Quantifying the individual impact of artificial barriers in freshwaters: A standardized and absolute genetic index of fragmentation

Abstract Fragmentation by artificial barriers is an important threat to freshwater biodiversity. Mitigating the negative aftermaths of fragmentation is of crucial importance, and it is now essential for environmental managers to benefit from a precise estimate of the individual impact of weirs and dams on river connectivity. Although the indirect monitoring of fragmentation using molecular data constitutes a promising approach, it is plagued with several constraints preventing a standardized quantification of barrier effects. Indeed, observed levels of genetic differentiation GD depend on both the age of the obstacle and the effective size of the populations it separates, making comparisons of the actual barrier effect of different obstacles difficult. Here, we developed a standardized genetic index of fragmentation (F INDEX), allowing an absolute and independent assessment of the individual effects of obstacles on connectivity. The F INDEX is the standardized ratio between the observed GD between pairs of populations located on either side of an obstacle and the GD expected if this obstacle completely prevented gene flow. The expected GD is calculated from simulations taking into account two parameters: the number of generations since barrier creation and the expected heterozygosity of the populations, a proxy for effective population size. Using both simulated and empirical datasets, we explored the validity and the limits of the F INDEX. We demonstrated that it allows quantifying effects of fragmentation only from a few generations after barrier creation and provides valid comparisons among obstacles of different ages and populations (or species) of different effective sizes. The F INDEX requires a minimum amount of fieldwork and genotypic data and solves some of the difficulties inherent to the study of artificial fragmentation in rivers and potentially in other ecosystems. This makes the F INDEX promising to support the management of freshwater species affected by barriers, notably for planning and evaluating restoration programs.


