Sophie Lanciano

Gael Cristofari
email: gael.cristofari@univ-cotedazur.fr

Flip-flop genomics: charting inversions in the human population

Flip-flop genomics: Charting inversions in the human population

Sophie Lanciano, Gael Cristofari

MAIN TEXT

Concomitant with the development of high throughput sequencing technologies, a wide variety of genetic variants have been detected in human genomes, ranging from singlenucleotide variants (SNVs), and small (< 50 base pairs) insertions or deletions (indels) to large (kilobase to megabase range) structural variants (SVs) (Figure 1A). SVs are extremely heterogeneous in nature and size and include copy number variations (large deletions or insertions, transposable element insertions, duplications and other amplifications) and translocations. These alterations have been associated with a broad range of genetic diseases, including neurodevelopmental disorders. Thus detecting them is essential to interpret genomic data [START_REF] Carvalho | Mechanisms underlying structural variant formation in genomic disorders[END_REF][START_REF] Ho | Structural variation in the sequencing era[END_REF]. In this issue of Cell, Porubsky et al. tackle another type of SVs, inversions, which have been largely overlooked until now [START_REF] Porubsky | Recurrent inversion polymorphisms in humans associate with genetic instability and genomic disorders[END_REF].

While SNVs and indels are relatively easy to identify from short-read sequencing data, the identification of larger genetic rearrangements can be more challenging (Figure 1A). In theory, the boundaries of an inversion could be easily detected by paired-end short-read sequencing using discordant read pairs with abnormal orientation between reads of the same pair, and split reads that span the inversion breakpoint. Unfortunately, in practice, inversions are frequently embedded in repeated sequences such as transposable elements or segmental duplications, and are hardly accessible using common short-read strategies [START_REF] Ho | Structural variation in the sequencing era[END_REF]. It is estimated that more than 50% of human inversions are flanked by segmental duplications [START_REF] Chaisson | Multi-platform discovery of haplotype-resolved structural variation in human genomes[END_REF]. The latter are large blocks of DNA (up to hundreds of kilobases) that are present at least twice in a genome. An unexpectedly high number of these duplicated regions are present in primate genomes as compared to other mammals. The current model proposes that non-allelic homologous recombination (NAHR) between such repeats, when oriented in opposite direction, promotes the apparition of recurrent and internal inversions [START_REF] Carvalho | Mechanisms underlying structural variant formation in genomic disorders[END_REF], also referred as "inversion toggling" [START_REF] Zody | Evolutionary toggling of the MAPT 17q21.31 inversion region[END_REF] (Figure 1B).

Emerging technologies that overcome the limitations of short-read sequencing improve the detection of SVs in repetitive regions [START_REF] Ho | Structural variation in the sequencing era[END_REF] (Figure 1A). For instance, long reads (tens of kilobases) offered by Pacific Bioscience (PacBio) or Oxford Nanopore Technologies (ONT) disambiguate mapping location in repeated regions and can directly detect SV breakpoints. These long reads sometime span the entire SV sequence, including potential internal rearrangements. Collectively, these information can provide structural insights into phased haplotypes [START_REF] Ho | Structural variation in the sequencing era[END_REF]. However, long read sequencing has a few drawbacks.

Beside an error rate that limits the accurate detection of SNVs and small indels, it is not fully adapted for the detection of very large genomic alterations, such as balanced inversions embedded in duplications of several hundred kilobases or in the order of megabases. As a means to provide a comprehensive characterization of structural variants in human and other primates, including complex inversion events, Porubsky et al. take advantage of single-cell strand sequencing (Strand-seq), a technique based on selective but shallow sequencing of the template strand in isolated daughter cells upon cell division, which can inform on the orientation of DNA at chromosome-length scale [START_REF] Sanders | Characterizing polymorphic inversions in human genomes by single-cell sequencing[END_REF]. This approach, applied to a human diversity panel of 41 individuals, with ancestry from several continents, provides the most complete genome-wide survey of inversions (> 50 bp) in the human population, revealing more than 700 inversion events, two third of which were validated by at least one orthogonal method, such as long-read sequencing or optical mapping. As expected, large balanced inversions are mainly located in repeat-rich regions, either segmental duplications or retrotransposons, supporting their role in human genome plasticity. Another common form of inversions are short inversions (<2 kb) frequently found at the 5' end of L1 retrotransposon insertions (Figure 1A) and resulting from an alternative integration pathway during their mobilization, known as twin priming [START_REF] Ostertag | Twin Priming: A Proposed Mechanism for the Creation of Inversions in L1 Retrotransposition[END_REF]. The precise analysis of the internal breakpoints and 5' junctions reinforces the idea that microhomology-mediated end joining (MMEJ) plays a preponderant role in the resolution of L1 retrotransposition [START_REF] Zingler | Analysis of 5' junctions of human LINE-1 and Alu retrotransposons suggests an alternative model for 5'-end attachment requiring microhomology-mediated end-joining[END_REF].

Extensive analysis of large balanced inversions shows that at least 40 of them, representing as much as ~0.6% of the genome, are subject to inversion toggling (Figure 1B). Although this flip-flop property was already observed throughout the evolution of primate genomes [START_REF] Porubsky | Recurrent inversion toggling and great ape genome evolution[END_REF], this new study indicates that the process also acts on a much shorter evolutionary scale. In addition, toggling segments are not homogeneously distributed along chromosomes, but are enriched within the sex chromosomes. The absence of homologous recombination and X chromosome hemizygosity have long been proposed to promote NAHR and thus inversions associated with repeats [START_REF] Carvalho | Mechanisms underlying structural variant formation in genomic disorders[END_REF]. The authors now provide support for this model at the population level. They also document the dynamics of recurrent inversions. First, they estimate the rate of toggling between 3.4x10 -6 and 2.7x10 -4 per locus per generation. Second, by leveraging phased SNVs, they propose an evolutionary scenario for several recurrent inversions, and find evidence of both independent parallel events and serial events (Figure 1B). In the future, defining the precise break points of inversions within segmental duplications or retrotransposons could provide a direct way to trace back the history of inversions if these repeats are sufficiently divergent. Indeed, each recombination event is expected to occur at a distinct position.

Finally, the consequences of these inversion hotspots, when located nearby a gene, are multiple. They can lead to the formation of chimeric-transcripts or perturb interaction between genes and regulatory sequences, such as enhancers, by disrupting topologically associating domains (TADs) boundaries [START_REF] Ho | Structural variation in the sequencing era[END_REF]. Strikingly, regions of toggling also overlap with regions associated with neurodevelopmental genomic disorders. Beyond direct effects of inversions, the authors predict haplotypes that could act as pre-mutational states for subsequent morbid rearrangements (Figure 1B), which could have important implications for the diagnosis of genomic disorders [START_REF] Carvalho | Mechanisms underlying structural variant formation in genomic disorders[END_REF]. (or Alu and SVA, not shown) is a particular form of SV. L1 integration is often associated with an inversion at its 5' end (shown in red). SNV: single nucleotide variant; indel: insertion or deletion; L1: long interspersed element 1; TSD: target-site duplication; SV: structural variant.

