness and genericity of the results obtained by these so-called projection methods [START_REF] Caswell | Matrix Population Models[END_REF]. ABMs proceed by simulation to provide population outcomes with respect to different tested scénarios (e.g., évolution of population size). Nevertheless, we observe that a large proportion of structured population models dedicated to PPP abandons the analytical approach and proceeds by numerical simulations as well, in particular when describing transient dynam ics of response to puise exposure to PPP (see below recovery aspects) or to formalize population viability analysis via the empirical calculation of popu lation extinction probabilities. Furthermore, the vision that opposes generic structured models with low environmental realism versus complex hyperparameterized ABMs spécifie to each case study seems to be vanished by the literature, as both types of formalism can implement ail key determinisms and processes of population dynamics (density-dependence, spatialization, influ ences of environmental conditions, phenology) [START_REF] Topping | Risk assessment of uk skylark populations using life-history and individual-based landscape models[END_REF][START_REF] Wang | Population models in pesticide risk assessment: Lessons for assessing population-level effects, recovery, and alternative exposure scénarios from modeling a small mammal[END_REF][START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF][START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF]. On the other hand, several publications propose decision guides for the development of pop ulation models in PPP ERA (Schmolke et al., 2017;[START_REF] Awkerman | Guidance for developing amphibian population models for ecological risk assessment[END_REF][START_REF] Raimondo | Popguide: Population modeling guidance, use, interprétation, and development for ecological risk assessment[END_REF], stressing on the importance of selecting the processes encompassed in the population model consistently with the question that the modelling approach must answer. This point should always drive the tradeoffs to be made between ERA genericity, realism, and précision in each case, rather than the type of adopted formalism.

There is an unbalanced tendency to use ABMs in the assessment of the unintended population effects of PPP: ABMs represent half of the 56 pop ulation models in our corpus compared with only 15% in the 450 studies implementing population models in applied ecology reviewed by [START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF]. At the same time, structured models are less represented (33% of PPP studies compared to 75% of the studies in ERA in general). The habits and background of the modeler communities -with a strong contribution of the European CREAM project (https://cream-itn.eu/) to this development-, but above ail the choice of questions specihcally addressed in the majority of these studies (recovery, spatialization...) and the suitability of ABMs to treat these aspects, seem to explain this bias. However, we will see further (Section 5.2.3), how some authors propose to mobilize the different types of population models to broaden the scope of questions to be addressed when evaluating the effects of PPP on non-target species [START_REF] Raimondo | Projected population-level effects of thiobencarb exposure on the mysid, americamysis bahia, and extinc tion probability in a concentration-decay exposure System[END_REF][START_REF] Topping | Risk assessment of uk skylark populations using life-history and individual-based landscape models[END_REF][START_REF] Forbes | Assessing pesticide risks to threatened and endangered species using population models: Findings and recommendations from a croplife america science forum[END_REF][START_REF] Rico | Developing ecological scénarios for the prospective aquatic risk assessment of pesticides[END_REF][START_REF] Hayashi | Ecological Risk Assessment Of Herbicides In Japan: Integrating Spatiotemporal Variation In Exposure And Effects Using A Multimedia Model And Algal Density Dynamics Models[END_REF][START_REF] Thursby | Coupling toxicokinetictoxicodynamic and population models for assessing aquatic ecological risks to time-varying pesticide exposures[END_REF][START_REF] Rueda-Cediel | Comparative analysis of plant démographie traits across species of different conservation concern: Implications for pesticide risk assessment[END_REF].

M ulti-species m odels

In this section, we will présent both static descriptive statistical approaches like species sensitivity distributions (SSD, first sub-section), together with dynamic models inspired from population models (second sub-section).

Species Sensitivity Distributions (SSD)

Within the original corpus, 29 papers mentioned the use of Species Sen sitivity Distributions (SSD), or related ones, to study PPP effects on sets of several species under various environment types. If works by [START_REF] Van Straalen | Ecotoxicological évaluation of soil quality criteria[END_REF], [START_REF] Aldenberg | Uncertainty Of The Hazardous Concentration and Fraction Affected For Normal Species Sensitivity Dis tributions[END_REF], [START_REF] Solomon | Probabilistic risk assessment of cotton pyrethroids: I. Distributional analyses of laboratory aquatic toxicity data[END_REF] and [START_REF] Sanchez-Bayo | Ecological relative risk (Ecorr): Another approach for risk assessment of pesticides in agriculture[END_REF] can be seen as precursors of the SSD as known today, Van Straalen and Denneman (1989) already used the idea of the p% Hazard Concentration (HCP), the book from [START_REF] Posthuma | Species Sensitivity Distributions In Ecotoxicology[END_REF] posing ail the bases of this concept. SSD is assumed to reduce the uncertainty related to différences in sensitivity of standard test species and those expected to be exposed in field from the inter-specific variability in sensitivities to contami nants in order to predict effects at the community level [START_REF] Maltby | Insecticide species sensitivity distributions: Importance of test species sélection and relevance to aquatic ecosystems[END_REF]Van Den Brink et al., 2006). More broadly, SSD may allow quantifying relationships between species richness and single environmental factors, thus helping in better understanding and predicting biodiversity patterns, identifying envi ronmental management options and setting Environmental Quality Standards (EQS) [START_REF] Schipper | Deriving held-based species sensitivity distributions (f-ssds) from stacked species distribution models (s-sdms)[END_REF].

On a theoretical point of view, the SSD approach is dehned as a Cumulative Distribution Function (CDF) of the toxicity of a single compound or mixture to a set of species that is considered as an assemblage or a community. A small cut-off value in the left tail of the distribution is used to estimate a concentration below which a certain fraction of species exposed above their toxicity threshold level is considered acceptable. Usually a cut-off value of 5 or 10% is chosen and their corresponding concentrations are named HC$ and HCio (Hazardous Concentration to 5 or 10% of the species). The use of the SSD concept in ERA relies on several hypothèses, among the following ones:

1. The species sample on which the SSD is htted is a random and représenta tive sélection of the community of interest. 2. Interactions among species do not influence the sensitivity probability distribution. 3. Because functional endpoints are usually not incorporated in the SSD, the community diversity is the target of concern. 4. The laboratory sensitivity of a species approximates its field sensitivity. 5. The protection of the prescribed percentile of species ensures a sufficient protection of field ecosystems.

Note that HCP estimâtes based on laboratory toxicity tests do not provide information neither on the recovery potential of sensitive endpoints nor on indirect effects, which may be important for regulatory decision-making [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF].

Within a community, some species are very intolérant while others are more tolérant. Consequently, the CDF is expected to exhibit a sigmoidal increasing shape, and a low exposure concentration is expected to affect only a small proportion of the species. The dérivation of this trigger value (namely the HCP as mentioned above) thus requires to ht a presupposed probability distri bution (usually a log-normal or a log-logistic probability distribution) to the toxicity values of ail the sampled species. Even if some authors are still using No Observed Effect Concentrations (NOEC) or Lowest Effect Concentrations (LOEC) entries for SSD analyses [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF][START_REF] Zwart | Ecological Effects of Pesticide Use in The Netherlands: Modeled and Observed Effects in the Field Ditch[END_REF][START_REF] Iwasaki | Does The Choice Of Noec Or EclO Affect The Hazardous Concentration For 5% Of The Species?[END_REF][START_REF] Cederlund | Effects of spray drift of glyphosate on nontarget terrestrial Plantsa critical review[END_REF], the toxicity values used as SSD inputs usually corne today from DR models (thus being LCX or ECX values, with usually x = 50%), more rarely from TKTD model (e.g., the No Effect Concentration, Kon Kam [START_REF] Kam King | Hierarchical modelling of species sensitivity distribution: Development and application to the case of diatoms exposed to several herbicides[END_REF]. Then, the SSD is performed in two steps:

1. The choice of a probability distribution, suited to the data set to be analysed: parametric distributions or non-parametric methods are possible choices. Parametric distributions are more reasonable with small data sets, while log-normal and log-logistic distributions are the customary choices among parametric ones. 2. Using a parametric distribution, ail the parameters need to be estimated.

In this perspective, several methods exist [START_REF] Belanger | SSDs Revisited: Part II, practical Considérations In The Development and Use Of Application Factors Applied To Species Sensitivity Distributions[END_REF]):

• Moment matching as in the ETX free software (current version is 2.3), an Excel spreadsheet with embedded Visual Basic macro-driven calculation tools to calculate HCP and Potentially Affected Factions (PAF) from normally distributed toxicity data [START_REF] Van Vlaardingen | A program to calculate hazardous concentrations and fraction affected, based on normally distributed toxicity data[END_REF]; ETX is one of the most used software [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF]Van Den Brink et al., 2006;[START_REF] Daam | Does the actual standard of 0.1 mu g/L overestimate or underestimate the risk of plant protection products to groundwater ecosystems?[END_REF][START_REF] Silva | Predicting the aquatic risk of realistic pesticide mixtures to species assemblages in Portuguese river basins[END_REF][START_REF] Van Den | Exposure Pattern-Specihc Species Sensitivity Distri butions For The Ecological Risk Assessments Of Insecticides[END_REF] 2019) used it to dérivé a combined SSD for acute toxicity of nine pyrethroids to aquatic animais. • Maximizing the likelihood, i.e., selecting parameters for which the probability of observing the data is the highest, as e.g., in the software Burrlioz (current version 2.0) used as the standard software to dérivé water quality guideline values for toxic compounds in Australia and New Zealand (Campbell et al., 2000;[START_REF] Barry | Burrlioz 2.0. commonwealth science and industrial research organization[END_REF]: Burrlioz uses a loglogistic distribution for data sets that comprise less than eight toxicity values and a Burr Type III distribution for data sets of eight or more toxicity values [START_REF] Anzecc | Australian and new zealand guidelines for fresh and marine water quality. Australian and New Zealand Environment and Conservation Council and Agriculture and Resource Management Council Of Australia and New Zealand[END_REF]. Regarding PPP, Burrlioz has been used by [START_REF] Chen | Aquatic risk assessment of a novel strobilurin fungicide: A microcosm study compared with the species sensitivity distribution approach[END_REF]; [START_REF] Li | Application Of Species Sensitivity Distribution In Aquatic Probabilistic Ecological Risk Assessment Of Cypermethrin: A Case Study In An Urban Stream In South China[END_REF]. 2021). • An amalgam of the above algorithms (maximum likelihood, moment estimators, linearization and the Metropolis-Hastings algorithm), also handling censored data to support htting and visualization of simple SSD according to the choice of a distribution among six possibilities, in the SSD Toolbox from the US EPA [START_REF] Etterson | Technical manual: Ssd toolbox version 1[END_REF].

Ail above software are based on a frequenstist inference method, while other authors attempted to use Bayesian approaches: [START_REF] Jesenska | Validation of the species sensitivity distribution in rétrospective risk assessment of herbicides at the river basin scale-the Scheldt river basin case study[END_REF] htted SSD in the R software (R Core Team, 2021) with the winBUGS language; He et al. ( 2014) developed a novel platform, named the Bayesian Matbugs Calculator (BMC), in order to select the best SSD ht to assess ecological risk at high-, mid-and low-levels of the 95% crédible interval and to set the priority of toxic substances.

Food web and Community models

The food web and community models represented 21 papers within the final bibliometric corpus. They encompass a wide diversity of models, from simple ones involving only two species in compétition [START_REF] Damgaard | Modeling effects of herbicide drift on the compétitive interactions between weeds[END_REF][START_REF] Joncour | Sublethal Concentration Of Insecticide Amplifies Interférence Compétition In A Tortrix Moth[END_REF], to the most complex ones considering as many as possible species for held studies, the one of [START_REF] Galic | Predicting impacts of Chemicals from organisms to ecosystem service delivery: A case study of insecticide impacts on a freshwater lake[END_REF], further developed by [START_REF] Bartell | The Comprehensive Aquatic Systems Model (CASM): Advancing Computational Capability for Ecosystem Simulation[END_REF], the CASM model, being maybe the most complété, addressing even ecosystem services within a lake. Most of the models are spécifie to particular situations which makes it difficult to présent a short overview and to identify common denominator as there are so many different mathematical formalisms that hâve been used, as well as species-contaminant combinations that hâve been studied.

Nevertheless, we can distinguish food-web models from those accounting for other types of ecological interactions such as compétition for example. The simplest food-web model we identified is the one of De Hoop et al. ( 2013) only involving two species whose dynamics is described by the Rosenzweig-MacArthur équation (namely a two-dimensional ODE System). Pioneer works with food-web models were done by [START_REF] Rose | Stepwise itérative calibration of a multi-species phytoplankton-zooplankton simu lation model using laboratory data[END_REF], calibrating a multispecies phytoplankton-zooplankton simulation model from laboratory data, [START_REF] Hommen | Simulation models to predict ecological risk of toxins in freshwater Systems[END_REF], predicting pollutant effects on freshwater plankton communities, or [START_REF] Hanratty | Evaluation of model prédictions of the persistence and ecological effects of diflubenzuron in a littoral ecosystem[END_REF], modelling the effects of diflubenzuron within a littoral ecosystem. Some years later, [START_REF] Traas | A freshwater food web model for the combined effects of nutrients and insecticide stress and subséquent recovery[END_REF] proposed a food-web model to analyse a microcosm experiment studying the combined effects of nutrients and insecticides for their impact on recovery of a model freshwater ecosystem; the final aim was to link eutrophisation and contamina tion. De Laender et al. ( 2011) also focused on microcosms to study the effect of linuron, a PPP also studied by [START_REF] Viaene | Using additive modelling to quantify the effect of Chemicals on phytoplankton diversity and biomass[END_REF] with the use of diver sity indices; while [START_REF] Nfon | Development of a dynamic model for estimating the food web transfer of Chemicals in small aquatic ecosystems[END_REF] developed a dynamical combined fateand food-web model to estimate the food-web transfers of Chemicals in small aquatic ecosystems. Their innovation lies in the fact that aquatic macrophytes were included in the fate model and also as a food item in the food-web model. Based on simulation, [START_REF] Nfon | Development of a dynamic model for estimating the food web transfer of Chemicals in small aquatic ecosystems[END_REF] were able to détermine the influence of macrophytes on fate and bioaccumulation of several hypothetical PPP showing in particular that macrophytes hâve a significant effect on the fate and food-web transfer of highly hydrophobie compounds. More recently, [START_REF] Bartell | Modeling the effects of thiamethoxam on Midwestern farm ponds and emergent wetlands[END_REF] proposed two integrated bio-energetics-based and habitat quality models to describe the daily biomass values of selected producer and consumer populations both in ponds and wetlands within farms.

The bee biological species has been used in two models to deal with the com munity level of biological organization. [START_REF] Becher | Bumble-beehave: A Systems model for exploring multifactorial causes of bumblebee décliné at individual, colony, population and community level[END_REF] capitalized on the already existing BEEHAVE model [START_REF] Becher | BEEHAVE: A Systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure[END_REF] to simulate the colony, population and community dynamics of up to six UK bumblebee species living in any mapped landscape, based on an agent-based spatially-explicit model.

CONTENTS

This kind of modelling approach has also been used for example by [START_REF] Reeg | Modelling direct and indirect effects of herbicides on non-target grassland communities[END_REF], Reeg et al. (2018) and Reeg et al. (2018) to extrapolate individual-level effects to the population and community level of non-target plant communities (the individual-based plant community or IBC-grass model). It has also been used to extrapolate from laboratory to held information in order to highlight herbicide effects with direct and indirect effects on population level. The herbicide effect extent dépends not only on the distance to the held, but also on the spécifie plant community, its disturbance régime and the resource level. [START_REF] Strauss | The Power Of Hybrid Modelling: An Example From Aquatic Ecosystems[END_REF] successfully merged an individualbased population model for Daphnia magna with a dynamic ecosystem lake model, utilising the accuracy of the former and the dynamic environment of the latter to simulate realistic held populations. They thus created the DaLaM model (Daphnia Lake Model) to simultaneously predict population dynamics of D. magna and phytoplankton within a simplihed daphnid-dominated food web under relevant variable held environmental conditions, such as underwater light climate, water température, turbulence and nutrient availability. As a main resuit, their hybrid modelling approach is capable of extrapolating singlespecies data from the laboratory to the held level as well as of decreasing the model uncertainty by including an appropriate level of complexity. Regarding lake ecosystems, two other types of models hâve been proposed: (1) Ren et al. ( 2017) applied a fugacity-based dynamic bioaccumulation model (namely mass-balanced équations) to study short food chains in high-altitude alpine lakes, that was specihcally adapted to the hsh species living in the Central Tibetan Plateau; (2) [START_REF] Galic | Predicting impacts of Chemicals from organisms to ecosystem service delivery: A case study of insecticide impacts on a freshwater lake[END_REF] used the existing AQUATOX frame work [START_REF] Park | Aquatox: Modeling Environmental Fate and Ecological Effects In Aquatic Ecosystems[END_REF] to quantify insecticide-induced impacts on ecosystem services provided by a lake from toxicity data for organism-level endpoints. The AQUATOX framework allows to integrate environmental fate of Chemicals and their impacts on food webs in aquatic environments. [START_REF] Galic | Predicting impacts of Chemicals from organisms to ecosystem service delivery: A case study of insecticide impacts on a freshwater lake[END_REF] highlighted that complex response of hshing services are mainly due to nonlinear feed-backs in the lake food web, and that the water clarity increased with reduced insecticide use being mostly driven by changes in food web dynam ics. The AQUATOX framework was also used by [START_REF] Scholz-Starke | Simulation-based assessment of the impact of fertiliser and herbicide application on freshwater ecosystems at the Three Gorges Réservoir in China[END_REF] to simulate the dynamics of trophic guilds of aquatic organisms, hydrodynamics and nutrients including the dynamics of the exposure substance and its métabolites. They found that there were several interconnected trophic levels and a signiheant biomagniheation of métabolites.

As [START_REF] Strauss | The Power Of Hybrid Modelling: An Example From Aquatic Ecosystems[END_REF] with their DaLaM (Daphnia Lake) model, [START_REF] Kattwinkel | Modeling Macroinvertebrate Community Dynamics in Stream Mesocosms Contaminated with a Pesticide[END_REF] took advantage of ecotoxicological mesocosm data to develop a mechanistic food-web model that they specihcally called Streambugs, in order to investigate the dynamics of the macro-invertebrate community exposed to puises of the insecticide thiacloprid. They used Bayesian inference to estimate parameters (in particular their uncertainty) then investigated vital rates (such as the emergence process and sub-lethal effects) and limiting environmental factors in the model. They thus yielded insights into recovery dynamics and supported the use of more accurate modeling approaches in gen eral. A statistical model based on multiple linear régressions was specifically used for biofilms [START_REF] Bhowmick | Assessing The Effect Of Herbicide Diuron On River Biohlm: A Statistical Model[END_REF] to better understand the influ ence of diuron, chlorophyll a concentrations and photosynthetic efficiency on changes in the river biohlm community structure and growth pattern of lotie ecosystems.

Even if of strong interest [START_REF] Crocker | Estimating the exposure of birds and mammals to pesticides in long-term risk assessments[END_REF], birds and mammals are probably the less studied category of animais. Let's cite the recent proposai by [START_REF] Dittrich | Multiyear Monitoring Of Bird Communities In Chlorpyrifos-Treated Orchards In Spain and The United Kingdom: Spa tial and Temporal Trends In Species Composition, Abundance, and Site Fidelity[END_REF] who assessed the potential effects of chlorpyrifos on bird communities based on a multi-year and multi-site monitoring program that was carried out in treated cider orchards (in the UK) and in treated citrus orchards (in Spain). The authors used N-mixture models htted to the number of trapped birds (capture data) using the p-count function of [START_REF] Royle | N-Mixture Models For Estimating Population Size From Spatially Replicated Counts[END_REF]. They corne to the conclusion that the abundance of most bird species was strongly and signihcantly affected by seasonality, while no species showed any tendency of réduction in their population size over the years.

Landscape models

At the frontier with population models, our literature searches identihed a corpus of 24 studies that introduce a spatial représentation to implement integrated modeling approaches at the scale of agricultural landscapes assessing unintended ecological impacts of PPP. Seventy-hve percent of them concern terrestrial species (more than half in mammals or birds). Population endpoints related to the maintenance of non-target species inhabiting the landscape constitute the outputs of the model in two thirds of the studies. The other ones predict contamination levels in non-target species (e.g., in hare Kleinmann and Wang 2017; [START_REF] Mayer | European hares do not avoid newly pesticide-sprayed fields: Overspray as unnoticed pathway of pesticide exposure[END_REF] or the exceeding of toxicity thresholds at the individual level (e.g., in a warbler, [START_REF] Moore | A Probabilistic Risk Assessment for the Kirtland's Warbler Potentially Exposed to Chlorpyrifos and Malathion During the Breeding Season and Migration[END_REF], or an owl, [START_REF] Engelman | Modelling effects of Chemical exposure on birds wintering in agricultural landscapes: The western burrowing owl (athene cunicularia hypugaea) as a case study[END_REF]) as a function of habitat occupancy, spatial or dietary behaviors, or landscape structure. Two thirds of the 24 landscape studies consider a spatially explicit représentation of the transfer and fate of PPP, 85% the spatialization of species life cycle (in particular for the use of trophic resources or habitats). Surprisingly, only less than 50% of them consider the contamination history of individuals with regard to the realization of the whole life cycle in heterogeneous landscape conditions. ABMs are again very much used (90% of the studies) for the intégration of spatial and temporal dynamics of life cycles, and they are recommended for tracing the complex historiés of individual exposures in landscape contexts (EFSA PPR Panel, 2018b). Contrary to our expecta tions, the spatialization of population dynamics (metapopulation, sink-source relationships, migration, colonization... ) is of interest to only two-thirds of the PPP landscape-scale studies. Landscape models thus gather a set of rather heterogeneous objects with different objectives, where landscape spatio-temporal dynamics can be taken into account either in the environmental fate of the PPP, or/and in the realization of the life cycle of the individuals, or/and in the démographie response of the populations, depending on the objectives of each study or risk évaluation to be carried out. The spatio-temporal dimension of the chain "PPP application -transport and fate -exposure -toxicological effectecological impact" is a major aspect of the understanding and the management of untargeted effects of PPP on biodiversity in agricultural ecosystems. For this reason, we chose to gather in a spécifie category ail the mechanistic modeling studies, when any element of which falls within a landscape framework. Our literature searches also revealed the existence of a few PPP studies at the land scape level that are based on spatial statistical approaches (species distribution models, [START_REF] Szabo | Predicting avian distributions to evaluate spatiotemporal overlap with locust control operations in eastern australia[END_REF][START_REF] Richardson | A probabilistic co-occurrence approach for estimating likelihood of spatial overlap between listed species distribution and pesticide use patterns[END_REF], pressure-impact relationships, Kattwinkel et al. 2011). These studies, while not based on dynamic mechanistic models, do incorporate various éléments of spatially explicit mod eling related to PPP uses and environmental fate, or ecological determinisms of non-target population exposure.

