Maelys Boennec
email: maelys.boennec@umontpellier.fr

Vasilis Dakos

Vincent Devictor

Sources of confusion in global biodiversity trends

Populations and ecological communities are changing worldwide, and empirical studies exhibit a mixture of either declining or mixed trends. Confusion in global biodiversity trends thus remains while being of major social, political, and scientific importance. Part of this variability may arise from the difficulty to reliably assess global biodiversity trends. Here, we conducted a literature review of studies documenting the temporal dynamics of global biodiversity. We classified the differences among approaches, data and methodology used by the reviewed papers to reveal common findings and sources of discrepancies. We show that reviews and meta-analyses, along with the use of global indicators, are more likely to conclude that trends are declining. On the other hand, the longer the data are available, the more nuanced are the trends they generate. Our results also highlight the lack of studies providing information on the impact of synergistic pressures on a global scale, making it even more difficult to understand the driving factors of the observed changes and how to decide conservation plan accordingly. Finally, we stress the importance of taking into account the sources of confusion identified, as well as the complexity of biodiversity changes, in order to implement effective conservation strategies. In particular, biodiversity dynamics are almost systematically assumed to be linear, while non-linear trends are largely neglected. Clarifying the sources of confusion in global biodiversity trends should strengthen large scale biodiversity monitoring and conservation.

Introduction

Providing a coherent synthesis of the ongoing biodiversity crisis through the quantification of various aspects of temporal changes of biological diversity is a challenge of both scientific and political importance. The accumulation of studies reporting a loss of biodiversity, either in species number (IUCN, 2019), population abundances (WWF, 2022) or at the assemblage or community scale [START_REF] Mckinney | Biotic Homogenization : A Few Winners Replacing Many Losers in the Next Mass Extinction[END_REF][START_REF] Olden | Ecological and evolutionary consequences of biotic homogenization[END_REF][START_REF] Sax | Species diversity : From global decreases to local increases[END_REF], leave no doubt regarding the fact that biodiversity is being depleted. However, empirical reports of temporal changes in biological diversity depict a nuanced and complex picture regarding the magnitude and direction of biodiversity loss, encompassing findings that may intuitively be seen as opposite. In addition to studies quantifying a global decline of biological diversity, others have suggested that biodiversity is not, on average, in decline [START_REF] Blowes | The geography of biodiversity change in marine and terrestrial assemblages[END_REF][START_REF] Dornelas | Assemblage Time Series Reveal Biodiversity Change but Not Systematic Loss[END_REF][START_REF] Dornelas | A balance of winners and losers in the Anthropocene[END_REF][START_REF] Vellend | Global meta-analysis reveals no net change in local-scale plant biodiversity over time[END_REF]. While highlighting a significant turnover in species composition, these analyses found no evidence of a systematic decline in species richness. Other recent studies revealed that only a few declining species were mostly responsible for the negative trends in overall indices [START_REF] Leung | Clustered versus catastrophic global vertebrate declines[END_REF], and demonstrated a rather balanced number of increasing and decreasing population trends worldwide [START_REF] Daskalova | Landscape-scale forest loss as a catalyst of population and biodiversity change[END_REF][START_REF] Dornelas | A balance of winners and losers in the Anthropocene[END_REF].

These heterogeneities in results entails several risks if their sources and uncertainties are not addressed. Firstly, it could lead to sub-optimal or, worse, ineffective conservation policies, as many conservation measures rely on the estimation of indicators or discussion of scenarios covering global biodiversity trend for all taxa on a global scale [START_REF] Agardy | Global marine conservation policy versus site-level implementation : The mismatch of scale and its implications[END_REF][START_REF] Pressey | Conservation planning in a changing world[END_REF].

Furthermore, avoiding to question the sources of the heterogeneity of these results and the uncertainties in the conclusions could encourage a "biodiversity-skepticism" by creating the idea that there is a lack of scientific consensus on the existence of a biodiversity crisis. Similarly, climate-skepticism partly emerged from the belief that there were significant disagreements about global warming among scientists [START_REF] Joslyn | Climate Projections and Uncertainty Communication[END_REF][START_REF] Leiserowitz | Climate Change in the American Mind : Americans' Global Warming Beliefs and Attitudes in April 2013[END_REF]. Such distorted perception was reduced by incorporating uncertainties into IPCC reports, clarifying the fact that much of the variability was due to predictive processes rather than fundamental differences in scientific opinion [START_REF] Howe | Acknowledging uncertainty impacts public acceptance of climate scientists' predictions[END_REF][START_REF] Reilly | Uncertainty and Climate Change Assessments[END_REF]. Thus, conservation science and knowledge on biodiversity loss should also benefit from such clarification and be consolidated by adopting a transparent and quantitative approach to major biases in the global estimates.

If these heterogeneous results have also caused a vivid controversy in the scientific community [START_REF] Cardinale | Overlooked local biodiversity loss[END_REF][START_REF] Cardinale | Is local biodiversity declining or not? A summary of the debate over analysis of species richness time trends[END_REF][START_REF] Gonzalez | Estimating local biodiversity change : A critique of papers claiming no net loss of local diversity[END_REF], it is to some extent probably resulting from the multiple meanings of the term biodiversity. The formal definition largely popularized by the Rio Earth Summit in 1992 equates biodiversity to "the variability among living organisms from all sources […] this includes diversity within species, between species and of ecosystems" (CBD, 1992). This definition itself creates a lot of confusion. For example, the WWF considers biodiversity at the population level (WWF, 2020(WWF, , 2022)). In contrast, others (e.g. [START_REF] Dornelas | Assemblage Time Series Reveal Biodiversity Change but Not Systematic Loss[END_REF]) consider biodiversity at the species or community level. As declines in population sizes and species richness are not necessarily related, both an increase and decrease in "biodiversity" can be concluded depending on the ecological level of interest. Clarifying the trends for each level of biodiversity should, in principle, limit the confusion. In practice however, trends within the same ecological levels show both a decline globally or no net changes; either at species scale (IUCN, 2019;[START_REF] Dornelas | Assemblage Time Series Reveal Biodiversity Change but Not Systematic Loss[END_REF][START_REF] Vellend | Global meta-analysis reveals no net change in local-scale plant biodiversity over time[END_REF] or at population scale [START_REF] Daskalova | Landscape-scale forest loss as a catalyst of population and biodiversity change[END_REF][START_REF] He | The global decline of freshwater megafauna[END_REF][START_REF] Leung | Clustered versus catastrophic global vertebrate declines[END_REF][START_REF] Wagner | A window to the world of global insect declines : Moth biodiversity trends are complex and heterogeneous[END_REF]. Beyond the ecological level considered other factors are therefore also generating confusion in the observed results.

The same difficulties affect the understanding of which and how pressures drive temporal changes of biodiversity on a global scale. The drivers of biodiversity loss are widely documented [START_REF] Ceballos | Accelerated modern human-induced species losses : Entering the sixth mass extinction[END_REF]IPBES, 2019;[START_REF] Pereira | Global Biodiversity Change : The Bad, the Good, and the Unknown[END_REF][START_REF] Pievani | The sixth mass extinction : Anthropocene and the human impact on biodiversity[END_REF][START_REF] Pimm | Human impacts on the rates of recent, present, and future bird extinctions[END_REF]. The effects of climate change and of anthropogenic drivers -e.g. habitat fragmentation -have been studied at the individual level -e.g. through changes in physiology [START_REF] Willis | Biodiversity and Climate Change[END_REF]) -, at the species and population levels, or at the community level -e.g. through changes in interspecific relationships [START_REF] Gilman | A framework for community interactions under climate change[END_REF][START_REF] Walther | Community and ecosystem responses to recent climate change[END_REF] -, or either spatially -e.g. through range shifts [START_REF] Erauskin-Extramiana | Are shifts in species distribution triggered by climate change? A swordfish case study[END_REF][START_REF] Paprocki | Regional distribution shifts help explain local changes in wintering raptor abundance : Implications for interpreting population trends[END_REF] -, or temporally -e.g. through changes in phenology [START_REF] Du | Diverging shifts in spring phenology in response to biodiversity loss in a subtropical forest[END_REF][START_REF] Radchuk | Adaptive responses of animals to climate change are most likely insufficient[END_REF][START_REF] Wolf | Flowering phenology shifts in response to biodiversity loss[END_REF]. However, the responses of different ecological levels to specific drivers are mostly documented at the local scale. The understanding of how global change drivers influence the heterogeneous biodiversity patterns at the global scale is therefore also limited, and filled with controversies. For instance, some studies suggest that habitat fragmentation may be beneficial to biodiversity [START_REF] Fahrig | Forty years of bias in habitat fragmentation research[END_REF][START_REF] Haddad | Experimental evidence does not support the Habitat Amount Hypothesis[END_REF] or that protected areas often fail to reduce biodiversity loss [START_REF] Brooke | Rates of movement of threatened bird species between IUCN red list categories and toward extinction[END_REF][START_REF] Mora | Ongoing global biodiversity loss and the need to move beyond protected areas : A review of the technical and practical shortcomings of protected areas on land and sea[END_REF] and can even be detrimental to biodiversity [START_REF] Geldmann | A global-level assessment of the effectiveness of protected areas at resisting anthropogenic pressures[END_REF].