(B) The landscape of inversions obtained in a human diversity panel of 41 individuals highlights the evolutionary history of recurrent inversions. Some events were inferred to have occurred independently in several lineages (parallel inversions). Evidence for serial toggling along the same lineage were also observed (serial inversions). The study also identifies premutational states for genomic disorders, i.e. alleles for which the inversion event can predispose to subsequent morbid rearrangements (right). A hypothetical situation is shown here, where a functional element (e.g. gene, promoter, enhancer, etc) (solid grey arrow) is flanked by a large (green triangles) and a short (yellow triangles) segmental duplications.

Upon inversion between the green inverted repeats, one of the yellow repeats is inverted. In the new configuration, the pre-mutational state, the pair of yellow repeats is now in direct orientation. In turn, they can recombine by non-allelic homologous recombination leading to the deletion of the functional element, the formation of a morbid allele and a genomic disorder. Similarly, inversions can produce "protective haplotypes" that prevent further morbid rearrangement (not shown).

  SV-detection has been driven by methodological advances in genome-wide genotyping assays, each technological advance providing access to a new type of variations. Almost 20 years after the initial release of the reference human genome, Porubsky et al. make a giant effort to characterize the inversion landscape of the human genome, an important resource for human genetics, and set a new standard for future genomics studies.

FIGUREFigure 1 -

 1 FIGURE

ACKNOWLEDGMENTS

Work in the laboratory of GC is supported by the French government, through the Agence Nationale de la Recherche (Idex UCAJEDI, ANR-15-IDEX-01; Labex SIGNALIFE, ANR-11-LABX-0028-01; ImpacTE, ANR-19-CE12-0032; ActiveLINE, ANR-21-CE12-0001), the Fondation pour la Recherche Médicale (FRM, DEQ20180339170), Inserm (GOLD crosscutting program on genomic variability), CNRS (GDR 3546).

DECLARATION OF INTERESTS

SL declares not competing interests. GC is an unpaid associate editor of the journal Mobile DNA (Springer-Nature).


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text:
Marianne Lefebvre
email: marianne.lefebvre@univ-angers.fr

Masha Maslianskaia-Pautrel

Pauline Laille

Alternative adaptation scenarios towards pesticide-free urban green spaces: welfare implication for French citizens

Keywords: JEL classification : Q24, Q26, C25 Choice experiment, France, Pesticides, Urban green spaces, Welfare measure

Adaptation of urban green spaces (UGSs) to allow their maintenance without pesticides is likely to impact the value attached to these green infrastructures by urban citizens. To understand citizens' preferences for UGSs in this context, a Discrete Choice Experiment was administered in France in 2017, when a pesticide ban in all UGSs was implemented. It allows evaluating the impact on citizens' welfare of different UGSs management scenarios without pesticides. The scenario offering new recreational opportunities is by far the most valued by citizens. Only a minority is worse-off in the "laisser-faire" scenario, where the vegetation is much less controlled. Citizens suffer from welfare losses in the scenario "apparently as before" since it comes at the cost of deteriorated working conditions for maintenance teams. The policy recommendations drawn can contribute to greater social acceptance of the transition towards pesticide-free UGSs.

Introduction

The European Commission announced two pesticide reduction targets as part to the Farm to Fork Strategy in May 2020. These are a 50% reduction in the use and risk of chemical pesticides and a 50% reduction in the use of more hazardous pesticides by 2030. This reduction concerns not only agricultural land, but also other types of land such as urban green spaces (UGSs). Pesticide use on amenity areas accounts for less than 3% of total pesticide use per year, but with strong environmental impacts, in particular on water contamination [START_REF] Kristoffersen | A review of pesticide policies and regulations for urban amenity areas in seven european countries[END_REF]. Some European countries officially extended their pesticide reduction efforts to non-agricultural areas well before this EU legislation. In France for example, following a law voted in 2014, pesticides are banned in public gardens, parks and other green spaces since 2017. While some cities had started to reduce pesticide use well before the ban, the challenge for most municipalities is to adopt suitable technical solutions for pesticide-free management whose consequences on the UGSs will be accepted by the population. While the risk reduction associated to the consumption of food produced with less pesticides is now well acknowledged by citizens, the consequences of UGS management without pesticides are less tangibles for the users of the recreational services offered by UGSs. 4 Our research aims at understanding the conditions for social acceptance, necessary for a successful transition towards pesticide-free UGSs.

Discrete choice experiment (DCE) is now acknowledged as a relevant method to evaluate citizens' preferences for natural environment in cities, in particular to highlight their multiple dimensions and their non-use values. For instance, the method has been used to assess preferences for parks [START_REF] Bullock | Valuing urban green space: Hypothetical alternatives and the status quo[END_REF][START_REF] Tu | Preferences for urban green spaces and peri-urban forests: An analysis of stated residential choices[END_REF][START_REF] Campagnaro | General, stress relief and perceived safety preferences for green spaces in the historic city of padua (italy)[END_REF], tree lines [START_REF] Giergiczny | From valuation to governance : Using choice experiment to value street trees[END_REF], urban recreational trails [START_REF] Arnberger | The influence of age on recreational trail preferences of urban green-space visitors: a discrete choice experiment with digitally calibrated images[END_REF] or for UGSs overall management plan in one city [START_REF] Kim | Understanding services from ecosystem and facilities provided by urban green spaces: A use of partial profile choice experiment[END_REF]. This approach is especially valuable when preferences cannot be observed, since users rarely have in their everyday life the opportunity to choose among different UGCs [START_REF] Liotta | Planning for environmental justice -reducing well-being inequalities through urban greening[END_REF]. The DCE method also allows estimating compensating surplus for shifts in UGSs management scenarios [START_REF] Mcintosh | Using discrete choice experiments to derive welfare estimates for the provision of elective surgery: Implications of discontinuous preferences[END_REF]. Knowing the distribution of the welfare impacts of a policy change allows making judgements concerning its social acceptability. This method has been used previously to measure the welfare impacts of alternative agricultural land and forest management scenarios. For example, Rodriguez-Entrena et al.(2012) have valued different soil management programs in order to value the carbon sink function of the Andalusian olive groves. [START_REF] Meyerhoff | Benefits of biodiversity enhancement of nature-oriented silviculture: Evidence from two choice experiments in germany[END_REF] have provided welfare measures for a more nature-oriented forest conversion program in Lower Saxony, Germany. We provide here a new case study for urban land management.

Building on the analysis of preferences for specific characteristics of UGSs managed without pesticides developed in [START_REF] Laille | Individual preferences regarding pesticide-free management of green-spaces: a discrete choice experiment with french citizens[END_REF], we calculate the welfare impacts of three UGSs management scenarios without pesticides. They are compared to a benchmark hypothetical situation where all UGSs' attributes would be unchanged compared to the situation before the pesticide ban. To do so, we rely on the estimates of a random parameter logit model applied to data collected with a DCE survey administered to a representative sample of the French metropolitan population. In this survey, each respondent was asked to choose between different hypothetical management schemes of the parks and gardens in his city (all without pesticides) defined by six characteristics likely to be impacted by the transition to pesticide-free management. The welfare measures obtained are useful to define the conditions for the transition to be accepted.