| INTRODUC TI ON
Heavily impacted by human activities, rivers are at the heart of biodiversity conservation issues (Dudgeon et al., 2006;Reid et al., 2018). Among the various threats to these ecosystems, river fragmentation by artificial barriers is considered as the most widespread and worrying (Couto & Olden, 2018;Nilsson, 2005;Turgeon, Turpin, & Gregory-Eaves, 2019). Weirs and dams, but also pipes and culverts, have long been, and are still, constructed for flow regulation and/or hydropower supply but they often imply a loss of habitat and a reduction in riverscape functional connectivity (that is, species-specific) in freshwater organisms (Birnie-Gauvin, Aarestrup, Riis, Jepsen, & Koed, 2017;Jansson, Nilsson, & Malmqvist, 2007). For fish, artificial fragmentation is known to impact key biological processes such as migration, dispersal, and recruitment, and thus viability and productivity of populations and communities (Blanchet, Rey, Etienne, Lek, & Loot, 2010;Poulet, 2007;Turgeon et al., 2019). Given the central role of hydropower as a source of energy, mitigating these negative aftermaths is now of high importance (Couto & Olden, 2018;Gibson, Wilman, & Laurance, 2017).
Different restoration and mitigation measures may be considered to enhance longitudinal river connectivity, including the removal of obstacles, periodic turbine shutdowns, and fishpasses setting (Bednarek, 2001;Poff & Schmidt, 2016;Silva et al., 2018). However, these measures may all result in unintended outcomes (McLaughlin et al., 2013), or unsatisfactory trade-offs between conservation of biodiversity, preservation of historical and cultural legacy and the maintenance of services provided by obstacles (Gibson et al., 2017;Hand et al., 2018;Roy et al., 2018;Song et al., 2019). In terms of conservation planning, it is therefore essential that environmental managers benefit from precise estimates of the actual impacts of different obstacles on river connectivity, or from precise estimates of the gain in connectivity resulting from restoration actions, in order to guide the prioritization of conservation efforts and to evaluate their efficiency (Cooke & Hinch, 2013;Januchowski-Hartley, Diebel, Doran, & McIntyre, 2014;Raeymaekers, Raeymaekers, Koizumi, Geldof, & Volckaert, 2009).
The direct monitoring methods conventionally used in rivers to quantify the functional permeability of an obstacle or the efficiency of a restoration action are video counting, telemetry, and capturerecapture protocols. Although efficient (Cooke & Hinch, 2013;Hawkins, Hortle, Phommanivong, & Singsua, 2018;Junge, Museth, Hindar, Kraabøl, & Vøllestad, 2014;Pracheil, Mestl, & Pegg, 2015), these methods are associated with technical constraints. In particular, ecological studies based on video counting or telemetry are often conducted on a limited number of obstacles, whereas robust capture-recapture protocols imply repeated and exhaustive capture sessions, ideally over several years, which involves the mobilization of substantial human and financial resources (Cayuela et al., 2018).
An alternative method to quantify the permeability of an obstacle from molecular data is simply to measure the level of neutral genetic differentiation between populations located in the immediate upstream and downstream vicinity of an obstacle (i.e., located a few hundreds of meters to one kilometer apart, an adjacent sampling strategy), an approach that does not necessarily require large sample sizes (i.e., n ~ 20-30 per population) or heavy computation: Any drop in local functional connectivity due to the creation of a barrier to gene flow is expected to translate into an increase in neutral genetic differentiation (Raeymaekers et al., 2009). However, measures of neutral genetic differentiation may only be considered as correct estimates of actual barrier effects when comparing obstacles of the same age (in terms of number of generations since barrier creation) and/or separating populations of similar effective size. This is because genetic differentiation primarily stems from genetic drift, that is, from the random fluctuation of allelic frequencies naturally occurring in all populations (Allendorf, 1986). When populations are separated by an obstacle to gene flow, these fluctuations tend to occur independently in each population, leading to a differential distribution of allelic frequencies on either side of the barrier.
However, this process is progressive, taking place over several generations (Landguth et al., 2010), and is all the more slow as effective population sizes N e are large (Kimura, 1983). As a consequence, it is impossible to attribute the differences in levels of genetic differentiation observed between obstacles varying in age and/or in the effective size of populations they separate to differences in their actual barrier effects; older obstacles or obstacles separating smaller populations should show higher genetic differentiation than more recent obstacles or obstacles separating larger populations, despite similar actual barrier effects. Given this drawback, there is an urgent need for the development of a standardized and absolute genetic index of fragmentation that takes into account the contribution of both the age of the obstacle (expressed in the number of generations since barrier creation) and the effective size N e of populations (or a proxy of it since this parameter is notoriously difficult to quantify; Wang, 2005) to observed measures of genetic differentiation. Such an index might allow a quick and robust quantification of individual and actual barrier effects whatever their characteristics, paving the way for informed management prioritization and proper evaluation of restoration measures, along with inter-basins and interspecific comparative studies.
Here, we bridge that gap by developing a user-friendly and standardized genetic index of fragmentation (see Appendix S1 for a walkthrough), allowing an absolute and independent assessment of the individual effects of obstacles on gene flow. The proposed index (F INDEX ) is expressed as a percentage and directly quantifies the relative loss of gene flow resulting from the presence of an obstacle. It is based on the comparison of measures of genetic differentiation observed between populations located in the immediate upstream and downstream vicinity of a putative obstacle with the theoretical measures of genetic differentiation that would be expected if the obstacle was a total barrier to gene flow. These theoretical measures of genetic differentiation are inferred from numerous genetic simulations, here used to reflect the expected changes in allelic frequencies resulting from the interplay between the age of the obstacle and the expected heterozygosity of populations, a proxy for N e : the closer the observed measure of genetic differentiation from the one that would be expected in the worst-case scenario (total barrier to gene flow), the higher the index of fragmentation. We first present the logic and principles underlying our index. We then use both simulated and published empirical genetic datasets to explore and discuss the validity and the limits of the proposed index. We finally propose several perspectives to use the index and, because setting bio-indicators takes time, we present potential improvements that should be considered to make this index even more useful to managers.