Acknowledging our current sources of (mis)understanding of the temporal changes of biodiversity and of their drivers at the global scale is urgently needed [START_REF] Tekwa | Detecting and attributing the causes of biodiversity change : Needs, gaps and solutions[END_REF]. International legislation and objectives (such as those discussed at United Nations Biodiversity Conference of the Parties) directly rely on our general knowledge and understanding of global biodiversity dynamics.

The objective of this study is therefore to critically examine this general knowledge. More specifically, we want to review how global biodiversity change is currently quantified, and to identify the most salient sources of confusion when assessing biodiversity trends or the effect of its drivers.

Several hypotheses can be formulated. First, with regard to trends, the data used can be expected to affect the results. The prevalence of certain threatened groups [START_REF] Houlahan | Quantitative evidence for global amphibian population declines[END_REF][START_REF] Marsh | Fluctuations in amphibian populations : A meta-analysis[END_REF], the lack of spatial representation (e.g. tropics are highly biodiverse [START_REF] Laurance | Have we overstated the tropical biodiversity crisis?[END_REF] but lack data representation [START_REF] Feeley | The data void in modeling current and future distributions of tropical species[END_REF]), or the temporal extent of the time series used [START_REF] Duchenne | Controversy over the decline of arthropods : A matter of temporal baseline?[END_REF][START_REF] Gonzalez | Estimating local biodiversity change : A critique of papers claiming no net loss of local diversity[END_REF][START_REF] Vellend | Global meta-analysis reveals no net change in local-scale plant biodiversity over time[END_REF] are likely to impact the conclusions. We also hypothesise that the methods with which trends are quantified play a role. Several studies have already pointed out that summarizing complex data using global indicators can hide meaningful variation [START_REF] Daskalova | Landscape-scale forest loss as a catalyst of population and biodiversity change[END_REF][START_REF] Leung | Clustered versus catastrophic global vertebrate declines[END_REF], but it is not clear to what extent and whether this is the case for other methods. Finally, different approaches, from meta-analyses and reviews of local studies to the analysis of globally aggregated empirical data, might also affect the conclusions.

Regarding the influence of drivers, we also expect that the biodiversity data used impact the results.

Focusing research on specific areas of the world can bias our knowledge. For example, the Arctic is projected to warm at two up to four times the rate of the global average but it is understudied [START_REF] Ipcc | Summary for Policymakers[END_REF]. A patchy data collection across taxa (or periods) also risks missing particularly (un)sensitive groups (or (un)stable periods) [START_REF] Mihoub | Setting temporal baselines for biodiversity : The limits of available monitoring data for capturing the full impact of anthropogenic pressures[END_REF]. Variations are also expected depending on the approach, the methods and the drivers considered.

Here, we conduct a literature review to clarify those sources of confusion, and to review the remaining challenges for future research and conservation science.

Methods

Literature review

We conducted a literature review in February 2022 aiming to identify papers providing an assessment of recent temporal changes of biodiversity globally. We were looking both for papers that studied the changes themselves, but also those that sought to explain the changes by studying the impact of the drivers. Different searches were initially launched in the Web of Science. We tested different search terms to refine the results. We wanted to minimise the number of irrelevant references while ensuring that some commonly known relevant articles (e.g. [START_REF] Dornelas | A balance of winners and losers in the Anthropocene[END_REF] fell within our scope. In the process, we identified broad terms (e.g. "population") that encompassed areas of research beyond our topic. We also found that restricting the search to terms in the titles and abstracts, rather than in the topics of the articles in general, allowed us to limit the search to a manageable number of articles (Appendix S1). The final search we launched in the Web of Science WC=("meteorology atmospheric sciences" OR "infectious disease" OR "biochemistry molecular biology" OR "paleontology" OR "microbiology"). TI is title, AB is abstract and WC is Web of Science Categories. This query resulted in 2,008 matches.

Each of these papers was then reviewed individually by titles, abstracts and then subjected to a full review to check their relevance to our study objective. We included studies that either assess or discuss the assessment of (i) temporal changes of biodiversity ; (ii) during the last century ; (iii) on a broad scale (at least two continents or two oceans). We included studies analysing temporal changes on biodiversity relying on empirical data, but also reviews based on empirical assessments as well as methodological studies explicitly questioning the assessment of global biodiversity changes. For studies relying on data, we excluded those using exclusively human-manipulated or simulated data. Figure 1A summaries this selection process and shows the number of articles excluded on the basis of their failure to meet the above criteria. In addition, we included four reports from the 'Grey literature' (IPBES, 2019;IUCN, 2022;[START_REF] Pörtner | IPBES-IPCC co-sponsored workshop report on biodiversity and climate change[END_REF]WWF, 2020), produced by organisations among the best known that provide assessments of temporal changes of biodiversity globally. 91 references constituted the final database, that we classified into four different categories: (i) biodiversity empirical analysis (n=48) ; (ii) reviews (n=20) ; (iii) methodological papers (n=19) ; (iv) reports (n=4).

Metadata extraction

Methodological papers were considered for discussion purposes. For the other references, we extracted detailed metadata and information to investigate potential sources of heterogeneities regarding the Global Biodiversity Changes (Fig. 1B). We distinguished papers mostly focused on biodiversity trends from those mostly focused on drivers. Papers that were studying both trends and drivers were considered both for analysing trends but also for analysing drivers, as we analyzed these issues separately (n=6).

For papers analyzing biodiversity trends, we recorded bibliometric data, the main conclusions, the type of assessment approach, and, when relevant, information regarding the data and methods used to quantify the changes (Fig. 1B). Conclusions were classified into decreasing trends, increasing trends, mixed trends (i.e. there were as many increasing trends as decreasing, or a majority of no trends) and factor-dependent trends (i.e. directions that varied according to certain factors, such as location).

While retrieving those information, we identified two main assessment approaches adopted in the corresponding studies to produce a global picture of biodiversity changes. First, a bottom-up approach, which correspond to reviews or meta-analyses aggregating results of studies analyzing individual datasets with varying methodologies from one study to the other (e.g. [START_REF] Pereira | Global Biodiversity Change : The Bad, the Good, and the Unknown[END_REF][START_REF] Pievani | The sixth mass extinction : Anthropocene and the human impact on biodiversity[END_REF]. Second, a top-down approach that produces a global result analyzing heterogeneous data aggregated in large databases within the same methodological framework (e.g. [START_REF] Dornelas | A balance of winners and losers in the Anthropocene[END_REF][START_REF] Wilson | Insect responses to global change offer signposts for biodiversity and conservation[END_REF]. We recorded the assessment approach for each reference and decided to investigate to what extent these could explain part of the observed heterogeneous results.

When relevant and available, we also retrieved information on the data used, the ecological level targeted and the methodological processes used to quantify the changes. We recorded the databases used, temporal and spatial scope, taxonomic scope, and number of species.

There are many measures of biodiversity, but in the papers selected we found measures of biodiversity at the population scale (abundance, density or biomass), at the species scale (mostly species richness), and at the community scale (assemblage composition, studied through similarity indices).

We categorised the methods used to quantify the changes into three main categories. The first category we identified concerns papers that studied the changes through linear trends of individual ecological level. These papers performed linear regressions (and all variations, e.g. state space models [START_REF] Daskalova | Landscape-scale forest loss as a catalyst of population and biodiversity change[END_REF] or logged annual growth rate [START_REF] Williams | Vertebrate population trends are influenced by interactions between land use, climatic position, habitat loss and climate change[END_REF]) on biodiversity measures either population by population or species by species. These results were then used to reach conclusions about the general direction of change. We will refer to these methods as "linear models on individual time series". The second category we identified corresponds to papers producing global indicators built upon populations (e.g. Living Planet Index (LPI) [START_REF] Loh | The Living Planet Index : Using species population time series to track trends in biodiversity[END_REF]) or species (e.g. Red List Index (RLI)), and estimating global trends of those single aggregated metrics. The last category we identified are the other methods that were used more sporadically, quantifying other aspects than the linear changes in abundance or species richness (e.g. quantifying the coefficient of variation [START_REF] Marsh | Fluctuations in amphibian populations : A meta-analysis[END_REF], non-linear changes [START_REF] Keith | Temporal correlations in population trends : Conservation implications from time-series analysis of diverse animal taxa[END_REF], or other aspects like resistance and recovery [START_REF] Capdevila | Global patterns of resilience decline in vertebrate populations[END_REF]).

For papers analyzing drivers of biodiversity changes, we recorded bibliometric data, the main conclusions, the type of assessment approach, and, when relevant, information regarding the biodiversity data used and the identity of the studied drivers (Fig. 1B). Conclusions were classified into different categories based on the nature of the impacts into negative, none or positive, and factor-dependent. The assessment approaches and information regarding the biodiversity data were the same as the ones described regarding the examination of the trends in biodiversity. The information provided on the drivers and the methods used to quantify the drivers' impacts on biodiversity was scarce and heterogeneous. As a result, we did not address the issue of the sensitivity of the results to the drivers data and methods used in depth. We rather examined the impact of the identity of the drivers studied. We declined the drivers between climate change, other anthropogenic pressures (mainly land use change) and conservation policies (protected areas).

