Elodie Brisset
email: elodie.brisset@gmail.com

Frédéric Guiter

Cécile Miramont

Tiané Troussier

Pierre Sabatier

Yoann Poher

Rosine Cartier

Fabien Arnaud

Emmanuel Malet

Edward J Anthony

The overlooked human influence in historic and prehistoric floods in the European Alps

Understanding the role of climate and humans in generating mountain slope instability is crucial because such instability influences downstream fluvial activity and is a major threat to societies. Here, we use the sedimentary archive of Lake Allos (southeastern France), a mountain lake in the European Alps, to characterize mountain flood deposits and vegetation dynamics over the past 7000 yr. Our results support the interpretation of a critical threshold in catchment sensitivity to erosion at 1700 calibrated (cal.) yr B.P. (A.D. 250) probably resulting from long-term, uninterrupted impacts of human activity. The frequency and severity of floods increased dramatically after this date. These results demonstrate that underestimation of human impacts over the Holocene may pose a challenge to a clear understanding of past climate changes because paleoflood records are highly likely to have been affected by geomorphic thresholds. Natural reforestation since the end of the 19 th century does not appear to be sufficient to induce a flood regime comparable to that which occurred prior to 1700 cal. yr B.P. This poses the question as to whether forest restoration in high-altitude environments is liable to foster a return to a low-erosion regime over the next decades, or whether the overall severity of soil degradation has been such as to preclude a return to previous conditions.

INTRODUCTION

Accelerated erosion processes are a major environmental concern because they result from a combination of factors that include climate, geomorphology, and human pressure, particularly when landscape disturbances occur at watershed scales and cause a shift to a regime with mean levels and variances higher than those prior to disturbances [START_REF] Sharpe | Geomorphic aspects of normal and accelerated erosion: Eos[END_REF]. In mountain areas, accelerated erosion is expected to exacerbate torrential floods through mobilization of large amounts of sediments during highintensity rainfalls. The importance of climate as a hydrological driver depends on the sensitivity of the system in question. Springtime rain-onsnow events and heavy summertime convective rains generally drive floods in alpine regions [START_REF] Parajka | Seasonal characteristics of flood regimes across the Alpine-Carpathian range[END_REF]. Through their activities, humans may also have had a major role in flood hazards. Vegetation removal can lead to an increase in runoff efficiency, favoring flood generation and increasing erosion [START_REF] Cosandey | The hydrological impact of the Mediterranean forest: A review of French research[END_REF]. While it is commonly assumed that climate change weakens present and future watershed resilience to global change, it is crucial to investigate how humans have transformed the geomorphic response of mountain landscapes to floods beyond the millennial time scale.

North-central Europe and its mountain ranges, notably the Alps, is an exceptionally appropriate area to address these issues because the environment in this setting has been affected by humans for millennia [START_REF] Fyfe | From forest to farmland: Pollen-inferred land cover change across Europe using the pseudobiomization approach[END_REF]. The spread of human settlements in the Alps dates back to the end of the Neolithic and the Bronze Age [START_REF] Walsh | A historical ecology of the Ecrins (Southern French Alps): Archaeology and palaeoecology of the Mesolithic to the Medieval period: Quaternary International[END_REF]. From these times to the present day, human activities have been seasonal, with uplands dedicated to grazing and dairy production. Based on a case study of Lake Allos (southeastern France; 44°14′N, 6°42′35″E, 2230 m above sea level), a mountain lake in the European Alps (Appendices DR1 and DR2-A in the GSA Data Repository 1 ), we examined changes in vegetation, land use, and the sedimentology of flood deposits over the past 7000 yr. Lake Allos is a valuable archive 1 GSA Data Repository item 2017100, Appendices DR1 and DR2 (characteristic of the study site), Appendices DR3 and DR4 (analytical procedures), Appendix DR5 (pollen data), Appendices DR6 and DR7 (chronology), Appendix DR8 (statistical tests), and Appendix DR9 (old postcards), is available online at http://www.geosociety.org/pubs/ft2017.htm or on request from editing@geosociety.org. of torrential floods because its stacked bottom sediments comprise detrital layers detected by their distinct sedimentological signature, including a sharp and coarse base overlain by a finingupward basal unit and capped by a whitish, finegrained unit. [START_REF] Wilhelm | Is a regional flood signal reproducible from lake sediments?[END_REF] have further shown that historically documented floods in the main valley downstream of Lake Allos are well detected in the sediment archive. A core, ALO11, was sampled in the deepest part of the lake (Appendices DR2-B and DR2-C), where stream discharge triggers detrital deposition over the subbasin floor [START_REF] Wilhelm | 1400 years of extreme precipitation patterns over the Mediterranean French Alps and possible forcing mechanisms[END_REF][START_REF] Wilhelm | Is a regional flood signal reproducible from lake sediments?[END_REF][START_REF] Brisset | A new contribution to the chronology of the deglaciation in the Upper Verdon Valley[END_REF]. Flood layers identified from thin overlapping sections were counted at a resolution of 200 µm under a binocular microscope (Appendix DR3) and distinguished according to the diameter of the coarsest particle of the layer (Appendix DR4). A palynological analysis was carried out on the same core (Appendix DR5), and the chronology was derived from 16 AMS 14 C dates and short-lived isotopes (Appendices DR6 and DR7).

DISCREPANCIES BETWEEN FLOOD FREQUENCY AND CLIMATE VARIABILITY

The age-depth model of core ALO11 provides a record of deposition over the past 7000 yr (Appendix DR6) comprising 1721 flood layers. In order to investigate how human-induced geomorphic changes have impacted the flood record, we tested the hypothesis that flood layer frequency and amplitude have significantly changed over this time frame. This has been tested using regime shift detection [START_REF] Rodionov | A sequential algorithm for testing climate regime shifts[END_REF]. Figure 1A shows that flood layers (FLs) were more frequent after 1700 cal. (calibrated) yr B.P. (from 150 to 545 floods per 1000 yr) than in any previous period over the past 7000 yr (p < 0.01 using t-test).

From 7000 to 1700 cal. yr B.P., the Lake Allos flood frequency exhibited low variability (Fig. 1A) and shows poor correspondence with other records from the southern Alps. In the stacked flood record from five lakes published by [START_REF] Wirth | Holocene flood frequency across the Central Alps: Solar forcing and evidence for variations in North Atlantic atmospheric circulation[END_REF], the flood frequency shifted at 4000 cal. yr B.P. (p < 0.01, t-test) (Fig. 1E), while [START_REF] Sivan | Rythmes de la sédimentation et interprétations paléoclimatiques lors du Postglaciaire dans les Alpes du Sud. 14C et dendro-géomorphologie, deux chronomètres complémentaires[END_REF] showed that periods of alluvial deposition in lower valleys occurred at 4500-3900 cal. yr B.P. and 2500-2900 cal. yr B.P. (periods 7 and 5, Fig. 1C). Since 1700 cal. yr B.P., the flood variability at Lake Allos has appeared to be in agreement with known periods of climatic changes. Higher flood frequency occurred during the Late Antiquity and the Little Ice Age (periods 3 and 1 in Fig. 1), two periods characterized in the Alps by cold and humid conditions [START_REF] Magny | Assessment of the impact of climate and anthropogenic factors on Holocene Mediterranean vegetation in Europe on the basis of palaeohydrological records: Palaeogeography[END_REF] and glacier advances (Le [START_REF] Roy | Calendar-dated glacier variations in the western European Alps during the Neoglacial: The Mer de Glace record[END_REF] (Fig. 1B). Periods of lower flood frequency corresponded to the warmer and drier conditions of the Roman and the Medieval Periods (periods 4 and 2 in Fig. 1).

Discrepancies between these lake records from 7000 to 1700 cal. yr B.P., and agreement since 1700 cal. yr B.P., argue for the fact that climate alone was not the dominant forcing factor of flood variability. Although flood frequency proxies are likely to have been driven by precipitation changes, they are not necessarily a product of climate variability alone over the entire Holocene. This the idea that past floods identified from high-elevation lake records would have been driven exclusively by climate forcing.