We find that the attribute most valued by citizens is the non-deterioration of recreational opportunities. Moreover, most citizens are willing to accept an increase in the budget allocated to UGSs for management scenarios favoring the presence of fauna and areas with a natural visual appearance. While it is less visible by citizens, the respondents do care about the working conditions of the UGS maintenance teams. As a result, most respondents suffer from a welfare loss in the scenario where vegetation is controlled at the cost of deteriorated working conditions. On the contrary, the scenario consisting in the improvement of recreational opportunities to compensate citizens for the changes in UGSs appearance is by far preferred by most of the respondents. We also highlight the heterogeneity in preferences, partly explained by gender, education, visit frequency to UGSs and general knowledge on the pesticide ban. The method can be replicated to estimate the welfare impact of other scenarios that would be envisaged by authorities in charge of the pesticide-free transition in other contexts.

The article is structured as follows. Section 2 presents the experimental design. The method for data analysis is exposed in section 3, and data in section 4. Section 5 discusses the results and policy implications. The last section concludes and highlights avenues for future research.

Experimental design

The survey consisted of several choice sets, each containing two mutually exclusive hypothetical options between which respondents were forced to choose their preferred one. 5The options characterize an average UGSs in the city of the respondents and they are defined by a set of six attributes, each attribute taking one level.

Attributes and levels

The six attributes selected are the UGS characteristics of most interest for the users and most likely to be impacted by the transition to pesticide-free management. They are: recreational opportunities, visual appearance, fauna abundance, existence of information, working conditions for maintenance teams and the share of the city budget allocated to UGSs. The definition of attributes with their levels are presented in Table 1. They have been selected based on interviews with managers and local politicians in charge of UGSs, as well as technical references provided by the resource centre for UGSs management in France and the environmental economics and landscape management literature on preferences for UGSs. A pilot conducted with 75 citizens allowed testing their understanding of the attributes.

The originality of our approach is that the levels of the attributes have been defined to describe the evolution following the pesticide ban, therefore allowing the estimation of the welfare impacts according to the way the transition is managed. The reference level corresponds to an unchanged situation with respect to what could be obtained with chemical pesticides. The technical constraints have changed with the pesticide ban, but we assume that some of the UGS characteristics can be left unchanged. Recreational opportunities and working conditions are attributes which may be improved or deteriorated with the pesticide ban, leading to three levels: the second level corresponds to an improvement and the third level to a deterioration compared to the unchanged situation. Since it seems unrealistic to consider the case where the pesticide ban would generate a loss of wildlife and a reduction in the public budget allocated to UGSs6 , the second level for those attributes corresponds to a small increase and the third one to a major increase with respect to the "unchanged situation". The two remaining attributes have two levels. For the visual appearance, the reference level is "controlled" since it corresponds to the visual appearance obtained with pesticides, corresponding to the situation in most UGSs before the pesticide ban. The second level is a more "natural" appearance since UGS managers may decide to limit the control of the vegetation and accept more wildness. The information attribute takes the value "absent" (reference level) or "existing", if information campaigns directed towards citizens and maintenance teams are organized. An efficient factorial design was applied in this study, using the Ngene software. We used the D-error criterion (0.079) to optimize the efficiency of the experimental design on the basis of prior results gleaned from the pilot survey. The 72 scenarios generated were then organized in 36 choice cards with two scenarios labelled "option A" and "option B" (Figure 1). These choice cards were splitted into 4 blocks of 9 choices. But in order to control for learning and lassitude, we created two versions of each block varying the order of the choice cards, for a total of 8 blocks. Lastly, to check for consistency, we duplicated one of the choice card.7 To summarize, each respondent was randomly assigned to one

Scenarios

The DCE method allows providing estimates for the welfare impact of different transition scenarios, associated with multiple changes in attributes. We define an hypothetical benchmark scenario S0 and focus on three management scenarios Si defined by three different combinations of the six attributes described above, but the method can easily be used to assess the welfare impact of other scenarios. The correspondence between the three scenarios and the attributes is summarized in Table 2. While practitioners have developed typologies to differentiate UGSs according to the maintenance required -grass cutting, pruning, irrigating, weeding ...- [START_REF] Allain | La ville : un territoire nouveau pour la nature ? la gestion différenciée en europe[END_REF], our scenarios are described by attributes of interest for the users and likely to be impacted by the pesticide ban.

The benchmark scenario (S0) corresponds to a situation where attributes are unchanged compared to the situation before the pesticide ban: recreational opportunities, fauna abundance and the working conditions are unchanged, the visual appearance is controlled (as commonly observed when chemical pesticides was available) and no information nor training for workers is available. It is hypothetical since it is impossible to maintain UGS characteristics identical without the help of chemical pesticides. Nevertheless, this benchmark is useful since citizens may be reluctant to changes in the visual appearance and services offered by UGSs and may expect such scenario to take place. During the interviews conducted before launching the survey, managers mentioned the importance of information to explain that this scenario is not applicable. As a result, we consider three alternative scenario judged as realistic by practitioners and evaluate welfare change with names A and B were swapped.

S0 as a benchmark.

The apparently as before scenario (S1) consists in keeping as much as possible the attributes' levels similar to the situation before the pesticide (as in the benchmark situation S0). But without chemical pesticides, keeping the controlled visual appearance and allowing for the same recreational opportunities require extra work (for example for weeding) compared to the situation with access to pesticides. Agents' working conditions may be deteriorated. The change in the working conditions is thus the only difference between S0 and S1. This scenario is likely to be selected for the maintenance of iconic gardens such as those adjacent to the town halls.

The laisser-faire scenario (S2) consists in a drastic change in UGSs management in order to reduce the maintenance burden in the absence of the cheap and efficient solution to control vegetation (chemical pesticides). Weeds are more present, alternative landscaping management strategies are implemented, causing different textures and colors to appear (e.g. mulch). The visual appearance therefore evolves towards more "natural" or "wild", but can also be considered as "poorly maintained" by some. When the grass is cut less frequently, the recreational opportunities can be deteriorated. Users and workers are informed of the changes generated by the pesticide ban in order to understand why the laisser-faire is positive, in particular since it provides the opportunity for much more wildlife to develop in new habitats. With this reorganization, workers may appreciate an improvement of their working conditions.

In the new opportunities scenario (S3), the managers decide to reduce the maintenance burden by letting the vegetation evolving towards a more natural appearance. But contrarily to S2, investment in equipment are realized in order to improve the recreational opportunities and somehow compensate the change in the visual appearance. Fauna observation may also be a new opportunity offered to visitors. Workers may dedicate less effort to control the vegetation but will have to maintain these equipments. Their working conditions may therefore be neither improved nor deteriorated. While this reorganization is the consequence of the pesticide ban, the managers may decide not to communicate on the benefits of pesticide-free UGSs to the public and workers, but rather put the focus on the new recreational opportunities offered.