M ixture models

More and more studies are reporting the occurrence of various PPP in a variety of environmental compartments such as water, soil, or air, meaning that aquatic, terrestrial and aerial biodiversity is often exposed to cocktails of PPP and contaminants from different sources (e.g., [START_REF] Pelosi | Residues Of Currently Used Pesticides In Soils And Earthworms: A Silent Threat? Agriculture[END_REF]). In the early 20th century, several mathematical models hâve been developed to assess and support the prédiction of joint effects caused by mixtures of Chemicals [START_REF] Jonker | Signihcance Testing Of Synergistic/Antagonistic, Dose Level-Dependent, Or Dose Ratio-Dependent Effects In Mixture Dose-Response Analysis[END_REF][START_REF] Schell | Assessing the effects of held-relevant pesticide mixtures for their compliance with the concentration addition model -An experimen tal approach with Daphnia magna[END_REF] (Figure 8 ). Both CA and IA models assume no interaction among mixture components [START_REF] Schell | Assessing the effects of held-relevant pesticide mixtures for their compliance with the concentration addition model -An experimen tal approach with Daphnia magna[END_REF] while, in some mixtures, interactions between Chemicals can resuit in stronger (synergistic) or weaker (antagonistic) effects than those expected of the toxicity of single components. CA and IA models thus fail to predict cases where interactions occur (e.g., [START_REF] Olmstead | Insecticidal juvénile hormone analogs stimulate the production of male offspring in the crustacean Daphnia magna[END_REF]. Moreover, there are some limitations in the application of CA and IA models to predict the impacts of more complex multi-chemical (e.g., ternary or more) mixtures [START_REF] Jonker | Signihcance Testing Of Synergistic/Antagonistic, Dose Level-Dependent, Or Dose Ratio-Dependent Effects In Mixture Dose-Response Analysis[END_REF], and the exact modes of action are often unknown for the majority of compounds [START_REF] Ginebreda | Assess ment of multi-chemical pollution in aquatic ecosystems using toxic units: Compound prioritization, mixture characterization and relationships with biological descriptors[END_REF][START_REF] Wilkinson | Acute and additive toxicity of ten photosystem-Ii herbicides to seagrass[END_REF]. Considering the broad range of PPP applied on agricultural helds, it is likely that PPP mixtures in streams are composed of compounds with both similar and dissimilar MoA. Moreover, there is a growing awareness that the MoA of a PPP may vary among organisms. In addition, if the MoA of PPP is known for the target organisms, it remains largely unknown for the non-target species [START_REF] Verro | Predicting Pesticide Envi ronmental Risk in Intensive Agricultural Areas. Ii: Screening Level Risk Assessment of Complex Mixtures in Surface Waters[END_REF].

Although interactions of Chemicals cannot be tested directly from the CA and IA models, they can be detected from the déviations between predicted and actually observed values [START_REF] Qiu | Interaction Patterns and Toxicities Of Binary and Ternary Pesticide Mixtures To Daphnia Magna Estimated By An Accelerated Failure Time Model[END_REF][START_REF] Filimonova | Ecotoxicological and biochemical mixture effects of an herbicide and a métal at the marine primary producer diatom Thalassiosira weissflogii and the primary consumer copepod Acartia tonsa[END_REF][START_REF] Tao | Quan titative évaluation and the toxicity mechanism of synergism within three organophosphorus pesticide mixtures Tochlorella pyrenoidosa[END_REF]. Déviations from the CA and IA models are referred to as antagonism (when the toxicity of the mixture is less than that predicted by each model) and synergism (when the toxicity of the mixture is greater than that predicted by each model, [START_REF] Phyu | A comparison of mixture toxicity assessment: Examining the chronic toxicity of atrazine, permethrin and chlorothalonil in mixtures to Ceriodaphnia cf. dubia[END_REF]. The reported inability of the CA and IA models to consistently model mixture toxicity led [START_REF] Jonker | Signihcance Testing Of Synergistic/Antagonistic, Dose Level-Dependent, Or Dose Ratio-Dependent Effects In Mixture Dose-Response Analysis[END_REF] to propose three additional functions that may be added to the basic CA and IA models to describe the three types of biologically relevant déviations from additivity: antagonistic déviation, dose level-dependent déviation, and dose ratio-dependent déviation.

To explore the joint action of Chemical mixtures, the isobologram model (Combination Index (Cl)-isobologram équation) is a commonly used and powerful graphical approach [START_REF] Tagun | The Response of Lemna minor to Mixtures of Pesticides That Are Commonly Used in Thailand[END_REF]. By comparing the isoboles based on the CA and IA prédictions and experimental mixture data, con clusions can be drawn on the type(s) of interaction occurring [START_REF] Cedergreen | Quantifying Synergy: A Systematic Review of Mixture Toxicity Studies within Environmental Toxicology[END_REF]. Moreover, [START_REF] Dupraz | Toxicity of binary mixtures of pesticides to the marine microalgae Tisochrysis lutea and Skeletonema marinoi: Substance interactions and physiological impacts[END_REF] described the Hewlett and Vplund mod els that are extensions of the CA model. Other methods relying on the same approaches (CA/IA models) hâve been proposed such as the Computational Approach to the Toxicity Assessment of Mixtures [START_REF] Schmidt | Rna sequencing indicates that atrazine induces multiple détoxification genes in Daphnia magna and this is a potential source of its mixture interactions with other Chemicals[END_REF], the Accelerated Failure Time (AFT) model [START_REF] Qiu | Interaction Patterns and Toxicities Of Binary and Ternary Pesticide Mixtures To Daphnia Magna Estimated By An Accelerated Failure Time Model[END_REF], the CI method [START_REF] Yang | Mixture toxicity of four commonly used pesticides at different effect levels to the epigeic earthworm, Eisenia fetida[END_REF], the calculation of Mixture Toxicity Index (MTI) or Safety Factor Index (SFI) [START_REF] Toumi | Combined acute ecotoxicity of malathion and deltamethrin to Daphnia magna (Crustacea, Cladocera): Comparison of different data analysis approaches[END_REF]. Another commonly used tool is the MIX-TOX model (e.g., [START_REF] Maloney | Cumulative toxicity of neonicotinoid insecticide mixtures to Chironomus dilutus under acute exposure scénarios[END_REF][START_REF] Mansano | Effects of diuron and carbofuran and their mixtures on the microalgae Raphidocelis sub capitata[END_REF][START_REF] Robinson | Comparing bee species responses to Chemical mixtures: Common response patterns?[END_REF][START_REF] Raby | Acute Effects of Binary Mixtures of Imidacloprid and Tebuconazole on 4 Freshwater Invertebrates[END_REF][START_REF] Rocha | Sensitivities of three tropical indigenous freshwater invertebrates to single and mixture exposures of diuron and carbofuran and their commercial formulations[END_REF]), a regression-based, dose-response mixture analysis modeling framework. This tool hts ecotoxicity data to the conceptual models (CA or IA) and then évaluâtes if there are any déviations for synergism/antagonism or dose level or ratio dependencies (i.e., depending on low or high doses, or dépendent on the ratio of the Chemicals in the mixture, respectively). In the same way, the Model Déviation Ratio (MDR) technique is used to détermine the biological signihcance and reproducibility of observed mixture effects (e.g., [START_REF] Belden | How Well Can We Predict The Toxicity Of Pesticide Mixtures To Aquatic Life? Integrated[END_REF][START_REF] Lopez Aca | Léthal and Sublethal Responses In The Fish, {Odontesthes} Bonariensis, Exposed To Chlorpyrifos Alone Or Under Mixtures With Endosulfan And Lambda-Cyhalothrin[END_REF][START_REF] De Perre | Mixture Toxicity Of Phostebupirim And Cyfluthrin: Species-Specihc Responses[END_REF][START_REF] Belden | Incorporating the joint toxicity of coapplied pesticides into the ecological risk assessment process[END_REF][START_REF] Lanteigne | Mixture Toxicity of Imidacloprid and Cyfluthrin to Two Non-target Species, the Fathead Minnow Pimephales promelas and the Amphipod Hyalella azteca[END_REF]) by comparing predicted and observed results of mixture toxicity. If the MDR values are < 5, then the CA model applies since the additive MoA can be assumed. If the MDR val ues are > 5, there is a potential that synergistic MoA dominâtes [START_REF] Chen | Risk assessment for pesticide mixtures on aquatic ecosystems in China: A proposed framework[END_REF]. When the MDR value is > 2.5, high levels of uncertainty exist, and this decreases the applicability of the model to risk assessments [START_REF] Belden | Joint Toxicity Of Chlorpyrifos and Esfenvalerate To Fathead Minnows and Midge Larvae[END_REF]. In addition, an MDR value > 2 could resuit from test variability or could be a resuit of the analytical quantification techniques [START_REF] Lanteigne | Mixture Toxicity of Imidacloprid and Cyfluthrin to Two Non-target Species, the Fathead Minnow Pimephales promelas and the Amphipod Hyalella azteca[END_REF].

In risk assessment of mixtures, the mathematical model used should be protective for complex, environmentally relevant mixtures which do not show synergistic interactions [START_REF] Cedergreen | Quantifying Synergy: A Systematic Review of Mixture Toxicity Studies within Environmental Toxicology[END_REF]. Based on its more conservative approach, CA is often suggested as a default model for risk assessment of Chem ical mixtures [START_REF] Schell | Assessing the effects of held-relevant pesticide mixtures for their compliance with the concentration addition model -An experimen tal approach with Daphnia magna[END_REF]. Another advantage of CA is that frequently reported ECX are sufficient for the calculation, whereas IA requires informa tion about the whole concentration response function, which is rarely reported or available [START_REF] Verro | Predicting Pesticide Envi ronmental Risk in Intensive Agricultural Areas. Ii: Screening Level Risk Assessment of Complex Mixtures in Surface Waters[END_REF]. Finally, the assumptions on the MoA in the IA model are unlikely to be met in environmental mixtures [START_REF] Svendsen | Similarity, Independence, Or Interaction For Binary Mixture Effects Of Nerve Toxicants For The Nematode Caenorhabditis Elegans[END_REF].

Some authors reported the IA model to underestimate the mixture effects, as [START_REF] Hasenbein | Environmentally relevant concentrations of herbicides impact non-target species at multiple sublethal endpoints[END_REF] who studied the combined effect of diuron and hexazinone on the growth of the green algae Pseudokirchneriella subcapitata and on Daphnia magna. In order to be adequately protective of sensitive aquatic insect species, these authors proposed to consider a prédiction window that incorporâtes both reference models when interpreting cumulative effects, accounting for any potential greater-than-additive effects that may occur resulting from mixture exposure. [START_REF] Ginebreda | Assess ment of multi-chemical pollution in aquatic ecosystems using toxic units: Compound prioritization, mixture characterization and relationships with biological descriptors[END_REF] reported that CA tended to overestimate toxicity in controlled experiments as compared to IA, and some other authors found that the CA model slightly underestimated mixture effects, indicating potential synergistic interactions [START_REF] Knezevic | Getting More Ecologically Relevant Information from Laboratory Tests: Recovery of Lemna minor After Exposure to Herbicides and Their Mixtures[END_REF][START_REF] Liess | Predicting the synergy of multiple stress effects[END_REF]. [START_REF] Belden | Incorporating the joint toxicity of coapplied pesticides into the ecological risk assessment process[END_REF] explained that if the empirical data deviates from the CA model by a factor of greater than 5, then synergy is considered likely and the ERA is based on the empirical data. Otherwise, the ERA may use CA to calculate Risk Quotients (RQ) or be based on the most toxic active ingrédient. Another approach proposed by [START_REF] Ginebreda | Assess ment of multi-chemical pollution in aquatic ecosystems using toxic units: Compound prioritization, mixture characterization and relationships with biological descriptors[END_REF] can be used to describe how a compound ecotoxicity is statistically distributed rather than to predict the exact ecotoxicity value of the mixture (where a major part is unknown). They dehne a procedure whereby the compounds identihed in a sample are ranked in descending order according to their toxic load expressed in terms of toxic units, and then the shape of the distribution is characterized. This compound prioritization, depending on the sampling site, is important from a management point of view.

W h a t are th e m o d el usages?

Prédiction of P P P ecotoxicological properties based on their Chemical characteristics using (Q )SA R m odels

Our literature analysis, spécifie to the PPP, identified some (Q)SAR models predicting toxicokinetic parameters (mainly bioconcentration factor, BCF) and numéro us articles describing (Q)SAR models predicting acute toxicodynamic parameters. In addition, some (Q)SAR models were developed to deal with substance classification.

Toxicokinetic outputs

For the toxicokinetic parameters, the most commonly used (Q)SAR models are based on the established corrélation between BCF and the hydrophobicity (log1 0 (A'O U I)) of organic Chemicals [START_REF] Pavan | Review of literature-based quantitative structure-activity relationship models for bioconcentration[END_REF]. There is general agreement that these linear corrélations give a fair approximation of the BCF for non-ionic, non-metabolised substances with log 10(KOW) in the range of 1 to 6 [START_REF] Pavan | Review of literature-based quantitative structure-activity relationship models for bioconcentration[END_REF]. Numerous (Q)SAR studies hâve attempted to predict the BCF accurately for more hydrophobie substances as well as for the substances that are metabolised to an appréciable extent in the exposed organism, for example by including additional descriptors in the équation and using more complex non-linear approaches (reviewed in [START_REF] Pavan | Review of literature-based quantitative structure-activity relationship models for bioconcentration[END_REF][START_REF] Miller | Prédiction of bioconcentration factors in fish and invertebrates using machine learning[END_REF]. During the last twenty years, a large number of global (Q)SAR models (diverse substances, Tables 12345in [START_REF] Pavan | Review of literature-based quantitative structure-activity relationship models for bioconcentration[END_REF] were developed for predicting the BC F but, to the best of our knowledge, few new (Q)SAR models were developed to predict specihcally the BCF of PPP [START_REF] Jackson | Use of Quan titative Structural Analysis To Predict Fish Bioconcentration Factors for Pesticides[END_REF][START_REF] Miller | Prédiction of bioconcentration factors in fish and invertebrates using machine learning[END_REF][START_REF] Nendza | Screening for low aquatic bioaccumula tion (2): Physico-chemical constraints[END_REF].

Toxicodynamic outputs

Most of the (Q)SAR models identified in our bibliographie analysis predict the dose that gives the toxic effect in 50% of the organisms, and therefore pre dict only acute toxicity of the substances. For instance, oral LD50 (the Léthal Dose for 50% of the tested organisms) is used for birds (Basant et al., 2015b;[START_REF] Mazzatorta | A QSAR study of avian oral toxicity using support vector machines and genetic algorithms[END_REF], contact LD50 is reported in pg/bee for honeybees [START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF] and, for aquatic animais, the LC5 0 , the léthal water concentration likely to kill 50% of the organisms is used [START_REF] Devillers | A general QSAR model for predicting the acute toxicity of pesticides to Lepomis macrochirus[END_REF][START_REF] Khan | QSAR modeling of Daphnia magna and hsh toxicities of biocides using 2d descriptors[END_REF]. Finally, the ECso inhibiting the algae biomass growth rate [START_REF] Villain | Quantile régression model for a diverse set of Chemicals: Application to acute toxicity for green algae[END_REF][START_REF] Xiao | Inhibition effect of natural flavonoids on red tide alga Phaeocystis globosa and its quantitative structure-activity relationship[END_REF], even if the endpoint is not at an organism level, can be assimilated to the acute toxic endpoints.

Another toxicodynamic endpoint well investigated by the (Q)SAR models is the mutagen properties of the substances, frequently based on the resuit of the bacterial reverse mutation test often referred to the Ames test or OECD test guideline No. 471.12 [START_REF] Benigni | Evaluation of the applicability of existing (q)sar models for predicting the genotoxicity of pesticides and similarity analysis related with genotoxicity of pesticides for facilitating of grouping and read across: An efsa funded Project[END_REF][START_REF] Herrmann | Q)Sar tools for the prédiction of mutagenic properties: Are they ready for application in pesticide régulation?[END_REF]. For the Ames test, ail (Q)SAR models generated statistically signiheant prédictions, comparable with the experimental variability of the test. The reliability of the models for other assays/endpoints appears to be still far from optimality [START_REF] Benigni | Evaluation of the applicability of existing (q)sar models for predicting the genotoxicity of pesticides and similarity analysis related with genotoxicity of pesticides for facilitating of grouping and read across: An efsa funded Project[END_REF].

Very few (Q)SAR models were developed for ecologically relevant endpoints able to predict potential chronic effects of substances, and at biological level convenient to manage the risk (population, community or ecosystem). Among the reviewed papers, only one really recent study addresses these sorts of endpoints. [START_REF] Finizio | A quantitative structureactivity relationships approach to predict the toxicity of narcotic compounds to aquatic communities[END_REF] developed successfully two simple (Q)SAR models to predict the effect of narcotic compounds on aquatic communities (HCs, concentration at which 5% of the species exhibit an effect). To hll this gap, Inter-species Corrélation Estimation (ICE) -(Q)SAR models could also be used to détermine HCP without the need for additional in vivo testing to help prioritise which Chemicals with no or few ecotoxicity data require more thorough assessment [START_REF] Mombelli | A linear model to predict chronic effects of Chemicals on daphnia magna[END_REF][START_REF] Douziech | Reliable and représentative in silico prédictions of freshwater ecotoxicological hazardous concentrations[END_REF].

Classification and modes/mechanisms of action

Even if, for ecotoxicity assessment, most of the (Q)SAR models are régres sions referring to the dose that gives the toxic effect in 50% of the organisms, some authors proposed to work with classification [START_REF] Mazzatorta | QSAR in ecotoxicity: An overview of modem classification techniques[END_REF]. Classification is the process of dividing a data set into mutually exclusive groups so that the members of each group are as "close" as possible to one another, and different groups are as "far" as possible from each other, where distance is measured with respect to spécifie variable (s) involved in the pré diction [START_REF] Mazzatorta | QSAR in ecotoxicity: An overview of modem classification techniques[END_REF]. For example, [START_REF] Venko | Classification models for identifying substances exhibiting acute contact toxicity in honeybees (Apis mellifera)[END_REF] proposed to classihed compounds according to the thresholds as dehned in PPDB: lowly toxic (LD50 more than 1 0 0 /rg/bee), moderately toxic (LD^o between 1 and 100 /rg/bee) and highly toxic (LD50 less than 1 /ag/bee). These authors argue that classification offers two main advantages in ecotoxicology: (i) the regulatory values are indicated as toxicity classes and (ii) classification can allow better management of data which are often noisy [START_REF] Mazzatorta | QSAR in ecotoxicity: An overview of modem classification techniques[END_REF].

Among the models developed to classify the substances, some were devel oped to détermine the mode of action (MoA) or mechanism of action (MechoA) of the substances including PPP (Bauer et al., 2018b,a;[START_REF] Kienzler | Mode of action (moa) assignment classifications for ecotoxicology: an évaluation of approaches[END_REF][START_REF] Martin | Prédiction of aquatic toxicity mode of action using linear discriminant and random forest models[END_REF]. MechoA differs from MoA because it refers to the molecular interaction that a molécule will undergo, leading to a biological outcome, which can be the key starting point of the Adverse Outcome Pathway (AOP) for this substance, i.e., the Molecular Initiating Event (MIE) [START_REF] Boone | Target site model: Application of the polyparameter target lipid model to predict aquatic organism acute toxicity for various modes of action[END_REF]. MoA is not so clearly dehned, often referring to the pathological effects that can be seen at the whole organism level in terms of behaviour or death i.e., at the other end of the AOP [START_REF] Russom | Predicting modes of toxic action from Chemical structure: acute toxicity in the fathead minnow (pimephales promêlas)[END_REF]. The idea behind these works is that a good understanding of MoA or MechoA, and appropriate methods to détermine them, is crucial for the efficient prédiction of toxicity using local (Q)SAR models and AOP framework [START_REF] Boone | Target site model: Application of the polyparameter target lipid model to predict aquatic organism acute toxicity for various modes of action[END_REF][START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF]. To this goal, various structure-based classification schemes hâve been developed to categorize Chemicals based on the MoA or MechoA (Bauer et al., 2018b;[START_REF] Kienzler | Mode of action (moa) assignment classifications for ecotoxicology: an évaluation of approaches[END_REF]. In addition, several prédic tive methods were developed with narrow applicability domains, and recently new methods were proposed to predict the MoA/MechoA only from the Chem ical structure to a wide range of organic Chemicals including PPP [START_REF] Raimondo | Application of Interspecies Corréla tion Estimation (Ice) models and QSAR in estimating species sensitivity to pesticides[END_REF].

Quantification of biological tim e-dose responses to P P P exposure using D R and T K T D m odels

As recommended since décades in most of the OECD guidance documents to study the ecotoxicity of Chemical substances for a range of species under standard protocols, DR analyses are employed to directly link constant expo sure concentrations to endpoints of interest (such as survival, reproduction, growth... ) at the end of the experiment (see for example [START_REF] Felten | Microplastics enhance Daphnia magna sensitivity to the pyrethroid insecticide deltamethrin: Effects on life history traits[END_REF]. DR models are mainly used to calculate standard outputs such as ECX or LCX on which the Tier-1 assessment is based to make decisions regarding approval of active substance [START_REF] Brock | Toxicity of sedimentbound lufenuron to benthic arthropods in laboratory bioassays[END_REF]Charles et al., 2021). Let us mention here the original work of [START_REF] Nian | Evaluation of the time-concentration-mortality responses of Plutella xylostella larvae to the interaction of Isaria fumosorosea with the insecticides beta-cypermethrin and Bacillus thuringiensis[END_REF] who tried to take into account the temporal dimension of the effects in a classical DR model by an approach known as time concentration mortality (TCM) modelling. Note that TCM models originate from Complementary log-log (CLL) models describing the relationship between time, dose, and the cumulative probability of mortality [START_REF] Preisler | Analysis of Time-Dose-Mortality Data[END_REF][START_REF] Nowierski | Analysis and modeling of time-dose-mortality of Melanoplus sanguinipes, Locusta migratoria migratorioides, and Schistocerca gregaria (Oorthoptera: Acrididae) from Beauveria, Metarhizium, and Paecilomyces isolâtes from Madagascar[END_REF].