EFFECT OF EROSION REGIME SHIFTS ON THE FLOOD RECORD

In order to investigate how geomorphic response impacts the flood layer record, we analyzed the sedimentological characteristics of the FLs, which reflect rainfall intensity and catchment sensitivity to erosion. In general, the size of the coarsest FL particles reflects the maximum river flow velocity reached during a flood [START_REF] Lapointe | 1750 years of large rainfall events inferred from particle size at East Lake, Cape Bounty[END_REF], and thickness reflects the abundance of sediment supplied [START_REF] Schiefer | A lake sediment-based proxy of floods in the Rocky Mountain Front Ranges[END_REF]. However, changes in thickness might also reflect changes in catchment erodibility [START_REF] Giguet-Covex | Frequency and intensity of high-altitude floods over the last 3.5 ka in northwestern French Alps[END_REF]. The increase in FL frequency follows the increase in FL thicknesses, showing the same breaking point at 1700 cal. yr B.P. (Fig. 2). A subdivision of the FLs according to the coarsest particles of each layer (Fig. 2) was carried out in order to investigate the relationship between maximum grain size and thickness (type FL-1, fine silts from 0 to 20 µm; FL-2, medium silts from 20 to 50 µm; FL-3, fine sands from 50 to 100 µm; Appendix DR5). This subdivision shows (Fig. 2) a sudden increase at 1700 cal. yr B.P. of the number of FL-1 layers from a mean of 85 to 395 per 1000 yr . FL-2 and FL-3 have also been more frequent since 1700 cal. BP, but their frequency increase has only been twofold. Using the non-parametric two-sample Mann-Whitney test (p < 0.01), we evaluated the null hypothesis that FL thickness from two periods of different vegetation cover have identical distributions with equal medians, against the alternative that they do not have equal medians. Distributions of FLs are significantly different and FLs are thicker since 1700 cal. yr B.P. (Fig. 2; p < 0.01; Appendix DR8). As there is no relationship between bulk density and sediment depth (Appendix DR6), change in FL thickness indicates that whatever the velocity, floods have mobilized systematically more sediment since this date. This is particularly remarkable for FL-3, which has significantly shifted to a higher order of magnitude (from a median thickness of 6-20 mm sediment supply is significantly higher during high-velocity flood events. In addition, FL-1 type events have been more frequent (Fig. 2), indicating that the change in FL frequency at 1700 cal. yr B.P. has been principally caused by an increase in the number of lower-velocity floods. The erosion sensitivity of the source area to rainfall has increased, even for low-intensity ones. These results highlight a modification of the relationship between precipitation intensity and sediment supply. Altogether, the results indicate an increase in catchment erodibility in response to hydro-meteorological processes. The relationship between flood regime and precipitation has shifted to a higher order of magnitude due to local changes in catchment sensitivity.

A HUMAN-INDUCED REGIME SHIFT

Causes of the change in catchment sensitivity have been explored through pollen analysis (Appendix DR5). Two pollen groups are shown in Figure 2, summarizing the abundance in tree cover (arboreal pollen) and domestic livestock grazing (anthropogenic pollen: Rumex, Urtica, Mentha, Plantago, Cerealia, and Chenopodiaceae; [START_REF] Court-Picon | Modern pollen-vegetation relationships in the Champsaur valley (French Alps) and their potential in the interpretation of fossil pollen records of past cultural landscapes[END_REF]. These results bring out four dominant stages in the vegetation dynamics that range from a dense forest from 7000 to 6000 cal. yr B.P. to a progressively more open forest from 6000 to 3500 cal. yr B.P. Since 3500 cal. yr B.P., the impact of human activities has tended to grow, and became intensified from 1700 cal. yr B.P. (attested by the increase in cereals and the Urtica pollen curves). Comparison between pollen and FL grain-size patterns suggests that the increase in FL number and thickness has been related to an increase in human-induced vegetation change. But, what is unexpected is the timing of the regime shift, between the Iron Age and the Roman period. These periods are not clearly recognized by the numerous alpine archaeological investigations carried out to date, notwithstanding decades of research. With the exception of some valleys located along transalpine trade routes [START_REF] Della Casa | Valleys, pastures, and passes[END_REF] where "Romanization" initiated urban growth and new forms of rural land use, high-altitude landscapes were characterized by a reduction, or, at most, continuity, of pastoral activities [START_REF] Segard | Habiter dans les Alpes: La Romanisation des regions de moyenne et de haute montagne au filter de l'habitat[END_REF].

Looking at the situation in more detail, tree cover decline at Lake Allos started before the change in flood regime at 1700 cal. yr B.P. One drawback of pollen is that it may not systematically yield precise information about where changes in vegetation occurred: locally or at the scale of the watershed. However, it is likely that forest clearance and agro-pastoralism led to increased runoff locally, favoring flood generation and exacerbated erosion from 1700 cal. yr B.P.

NON-STATIONARY PALAEOCLIMATIC ARCHIVES

Since 1700 cal. yr B.P., a change in catchment sensitivity has modified the apparent frequency of floods archived in Lake Allos. This type of geomorphic change is liable to distort our perception of long-term climate variability, leading to a misinterpretation of flood frequency and intensity as stationary proxies of precipitation. Similar conclusions were set earlier for climate reconstructions based on paleoecological proxies in many alpine landscapes [START_REF] Lotter | The Holocene palaeolimnology of Sägistalsee and its environmental history: A synthesis[END_REF]. Several alpine paleoflood records show a similar but non-synchronous pattern of late Holocene flood frequency regime shift (Fig. 1) occurring at 1700 cal. yr B.P. in Lake Allos (Fig. 1A), 3400 cal. yr B.P. in Lake Anterne (France) (Fig. 1D), 4000 cal. yr B.P. for the southeastern Alps (Fig. 1E), and 2500 cal. yr B.P. for the northern Alps (Fig. 1F). Following the example of Lake Allos based on multiproxy analyses, accelerated erosion processes in European Alps are highly likely to have been driven by human activities. As human influence on landscapes has been heterogeneous in time, in intensity, and in quality [START_REF] Hoffmann | Human impact on fluvial regimes and sediment flux during the Holocene: Review and future research agenda[END_REF], the onset of accelerated erosion has differed among sites.

For the late Holocene, precautions are generally taken to disentangle the respective influence of climate and humans on flood reconstructions [START_REF] Giguet-Covex | Frequency and intensity of high-altitude floods over the last 3.5 ka in northwestern French Alps[END_REF]. Nonetheless, several studies have directly reconstructed paleoprecipitation variability by assuming that geomorphic settings were unaffected by ancient human practices, and by refuting evidence that human impact has occurred at different points of time in the Alps or that such impact generated multimillennial landscape transformations. Unaffected flood records may rather be found in glaciated or steep catchments unfavorable for human activities during the entire Holocene. Minor human impact may also be invoked for sites located at altitudes higher than that of the Holocene forest extension [START_REF] Lotter | The Holocene palaeolimnology of Sägistalsee and its environmental history: A synthesis[END_REF]. In those cases, neither vegetation nor soils may have significantly changed. The Lake Allos record demonstrates that catchment sensitivity to rainfall can affect the homogeneity of flood archiving in the sediment record. Underestimation of human impact during the Holocene might, therefore, influence the understanding of climate changes. Non-stationary processes [START_REF] Milly | Stationarity is dead: Whither water management?[END_REF], especially human-induced geomorphic ones, need to be investigated before using paleofloods as a long-term proxy for flood-risk assessment.

IMPLICATIONS FOR FLOOD-RISK MITIGATION

Changes in vegetation cover have been a decisive driver of the Holocene erosion acceleration at Lake Allos by affecting the flood regime. Prior to 1700 cal. yr B.P., the flood regime was characterized by a low mean level and low variability. In the Alps, forests reached their maximum altitudinal position from 8000 to 6000-4000 cal. yr B.P., depending on the catchment [START_REF] Brisset | Lateglacial/Holocene environmental changes in the Mediterranean Alps inferred from lacustrine sediments[END_REF]. The stable geomorphic conditions were then disrupted following the multimillennial regression of forests in response to intensive human exploitation. Thus, catchment sensitivity to erosion was significantly lower during the Holocene in comparison to the past 1700 yr. Given these results, it could be expected that reforestation of heavily eroded terrain would help to reinstate a lower flood regime as occurred during the mid-Holocene.