Method for data analysis

Discrete choice approach is based on Lancaster's demand theory [START_REF] Lancaster | A new approach to consumer theory[END_REF] and the econometric modeling is based on the random utility theory [START_REF] Mcfadden | Conditional logit analysis of quantitative choice behavior[END_REF]. Respondents are expected to select their preferred scenario from a set of hypothetical pesticide-free UGS management scenarios composed of six attributes (X).

The preferences of each individual i = 1, ..., N for different options j = 1, ..., J in choice set t = 1, ..., T are defined as:

U ijt = V ijt + ijt = X ijt β i + ijt (1)
with V ijt is a function of observable attributes of the options and ijt an unobserved random component.

An individual i will choose an option k from J options, if U k > U j ∀j = k. The probability, p kit , to observe the choice k of the individual i in choice set t is given by:

p ki = P rob   j =k (U kit > U jit )   = P rob   j =k ( jit < V kit -V jit + kit )   (2)
In the baseline framework the random error terms is assumed to be iid following Gumbel distributions. The probability p ki is thus given by:

p ki = exp(V ikt ) J j=1 (exp(V ijt )) (3)
In the Random Parameter Logit model (RPL), the parameters β i (equation 1) are randomly distributed and vary over decision makers following a given distribution in order to represent the heterogeneity in respondents' tastes and cognitive abilities [START_REF] Mariel | A more flexible model or simply more effort? on the use of correlated random parameters in applied choice studies[END_REF]. It can be decomposed into :

β i = β + Λz i + Γν i (4)
where β is a parameter vector representing the fixed means of the random parameter distribution, z i is the vector of observed individual-specific characteristics that affect the mean of the random parameter distribution and Λ is the associated parameter matrix, allows us to take into consideration a possible interaction of individual characteristics and attributes. The random unobserved taste variation is represented by ν i , a vector of uncorrelated random variables with mean zero and covariance matrix with known values on the diagonal, fixed by identification restrictions. Γ is a matrix defined a convariance structures among N random parameters. In the case of uncorrelated random parameters, Γ is a diagonal matrix, but individuals may have correlated preferences for different attributes (not only for different levels of the same attribute). In this case, Γ is a lower triangular matrix with non-zero off diagonal elements. [START_REF] Hess | Correlation and scale in mixed logit models[END_REF] demonstrate that the RPL model with full correlation among utility coefficients allow for all sources of correlation, including scale heterogeneity. As suggested by [START_REF] Mariel | A more flexible model or simply more effort? on the use of correlated random parameters in applied choice studies[END_REF], we compare the RPL model with full correlation among utility coefficients and the RPL with uncorrelated random parameters.

As commonly assumed in the literature [START_REF] Hensher | The mixed logit model: the state of practice[END_REF], the coefficient associated with the cost attribute is considered to be constant, whereas the other RPL parameters are assumed to be normally distributed across population.8 To account for non-linear relationships, all attributes were dummy-coded, except the budget attribute that was coded as continuous (+0%, +5% and +15%).

Comparing the impacts of different attributes: Marginal Rates of Substitution

We use Marginal Rate of Substitution (MRS) to interpret the relative impact of the attributes since they cannot be compared using attribute parameter size and significance. Indeed, the effect of an attribute can be due to a large weight relative to other attributes, but also to large differences in scale values associated with the levels, or some combination of both [START_REF] Lancsar | Several methods to investigate relative attribute impact in stated preference experiments[END_REF]. In particular here, distances between the levels of different qualitative attributes don't have the same meaning. Investigating the relative importance people place on the various attributes requires a common scale, provided by the MRS tool.

Because of linear assumption about individual utility function and dummy-coded attributes, the MRS associated with attribute a at his level l is equal to the corresponding coefficients ratio:

M RS a,l = β a,l β BU DGET (5)
where β a,l represents the coefficient of the corresponding non-monetary attribute, and β BU DGET represents a proxy for the marginal utility of income.

The MRS can be viewed as the average weight in trade-off when moving from the reference level of attribute a to level l, expressed in percentage point increase in the city budget allocated to UGSs. Because of the common denominator, MRS allow comparing different attributes and show the characteristics to be prioritized in a context of limited financial resources. The median MRS provides useful information on the share of the population with positive (and negative) preferences towards an attribute's level.

Welfare measures

In order to assess the acceptability of alternative pesticide-free management scenarios, we measure the welfare impacts of the scenarios described in Table 2. We calculate the welfare impact as a compensating surplus (CS) [START_REF] Espinosa-Goded | What do farmers want from agri-environmental scheme design? a choice experiment approach[END_REF][START_REF] Rodríguez-Entrena | Evaluating the demand for carbon sequestration in olive grove soils as a strategy toward mitigating climate change[END_REF][START_REF] Meyerhoff | Benefits of biodiversity enhancement of nature-oriented silviculture: Evidence from two choice experiments in germany[END_REF]. CS is the maximum amount of money a respondent would be willing to pay (or willing to accept) to have the same utility in the pesticide-free scenarios as in the hypothetical benchmark scenario. The welfare change is thus expressed as :

CS S = V 0 -V S -β budget (6)
where V 0 and V S represent the conditional indirect utility associated respectively with the benchmark and the scenarios, and β budget is the coefficient for the budget attribute.

A positive CS means that citizens are worse-off in the pesticide-free scenario compared to the benchmark: they request a compensation in the form of an increase in other municipal budget lines to accept the transition. A negative CS indicates that citizens are better-off with the transition: they are willing to accept an increase in the budget allocated to UGSs for this change.

Data

The sample is composed of 500 French citizens surveyed on line in fall 2017.9 Thanks to stratified random sampling, the final sample of 500 citizens is similar to the French population in terms of region, gender, occupation category, and age (Table 3 (top)). More than 500 respondents were interviews but those who did not make the same choice for the two identical choice cards were qualified as "inconsistent" and removed from the sample. Survey length was on average 12 minutes (5% took more than 30 minutes and 5% less than 5 minutes). The Electronic Supplementary Material includes the full text of the survey.

Since previous research suggested that individual preferences for urban landscapes are shaped by socio-demographic variables [START_REF] Giergiczny | From valuation to governance : Using choice experiment to value street trees[END_REF][START_REF] Tu | Preferences for urban green spaces and peri-urban forests: An analysis of stated residential choices[END_REF][START_REF] Chen | Identifying societal preferences for river restoration in a densely populated urban environment: Evidence from a discrete choice experiment in central brussels[END_REF], we also collected other information on respondents' characteristics, complementary to those used to build the representative sample (Table 3). 63% of the respondents have received higher education. More than half of the sample (55.2%) lives in large cities (more than 100000 inhabitants) and one third in small ones (less than 20000 inhabitants). City size may have an impact on preferences towards UGSs since small city inhabitants are more likely to have a private garden and the access to public parks and gardens is more limited in small cities. Those who have their own garden may also be more familiar with the efforts associated to controlling vegetation without pesticides. On the contrary, in large and medium size cities, there are more multiple dwellings, a minority of them with private parks.