Results

Global overview

Interestingly, we found only 91 papers that analyze temporal changes of biodiversity globally, while a plethora of examples accumulate at more local scales (e.g. [START_REF] Donald | Agricultural intensification and the collapse of Europe's farmland bird populations[END_REF][START_REF] Koleček | Global population trends in shorebirds : Migratory behaviour makes species at risk[END_REF]. These were published from 1991 to 2021, with a majority published after 2010 (Appendix S2). We identified an increasing interest in this question over time, although this tendency also reflects an overall increase in the number of papers published during the same period. Of the 91 papers, 48 directly relied on empirical datasets, 20 were reviews, 19 were methodological papers and 4 were reports that we added from grey literature.

Out of the 44 papers assessing temporal trends in biodiversity changes, 57% (n=25) concluded that biodiversity is globally in decline. More than a third of the papers concluded that trends are mixed or factor-dependent (36%, n=16). Only 3 of the reviewed papers showed evidence of increasing biodiversity trends. Out of the 34 studies focusing on drivers, 65% (n=22) concluded negative effects on biodiversity, 26% (n=9) concluded that the effects were factor-dependent, and only 3 papers concluded that there was no significant effect or that the effect was positive (the latter referring to the effect of conservation plans only).

(ncalc=3) 2,905 (ncalc=21)
Description of the five types of encountered databases providing time series data on different biodiversity levels. n tot represents the total number of articles considering each of the data source. n calc represents the number of articles used to calculate the averages (without those whose information is unavailable). * Single non-aggregated but marginal data sets (used in articles only once). ** Aggregation of several locally available data sets in individual studies.

Papers relying on empirical data used in majority aggregations of several data sets from individual studies (62,5%, n=30). Still, we found that three main global databases gathering biodiversity data were used: BioTIME [START_REF] Dornelas | BioTIME : A database of biodiversity time series for the Anthropocene[END_REF], the Living Planet Database (LPD) [START_REF] Loh | The Living Planet Index : Using species population time series to track trends in biodiversity[END_REF], and the Global Population Dynamics Database (GPDD) [START_REF] Inchausti | Investigating Long-Term Ecological Variability Using the Global Population Dynamics Database[END_REF]. The remaining papers relied on other unique but more sporadically used databases that were not open access. Table 1 highlights the characteristics and properties of the different data sources. The overwhelming majority of papers were based on terrestrial data covering all continents (67%, n=32), which is not surprising since our selection process was based in part on the choice to have global studies. Still, we accepted articles covering at least two continents, and we note that the only continents that were studied in pair were America and Europe. The temporal coverage of the data was quite heterogeneous, but mainly covered the last 70 years (Fig. 2A). This also confirms the strength of BioTIME's temporal coverage compared to other databases [START_REF] Dornelas | BioTIME : A database of biodiversity time series for the Anthropocene[END_REF]. The taxonomic coverage shows that the papers in our corpus mainly relied on data referring to several groups (Fig. 2B). As well as for the geographical extent, this is not surprising considering our selection process.

Still, there is a preponderance of data on mammals and birds, more generally on terrestrial vertebrates, and an under-representation of insects and invertebrates.

The empirical data were based on different levels of biodiversity (Fig. 2C). Papers relying on biodiversity at the population scale (e.g. abundances, biomass, density) represented 50% of our corpus (n=24), papers relying on biodiversity at the species scale (e.g. species richness, detection rates) represented 31% (n=15). The 19% remaining relied on grouped levels, i.e. several levels among population, species, or also community scale (studied through community composition).

Potential sources of heterogeneities in the assessment of biodiversity trends

We investigated three potential sources of heterogeneities. First, we examined the effect of using different assessment approaches. When papers used a bottom-up approach (i.e. aggregating local or regional results with varying methodologies into meta-analyses or reviews), they mostly concluded a decline in global biodiversity (69%, Fig. 3). In contrast, when papers used a top-down approach (i.e. performing analyses through a single methodology on global datasets), their conclusions were much more balanced: a bit more than 50% concluded that biodiversity was decreasing and almost 50% that trends were mixed or increasing (Fig. 3).

Figure 3. Proportions within conclusions depending on whether global biodiversity trends or drivers were assessed and depending on the assessment approach (i.e. top-down or bottomup).

Second, we examined the effect of using data with different characteristics. Among the 22 papers using aggregated databases, 45% concluded a decline, 41% mixed or factor-dependent trends and 14% identified increases in biodiversity globally. The LPD and the other individual datasets were mainly associated with a decline in global biodiversity, whereas studies using the BioTIME database mainly concluded that trends were mixed or factor-dependent (Fig. 4A). The conclusions between declining or mixed trends were balanced no matter the number of taxonomic groups considered (Fig. 4A). The time span did influence the conclusions however. The longer the data, the more heterogeneous the results were: 78% of articles based on time series of less than 30 years concluded that trends were declining, whereas this percentage dropped to 60% for time series between 30 and 49 years long, and to 22% for time series longer than 50 years. Third, we examined the effect of using different methods. Among the 12 papers we reviewed that used global indicators to assess biodiversity changes, 9 concluded that biodiversity was declining, and only 3 that trends were more mixed. On the other hand, papers using linear models on individual time series depicted a much more nuanced picture, with 9 papers concluding that trends were mixed, 3 that trends were declining and 2 that trends were increasing. The other methods weren't much represented but concluded declines in 4 papers out of 6. Surprisingly, papers focusing on the population level showed more declines than the ones focusing on the species level (67 % declines against 44 % declines respectively). The papers relying on several levels of biodiversity only concluded that trends were mixed. However, as Figure 4B illustrates, these conclusions seem to be highly driven by the underlying quantification methods. Indeed, declines identified at both species or population levels are in majority declines that are identified through the use of global indicators.

Potential sources of heterogeneities in the assessment of biodiversity drivers

We also explored the effect of three potential sources of heterogeneities when assessing biodiversity drivers' impacts. First, we examined the effect of using different assessment approaches. Among the papers using a top-down approach, there was an almost even split between concluding a negative effect of the drivers considered on biodiversity (46%) and a factor-dependent or no effect (54%). In contrast, 76% of the papers using a bottom-up approach concluded that the drivers identified had a negative impact (Fig. 5).

Figure 5. Alluvial plots representing the links between the potential sources of heterogeneity

and the conclusions when assessing the impact of the drivers. A (n=9) highlights the impact of the data characteristics. B (n=20) highlights the impact of the biodiversity level and the identity of the drivers. The height of the boxes is proportional to the number of papers. Flow thickness between boxes is proportional to the number of papers. Colours of the flow reflect the conclusions.

The second source of heterogeneity we explored is related to the characteristics of biodiversity data that were used. Patterns regarding the impact of drivers did not clearly show a data bias (Fig. 5A), probably because of the very low number of papers for which enough information was available (n=9). Only papers using single and rarely used databases or aggregated databases (associated with poor taxonomic and temporal coverage) concluded that drivers did not have an effect on observed changes (n=2). The majority of papers (n=6), regardless of the data used, concluded that drivers had a negative impact on biodiversity.

The third source of heterogeneity we tested was the identity of the assessed drivers. We highlighted that only conservation measures had a positive effect on biodiversity. Climate change affected biodiversity mostly negatively, but conclusions were more nuanced concerning other anthropogenic drivers (Fig. 5B).

Discussion

Quantification of temporal changes in biodiversity at large scales and attribution of drivers of these changes is a daunting task. Studies quantifying global declines are mixed with evidences of more heterogeneous changes, including declines, increases, and no net change at different levels of biological diversity. In a context of accelerated global change, clarifying and addressing these sources of heterogeneity in temporal changes of biodiversity is needed to inform conservation policies. Plus, far from weakening the knowledge on biodiversity loss, working on uncertainty is in fact the best way to consolidate what we know. Here, we explored how different methodological pathways to produce estimates of biodiversity changes likely influence the direction of trends in population abundance, species richness and community composition as well as the effect of the drivers of these trends. As our analysis is based on a single bibliographic database and additions from the grey literature, we recognize that the coverage of the literature is certainly not complete.

Moreover, with the explosion of open databases worldwide, the literature on this subject is flourishing and articles are accumulating very quickly (Appendix S2). There is therefore a gap between the representativity of the current knowledge compared to the one from the established corpus. However, the robustness of our methodology to target a broad range of papers within the initial query allows a certain degree of confidence regarding the approximations we may draw in the present paper.