Between the 19 th and 20 th centuries, grazing activities at Lake Allos decreased following rural exodus and forest-protection policies. A comparison of historic photographs of Lake Allos dating from the end of the 19 th century to the present (Appendix DR9) shows natural reforestation of the lakeshore. Reforestation and mountain slope management are likely to reduce erosion, as shown for the marly formations of the southern Alps over the past 120 yr [START_REF] Vallauri | An analysis of forest restoration 120 years after reforestation on badlands in the southwestern Alps[END_REF], and could contribute to mitigating flood risk. The last decade has been characterized by high flood frequencies (Fig. 2) and by the occurrence of one thick layer (41.2 mm) corresponding to a flood in A.D. 1994 [START_REF] Etienne | Influence of sample location and livestock numbers on Sporormiella concentrations and accumulation rates in surface sediments of Lake Allos, French Alps[END_REF]. This FL is thicker than all of the FLs deposited from 7000 to 1700 cal. yr B.P., while no significant compaction affects the sediment (bulk density is almost constant; Appendix DR6). Thus, this suggests that the flood regime level and sediment supply are still high. Forest altitudinal expansion does not seem to modify the flood regime at this time scale. Forests have still not yet recolonized the upper parts of the catchment, and the severity of inherited soil degradation might be a lasting obstacle to upslope migration of mature forests. Even though ecological simulations indicate that abandoned overgrazed grasslands could turn into woodlands within 20-50 yr in the southern Alps [START_REF] Albert | Land-use change and subalpine tree dynamics: Colonization of Larix decidua in French subalpine grasslands[END_REF], the establishment of mature forests may be conditioned by the requirement of having developed soils with a sufficient waterholding capacity [START_REF] Henne | Did soil development limit spruce (Picea abies) expansion in the Central Alps during the Holocene? Testing a palaeobotanical hypothesis with a dynamic landscape model[END_REF]. A return to previous conditions (mature forest, developed soils) may require much more time than hitherto assumed. The critical geomorphic threshold that occurred at 1700 cal. yr B.P. might thus be interpreted as a tipping point; a return to the previous state (low flood regime) may not be possible within the time scale of a few human generations [START_REF] Mori | Ecosystem management based on natural disturbances: Hierarchical context and non-equilibrium paradigm[END_REF]. A choice in favor of landscape reforestation and possible effects on flood mitigation would also require finding an optimal balance that also maintains mountain landscapes open to the promotion of biological diversity, the preservation of traditional shepherding, and the sustenance of tourism.

  Figure 1. Location map and comparison of lake flood frequency records of European Alps over the past 7000 yr, glacier advances, and slack water deposition. Phases of humid and cold con ditions corresponding to high flood layer (FL) frequency at Lake Allos (southeastern France) are shaded in dark gray; those not corresponding are in light gray. Number ing (0-7) refers to periods discussed in text (black, cold and humid; gray, warm and dry). Asterisks indicate the most signifi cant flood regime shifts (p < 0.01, ttests). A: 100 yr FL moving frequency, Lake Allos (this study). B: Glacier advances (Le Roy et al., 2015). C: Sediment supply of Durance River (southeastern France) (Sivan et al., 2006). D: 100 yr FL moving frequency, Lake Anterne (France) (GiguetCovex et al., 2012). E,F: Flood activ ity (%), southeastern and northern Alps, respec tively (Wirth et al., 2013). cal.-calibrated.

Figure 2 .

 2 Figure 2. Flood layer (FL) sedimentological characteristics compared to vegetation cover from 7000 cal. yr B.P. to present in Lake Allos, Alps (southeastern France). Arboreal pollen indi cates degree of forest openness, and anthropogenic pollen represents agropastoralism. FL subdivision is based on coarsest particle size (FL1, 0-20 µm; FL2, 20-50 µm; FL3, 50-100 µm). Number of FLs: 1000 yr moving time window. FL thickness distributions are shown by notchandwhisker box plots (box height is interquartile range; thick line is median; notch is median confidence interval, whiskers show 1.5× interquartile range). Asterisks point out significant change in FL thickness (p < 0.01, MannWhitney tests). cal.-calibrated.

ACKNOWLEDGMENTS

We thank D. Delanghe, R. Sinet, and M. Revel for field assistance, M. Kölher for slide preparations, and T. Nakagawa, A. Millon, and J. Vallauri for discussions. This work is part of the LADICIA program (Région PACA, France). We thank B. Ruddiman, L.L. Ely, L. Davis, and other, anonymous, reviewers for their constructive suggestions in improving the paper.


Corinne Frere

Katsushi Kobayashi

Claire Dunois

Jean Amiral

Pierre-Emmanuel Morange

Marie-Christine Alessi

Assessment of platelet function on the routine coagulation analyzer Sysmex CS-2000i

Assessment of platelet function on the routine coagulation analyzer Sysmex CS-2000i

Corinne Frère, Katsushi Kobayashi, Claire Dunois, Jean Amiral, Pierre-Emmanuel Morange & Marie-Christine Alessi

Abstract

Background: Light transmission aggregometry (LTA) is considered as the gold standard for testing platelet function in the setting of both platelet disorders suspicion and response to antiplatelet therapy evaluation. LTA requires however specialized equipment, substantial blood sample volumes, is technically challenging and time-consuming. Aim: To evaluate an automated platelet aggregation method performed on a routine coagulation analyzer Sysmex CS-2000i. Methods: 46 patients presenting a bleeding syndrome and 62 patients with acute coronary syndrome receiving dual antiplatelet therapy were studied in total. Platelet aggregations were performed on CS-2000i equipped with a dedicated software and on France) as the reference instrument. Aggregation was measured by monitoring the changes in light absorbance occurring in response to ADP 2.5, 5 and 10µM, collagen 3.3 µg/mL, epinephrin 10µM, ristocetin 1.25 mg/mL and arachidonic acid 0.5 mg/mL in platelet rich plasma (PRP). PRP were tested simultaneously on both CS-2000i and APACT-4004 devices. Platelet stirred speed were 800 rpm for both instruments. Results: Significant correlations were observed between CS-2000i and LTA after all stimulations (p< 0.001). Patients presenting a bleeding syndrome had similar aggregation profiles with both methods. A single patient presented a severe platelet disorder (Glanzmann Thrombasthenia) and its PRP showed defective aggregation in response to all agonists except ristocetin with both instruments. Finally, the inter-agreement rates for CS-2000i and APACT-4004 to detect low responders to thienopyridines or aspirine were strong (weighted kappa> 0.70). Conclusion: Platelet aggregation on the routine coagulation analyzer CS-2000i is an easily accessible, handy, reliable, standardized, and rapid tool to assess platelet function which allows to skirt most of the LTA limitations. Thromb Haemost 2016;116:638-650]. The PFA-100 and PFA-200 are used in most hospitals and were demonstrated to be highly sensitive for VWD and severe platelet defects, but sometimes insensitive for mild disorders such as storage pool disease and Hermansky-Pudlak syndrome. The multiplate platelet function analyzer is also used in some laboratories, particularly to tailor antiplatelet therapy. However, the light transmission aggregometry (LTA) remains the "gold standard" method for platelet function exploration [Born GV, Cross MJ. The aggregation of blood platelets. J Physiol 1963;168:178-195]. Using an optical aggregometer with a fixed wavelength spectrophotometer, LTA evaluates increase in transmitted light when aggregation occurs under stirring conditions in platelet-rich plasma (PRP) following stimulation with a platelet agonist. LTA presents, however, some limitations: it requires both specialized equipment and substantial blood sample volumes, it is technically challenging and time-consuming, and finally it lacks standardization [Cattaneo M, Cerletti C, Harrison P, Hayward CPM, Kenny D, Nugent D, Nurden P, Rao AK, Schmaier AH, Watson SP, Lussana F, Pugliano MT, Michelson AD. Recommendations for the standardization of light transmission aggregometry: A consensus of the working party from the platelet physiology subcommittee of SSC/ISTH. J Thromb Haemost JTH 2013; Breddin HK. Can platelet aggregometry be standardized? Platelets 2005;16:151-158]. Consequently, very few hemostasis laboratories undertake this analysis and patients must often be referred to specialized centers for LTA investigation, which is inconvenient to the patients and sometimes delays the diagnosis and treatment. The development of new technologies to assess platelet function more easily and less costly appears thus as necessary. Recently, in order to automate platelet aggregation testing, an analytical procedure was developed with dedicated software on the CS-2000i coagulation analyzer (Sysmex Corporation, Japan) [5 Lawrie AS, Kobayashi K, Lane PJ, Mackie IJ, Machin SJ. The automation of routine light transmission platelet aggregation. Int J Lab Hematol 2014;36:431-438]. The aim of the present study was to evaluate this automated platelet aggregation method and to compare it to a reference LTA method.