Most of the respondents are frequent users of UGSs: only less than 10% have never visited UGSs in the last 12 months, 42.20% of them visited at least once a week UGSs in the last 12 months and 49.20% visited them less than once a week. Frequent visits to parks and gardens are not so surprising since most of the respondents live in big cities and they have interest in the survey topic if they decided to respond to the panel invitation. We also collected information about respondents' knowledge about the pesticide ban through three questions (bottom of Table 3). We then built a synthetic indicator of self-declared knowledge with vary from 0 (no prior knowledge) to 3 (complete knowledge). Despite the fact that the survey was conducted the same year than the implementation of the pesticide ban (2017), half of the respondents declared to have no prior knowledge and only 6.4% of sample believed they were perfectly informed (they can distinguish a pesticide-free managed green space, they declare to know since when the UGSs of their city are managed without pesticides, and they declare to be more informed than the general public on the topic of the survey). 42.8% of the respondents declared to have partial knowledge (they answered "yes" to one or two of these questions).

The estimations presented in the next section account for potential interactions between the attributes and these socio-demographic and habits variables in order to measure to what extent they shape preferences' towards UGS characteristics.

KnowZP

Answers to the questions "Do you know since when the UGSs of your town are pesticide-free? Can you distinguish a green space managed with pesticides from one pesticide-free? Do you feel more informed than the general public on the topic of the survey (due to your job, studies or those of another household member)? " These answers capture the respondent's knowledge of the survey topic. 3 If the respondents answered "yes" to the tree questions 6.4 2 If the respondents answered "yes" to at least two of these questions 5 Results of the discrete choice analysis

We discuss here the results of two versions of the RPL model with uncorrelated random parameters (Table 4). 10 The first model does not account for respondents' characteristics, while the second extends the model by interacting attributes with such variables. MRS estimates (Table 5) and welfare measures (Figure 2) for the three scenarios are based on estimations of the RPL model with interactions.11

Preferences for UGSs' attributes

In the left-hand size of Table 4, the estimated means of coefficients are all statistically significant (at the 1% significance level) and have the expected signs: respondents evaluate improvements in UGS characteristics positively but perceive a budget increase as negative. The standard deviations of all coefficients are significant and high, confirming that preferences are highly heterogeneous and the RPL model provides a significantly better representation of the choices than the conditional logit model does.

The attributes corresponding to a deterioration compared to the baseline situation (recreational opportunities and working conditions) have the highest numerical weight, albeit negative. On average, ceteris paribus, a deterioration in the working conditions generates a higher loss than the gain associated with improved conditions (-1.054 vs 0.337). The same effect is observed for the recreational opportunities (-1.272 for a deterioration vs 0.480 for an improvement). This is in agreement with prospect theory [START_REF] Kahneman | Prospect Theory: An analysis of decision under risk[END_REF]. Furthermore, we provide a new input to the contrasted literature on citizens' preferences for wild-looking areas in cities [START_REF] Sang | The effects of naturalness, gender, and age on how urban green space is perceived and used[END_REF][START_REF] De Groot | Visions of nature and landscape type preferences: an exploration in the netherlands[END_REF][START_REF] Harris | Green space context and vegetation complexity shape people's preferences for urban public parks and residential gardens[END_REF][START_REF] Arnberger | Are urban visitors' general preferences for greenspaces similar to their preferences when seeking stress relief?[END_REF][START_REF] Tagliafierro | Landscape economic valuation by integrating landscape ecology into landscape economics[END_REF][START_REF] Bronnmann | The value of naturalness of urban green spaces: Evidence from a discrete choice experiment[END_REF]. According to our results, most respondents show strong preferences for a natural visual appearance as opposed to a more controlled appearance.

We rely on MRS (Table 5) to analyse the relative impact of the attributes to avoid scale issues. Since attributes are ranked according to the absolute values of the median MRS, attributes corresponding to a deterioration compared to the current situation are in the top of the ranking even if the MRS is negative. Improved recreational opportunities is the most preferred positive attribute (rank 3). While the attributes illustrating the concept of "nature in the city" are positively valued (rank 5 for the natural appearance and ranks 4 and 7 for the fauna abundance), respondents expect pesticide-free UGSs to offer at least the same level of recreational opportunities than before the pesticide ban. The respondents seem not to be bothered by animals since they prefer a major (rank 4) than a minor increase (rank 7) in fauna. The availability of information for citizens and workers and the improvement in working conditions are positively valued, but to a lesser degree (respectively rank 6 and 8). Still, it suggests that citizens are concern by the technical challenge of the transition to pesticide-free management and are able to empathize with maintenance teams. Two characteristics are less consensual. While a majority of the citizens are in favor of a natural visual appearance or the improvement of working conditions, still 34% prefer a controlled visual appearance and 37% are not willing to accept an increase in budget for the improvement of the working conditions. The RPL model with interactions allows understanding what are the socio-demographic and attitudinal characteristics of those persons with differing preferences.

The influence of socio-demographic and attitudinal variables on preferences

In the extended model (right-hand side model in Table 4), we test the effect of the socioeconomic and attitudinal variables described in Table 3 on the coefficients associated with each attribute. Only significant interactions are presented. Our results show the need to account for heterogeneity to provide relevant information on citizens' preferences. Gender, education, region, town size, knowledge on the pesticide ban and visit frequency seem to influence preferences, at least for some of the attributes. For example, respondents with higher self-reported knowledge on the pesticide ban give higher value to a natural visual appearance and a major increase in fauna abundance. This suggests information campaigns on the pesticide ban can increase the acceptability of the change in the visual appearance toward more natural. Those more informed are also less negatively impacted by the increase in budget. While the natural visual appearance is preferred on average, we observe heterogeneity with respect to town size: the preferences for the natural visual appearance is lower for citizens living in large cities compare to small cities and citizens living in medium size cities are on average more in favor of a controlled visual appearance. Surprisingly, the preferences towards information campaigns are not shaped by the selfdeclared knowledge of the topic, while we would have expected those who believe they are not well informed to value information. However, while males have no utility gains associated to information campaigns and training, females do. Visit frequency also shapes preferences: the utility gains associated with an improvement of the working conditions of the maintenance teams are largely reduced for those who visit UGSs at least once a week.

During their frequent visits, they may have the opportunity to observe maintenance teams and they form their judgement that their working conditions are good enough based on these observations. Females are more in favor of an improvement in working conditions than males. Citizens who have received higher education are more impacted by a budget increase. This may be explained by the fact that they are more likely to anticipate that an increase in the budget allocated to UGSs will end up to an increase in their local taxes (in particular if they are also the wealthiest since local taxes in France are based on housing size and property ownership). [START_REF] Krinsky | On approximating the statistical properties of elasticities[END_REF] procedure with 1000 draws. The lower and upper limits of a 95% confidence interval are given by the 26th and 975th sorted estimates of WTP, respectively [START_REF] Hole | A comparison of approaches to estimating confidence intervals for willingness to pay measures[END_REF].