Bottom-up approaches amplify publication bias

Producing biodiversity syntheses requires gathering empirical evidence of biodiversity changes distributed on a broad scale. We have identified two major ways of estimating global changes in biodiversity: either by synthesizing already available information ("bottom-up") or by producing estimates from raw global data ("top-down"). Our findings show that the bottom-up syntheses from reviews or meta-analyses most often conclude a decline in biodiversity. This could be due to biases in the selected studies when performing such bottom-up assessment. The political intent of governments or conservationists to monitor more endangered species results in a selection bias if the trend of those species is interpreted as an average trend for the entire taxonomic group considered [START_REF] Boakes | Distorted Views of Biodiversity : Spatial and Temporal Bias in Species Occurrence Data[END_REF]. Such selection bias might be further amplified due to a publication bias: as studies generally hypothesize a decline, any study showing neutral or positive change would fail to prove the hypothesis, which may encourage authors to select more results on declining trends [START_REF] Haddaway | Eight problems with literature reviews and how to fix them[END_REF][START_REF] Mlinarić | Dealing with the positive publication bias : Why you should really publish your negative results[END_REF]. Studies showing biodiversity declines are thus over-represented compared to studies showing neutral or positive changes. This tendency is exacerbated by bottom-up assessments as they rely on already published materials. We do not imply that reviews or meta-analyses should not be conducted, but rather that biodiversity syntheses should make sure publication bias is taken into account (see Haddaway et al., 2020 for recommendations).

Biodiversity syntheses are challenged by data characteristics

Quantification of trends is also based on empirical biodiversity data that are biased in terms of spatial coverage and taxa considered. Plus, these data often represent monitoring of populations or communities through short sampling periods, hence the challenges around the use and collection of these data. Our findings confirm the major geographical and taxonomic drawbacks when estimates are generated from empirical data, namely geographical and taxonomic ones. Europe and North America are the most assessed continents [START_REF] Boakes | Distorted Views of Biodiversity : Spatial and Temporal Bias in Species Occurrence Data[END_REF][START_REF] Manes | Endemism increases species' climate change risk in areas of global biodiversity importance[END_REF][START_REF] Saha | Tracking Global Population Trends : Population Time-Series Data and a Living Planet Index for Reptiles[END_REF], whereas information is least available in the tropics [START_REF] Feeley | The data void in modeling current and future distributions of tropical species[END_REF][START_REF] Saha | Tracking Global Population Trends : Population Time-Series Data and a Living Planet Index for Reptiles[END_REF] and in regions that are currently under pressure [START_REF] Pereira | Global Biodiversity Change : The Bad, the Good, and the Unknown[END_REF]. Regarding taxonomic groups, terrestrial organisms, and especially vertebrates [START_REF] Davison | Land-use change and biodiversity : Challenges for assembling evidence on the greatest threat to nature[END_REF][START_REF] Pereira | Global Biodiversity Change : The Bad, the Good, and the Unknown[END_REF][START_REF] Theobald | Global change and local solutions : Tapping the unrealized potential of citizen science for biodiversity research[END_REF], are more studied than marine ones [START_REF] Manes | Endemism increases species' climate change risk in areas of global biodiversity importance[END_REF]. Overall, there is an over-representation of endangered species [START_REF] Boakes | Distorted Views of Biodiversity : Spatial and Temporal Bias in Species Occurrence Data[END_REF][START_REF] Saha | Tracking Global Population Trends : Population Time-Series Data and a Living Planet Index for Reptiles[END_REF]. In addition to these already well-documented taxonomic and geographical biases, we show that the length of the period considered is influencing the conclusions: the reviewed studies that are based on short time series identify more declines. If species historically monitored are recovering, short time series may miss their recovery. Selecting longer time-series should buffer the decline in this scenario. These results contradict other findings though. For instance, [START_REF] Vellend | Global meta-analysis reveals no net change in local-scale plant biodiversity over time[END_REF] found that the length of the time series had no effect on the assessment of biodiversity change. On the contrary, [START_REF] Gonzalez | Estimating local biodiversity change : A critique of papers claiming no net loss of local diversity[END_REF] showed that the percentage of decline increased with the length of the time series.

Thus, the heterogeneity in the conclusions is probably related to heterogeneity in the data characteristics. Beyond being a simple source of heterogeneity, this indicates a lack of representativeness that may represent a bias and therefore influence the reliability of the estimated trends. The lack of representativity in certain groups or regions does not ensure the reliability of the trends, but recent studies highlighted that accounting for these biases (e.g. through weighting processes [START_REF] Mcrae | The Diversity-Weighted Living Planet Index : Controlling for Taxonomic Bias in a Global Biodiversity Indicator[END_REF]) is not sufficient to correctly assess the trends [START_REF] Dove | How much data do we need? Reliability and data deficiency in global vertebrate biodiversity trends[END_REF].

They showed that not only short time series are less reliable than longer ones [START_REF] Wauchope | When can we trust population trends? A method for quantifying the effects of sampling interval and duration[END_REF], but also that the assessment of temporal changes in biodiversity at the global scale depends more on the number of time series (considered here at population scale) than on the representativeness of the number of species present within each taxonomic group in the data [START_REF] Dove | How much data do we need? Reliability and data deficiency in global vertebrate biodiversity trends[END_REF].

To overcome these issues, a short-term solution would be to merge existing aggregated databases that are complimentary in order to increase the amount of data; although it should be noted that such synthesis requires caution regarding possible scale mismatches among datasets (temporal and/or spatial) and diversity in the metrics used [START_REF] Record | Novel Insights to Be Gained From Applying Metacommunity Theory to Long-Term, Spatially Replicated Biodiversity Data[END_REF]. Additionally, sensitivity analyses regarding the length of the time series used should be implemented systematically. The long-term solution is obviously to invest in maintaining monitoring schemes for collecting data in the long term and to make a special effort on covering overlooked taxa and areas.

Beyond linear trends

Another part of the observed heterogeneities arise from methodological issues. In particular, we identify two main methodological approaches. The first is the use of global indicators, and most notably in the papers reviewed here the use of the LPI as well as the RLI. The second approach is the use of individual models, very often linear, in order to characterize trends in time series evaluating population abundances or species richness.

We highlight the fact that the ecological level considered is not as important in the heterogeneities as might be thought, but that the aggregation of trends into single metrics masks the heterogeneities, providing an abundant proportion of declining results. Such indicators have already been criticized

for this reason, but also because of their sensitivity to random fluctuations and data gaps [START_REF] Buschke | Random population fluctuations bias the Living Planet Index[END_REF][START_REF] Leung | Clustered versus catastrophic global vertebrate declines[END_REF].

Our results show that linear models applied to individual time series seem to be a less biased modelling strategy compared to global indicators. Linear models are often used to estimate the rate of change of a variable [START_REF] Christensen | A century of fish biomass decline in the ocean[END_REF][START_REF] Donald | Agricultural intensification and the collapse of Europe's farmland bird populations[END_REF][START_REF] Sánchez-Bayo | Worldwide decline of the entomofauna : A review of its drivers[END_REF], the most widely used variable being species richness [START_REF] Hillebrand | Biodiversity change is uncoupled from species richness trends : Consequences for conservation and monitoring[END_REF]. However, species richness may not be the most appropriate variable to measure biodiversity change. Indeed, beyond being widely used, changes in species richness remain poorly informative. It has been proven to be insensitive to other form of biodiversity change [START_REF] Hillebrand | Biodiversity change is uncoupled from species richness trends : Consequences for conservation and monitoring[END_REF][START_REF] Santini | Assessing the suitability of diversity metrics to detect biodiversity change[END_REF] and unreliable to detect direction in trends despite the relative simplicity to calculate it [START_REF] Valdez | The undetectability of global biodiversity trends using local species richness[END_REF].

Plus, focusing on linear trends may hide other relevant components. First, there are many examples of non-linear dynamics in nature, both in pressures [START_REF] Steffen | The trajectory of the Anthropocene : The Great Acceleration[END_REF] and in responses [START_REF] Mcgill | Fifteen forms of biodiversity trend in the Anthropocene[END_REF]. Linear trends are also more likely to miss different periods within time series (e.g. the recent recovery of a given species monitored for a long time). For these reasons, describing nonlinear patterns should be even more straightforward than using simplistic linear approaches. Some complex methods like generalised linear models with polynomial regression splines [START_REF] Cunningham | A statistical methodology for tracking long-term change in reporting rates of birds from volunteer-collected presence-absence data[END_REF] or generalised additive models (GAM) [START_REF] Buckland | Monitoring change in biodiversity through composite indices[END_REF][START_REF] Fewster | Analysis of Population Trends for Farmland Birds Using Generalized Additive Models[END_REF] are already being used to describe non-linear dynamics. However, we suggest here to use simpler workflows, like the one described by [START_REF] Rigal | A method for classifying and comparing non-linear trajectories of ecological variables[END_REF] for instance, to avoid overfitting and allow comparisons between different species.

Also, most attention is given on trends while other characteristics in the pattern of biodiversity changes are most often ignored. Variability (and changes thereof) is a proxy of stability in ecological systems [START_REF] Donohue | Navigating the complexity of ecological stability[END_REF]). Yet, the variability in biodiversity dynamics is largely overlooked: variability is often studied at the scale of ecosystems or communities to characterize their stability [START_REF] Hughes | Multiscale regime shifts and planetary boundaries[END_REF][START_REF] Scheffer | Early-Warning Signals for Critical Transitions[END_REF], but very little at the scale of populations in the context of a global analysis. In the studies we reviewed, stability has only been investigated once [START_REF] Marsh | Fluctuations in amphibian populations : A meta-analysis[END_REF], and the few examples of studies that have assessed population stability at the global scale involve taxonomically and spatially biased data [START_REF] Leung | Trends in mean growth and stability in temperate vertebrate populations[END_REF][START_REF] Williams | Vertebrate population trends are influenced by interactions between land use, climatic position, habitat loss and climate change[END_REF]. Instead, most studies focus on the extinction of species [START_REF] Bellard | Impacts of climate change on the future of biodiversity[END_REF] and ignore fluctuations in populations, although fluctuations can indicate high vulnerability to extinction [START_REF] Clements | Factors Influencing the Detectability of Early Warning Signals of Population Collapse[END_REF].