Between January and May 2016, two different groups of patients were prospectively included in the study. The first group was constituted by patients not suffering from a VWD but presenting a history of bleeding or bleeding symptoms suggestive of platelet disorders as defined by petechiae, bruising, and mucosal bleeding such as gingival hemorrhage, epistaxis, and menorrhagia and referred to the "Centre d'Exploration des Pathologies Hémorragiques et Thrombotiques" (La Timone Hospital, Marseille, France) for LTA investigation. The second group was constituted by patients suffering from an ACS and receiving dual antiplatelet therapy (aspirin 100 mg and clopidogrel 75 mg once a day) and referred to our laboratory for antiplatelet therapy tailoring. Venous blood samples were collected after a short rest period by sterile venipuncture in vacutainer tubes (BD Life Science, Le Pont de Claix, France) filled to capacity containing buffered sodium citrate 0.105 M (approximately 3.2%) with a whole blood-to-anticoagulant ratio of 9:1. Samples were obtained with informed consent from all subjects. PRP and platelet-poor plasma (PPP) were prepared according to the platelet physiology subcommittee of SSC/ISTH recommendations for the standardization of LTA [Cattaneo M, Cerletti C, Harrison P, Hayward CPM, Kenny D, Nugent D, Nurden P, Rao AK, Schmaier AH, Watson SP, Lussana F, Pugliano MT, Michelson AD. Recommendations for the standardization of light transmission aggregometry: A consensus of the working party from the platelet physiology subcommittee of SSC/ISTH. J Thromb Haemost JTH 2013]. Briefly, the sample tubes were mixed by gentle inversion before centrifugation at 200 g for 10 min at ambient temperature (approximately 20-22°C). The resultant PRP was aspirated using plastic pipettes and transferred to polypropylene tubes capped and kept at ambient temperature until testing. The primary sample tube was centrifuged once again at 1500 g for 15 min at ambient temperature to produce PPP, which was removed as described for the PRP. Platelet counts were then performed on the PPP and PRP using a Sysmex XN analyzer (Sysmex, Kobe, Japan) and all patients included in the study had a PRP platelet count >150 G/L. Platelet aggregations were performed on CS-2000i equipped with a dedicated software and on APACT-4004 (Elitech, France) as the reference instrument. Aggregation was measured by monitoring the changes in light absorbance occurring in response to ADP 2.5, 5, and 10 µM, collagen 3.3 µg/mL, epinephrine 10 µM, ristocetin 1.25 mg/mL, and arachidonic acid 0.5 mg/mL (all from HYPHEN BioMed, France) in PRP. PRP were tested simultaneously on both CS-2000i and APACT-4004 devices. Platelet stirred speed was 800 rpm for both instruments. When using the CS-2000i instrument, after completion of reaction monitoring for all agonists for each PRP, the 100% light transmission reading is integrated with the measured and derived parameters from PRP reaction monitoring, and the aggregation traces are then viewed from the analyzer results file (Fig 1). The intra-serial imprecision (CV %) of maximal intensity of platelet aggregation assessed with the CS-2000i instrument was lower than 5% for each agonist. Reference intervals were previously established in 30 healthy volunteers in our laboratory.

In total, 46 patients presenting bleeding symptoms suggestive of platelet disorders and 54 patients with ACS receiving dual antiplatelet therapy were studied. The 46 patients presenting bleeding symptoms suggestive of platelet disorders had similar aggregation profiles with both devices. A single patient presented a severe platelet disorder (Glanzmann Thrombasthenia) confirmed by flow cytometry and its PRP showed defective aggregation in response to all agonists except ristocetin with both instruments. All the other patients had both normal occlusion times and aggregation traces. Concerning patients with ACS receiving dual antiplatelet therapy, the classification of the values for both methods by using ADP, in relation to the presence or absence of high on thienopyridines platelet reactivity [Cuisset T, Frere C, Quilici J, Gaborit B, Castelli C, Poyet R, Bali L, Morange P-E, Alessi M-C, Bonnet J-L. Predictive values of post-treatment adenosine diphosphate-induced aggregation and vasodilator-stimulated phosphoprotein index for stent thrombosis after acute coronary syndrome in clopidogrel-treated patients. Am J Cardiol 2009;104:1078-1082], 49 (91%) of the 54 patient samples tested were concordant. Good significant agreement was observed between the results obtained by the two tests (κ = 0.706; P < 0.0001). By using arachidonic acid, in relation to the presence or absence high on aspirin platelet reactivity [Cuisset T, Frere C, Quilici J, Morange P-E, Camoin L, Bali L, Lambert M, Juhan-Vague I, Alessi M-C, Bonnet J-L. Relationship between aspirin and clopidogrel responses in acute coronary syndrome and clinical predictors of non-response. Thromb Res 2009;123:597-603], 50 (94%) of the 53 patient samples tested were concordant. Good significant agreement was observed between the results obtained by the two tests (κ = 0.822; P < 0.0001).

Significant correlations between the CS-2000i and APACT-4004 were observed after stimulation with ADP 2.5 µM (r = 0.79; P < 0.0001), 5 µM (r = 0.92; P < 0.0001), and 10 µM (r = 0.8963; P < 0.0001); collagen 3.3 µg/mL (r = 0.92; P < 0.0001); epinephrine 10 µM (r = 0.94; P < 0.0001); ristocetin 1.25 mg/mL (r = 0.38; P = 0.0099); and arachidonic acid 0.5 mg/mL (r = 0.98; P < 0.0001). Bland and Altman plots showed that 95% of the differences were located within acceptable range with all agonists, allowing to conclude that the two compared devices could be considered as consistent (Fig 2).

In conclusion, this new method presents some limitations: the preparation of PRP remains time-consuming and the method is not suitable in the case of thrombocytopenia. However, this method presents benefits that allow to skirt some LTA limitations: it is easily accessible, more standardized, and it constitutes a more rapid tool to assess platelet function. This automated platelet aggregation method would thus potentially allow numerous hemostasis laboratories that are not equipped with an aggregometer to undertake an assessment of platelet function abnormalities and responsiveness to antiplatelet drugs.

:

  Laboratory investigations of platelet function are currently recommended in patients with bleeding symptoms suggestive of primary hemostatic disorders when thrombocytopenia and von Willebrand disease (VWD) have been excluded [Cattaneo M, Cerletti C, Harrison P, Hayward CPM, Kenny D, Nugent D, Nurden P, Rao AK, Schmaier AH, Watson SP, Lussana F, Pugliano MT, Michelson AD. Recommendations for the standardization of light transmission aggregometry: A consensus of the working party from the platelet physiology subcommittee of SSC/ISTH. J Thromb Haemost JTH 2013.]. Platelet function tests are also useful to assess both thienopyridines and aspirin responses in acute coronary syndrome (ACS) patients in some cases [Le Quellec S, Bordet J-C, Negrier C, Dargaud Y. Comparison of current platelet functional tests for the assessment of aspirin and clopidogrel response. A review of the literature.


Jérôme G Prunier
email: jerome.prunier@gmail.com

Vincent Dubut

Lounes Chikhi

Simon Blanchet

| Lounès Chikhi

Contribution of spatial heterogeneity in effective population sizes to the variance in pairwise measures of genetic differentiation

| INTRODUCTION

The maintenance of effective dispersal capacities among demes is of tremendous importance for the viability of spatially structured populations [START_REF] Wiens | 3 -Metapopulation dynamics and landscape ecology[END_REF]. Given the technical challenges of directly monitoring individual movements, landscape genetics has emerged as an efficient way of assessing functional landscape connectivity [START_REF] Tischendorf | On the usage and measurement of landscape connectivity[END_REF], i.e. the influence of landscape configuration on effective dispersal between populations (i.e. gene flow; [START_REF] Barton | The barrier to genetic exchange between hybridising populations[END_REF], by combining methods from population genetics, landscape ecology and spatial statistics [START_REF] Manel | Landscape genetics: Combining landscape ecology and population genetics[END_REF]; but see [START_REF] Dyer | Is there such a thing as landscape genetics?[END_REF].

One of the main assets of landscape genetics is that it allows assessing functional landscape connectivity without the need for the quantitative inference of dispersal parameters (dispersal rate, dispersal distance or effective numbers of migrants; see [START_REF] Broquet | Molecular estimation of dispersal for ecology and population genetics[END_REF] for a review). Pairwise measures of neutral genetic differentiation (or "genetic distances") such as F-statistics (e.g. F st ; [START_REF] Wright | Isolation by distance[END_REF] are supposed to contain information about past effective dispersal events [START_REF] Jaquiéry | Inferring landscape effects on dispersal from genetic distances: How far can we go[END_REF] and are thus considered a proxy for gene flow. The direct use of F-statistics as a proxy for gene flow ensues from the seminal work by [START_REF] Wright | Isolation by distance[END_REF] who showed that, under the specific assumptions of the island model, gene flow (the product of effective deme size N e and immigration rate m) between two populations could be derived from a measure of neutral genetic variance, following F st = 1/(4Nm + 1). Genetic distances are thus often used as dependent variables in correlative analyses to elucidate how neutral genetic variation is affected by landscape configuration [START_REF] Guillot | Statistical methods in spatial genetics[END_REF][START_REF] Holderegger | Landscape genetics[END_REF]. When carried out within a hypothesis-testing framework depicting the expected statistical relationships between landscape and neutral genetic data [START_REF] Richardson | Navigating the pitfalls and promise of landscape genetics[END_REF], correlative analyses allow identifying the possible determinants of spatial genetic structures, thus providing a valuable way of assisting both landscape management and wildlife conservation [START_REF] Segelbacher | Applications of landscape genetics in conservation biology: Concepts and challenges[END_REF].