In essence, DR models do not allow any considération of the time dimen sion of the effects. They also do not include exposure modelling, so that they are purely descriptive and unusable to perform prédictions under timevariable exposure scénarios, more environmentally realistic. However, recent work has attempted to include pulsed exposures (Copin et al., 2015;Copin and Chevre, 2015;[START_REF] Copin | Modelling the effect of exposing algae to puises of S-metolachlor: How to include a delay to the onset of the effect and in the recovery[END_REF][START_REF] Copin | Modelling the effects of Psii inhibitor puise exposure on two algae in co-culture[END_REF]. Other work has extended the use of DR models for example to take into account the seasonal and the gender variability on ECso values [START_REF] Dalhoff | Seasonal sensitivity of Gammarus pulex towards the pyrethroid cypermethrin[END_REF], to account for hormesis [START_REF] Jager | Hormesis On Life-History Traits: Is There Such Thing As A Free Lunch?[END_REF][START_REF] Tyne | Hormesis dépends upon the life-stage and duration of exposure: Examples for a pesticide and a nanomaterial[END_REF], or to make a link with biological traits [START_REF] Rubach | Species traits as predictors for intrinsic sensitivity of aquatic invertebrates to the insecticide chlorpyrifos[END_REF]. More interestingly, [START_REF] Monti | Log-ratio approach in curve htting for concentration-response experiments[END_REF] addressed the thorny issue of systematically considering a normal dis tribution of toxicity data, while it is well-known that such an assumption may be wrong for binary or count data for example [START_REF] Forfait-Dubuc | Survival Data Analyses In Ecotoxicology: Critical Effect Concentrations, Methods and Models[END_REF][START_REF] Delignette-Muller | Statistical Handling Of Reproduction Data For Exposure-Response Modeling[END_REF]OECD, 2016). [START_REF] Monti | Log-ratio approach in curve htting for concentration-response experiments[END_REF] proposed an alternative approach to deal with proportion data while the initial number of individuals remains unknown; their innovation lies in the use of the Beta probability distribution, without classical optimization techniques but the use of the log-ratio. Finally, cite work from [START_REF] Baillard | Effect of interspecific compétition on species sensitivity distribution models: Analysis of plant responses to Chemical stress[END_REF] who proposed including ecological interactions in ERA, by studying how inter-specihc com pétition affects plant species response to herbicides and more specihcally how it may modify DR curves and the resulting toxicity indices.

Regarding TK models, our literature review reveals two clusters of papers. The first cluster encompasses classical TK models. TK models are mainly used for calculating bioaccumulation metrics such as bioconcentration, biotasediment accumulation or biomagnification factors. The type of factor dépends on whether the exposure is via water, sédiment or food, respectively, providing the so-called BCF, B S AF and B M F values, respectively, as required by regulators for ERA. The most used is clearly the BCF, originally developed to analyse bioaccumulation in hsh according to the OECD guideline 305 (OECD, 2012). Regarding PPP, we hâve unearthed two old publications in which the bioaccumulation model is not formalised as it is today by ordinary differential équations describing the dynamics of the different compartments that are considered [START_REF] Elliott | Assessing breeding potential of peregrine falcons based on chlorinated hydrocarbon concentrations in prey[END_REF][START_REF] Satyanarayan | Bioaccumulation kinetics and bio concentration factor of chlorinated pesticides in tissues of Puntius ticto (Ham.)[END_REF]. The other papers on TK models applied to PPP divide in work providing BC F [START_REF] Brox | Toxicokinetics of Polar Chemicals in Zebrafish Embryo (Danio rerio): Influence of Physicochemical Properties and of Biological Processes[END_REF][START_REF] El-Amrani | Bioconcentration of pesticides in Zebrahsh eleutheroembryos (Danio rerio)[END_REF][START_REF] Loureiro | Assimilation efficiency and toxicokinetics of C-14-lindane in the terrestrial isopod Porcellionides pruinosus: The rôle of isopods in dégradation of persistent soil pollutants[END_REF] or B M F values [START_REF] Carafa | A bioaccumulation model for herbicides in Ulva rigida and Tapes philippinarum in Sacca di Goro lagoon (Northern Adriatic)[END_REF][START_REF] Lazartigues | Accumulation and half-lives of 13 pesticides in muscle tissue of freshwater hshes through food exposure[END_REF][START_REF] Fraser | Modeling biomagnification and metabolism of contaminants in harp seals of the Barents Sea[END_REF].

In the second cluster, with more elaborated TK models, three studies emphasize the importance of considering biotransformation, that is the possi ble dégradation of the parent compound into métabolites, that may be even more toxic [START_REF] Firdaus | Fate, Uptake, and Distribution of Nanoencapsulated Pesti cides in Soil-Earthworm Systems and Implications for Environmental Risk Assessment[END_REF][START_REF] Gao | Enantiomerization and Enantioselective Bioaccumulation of Benalaxyl in Tenebrio molitor Larvae from Wheat Bran[END_REF][START_REF] Wu | Prédiction Of Organic Contaminant Uptake By Plants: Modihed Partition-Limited Model Based On A Sequential Ultrasonic Extraction Procedure[END_REF], the work by [START_REF] Wu | Prédiction Of Organic Contaminant Uptake By Plants: Modihed Partition-Limited Model Based On A Sequential Ultrasonic Extraction Procedure[END_REF] having the particularity to concern plants. One study has accounted for time-variable exposure [START_REF] Rubach | Toxicokinetic Variation In 15 Freshwater Arthropod Species Exposed To The Insecticide Chlorpyrifos[END_REF] going so far as to propose the 95% dépuration time (£9 5 ) as a complément to the BCF. The dépuration time is important as it dehnes the minimum length of the inter val between repeated exposure events required for the organisms to recover. Consequently, it could be particularly useful in ERA when evaluating effects due to pulsed exposure. Last but not least, [START_REF] Roesch | Mechanistic Understanding of the Synergistic Potential of Azole Fungicides in the Aquatic Invertebrate Gammarus pulex[END_REF] propose a TK model to deal with binary mixtures, focusing on the synergistic potential of azole fungicides from the CA hypothesis (see Section 4.1.6).

In essence, TKTD models are of course best able to quantify the dynamics of Chemical effects on life-history traits of exposed organisms, whatever the type of effects they account for (léthal or sub-lethal). See section 4.1.2 were they are presented.

Extrapolation of effects of a tested exposure pattern to others, untested, exposure patterns

At the individual level, only TKTD models really enable to extrapolate effects under a tested exposure pattern to other untested ones (EFSA PPR Panel, 2018a). As already stated above, TKTD models hnely describe the internai dynamic of the damages due to a (time-variable) Chemical exposure, leading to effective or léthal changes on living organisms. TKTD models actually bring together several types of models depending on the biological traits that are observed (see Table 4 and Figure 1 in EFSA PPR Panel 2018a).

Regarding our literature review on PPP, GUTS models appear as the most used. As described in the founding article [START_REF] Jager | General Unihed Threshold Model Of Survival-A Toxicokinetic-Toxicodynamic Framework For Ecotoxicology[END_REF], and later in more details [START_REF] Jager | Modelling Survival Under Chemical Stress. A Comprehensive Guide To The GUTS Framework[END_REF], GTJTS models specifically describe the survival probability as a function of time and exposure concentration, this latter may vary over time. Note that the GUTS name dates from 2011 [START_REF] Jager | General Unihed Threshold Model Of Survival-A Toxicokinetic-Toxicodynamic Framework For Ecotoxicology[END_REF]; before that, a large number of very different TKTD approaches for survival existed in the literature with just as many different names. For clarity reasons, the GUTS name is used hereafter, whatever the TKTD model for survival is mentioned.

Mostly used for research purposes, initially at constant exposure concen trations [START_REF] Jager | Modeling receptor kinetics in the analysis of survival data for organophosphorus pesticides[END_REF][START_REF] Hesketh | Extending standard testing period in honeybees to predict lifespan impacts of pesti cides and heavy metals using dynamic energy budget modelling[END_REF][START_REF] Kretschmann | Toxicokinetic and toxicodynamic model for diazinon toxicity-mechanistic explanation of différences in the sensitivity of Daphnia magna and Gammarus pulex[END_REF], GUTS is today more and more employed to account for time-variable exposure [START_REF] Ducrot | Modelling effects of diquat under realistic exposure patterns in genetically differentiated populations of the gastropod Lymnaea stagnalis[END_REF][START_REF] Focks | Calibration and validation of toxicokinetic-toxicodynamic models for three neonicotinoids and some aquatic macroinvertebrates[END_REF][START_REF] Nyman | Toxicokinetictoxicodynamic modelling of survival of Gammarus pulex in multiple puise exposures to propiconazole: Model assumptions, calibration data requirements and prédictive power[END_REF][START_REF] Gabsi | Short-Term To Long-Term Extrapolation Of Léthal Effects Of An Herbicide On The Marine Mysid Shrimp Americamysis Bahia By Use Of The General Unihed Threshold Model Of Survival (Guts)[END_REF]. GUTS models are also used for ERA, for example at Tier-2C assessment in combination with Tier-2B assessment based on SSD approaches (see Brock et al. 2021, and Figure 6 in EFSA PPR Panel 2018a). Extensions of GUTS models hâve recently been published to deal with Chemical mixtures [START_REF] Arlos | Improving Risk Assessment by Predicting the Survival of Field Gammarids Exposed to Dynamic Pesticide Mixtures[END_REF][START_REF] Bart | Predicting Mixture Effects over Time with Toxicokinetic-Toxicodynamic Models (Guts): Assumptions, Experimental Testing, and Prédictive Power[END_REF], in combination with a shortage of food resources [START_REF] Nyman | The Insecticide Imidacloprid Causes Mortality of the Freshwater Amphipod Gammarus pulex by Interfering with Feeding Behavior[END_REF], while [START_REF] Dalhoff | Linking Morphology, Toxicokinetic, and Toxicodynamic Traits Of Aquatic Invertebrates To Pyrethroid Sensitivity[END_REF] hâve proposed to relate GUTS models with morphological and physiological traits.

For explaining effects on sub-lethal individual life-history traits (such as growth and reproduction endpoints), DEBtox models are today the leading TKTD models [START_REF] Jager | Revisiting Simplihed Debtox Models For Analysing Ecotoxicity Data[END_REF]. EFSA even recognizes the great potential of DEBtox models for future use in prospective ERA for PPP, although the DEBtox modelling approach is currently limited to research applications (EFSA PPR Panel, 2018a). Regarding the use of DEBtox models for PPP, we only found few relevant papers. [START_REF] Pieters | Modeling responses of Daphnia magna to pesticide puise exposure under varying food conditions: Intrinsic versus apparent sensitivity[END_REF] exposed daphnids to PPP puises with either low or high food availability, leading them to conclude that effect of PPP application on field populations of daphnids will dépend not only on the trophic State of the receiving water body, but also on the reproductive state and size of the animais. [START_REF] Jager | Chronic exposure to chlorpyrifos reveals two modes of action in the springtail Folsomia candida[END_REF] exposed Folsomia to chlorpyriphos via food, simultaneously modelling survival (this part being similar to a GUTS model in its Stochastic Death (SD) version), growth and reproduction, then making the link to the population dynamics via the Euler-Lotka équation. [START_REF] Zimmer | Modelling effects of time-variable exposure to the pyrethroid beta-eyfluthrin on rainbow trout early life stages[END_REF] proposed a model for the effects of time-variable exposure to the /3-cyfluthrin pyrethroid on rainbow trout early life stages. And very recently, [START_REF] Vignardi | Conventional and nano-copper pesticides are equally toxic to the estuarine amphipod Leptocheirus plumulosus[END_REF] proposed a DEBtox-like modelling approach to study how aquatic species respond to incidental exposure to Cu-based nano-engineered PPP, pointing out that future efforts should focus on toxicity studies and TKTD model development for nano-pesticides to make advance in ERA. Jager (2020) also proposed some directions that could improve ERA, like including a starvation module in DEBtox models to account for time-variable exposure profiles in particular, and performing more experiments under time-variable exposure in order to support the validation of DEBtox models for ERA.

In terms of innovation with TK models, the combined TK-IBM framework proposed by [START_REF] Liu | Incorporating toxicokinetics into an individual-based model for more realistic pesticide exposure estimâtes: A case study of the wood mouse[END_REF] revealed particularly interesting to better assess the PPP risk on wood mouse when the temporal pattern of feeding and time spent in exposed area by individuals is accounted for. Also, works of Chaumet et al. (2019)a andChaumet et al. (2019)b on biofilms is worth mentioning, as well as work of [START_REF] Roeben | Towards A Spatiotemporally Explicit Toxicokinetic-Toxicodynamic Model For Earthworm Toxicity[END_REF] including both time and space explicitly as explanatory variables in addition to the exposure concentration. Those studies then employed an explicitly spatialized TKTD model combined with a trait-based approach and a population dynamic model in a modular approach that revealed particular efficient. Last but not least, [START_REF] Mit | Modeling Acétylcholine Esterase Inhibition Resulting From Exposure To A Mixture Of Atrazine and Chlorpyrifos Using A Physiologically-Based Kinetic Model In Fish[END_REF] are the first to illustrate how PBTKTD models (that is considering several compartments for the TK part) may be used to better characterize and understand the interactions of Chemical compounds within a binary mixture.

Coupled with TKTD models, population models -whether they are unstructured, structured or ABMs -allow understanding the ecological con séquences of complex exposure scénarios, especially time-varying patterns particularly relevant in the case of PPP, e.g., [START_REF] Galic | Modeling the contribution of toxicokinetic and toxicodynamic processes to the recovery of gammarus pulex populations after exposure to pesticides[END_REF] 2016). When coupled with fate models in the frame of landscape models, these models can act as a toolbox in which a range of PPP exposure scénarios can be simulated. This allows to better inform the possible effects of these substances in realistic landscapes and realistic agricultural application patterns [START_REF] Dalkvist | Population-level impacts of pesticide-induced chronic effects on individuals dépend more on ecology than toxicology[END_REF]Focks et al., 2014;EFSA PPR Panel, 2018b). Various studies in both terrestrial and aquatic environments illustrate how this approach makes it possible to identify the influence of agricultural practices on the ecological risk for non-target species [START_REF] Topping | Landscape Structure and Man agement Alter The Outcome Of A Pesticide Era: Evaluating Impacts Of Endocrine Disruption Using The Almass European Brown Hare Model[END_REF], the effect of land use change, for example in an owl [START_REF] Engelman | Modelling effects of Chemical exposure on birds wintering in agricultural landscapes: The western burrowing owl (athene cunicularia hypugaea) as a case study[END_REF] or the woodpigeon [START_REF] Kulakowska | Using an individual-based model to select among alternative foraging strategies of woodpigeons: data support a memory-based model with a flocking mechanism[END_REF], or the beneht of mitigation actions such as the establishment of buffer zones, e.g., in rodents [START_REF] Dalkvist | Landscape structure médiates the effects of a stressor on held vole populations[END_REF], carabid beetles [START_REF] Topping | Towards a landscape scale management of pesticides: Era using changes in modelled occupancy and abundance to assess long-term population impacts of pesticides[END_REF], aquatic invertebrates [START_REF] Dohmen | Population-level effects and recovery of aquatic invertebrates after multiple applications of an insecticide[END_REF], or hsh [START_REF] Schmolke | Applying a hybrid modeling approach to evaluate potential pesticide effects and mitigation effectiveness for an endangered hsh in simulated oxbow habitats[END_REF].

Natural and Chemical stressors occur simultaneously in the different compartments of the environment [START_REF] De Coninck | Interactive effects of a bacterial parasite and the insecticide carbaryl to life-history and physiology of two Daphnia magna clories differing in carbaryl sensitivity[END_REF]. Population or community models can be used to assess effects of a PPP in different environmental settings including stressors ignored in the lab tests (e.g. increased température, reduced soil moisture, resource limitation, prédation pressure). Moreover, mathematical models used for joint effects caused by mixtures of Chemicals can be used to assess the effects of combined stressors, e.g., soil moisture in [START_REF] Morgado | Toxicity interaction between chlorpyrifos, mancozeb and soil moisture to the terrestrial isopod Porcellionides pruinosus[END_REF]; ultraviolet-B radiation in [START_REF] Yu | Joint effects of pesticides and ultraviolet-B radiation on amphibian larvae[END_REF]; food limitation in [START_REF] Shahid | Environmental Stress Increases Synergistic Effects of Pesticide Mixtures on Daphnia magna[END_REF]; bacterial parasite in De Coninck et al.

(2013); prédation in [START_REF] Pestana | Pesticide exposure and inducible antipredator responses in the zooplankton grazer, Daphnia magna Straus[END_REF]; prédation threat, parasitism and carbaryl in [START_REF] Coors | Synergistic, antagonistic and additive effects of multiple stressors: Prédation threat, parasitism and pesticide exposure in Daphnia magna[END_REF]. Thus, current efforts aim at including the additional risk of PPP mixtures and environmental stressors into the environmental risk assessment of PPP. Generally, the IA model, used to study combined effects of dissimilarly acting stressors, is chosen to assess the effects of combined stressors [START_REF] De Coninck | Interactive effects of a bacterial parasite and the insecticide carbaryl to life-history and physiology of two Daphnia magna clories differing in carbaryl sensitivity[END_REF]. [START_REF] Liess | Predicting the synergy of multiple stress effects[END_REF] developed the Stress Addition Model (SAM) that assumes that each individual has a general stress capacity towards ail types of spécifie stress that should not be exhausted. This model relies on three principal assumptions that provide a mechanistic understanding of the combined impact of independent stressors, in this case a Chemical in combination with one environmental stressor: (i) each individual has a certain tolérance towards ail types of stress, its general stress capacity; (ii) every spécifie unit of a given stressor (e.g., gg/L for Chemi cals, °C for température) can be transferred into a general stress level ranging from 0 to 1 as a "common currency" for ail stressors (the main challenge); (iii) general stress levels of independent stressors are additive, with the sum determining the total stress exerted on a population. This model was used by [START_REF] Shahid | Environmental Stress Increases Synergistic Effects of Pesticide Mixtures on Daphnia magna[END_REF] who compared it to CA and Effect Addition (EA) in order to assess the combined effects of food limitation and of a pyrethroid insecti cide or an azole fungicide. The combined effects of PPP and food stress was best predicted with the SAM that showed the lowest mean déviation between effect observation and prédiction.

A ssessm ent of the relevance of P P P effects observed on individuals for the population level

Some works emphasize that linking TKTD models to population dynamic models would be a further step toward a more effective risk assessment [START_REF] Horig | The Advantage Of A Toxicokinetic Model Of The Honey Bee Colony In The Context Of The Risk Assessment Of Plant Protection Products[END_REF][START_REF] Kretschmann | Toxicokinetic and toxicodynamic model for diazinon toxicity-mechanistic explanation of différences in the sensitivity of Daphnia magna and Gammarus pulex[END_REF]. More concretely, [START_REF] Vignardi | Conventional and nano-copper pesticides are equally toxic to the estuarine amphipod Leptocheirus plumulosus[END_REF] enlightened potential population-level effects of exposure to very low-levels of nano-pesticides from their TKTD modelling outputs. Based on an integrated multi-faceted modelling approach, [START_REF] Roeben | Towards A Spatiotemporally Explicit Toxicokinetic-Toxicodynamic Model For Earthworm Toxicity[END_REF] were able to make the link between PPP exposure, ecology and toxicological effects on earthworms.

The most basic aim of using population models for the ERA of PPP is to establish the démographie outcome of the répétition of organism-level toxic events during the development of successive générations, through either sim ulation or projection exercises [START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF]. In connection with the cyclic répétition of agricultural treatments, they thus consider the cumulative outcome of mortality events [START_REF] Topping | Towards a landscape scale management of pesticides: Era using changes in modelled occupancy and abundance to assess long-term population impacts of pesticides[END_REF], réductions of reproductive capacities {e.g., insecticides in pollinators Cresswell 2017 and seabirds [START_REF] Goutte | Démographie, Endocrine and Behavioral Responses To Mirex In The South Polar Skua[END_REF] or disturbances of ail the phases of the life cycle [START_REF] Chandler | Population conséquences of hpronil and dégradâtes to copepods at held con centrations: An intégration of life cycle testing with leslie matrix population modeling[END_REF]. But the first great value recognized in these models is that they simultaneously integrate ail the toxic effects of PPP exposure (survival, reproduction, growth, behavior, etc.), taking into account the characteristics of the life cycle of the species of concern when predicting the PPP consé quences on population persistence [START_REF] Stark | Population-level effects of pesticides and other toxicants on arthropods[END_REF][START_REF] Topping | Risk assessment of uk skylark populations using life-history and individual-based landscape models[END_REF][START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF]. Some authors establish dose-response relationships at the population level using as output different indicators of population size, population growth capacity or extinction risk calculated by these models [START_REF] Stark | Estimating susceptibility of biological control agents to pesticides: influence of life history strategies and population structure[END_REF][START_REF] Lopes | Ecotoxicology and population dynamics: Using debtox models in a leslie modeling approach[END_REF][START_REF] Preuss | The potential of individual based population models to extrapolate effects measured at standardized test conditions to relevant environmental conditions-an example for 3, 4-dichloroaniline on daphnia magna[END_REF][START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF][START_REF] Stark | Demography and modeling to improve pesticide risk assess ment of endangered species[END_REF][START_REF] Goutte | Démographie, Endocrine and Behavioral Responses To Mirex In The South Polar Skua[END_REF]. Although highly conditioned by the choice of processes and conditions considered in each model, these studies propose to define protective concentration thresholds for the population by confronting these outputs with theoretical thresholds of maintenance or good démographie state of the populations.