| Principle of the proposed genetic index of fragmentation F INDEX
The proposed genetic index of fragmentation F INDEX is designed as a standardized estimate of the reduction in gene flow between two adjacent populations separated by an obstacle. It simply consists in rescaling the observed measure of genetic differentiation GD obs within its theoretical range of variation, taking into account the expected temporal evolution of allelic frequencies resulting from the interplay between the age of the obstacle and the averaged expected heterozygosity of populations, a proxy for their effective population size N e . This theoretical range of variation spans from GD min to GD max . GD min stands for the theoretical measure of genetic differentiation that would be expected if the obstacle was totally permeable to gene flow (crossing rate m ≈ 0.5). GD min should theoretically equal 0 but the background noise resulting from the concomitant influences of genetic drift, mutations, and incomplete genetic sampling may actually lead to non-null-though very low-measures of genetic differentiation. On the other hand, GD max stands for the theoretical measure of genetic differentiation that would be expected under the worst-case scenario, that is, under the hypothesis that the considered obstacle is a total barrier to gene flow (m = 0). GD max is expected to increase with time since barrier creation and to decrease with the increase in effective population sizes (Gauffre, Estoup, Bretagnolle, & Cosson, 2008;Landguth et al., 2010) and thus with H e . For any measure k of genetic differentiation GD k , the genetic index of fragmentation F INDEX is then computed as follows (see Appendix S2 for details): The F INDEX ranges from 0% (the observed measure of genetic differentiation is minimum-but not null-and equals the expected value GD min under the assumption that the considered obstacle has no impact on gene flow) to 100% (the observed measure of genetic differentiation is maximum and equals the expected value GD max under the assumption that the considered obstacle acts as a total barrier to gene flow). The F INDEX thus directly quantifies the loss of gene flow resulting from the presence of an obstacle. GD obs is directly calculated from observed genotypic data collected in populations located at the immediate upstream and downstream vicinity of the obstacle (a few hundred of meters to one kilometer apart depending on the target species; see below), whereas GD min and GD max are predicted from theoretical datasets simulated according to three main parameters (see the next section for details): the mutation rate µ of considered genetic markers, and, for GD max only, the age T of the total barrier to gene flow (expressed in number of generations since barrier creation; Landguth et al., 2010;Lowe & Allendorf, 2010) and the averaged expected heterozygosity H e of the two considered populations. H e is here considered as a proxy for effective population sizes N e , since both theoretical and empirical works indicate that genetic diversity should increase with the increase in N e (Hague & Routman, 2016;Kimura, 1983; see Appendix S5). We used the average of expected levels of heterozygosity since most pairwise metrics of genetic differentiation assume similar effective population sizes between populations (Prunier, Dubut, Chikhi, & Blanchet, 2017).

| Expected measures of genetic differentiation
We used QuantiNemo2 (Neuenschwander, Michaud, & Goudet, 2019), an individual-based simulator for population genetics, to simulate theoretical datasets that will in turn be used to predict GD min and GD max values. We designed a very simple metapopulation model composed of two adjacent demes. Both demes had the same carrying capacity K, with K ranging from 30 to 2,000 individuals (93 levels; see Figure S5a for visualization) and kept constant over time. We used forward simulations of gene flow between these two demes over 1,000 nonoverlapping generations.
Genotypes were randomly assigned to individuals at the beginning of simulations. The inter-deme migration rate was set to 0.5 for the first 400 generations, these parameters providing an optimal mixing of populations and mimicking a natural situation without barrier. The inter-deme migration rate was then dropped to zero for the last 600 generations, mimicking the creation of a total barrier to gene flow, splitting a "single" population into two adjacent subpopulations.
With populations being isolated for 600 generations, we made sure our simulations covered a time frame long enough to account for the effect of the oldest artificial barriers: Although most obstacles in freshwater ecosystems around the world are recent (constructed over the last 100 years), many others, especially in Europe, date from the 12th-15th centuries, which corresponds to ~250-400 generations in most aquatic organisms such as fish species (assuming a generation time of 2 years). For each carrying capacity K (93 levels) and each mutation rate µ (2 levels), we ran ten simulation replicates, and 30 genotypes were sampled every ten generations from generation 300 to generation 1,000 (71 levels) to monitor the setting up of genetic differentiation over time. This procedure resulted in a total of 93 × 2×71 × 10=132,060 simulated genetic datasets in the Fstat format (Goudet, 1995) and further converted into the genepop format (Rousset, 2008) using R (R Development Core Team, 2014).
For each simulation, we computed the two following pairwise metrics of genetic differentiation: the Hedrick's G″st (Hedrick, 2005;Meirmans & Hedrick, 2011) and the Meirmans' φ′st (Meirmans, 2006), both computed using the R-package mmod (Winter, 2012). Nine other metrics were initially considered, but preliminary analyses revealed that some were dependent on sample size (e.g., the proportion of shared alleles or the Cavalli-Sforza and Edwards' Chord distance; Bowcock et al., 1994;Cavalli-Sforza & Edwards, 1967; see Appendix S3 for details), while others were sensitive to mutation rate and/or did not show enough variability (e.g., the Weir and Cockerham's θst or the Jost's D; Jost, 2008;Weir & Cockerham, 1984; see Appendix S4 for details): They were thus discarded to avoid jeopardizing the validity of the proposed index.
We found that the two retained metrics G″st and φ′st were robust to variations in mutation rate and increased quickly after barrier creation, especially in the case of small effective population sizes  (Hague & Routman, 2016;Kimura, 1983). We here focused on mean heterozygosity because, unlike metrics such as allelic richness, heterozygosity values are bound between 0 and 1, which facilitates comparison between case studies. Moreover, this metric is much more straightforward to calculate for managers than the actual effective population size, since the latter is notoriously difficult to estimate in complex landscapes (Paz-Vinas et al., 2013;Wang, 2005). Note also that the use of two different realistic mutation rates yielded two levels of H e across simulations (a low level at the low mutation rate and a high level at the high mutation rate; Appendix S5b), thus mimicking uncertainty in our proxy for effective population sizes. In addition to the two metrics of genetic differentiation G″st and φ′st and to the expected heterozygosity H e , we also kept record of the simulation replicate number, the mutation rate µ, the generation t at which genotypes were collected, the age T of the barrier (computed as T = t−400 and expressed in number of generations since barrier creation), and the carrying capacity K of simulated populations.
The 111,600 simulations associated with T > 0 (i.e., after the creation of the barrier) were used as a training set in the regression implementation of a random forest machine-learning algorithm (Breiman, 2001). This approach was chosen as it is currently one of the most efficient statistical techniques for making predictions from nonlinear data, with only a few parameters to tune (