Depending on the complexity of the landscape, several competing hypotheses can be combined within the same analysis, such as isolation-by-distance (IBD) or isolation-by-resistance (IBR; [START_REF] Zeller | Estimating landscape resistance to movement: A review[END_REF]. These hypotheses are formulated on the basis of how specific landscape features (coded as pairwise Euclidean or cost distances) are assumed to impact genetic differentiation and, by extension, gene flow. Isolation-by-distance is notably a baseline hypothesis in landscape genetics [START_REF] Jenkins | A meta-analysis of isolation by distance: Relic or reference standard for landscape genetics[END_REF]. In organisms whose dispersal ability is spatially constrained, the IBD hypothesis depicts the expected increase in genetic differentiation (and its variance) between populations as geographical distance increases. At a given spatial scale (e.g. [START_REF] Bradbury | Non-linear genetic isolation by distance: Implications for dispersal estimation in anadromous and marine fish populations[END_REF], a significant positive correlation between Euclidean distances and genetic distances would give support to the tested hypothesis, suggesting that dispersal movements decrease as geographic distance increases [START_REF] Slatkin | Isolation by distance in equilibrium and nonequilibrium populations[END_REF]; but see [START_REF] Edelaar | Non-random gene flow: An underappreciated force in evolution and ecology[END_REF].

However, it has to be emphasised that F-statistics are not estimates of gene flow per se but are primarily measures of the balance between genetic drift on the one hand, and migration (and mutations) on the other hand: high values of pairwise F st indicate that genetic variation is mostly driven by drift, whereas low values indicate that genetic variation is mostly determined by dispersal, counterbalancing the effects of drift. Genetic drift is the evolutionary process of random fluctuations in allelic frequencies naturally occurring in all populations, whatever their size, though compounded in small ones [START_REF] Allendorf | Genetic drift and the loss of alleles versus heterozygosity[END_REF]. If not fully compensated by gene flow, these random fluctuations should ultimately lead to genetic differentiation, especially if at least one of the two considered demes is small. In other words, genetic distances may increase because of reduced landscape connectivity (and thus dispersal) between populations, but also because of spatial variations in population sizes [START_REF] Jaquiéry | Inferring landscape effects on dispersal from genetic distances: How far can we go[END_REF][START_REF] Richardson | Navigating the pitfalls and promise of landscape genetics[END_REF] see Appendix S1a for an illustration). Spatial heterogeneity in the intensity of genetic drift alone may thus be responsible for spurious relationships between measures of genetic differentiation and landscape predictors, erroneously providing support for alternative hypotheses such as IBD or IBR and possibly leading to counterproductive management and conservation measures. This risk of spurious conclusions is all the more important when the heterogeneity in the intensity of drift is not random but follows spatial patterns (such as upstream-downstream gradients in rivers or altitudinal gradient in mountains) that may in some cases be falsely captured by alternative landscape hypotheses (Appendix S1b). In any case, quantifying the contribution of spatial heterogeneity in local drift to the variance in genetic differentiation may provide crucial insights into the actual drivers of genetic structures.

In the same way that IBD or IBR hypotheses depict the expected contribution of landscape characteristics to the variance in genetic distances, we here propose an additional hypothesis relating the influence of spatial heterogeneity in local effective population sizes (Ne) over patterns of genetic differentiation: the Spatial-Heterogeneity-in-Ne (SHNe) hypothesis. This SHNe hypothesis, based on the computation of distance-based metrics from estimates of Ne, naturally falls within the hypothesis-testing framework classically used in landscape genetics, and is aimed at quantifying the contribution of heterogeneity in population sizes in shaping spatial patterns of genetic differentiation, thus providing further insight into acting evolutionary forces. Note that we did not intend to compute a measure of genetic differentiation "corrected" for Ne (as in [START_REF] Relethford | Genetic drift can obscure population history: Problem and solution[END_REF][START_REF] Jost | G ST and its relatives do not measure differentiation[END_REF], but rather to provide metrics allowing a direct quantification of the amount of variance explained by SHNe.

K E Y W O R D S
dispersal, evolutionary forces, genetic drift, landscape genetics, population genetics, variance partitioning In this study, we first described how estimates of Ne can be used to compute two distinct SHNe metrics stemming from the theoretical model of pure random genetic drift. We then investigated the influence of SHNe on the variance in F st values and on the behaviour of each metric in a simple two-deme situation. We then tested the ability and efficiency of each metric to account for heterogeneity in population sizes when they are directly computed from Ne, using simulations in various genetic models of population structure. Given the inherent difficulty in estimating Ne [START_REF] Wang | Estimation of effective population sizes from data on genetic markers[END_REF], we used similar simulations to assess whether SHNe metrics were still efficient when computed from environmental proxies for local carrying capacities K, assuming that K is an imperfect proxy of Ne. We further assessed the efficiency of each metric in an empirical case study involving a freshwater fish species (Gobio occitaniae) using environmental estimates of population sizes. We finally discussed how and why these metrics should be used in landscape genetics studies.

| MATERIALS AND METHODS

| Distance-based metrics of SHNe

The di metric (for distance based on the inverse) was first proposed by [START_REF] Relethford | Genetic drift and anthropometric variation in ireland[END_REF] and directly ensues from the classical formula depicting the expected loss of heterozygosity in an ideal Wright-Fisher population of constant size N over time but experiencing genetic drift (e.g. [START_REF] Hartl | Principles of population genetics[END_REF]:

where F t is the fixation index at generation t. Extrapolated to a spatial context and with F 0 set to 0, the same equation can be used to depict the expected divergence of two subpopulations of size N i relative to a founding population, in a situation where subpopulations are totally isolated, of constant size over time and with genetic drift being the only acting evolutionary force [START_REF] Crow | An introduction to population genetics theory[END_REF]. After transformation [START_REF] Relethford | Genetic drift and anthropometric variation in ireland[END_REF], it can be shown that F st between populations 1 and 2 is proportional to di (Appendix S2b), with:

and N 1 and N 2 the (ideally effective) population sizes of populations 1 and 2, respectively.

The dhm metric (for distance based on the harmonic mean) was proposed by [START_REF] Serrouya | Population size and major valleys explain microsatellite variation better than taxonomic units for caribou in western Canada[END_REF] and also directly ensues from Equation 1. In the case of fluctuating population sizes over time, it can be shown that the effective size Ne of a population is the harmonic mean of census population sizes N over time [START_REF] Hartl | Principles of population genetics[END_REF]. The harmonic mean weights smaller populations more heavily: in biological terms, it means that a single period of small population size (bottleneck) can result in a serious loss of heterozygosity. Extrapolated to a spatial context, the use of the harmonic mean entails that the smaller one of the two populations, the higher the pairwise genetic distance under a pure genetic drift model (Appendix S2a). We thus expect F st between populations 1 and 2 to be proportional to dhm, with:

Note that we considered the opposite to the harmonic mean of N because the untransformed harmonic mean shows negative relationships with F st [START_REF] Serrouya | Population size and major valleys explain microsatellite variation better than taxonomic units for caribou in western Canada[END_REF], and thus does not behave as a classical distance-based metric. Metrics di and dhm are inversely related and are thus expected to show different mathematical properties for the same combination of population sizes (Figure 1b; Appendix S2c).

Directly accounting for SHNe through the use of Ne is probably the most straightforward approach, but implies a major difficulty: estimating this demographic parameter, a task that may turn out to be tricky [START_REF] Wang | Estimation of effective population sizes from data on genetic markers[END_REF]. Alternatively, we thus propose to consider the use of environmental estimates of local carrying capacities (K) as a proxy for effective population sizes. Carrying capacity reflects the upper asymptote of the logistic growth curve of a population given the distribution and abundance of resources determined by local environmental conditions [START_REF] Hanski | A practical model of metapopulation dynamics[END_REF] and can be approximated using specific environmental variables such as habitat patch size or habitat quality (e.g. [START_REF] Raeymaekers | Modeling genetic connectivity in sticklebacks as a guideline for river restoration[END_REF].