In a cognitive mode of use, population models and sensitivity-elasticity analyses [START_REF] Caswell | Matrix Population Models[END_REF] -frequently used in species conservation manage ment -allowed to understand the crucial rôle that life history traits plays in the démographie impacts of PPP. Numéro us modeling studies hâve emphasized the importance of species life cycle characteristics in the démographie impact of PPP on animais or plants [START_REF] Stark | Population-level effects of pesticides and other toxicants on arthropods[END_REF][START_REF] Stark | Estimating susceptibility of biological control agents to pesticides: influence of life history strategies and population structure[END_REF][START_REF] Raimondo | Projected population-level effects of thiobencarb exposure on the mysid, americamysis bahia, and extinc tion probability in a concentration-decay exposure System[END_REF][START_REF] Lindsay | Impacts of stage-specihc acute pesticide exposure on predicted population structure of the soft-shell clam, mya arenaria[END_REF][START_REF] Stark | Incorporating variability in point estimâtes in risk assessment: bridging the gap between lc50 and popu lation endpoints[END_REF]Schmolke et al., 2017Schmolke et al., , 2018;;[START_REF] Thursby | Coupling toxicokinetictoxicodynamic and population models for assessing aquatic ecological risks to time-varying pesticide exposures[END_REF][START_REF] Banks | The trouble with surrogates in environmental risk assessment: a daphniid case study[END_REF]. Structured population models are widely used in this framework of ERA [START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF][START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF], which is also found for PPP in our corpus of case studies: 50% of structured models versus only 15% for ABMs address the issue of differential démographie sensitivities between life cycle stages. Another major point relating to life cycle characteristics in PPP ecological models is the phenology and timing of exposure in relation to cultural practices that influence the risk of population exposure, the capacities of démographie compensation, or the recovery after short-term exposure. These temporal aspects, which hâve been extensively studied in pest management and biocontrol [START_REF] Stark | Estimating susceptibility of biological control agents to pesticides: influence of life history strategies and population structure[END_REF][START_REF] Tonnang | Advances in crop insect modelling methods-towards a whole System approach[END_REF][START_REF] Tang | A general model of hormesis in biological Systems and its application to pest management[END_REF], are now being emphasized as determining factors in the vulnerability of non-target species, and in the relative severity of impacts of PPP treatment practices: reproductive phenology in bird species [START_REF] Etterson | Quantifying the effects of pesticide exposure on annual reproductive success of birds[END_REF][START_REF] Etterson | Mechanistic modeling of insecticide risks to breeding birds in North American agroecosystems[END_REF][START_REF] Moore | A Probabilistic Risk Assessment for the Kirtland's Warbler Potentially Exposed to Chlorpyrifos and Malathion During the Breeding Season and Migration[END_REF][START_REF] Crocker | Estimating The Potential Effects Of Pesticide Seed Treatments On The Reproductive Success Of Arable Birds[END_REF], annual devel opment cycle in pollinators [START_REF] Thompson | The effects of four insect growth-regulating (igr) insecticides on honeybee (apis mellifera 1.) colony development, queen rearing and drone sperm production[END_REF], in aquatic invertebrates [START_REF] Galic | Simulating population recovery of an aquatic isopod: Effects of timing of stress and landscape structure[END_REF][START_REF] Sorensen | Pesti cide risk indicator for terrestrial adult stages of aquatic insects[END_REF] or in plants exposed to herbicides [START_REF] Schmitt | Mechanistic TK/TDmodel simulating the effect of growth inhibitors on Lemna populations[END_REF]. The other overarching element considered is the spatial dimension in the processes of exposure or in population dynamics response [START_REF] Topping | Modeling the influence of temporal and spatial factors on the assessment of impacts of pesticides on skylarks[END_REF][START_REF] Dalkvist | Population-level impacts of pesticide-induced chronic effects on individuals dépend more on ecology than toxicology[END_REF][START_REF] Forbes | Assessing The Risks Of Pesticides To Threatened And Endangered Species Using Population Modeling: A Critical Review and Recommendations For Future Work[END_REF]Schmolke et al., 2017;[START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF]. PPP population and landscape models thus make it possible to retrace (i) the complex ecology of certain species (amphibians in EFSA PPR Panel 2018b; endangered mammals in [START_REF] Nogeire | Land use as a driver of patterns of rodenticide exposure in modeled kit fox populations[END_REF]; or fish in [START_REF] Schmolke | Applying a hybrid modeling approach to evaluate potential pesticide effects and mitigation effectiveness for an endangered hsh in simulated oxbow habitats[END_REF]), (ii) the spatial heterogeneity of resources (soil invertebrates in [START_REF] Johnston | Earthworm distribution and abundance predicted by a process-based model[END_REF]; birds in [START_REF] Topping | Modeling the influence of temporal and spatial factors on the assessment of impacts of pesticides on skylarks[END_REF]bees in Becher et al. 2014;[START_REF] Thorbek | Using Beehave to explore pesticide protection goals for European honeybee (Apis melifera L.) worker losses at different forage qualifies[END_REF][START_REF] Gegear | Modeling scale up of anthropogenic impacts from individual pollinator behavior to pollination Systems[END_REF][START_REF] More | EFSA is working to protect bees and shape the future of environmental risk assessment[END_REF]), (iii) the migratory links between habitats or throughout the population distribution area [START_REF] Galic | Simulating population recovery of an aquatic isopod: Effects of timing of stress and landscape structure[END_REF]Focks et al., 2014), which can compensate for local PPP effects or on the contrary export the démographie impacts to non-contaminated areas [START_REF] Chaumot | Ecotoxicology and spatial modeling in population dynamics: An illustration with brown trout[END_REF][START_REF] Schaefer | Assessing recovery of stream insects from pesticides using a two-patch metapopulation model[END_REF]. Various studies hâve thus highlighted the influence of landscape structure on the impacts of various agricultural PPP practices on non-target populations (e.g., in vole, [START_REF] Wang | Population models in pesticide risk assessment: Lessons for assessing population-level effects, recovery, and alternative exposure scénarios from modeling a small mammal[END_REF][START_REF] Dalkvist | Landscape structure médiates the effects of a stressor on held vole populations[END_REF]hare, Topping et al. 2016) and identihed spécifie areas of the landscape that are particularly at risk for species of conservation concern [START_REF] Engelman | Modelling effects of Chemical exposure on birds wintering in agricultural landscapes: The western burrowing owl (athene cunicularia hypugaea) as a case study[END_REF] or important for ecosystem functioning [START_REF] Kattwinkel | Climate change, agricultural insecticide exposure, and risk for freshwater communities[END_REF].

The démographie framework also led some studies to emphasize the possibility of compensation between PPP-induced mortality or reduced fecundity and the release of natural density-dependent Controls (e.g., compétition) that buffer PPP population impacts [START_REF] Stark | Population-level effects of pesticides and other toxicants on arthropods[END_REF][START_REF] Stark | Demography and modeling to improve pesticide risk assess ment of endangered species[END_REF]. These processes hâve been investigated in wild rodents [START_REF] Wang | Démographie uncertainty in ecological risk assessments[END_REF][START_REF] Wang | Population models in pesticide risk assessment: Lessons for assessing population-level effects, recovery, and alternative exposure scénarios from modeling a small mammal[END_REF], in relation to territorial behavior in hsh [START_REF] Mintram | Assessing population impacts of toxicant-induced disruption of breeding behaviours using an individual-based model for the three-spined stickleback[END_REF] or hare [START_REF] Kleinmann | Modeling Individual Movement Decisions Of Brown Hare Lepus Europaeus As A Key Concept For Realistic Spatial Behavior And Exposure: A Population Model For Landscape-Level Risk Assessment[END_REF], in soil invertebrates [START_REF] Reed | A Risk Assessment Example For Soil Invertebrates Using Spatially Explicit Agent-Based Models[END_REF], in pollinators [START_REF] Bryden | Chronic sublethal stress causes bee colony failure[END_REF], and in plants (Schmolke et al., 2018). This effect of density level led some authors to point out the specihcity of the démographie response of rare or endangered species to PPP exposure [START_REF] Topping | Risk assessment of uk skylark populations using life-history and individual-based landscape models[END_REF]. Taking into account density-dependence phenomena can complicate the mathematical analysis of structured models, as well as the degree of knowledge required for the parameterization of simulation models. Similarly to the habits in generic ERA [START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF], our PPP case studies show that 80% of ABMs include density-dependence against only 40% of structured models. One of the great advantages of ABMs is to make these density-dependence phenomena emerge from individual behaviors and thus mechanistically include the effects of PPP at the heart of these processes, as illustrated by the interplay of the démographie effect of neonicotinoids and the size of bumblebee colonies [START_REF] Crall | Social buffering of pesticides in bumblebees: Agent-based modeling of the effects of colony size and neonicotinoid exposure on behavior within nests[END_REF].

One current perspective for increasing the ecological relevance of popula tion models is the considération of PPP multigenerational effects in ERA. As illustrated by pioneer studies on the transgenerational effects of fungicides acting as endocrine disruptors in wild rodent populations [START_REF] Dalkvist | Population-level impacts of pesticide-induced chronic effects on individuals dépend more on ecology than toxicology[END_REF][START_REF] Dalkvist | Landscape structure médiates the effects of a stressor on held vole populations[END_REF], ABMs are particularly well suited to take into account the exposure history according to the pedigree of individuals and the transfer of effects between générations. Moreover, while population genetic models hâve been integrated in the study of PPP résistance for several years [START_REF] Onstad | Modeling évolution of diabrotica virgifera virgifera (coleoptera: Chrysomelidae) to transgenic corn with two insecticidal traits[END_REF], the micro-evolutionary aspects possibly leading to adaptation and associated htness costs are up to now totally absent from PPP population modeling for non-target species. But here again, ABMs seem particularly promising for integrating this type of long-term effects once they are better documented in the ecotoxicological literature, following the example of quantitative genetics modeling practices used in pest résistance management [START_REF] Ives | Spatio-temporal variation in landscape composition may speed résistance évolution of pests to bt crops[END_REF][START_REF] Slater | Use Of An Individual-Based Simulation Model To Explore And Evaluate Potential Insecticide Résistance Management Strategies[END_REF].

Intégration of recovery processes, from individual to population level recovery

Population models place the assessment of PPP effects at larger spatial and temporal scales than the évaluation solely focused on toxicological individual responses [START_REF] Forbes | Ecological models in support of regulatory risk assessments of pesticides: developing a strategy for the future[END_REF]. Agricultural treatments cause toxic stresses that may be episodic and punctual (puise exposure) or localized in the habitat space of non-target populations. Various population studies hâve thus focused on the capacity for population recovery after exposure to PPP [START_REF] Wang | Démographie uncertainty in ecological risk assessments[END_REF][START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF][START_REF] Wang | From home range dynamics to population cycles: Validation and realism of a common vole population model for pesticide risk assessment[END_REF][START_REF] Mintram | Assessing population impacts of toxicant-induced disruption of breeding behaviours using an individual-based model for the three-spined stickleback[END_REF], implying the capacity for recolonization from uncontaminated refuge areas on small spatial scales [START_REF] Van Den | An individual-based approach to model spatial population dynamics of invertebrates in aquatic ecosystems after pesticide contamination[END_REF][START_REF] Galic | Simulating population recovery of an aquatic isopod: Effects of timing of stress and landscape structure[END_REF][START_REF] Galic | Modeling the contribution of toxicokinetic and toxicodynamic processes to the recovery of gammarus pulex populations after exposure to pesticides[END_REF] or at larger distances, e.g., river network (Focks et al., 2014). This issue is very prédominant in the literature on the use of ecological models for PPP ERA: 60% of the case studies of population models in our corpus ht into such a framework of puise exposure, as well as 40% of the landscape studies. These developments are partly driven by the proposai to use population models to apply an ecological recovery option in PPP ERA, where législation explicitly allows limited adverse effects of PPP if recovery of exposed populations can be achieved within a given time period [START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF]Focks et al., 2014;[START_REF] Galic | Modeling the contribution of toxicokinetic and toxicodynamic processes to the recovery of gammarus pulex populations after exposure to pesticides[END_REF]. The literature offers different définitions and a mul titude of recovery indicators, which refer to a return to a pre-exposure State, or a state simulated in a control scénario. This population state can be of dif ferent natures, based on the abundance or on the level of occupancy of the different patches of the population distribution area [START_REF] Topping | Towards a landscape scale management of pesticides: Era using changes in modelled occupancy and abundance to assess long-term population impacts of pesticides[END_REF]. PPP impacts and their acceptability are dehned in terms of recovery capac ity, recovery time, response amplitude, probability of extinction, or duration of low-level density period, e.g., [START_REF] Wang | Démographie uncertainty in ecological risk assessments[END_REF]; [START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF]; [START_REF] Hayashi | Ecological Risk Assessment Of Herbicides In Japan: Integrating Spatiotemporal Variation In Exposure And Effects Using A Multimedia Model And Algal Density Dynamics Models[END_REF]; [START_REF] Thursby | Coupling toxicokinetictoxicodynamic and population models for assessing aquatic ecological risks to time-varying pesticide exposures[END_REF]. Population models can be used to identify the déterminants of recovery capacity, in particular to distinguish between autogenic (local démographie recovery) and allogenic (recolonization) capacity, e.g., [START_REF] Van Den | An individual-based approach to model spatial population dynamics of invertebrates in aquatic ecosystems after pesticide contamination[END_REF]; EFS A PPR Panel (2018b); Schaefer et al. (2017). From an applied point of view, highlighting the importance of migratory processes in population recovery within agricultural landscapes justifies the préservation of spatial connectivity and the importance of refuge zones [START_REF] Galic | Simulating population recovery of an aquatic isopod: Effects of timing of stress and landscape structure[END_REF][START_REF] Galic | Modeling the contribution of toxicokinetic and toxicodynamic processes to the recovery of gammarus pulex populations after exposure to pesticides[END_REF]Focks et al., 2014). Modeling can also allow the évaluation of sustainable levels of treatment frequency for populations (Focks et al., 2014) following similar méthodologies developed in biocontrol and for the pest management [START_REF] Stark | Estimating susceptibility of biological control agents to pesticides: influence of life history strategies and population structure[END_REF][START_REF] Tonnang | Advances in crop insect modelling methods-towards a whole System approach[END_REF][START_REF] Tang | A general model of hormesis in biological Systems and its application to pest management[END_REF].

A ssessm ent of P P P im pacts at the com m unity level

Statistical extrapolation using SSD approaches

There are two main types of standard outputs when performing SSD anal yses. When SSD is used in a prospective risk assessment, the final aim is to dérivé Predicted No-effect Concentrations (PNEC) and the derived Toxicity Exposure Ratios (TER). The PNEC is a prospective level of environmental safety corresponding to the concentration below which adverse effects are not expected to occur (European Commission, 2003). The TER is dehned as the ratio of the measure of the effects (e.g., LD^o, LC$o, NOËL) to the estimated exposure. It is the reciprocal of a risk quotient (RQ) or a hazard quotient (HQ, [START_REF] Stephenson | Glossary of terms relating to pesticides (ITJPAC Recommendations 2006)[END_REF]). In a rétrospective assessment of the level of environmental safety, EQS are preferred, especially in the context of the Water Framework Directive (WFD, Technical Guidance Document (2011), [START_REF] Lepper | Towards the Dérivation of Quality Standards for Priority Substances in the Context of the Water Framework Directive[END_REF]). Within the WFD, a distinction is even made between the annual average EQS (AA-EQS) and the maximum allowable concentration EQS (MAC-EQS) values [START_REF] Brock | Aquatic Risks of Pesticides, Ecological Protection Goals, and Common Aims in European Union Législation[END_REF].

For both types of apical criteria (namely, final decision criteria that will be used by regulators), the main standard output derived from SSD is the HCP statistically corresponding to the pth percentile of the probability distribution that is htted to toxicity input values. As stated by [START_REF] Posthuma | Species Sensitivity Distributions In Ecotoxicology[END_REF], the HCP is the exposure concentration assumed to be protective for (1 -p)% of the species within the considered ecosystem. Most of the time, the HC$ is calculated, at least for PPP [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF]Van Den Brink et al., 2006;[START_REF] Daam | Does the actual standard of 0.1 mu g/L overestimate or underestimate the risk of plant protection products to groundwater ecosystems?[END_REF][START_REF] Mensah | Dérivation of South African water quality guidelines for Roundup (R) using species sensitivity distribution[END_REF][START_REF] Ramo | Environmental risk assessment of pesticides in the River Madré de Dios, Costa Rica using Perpest, Ssd, and Mspaf models[END_REF][START_REF] Iwasaki | Does The Choice Of Noec Or EclO Affect The Hazardous Concentration For 5% Of The Species?[END_REF][START_REF] Van Den | Exposure Pattern-Specihc Species Sensitivity Distri butions For The Ecological Risk Assessments Of Insecticides[END_REF][START_REF] Baillard | Effect of interspecific compétition on species sensitivity distribution models: Analysis of plant responses to Chemical stress[END_REF]. Almost ail tools associate uncertainty limits around the mean or the médian of the delivered HCp esti mâtes. The PNEC can be calculated from the HC$ (Tier-2 PNEC), accounting for uncertainty by dividing the HC$ by a certain coefficient. According to authors, the relationship between the HC$ and the PNEC may differ: it can be assumed equal to the médian HC$ [START_REF] Brock | Aquatic Risks of Pesticides, Ecological Protection Goals, and Common Aims in European Union Législation[END_REF], to its lower-limit [START_REF] Daam | Does the actual standard of 0.1 mu g/L overestimate or underestimate the risk of plant protection products to groundwater ecosystems?[END_REF], to the ratio of the HC$ by an uncertainty factor [START_REF] Mentzel | Development Of A Bayesian Network For Probabilistic Risk Assessment Of Pesticides[END_REF]; in the regulatory context, either to the ratio of the HC$ by an appropriate Assessment Factor (AF, European Commission 2003) or also equal to the médian HCz estimate [e.g., EFSA PPR Panel (2015b)). Note that ratios based on SSD outputs are now preferred: for example the Tier-1 Regulatory Acceptable Concentration (RAC) is an EC^o/AF, while the Tier-2B RAC is an EfC^/AF as usually preferred in aquatic risk assessment [START_REF] Efsa Ppr Panel | Scientihc Opinion On Good Modelling Practice In The Context Of Mechanistic Effect Models For Risk Assessment Of Plant Protection Products[END_REF]. Note that in EFSA PPR Panel (2013), the TER is rather denoted as ETR (standing for exposure-toxicity ratio), dehned as the Pre dicted Environmental Concentration (PEC) over the RAC. A value of ETR < 1 (that is PEC < RAC) indicates an acceptable risk. Other calculations from single or very few toxicity indices for isolated species are more related to the REACH terminology, such as for example the RQ equal to the PEC over the PNEC [START_REF] Iwasaki | Does The Choice Of Noec Or EclO Affect The Hazardous Concentration For 5% Of The Species?[END_REF][START_REF] Sorgog | Quantifying the précision of ecological risk: Conventional assessment factor method vs. species sensitivity distribution method[END_REF].

The application of S SD in a rétrospective risk assessment of Chemicals consists in predicting a fraction of the community which is likely to be impacted by a spécifie concentration of a given substance. Then, the standard output is the Potentially Affected Fraction (PAF) [START_REF] Zwart | Ecological Effects of Pesticide Use in The Netherlands: Modeled and Observed Effects in the Field Ditch[END_REF].

Regarding mixtures studied via SSD, most analyses aim at calculating multiple-substance P AF or m sPAF. Such outputs corne from a combination of SSD for each individual compound with CA or RA models [START_REF] Jesenska | Validation of the species sensitivity distribution in rétrospective risk assessment of herbicides at the river basin scale-the Scheldt river basin case study[END_REF]. In particular, [START_REF] Jesenska | Validation of the species sensitivity distribution in rétrospective risk assessment of herbicides at the river basin scale-the Scheldt river basin case study[END_REF] evaluated the impact of different data validation approaches (such as removal of duplicate values and outliers, testing of different exposure durations and purity levels of studied herbicides, using different sets of input data, namely NOEC vs. EC50, and considering different taxonomie groups) in a rétrospective model case study. Interestingly, they conclude that the use of rough non-validated data seems to provide robust results, especially when few ecotoxicity values are available for certain compound(s).

Analysis and prédiction of possible indirect PPP effects within communities

Even if the SSD method does not account for any species interaction, comparing the SSD method used at Tier-2 to food-chain models at Tier-3 of ERA, [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF] stated that a protection level based on direct effects (such as reflected by the F[C$ estimate) could also protect against indirect effects. Nevertheless, while unavoidable within community experiments, indirect effects are not very often directly studied and accounted for in models at the commu nity level, in general. Only [START_REF] Clemow | A Rehned Ecological Risk Assessment for California Red-legged Frog, Delta Smelt, and California Tiger Salamander Exposed to Malathion[END_REF] used an SSD-based approach to highlight both direct and indirect effects for hsh and aquatic invertebrates exposed to malathion. Compared to the SSD concept and food-chain models, the PERPEST model was proposed to account for more information on ecological risks when a common toxicological MoA is evaluated [START_REF] Van Den | Perpest model, a case-based reasoning approach to predict ecological risks of pesticides[END_REF], 2006); indeed the PERPEST model considers both recovery and indirect effects. In brief, the PERPEST simultaneously predicts the probability of classes of effects (no, slight, or clear effects, plus an optional indication of recovery) on various grouped endpoints of a particular concentration of a PPP on community endpoints (e.g., community metabolism, phytoplankton, and macro-invertebrates). It is entirely based on literature data gathered in a database to perform prédiction where no effects on a semi-held scale hâve been published. The PERPEST model was specihcally emplopyed to address direct and indirect effects in Van Den Brink et al. (2006) and successfully applied to PPP [START_REF] Daam | Does the actual standard of 0.1 mu g/L overestimate or underestimate the risk of plant protection products to groundwater ecosystems?[END_REF][START_REF] Ramo | Environmental risk assessment of pesticides in the River Madré de Dios, Costa Rica using Perpest, Ssd, and Mspaf models[END_REF]. [START_REF] Reeg | Modelling direct and indirect effects of herbicides on non-target grassland communities[END_REF] studied direct and indirect effects of herbicides on non-target grassland communities.