Integrating interacting drivers into biodiversity monitoring and changes assessments

Understanding the biodiversity crisis also requires to understand how global change drivers impact biodiversity across spatial and temporal scales. There are many local or regional examples in which pressure-response links have been established, especially with habitat destruction or land-use practices [START_REF] Donald | Agricultural intensification and the collapse of Europe's farmland bird populations[END_REF][START_REF] Kohsaka | Local Assessment of Tokyo : Satoyama and Satoumi -Traditional Landscapes and Management Practices in a Contemporary Urban Environment[END_REF][START_REF] Liu | Local Assessment of Shanghai : Effects of Urbanization on the Diversity of Macrobenthic Invertebrates[END_REF][START_REF] Nowakowski | Amphibian sensitivity to habitat modification is associated with population trends and species traits[END_REF], but our work reveals that the way in which pressures aggregate on a global scale and impact the spatiotemporal dynamics of biodiversity remains poorly understood. We also highlight that while links to climate change can be established [START_REF] Comte | Decoupled land-sea biodiversity trends[END_REF][START_REF] Knape | Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?[END_REF][START_REF] Parmesan | A globally coherent fingerprint of climate change impacts across natural systems[END_REF], the difficulty of making links between other anthropogenic pressures and biodiversity changes at the same time remains (only few examples, e.g. [START_REF] Mantyka-Pringle | Interactions between climate and habitat loss effects on biodiversity : A systematic review and meta-analysis[END_REF][START_REF] Nunez | Exploring interaction effects from mechanisms between climate and land-use changes and the projected consequences on biodiversity[END_REF][START_REF] Oliver | Interactions between climate change and land use change on biodiversity : Attribution problems, risks, and opportunities[END_REF]. This observation confirms [START_REF] Mazor | Global mismatch of policy and research on drivers of biodiversity loss[END_REF]: they found that 40,3% of the research effort on drivers of biodiversity loss focus on climate change, while only 5,4% focus on pollution and 5% on overexploitation. However, many studies have suggested that climate change and other threats to biodiversity may interact to lead to even greater consequences [START_REF] Bowler | Mapping human pressures on biodiversity across the planet uncovers anthropogenic threat complexes[END_REF][START_REF] Brook | Synergies among extinction drivers under global change[END_REF][START_REF] Oliver | Interactions between climate change and land use change on biodiversity : Attribution problems, risks, and opportunities[END_REF][START_REF] Sala | Global Biodiversity Scenarios for the Year 2100[END_REF].

Such lack of global scale integration jeopardises our understanding of the human induced drivers of biodiversity changes at large scale, leading to inappropriate management strategies and missed conservation opportunities [START_REF] Sirami | Impacts of global change on species distributions : Obstacles and solutions to integrate climate and land use[END_REF].

Conservation perspectives

Although some of the biases we report here potentially lead to over or under estimate the overall decline in biodiversity, we do not question the magnitude of the biodiversity crisis. We are now moving forward with the post-2020 Global Biodiversity Framework and all the Aichi Targets for 2020 have been only partially achieved or not achieved at all. The Intergovernmental Platform on Biodiversity and Ecosystem Services (IPBES) has published a very alarming global biodiversity assessment report in 2019. In this context, characterizing the state of biodiversity, the impact of drivers and responses is a key step to take action and "bend the curve of biodiversity loss" [START_REF] Tekwa | Detecting and attributing the causes of biodiversity change : Needs, gaps and solutions[END_REF]. While we urgently need reliable assessments to quantify temporal changes in biodiversity and their links to global drivers, we call for more attention to overlooked and yet informative components of biodiversity changes.

For instance, the Group on Earth Observations Biodiversity Observation Network (GEO BON)

initiative emerged in 2013 with the concept of "Essential Biodiversity Variables" defined as "measurement required for study, reporting, and management of biodiversity change", focusing on the status and trend of biodiversity components [START_REF] Pereira | Essential Biodiversity Variables[END_REF]. These metrics transform data from a variety of sources into indicators that provide a synthetic description of different levels of biodiversity organization, thus facilitating the translation of biodiversity data into policy information.

We suggest that conservation actions should be based not only on Essential Biodiversity Variables but more globally on Essential Biodiversity Data, with requirements on taxonomic, geographic and temporal coverage ensuring the reliability of estimated trends and thus being able to guide strategies based on the least biased observations possible. Similarly, the implementation of a framework such as Essential Biodiversity Assessment Methods, including the need to systematically take into account different levels of biodiversity, as well as the measurement not only of linear dynamics, should be considered collectively and on a large scale.

Eventually, examining the drivers of temporal changes of biodiversity also provides evidence for conservation decision-making [START_REF] Ehrlén | Predicting changes in the distribution and abundance of species under environmental change[END_REF][START_REF] Hefley | When can the cause of a population decline be determined?[END_REF]. Conservation can only be considered in conjunction with an examination of the drivers of these trends, which are of course complex and heterogeneous. Our results plead for an urgent need to develop guidance on the necessary quality required for drivers data, their spatial and temporal coverage, the number of drivers to be considered, and their identity. Methods establishing links also need to be considered, and perspectives are to be explored in terms of not only correlative but also causal links [START_REF] Rigal | Farmland practices are driving bird population decline across Europe[END_REF].

The results of our review confirm the idea that a multifaceted view of biodiversity is needed to capture all trajectories and the risk of relying solely on global indicators. Empirical evidence for the ongoing biodiversity crisis will never reduce to a silver bullet and univocal metric of global biodiversity change. Eventually, denialism and inaction can be encouraged by the fiction that the state and fate of global biodiversity can be encapsulated in a given metric. A pernicious effect of relying on global metrics would be to consider that the situation is satisfactory providing that a given metric is stable if declining populations are "compensated" or "balanced" by increasing ones.

But declines and increases in specific components of biodiversity caused by human activities are by no means cancelling out each other. Any decline of a population or an extinction of a species caused by human activities is a conservation and ethical concern. By quantifying the nuance and full distribution of the impacts of drivers on temporal changes of biodiversity, we should better understand ongoing changes in biodiversity and make sure that conservation actions are making differences.

Data, scripts, code, and supplementary information availability

The R code for metadata manipulation and visualization is available on GitHub (https://github.com/MaelysBoennec/Sources-of-confusion-in-global-biodiversity-trends).

  was thus: TI=((biodiversity OR population* OR communit* OR indicator* OR natur* OR richness OR species OR "biological diversity" OR abundance OR assemblage OR *flora OR *fauna) AND (trend* OR dynamic* OR "time series" OR declin* OR loss OR extinct* OR increas* OR gain OR coloni* OR change* OR fluctuat* OR trajector* OR tempo*)) AND AB=(("temporal" OR time) AND ("analys*" OR "model*" OR stud* OR quantifi*)) NOT TI=("human population" OR "urban population") AND (TI=(global OR worldwide) OR AB=(global OR worldwide)) NOT

Figure 1 .

 1 Figure 1. Summary of the sampled literature and extracted metadata. (A) Diagram representing the different steps of the screening process. List of studies extracted from the Web of Science, including excluded studies with reasons for exclusion are in the Appendix S3. (B) Summary of the metadata collected for the database. The potential sources of heterogeneities we investigate are highlighted in yellow.

Figure 2 .

 2 Figure 2. Information on the biodiversity data on which the reviewed papers are based. (A) Temporal extent of the data, colored based on the data source (see Table 1). (B) Taxonomic extent of the data. Number of papers considering each group, wheter considered alone or combined (i.e. when the study does consider several groups at a time). For instance, 2 papers were examining the fate of mammals only and 30 were examining the fate of mammals and other groups at the same time. (C) Ecological level representation. Number of papers and percentages are indicated. « Grouped » category reprensent papers examining several ecological levels within the same paper.

Figure 4 .

 4 Figure 4. Alluvial plots representing the links between the potential sources of heterogeneity and the conclusions when assessing trends. A (n= 27) highlights the impact of the data characteristics. B (n=32) highlights the impact of the methods and the ecological level. The height of the boxes is proportional to the number of papers. Flow thickness between boxes is proportional to the number of papers. Colours of the flow reflect the conclusions.