Welfare impact of different management scenarios

In order to measure the acceptability of alternative ways to realize the transition towards pesticide-free UGSs, we provide in Figure 2 estimates for the welfare impact of three pesticide-free management scenarios, compared to an hypothetical benchmark situation S0, where attributes are unchanged compared to the situation before the pesticide ban. Figure 2 presents the distribution of the compensation requested by citizens for each scenario, expressed in percentage points of budget allocated to UGSs. We focus the discussion on the median value since it's informing whether the majority of the population benefit from a positive welfare change, an indicator of social acceptance.

The median compensating surplus of the apparently as before scenario (S1) is positive (+11.20 percentage point of UGS budget), indicating that more than half of the respondents will suffer from a loss in utility if this scenario is chosen. Indeed, S1 consists in keeping unchanged the quality of use, visual appearance and fauna abundance (as before the pesticide ban), but it necessarily comes at the cost of deteriorated working conditions. To receive support from the majority of the respondents, the budget allocated to UGS in S1 should be reduced by 11 percentage points. But since workers need to use more time-consuming weeding techniques, this scenario is also likely to be the costlier. One could have think that the extra-efforts necessary to obtain a controlled visual appearance without pesticide would be valued by citizens but our results show the contrary since citizens empathize with workers. This scenario should therefore be avoided, at least not as a general rule for maintenance of all parks and gardens in a city. While the generalization of S1 is not desirable, it may be a relevant option in the case of an iconic garden surrounding a town-hall or major historical monument for example. In this case, if the extra-work is restricted to the maintenance of very specific areas and less labor-intensive scenarios are implemented in other types of UGSs, the deterioration of the working conditions and the associated welfare losses for citizens could be avoided.

The laisser-faire scenario (S2) was selected as a potential option to limit the maintenance burden in the absence of pesticides. The median compensating surplus for S2 is slightly negative (-1.75), suggesting that slightly more than half of the citizens are betteroff if this scenario is chosen. This comes from the fact that citizens value the natural visual appearance and the abundance of fauna, while it was initially expected these attributes' levels could be associated with welfare losses. Moreover, citizens value positively the improved working conditions of the maintenance teams and the information campaigns, which further increase the welfare associated to S2. Still, the deterioration of recreational opportunities associated with this "laisser-faire" is strongly negatively valued by citizens and therefore limit the welfare gains in this scenario. Moreover, the confidence interval is very large, indicating that many users (47%) would require a compensation (in the form of an increase in other public services for example) to make up for those changes. This scenario is likely to be the cheapest to implement. It could therefore be implemented in areas where the public had anyway limited recreational opportunities before the pesticide ban or in peripheral parks where the experience of "nature-in-the-city" is particularly sought.

The new opportunities scenario (S3) is associated with the largest welfare improve-ment and is preferred by most of the respondents. According to our estimations, 50% of the respondents would be willing to bear an increase of more than 8.07 percentage point in UGS budget for this scenario to be implemented. This scenario offering new recreational opportunities was initially imagined as a compensation for the deteriorated visual appearance. But since citizens also positively value the natural visual appearance, the new opportunities available in S3 and not in S2 further improve welfare. This is true even if the need for the maintenance of new recreational equipment does not guarantee the improvement of the working conditions (contrarily to S2), and this scenario does not encompass information campaigns and training on pesticide-free management. S3 is also more consensual than S2 since the confidence interval is smaller. Still, a little more than a quarter of the population (26.2%) would suffer from a welfare loss. If the choice set would be restricted to the three scenarios analysed here, S3 should be favored, in particular if the improvement in recreational opportunities can be implemented at low cost. Previous available evidence already suggested that citizens highly value the presence of recreational facilities in UGSs [START_REF] Arnberger | Are urban visitors' general preferences for greenspaces similar to their preferences when seeking stress relief?[END_REF][START_REF] Campagnaro | General, stress relief and perceived safety preferences for green spaces in the historic city of padua (italy)[END_REF][START_REF] Kim | Understanding services from ecosystem and facilities provided by urban green spaces: A use of partial profile choice experiment[END_REF] Our results show that there is no obvious scenario to be generalized since none are consensual. Indeed, in S2 and S3 some respondents are worse-off while the majority is better-off compare to the benchmark (and the opposite for S1). This suggests that onesize-fits-all approach is not only technically impossible but also socially undesirable, thus confirming the relevance of differentiated management, a common way of dealing with the pesticide ban when human and financial resources are constrained. It consists in applying to each public green area a specific treatment, with varying levels of performance depending on its category (park, garden or infrastructure), its cultural, social and biological function and its role in the city [START_REF] Allain | La ville : un territoire nouveau pour la nature ? la gestion différenciée en europe[END_REF][START_REF] Aggéri | Inventer les villes-natures de demain: gestion différenciée, gestion durable des espaces verts[END_REF]. Our approach can help to balance the costs of these different treatments with the value citizens place on each type of management scenario.

Conclusion

Discrete choice modelling has been applied to measure the welfare impacts of alternative transition scenarios towards pesticide-free UGSs. The question addressed in the article is not whether stopping pesticide use is beneficial for the population but how the transition to pesticide-free UGSs can be implemented so that it increases welfare for the majority of the population. We identified the UGS characteristics most preferred by the users and the trade-offs they are willing to make in a context of bounded budget. These estimations allow for the calculation of the compensating surplus requested by users to cover for welfare losses due to the change in UGS management to comply with the pesticide ban, according to three different scenarios. Thanks to stratified random sampling based on age, gender, occupation category and region, the study allows drawing conclusions taking as example the French population. The method used can also be extrapolated to other management scenarios.

Managers and local politicians have their own opinion on the acceptability by urban citizens of the changes resulting from the transition towards pesticide-free UGSs. During focus groups with UGS managers and local politicians, we heard the following: "citizens strongly dislike weeds and UGSs should not look like wild areas"; "less pesticides can benefit to fauna, but many urban citizens associate fauna with potential trouble making"; "dedicating a large share of the budget to communication with the general public is crucial". Our results challenge some of these opinions and allow providing evidence-based recommendations, that can help to remove barriers to a successful transition towards pesticide-free UGSs. In particular, we found that citizens have a strong preference for a natural visual appearance, which suggests that the costly control of the vegetation is not always desirable. We also observed that fauna abundance and the improvement in the recreational opportunities available in UGSs are valued by a large majority of respondents. On the contrary, information is only valued by females. With regard to attributes less visible by citizens, the respondents do care about the working conditions of the UGS maintenance teams: a majority prefer their working conditions are improved, and even more numerous are those who are strongly against their deterioration. We found evidence of loss aversion since citizens' utility is on average more impacted by the degradation of working condition or recreational opportunities than their upgrading. Overall, the transition is more likely to be accepted by making sure that recreational opportunities are not restricted and workers' conditions do not deteriorate.