In fact, food-web models are more appropriate to deal with indirect effects. For example, [START_REF] Traas | A freshwater food web model for the combined effects of nutrients and insecticide stress and subséquent recovery[END_REF] 2018) appeared as addressing the issue of biomagnification. Indeed, they employed the AQUATOX framework to simulate aquatic trophic guild dynamic accounting for hydrodynamics and nutrients together with the dynamics of the exposure substance and its métabolites: they showed a significant biomagnification of métabolites. However, the issue of bioaccumulation is mentioned several times within food-web studies [START_REF] Nfon | Development of a dynamic model for estimating the food web transfer of Chemicals in small aquatic ecosystems[END_REF][START_REF] Ren | Biomagnihcation of persistent organic pollutants along a high-altitude aquatic food chain in the Tibetan Plateau: Processes and mechanisms[END_REF], while it has been far more basically addressed by [START_REF] Sanchez-Bayo | Ecological relative risk (Ecorr): Another approach for risk assessment of pesticides in agriculture[END_REF] via the use of the Ecological Risk Ratio (EcoRR) approach.

Development of tools that integrate both exposure and effects

From a particular case study on bees, [START_REF] Crenna | Characterizing Honey Bee Exposure and Effects From Pesticides For Chemical Prioritization and Life Cycle Assessment[END_REF] underlined how important it is to consider both exposure and effects across ail applied PPP, instead of focusing only on PPP with high ecotoxicity potentials or modes of action specihcally targeting insects. Nevertheless, combined studies that looked at both exposure and effects are rather rare within our corpus. At the community level, a hrst attempt was made by [START_REF] Sanchez-Bayo | Ecological relative risk (Ecorr): Another approach for risk assessment of pesticides in agriculture[END_REF] with its EcoRR approach, while a deeper intégration of both aspects came later with [START_REF] Nfon | Development of a dynamic model for estimating the food web transfer of Chemicals in small aquatic ecosystems[END_REF] who combined fate and food-web models to estimate the food-web transfer of Chemicals in small aquatic ecosystems. Then, thanks to the AQUATOX models, improvements in integrating both exposure and effect modelling was undertaken either for trophic guilds of aquatic organisms [START_REF] Scholz-Starke | Simulation-based assessment of the impact of fertiliser and herbicide application on freshwater ecosystems at the Three Gorges Réservoir in China[END_REF] or lake ecosystems [START_REF] Galic | Predicting impacts of Chemicals from organisms to ecosystem service delivery: A case study of insecticide impacts on a freshwater lake[END_REF].

The SYNOPS-WEB model [START_REF] Strassemeyer | Synops-Web, an online tool for environmental risk assessment to evaluate pesticide strategies on held level[END_REF] allows quantita tive assessment of the potential risk of PPP for the environment (leaching to groundwater) and for various Reference Species (RS) in soil (RS: earthworms), surface water (RS: algae, Lemna sp., Daphnia sp., Chironomus sp. and hsh) and held margins (RS: bees). The acute and chronic risk indices are calculated as exposure toxicity ratio (ETR) where the PEC (in soil, surface water or held margin) is related to a toxicity value of the considered RS. For multi ple application events and multiple active ingrédients, the acute risk of a full application strategy is considered as the maximum risk posed by ail appli cation events and ail active ingrédients applied within one végétative period. The chronic risk values are aggregated additively for each RS according to the concept of CA. The chronic risk aggregation of an application pattern is carried out in two steps: hrst, the chronic risk values are calculated for each applied active ingrédient and added on a daily basis to dérivé curves of ETR sums; second, the maximum of these ETR-sum-curves is derived thus constituting the chronic risk of the full application strategy. It was demonstrated that SYNOPS-WEB reliably modelled the PPP exposure of aquatic organ isms. The model could be improved with the intégration of more mitigation measures such as strip till techniques, mulch seeding, création of buffer strips or multi-functional held margins [START_REF] Strassemeyer | Synops-Web, an online tool for environmental risk assessment to evaluate pesticide strategies on held level[END_REF].

Among models accounting for both exposure and effects, there is also the work by Baudrot et al. (2020) who developed a heuristic non-spatialized model including montane water voles, specialist vole predators and the red fox as a generalist predator consuming voles, mustelids and other preys. Thanks to a broad-range sensitivity analysis on poorly informed toxicological parameters, they investigated the impact of hve farmer functional responses (that is varying amounts of anticoagulant rodenticide spread according to different thresholds in vole densities) on predator-prey relationships, anticoagulant rodenticide transfer across the trophic chain and population effects.

At last, Baudrot et al. ( 2021) made a step further developing a spatiallyexplicit exposure-hazard model considering both the dynamics of pollen dispersai obtained by convolving genetically modihed plants émission with a dispersai kernel and a TKTD model accounting for the impact of toxin inges tion on individual survival of on non-target Lepidoptera. This exposure-effect combined modelling approach allowed authors to better assess the ecological risk of Bt-maize at the landscape scale.

S tren g th s an d lim ita tio n s o f th e em p lo y m en t o f th e different m o d el ca teg o ries in P P P E R A

G e n e ricity and tr a n sv ersa lity

A pplicability of population models: from general to local case-study spécifie ERA

There is a consensus in the literature on the complementarity between simple generic population models addressing large scale questions for ERA of PPP {e.g., identification of species at risk at a national level with respect to a cer tain type of PPP use) and more précisé and spécifie modeling at local scales (e.g., influence of landscape éléments, or spécifie agricultural practices on a species locally at risk) [START_REF] Topping | Risk assessment of uk skylark populations using life-history and individual-based landscape models[END_REF][START_REF] Forbes | Assessing pesticide risks to threatened and endangered species using population models: Findings and recommendations from a croplife america science forum[END_REF]. Decision guides for the choice of population models now make it possible to identify the trade-offs to be made between genericity, realism and précision of an ERA according to its objectives [START_REF] Raimondo | Popguide: Population modeling guidance, use, interprétation, and development for ecological risk assessment[END_REF]. One of the strong aspects of population model frameworks is their portability between species, as already illustrated for birds [START_REF] Etterson | Mechanistic modeling of insecticide risks to breeding birds in North American agroecosystems[END_REF], pollinators [START_REF] Becher | Bumble-beehave: A Systems model for exploring multifactorial causes of bumblebee décliné at individual, colony, population and community level[END_REF], earthworms [START_REF] Forbes | Mechanistic effect modeling of earthworms in the context of pesticide risk assessment: synthesis of the foresee workshop[END_REF], and plants (Schmolke et al., 2018). This rapid cross-species transposition of population models (especially structured models) benefits from the recent constitution of large ecological databases of démo graphie traits in conservation science (e.g., in birds, fish, mammals, plants). It allows the rapid parameterization of population models on a large number of species and it could help in the relative ranking of species vulnerabilities to the different uses of PPP [START_REF] Forbes | Assessing pesticide risks to threatened and endangered species using population models: Findings and recommendations from a croplife america science forum[END_REF][START_REF] Etterson | Mechanistic modeling of insecticide risks to breeding birds in North American agroecosystems[END_REF][START_REF] Rueda-Cediel | Comparative analysis of plant démographie traits across species of different conservation concern: Implications for pesticide risk assessment[END_REF]. On the other hand, mechanistic population models can also be adapted to local or population-specific conditions by incorporating the influ ence of environmental parameters on individual biological input variables and species phenology (50% of the case studies in our corpus integrate such influ ence). The assessment of PPP population impacts is then refined, for example, according to température conditions in chironomids [START_REF] Diepens | Dynamics and Recovery Of A Sediment-Exposed Chironomus Riparius Population: A Modelling Approach[END_REF] or in aquatic plants [START_REF] Schmitt | Mechanistic TK/TDmodel simulating the effect of growth inhibitors on Lemna populations[END_REF], according to trophic and dietary con ditions, such as in daphnids [START_REF] Preuss | The potential of individual based population models to extrapolate effects measured at standardized test conditions to relevant environmental conditions-an example for 3, 4-dichloroaniline on daphnia magna[END_REF], bee [START_REF] Abi-Akar | Simulating honey bee large-scale colony feeding studies using the beehave model-part ii: analysis of overwintering outcomes[END_REF], partridge [START_REF] Millot | Little field evidence of direct acute and short-term effects of current pesticides on the grey partridge[END_REF], or in function of different landscape structures (Focks et al., 2014;[START_REF] Topping | Landscape Structure and Man agement Alter The Outcome Of A Pesticide Era: Evaluating Impacts Of Endocrine Disruption Using The Almass European Brown Hare Model[END_REF]. This also enables the projection of scénarios of climate change or land use évolution [START_REF] Nogeire-Mcrae | Land use change and rodenticide exposure trump climate change as the biggest stressors to san joaquin kit fox[END_REF] as can be done in the field of pest control [START_REF] Donatelli | Modelling The Impacts Of Pests and Diseases On Agricultural Systems[END_REF]. These environmental factors may constitute stressors additional to PPP, and population models are mobilized to compare PPP relative impacts in multi-stress contexts (hypoxia and insecticides in salmon, [START_REF] Landis | Intégration of chlorpyrifos acetylcholinesterase inhibition, water température, and dissolved oxygen concentration into a régional scale multiple stressor risk assessment estimating risk to chinook salmon[END_REF], insecticides and parasitism in pollinators in [START_REF] Becher | BEEHAVE: A Systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure[END_REF][START_REF] Schmolke | Honey bee colony-level exposure and effects in realistic landscapes: An application of beehave sim ulating clothianidin residues in corn pollen[END_REF], flooding régime and herbicides in a threatened plant in Schmolke et al. 2017).

Lim itation and applicability of m ixture m odels to environm ental case studies

Regarding environmental monitoring and risks, mixture models hâve been used for many years to assess the risks estimated from monitoring data on envi ronmental concentrations [START_REF] George | Assessment of the probabilistic ecological risk assessment-toxic équivalent combination approach for evaluating pesticide mixture toxicity to zooplankton in outdoor micro cosms[END_REF][START_REF] Schuler | Aquatic risk assessment of herbicides in freshwater ecosystems of south Florida[END_REF][START_REF] Vaj | Assessing, mapping and validating site-specihc ecotoxicological risk for pesticide mixtures: A case study for small scale hot spots in aquatic and terrestrial environments[END_REF][START_REF] Chen | Risk assessment for pesticide mixtures on aquatic ecosystems in China: A proposed framework[END_REF]. [START_REF] Cruzeiro | Environmental assessment of pesticides in the Mondego River Estuary (Portugal)[END_REF] measured 56 priority PPP belonging to distinct categories (insecticides, herbicides and fungicides) in 42 surface water samples. Based on the CA and IA models, they used a two-tiered approach to assess the hazard of the PPP mixture, at the maximum concen tration found, reflecting a potential risk. In the same way, [START_REF] Kuzmanovic | Ecotoxicological risk assessment of Chemical pollution in four Iberian river basins and its relationship with the aquatic macroinvertebrate community status[END_REF] assessed ecotoxicological risks of Chemical pollution in four Iberian river basins and its relationship with the aquatic macro-invertebrate community status using a data set including more than 200 emerging and priority compounds measured at 77 sampling sites along four river basins. The Toxic Units (TU) approach was used to assess the risk of individual compounds and the CA model to assess the site-specific risk. A difficulty highlighted by [START_REF] Perez | Growth rate of Pseudokirchneriella subcapitata exposed to herbicides found in surface waters in the Alqueva réservoir (Portugal): A bottom-up approach using binary mixtures[END_REF] is that shifts for synergism and/or antagonism might occur depending on the dominant Chemical présent. However, [START_REF] Verro | Predicting Pesticide Envi ronmental Risk in Intensive Agricultural Areas. Ii: Screening Level Risk Assessment of Complex Mixtures in Surface Waters[END_REF] exposed several considérations that support the suitability of the CA model for assessing risk for ecologically relevant PPP mixtures. These authors said that a few Chem icals are responsible for > 80% of the toxicity, rendering différences between CA and IA prédictions very small. Moreover, the most toxic components of the mixtures often hâve the same MoA. A geo-referenced représentation of results allows analyzing the spatial pattern of toxic mixture assemblage in order to prioritize the locations at risk and to detect the group of compounds causing the greatest risk at different scales [START_REF] Faggiano | Patterning ecological risk of pesticide contamination at the river basin scale[END_REF]. However, predicting the effect from mixture assumes that the compounds will co-occur spatially and temporally which is not always the case [START_REF] Faggiano | Patterning ecological risk of pesticide contamination at the river basin scale[END_REF].

Moreover, évaluation of effects on organisms at stimulatory doses of Chem icals, known as hormesis, lacks a common statistical approach for mixtures [START_REF] Belz | Predicting hormesis in mixtures of herbicidal compounds -where are we and how far can we go?[END_REF]. Prédiction of effective hormetic doses can be facilitated by using joint action models but to date there is no mechanistic models to predict the hormetic magnitude in mixtures. The IA model assumes a dissimilar MoA and multiplicity of effects up to a maximum response of 100% [START_REF] Streibig | Actions of herbicides in mixtures[END_REF], which is inappropriate to model hormetic doses leading to a response of > 100 [START_REF] Belz | Predicting hormesis in mixtures of herbicidal compounds -where are we and how far can we go?[END_REF]. Nevertheless, some promising attempts were made to predict the hormetic magnitude. The sélection of a reference model like CA can be used to describe mixtures of dissimilarly and similarly acting compounds [START_REF] Belz | Predicting hormesis in mixtures of herbicidal compounds -where are we and how far can we go?[END_REF]. If the observed mixture data deviates synergistically or antagonistically from a reference model, the predefined curved isobole models of Hewlett or Vqlund are available to model observed déviation patterns [START_REF] Sorensen | An Isobole-Based Statistical Model and Test For Synergism/Antagonism In Binary Mixture Toxicity Experiments[END_REF].

U n c e r ta in ty an d m o d ellin g p ra ctices

In the guidance on how to characterize, document and explain uncertainties in risk assessment recently published by EFSA (EFSA Scientific Committee, 2018), uncertainty analyses are the process of identifying limitations in sci entific knowledge and evaluating their implications for scientific conclusions. ERA relies on a very general définition of the uncertainty, that is referring to ail types of limitations in available knowledge that affect the range and probability of possible answers to an assessment question. Focusing on the modelling cycle, it is strongly recommended, if not mandatory, to quantify the parameter uncertainty (for example with 95% confidence or credibility intervals), but also to include a sensitivity analysis, an uncertainty analysis and the comparison of prédictions with observed data when setting up the model (EFSA PPR Panel, 2014). In particular, if the model is eventually to be used to extrapolate from one situation to another, the resulting effect on the level of uncertainty should be clearly stated.

In support of the above general statement, note that within the guidance document on tiered risk assessment of PPP for aquatic organisms in edgeof-field surface waters (EFSA PPR Panel, 2013), it is clearly recommended that:

• A qualitative évaluation of the uncertainties affecting refined RA should be provided based on a tabular approach. In case of multiple fines of evidence, uncertainties affecting each line should be evaluated separately. • If the qualitative évaluation of uncertainty reveals not sufficient to détermine whether an unacceptable level of impact may occur, it is required to either (i) make an effort to get additional data to reduce the uncertainty, or (ii) use deterministic or probabilistic methods to refine uncertainty quantification.

(Q )SA R m odels

In general, the uncertainty of the (Q)SAR models is well characterized due to the conformation of the models to the OECD (Q)SAR validation principles (see Section 4.1.1). First, the recent (Q)SAR models were always developed using a training and a validation data set (80% -20% of the data set generally) and could also be evaluated on another external data set (Figure 7). In addition, several traditional validation metrics are applied to assess the accuracy, the stability/robustness and the reliability of the (Q)SAR models (reviewed in Gramatica and Sangion 2016):

• G oodness-of-fit: Root Mean Square Error (RMSE), détermination coeffi cient (R2), détermination coefficient adjusted (R2dj), and Lack Of Fit (LOF) which was dehned as being proportional to the least-squares error corrected by the number of descriptors and the number of training data [START_REF] Furuhama | Development of Qsaar and Qaar models for predicting fish early-life stage toxicity with a focus on industrial Chemicals[END_REF] Elsewhere, numerous quantitative and graphical quality indicators for clas sification models can be applied [START_REF] Venko | Classification models for identifying substances exhibiting acute contact toxicity in honeybees (Apis mellifera)[END_REF]. In binary classifications, such as toxic (positive) or non-toxic (négative), several metrics were computed to assess the model qualities: accuracy (proportion of any substances correctly classihed), sensitivity (proportion of true positives correctly classihed), specihcity (proportion of true négatives correctly classihed), and efficacy (pro portion of de-prioritization candidates) [START_REF] Benigni | Evaluation of the applicability of existing (q)sar models for predicting the genotoxicity of pesticides and similarity analysis related with genotoxicity of pesticides for facilitating of grouping and read across: An efsa funded Project[END_REF][START_REF] Herrmann | Q)Sar tools for the prédiction of mutagenic properties: Are they ready for application in pesticide régulation?[END_REF].

The reliability of the (Q)SAR model prédictions is also due to their domain of applicability. Leverage is one of the standard methods for the analysis of the domain of applicability of the model. The leverage value hd for the ith PPP is calculated from the descriptor matrix and compared to their critical leverage value (h*) depending on the number of variables used in the model and on the number of training compounds (Basant et al., 2015b). The value of hi > h* indicates that the structure of the compound substantially dif fère from those used for the calibration. Therefore, the compound is located outside the optimum prédiction space. Frequently, the Williams plot is considered for representing the domain of applicability of the (Q)SAR models. This graph represents the standardized residual value according to the lever age value (Figure 7) (Basant et al., 2015b). Some software, such as the open source platform VEGA-HUB, assess the reliability of the prédiction using the Applicability Domain Index (ADI) . This index is an aggregated resuit taking into account several aspects: (i) similar molécules with known experimental value and their accuracy (or average error) in their prédiction, (ii) concordance among the target and similar molécules for the experimental data, (iii) Atom Centered Fragments (ACF) similarity check, (iv) descriptors noise sensitivity analysis, and (v) model descriptors range check [START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF].

Finally, accuracy, stability/robustness and reliability of most of the (Q)SAR models were generally checked during the last fifty years on PPP toxicity (Basant et al., 2015a[START_REF] Basant | Modeling the toxicity of Chemical pesticides in multiple test species using local and global qstr approaches[END_REF][START_REF] Carnesecchi | Integrating QSAR models predicting acute contact toxicity and mode of action pro filing in honey bees ( A. mellifera ): Data curation using open source databases, performance testing and validation[END_REF][START_REF] Hamadache | Qsar mod eling in ecotoxicological risk assessment: application to the prédiction of acute contact toxicity of pesticides on bees (apis mellifera 1.)[END_REF][START_REF] Venko | Classification models for identifying substances exhibiting acute contact toxicity in honeybees (Apis mellifera)[END_REF]. In addition, some of the papers published before hâve been re-assessed for their consistency with these principles [START_REF] Pavan | Review of literature-based quantitative structure-activity relationship models for bioconcentration[END_REF]. Moreover, according to the OECD guidance document (OECD, 2014), the consensus approach can be applied when several complementary models are available. Thus, the newly developed models would contribute to more reliable prédictions of toxicity of PPP [START_REF] Venko | Classification models for identifying substances exhibiting acute contact toxicity in honeybees (Apis mellifera)[END_REF]. Concordance with ail these principles guarantees rigorous and independent validation of (Q)SAR models which is an essential step toward their regulatory acceptance [START_REF] Eriksson | Methods for reliability and uncertainty assessment and for applicability évaluations of classihcation-and regression-based qsars[END_REF].

D R and T K T D m odels

Most probably due to old habits in ERA, but maybe also due to a lack of computer resources some décades ago, uncertainties associated with the use of DR models are still rarely fully reported, meaning not systematically, usually only summarized by rough standard déviations. On the contrary, among works based on TKTD models, there is an increasing number of contributions providing information on uncertainties, in various forms depending on the inference method used. [START_REF] Baudrot | Recommendations To Address Uncertainties In Environmental Risk Assessment Using Toxicokinetics-Toxicodynamics Models[END_REF] even proposed some useful recommendations to address uncertainties in ERA using TKTD models. [START_REF] Fraser | Modeling biomagnification and metabolism of contaminants in harp seals of the Barents Sea[END_REF] discussed of uncertainty in biomagnihcation factors and half-lives of métabolites, while [START_REF] Weijs | Applica tion of Bayesian Population Physiologically Based Pharmacokinetic (Pbpk) Modeling and Markov Chain Monte Carlo Simulations to Pesticide Kinetics Studies in Protected Marine Mammals: Ddt, Dde, and Ddd in Harbor Porpoises[END_REF] used a Morris sensitivity analysis followed by the eFAST test to quantitatively test the influence of the most sensitive parameters on their model output. We also noticed an increas ing use of probabilistic methods, such as Bayesian inference [START_REF] Weijs | Applica tion of Bayesian Population Physiologically Based Pharmacokinetic (Pbpk) Modeling and Markov Chain Monte Carlo Simulations to Pesticide Kinetics Studies in Protected Marine Mammals: Ddt, Dde, and Ddd in Harbor Porpoises[END_REF] or Bayesian Networks (BN) [START_REF] Kaikkonen | Bayesian Networks In Environmental Risk Assessment: A Review[END_REF][START_REF] Mentzel | Development Of A Bayesian Network For Probabilistic Risk Assessment Of Pesticides[END_REF], which hâve proven their efficiency in quantifying uncertainties. And to go in the same direction, [START_REF] Rubach | Toxicokinetic Variation In 15 Freshwater Arthropod Species Exposed To The Insecticide Chlorpyrifos[END_REF] hâve even illustrated that a complementary use of least-squares htting with the Levenberg-Marquardt (LM) algorithm and Monte Carlo Markov Chain (MCMC) methods is much more useful than the use of LM alone.