(1) 1 -F t = 1 - 1 2N t (1 -F 0 ) (2) di = 1 N 1 + 1 N 2 = N 1 + N 2 N 1 N 2 (3) dhm = - 2 1 N 1 + 1 N 2 = - 2N 1 N 2 N 1 + N 2 F I G U R E 1 Behaviour of F st (a)

| Simulated datasets

For all simulations, we used a computational pipeline including the programs ABCsAmpler [START_REF] Wegmann | ABCtoolbox: A versatile toolkit for approximate Bayesian computations[END_REF]), simCoAl2.1.2 (Laval & Excoffier, 2004) and ArlsumstAt [START_REF] Excoffier | Arlequin suite ver 3.5: A new series of programs to perform population genetics analyses under Linux and Windows[END_REF] In all simulations, a maximum of 30 haploid genotypes (that is, 15 diploid individuals) were sampled from each deme at the end of simulations and were used to compute pairwise F st among demes using ArlsumstAt.

di and dhm metrics were computed on the basis of demes' local carrying capacities K, with K = N + αN. The parameter α represents the uncertainty in the estimates of effective population sizes through an environmental proxy such as habitat patch size. The estimates of N were considered as unbiased for α = 0 (since K = N) or uncertain for α ≠ 0.

To control for heterogeneity in local genetic drift, effective population sizes N i were computed from a maximum population size N max following N i = N max -γN max , with N max fixed at 1,000 or randomly picked from a uniform distribution ranging from 100 to 1,000 (see details below)

and γ a correcting parameter randomly picked from a uniform distribution ranging from 0 to 0.95 so that N i ≤ N max . Levels of heterogeneity across effective population sizes were estimated using the coefficient of variation CV = s∕N, with s and N the standard deviation and the mean of effective population sizes, respectively. All statistical analyses were performed in R 3.1.2 (R Development Core Team, 2014).

| Main characteristics of SHNe metrics

We first investigated the influence of SHNe on the variance in F st values and on the behaviour of each SHNe metric in a simple two-deme situation. We simulated 10 5 genetic datasets with m fixed at 0.02 and α set to 0. Effective population size for deme 1 (N 1 ) was fixed at N max = 1,000 (i.e. 500 diploid genotypes), while effective population size for deme 2

(N 2 ) was computed from N 1 following N 2 = N 1 -γN 1 . For each dataset,
we computed pairwise F st , di and dhm metrics, and CV. We then plotted F st values as well as z-transformed di and dhm values against N 2 .

| Contribution of SHNe metrics to the variance in F st

We then assessed the contribution of each SHNe metric to the variance in F st in four complex situations differing according to both the network structure and the migration model used for simulations (Appendix S3). We considered two different network structures: a one-dimensional 16-deme linear network and a two-dimensional 16deme lattice network. We considered two distinct migration models: a spatially structured island model [START_REF] Wright | Isolation by distance[END_REF] in which m decreases with Euclidean distance following an inverse-square function, and a spatially structured stepping-stone model [START_REF] Kimura | The stepping stone model of population structure and the decrease of genetic correlation with distance[END_REF] where demes can only exchange migrants with adjacent demes. For each situation, 10,000 genetic datasets were simulated with α set to 0, m randomly picked from a uniform distribution ranging from 0.0001 to 0.3 and N max randomly picked from a uniform distribution ranging from 100 to 1,000 was used to estimate the respective unique contribution (U) of each predictor to the variance in the dependent variable. The unique contribution is the part of the total variance in the dependent variable that is explained by the sole effect of the predictor being considered (mr, di or dhm). On the contrary, common contributions (shared variance among predictors) can help identify statistical suppression situations, responsible for artefactual distortions in parameter estimates [START_REF] Paulhus | Two replicable suppressor situations in personality research[END_REF][START_REF] Prunier | Regression commonality analyses on hierarchical genetic distances[END_REF]. Datasets were finally pooled according to their migration rate into 30 classes defined every 0.01 units (about 330 datasets per class). For each class, we computed the mean and the standard deviation of unique contributions of each predictor. A unique contribution was considered as negligible as soon as the dispersion around the mean included zero.

| Minimum level of heterogeneity accounted for by SHNe metrics

To determine the minimum level of SHNe likely to affect pairwise F st , we used the same approach as described above but with a single migration rate (m = 0.02). For each simulated dataset, we additionally computed the coefficient of variation CV, and plotted the unique contribution of each predictor (mr, di or dhm) along with their respective standard deviation against CV.

| Metrics measured from an environmental proxy

Finally, we investigated the influence of uncertainty in the estimation of Ne through an environmental proxy. We used the same approach as described above with m randomly picked from a uniform distribution ranging from 0.0001 to 0.3 and the parameter α picked, independently for each population, from a uniform distribution ranging from -0.9 to 0.9 (Appendix S4).

| Empirical dataset

As an empirical example, we considered neutral genetic data collected in the gudgeon (G. occitaniae), a small benthic freshwater fish. We further investigated the observed pattern using piecewise regression to identify the scale of migration-drift equilibrium, that is, the distance at which different linear relationships are observed. Estimations of breakpoints and slope parameters, as well as 95% confidence intervals, were performed using the R-package segmented [START_REF] Muggeo | Segmented: An R package to fit regression models with broken-line relationships[END_REF].

Given the difficulty in estimating effective population sizes in the wild, we used a proxy for local carrying capacities to estimate di and dhm. The proxies we used were the width of the river at each sampling site and the estimated home-range size of each population

F I G U R E 3 Averaged R 2 (red)
(g) (h) [START_REF] Raeymaekers | Modeling genetic connectivity in sticklebacks as a guideline for river restoration[END_REF]. The home-range size of each deme was computed as the product of length and width of the river network (including tributaries) delimited by any downstream or upstream weir (see Blanchet, Rey, Etienne, Lek, & Loot, 2010 for a description of weirs in this river). This corresponded to the water area in which gudgeons were free to move. Matrices of pairwise di and dhm were then computed from these estimates and were independently confronted to the matrix of pairwise F st using MRDM with 1,000 permutations and with mr as a covariate. Commonality analyses were then used to disentangle the relative contribution of each predictor to the variance in pairwise F st .

Finally, we plotted the residuals of the linear regression between F st and the di metric (based on measures of river width) against mr and used a simple Mantel test to assess significance of the relationship. We

| RESULTS

| Simulated datasets

| Main characteristics of SHNe metrics

The aim of the first simulation study was to assess the behaviour of SHNe metrics in a very simple system in response to the variance in effective population sizes. Simulations were conducted so that any increase in heterogeneity in effective population sizes (as measured by CV) was the result of a decrease in the size of one of the two populations (N 2 ), the size of the other population (N 1 ) being held constant. As expected, the increase in heterogeneity in Ne led to an increase in the variance in F st (Figure 1a): F st values ranged from 0 to 0.25 for a CV of 1.2 (N 2 ≈ 5) while they did not exceed 0.05 for a CV of 0 (N 2 ≈ 1,000). The dhm metric showed a regular (though non-linear) increase with the increase in CV, while the di metric showed limited increase for CV ≤ 0.6, followed by a steep increase for CV > 0.6 (Figure 1b). When F st and SHNe metrics were scaled to range from 0 to 1, SHNe metrics followed patterns similar to that observed for F st , although di tends to better fit the general F st pattern than dhm (Appendix S7).

| Contribution of SHNe metrics to the variance in F st

In the absence of uncertainty in the estimation of effective population sizes (α = 0), both di and dhm explained a non-negligible part of the total variance in pairwise F st (i.e. from 5% to more than 60%;

Figure 2). Dispersion around the means further indicated that the unique contribution of SHNe metrics can be substantial, whatever the maximum population size in the system (N max ranging from 100 to 1,000) and for migration rates as high as 0.135 (Figure 2). For m < 0.135, the unique contributions of di and dhm were the lowest for a linear network with stepping-stone migration (Figure 2a,b) and were the highest in a lattice network with spatially limited dispersal (Figure 2g,h). In this latter case, di and dhm explained much more variance than the traditional covariate mr as soon as m < 0.05. In other genetic models, the unique contributions of di and dhm were as high as or slightly higher than the unique contribution of mr (Figure 2c-f).