Table 1 . Overview of the different sources of data identified. Data source Biotime (ntot=7)

 1

			Living Planet	Global Population	Other*	Aggregation**
			Database (LPD)	Dynamics Database	(ntot=5)	(ntot=30)
			(ntot=8)	(GPDD) (ntot=4)
	Contant	Time series data of	Time series data	Time series data of	Time series data of	Time series data of
		ecological	of individual	individual species'	several	several biodiversity
		assemblages	species'	abundance (mainly	biodiversity	measures
		(mainly used at	abundance	used at population	measures	(mainly used at
		community and	(mainly used at	level)	(both species and	species or
		species level)	population level)		population level)	population level)
	Taxa	Vertebrates,	Vertebrates (5 in	Vertebrates,	3 on average	3 on average
		invertebrates and	total)	invertebrates and
		plants (8 in total)		plants (8 in total)
	Realms	Marine, terrestrial	Marine,	Marine, terrestrial	Marine and	Marine, terrestrial
		and freshwater	terrestrial and	and freshwater	terrestrial	and freshwater
			freshwater
	Average	13,726 (ncalc=6)	847(ncalc=8)	424 (ncalc=3)	30,553
	number of
	species

Conflict of interest disclosure

The authors declare that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article.


Izabel C Medeiros-Costa

Eddy Dib

Florent Dubray

Jean-Pierre Gilson

Jean-Pierre Dath

Nikolai Nesterenko

Hristiyan A Aleksandrov

Georgi N Vayssilov

Svetlana Mintova

Unraveling the effect of silanol defects on the insertion of single site Mo in the MFI zeolite framework

Keywords: . Defects, silanols, metals, zeolites, nanocrystals

The preparation of defect-free MFI crystals containing single site framework Mo through a hydrothermal post-synthesis treatment is reported. The insertion of single Mo sites in the MFI zeolite samples with different crystal sizes of 100, 200 and 2000 nm presenting a diverse concentration of silanol groups is revealed. The nature of the silanols and their role in the incorporation of Mo into the zeolite structure are elucidated through an extensive spectroscopic characterization ( 29 Si NMR, 1 H NMR, 31 P NMR and IR) combined with X-ray diffraction and HRTEM. In addition, a DFT based theoretical modeling of a large Si 154 O 354 H 92 nanoparticle containing 600 atoms is carried out to understand the expansion of the unit cell volume measured by X-ray diffraction. An accurate quantification of the silanols in the MFI crystals with different particle sizes and the insertion of Mo in the zeolitic framework is reported for the first time. The results confirmed that the non H-bonded silanols seem to be the gateway for the insertion of single Mo atoms in the zeolite structure. Such materials with single metal sites present high crystallinity and perfect structure thus providing great stability in catalytic applications.

INTRODUCTION

Zeolites are microporous aluminosilicates with great applications in several areas as ion exchange, adsorption and catalysis. [START_REF] Dusselier | Small-Pore Zeolites: Synthesis and Catalysis[END_REF][START_REF] Weckhuysen | Recent Advances in Zeolite Chemistry and Catalysis[END_REF][START_REF] Kulprathipanja | Overview in Zeolites Adsorptive Separation[END_REF] The introduction of transition metals in zeolites e.g. Ti, Fe, V, Cu etc. [START_REF] Taramasso | Preparation of Porous Crystalline Synthetic Material Comprised of Silicon and Titanium Oxides[END_REF][START_REF] Millini | Synthesis and Characterization of Boron-containing Molecular Sieves[END_REF][START_REF] Dzwigaj | Role of Silanol Groups in the Incorporation of V in β Zeolite[END_REF] has been used as a way to enhance the zeolites performances and broaden their spectrum of use. The incorporation of metals can occur mainly in three different ways: ion exchange, impregnation of extra-framework metal oxides or isomorphic substitution. [START_REF] Clatworthy | Emphasis on the Properties of Metal-Containing Zeolites Operating Outside the Comfort Zone of Current Heterogeneous Catalytic Reactions Angewandte[END_REF] The way metals are incorporated into zeolites can change their properties considerably. Recently, it was shown that for the conversion of glycerol, Fe (III) in tetrahedral position was able to selectively generate acrylic acid, while, extra framework Fe (II) oxides selectively produced acrolein. [START_REF] Diallo | Influence of the Preparation Procedure and Crystallite Size of Fe-MFI Zeolites in the Oxidehydration of Glycerol to Acrolein and Acrylic Acid[END_REF] In the case of Mo-MFI catalysts used for methane conversion, the isomorphic substitution of Mo in a tetrahedral position appears as the most promising choice. In a previous publication of our group, [START_REF] Konnov | Novel Strategy for the Synthesis of Ultra-Stable Single-Site Mo-ZSM-5 Zeolite Nanocrystals[END_REF] it was shown that the incorporation of single Mo atoms into the ZSM-5 framework was able to promote the activity, stability and reduce coke deposition when applied in methane conversion. On the other hand, the Mo impregnated ZSM-5 displayed fast deactivation because of the sintering and migration of molybdenum carbide species. [START_REF] Konnov | Novel Strategy for the Synthesis of Ultra-Stable Single-Site Mo-ZSM-5 Zeolite Nanocrystals[END_REF] The Mo is inserted in the zeolite framework through a post-synthesis treatment. [START_REF] Dubray | Direct Evidence for Single Molybdenum Atoms Incorporated in the Framework of MFI Zeolite Nanocrystals[END_REF] A significant reduction in the silanol defects concentration in the zeolite is noticed after the incorporation of Mo, which is an evidence of their role in Mo insertion. Thus, in addition to creating new active sites, the introduction of Mo in the zeolitic structure favor the healing of silanol defects, commonly present in zeolites.

Consequently, healing silanols with metals should also represent a step forward in applications where hydrophobic and/or highly stable zeolites are required. This approach might be useful for producing catalysts for applications such as non-oxidative methane conversion, hydrocracking and fluid catalytic cracking. The reduction of silanols content has also been shown to be important in several catalytic applications, where it is directly related to the reduction of coke deposition and to the increase of the catalyst lifetime. [START_REF] Lee | Cooperative Effects of Zeolite Mesoporosity and Defect Sites on the Amount and Location of Coke Formation and Its Consequence in Deactivation[END_REF][START_REF] Prokopyeva | Methanol-to-Olefins Process over Zeolite Catalysts with DDR Topology: Effect of Composition and Structural Defects on Catalytic Performance[END_REF][START_REF] Grahn | Small ZSM-5 Crystals with Low Defect Density as an Effective Catalyst for Conversion of Methanol to Hydrocarbons[END_REF][START_REF] Qin | Comparative Study of Nano-ZSM-5 Catalysts Synthesized in OH -and F -Medium[END_REF] Thus, the healing of silanol defects through the introduction of metals represents an attractive alternative to the classical method using hydrofluoric acid. [START_REF] Axon | Synthesis and Characterization of Defect-Free Crystals of MFI-Type Zeolites[END_REF] Therefore, the relationship between the introduction of transition metals and silanol defects is highly important and needs to be investigated. In this contribution, we follow the post-synthesis approach to insert Mo in pure silica MFI zeolites having different characteristics regarding the size of crystals and the amount and type of silanol defects. A full characterization of the zeolites before and after treatment with Mo permits to understand the mechanism of incorporation and distribution of Mo within the zeolite framework. The incorporation of Mo is more favorable in crystals presenting smaller size, which is likely related to the abundance of a specific type of silanols. Besides, a correlation was observed between the expansion of the unit cell volume and the amount of Mo incorporated, which agrees with the hypothesis of Mo isomorphic substitution.

A, DFT based theoretical simulation indicates that Mo (VI) is the most stable oxidation state for this metal, when incorporated in the zeolite framework.

RESULTS AND DISCUSSION

Pure silica MFI zeolites were synthesized following the procedures described in the experimental section. The samples were named as MFI-x, where "x" represents the size of the zeolite crystals in nanometers. Samples MFI-100 MFI-200 and MFI-2000 contain zeolite crystals with particle size of 100, 200 and 2000 nm. The incorporation of Mo in these zeolite samples was carried out following the post-synthesis hydrothermal treatment procedure as described in our previous work. [START_REF] Dubray | Direct Evidence for Single Molybdenum Atoms Incorporated in the Framework of MFI Zeolite Nanocrystals[END_REF] Additional information is also provided in the method section. The Furthermore, the morphology and the size of the crystals was not affected by the hydrothermal post-synthesis treatment (Figure S1). Figure 2A shows the X-ray diffraction patterns of the zeolite samples before and after insertion of Mo. All zeolite samples present good crystallinity, which is maintained after the Mo incorporation. No Mo oxide phases were identified in the diffractograms, which is also supported by Raman analysis (Figure S2). The XRD patterns of the samples are presented in the range of 22.5° and 25 °2θ (Figure 2A); a splitting of the peaks at ~ 23.3°, 23.8° and 24.5° into two peaks marked with asterisks is observed for all Mo-containing samples, which evidences the monoclinic symmetry of the crystals. All as synthesized zeolite samples (MFI-100, -200 and -2000) before treatment with Mo, present orthorhombic symmetry, while after the incorporation of Mo (Mo-MFI-100, -200 and -2000) present monoclinic symmetry. The transition from orthorombic to monoclinic symmetry has already been observed after insertion of Al in the MFI zeolite framework. [START_REF] Van Koningsveld | On the Preparation of a Monoclinic (Nearly) Single Crystal of Zeolite HZSM-5[END_REF] The change in symmetry after the introduction of Mo in the zeolitic structure is accompanied by an increase in the unit cell volume. The unit cell volume of the as synthesized MFI-100, -200 and -2000 and Mo-containing Mo-MFI-100, -200 and -2000 zeolite samples obtained using Le Bail refinement considering the orthorombic and monoclinic symmetry, respectievely are shown in Figure 2B and Table S1. After the incorporation of Mo, the unit cell volume of all zeolite samples increases, even though the difference in the unit cell volume before and after incorporation of Mo is not the same for the different zeolites. A greater change in the unit cell volume for the samples with small zeolite crystal sizes (MFI-100 and MFI-200) is measured whereas that change is reduced in the case of big crystals (MFI-2000).