Population and landscape m odels

The uncertainty associated with the outputs of population or landscape mod els is very often addressed by these up-scaling tools, which methodologically rely on different sensitivity or elasticity analyses (50% of the models in the corpus) or which integrate environmental stochasticity into the scénarios tested (60% of the studies). The outputs of these models are thus most often expressed in the form of distributions of values or probabilities of démo graphie effects. However, the fact that an uncertainty is almost systematically expressed in the outputs of these models should not make us forget the reductionist aspect of these modelling approaches which, by définition, can only focus on a limited number of processes. Also, this issue is of high relevance considering that the use of population and landscape models is proposed in the literature to contribute to higher Tier assessment of PPP (refinement for population-level endpoints) [START_REF] Forbes | Ecological models in support of regulatory risk assessments of pesticides: developing a strategy for the future[END_REF]EFSA PPR Panel, 2018b). These models are indeed sometimes seen as surrogate cost-effective methods of achieving higher levels of ecological relevance when higher Tier data (mesocosms, field studies) are lacking [START_REF] Hanson | Utility of population models to reduce uncertainty and increase value relevance in ecological risk assessments of pes ticides: An example based on acute mortality data for daphnids[END_REF]. However, like any bottom-up approach, it only accounts for the toxic effects and environmen tal variables that are considered in the modelling processes. It is therefore important for risk assessors to bear in mind this reductionist aspect of the up-scaling approach, which is often falsely erased in view of the intégrative and population-level dimension of the outputs of these models. Hence, the efforts to propose sound decision guides, e.g., Schmolke et al. (2017); [START_REF] Raimondo | Popguide: Population modeling guidance, use, interprétation, and development for ecological risk assessment[END_REF], which explicitly State the hypothèses taken into account in the modelling process and the scope of the questions addressed for the ERA, become very important for this issue. As a warning illustration, we were able to document in our corpus some adverse effects of PPP that are mostly ignored despite their importance for population effects, and the suitability of ecological models to integrate these effects. Models, particularly ABMs, are for instance very adapted to take into account individual behaviors in the emergence of population dynamics [START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF], especially spatial behaviors. However, it appears from our case studies data set that direct behavioral disruption by PPP is actually considered in only 15% of popula tion models for animal species while more than half of these models deliver an impact assessment in a spatial frame, and less than 10% in landscape-scale studies. Another finding from our analysis of population case studies is that less than 50% of them consider sub-lethal effects (75% for structured models but 40% for ABMs). This also illustrâtes the gap that may exist between the intégrative possibilities offered by the population-modelling framework and the reductionism of the proposed assessment. This gap is mainly explained by a problem of experimental data availability on PPP sublethal effects in environmental species (effects on reproduction, individual growth, develop ment, behaviour) but also in some cases to deliberate choices in modeling assumptions. Indeed, studies that integrate only mortality for animais or population growth inhibition phenomena in algae and plants represent 50% of the studies between 2000 and 2010, 70% between 2011 and 2015 and again 50% from 2016 to 2020. This is partly related to the strong development of population recovery studies that only consider the acute léthal toxic effects of PPP during short peaks of exposure and ignore the delayed or long-term effects of environmental imprégnation by PPP.

M ulti-species m odels

SSD approaches On a general point of view, SSD analyses are expected to pro vide smaller uncertainties on apical risk assessment indices in comparison with the approach using AF that is applied for a limited number of toxicity values [START_REF] Borges | Scientific Advice on Guidance Document 21: Technical Guidance for Deriving Environmental Quality Standards[END_REF][START_REF] Jesenska | Validation of the species sensitivity distribution in rétrospective risk assessment of herbicides at the river basin scale-the Scheldt river basin case study[END_REF]. Such indices are for example the RAC as dehned in the guidance document on tiered risk assessment for PPP for aquatic organisms in edge-of-held surface waters (EFSA PPR Panel, 2013). In addition to the EU PPP régulation, water bodies are also regulated by the WFD Technical Guidance Document (2011); European Commission (2002a) which provides a framework to evaluate the Chemical and ecological quality of the water bodies in the EU from EQS. Short-term (Maximal Acceptable Con centrations, MAC-EQS) and long-term (Annual Average, AA-EQS) EQS are based on ECso and EC io values, respectively, or SSD calculations.

Even if not systematically provided when delivering HCp estimâtes, the uncertainty is nevertheless sometimes taken into considération [START_REF] Daam | Does the actual standard of 0.1 mu g/L overestimate or underestimate the risk of plant protection products to groundwater ecosystems?[END_REF]Van Den Brink et al., 2006). [START_REF] Van Dam | Ecological risk assessment of tebuthiuron following application on tropical Australian wetlands[END_REF] tried to identify possible uncertainty sources in using SSD. First, they noted that small sample sizes when characterizing SSD added substantial uncertainty to the assessment. Another factor contributing to uncertainty is the unknown ability of the considered species to recover following exposure to the compounds under study. They also established that uncertainty may surround the expo sure characterization. [START_REF] Van Dam | Ecological risk assessment of tebuthiuron following application on tropical Australian wetlands[END_REF] concluded that, although the uncertainty can be quantihed using the confidence limits around the htted probability distributions, which in some cases spanned an order of magnitude of the reported ELPp values, the data variability is usually high, a part never explained by the models. Very interestingly, Kon Kam King et al. ( 2015) innovated with a hierarchical approach of the SSD exploiting its founding basis that ail tested species represent a random sample from a theoretical community so that their responses follow a distribution; this means that parameters describing the DR of each species within the sample follow a probability distribution themselves. In this approach, species for which the response is characterized with large uncertainty on the parameters of the DR, or where data are missing, contribute less to final htted SSD. Kon Kam [START_REF] Kam King | Hierarchical modelling of species sensitivity distribution: Development and application to the case of diatoms exposed to several herbicides[END_REF] were hnally able to provide EtC$ estimâtes accounting for the uncertainty of the original raw data. At last, even if identihed a long time ago [START_REF] Aldenberg | Uncertainty Of The Hazardous Concentration and Fraction Affected For Normal Species Sensitivity Dis tributions[END_REF][START_REF] Verdonck | Uncertainty techniques in environmental risk assessment[END_REF][START_REF] Forbes | Are current species extrapo lation models a good basis for ecological risk assessment?[END_REF][START_REF] Forbes | Species Sensitivity Distributions Revisited: A Critical Appraisal[END_REF], great progress and improvements hâve only been made recently to account for uncertainties in SSD approaches. For example, to overcome some theoretical criticisms of the SSD, Bayesian inference may be used to ht SSD [START_REF] He | Ecological risk assessment and priority setting for typical toxic pollutants in the water from Beijing-Tianjin-Bohai area using Bayesian matbugs calculator (Bmc)[END_REF]. Also [START_REF] Grist | Bayesian and time-independent species sensitivity distributions for risk assessment of Chemicals[END_REF] demonstrated that it could reduce the uncertainty. More generally, Bayesian inference and MCMC methods gradually become popular in the field of environmental science like with water quality models and hydrological models [START_REF] Jeremiah | Efficient hydrological model parameter optimization with sequential monte carlo sampling[END_REF] as it allows considering multiple issues and System components as well as handling missing data and uncertainty easily. Bayesian inference is now also successfully used in the field to environmental risk assessment (see for exam ple [START_REF] Chen | Good practice in bayesian network modelling[END_REF][START_REF] Baudrot | Recommendations To Address Uncertainties In Environmental Risk Assessment Using Toxicokinetics-Toxicodynamics Models[END_REF]Charles et al. 2021).

Community models

Usually involving a large number of parameters, community models inevitably exhibit a higher parameter uncertainty [START_REF] Strauss | The Power Of Hybrid Modelling: An Example From Aquatic Ecosystems[END_REF], compared to simpler models such as DR or even TKTD models. This is indeed a matter of fact that having more parameters to estimate (what in essence characterizes community models), if the sample size of input data sets is limited, then parameter estimâtes will be less précisé. This can be due to difficulties in making converge the optimizing algorithm in particular. The use of Bayesian inference to estimate the parameters of the mechanistic food-web model Streambugs [START_REF] Kattwinkel | Modeling Macroinvertebrate Community Dynamics in Stream Mesocosms Contaminated with a Pesticide[END_REF] perfectly illustrâtes how to adequately handle uncertainties, and how it is particularly helpful to identify potential improvements in the model structure and in the experimental design.

M ixture models

In mixture models, uncertainties will be generally larger than in assessments of single Chemical substances as there are more sources of uncertainties. As for other models, it is important to consider the uncertainties when interpreting the results. Thus, uncertainties hâve to be identihed in each stage of the mix ture model framework and an overall uncertainty analysis has to be integrated in the risk characterisation. The EFSA guidance on risk assessment of mul tiple Chemicals (EFSA Scientihc Committee, 2019) lists the most important aspects of uncertainty analysis for each step of the risk assessment of combined exposure to multiple Chemical substances.

R e p r o d u c ib ility o f m o d el o u tp u ts

The issue of reproducibility is more generally related to scientihc integrity, an issue reviewed by [START_REF] Mebane | Scientihc integrity issues in environmental toxicology and chemistry: Improving research reproducibility, credibility, and transparency[END_REF] for applied environmental sciences, with a particular emphasis on ecotoxicology. Reproducibility is only one of the prerequisites for a crédible research [START_REF] Wilkinson | The fair guiding principles for scientific data management and stewardship[END_REF] and differently concerns materials, especially data (e.g., [START_REF] Rubach | Toxicokinetic Variation In 15 Freshwater Arthropod Species Exposed To The Insecticide Chlorpyrifos[END_REF]; Reeg et al. (2018); EFSA PPR Panel (2017)), methods and results (e.g., [START_REF] Tyne | Hormesis dépends upon the life-stage and duration of exposure: Examples for a pesticide and a nanomaterial[END_REF] as described in papers. Focusing on model outputs, only few authors gave enough information for full reproducibility, given that some results cannot of course be exactly reproduced due to stochastic processes in the modelling approach [START_REF] Carr | SSDs Revisited. I. A Framework For Sample Size Guidance On Species Sensitivity Distribution Analysis[END_REF][START_REF] Schneckener | A workflow to build Pbtk models for novel species[END_REF]Charles et al., 2021;Charles et al., 2021).

M o d ellin g ap p roach es in th e E u ro p ea n P P P rég u la tio n 6.1 R e g u la to r y c o n te x t

In the European Union, the approval of an active substance and the placing of a PPP on the market require, among others, to assess their ecotoxicological effects and the corresponding risks. The soil, water (including sédiments) and air compartments are considered. The overall objective is to approve only the compounds which do not hâve any harmful effect on human or animal health or any unacceptable effects on the environment (European Commission, 2009) (see Section 2). Therefore, the régulation holds on strict approval and exclusion criteria for active substances (European Commission, 2020). In this context, prospective risk assessment based on modelling approaches is of great interest.The ecotoxicological risk assessment phase is detailed in the régulation and in the guidance documents notified at the European level (i.e., approved by the different member states), leading to a harmonized procedure between member states. In the light of the diversity of organisms potentially exposed in situ to the different PPP and their active substances, the assessment has to be done for several biological groups which are related to a wide range of environmental media: birds, aquatic organisms, arthropods, earthworms, soil non-target microorganisms, and other non-target organisms (flora and fauna) believed to be at risk. Each biological group is associated to spécifie protection goals, which will drive the choice of the methods to use (e.g., kind of tests and models) for risk assessment.

R isk a sse ssm e n t in P P P rég u la tio n

Whatever the investigated biological group, the risk assessment follows a tiered-approach which is since décades widely used within the scientific community. The tiered-approach consists of structuring the risk assessment process along a gradient of environmental representativeness, and complexity of experi mental System, leading to a refinement of the risk (Figure 9). The risk is usually assessed by comparing effect (hazard identification and characterization) and exposure. The first Tier (Tier-1) is intended to be simple and protective. It mostly relies on the use of norrnalized or standardized tests (e.g.. DR exposiue design) performed in laboratory and including one taxa (e.g., 0 1 1 e micro-algal species) exposed to one compound under controllcd conditions. As snob tests are relatively easy to rcproducc and to perforai, lhey ncglect the cffccls of various otber factors sucli as tbc biotic interactions into stress organism rcsponscs. The following tiers rely on approacbes eliaracterized by a liigber degree of environment-aï représentât iveness. Tins kind of approach aims at refining tlie risk assessment and at prodiic.ing more realistic thresbolds. In the different guidance documents, going from Tier-1 to higher tiers means, for example, to intégrale more realistic cxposurc concentra Lions into tbc risk assessment, to consider organisms susceptible to bc particularly exposed (e.g., according to tbeir habitat, feeding habits, life-cycle), to intégrale additional sensitivity data or to use more sophisticated models or experimental devices such as mesocosms (EFSA PPR Panel, 2013).

C u rren t u se o f m o d elin g in P P P r ég u la tio n

Currently, most of tbc nolified guidance document recommendations are linked to the type of tests to perforai (e.g., organism, exposure duration) and to the metliods to assess and to refine the risk assessment. Nevertheless, the use of various kinds of model is already recommended in several cases [START_REF] Efsa Ppr Panel | Scientihc Opinion On Good Modelling Practice In The Context Of Mechanistic Effect Models For Risk Assessment Of Plant Protection Products[END_REF][START_REF] Efsa | Guidance document on risk assessment for birds & mammals on request from efsa[END_REF].

First, DR modcls are widcly used for dossier constitution as il supports tbc dérivation of a sensitivity value (e.g., E C r) which can be la ter used to dérive for example an HCP as well as to assess the risk (e.g., TER). This type of model can be applied at every Tier as long as it fits modelling good practice (e.g., enough tested concentrations) but is especially of great importance in Tier-1 studies to model the required organism responses (e.g., mortality, growth, reproduction) to an increasing gradient of stress (here, Chemical concentra tion). For example, the normalized tests performed on aquatic organisms, as well as on birds or mammals, rely on such models. However, DR model can also be recommended in the context of higher Tier experiments, as it can potentially support the development of more sophisticated models.

Second, notihed guidance documents also recommend for Tier-2 approaches the use of SSD models. In the regulatory context, the SSD models présent the advantage to induce less uncertainty compared to Tier-1 approaches, as they are based on the sensitivity values of various taxa (hve to eight are at least requested depending on the biological group). For example, the use of SSD models is recommended for aquatic organisms, non-target plants and soil organisms but, in this last case, a methodological guidance for this kind of organisms is still required. However, SSD are not suitable models for ail of the biological groups involved in the PPP régulation (e.g., EFSA PPR Panel (2015a)).

Within the multi-species category, community models are also of great interest for regulatory purposes, especially for higher tier studies dedicated to refine risk assessment. However, working at such an ecological level could constrain their use by regulators because these community models are ail casestudy dépendent.

Finally, notihed guidance documents also recommend the use of (Q)SAR models to estimate sensitivity values, to reduce the number of tests on the biota, and to explore PPP métabolites (e.g., potential to bioaccumulate).

Over the above-cited modeling approaches, the notihed guidance docu ments also deal with other models to develop or to validate (if those models already exist but are not enough tested for a use in the regulatory context). For example, in 2013, the notihed guidance document for the aquatic organ isms (EFSA PPR Panel, 2013) highlighted that mechanistic models such as TKTD, population or food-web models hâve a great potential for effect and risk assessment. But the insuhicient insights regarding those models hâve so far prevent their use in the regulatory context. It has to be underlined that, since 2013, EFSA hâve published several documents to promote the development of models for PPP regulatory purpose, and to give to the assessors enough élé ments to understand and assess these models. These documents are detailed in the following section.

T ow ards th e im p lé m en ta tio n o f m ore m o d els in th e r eg u la to ry c o n te x t

The hndings drawn from the guidance documents currently notihed is that only few models are approved in the context of PPP régulation, and can be used routinely for ecotoxicological risk assessment. If the documents make authority and are the references for the decision-makers to state if a dossier is admissible or not, the other publications of the EFSA journal (e.g., Scientihc Opinion, CONTENTS Technical Report) draw the perspectives and provide new Unes of thinking for the next guidance documents. Figure 10 shows, in a chronological, order the publications of the guidance documents (dark blue) for the different biological groups, and the other publications such as " Scientific Opinion" and "Technical reports'' (grey) which are directly or indirectly related to the use of modeling in PPP régulation. As indicated above, several documents hâve been published in the EFSA journal since 2013 highlighting the increasing interest of EFSA for the use of modeling in this context. Those publications can be spécifie to one biological group or addressed to several groups. In 2014, the Scientific Opinion dealing with the good modeling practice in the context of mechanistic effect models for risk assessment of PPP [START_REF] Efsa Ppr Panel | Scientihc Opinion On Good Modelling Practice In The Context Of Mechanistic Effect Models For Risk Assessment Of Plant Protection Products[END_REF] showed EFSA encourages the use of mechanistic models in régulation, and the need of an harmonized procedure at the EU level for the development and the validation of new models. The crucial rôle of modeling and its application at the different lcvels of the tiered-approach is illustrâted in Figure 9. The EFSA Scientific Opinion highlights the relevance of effect models but déploré the rejection of several models used in dossiers because of: (i) the lack of harmonizalion in their development, (ii) the lack of qnality control, and (iii) disagreement between the member states. Moreover, this Scientific Opinion highlights varions points to consider during the develop ment of a model that will be used under the régulaiory context and notes tliat tliere is still a rooni for improvement regarding modeling development or validation. Currently, the models of interest for PPP régulation are mechanistic models such as organism level effect (TKTD) models, population models {e.g., Individual-Based Modelling), community models (e.g., food web model) or those combining several of them.

The lack of data constitutes one of the major limiting factors to develop new models and/or to validate the existing ones. Except the DR models and the (Q)SAR models which are already used and accepted in the dossiers, it appears from the EFS A documents that there is a real need to use the S SD models on more biological groups (limits explained in the above section), as well as the TKTD, population and food web models (Figure 9). However, models like SSD, QSARs or TKTD which require testings are of course not compatible with the animal welfare considération. Thus, the choice of the models dépends on the biological group and on the bio-ecological characteristics (e.g., ability to move and at what scale, stages of life, physiology) of the organisms targeted by each document.

TKTD models are of high interest for the dossiers (EFSA PPR Panel, 2018a; EFSA, 2009). For example, DEBtox models based on energetic bud gets deal with sublethal effects and thus présent a great potential for various organisms. Also, the GIJTS model, based on survival data, is of high poten tial for hshes, benthic macro-invertebrates and aquatic stages of amphibians. Regarding primary producers, for which the sensitivity to a PPP is mostly characterized using growth as endpoint, a TD model developed for microalgae [START_REF] Weber | Combination of a higher-tier flow-through System and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspicatus and Pseudokirchneriella subcapitata[END_REF]) and a TKTD model developed for the macrophyte Lemna [START_REF] Schmitt | Mechanistic TK/TDmodel simulating the effect of growth inhibitors on Lemna populations[END_REF] hâve been reported. TKTD models can also be used for the reptiles and amphibians but the lack of data for those groups hâve prevented any progress (EFSA PPR Panel, 2018b).

Population models also présent a high potential for most of biological groups involved in PPP régulation. Based on their bio-ecological characteris tics, the population models at the landscape scale would be the most suitable ones to characterize the risk induced by the PPP for non-target arthropods, and for reptiles and amphibians. For example, the reptiles and the amphib ians can be associated to different media depending on their stages of life, and they are able to move at the landscape scale. For this group, it is recommended to use population models such as ALMaSS (Animal, Landscape and Man Simulation System, [START_REF] Topping | Almass, an agent-based model for animais in temperate european landscapes[END_REF] which takes into considération these different variables. Finally, the birds and mammals group may beneht from population models but the notihed guidance document of 2013 déploré the lack of methodology and guidance for their use.

The Figure 10 also demonstrates that bees received a spécifie attention during the last years with the setting in 2013 of a dedicated guidance doc ument (EFSA, 2013). However, as this document was not accepted at the European scale, the SANCO document from 2002 is still the official guidance document (European Commission, 2002b). In 2015, the BEEHAVE model was also in the heart of a Scientific Opinion for its use in the regulatory context (EFSA PPR Panel, 2015d). This model aims at estimating the decrease of a colony after PPP exposure. Its assessment by EFSA experts revealed its reliability for bees but not for wild bees because of the lack of experimental data. More recently, an éditorial document has announced the development of the ApisRAM model [START_REF] More | EFSA is working to protect bees and shape the future of environmental risk assessment[END_REF] dealing with data directly obtained from hives, and deriving the risk assessment of Chemical factors alone or combined at large spatial and temporal scales, among others. In both cases, BEEHAVE and ApisRAM are based on population models.

Finally, food-web models are of high interest for sédiment organisms (EFSA PPR Panel, 2015c). The sédiment compartment can play the rôle of sink for persistent substances and/or hydrophobie ones (log10 K ow > 3), and can change the exposure of the organisms living in the sédiment. In this case, the use of such model could support the considération of biomagniheation into PPP ERA. Guidances are expected (EFSA PPR Panel, 2015c).

Beyond ail of the above-cited models, those dealing with PPP mixture toxicity prédiction should also be considered in the regulatory framework (European Commission, 2020;EFSA, 2013;[START_REF] Efsa Ppr Panel | Scientihc Opinion On Good Modelling Practice In The Context Of Mechanistic Effect Models For Risk Assessment Of Plant Protection Products[END_REF]. Recently, the Court of Justice of the European Union conhrmed the need to consider the join toxicity of ail of the components (e.g., active substance, safener, synergist, co-formulant) before the placing on the market of a PPP (CJEU, lst oct. 2019, C-616/17, pt 75). Also, mixtures are integrated to the régulation (EC) No 1272/2008 on classification, labelling and packaging of substances and mixtures. Two models are frequently used in the scientific community: the CA and the IA models. The first one is mainly recommended by the guidance documents as it tends to be more conservative [START_REF] Efsa Ppr Panel | Scientihc Opinion On Good Modelling Practice In The Context Of Mechanistic Effect Models For Risk Assessment Of Plant Protection Products[END_REF].

At the end, the use of modelling approaches in registration dossiers will mostly rely on the targeted biological group, on the required level of risk rehnement (e.g., Tier-2 or more), and on the available data to parameterize the models. However, among the different models which are recommended in EFSA documents, one can suspect a temporal évolution in the category of used mod els. For example, "simple" ones like SSD hâve a long history in PPP régulation as they were already recommended in 2002 for non-target plants (European Commission, 2002b), while more developed ones still required guidance for users and assessors. This calls for a comprehensive analysis of the dossiers to characterize the real usage of modelling approaches in PPP régulation. (Q)SAR models hâve the potential to provide rapid, in silico estimâtes of ecotoxicological endpoints. In addition, they can be an important tool for environmental risk assessment of the dégradation products, métabolites and impurities, when it cannot be performed experimentally.