| Computing the genetic index of fragmentation F INDEX
Equation 1 allows computing a unique index of fragmentation for each combination of both a mutation rate µ (5 × 10 -5 or 5 × 10 -4 ) and a metric of genetic differentiation GD (G″st or φ′st). The whole procedure was automated within a user-friendly R-function (the FINDEX R-function; see Appendix S1). Users are simply expected to provide empirical genotypic datasets (in the genepop format) and a parameter file indicating for each considered obstacle the name of the two adjacent populations (as given in the genotypic datasets) and the number of generations elapsed since barrier creation. This number of generations is to be estimated from the life-history traits of the considered species. Figure 1 provides a flowchart allowing an overall visualization of the process.
F I G U R E 1 Flowchart illustrating the major steps in calculating the genetic index of fragmentation for two independent obstacles. This flowchart refers to a user-friendly script made publicly available. After the sampling of populations located at the immediate upstream and downstream vicinity of each obstacle, users only have to provide a file of genotypes in the genepop format and a file of parameters indicating, for each obstacle, the names of the sampled populations and the number T of generations elapsed since the creation of the obstacle. Observed measures of genetic differentiation GD obs and mean expected heterozygosity H e are automatically computed from provided genotypic data. GD min and GD max values, both delimiting the theoretical range of variation of GD obs , are automatically predicted from pre-existing.rda files, GD max values depending on both H e and T. The computation of the index basically amounts to rescaling GD obs within its theoretical range (see main text for details), thus allowing standardized comparisons of the permeability of various obstacles, whatever their age, the considered species or the effective size of sampled populations

| Validation of the F INDEX from simulated data
To assess the validity of the proposed F INDEX in response to different levels of obstacle permeability, we again used the program QuantiNemo2 to simulate gene flow over 1,000 nonoverlapping generations between two adjacent demes of constant carrying capacity K, with K = 50, 100, 250, 500, or 1,000 individuals. To mimic realistic genetic datasets, each microsatellite locus was given a unique stepwise mutation rate µ randomly picked from a log-normal distribution ranging from 5 × 10 -5 to 5 × 10 -3 with a mean of 5 × 10 -4 (see Appendix S7 for details). The inter-deme migration rate was set For each simulated dataset, we computed the averaged expected heterozygosity H e and the two pairwise measures of genetic differentiation G″st and φ′st. We then used parameters T and H e to predict the corresponding measures of genetic differentiation GD min and GD max (for both G″st and φ′st) expected under the two mutation rates 5 × 10 -5 and 5 × 10 -4 using the predict.randomForest function and the previously created.rda files (Appendix S1). For each dataset, the four indices of fragmentation were then computed using Equation 1. To average datasets across replicates, we finally used intercept-only mixed-effect models (with dataset as a random effect) to get the final mean F INDEX (along with a 95% confidence interval) corresponding to each combination of K, T, and m.
We finally explored the sensitivity of the F INDEX to uncertainty in the estimates of N e and T and to reduced numbers of markers.
Details are provided in Appendices S12 to S14.