The increase in unit cell volume of the Mo-MFI zeolites results from the incorporation of Mo in a tetrahedral position in the framework, since Mo (55 pm) has larger ionic radius than Si (40 pm). [START_REF] Deka | Comparison of All Sites for Ti Substitution in Zeolite TS-1 by an Accurate Embedded-Cluster Method[END_REF][START_REF] Borin | Synthesis of TS-1 Molecular Sieves Using a New Ti Source[END_REF][START_REF] Tuel | Influence of the Nature of Silicon and Titanium Alkoxides on the Incorporation of Titanium in TS-1[END_REF] Therefore, the more pronounced difference in unit cell volume in the case of smaller crystals is attributed to a greater incorporation of Mo atoms in the zeolitic framework. Therefore, small crystals can more easily receive a large amount of Mo in comparison to big crystals. Experimental studies have been supplemented by computational modeling based on periodic density functional calculations performed using the Vienna ab initio simulation package (VASP) [START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium[END_REF] with the gradient corrected Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] functional (see Experimental section for computational details). In order to clarify which is the most stable type of molybdenum ions in the zeolite framework we modeled three types of Mo-containing species incorporated in the MFI framework (Figure 4 A-C). Similar to the situation with W-MFI zeolites [START_REF] Borin | Synthesis of TS-1 Molecular Sieves Using a New Ti Source[END_REF] structure; a similar results for W-containing MFI zeolites was also found where the MFI-[WVIO] is more stable than the MFI-[WIV] structure by >350 kJ/mol. [START_REF] Borin | Synthesis of TS-1 Molecular Sieves Using a New Ti Source[END_REF] In order to investigate the volume expansion of the MFI zeolite samples after Mo incorporation, we modeled a large Si 154 O 354 H 92 nanoparticle containing 600 atoms (Figure S3). It was a cut from the periodic MFI structure and the terminal oxygen centers were saturated by hydrogen, forming hydroxyl groups. The maximal distances between Si atoms at both ends of the nanoparticle at each direction (A, B, and C) are 17.23, 24.89, and 16.68 Å, respectively, thus the calculated volume of the nanoparticle is 7153.34 Å 3 (Table 1). To be more precise we averaged three equivalent Si-Si distances at each direction. Two or four silicon centers were substituted by [MoVIO] or by [MoVI(OH) 2 ] species, which corresponds to about 1.9 or 3.7 wt. % Mo in the zeolite nanoparticle, respectively. After incorporation of two and four

[MoVIO]/[MoVI(OH) 2 ]
species, the volume of the zeolite nanoparticles increases to 7234.78/7216.08 and 7325.05/7322.11 Å 3 , respectively (Table 1). This increase corresponds to 0.9-1.1% and 2.3-2.4 % expansion of the unit cell volume of the zeolite nanoparticles containing two and four molybdenum, respectively. These results are in a good agreement with experimental data (Figure 2). It is obvious from the 1 H NMR spectra that H-bonded silanols are completely healed by the introduction of Mo [START_REF] Dubray | Direct Evidence for Single Molybdenum Atoms Incorporated in the Framework of MFI Zeolite Nanocrystals[END_REF][START_REF] Grand | One-Pot Synthesis of Silanol-Free Nanosized MFI Zeolite[END_REF] Most of the non H-bonded silanols are also eliminated after the insertion of Mo in the zeolite framework. As shown in Figure S4, a correlation can be drawn between the quantity of healed non H-bonded silanols and the quantity of Mo incorporated in the zeolite crystals, where samples with higher amount of non H-bonded silanols also present higher amount of Mo after the hydrothermal post-treatment (Mo-MFI-100>Mo-MFI-200>Mo-MFI-2000). On the other hand, no trend is observed when correlating H-bonded silanols and the quantity of Mo in the samples. For this reason, we believe that Mo atoms are preferentially bonded to non Hbonded silanols, which present convenient configuration with free space to receive Mo atoms.

In order to provide more insights into the relationship between the healing of silanols and Mo insertion in the zeolitic structure, 1 H NMR (silanols) and [START_REF] Baerlocher | Database of Zeolite Structures[END_REF] The healing of H-bonded silanols is also achieved by the hydrothermal treatment, however it should not be directly linked to the incorporation of Mo. This approach presents a high potential for introduction of single site metal species in zeolite crystals containing various defect sites. The single site metal catalysts are of great importance sine high stability of the catalysts working outside of the comfort zone is required.

METHODS

Synthesis of parent MFI zeolites.

As shown in Table 2, the MFI zeolites were prepared from precursor suspensions with various molar compositions. Double distilled water and TPAOH (tetra n-propylammonium hydroxide, 20 wt% in water solution, Alfa Aesar) were initially mixed for about 30 minutes, followed by dropwise addition of TEOS (tetraethyl orthosilicate, 98%, Aldrich). The precursor solutions were kept under magnetic stirring for 1 h after adding TEOS, then aged for 18 hours at room temperature on an orbital shaker. The hydrothermal treatment of the aged suspensions was carried out in polypropylene bottles at 90 °C or in Teflon lined stainless steel autoclaves at 140 °C. In both cases, the syntheses were performed under autogenous pressure and static conditions. After the crystallization period (detailed for each sample in Table 2), the samples were purified, dried overnight at 90 ° C and calcined at 550 ° C/ 5h. S1). [START_REF] Petříček | Crystallographic Computing System JANA2006: General Features[END_REF] Transmission Electron Microscopy (TEM). The crystal size and morphology were measured by transmission electron microscopy (TEM); experiments were carried out on an Analythical double (objective and probe) corrected JEOL ARM200CF equipped with a 100 mm Centurio EDS detector and a Quantum GIF for the EELS. A probe of 0.1 nm was used to scan the specimen in STEM mode and Bright Field, and high Angular Annular Dark Field detectors were simultaneously employed for imaging. The camera length was fixed at 8 cm. To avoid material degradation, the STEM-EDS analytical essays were carried out at 80 kV with a high scanning speed of 3 µs/px and for a mean duration of 60 minutes.

Fourier Transform Infrared Spectroscopy (FTIR). FTIR spectra were obtained by using a Nicolet Magna 550-FT-IR spectrometer (4 cm-1 optical resolution). Zeolite wafers with an average area of 1cm2 and about 20 mg were hydraulic pressed (1.5 t.cm-²). The self-supported wafers were activated at 500 °C for 4 hours under secondary vacuum prior to the measurements.

Nuclear Magnetic Resonance Spectroscopy (NMR)

. [START_REF] Dusselier | Small-Pore Zeolites: Synthesis and Catalysis[END_REF] H, [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF] Si and 31 P NMR analyzes were performed on a 11.7 T Bruker Avance 500 spectrometer operating at a frequency of 500.07 MHz, 99.35 MHz and 202.4 MHz, respectively. In the case of 31 P and [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF] Si NMR, the samples were packed into 3.2 mm zirconia rotors that spun at 22 kHz. In order to obtain higher resolution in the case of 1 H NMR, 1.9 mm zirconium rotor was used at a spinning rate of 40 kHz. Flip angles of 30° was used when measuring [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF] Si NMR spectra, while 90° flip angles were used for 1 H and 31 P NMR spectra. The number of scans of single-pulse 1 H, [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF] Si and 31 P MAS NMR was 64, 2048 and 256, respectively. Tetramethyl silane (TMS) was used as a reference for the chemical shift of 1 H and [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF] Si NMR and phosphoric acid (H 3 PO 4 ) for 31 P NMR experiments.

Sample preparation for 31 P NMR: The presence of Mo atoms in the zeolitic structure was investigated through 31 P NMR by using trimethylphosphine oxide (TMPO) as a probe molecule.

The samples were initially activated under secondary vacuum at 400 °C for 5 h. Then, the cell containing the sample was sealed and placed in a glovebox under Ar. The TMPO was weighed inside the glovebox, dissolved with dichloromethane and the solution was transferred to the cell containing the sample with the aid of a syringe. The volume of TMPO/ dichloromethane solution was about 0.8 ml and it was sufficient to immerse the zeolite powder. The cell was then placed in the ultrasound bath for 15 min and the zeolite/TMPO-dichloromethane mixture was kept inside the cell overnight. The next day the dichloromethane was evaporated in a rotavapor and the cell was again placed under secondary vacuum in order to remove any traces of the solvent. As a result, the solid zeolite + adsorbed TMPO was obtained and used to fill the 3.2 mm zirconium NMR rotor (under Ar atmosphere). Sample preparation for 1 H NMR: Before measurements samples were activated at 350 ° C/10 h under secondary vacuum. The 1.9 mm zirconium rotor filled with the dehydrated zeolite were closed under Ar atmosphere.