The potential for application in PPP régulation seems there as (Q)SAR approaches properly used can be a valuable tool for providing prédictions on Chemical toxicity [START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF][START_REF] Mombelli | Evaluation of the oecd qsar toolbox automatic workflow for the prédiction of the acute toxicity of organic Chemicals to fathead minnow[END_REF]. In addition, several available tools already exist and, for a given substance, may fall into the applicability domain of a multitude of in silico models, raising the question of which model(s) and/or tool(s) to apply [START_REF] Herrmann | Q)Sar tools for the prédiction of mutagenic properties: Are they ready for application in pesticide régulation?[END_REF]. Nevertheless, there are several areas for improvement to facilitate the work of decision-makers. It is necessary to allow them to establish with a maximum of certainty if: (i) the (Q)SAR model is scientihcally valid, (ii) the predicted effect is of regulatory utility, and (iii) the model is applicable to the substance of interest.

As far as scientihc validity is concerned, (Q)SAR models can provide pré dictions in case of unknown MoA, but a prerequisite is the availability of appropriate training data for model development [START_REF] Herrmann | Q)Sar tools for the prédiction of mutagenic properties: Are they ready for application in pesticide régulation?[END_REF] and appropriate supporting information such as (Q)SAR Model Reporting For mats (QMRF) (e.g., JRC QSAR model Database). Overall, it appears that, if properly used and evaluated, (Q)SAR approaches can be a valuable tool for providing ht-for-purpose prédictions in the framework of régulations on Chemical toxicity [START_REF] Mombelli | Evaluation of the oecd qsar toolbox automatic workflow for the prédiction of the acute toxicity of organic Chemicals to fathead minnow[END_REF]. For example, [START_REF] Mombelli | Evaluation of the oecd qsar toolbox automatic workflow for the prédiction of the acute toxicity of organic Chemicals to fathead minnow[END_REF] highlighted the regulatory relevance and robustness of (Q)SAR prédictions for acute hsh toxicity and demonstrated a level of reliability of the prédiction comparable to the experimental data. This kind of validation exercises conducted by third parties can also contribute to enhance knowledge about models and their intrinsic limitations so that informed decision-making can take places [START_REF] Mombelli | Evaluation of the oecd qsar toolbox automatic workflow for the prédiction of the acute toxicity of organic Chemicals to fathead minnow[END_REF].

For a ready regulatory applicability usefulness, focusing the development of (Q)SAR models as a function of endpoints of regulatory interest formalized by OECD guidelines would render their application straightforwardly relevant. Always from a regulatory point of view, it would be very useful to extensively cover the different trophic levels and biological organization levels since, for instance, only a minority of work on (Q)SAR provided models for algae or for long term risk at the population or community level. (Q)SAR approaches are constrained by the experimental data availability and quality, so the data sets are one of the most important (Q)SAR éléments. Consequently, to improve their ecological relevance, the scientihc community has to work on the lack of ecotoxicological data for PPP covering the whole biodiversity and investigating sub-lethal and chronic effects.

To overcome this limitation, the development of the quantitative form of AOP (qAOP) (see for example, [START_REF] Conolly | Quantitative adverse outcome pathways and their application to prédictive toxicology[END_REF])and their association with (Q)SAR models seems very promising. Indeed, MechoA approach in (Q)SAR aiming at predicting the Molecular Initiating Event (MIE) sounds convenient to provide input to qAOP, which are able to translate subtle functional déficits within individuals into population-level effects under different ecological and environmental scénario.

For the applicability to a given substance, the framework proposed by VEGA hub [START_REF] Benfenati | Vega-qsar: Ai inside a platform for prédictive toxicology[END_REF] seems very promising (ADI), and uncertainty associated to the model prédiction should be more systematically communicated. However, an identihed limitation of the (Q)SAR model cornes from the difficulty to explain data from complex MoA using relatively sim ple models, and therefore the causal toxicological mechanisms generally stay unknown even if the physico-chemical déterminants can be accurately described [START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF]. Lastly, even if tools are available, an expert judgment should as often as possible be consulted. For example, a (Q)SAR prédiction can be compared with a read-across prédiction based on the closest structural analogues to hâve an idea of the relevance of the prédiction. To improve applicability, different studies hâve explored strategies for combining prédictions from multiple (Q)SAR tools to improve the prédiction of several endpoints. These consensus models show better overall prédictive capacity than individual (Q)SAR tools and sound promising [START_REF] Villaverde | Qsar/qspr models based on quantum chemistry for risk assessment of pesticides according to current european législation[END_REF].

The intégration of TKTD and (Q)SAR modelling represents an interesting and promising held of research. In such an integrated scheme, (Q)SAR models provide interpolation for toxicological responses and toxicokinetic parameters. Indeed, this synergy between the two modelling approaches can greatly reduce the need for animal testing while optimizing in cost-efficient ways toxicological resources [START_REF] Mombelli | Evaluation of the oecd qsar toolbox automatic workflow for the prédiction of the acute toxicity of organic Chemicals to fathead minnow[END_REF]. Finally, the promotion of capacity building in governmental agencies aiming at increasing awareness about in silico tools would rapidly resuit into an enhanced and informed use of in silico approaches during decision-making.

T K T D m o d els

Below are some possible directions that can be learned from the analysis of the literature on TKTD models in terms of prospects for the future, both from a purely research point of view, and to improve ERA:

• For regulatory purposes and for use by non-experts, TKTD models need to be as simple (i.e., simple enough to be used on -somewhat extendedstandard toxicity test data) and transparent as possible [START_REF] Jager | Revisiting Simplihed Debtox Models For Analysing Ecotoxicity Data[END_REF]. • TKTD models should be as représentative as possible of the widest diversity of PPP, both in their bioavailability and MoA [START_REF] Crenna | Characterizing Honey Bee Exposure and Effects From Pesticides For Chemical Prioritization and Life Cycle Assessment[END_REF]. • TKTD models should be both calibrated and validated on data collected under time-variable exposure, agreeing that this type of scénario is more realistic from an environmental point of view [START_REF] Van Den | Exposure Pattern-Specihc Species Sensitivity Distri butions For The Ecological Risk Assessments Of Insecticides[END_REF]; in other words they should include the exposure history of organisais [START_REF] Jager | Modeling receptor kinetics in the analysis of survival data for organophosphorus pesticides[END_REF]. • Tested species should be relevantly chosen regarding their representativeness of field conditions, rather than being selected for their accessibility in laboratories [START_REF] Arlos | Improving Risk Assessment by Predicting the Survival of Field Gammarids Exposed to Dynamic Pesticide Mixtures[END_REF][START_REF] Roeben | Towards A Spatiotemporally Explicit Toxicokinetic-Toxicodynamic Model For Earthworm Toxicity[END_REF][START_REF] Bart | Predicting Mixture Effects over Time with Toxicokinetic-Toxicodynamic Models (Guts): Assumptions, Experimental Testing, and Prédictive Power[END_REF]. • TKTD models could be improved by considering ecologically relevant biological traits, such as the movement behaviour [START_REF] Roeben | Towards A Spatiotemporally Explicit Toxicokinetic-Toxicodynamic Model For Earthworm Toxicity[END_REF], the actual size [START_REF] Dalhoff | Seasonal sensitivity of Gammarus pulex towards the pyrethroid cypermethrin[END_REF] or the membrane permeability [START_REF] Crenna | Characterizing Honey Bee Exposure and Effects From Pesticides For Chemical Prioritization and Life Cycle Assessment[END_REF], to name but a few examples. • TK models should consider several routes of exposure as well as the possi ble presence of métabolites in order to also quantify their bioaccumulation; indeed, sometimes métabolites can be more toxic than the parent compound to which they dérivé. In addition there is no longer technical reasons to limit ourselves to simplistic TK models since ready-to-use tools exist to perform relevant TK modelling analyses in all-in-one facilities [START_REF] Ratier | New Perspectives On The Calculation Of Bioaccumulation Metrics For Active Substances In Living Organisms[END_REF]. • Field studies are still too rare, while they would be really useful to test the prédictive power of model outputs.

Of course, such improvements for a better use of TKTD models should not make us forget that in recent years, there has been a widespread drive to hâve more relevant testing strategies, accounting for the animal welfare and including the 3R principles European Commission (2009). Already a current practice in REACH [START_REF] Lilienblum | Alternative methods to safety studies in experimental animais: Rôle in the risk assessment of Chem icals under the new European Chemicals Législation (REACH)[END_REF], but first introduced few décades ago [START_REF] Russel | The principles of Humane Experi mental Technique[END_REF] and still debated [START_REF] Goldberg | The Principles of Humane Experimental Technique: Is It Relevant Today[END_REF][START_REF] Balls | It's Time to Reconsider The Principles of Humane Experi mental Technique[END_REF], the 3R principles refers to the principle of réduction, replacement, and rehnement of animal studies. The objective of réduction is to decrease the number of animais used for research and regulatory purposes. The replacement approach includes in vitro or in silico methods. Rehnement involves reducing, eliminating, or relieving animais' pain or distress, and thereby improving their well-being [START_REF] Tan | Opportunities and challenges related to saturation of toxicokinetic processes: Implications for risk assessment[END_REF]. Additionally, there is a need to change the classical, animal testing-based approach towards more modem tools that are more prédictive for humans. This has been particularly explored for TK and TKTD models [START_REF] Heringa | Intégration of toxicokinetics and toxicodynamics testing essential for risk assessment[END_REF][START_REF] Terry | Application of a novel integrated toxicity testing strategy incorporating "3R" principles of animal research to evaluate the safety of a new agrochemical sulfoxaflor[END_REF].

P o p u la tio n and la n d sca p e m o d els

Various authors suggest, in the reviewed papers, that ecological models are very little applied in regulatory PPP ERA (Hommen et al., 2016;[START_REF] Accolla | A review of key features and their implémentation in unstructured, structured, and agent-based population models for ecological risk assessment[END_REF][START_REF] Raimondo | Popguide: Population modeling guidance, use, interprétation, and development for ecological risk assessment[END_REF]. A spécifie analysis of PPP registration dossiers actually submitted to régulation agencies should be conducted to conhrm this statement. This probable underuse of population models in regulatory ERA is surprising when compared to the wide use of similar population models in species conservation or hsheries resource management. Nevertheless, there is a strong consensus among stakeholders on the potential contribution of ecologi cal models to PPP ERA. One possible explanation emerging from our literature review in using population and landscape models in ERA is an obvious lack of easy running tools for people not advertised in modelling in general, in these type of models in particular. Filling this gap could be a new challenge in a near future.

Firstly, models could inform the ecological criteria to be taken into account at ail tiers of prospective ERA [START_REF] Forbes | Assessing pesticide risks to threatened and endangered species using population models: Findings and recommendations from a croplife america science forum[END_REF], e.g., choice of test species and life stages fixed by regulators for lower Tier assessments, définition of ecological scénarios to be tested in higher Tier assessments with a worst-case scénario approach [START_REF] Rico | Developing ecological scénarios for the prospective aquatic risk assessment of pesticides[END_REF]. Secondly, they allow the uncertainty sources attached to the évaluation criteria to be tested in silico. They should make it possible to reexamine the arbitrary safety factors applied in ERA to guaranty ecosystem protection when extrapolating to the multitude of contexts of PPP use (Focks et al., 2014). But while ignoring the fact that most of these mechanistic models are rather cognitive tools to inform on the ecological complexities in PPP impacts [START_REF] Forbes | Ecological models in support of regulatory risk assessments of pesticides: developing a strategy for the future[END_REF], the debate for their use in ERA is most often unfortunately conhned to the sole question of validating their prédictive capacity as stated by [START_REF] Wang | From home range dynamics to population cycles: Validation and realism of a common vole population model for pesticide risk assessment[END_REF], the models then being only considered as mere forecasting tools in the same way as meteorological models for weather prédiction. Yet, as pointed 30 years ago by [START_REF] Barnthouse | The rôle of models in ecological risk assessment: A 1990's perspective[END_REF], the real issue in determining whether models can contribute to regulatory risk assessment should be credibility rather than validity.

In addition to prospective ERA, population and landscape models can con tribute to understand held ecological impacts of PPP by providing information on their relative contribution to dégradation of biodiversity, particularly for non-target species of patrimonial value or keystone species for ecosystem functioning (e.g., [START_REF] Topping | Modeling the influence of temporal and spatial factors on the assessment of impacts of pesticides on skylarks[END_REF][START_REF] Abi-Akar | Simulating honey bee large-scale colony feeding studies using the beehave model-part ii: analysis of overwintering outcomes[END_REF][START_REF] Landis | Intégration of chlorpyrifos acetylcholinesterase inhibition, water température, and dissolved oxygen concentration into a régional scale multiple stressor risk assessment estimating risk to chinook salmon[END_REF]. Similarly, they can be used to evaluate future population trajectories under different scénarios of climatic, agricultural or landscape évolution (as in [START_REF] Nogeire-Mcrae | Land use change and rodenticide exposure trump climate change as the biggest stressors to san joaquin kit fox[END_REF].

The informative value of model outputs regarding population and ecosys tem threat in agricultural landscapes is crucial for their acceptance in environmental risk management. Some works already illustrâtes how ecologi cal models can be used to establish the relevance of traditional risk assessment endpoints with respect to the recovery capacities of populations [START_REF] Hayashi | Ecological Risk Assessment Of Herbicides In Japan: Integrating Spatiotemporal Variation In Exposure And Effects Using A Multimedia Model And Algal Density Dynamics Models[END_REF]. They may also inform the choices of évaluation endpoints regarding their relationship with key ecosystem services [START_REF] Croft | Evalu ating european food safety authority protection goals for honeybees (apis mellifera): What do they mean for pollination? Integrated environmental assessment and management l f[END_REF]. However, the endpoints derived from population projection models or the indicators quantifying population extinction risk in simulation approaches currently lack any reference grid for their interprétation in terms of impact severity and possi ble population collapse. Conservation science (e.g., for the définition of species conservation status by the International Union for Conservation of Nature), but also the widely-accepted use of models in hsheries management or in épi démie forecasting, may well inspire the évolution of future PPP ERA practices [START_REF] Thursby | Coupling toxicokinetictoxicodynamic and population models for assessing aquatic ecological risks to time-varying pesticide exposures[END_REF]. The harmonization and the common définition of ref erence thresholds of population vulnerability to be applied to these endpoints could indeed operationalize the use of ecological models in the management of PPP risk for non-target species and better inform decision-making in PPP environmental management. This could présent a high value for ERA since Spécifie Protection Goals (SPG) are in most cases defined on the population level. Thus, the use of ecological models offers a promising avenue to link typical test results on the organism level and the SPG of PPP ERA.

M u lti-sp ec ie s m o d els

SSD models

Ecological interactions are rarely taken into account in ERA, while it is important to consider both direct and indirect effects of Chemical exposure (e.g., [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF]). Nevertheless, SSD approaches currently hâve large implications in législation and risk management, so that they are discussed a lot [START_REF] Posthuma | Species Sensitivity Distributions In Ecotoxicology[END_REF]. Critical issues are both fundamental (e.g., its statistical rather than its ecological basis) and technical (e.g., the necessary number of input data). Also, it is not conhrmed to what extent classical outputs, such as PAF (for substance alone) and msPAF (for mixtures) could be considered predictors in a rétrospective perspective of mixture impacts on held communities [START_REF] Posthuma | Predicted Effects Of Toxicant Mix tures Are Conhrmed By Changes In Fish Species Assemblages In Ohio, Usa, Rivers[END_REF]; this motivated a lot of model confirmation studies that were mainly focused on the 5th percentile of the htted SSD namely the HC$ (see [START_REF] Posthuma | Species Sensitivity Distributions In Ecotoxicology[END_REF]. Recently, the SSD method was scrutinized in detail for its potentiality to support ERA within the framework of the European WFD which suggests using models to assess the likelihood that Chemicals affect water quality for management prioritization. Deriving SSD analyses for more than 12000 Chemicals, [START_REF] Posthuma | Species Sensitivity Distributions For Use In Environmental Protection, Assessment, and Management Of Aquatic Ecosystems For 12 386 Chemicals[END_REF] concluded that SSD is a versatile and comprehensive approach to prevent, assess, and manage Chemical pollution problems.

Recently, [START_REF] Fox | Recent Developments In Ssd Modeling[END_REF] published a summary of the current status of SSD approaches, and elaborated on several recent developments for SSD methods, specihcally, model averaging, multi-modality and software development. Identifying several technical issues to urgently deal with for SSD improvements, [START_REF] Fox | Recent Developments In Ssd Modeling[END_REF] also proposed some future directions with respect to the use of SSD, ultimately aiming at facilitating wider international col laboration and, further, a possible harmonization of SSD methods. Regarding technical issues, to name but a few, [START_REF] Fox | Recent Developments In Ssd Modeling[END_REF] mention the choice of a parametric or a non-parametric (i.e., distribution-free) modelling, the choice of frequentist versus Bayesian inference, the tricky question of the sample size (also stated by Carr and Belanger 2019), the expected shape of the distribu tion, the representativeness of species sample possibly leading to bi-modality when there are clearly two groups of species sensitivities or because of a very spécifie MoA of Chemical compound.

SSD methods hâve also been used in combination with complementary approaches in order to account for additional influencing phenomena on species sensitivities. [START_REF] Nagai | Estimation Of Herbicide Species Sensitivity Distribution Using Single-Species Algal Toxicity Data And Information On The Mode Of Action[END_REF] showed that considering the MoA of compounds improved the accuracy of estimating SSD markedly. The PERPEST model is also an approcha allowing to include the considération of MoA [START_REF] Van Den | Perpest model, a case-based reasoning approach to predict ecological risks of pesticides[END_REF], 2006). Based on the tact that SSD is a probabilistic risk assessment model, [START_REF] Giddings | Ecological risks of diazinon from agricultural use in the Sacramento-San Joaquin River Basins, California[END_REF] evaluated potential toxic effects of diazinon in the Sacramento-San Joaquin System, based on data sets collected from laboratory toxicity tests for 63 species. [START_REF] Qu | Ecological risk assessment of pesticide residues in Taihu Lake wetland, China[END_REF] illustrated the improvement in the RQ method expressing the ecological risk as the degree of overlap between the distribution of environmental exposure concentrations and the distribution of toxicity values. A step further was made in the study of mix tures effects using SSD [START_REF] Cedergreen | Species-specihc sensitivity of aquatic macrophytes towards two herbicide[END_REF][START_REF] Jesenska | Validation of the species sensitivity distribution in rétrospective risk assessment of herbicides at the river basin scale-the Scheldt river basin case study[END_REF][START_REF] Li | Application Of Species Sensitivity Distribution In Aquatic Probabilistic Ecological Risk Assessment Of Cypermethrin: A Case Study In An Urban Stream In South China[END_REF][START_REF] Silva | Predicting the aquatic risk of realistic pesticide mixtures to species assemblages in Portuguese river basins[END_REF], some authors also accounting for the effects of environmental factors [START_REF] Rico | Effects of malathion and carbendazim on Amazonian freshwater organisms: Comparison of tropical and temperate species sensitivity distributions[END_REF][START_REF] Rico | Effects of imidacloprid and a neonicotinoid mixture on aquatic invertebrate communities under Mediterranean condi tions[END_REF]. [START_REF] Clemow | A Rehned Ecological Risk Assessment for California Red-legged Frog, Delta Smelt, and California Tiger Salamander Exposed to Malathion[END_REF] proposed a rehnement of the SSD including exposure simulation aiming at identifying direct and indirect effects of malathion on amphibians. Nevertheless, [START_REF] Clemow | A Rehned Ecological Risk Assessment for California Red-legged Frog, Delta Smelt, and California Tiger Salamander Exposed to Malathion[END_REF] agréé that their approach does not allow for representing the daily fluctuations of malathion over the course of multiple applications. However, taking into account a time-variable exposure was early identihed as a crucial issue [START_REF] Cedergreen | Species-specihc sensitivity of aquatic macrophytes towards two herbicide[END_REF][START_REF] Van Dam | Ecological risk assessment of tebuthiuron following application on tropical Australian wetlands[END_REF]; so the combination of SSD with TKTD models could be the next step further in improving Tier-2 ERA based on SSD, especially for PPP [START_REF] Van Den | Exposure Pattern-Specihc Species Sensitivity Distri butions For The Ecological Risk Assessments Of Insecticides[END_REF].

Last but not least, held study data hâve been highlighted for their addedvalue in SSD analyses to better characterize the exposure, as for example De [START_REF] Zwart | Ecological Effects of Pesticide Use in The Netherlands: Modeled and Observed Effects in the Field Ditch[END_REF] who used a Géographie Information System (GIS) map to predict aquatic exposure to PPP in held ditches; [START_REF] Van Dam | Ecological risk assessment of tebuthiuron following application on tropical Australian wetlands[END_REF] who htted a break-point régression model to held monitoring data, providing a time-dependent estimate of exposure to tebuthiuron; or [START_REF] Li | Application Of Species Sensitivity Distribution In Aquatic Probabilistic Ecological Risk Assessment Of Cypermethrin: A Case Study In An Urban Stream In South China[END_REF] who combined effect data with the probability distributions of environmental exposures of contaminants. But held study data hâve also been highlighted to beneht from held ecotoxicity information issued from microcosm or mesocosm studies. For example, [START_REF] Brock | Comparing aquatic risk assessment methods for the photosynthesisinhibiting herbicides metribuzin and metamitron[END_REF] concluded that the SSD approach cannot be seen as a complété alternative to semi-held experiments, even if a protection level based on direct effects (e.g., the HCs) will also protect against indirect effects. Van Den Brink et al. (2006) then proposed the con cept of NO ECecosystem (dehned as the highest test concentration causing no observed effects in microcosm or mesocosm experiments) to be used to extrapolate from laboratory to held data. Today, NO EC ecosystem is not used anymore, replaced by the concept of effect classes and the dérivation of Ecolog ical Threshold Option (ETO)-and Ecological Recovery Option (ERO)-RAC from mesocosm studies (EFSA PPR Panel, 2013). [START_REF] Schipper | Deriving held-based species sensitivity distributions (f-ssds) from stacked species distribution models (s-sdms)[END_REF] presented a different approach from the previous ones, based on the Stacked Species Distribution Modeling (S-SDM). Establishing an S-SDM for several species to describe their probability of occurrence in relation to multiple envi ronmental factors, they were able to study the variation of this probability of occurrence along the gradient of each environmental factor with the remaining ones hxed. Hence, [START_REF] Schipper | Deriving held-based species sensitivity distributions (f-ssds) from stacked species distribution models (s-sdms)[END_REF] investigated how held-based SSD (f-SSD) for a given environmental factor changed under confounding inhuences, such as low, medium or high environmental disturbance.