The method used has some limitations. In particular, the results may be biased by framing effects, inherent to stated preferences surveys as responses are contingent on the ways in which information has been formulated and presented in the questionnaire. For example, one may question the implications of using a percentage to describe the change in the budget, instead of using real amounts [START_REF] Kragt | Attribute in choice experiments: How do attribute level descriptions affect value estimates?[END_REF] found no impact of the wording of attribute levels as total versus proportional quantities). One may also question the relevance of having the same images with only an indication of the evolution trend (=, +, -). We are not aware of any reference in the literature assessing the difficulty for respondents to figure-out the differences across levels with such a presentation of the choice cards. Moreover, beyond these purely methodological aspects, the results do not provide information on preferences for UGSs diversity within one city (we only shed light on preferences for an average park or garden in the city of the respondents). This would be of particular interest for managers, since in the cities who have successfully managed the transition, differentiated management is implemented, relying on different management options according to the areas. Analyzing preferences for this diversity within a city would be an interesting addition to our research. Moreover, to be operational, the result indicating strong preferences for a natural visual appearance should be further investigated. Indeed, the exact meaning of a natural visual appearance is ambiguous when associated to areas such as urban green spaces where human interventions are necessaries [START_REF] Allain | La ville : un territoire nouveau pour la nature ? la gestion différenciée en europe[END_REF]. The definition of a natural visual appearance are likely to differ across individuals. Lastly, if data on the cost of the alternative management options would be available, complementary research could include weighing citizens' welfare measures against the costs of alternative pesticide-free management scenarios in order to carry out a comprehensive cost-benefit analysis.

In summary, this study demonstrates how stated preference methods (and DCE in particular) and the calculation of welfare measures can provide valuable and policy-relevant inputs that can support managers in the transition towards zero pesticide in UGS. These inputs include a deeper understanding of public preferences and their heterogeneity, but also quantitative welfare measures for the considered management scenarios.

Figure 1 :

 1 Figure 1: Example of choice card

  top part presents variables used for quota sampling. The last column contains data for the French metropolitan population (Source: INSEE job survey 2012 and Recencement de la population 2017 and OECD(2019) for higher education). The bottom part describes control variables collected in the survey and used in the estimation.

Figure 2 :

 2 Figure 2: Individual compensating surplus to accept the transition to pesticide-free scenarios

  05, * p<0.1 Estimations obtained based on maximum likelihood simulations (1000 Halton draws) Estimated with STATA14 "mixlogit" package LR (model with interactions)= -2 × ((-2387.0099) -(-2384.489)) = 5.04 < 41, 34 = χ 2 (28)0.05Table A2: Estimated correlation matrix of the random parameters (RPL correlated without interactions)

Table 1 :

 1 Attributes

	Attributes	Description

Table 2 :

 2 Attribute levels associated with different scenarios

		S0	S1	S2	S3
		Benchmark Apparently as before	Laisser-faire	New opportunities
	Recreational opportunities Unchanged	Unchanged	Deteriorated	Improved
	visual appearance	Controlled	Controlled	Natural	Natural
	Fauna abundance	Unchanged	Unchanged	Major increase	Minor increase
	Training & Information	Absent	Absent	Existing	Absent
	Working conditions	Unchanged Risk of deterioration	Improved	Unchanged

Table 3 :

 3 Definitions and descriptive statistics of socio-economic control variables

	Variable	Description	% Sample	% French
				population
	VARIABLES USED FOR STRATIFIED RANDOM SAMPLING
	Region	French geographical region where the respondent lives -5 modalities:
	IDF Paris and Parisian region (Ile-de-France)	19	18
	NW North West	23	23
	NE North East	22	22
	SW South West	11	11
	SE South East	25	25
	Age	Age category of respondent -5 modalities:
	1 Between 18 and 24 years old	9.2	10
	2 Between 25 and 34 years old	16.2	15
	3 Between 35 and 49 years old	24.6	25
	4 Between 50 and 64 years old	24.6	25
	5 Above 65 years old	25.4	24
	CSP	Occupational category -4 modalities:
	High Higher socio-economic status	30.6	28
	Low Lower socio-economic status	27.6	29
	Retired Retired	27.8	26
	Unempl Other Unemployed	14	17
	Female
	1 if the respondent is a women	51	52
	OTHER VARIABLES
	HigherEducation
	1 if the respondent has received higher education	63	63
	Townsize	Size of the city where the respondents currently live:
	small Less than 20000 inhabitants	33.8	62
	medium Between 20000 and 100000	11	23
	large More than 100000	55.2	15
	VisFreq	Answer to the questions "In the last 12 months, how often have you visited UGSs on average? "
	0 I don't visit UGSs	8.6
	1 Less than once a week	49.2
	2 At least once a week	42.2

Table 4 :

 4 RPL models with independant random parameters

		RPL uncorrelated	RPL uncorrelated with interactions
	VARIABLES	Mean	SD	Mean	SD
	USE(-)	-1.304***	1.277***	-1.159***	1.305***
		(0.106)	(0.121)	(0.136)	(0.123)
	USE(+)	0.550***	0.846***	0.575***	0.878***
		(0.0848)	(0.135)	(0.0875)	(0.136)
	VISUAL(nat)	0.456***	1.128***	0.634***	1.116***
		(0.0737)	(0.0976)	(0.146)	(0.0998)
	FAUNA(+)	0.288***	0.344*	0.303***	0.406**
		(0.0683)	(0.200)	(0.0706)	(0.180)
	FAUNA(++)	0.460***	0.878***	0.254**	0.896***
		(0.0910)	(0.128)	(0.114)	(0.131)
	INFO	0.305***	0.584***	0.101	0.570***
		(0.0624)	(0.105)	(0.0861)	(0.110)
	WORK(-)	-1.087***	1.102***	-1.108***	1.130***
		(0.0960)	(0.118)	(0.0991)	(0.122)
	WORK(+)	0.279***	-0.554***	0.307**	-0.567***
		(0.0813)	(0.158)	(0.130)	(0.157)
	BUDG	-0.0921***		-0.0941***
		(0.00614)		(0.00983)
	USE(-)xFemale			-0.366**
				(0.176)
	VISUAL(nat)xKnowZP			0.171**
				(0.0772)
	VISUAL(nat)xTownsize medium			-0.685***
				(0.247)
	VISUAL(nat)xTownsize large			-0.414***
				(0.158)
	FAUNA(++)xKnowZP			0.272***
				(0.0911)
	INFOxFemale			0.430***
				(0.123)
	WORK(+)xFemale			0.256*
				(0.150)
	WORK(+)xVisFreq 2			-0.342**
				(0.152)
	BUDGxRegion NW			0.0235**
				(0.0116)
	BUDGxHigherEducation			-0.0348***
				(0.0105)
	BUDGxKnowZP			0.0194***
				(0.00544)
	Nb of observations	4500		4500
	Nb of individuals	500		500
	Log likelihood	-2427.307		-2387.010
	Chi2	312.428		319.393
	AIC	4888.615		4830.020
	BIC	5009.400		5028.959
		Standard errors in parentheses
	*** p<0.01, ** p<0.05, * p<0.1
	Estimations obtained based on maximum likelihood simulations (1000 Halton draws)
	Estimated with STATA14 "mixlogit" package