Overall, di and dhm behaved very similarly in all situations, although di showed both higher mean contribution and slightly higher dispersion around the mean than dhm.

| Minimum level of heterogeneity accounted for by SHNe metrics

When m was fixed at 0.02, the unique contribution of dhm and di were negligible when CV were below a value ranging from 0.23 (Figure 3c-h) to 0.28 (linear network with stepping-stone migration;

Figure 3a,b). At maximum heterogeneity (CV ≈ 0.8), unique contributions ranged from 10 to 50% (Figure 3). As previously, di and dhm behaved very similarly, although mean contribution as well as dispersion around the mean were slightly higher for di than for dhm in all situations. In most situations, the averaged model fit R 2 (the sum of unique and common contributions; [START_REF] Prunier | Multicollinearity in spatial genetics: Separating the wheat from the chaff using commonality analyses[END_REF] also increased with the increase in CV (e.g. from 10 to 60%; Figure 3g,h).

The observed decrease in the unique contribution of mr as the unique contribution of SHNe metrics increases (Figure 3a-f) was not due to an increase in the common contribution of mr and SHNe metrics (data not shown), indicating that the relative support for alternative hypotheses such as IBD or IBR may be impaired in the presence of SHNe.

| Metrics measured from an environmental proxy

When uncertainty was included in the estimation of effective population sizes so as to mimic an environmental proxy for K (using α ϵ [-0.9, 0.9]), mr showed similar patterns to those in the absence of uncertainty (Figure 4). SHNe metrics behaved similarly to situations where true estimates of N were used, although unique contributions were systematically lower (but still up to 30% for m values lower than a threshold ranging from 0.025 to 0.105). Furthermore, dispersion around the mean was generally noticeably larger for di than for dhm.

| Empirical dataset

The pattern of IBD in G. occitaniae was characterised by a slightly positive though insignificant relationship between F st and mr (Table 1).

Piecewise regression explained a slightly higher proportion of the variance in F st (6.7%) than classical linear regression (2.9%). However, the upper bound of the confidence interval around the putative breakpoint (estimated at 74.8 ± 7.7 km) was located beyond spatial extent of the study.

When K values were estimated from river width or home-range sizes, coefficients of variation were respectively 0.432 and 0.927, suggesting high SHNe in this system. On the whole, model fit indices R 2 were higher when K values were estimated from river width rather than from home-range sizes (Table 1), indicating that river width was a better proxy for carrying capacities than home-range size in this dataset. Whatever the proxy used for K, mr showed limited unique contribution to the variance in measures of genetic differentiation, with values ranging from 3.4 to 7.8% (Table 1). This variability in unique contributions of mr stemmed from collinearity with distancebased metrics of genetic drift, as revealed by common contributions C [START_REF] Prunier | Multicollinearity in spatial genetics: Separating the wheat from the chaff using commonality analyses[END_REF]: indeed, the highest unique contribution of mr (U = 7.8%) was also associated with the highest negative common contribution (C = -4.8%), indicating statistical suppression, a situation responsible for an artificial boost in both the regression coefficient and its significance [START_REF] Paulhus | Two replicable suppressor situations in personality research[END_REF]Prunier et al., 2017). The observed variability in model fits (ranging from 4% to 44.2%) thus mostly ensued from the variability in SHNe metrics' unique contributions to the variance in F st . When K values were estimated from homerange sizes, the effect of di was not significant (unique contribution of 1.1%) whereas dhm uniquely accounted for 9.8% of variance in F st .

When K values were estimated from river width, the unique contribution of di and dhm strongly increased, reaching 41.3% and 36.7% respectively (Table 1).

When exploring the relationship between residuals of the linear regression between F st and the di metric (based on measures of river width) and mr, piecewise regression explained a substantially higher proportion of the variance in F st (23.8%) than linear regression (12.5%). The scatterplot showed an increase in residual values up to 8.9 ± 3.3 km and a clear-cut plateau beyond this threshold (Figure 5b).

This pattern suggests that, once the influence of SHNe is taken into account, the scale of IBD may be better inferred, with the divergence between populations located more than 8.9 km apart being mostly determined by drift.

| DISCUSSION

The possible influence of Spatial-Heterogeneity-in-Effective-Population-Sizes (SHNe) on the raw material of most landscape genetic studies, namely the variance in inter-deme measures of genetic differentiation, is rarely taken into consideration (but see [START_REF] Leblois | Influence of spatial and temporal heterogeneities on the estimation of demographic parameters in a continuous population using individual microsatellite data[END_REF] for an example), although it may lead to erroneous or incomplete interpretations of observed genetic patterns.

Our study demonstrates that considering SHNe metrics (i.e. distance metrics measured from estimates of Ne or from environmental proxies for local carrying capacities) is a relevant approach to quantify the contribution of SHNe to the variance in pairwise measures of genetic differentiation, providing substantial information as to the actual drivers of observed patterns of genetic differentiation in addition to alternative hypotheses such as IBD. The proposed framework is based on a simple variance-partitioning procedure and does not require any complex parameterisation.

| Comparison of SHNe metrics

In a simple two-deme situation with constant migration rate, SHNe to 80% for a higher mutation rate; see Appendix S8) at low migration rate, but still showed substantial contributions for migration rates as high as 0.135 (0.225 for a higher mutation rate). It is however noteworthy that the amounts of explained variance strikingly depended on the configuration of the network (1D vs. 2D), the migration model (presence versus absence of long distance migration events) and the mutation rate (Appendices S8 and S9).

When applied to the G. occitaniae dataset, the use of di and dhm allowed explaining large amounts of variance in genetic differentiation when river width was used as a proxy for local carrying capacities. Only 2.9% of variance in measures of genetic differentiation was accounted for with mr as the only predictor. On the contrary, up to 44.2% of variance was explained when either di or dhm were used as additional explanatory variables. This suggests that the observed variance in measures of genetic differentiation was mostly driven by SHNe and much less by IBD. Interestingly, taking this effect into consideration through the use of residuals increased the scatterplot signal-tonoise ratio and revealed that genetic differentiation actually increased with riparian distance as long as populations were less than 8.9 km apart. This threshold corresponds to the scale of spatial autocorrelation in measures of genetic differentiation and may provide an upper estimate for effective dispersal distance [START_REF] Anderson | Considering spatial and temporal scale in landscape-genetic studies of gene flow[END_REF]. This parameter is of particular interest as it may be used to inform conservation policies, for instance to support decisions in management of weirs or dams. Note, however, that taking the influence of SHNe into account in simulated datasets did not systematically lead to such an increase in signal-to-noise ratio (data not shown), probably because of variations in the spatial scale of simulated processes [START_REF] Bradbury | Non-linear genetic isolation by distance: Implications for dispersal estimation in anadromous and marine fish populations[END_REF]. Further studies are hence needed to identify the specific conditions under which such improvement can be achieved: for instance, the upstream-downstream increase in carrying capacities encountered in river systems is responsible for a specific longitudinal pattern of SHNe (Appendix S1b) that may be more easily captured using this procedure than in the case of random SHNe (as simulated in this study).

When uncertainty was introduced in estimates of Ne, mimicking the use of an environmental proxy such as local carrying capacities, simulations showed that both di or dhm were still efficient at accounting for the influence of SHNe on the variance in F st . However, dhm slightly outperformed di at intermediate migration rates (i.e. for m lower than 0.1) as di's unique contribution to the variance in F st showed higher dispersion around the mean than dhm. This trend was confirmed by the empirical dataset: when local carrying capacities were estimated from home-range sizes, di failed to detect any contribution of SHNe to the variance in genetic differentiation, whereas dhm -though less efficient than with river width as a proxy-still explained about 10% of variance. This difference stems from the inner characteristics of each metric. Given the use of a harmonic mean in its computation, dhm tends to increase as soon as one of the two demes shows a low to intermediate Ne. While di values show a rapid decrease as soon as one of the two demes shows an increase in Ne, the decrease in dhm values is smoother, thus still allowing the detection of the effect of SHNe despite higher uncertainty in the estimates of Ne. The dhm metric may actually be more robust when using environmental proxies for local carrying capacities and should therefore be preferred (or compared) to di. It is noteworthy that the two metrics can easily be combined in a single model and, provided collinearity patterns are inspected [START_REF] Prunier | Multicollinearity in spatial genetics: Separating the wheat from the chaff using commonality analyses[END_REF], the best at fitting the dataset be selected according to its unique contribution (see Appendix S10 for an illustration).