Community and food web models

What is particularly striking about the community models in terms of gaps is different according to the type of models. ABM/IBM-type models, together with BN models, account for a lot of refined biological processes combined with stochastic links, thus making it difficult to keep a critical eye on the relevancy of model outputs at the community level: do they really emerge from the modelling itself? Are they only artifactual, due to spécifie initial condition in simulations, for example? These models also rarely quantify uncertainties on outputs while they include both uncertainty and variability as input by essence.

Food-web models, also rarely accounting for uncertainties, reveal a noticeable gradient from the simplest ones [START_REF] Damgaard | Modeling effects of herbicide drift on the compétitive interactions between weeds[END_REF] to the most complex ones [START_REF] Nfon | Development of a dynamic model for estimating the food web transfer of Chemicals in small aquatic ecosystems[END_REF] giving rise to the question of the best compro mise to find. There is a real challenge to be realistic enough from a biological point of view (enough species and ecological processes to account for) but sim ple enough from a modeling point of view (based on the parsimony principle) so that the model appears finally sound. However, to find the best compro mise may strongly be related to the available experimental data, obviously not manipulable afterwards. Hence, simple food-web models will usually be employed with microcosm data [START_REF] Traas | A freshwater food web model for the combined effects of nutrients and insecticide stress and subséquent recovery[END_REF], while more complex ones will be suitable for mesocosm data [START_REF] Bartell | Modeling the effects of thiamethoxam on Midwestern farm ponds and emergent wetlands[END_REF][START_REF] David | Modelling population dynamics in mesocosms using an individual-based model coupled to a bioenergetics model[END_REF]. Some food-web models also seldom proved helpful because strictly dépendent on a particular species (e.g., bumble bees with bumble- BEEHAVE Becher et al., 2018or ApisRAM More et al. 2021).

A probabilistic RQ is a more informative alternative to the traditional single-value RQ, which is often interpreted as a binary outcome. Indeed, it can be useful useful for ranking of different scénarios as well as prioritizing among alternative risk scénarios (in Campbell et al. (2000), cited in [START_REF] Mentzel | Development Of A Bayesian Network For Probabilistic Risk Assessment Of Pesticides[END_REF]). Among probabilistic approaches, the Bayesian Network (BN) models are increasingly being used to model environmental Systems, in order to: integrate multiple issues and System components; utilise information from different sources; and handle missing data and uncertainty [START_REF] Chen | Good practice in bayesian network modelling[END_REF]. As illustrated by [START_REF] Mentzel | Development Of A Bayesian Network For Probabilistic Risk Assessment Of Pesticides[END_REF], a BN has been developed and parameterised for three PPP based on monitoring data from a catchment located in South-East Norway. The authors used toxic effects data for several freshwater species representing various taxonomie groups (namely, N O EC values for growth and reproduction).

M ix tu r e m o d els

Mixture models should include the assessment of dose-level dépendent dévi ation as it was suggested that concentrations of Chemicals can influence interactions between PPP [START_REF] Lopez Aca | Léthal and Sublethal Responses In The Fish, {Odontesthes} Bonariensis, Exposed To Chlorpyrifos Alone Or Under Mixtures With Endosulfan And Lambda-Cyhalothrin[END_REF][START_REF] Sanches | Léthal and sublethal toxicity of abamectin and difenoconazole (individually and in mixture) to early life stages of zebrahsh[END_REF][START_REF] Kristofco | Comparative Pharmacology and Toxicology of Pharmaceuticals in the Environment: Diphenhydramine Protection of Diazinon Toxicity in Danio rerio but Not Daphnia magna[END_REF]. For instance, in [START_REF] Chen | Combined toxicity of butachlor, atrazine and OEa-cyhalothrin on the earthworm Eisenia fetida by combination index (Ci)-isobologram method[END_REF], it is reported that CA had severe limitations when the dose-response curves of the individual Chemicals were not identical at low effect concentrations. Similarly, [START_REF] Ritz | How to use statistics to daim antagonism and synergism from binary mixture experiments[END_REF] found that fixed-ratio designs (PPP and their mixture are used at increasing doses) should be preferred as they allow validation of the assumed dose-response relationship and, consequently, provide much stronger claims about antagonistic and synergistic effects than factorial designs (lots of PPP are only available at a single dose level and a mixture simply combines these doses). For this reason, [START_REF] Marques | Ecotoxicological Effects of Mikado (R) and Viper (R) on Algae and Daphnids[END_REF] or [START_REF] Pestana | Pesticide exposure and inducible antipredator responses in the zooplankton grazer, Daphnia magna Straus[END_REF] underlined the need for higher number of testing combinations and concentrations of each stressor to improve model calibration.

Moreover, mixture models should include the status of test species at different time points (time-to-event), as suggested by [START_REF] Qiu | Interaction Patterns and Toxicities Of Binary and Ternary Pesticide Mixtures To Daphnia Magna Estimated By An Accelerated Failure Time Model[END_REF] who used the AFT model, that assesses the relationships between the time-toevent and treatments. The AFT model, which prédictive power and accuracy can be improved by setting more observation time points in experimental design, provides a simple and valuable method to quantify the interactions and to evaluate the outcomes of exposure to a mixture of Chemicals. This is in accordance with [START_REF] Broerse | Mixture effects of nickel and chlor pyrifos on Folsomia candida (Collembola) explained from development of toxicity in time[END_REF] who explained that analyzing mixture toxicity at successive time points may be a good way to explain observed mixture effects. Indeed, this allows the application of process-based models (time-toxicity relationships, DEBtox) that estimate time-independent parameters (uptake and élimination rate constants) besides only time-dependent toxicity estimâtes (LCX or ECX), which may enable extrapolations beyond the standard exposure time.

Finally, [START_REF] Carnesecchi | Investigating combined toxicity of binary mixtures in bees: Meta-analysis of laboratory tests, modelling, mechanistic basis and implications for risk assessment[END_REF], working on bees, proposed the following perspectives for mixture and other models:

• Development of in silico tools such as (Q)SAR models to predict combined toxicity of mixtures.

• Characterization of the synergistic potential of Chemicals including TK inter actions either through inhibition or induction of metabolism or through direct TD interactions. The CA and IA models provide a validated initial risk assessment approach to predict mixture toxicity, but they are mechanistically uninformative [START_REF] Lister | Modelling the joint effects of a métal and a pesticide on reproduction and toxicokinetics in Lumbricid earthworms[END_REF]. Accounting for Chemical uptake and élimination in mixtures is an essential requirement for mechanistic understanding of Chemical interactions. [START_REF] Svendsen | Similarity, Independence, Or Interaction For Binary Mixture Effects Of Nerve Toxicants For The Nematode Caenorhabditis Elegans[END_REF] explained that where interactions occurred between the hve tested PPP, these could be explained by information on the potential mechanisms of compound toxicokinetics. These authors concluded that detailed analysis of toxicokinetics and toxicodynamics can aid in further understanding of interactions in mix tures. A need exists for a better understanding of the dynamics of the effects of mixtures, underlining the need for measurements with intermediate time points [START_REF] Baas | Modeling The Effects Of Binary Mixtures On Survival In Time[END_REF]. To select CA or IA as the most appropriate model for any given mixture, knowledge about the MoA of Chemicals included is required. This mechanistic classification is achieved using knowledge of the toxicodynamics rather than, for example, the toxicokinetics of the Chemical.

• For multiple species or the whole ecosystem, S SD can be applied to estimate HCX (hazardous concentration for < x% of the species) for multiple Chem icals of concern with the aim to identify whether the estimated exposure exceeds the HCX, as the médian for x% species affected in the SSD (EFSA Scientihc Committee, 2019).

In brief, to better understand mixture effects of PPP, efforts must be done on:

• Understanding the mechanisms (uptake and élimination, effects) • Predicting time sériés of exposure.

• Using more concentrations in tests with mixtures.

• Coupling mixture models to other modelling approaches; for instance, [START_REF] Bart | Predicting Mixture Effects over Time with Toxicokinetic-Toxicodynamic Models (Guts): Assumptions, Experimental Testing, and Prédictive Power[END_REF] combined both CA and IA models to GUTS models to account for both mixtures and the time course of processes leading to toxicity.

C on clu sio n and p ersp e ctiv es

The basic expectation from the use of computational prédiction models in PPP ERA is to avoid testing ail the PPP and métabolites. Hence, they can be used to link Chemical structure or concentrations of PPP with activity and toxicity on organisms. Models also hâve the potential to assess PPP effects on sets of several species under various environment types, to extrapolate adverse effects across levels of biological organization, to decipher their underlying mecha nisms, and to support the prédiction of joint effects caused by mixtures of Chemicals. This review led thus to the conclusion that (Q)SAR, DR, TKTD, population, landscape, and community models are increasingly recognized for the risk assessment of PPP, notably under the impetus of regulatory authorities having encouraged the development of good modeling practice guides, harmonization and reference modeling procedures. In the framework of the prospective ERA, (Q)SAR models are already used to supply in silico ecotoxicological endpoints hlling in the toxicity data gaps for the multitude of PPP and species diversity, and reducing the breadth of the experimental task. While the value of ecological models addressing population, landscape and commu nity scales is undisputed for PPP ERA, their possible place is still ambiguous in assessment schemes, oscillating between strict simulating tools of ecolog ical outcomes used as endpoints for risk assessment, versus cognitive tools informing on species vulnerabilities and critical environmental factors in PPPexposed ecosystems to be considered in assessment procedures. These tools still suffer from unfriendliness to be routinely used in ERA.

The vision of models as surrogate cost-effective methods for ecotoxicological assessment offering cross species/substances extrapolation facilities, between climatic or geographical conditions extrapolation, and up-scaling intégration of multiple PPP effects should not hide the still major weakness of available experimental data informing on chronic and non-lethal effects of PPP among ecological communities. This point is still a major limitation for a Sound appli cation of models as prédictive tools of PPP ecological impacts. At the same time, although more information is needed to better depict and predict the effects of PPP on living organisms at different scales, models should be parsimonious, meaning that they must accomplish the desired level of explanation or prédiction with as few predictor variables and parameters as possible. Decision guides are increasingly proposed to help modelers to select relevant modelling options adapted to each spécifie risk assessment questioning. With a too large number of input parameters, models exhibit a higher uncertainty which has to be characterized. Moreover, the parameters which drives the model should be estimated as accurately as possible to decrease the uncertainty. Thus, to be relevant, prédiction models should include a sensitivity analysis, an uncer tainty analysis and the comparison of prédictions with observed data. In that, Bayesian inference is a relevant and promising approach to estimate the param eters, to handle uncertainties, and to identify potential improvements in the model structure and experimental designs.

Some future developments of models also emerged from this review such as the considération of PPP multigenerational effects or the study of "multiple stressors". These terms generally refer to the combination of natural stressors (abiotic and biotic) and Chemical exposure, thus including "cocktail effects" due to Chemicals mixture. Effect modelling can help to gain knowledge on interac tions between multiple stressors and their joint effects. Moreover, in order to address the "things that matter" in protecting the environment, i.e., keystone species and ecosystem services, ecotoxicological models describing effects on organisms could be coupled with ecological models informing on interactions between organisms and the functions they fulhll. Thus, modelling the effects of PPP and other stressors on living organisms, from their application in the held (exposure) to their functional conséquences on the ecosystems at different scales of time and space would help going towards a more sustainable man agement of natural resources. However, a lot of data and knowledge remain to be acquired, whether on ecological or ecotoxicological part. For instance, food web and community models at scales relevant for ecological processes are still not enough developed. Also, modelling approaches based on emerging methods such as the so-called "omics" are still lacking despite their great potential for ERA (e.g., detect early effects, improve mechanistic understanding). In addi tion, the considération of the different reviewed modeling facets is still poorly developed in the framework of rétrospective ERA of PPP, while their use for the interprétation of ecological monitoring data in view of PPP use practices, and a dialog with the domains of species conservation and wildlife exploitation management which routinely use models, could constitute wealthy avenues to facilitate the use of models in ecotoxicology, and improve the knowledge and the prédiction of PPP effects on biodiversity.

D écla ra tio n s

Acknowledgm ents The authors acknowledge the Trench Ministries for Ecology, for Research, and for Agriculture who commissioned the collective scientihc assessment (CSA) on the effects of plant protection products on biodiversity and ecosystem services to which this work contributed to. The authors would also like to thank Sophie Leenhardt (INRAE), project manager of the CSA; and Dr Stéphane Pesce (INRAE) and Dr Wilfried Sanchez (Ifremer), sci entihc leaders of the CSA (together with Dr Laure Mamy (INRAE). This work benehted from the Trench GDR "Aquatic Ecotoxicology" framework which aims at fostering stimulating scientihc discussions and collaborations for more intégrative approaches in ecotoxicology. The authors would also like to thank Prof. Hubert Charles (INRAE, INS A Lyon) for his expertise in biology and ecology, in biodiversity more specihcally, what advantageously benehted to this review. Finally, the authors thank Dr Udo Hommen who extensively reviewed the hrst version of this manuscript, providing a lot of constructive comments leading to signihcant improvements. Ethics approval Not applicable.

Consent to participate Not applicable.

Consent for publication Not applicable.

A uthors contributions This study was conducted under the umbrella of the collective scientihc assessment (CSA) on the effects of plant protection products on biodiversity and ecosystem services, INRAE and Ifremer were asked to lead by the Trench Ministries for Ecology, for Research and for Agriculture. LM and RB coordinated discussions with the CSA project team and within the dedicated working group on modelling. LM reviewed the entire manuscript for harmonization, structuring and scientihc consistency. SC coordinated the technical writing in DT^X. MLG conducted the literature search, the paper collection and the bibliometric analysis. FL, SC, AC, CP, RB equally contributed to the study and to the paper drafting. Ail authors read and approved the hnal manuscript.

Funding This work was funded by the French Office for Biodiversity (OFB) through the national ECOPHYTO plan.

C om peting interests

The authors déclaré no competing interests.

Availability of data and m aterials

Ail data generated and analysed during this study are available at https://doi.org/10.5281/zenodo.5884878 as supplementary hles.

T a b le 2

 2 C om b in atio n of th e keyword lists com posing th e first bibliographie query. C olum ns were joined to g e th e r w ith th e logical o p e ra to r AND. Ail keyword lists are available in S u p p lem en tary Inform ation a t h ttp s ://d o i.o rg /1 0 .5 2 8 1 /ze n o d o .5 7 7 5 0 3 8 (L arras et al., 2021).

  Network betw een h o st in stitu tio n s of first a u th o rs .T h e in stitu tio n s represented hâve p ublished a t least th re e p a p e rs a n d th re e c o -publications w ith o th er in stitu tio n s.

F

  ig . 3 M ain co n cep ts a p p e a rin g a t least 35 tim es w ith in th e p a p er collection; th e different colors correspond to th e sem antic pro x im ity of w ords.

F

  ig . 4 T im e course of référencés sub-divided by m odel categories. M odel classes were dcfincd according to th e kcyword lists prcscntcd in T able 1. Methods rcfcrs to general m ethodological p a p ers n o t necessarily re la te d to P P P .

F

  ig . 5 D istrib u tio n of m odela by biological groupa, eacli c ategory being su b-divided accord ing to th e m odel categories. T h e Methods word refera to general p a p e rs an d ,/o r those including several m odel categories. A b b re v iatio n HA m eans N ot Available.

  of th e level of biological organi2a tio n accounted for in th e m odels for each ty p e of species living environm ent. A bb rev iatio n NA m eans N ol Available. 4 E R A m o d ellin g for P P P effect on organisons, p o p u la tio n s, co m m u n ities an d ec o sy stem s 4.1 D e sc rip tio n an d c la ssifica tio n o f e x istin g m o d els

  c h a rt adaptccl from B a sa n t e t al. (2015b) show ing th e (Q )S A R m odcling p ro cedure. pLD50 is effective c o n ce n tra tio n d a ta converted to a m olar basis a n d lo g arithm ically transform ée!. exp a n d p re d are e x p erim e n tal a n d p re d ic le d d a ta , respectively.

  rs re fe r t o tw o o r d in a r y d iff e r e n tia l é q u a tio n (O D E ) m o d e ls (B o o to n e t a l., 2018; P is a n i e t al., 2008) a n d o n e m o d e l b a se d o n s te p w is e b e h a v io u ra l re s p o n s e s c o m b in e d w ith a S e lf-O rg a n iz in g M ap (R e n e t a l., 2013). T a b le 4 Q u a n tita tiv e overview of dose-response (D R) a n d toxicokinetic-toxicodynam ic (T K T D ) m odels (n = 58).

F

  ig . 8 T icr-2 approach to analyzc th c m ix tu res of c o n ta m in a n ts, te s te d for in teractio n s (régressions). T h e in te rac tio n s are th e n ch aracterized by a q u a lita tiv e cornparison of tire m ixing d a ta w ith co n ce n tra tio n ad d itio n (CA ) and in d ep e n d en t action (IA) m odels (from Hoffmann et al. 2016). 1. The Concentration Addition (CA) model assumes tliât ail eomponents of a mixture sliarc a conimon Mode of Action (MoA) (Claudio Cacciatorc et al., 2018). The CA niodel is also known as "toxio unit summation" since onc Chemical can bc rcplaced by an cqual fraction of an cqui-effcctivc concentration of another, without changing the overall effect (Qiu et al., 2017). 2. The Independent Action (IA) niodel, also ealled RA (Response Addition) or Multiplicative Survival Model (MSM), addresses mixtures of Chemicals with dissimilar MoA (Garcia-Gomez et al., 2019; Englert et al., 2017) as it considers that the probability of the effect of one Chemical is independent of the probability of the effect of the other Chemicals in the sample. 3. The Simple Interaction (SI) model assumes that one substance in the mixture, at a non-toxic concentration, is able to influence the toxicity of other substance through an indirect mechanism. These interactions between Chemicals can be due to Chemical and physico-chemical interactions with the constituents of the matrix (e.g., soil), toxicokinetic interactions affecting uptake and élimination (e.g., Roesch et al. (2017) or toxicodynamic interactions affecting compound metabolism or associations at the target site (Gomez-Evles et al., 2009).

  ; Thursby et al. (2018); Weber et al. (2019); Ashauer et al. (2020); Schmolke et al. (2021). These integrated mechanistic models are most often used to theoretically extrapolate the conséquences of PPP use scénarios to other exposure patterns, other ecosystems, or new climate conditions, e.g., Dohmen et al. (2016); Hommen et al. (

  studied indirect effects of PPP on biomass and recovery within a microcosm. With very simple models, De Hoop et al. (2013) concluded to the existence of food mediated indirect effects of atrazine on zoobenthos populations, while Joncour and Nelson (2021) demonstrated the direct and indirect impact of spinosad on insect life-histories. CONTENTS PPP bioaccumulation and biomagnification within food chains / food webs Within our bibliographie corpus, only the paper by Scholz-Starke et al. (

  | l In S cientific O pin ion (SO) o r Technical Report (TR) S i In SO o r TR and: O f interest but not yet d eveloped ■ J Toxicity not required in dossiers dlffrcult to u?e because o f lack o f data or need o f more guidance F ig . 9 Tierce! approach illu stra tc d across th e six categories of m odcls (in rows) an d th e different biological groupa (in colurrms) considérée! for re g istra tio n dossiers, according to E FSA docum ents re la te d to P P P rég u latio n (G uidance D ocum ents, Scientific O pinions and T echnical R ep o rts). In T iers, n.c. m cans not classified.

F

  ig . 10 P u blication tim clin c of th e G uidance docum ents (blue), th e Scientific O pinions, and th e T echnical R eports (grey) dealing w ith m odelling a n d directly or in directly related to P P P régulation. ' A pisR A M is a m odel u n d e r developm ent to be relcased in 2025(M ore et al., 2021).

  Table 2). List of keywords used in the different sub-queries were established a priori from the authors' expertise (see SI at https://doi.org/10.5281/zenodo.5775038, Larras et al. 2021).

	Item	Spécifie	Global	Nbr of
	nbr	item	item	references
	1	(Q)SAR model		427
	2	DR and TKTD	Pesticides	143
	3	Population	General	392
	4	Multi-species	Modelling	79
	5	Landscape	Ecotoxicology	202
	6	Mixture		398
	7	Régulation		399

  .

	Taxa	% of reviewed (Q)SAR papers (n = 39)
	Fish	33%
	Aquatic invertebrates	22%
	Terrestrial invertebrates 16%
	Birds	10%
	Algae	10%
	Mammals	6%
	Plants	4%

  . • Least-square régression on the empirical CDF as in the Excel spreadsheet with the built-in macro SSD generator (current version VI) developed from the Causal Analysis/Diagnosis Decision Information System (CAD-

DIS) of the US Environmental Protection Agency based on the US EPA's 2000 Stressor Identification Guidance document (US EPA, 2000, 2018). Mensah et al. (2013) used the US EPA SSD generator to deal with indigenous aquatic biota in South Africa, while Giddings et al. (

  . • Robustness: cross-validation corrélation coefficient, i.e., Q2 LOO (Leave-One-Out) which shows the prédictive ability for internai validation of the model (based on the training set compounds), and leave-one out crossvalidated R M S E , and R 2d;j (i.e., R M S E C V and Q2dj). The absence of corrélation could be checked by low values of R2 calculated on scrambled response (Galimberti et al., 2020). • Reliability: Q2 metrics (prédictive performance or R 2 Prédiction) measures the reliability of a model, which will not be enough to dehne the model performance when new molécules are engaged (see application domain). Q2 can be calculated using different formulae (referred as F\, F2 or Fs). Q2 and the Concordance Corrélation Coefficient (CCC) are the typical statistical metrics used for the external validation of the developed model Pandey et al.

(2020).

& * * i? # v ' F & -r ■fi*

AFT AMBIT ANN AOP B CF BMC BMF BN BSAF