Computational Modeling. The periodic plane wave quantum chemical calculations performed with the Vienna ab initio simulation package (VASP) [START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium[END_REF] were based on the density functional theory method using a cutoff energy of 415 eV. The gradient corrected Perdew-Burke-Ernzerhof (PBE), [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] exchange-correlation functional with the additional empirical dispersion correction (PBE+D2) [START_REF] Grimme | Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction[END_REF] and PAW pseudopotentials were employed. [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] For the bulk calculations Å, c = 33.664 Å. Due to the large size of the unit cells, the Brillouin zone using only the Γ point was samples. [START_REF] Jeanvoine | Brønsted Acid Sites in HSAPO-34 and Chabazite: An Ab Initio Structural Study[END_REF] All atoms of zeolite structures were allowed to relax until the force on each atom becomes less than 510 4 eV/pm during the geometry optimization.

Corresponding Author

*svetlana.mintova@ensicaen.fr

  nomenclature of zeolites after insertion of Mo was obtained by adding the prefix Mo-before the name of the parent zeolites (Mo-MFI-100, Mo-MFI-200 and Mo-MFI-2000). As shown in Figure 1, the zeolite crystals of sample Mo-MFI-100 have spherical morphology while the MFI-200 have more defined faces with hexagonal morphology. In turn, MFI-2000 presents twin zeolite crystals with the typical coffine-like shape morphology. The STEM-EDS elemental mapping shows a homogeneous distribution of Mo in the zeolite crystals with a mean Mo content of about 1.2, 1.0 and 0.16 wt. % for samples Mo-MFI-100, Mo-MFI-200 and Mo-MFI-2000, respectively.

Figure 1 .

 1 Figure 1. TEM micrographs and STEM-EDS elemental maps of samples (A) Mo-MFI-100, (B)

Figure 2 .

 2 Figure 2. (A) X-ray diffraction patterns of samples MFI-100, MFI-200 and MFI-2000, Mo-MFI-

Figure 3 .

 3 Figure 3. 31 P NMR spectra of samples Mo-MFI-100, Mo-MFI -200 and Mo-MFI -2000 (A).

Figure 4 .

 4 Figure 4. Optimized periodic bulk systems with Mo moieties incorporated in T11 position in the

Figure 5 .

 5 Figure 5. Characterization of silanol defects by IR spectroscopy: (a) MFI-100 (blue), (b) MFI-

  P NMR (Mo) quantitative data are presented in Figure7. To enable the comparison between the amount of healed silanols and the amount of Mo introduced into the zeolite framework, both molar amounts of H-bonded and non H-bonded silanols were divided by four, respecting the 4 SiOH: 1 Mo stoichiometry. This stoichiometry was deduced from theoretical calculations, which indicate that the most stable configuration for the Mo atom is found when it is linked to the zeolitic structure through four bonds. Thus, an excess of healed silanols is measured relatively to the amount of Mo inserted into the zeolite samples (Mo-MFI-100, -200 and -2000) (Figure7). Excess silanols are observed regardless the type of silanol: H-bonded or non H-bonded silanols. An extreme case for the Mo-MFI-2000 sample, where the crystals have large amounts of H-bonded healed silanols, although it presents a small incorporation of Mo is found. These information led us to conclude that Mo is not the only agent responsible for the defects healing. A partial recrystallization of the zeolite structure during the post synthesis hydrothermal treatment is possibly occurred leading to defects healing.

Figure 6 . 1 H

 61 Figure 6. 1 H NMR spectra of samples (a) MFI-100, (b) Mo-MFI-100, (c) MFI-200, (d) Mo-

Figure 7 .

 7 Figure 7. Comparison between the quantities of Mo (gray bars) and different types of silanols

Figure 8 .

 8 Figure 8. 29 Si NMR spectra of samples (a) MFI-100, (b) Mo-MFI-100, (c) MFI-200, (d) Mo-

  and stirred for one hour at room temperature. The bottles were then placed in the oven at 90 °C under static conditions for a period of 7 days. After hydrothermal treatment, the zeolites were washed extensively with double deionized water. The solids recovered by centrifugation were dried overnight at 90 ° C and calcined at 550 °C/ 5h. After calcination, the samples were ion exchanged with 0.2 M NH 4 Cl solution. Two cycles of ion exchange were performed and in each cycle the mixture was stirred for one hour at room temperature and the zeolites recovered by centrifugation. At the end of the second cycle, the solids were rinsed with double distilled water, recovered again by centrifugation and placed in the oven at 90 °C, where they were dried overnight and then calcined at 550 ° C / 5h. After treatment with Mo and subsequent ion exchange, the samples were named by adding Mo to the respective names of the parent zeolites: Mo-MFI-100, Mo-MFI-200 and Mo-MFI-2000.X-Ray Diffraction (XRD).X-Ray diffraction patterns were acquired using a PANanalytical X'Pert Pro diffractometer equipped with a Johansson monochromator, Kα1 radiation λ = 1.540598 Å. The patterns were measured with a step of 0.0167 °. JANA2006 software was used to perform Le Bail profile refinement and thus determine unit cell parameters (Table

  an orthorhombic unit cell of the MFI type zeolite framework, consisting of 96 T atoms with dimensions a = 20.271 Å, b = 19.925 Å, c = 13.332 Å was used, 31 while the Si 154 O 354 H 92 nanoparticle were model in an orthorhombic unit cell with dimensions: a = 27.271 Å, b = 26.925

  the most stable Mo-containing species incorporated in the MFI framework are Mo in oxidation state VI interacting with one additional O atom, MFI-[MoVIO]. When a H 2 O molecule is dissociated at those MFI-[MoVIO] species and two hydroxyl groups are formed, the obtained MFI-[MoVI(OH)2] species is more stable by 11 kJ/mol than the MFI-[MoVIO], though one can expect that such a small energy difference can be easily overcome by the entropy contribution at room temperature and the water molecule is expected to desorb. The incorporation of МоIV species in oxidation state IV in the zeolite framework is considered as well. The obtained structure, MFI-[МоIV], is by 319 kJ/mol less stable than the most stable MFI-[MoVIO]

Table 1 .

 1 Si-Si distances (Å) between Si atoms located at the ends of the pristine pure silica zeolite nanoparticle as well as the nanoparticles containing two and four [MoVIO] or [MoVI(OH) 2 ] species incorporated in the pure silica zeolite nanoparticle. The unit cell volume (Å 3 ) of the pure silica and molybdenum containing zeolite nanoparticles and the volume expansion under incorporation of Mo in the structure are calculated. So far, it is clear that the size of the crystals plays a role in the incorporation of Mo in the zeolitic framework. However, we have not yet addressed other features, as silanol defects, that also may affect the Mo incorporation. Just as the different zeolites presented throughout this work have different morphologies and crystal sizes, such zeolites also display different characteristics regarding the composition of silanol defects. Figures 5 and 6 show the IR and 1 H

		Direction A Direction B Direction C Volume Expansion, %
	Si 154 O 354 H 92	17.23	24.89	16.68	7153.34
	[MoO] 2 Si 152 O 354 H 92	17.22	24.99	16.81	7234.78	1.13
	[Mo(OH) 2 ] 2 Si 152 O 354 H 92	17.26	24.95	16.76	7216.08	0.87
	[MoO] 4 Si 150 O 354 H 92	17.27	25.04	16.93	7325.05	2.34
	[Mo(OH) 2 ] 4 Si 150 O 354 H 92	17.25	24.99	16.98	7322.11	2.30

Table 2 .

 2 Molar composition of the precursor suspensions used for the synthesis of zeolites and

	the respective hydrothermal (HT) conditions
	MFI-100
	Molar composition	1SiO 2 :0.28 TPAOH: 40 H 2 O
	HT conditions	48 h/ 90 °C
	MFI-200
	Molar composition	1SiO 2 :0.28 TPAOH: 40 H 2 O
	HT conditions	6 h/ 180 °C
	MFI-2000
	Molar composition	1SiO 2 :0.14 TPAOH: 40 H 2 O
	HT conditions	15 days/ 140 °C

Incorporation of Mo in MFI zeolites.

  The calcined zeolites were treated with a 3% wt. solution of Na 2 MoO 4 .2H 2 O in a ratio of 21.5 g of solution per 1 gram of zeolite samples. The mixtures of zeolite and sodium molybdate solution were placed in closed polypropylene bottles

by the European Regional Development Fund and the Operational Program "Science and Education for Smart Growth" under contract UNITe No. BG05M2OP001-1.001-0004-C01.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT

This research was supported by TOTAL and Industrial Chair ANR-TOTAL "Nanoclean energy", the Normandy University, and the Lable of Excellence for the Centre of Zeolites and Nanoporous Materials by the Region of Normandy. H. A. A. and G. N. V. acknowledge support

Supporting Information

A supporting information file is available presenting SEM and Raman analyses, as well as correlations between [START_REF] Dusselier | Small-Pore Zeolites: Synthesis and Catalysis[END_REF] H NMR data and Mo quantification. Additional details on LeBail calculation and molecular modeling are also presented.