| Test of the F INDEX with empirical data
To assess the behavior of the proposed F INDEX in real situations, we used two published empirical datasets. The first one is from Gouskov, Reyes, Wirthner-Bitterlin, and Vorburger (2016

| Expected measures of genetic differentiation
The first set of simulations was designed to predict GD min and

| Validation of the F INDEX from simulated data
The second set of simulations was designed to assess whether the   Sensitivity analyses showed that the F INDEX is highly robust to a ~50% uncertainty in the estimates of T (Appendix S12) and that 95% CI about F INDEX values correctly capture uncertainty associated with the use of H e as a proxy for N e (Appendix S13). Finally, we found that the F INDEX is highly robust to a limited number of microsatellite markers, but tends to slightly underestimate barriers effects when using low polymorphic markers (Appendix S14).

| Test of the F INDEX with empirical data
In the first empirical dataset (Gouskov et al., 2016), monitored dams were created from 1893 to 1964, which corresponds to ~15 to 39 generations in S. cephalus (Table 1). Averaged levels of expected heterozygosity were high and showed little variability (ranging from 0.69 to 0.77), whereas observed measures of genetic differentiation were pretty low, ranging from 0 to 0.028 for φ′st and from 0 to 0.025 for G″st. We found that three dams showed a F INDEX value ranging from 49% to 62%, suggesting a 49% to 62% local decrease in genetic connectivity (Figure 4a). The other three dams all showed null F INDEX F I G U R E 2 For each mutation rate (panels A and B) and each metric of genetic differentiation (G″st on the left and φ′st on the right), predicted GD max variations across the parameter space defined by the number T of generations elapsed since total barrier creation (from 0 to 600 generations) and the averaged expected heterozygosity (H e , ranging from 0 to 0.93) for pairs of adjacent populations. GD min values are represented at the bottom of each graph. GD min and GD max surfaces together delimit the theoretical range of variation for any observed measure of genetic differentiation GD obs

| D ISCUSS I ON
Restoring riverscape connectivity is of crucial importance in terms of biodiversity conservation, and it is now often subject to regulatory obligations (e.g., in Europe, the Water Framework Directive 2000/60/EC). However, rivers are subject to many and sometimes contradictory uses (Reid et al., 2018): For practitioners to be able to propose informed trade-offs between restoring riverscape connectivity and maintaining infrastructures and their associated socioeconomic benefits (Hand et al., 2018;Roy et al., 2018;Song et al., 2019), new tools have to be developed, allowing a rapid and reliable quan-

Box 1 Guidelines for the use and the interpretation of the F INDEX
The F INDEX allows an individual and standardized quantification of the impact of artificial barriers on riverscape functional connectivity from snapshot measures of genetic differentiation. Here, we provide a guideline for practitioners: • Species: Any freshwater species whose local effective population sizes are lower than 1,000 can be considered.
• Obstacle: Any obstacle whose age corresponds to a minimum of 10-15 generations and a maximum of 600 generations for the studied species can be considered.
• Sampling: Populations are sampled in the immediate upstream and downstream vicinity of the obstacle, with a minimum of 20-30 individuals per population.
• Genetic data: Individual genotypes are based on a set of highly polymorphic microsatellite markers.
• Computation: The F INDEX is computed in R thanks to a user-friendly script made publicly available (see Data Archiving statement and Appendix S1 for a walkthrough).
• Interpretation for F INDEX > 90%: A F INDEX value higher than 90% (or whose 95% confidence interval includes the 90% threshold) indicates no gene flow between populations (total barrier effect), whatever the age of the obstacle or the effective size of populations.
• Interpretation for F INDEX < 20%: A F INDEX value lower than 20% (or whose 95% confidence interval includes the 20% threshold) indicates full genetic connectivity (no barrier effect), whatever the age of the obstacle or the effective size of populations. •