Table 5 :

 5 Marginal rates of substitution: trade-off between increase in UGS budget and other UGS characteristics

	Attribute	Median	95% CI	Rank	Frequency
						Negative Positive
	USE(-)	-13,91	[-42,91; 14,23]	1	85%	15%
	USE(+)	6,52	[-10,77; 24,42]	3	25%	76%
	NATU	4,87	[-17,56; 27,14]	5	34%	66%
	FAUNA(+)	3,17	[-5,16;	11,14]	7	21%	79%
	FAUNA(++)	4,97	[-12,80; 23,07]	4	28%	72%
	INFO	3,39	[-8,01;	14,91]	6	27%	73%
	WORK(-)	-11,19	[-33,73; 10,43]	2	82%	18%
	WORK(+)	1,90	[-9,87;	13,66]	8	37%	63%
	Note: Attributes are ranked according to the absolute value of the median MRS.
	MRS estimated following the

Table A1 :

 A1 RPL models with correlated random parameters

		RPL correlated	RPL correlared with interactions
	VARIABLES	Mean	Mean
	USE(-)	-1.455***	-1.363***
		(0.120)	(0.155)
	USE(+)	0.581***	0.609***
		(0.0951)	(0.0998)
	VISUAL(nat)	0.456***	0.666***
		(0.0851)	(0.159)
	FAUNA(+)	0.379***	0.389***
		(0.0873)	(0.0892)
	FAUNA(++)	0.659***	0.489***
		(0.126)	(0.145)
	INFO	0.331***	0.109
		(0.0720)	(0.0954)
	WORK(-)	-1.226***	-1.248***
		(0.110)	(0.116)
	WORK(+)	0.343***	0.343**
		(0.0981)	(0.149)
	BUDG	-0.100***	-0.100***
		(0.00717)	(0.0109)
	USE(-)xFemale		-0.262
			(0.182)
	VISUAL(nat)xKnowZP		0.206**
			(0.0833)
	VISUAL(nat)xTownsize medium		-0.791***
			(0.269)
	VISUAL(nat)xTownsize large		-0.381**
			(0.177)
	FAUNA(++)xKnowZP		0.284***
			(0.0971)
	INFOxFemale		0.465***
			(0.131)
	WORK(+)xFemale		0.249
			(0.168)
	WORK(+)xVisFreq 2		-0.289*
			(0.170)
	BUDGxRegionNW		0.0234*
			(0.0124)
	BUDGxHigherEducation		-0.0419***
			(0.0112)
	BUDGxKnowZP		0.0216***
			(0.00581)
	Nb of observations	4500	4500
	Nb of individuals	500	500
	Log likelihood	-2380.7648	-2384.489
	Chi2	412.478	311.283
	AIC	4851.530	4828.978
	BIC	5171.254	5042.127
		Standard errors in parentheses
	*** p<0.01, ** p<0.

Moreover, most of the literature focuses on willingness to pay for food products with less pesticides[START_REF] Florax | A meta-analysis of the willingness to pay for reductions in pesticide risk exposure[END_REF][START_REF] Travisi | Valuing environmental and health risk in agriculture: A choice experiment approach to pesticides in italy[END_REF][START_REF] Costa | Estimating the demand curve for sustainable use of pesticides from contingent-valuation data[END_REF] and at the margin for other agricultural goods like flowers[START_REF] Michaud | Willingness to pay for environmental attributes of non-food agricultural products: a real choice experiment[END_REF]. Preferences for pesticide reduction in non-agricultural goods and services, such as access to UGSs, have hardly been studied in the literature.

There is no opt-out in our design since the transition to pesticide-free management is compulsory and the status-quo is not an available option. When opt-out is not allowed, respondents cannot sidestep the cognitive task of comparing alternatives[START_REF] Dhar | The effect of forced choice on choice[END_REF][START_REF] Dhar | Consumer preference for a no-choice option[END_REF].

Cheval et al. (2017) have found that the savings due to stopping the purchase of pesticides are largely lower than the increase in labor costs to manage UGSs without pesticides.

The options proposed to each respondent were the same for the first and seventh choices, but the

Even if assuming that there is no heterogeneity among the respondents in relation to budget is somewhat unrealistic, the budget parameter was specified as fixed in order to be able to compute the marginal rate of substitutions between the monetary attribute and the others.

The respondents were selected from the Opinionway Internet panel composed of

100,000 persons. The panelists receive a financial compensation for participation to each survey. They are recruited through various channels to reduce sampling bias.

Estimations of the RPL with correlated parameters, together with the correlation matrix are presented in the appendix (TablesA1 and A2). We find high correlations among some of the attributes but we cannot reject the null hypothesis that all out-of-diagonal elements of the correlation matrix of the random parameters are zero (see likelihood-ratio test below TableA1).

Ranking of attributes are similar using the RPL with or without interactions, which shows that our estimates are robust.

Ministry for Agriculture and Food and the Ministry for an Ecological and Solidarity Transition, with the financial support of the French Biodiversity Agency on "Call for research & innovation projects on the development of alternative solutions to plant protection products in gardens, green spaces and infrastructures" research call, with the fees for diffuse pollution coming from the Ecophyto plan. We thank Rafiou Alfa Boukari for his contribution to data collection, Maria Espinosa, Raphaële Préget et Sophie Thoyer for helpful comments on the experimental design and data analysis and


domain: info math sdv.ba

text:
1Francesco

  Search via Parallel Lévy Walks on Z 2Lévy walk (informal):A Lévy walk is a random walk whose step-length density distribution is proportional to a power-law, namely, for each d ∈ R + , f (d) ∼ 1/d α , for some α > 1 Note: the speed of the walk is constant Lévy walks are used to model movement patterns [Reynolds, Biology Open 2018] Examples: Rhytidoponera mayri workers. Credit: Associate Professor Heloise Gibb, La Trobe University • T cells within the brain • swarming bacteria • midge swarms • termite broods • schools of fish • Australian desert ants • a variety of molluscs Lévy walks are used to model movement patterns [Reynolds, Biology Open 2018] Examples: Rhytidoponera mayri workers. Credit: Associate Professor Heloise Gibb, La Trobe University • T cells within the brain • swarming bacteria • midge swarms • termite broods • schools of fish • Australian desert ants • a variety of molluscs Widely employed in the Foraging theory Optimality results: Lévy walks are optimal in different search problems [Viswanathan et al., Nature 1999], [Guinard and Korman, Sciences Advances 2021]

The Lévy flight foraging hypothesis

The Lévy flight foraging hypothesis [Viswanathan et al., Physics of Life 2008]: since Lévy flights/walks optimize random searches, biological organisms must have evolved to exploit Lévy flights/walks

Formulation of an evolutionary hypothesis

The Lévy flight foraging hypothesis

-2

The ANTS problem