Box 2 Future directions for improving the F INDEX
The F INDEX is already operational but it is, however, still in its infancy. We identified several research avenues that may allow further improving it or help answer specific needs. They are here presented by our order of priority.
• Taking asymmetric crossing into consideration: The proposed F INDEX currently relies on the use of classical pairwise measures of genetic differentiation that assume symmetric gene flow. It will be first necessary to assess the sensitivity of the current version of the F INDEX to asymmetric barrier effects and, if needed, to determine whether existing asymmetric measures of genetic differentiation (Sundqvist, Keenan, Zackrisson, Prodöhl, & Kleinhans, 2016) could be used to improve its efficiency. This task may otherwise require the development of new metrics of genetic differentiation.
• Dealing with nonadjacent sampling designs: The proposed F INDEX relies on a strict adjacent sampling strategy, with populations sampled in the immediate upstream and downstream vicinity of the considered obstacle. However, this sampling design might be difficult to implement in some situations (e.g., dams with a large reservoir). When the two sampled populations are distant from each other, GD obs values may nevertheless result from the interplay between the actual barrier effect (the quantity of interest) and other processes such as Isolation-by-Distance. In such situations, the F INDEX should be computed using ad hoc GD min and GD max .
values, both taking into account the additional processes responsible for GD obs values. To that aim, a solution could be to consider a space-for-time substitution sampling design (Coleman et al., 2018), with the additional sampling of (at least) two control populations that are not disconnected by any barrier, are located within the same river stretch and are separated by approximately the same distance as the two focal populations.  fragmentation but also from other processes such as Isolation-by-Distance (Coleman et al., 2018). We thus strongly encourage practitioners to consider an adjacent sampling design as often as possible, although we readily acknowledge that this may not always be an easy task given safety and accessibility considerations. Furthermore, fish may not always be found in the direct vicinity of obstacles. For instance, the conversion of a river into a reservoir after the creation of a dam often leads to major habitat modification and shifts in species composition (Bednarek, 2001) (Figure 2; see also Box 2). It is in this perspective that the provided R-function already allows users to integrate their own GD min . and GD max . values (Appendix S1). However, we believe that the variety, the complexity, and the specificity of such scenarios would preclude the computation of standardized F INDEX scores, comparable among obstacles, species, and studies. Although it might in some instances be considered a technical constraint, we argue that only a strict adjacent sampling design can warrant unbiased and reliable F INDEX estimates.
Finally, the proposed F INDEX does not take into account the possible asymmetric gene flow (and associated asymmetry in effective population sizes) created by barriers, as fish might struggle or even fail to ascent an obstacle (sometimes despite the presence of dedicated fishpasses; Silva et al., 2018) whereas dam discharge might on the contrary further increase or even force downstream movements (Pracheil et al., 2015). Although quantifying the asymmetric permeability of obstacles appears of crucial importance for informed conservation measures, the proposed F INDEX currently relies on the use of classical pairwise measures of genetic differentiation that assume symmetric gene flow and similar effective population sizes on either side of an obstacle. This may for instance partly explain why we did not find any F INDEX higher than 65% for weirs  and 61% for dams (Gouskov et al., 2016; (Cayuela et al., 2018). Future developments will be required to allow the F INDEX to provide unbiased and distinct standardized scores for both upstream and downstream barrier effects (see Box 2). In the meanwhile, it may be interesting to also assess the validity of the F INDEX in quantifying the effects of terrestrial obstacles, since asymmetric gene flow is not necessarily as pronounced as in river systems: Provided that populations are sampled in the direct vicinity of the obstacle, the F INDEX might as well provide a standardized quantification of road-induced fragmentation.

| CON CLUS ION
We here laid the groundwork for an operational tool dedicated to the individual and standardized quantification of the impact of artificial barriers on riverscape functional connectivity from measures of genetic differentiation. The proposed genetic index of fragmentation F INDEX is designed to take into account the temporal inertia in the evolution of allelic frequencies resulting from the interplay between the age of the obstacle and the effective sizes of populations. Provided only adjacent populations are sampled, the F INDEX allows a rapid and thorough ranking of obstacles only a few generations after their creation. The F INDEX in its current form still suffers from some limitations, and it should be seen as the preliminary version of a future powerful bio-indicator of habitat fragmentation, rather than as an end-product.
We call conservation and population geneticists to pursue the development of such an index, as we-as scientists-need to help managers resolve complex and urging social problems. In Box 2, we hence

ACK N OWLED G EM ENTS
We warmly thank all the colleagues and students who helped with field sampling. We are also grateful to Dr. A. Gouskov and C.
Vorburger for details about their data. This work has been financially supported by grants to SB from the Agence Française pour la Biodiversité and from the Région Occitanie (CONAQUAT).

DATA AVA I L A B I L I T Y S TAT E M E N T
The two simulated datasets as well as R-objects allowing the computation of the F INDEX (Prunier et al., 2019)