| Biologically relevant metrics

Simulations indicated that the influence of SHNe was still perceptible for migration rates up to 0.15, irrespective of the model of population structure being considered (Figures 2 and4). Interestingly, this range of values is higher than migration rates likely to be encountered in most natural systems. Indeed, summary statistics from 49 recent empirical studies that used BAYESASS [START_REF] Wilson | Bayesian inference of recent migration rates using multilocus genotypes[END_REF] to estimate interpatch migration rates (collected from a literature survey by [START_REF] Meirmans | Nonconvergence in Bayesian estimation of migration rates[END_REF]; see Appendix S11 and Appendix S14 for details) indicated that the median value of average migration rates was 0.023, with more than 95% of studies showing average estimates lower than 0.1 (Appendix S12). For instance, the average estimate of migration rates in G. occitaniae in our empirical dataset was about 0.02 (unpublished data), as estimated using GENECLASS [START_REF] Cornuet | New methods employing multilocus genotypes to select or exclude populations as origins of individuals[END_REF]. These observations suggest that SHNe is likely to be an important driver of spatial genetic variation in many empirical datasets, considering that natural variability in deme sizes is most probably far from being an exception. Because of their ability to explain substantial additional amounts of variance in observed measures of genetic differentiation, we argue that considering the use of simple distance-based metrics such as di or dhm in future landscape genetic studies should thoroughly improve our understanding of observed spatial patterns of genetic variation.

| Limitations of SHNe metrics

Considering the difficulties in accurately estimating Ne from genetic data [START_REF] Wang | Estimation of effective population sizes from data on genetic markers[END_REF], the use of alternative estimates of population size such as observed local densities (e.g. [START_REF] Blanchet | Species-specific responses to landscape fragmentation: Implications for management strategies[END_REF] or habitat patch size (e.g. [START_REF] Raeymaekers | Modeling genetic connectivity in sticklebacks as a guideline for river restoration[END_REF][START_REF] Verboom | European nuthatch metapopulations in a fragmented agricultural landscape[END_REF] to compute SHNe metrics is particularly appealing, but has yet to be considered with caution.

The validity of such metrics indeed proceeds from the assumption that effective population sizes have remained constant over time (Appendix S2). This assumption theoretically limits the practical use of SHNe metrics to systems in which populations are not subject to abrupt changes in genetic drift. For populations having suffered from bottleneck events [START_REF] Nei | The bottleneck effect and genetic variability in populations[END_REF] or from founder effects [START_REF] Ellstrand | Population genetic consequences of small population-size -Implications for plant conservation[END_REF], local environmental variables such as patch size may not properly mirror the actual effective population size, thus making SHNe metrics poor predictors of spatial patterns of genetic differentiation. In these situations, estimating effective population sizes from molecular data -although a delicate exercise-probably remains the best option (see [START_REF] Wang | Estimation of effective population sizes from data on genetic markers[END_REF] for a review synthesizing methods used to estimate Ne). It is also noteworthy that the use of SHNe metrics, as proposed here, does not provide a definitive way of controlling for the variance in populations sizes. Next important steps will be to test whether inferences of dispersal estimates could be improved by incorporating such metrics into IBD models (e.g. [START_REF] Rousset | Genetic differentiation and estimation of gene flow from F-statistics under isolation by distance[END_REF] and to develop new theoretical work allowing accurate IBD predictions while taking SHNe into account. More generally, integrating the demographic processes affecting Ne over time will be an important challenge to overcome so as to make landscape genetics an integrative discipline accounting for the complexity of spatially and temporally dynamic populations [START_REF] Lowe | What can genetics tell us about population connectivity?[END_REF].

| CONCLUSION

Habitats modifications by humans have two components [START_REF] Fischer | Landscape modification and habitat fragmentation: A synthesis[END_REF]; one leading to a decrease in connectivity (fragmentation) and another leading to a decrease in habitat and resource availability (habitat loss and degradation). By reducing the size of available habitats and by decreasing connectivity among habitats, humans are rapidly making the ground more and more fertile for genetic drift, and therefore spatial heterogeneity in local drift, to become an increasingly influential evolutionary process. As the combined use of SHNe metrics and classical (IBD, IBR, etc.) landscape predictors in regression commonality analyses may substantially improve our understanding of how each process respectively contributes to observed spatial patterns of genetic variation, we believe that the time is ripe to systematically quantify the influence of SHNe on the spatial genetic structure of wild populations, in order to identify cases where genetic differentiation is actually increasing as a consequence of spatial heterogeneity in resource availability.

  and each z-transformed SHNe metric (b) in a simple two-deme system as a function of effective population size N 2 (d: value of SHNe metrics; CV, Coefficient of variation)

  to simulate and analyse microsatellite genetic datasets, with 15 independent loci following a stepwise mutation model and a single mutation rate μ = 0.0005 (see Appendices S8 and S9 for results with μ = 0.01). Parameter values (symmetrical migration rates m i and local demes' effective population sizes Ne (in number of haploid genotypes), hereafter only denoted as N) were picked from uniform distributions using ABCsAmpler and were then used as inputs in Simcoal 2.1.2 to simulate genetic data based on a coalescent approach.

Fieldwork

  was conducted in accordance with French laws and with the approval of the Prefecture du Lot (the administrative region where the samples were collected). A total of 562 individuals were caught in 2011 by electro-fishing in 19 sampling sites scattered along the mainstream channel of the river Célé (Appendix S5). Pairwise F st were computed between all pairs of sites using 11 microsatellite loci (Appendix S13). See Appendix S6 for details on laboratory procedures F I G U R E 2 Unique contribution of metrics mr and di (left panels) or mr and dhm (right panels) as a function of the migration rate m for α = 0. Results are for a linear network with stepping-stone migration (a, b), a linear network with spatially limited dispersal (c, d), a lattice network with stepping-stone migration (e, f) and a lattice network with spatially limited dispersal (g, h). Circles represent the average unique contribution of each variable and coloured areas represent the dispersion of unique contributions around the mean, as defined by standard deviations. Vertical dashed lines indicate the migration rate m above which the unique contribution of SHNe metrics become negligible (lower bound for SD < 0) and acquisition of landscape data. The riparian distance among sites was used as a measure of matrix resistance mr among sites. We first used a simple Mantel test to assess significance of the relationship.

  and unique contribution of metrics mr and di (left panels) or mr and dhm (right panels) as a function of heterogeneity in Ne (CV, coefficient of variation) for m = 0.02 and α = 0. See legend in Figure2for other details

F I G U R E 4

 4 Unique contribution of metrics mr and di (left panels) or mr and dhm (right panels) as a function of the migration rate m for α ranging from -0observed pattern using piecewise regression to identify the distance threshold at which different linear relationships could be observed.

  metrics exhibited patterns similar to F st , thus properly rendering the influence of spatial heterogeneity in local drift on deme genetic differentiation. In more realistic scenarios, these metrics allowed quantifying the influence of SHNe on the variance in pairwise F st from CV of about 25%. In other words, pairwise F st in a set of three populations of mean size 100 and exchanging 2% of migrants at each generation (m = 0.02) may be affected by SHNe for differences in population sizes as low as 25 (e.g. N = 75, 100 and 125). The SHNe metrics explained up to 60% of variance in measures of genetic differentiation (and up F I G U R E 5 Scatterplot of pairwise F st against (a) pairwise riparian distances (mr) and (b) residuals of the linear regression between F st and the di metric (computed from river width) in the empirical dataset. Piecewise regression lines are in black. In red, solid vertical lines indicate the distance thresholds on either side of which different linear relationships can be observed, with 95% confidence intervals represented by dashed lines

  . For each simulated dataset, we computed four pairwise matrices (F st , di, dhm and Euclidean distances mr, the latter acting as a simple measure of inter-deme matrix resistance) and performed multiple regressions on distance matrices (MRDM;[START_REF] Smouse | Multiple-regression and correlation extensions of the mantel test of matrix correspondence[END_REF] between F st and each SHNe metric, with mr as a unique covariate (F st = mr + di or F st = mr + dhm). All variables were

z-transformed to standardise parameter estimates. Commonality analysis (a variance partitioning procedure assessing the reliability of model parameters in face of multicollinearity;

[START_REF] Prunier | Multicollinearity in spatial genetics: Separating the wheat from the chaff using commonality analyses[END_REF][START_REF] Ray-Mukherjee | Using commonality analysis in multiple regressions: A tool to decompose regression effects in the face of multicollinearity[END_REF]

ACKNOWLEDGEMENTS

We thank G. Loot, I. Paz-Vinas, O. Rey and C. Veyssière for their help on the field and in laboratory, as well as K. Saint-Pé for proofreading. We are grateful to Mark Beaumont for reading carefully a previous draft and providing comments that helped us clarify the manuscript significantly. We also thank the Office Nationale de l'Eau et des Milieux Aquatiques (ONEMA) for financial support. Data used in this work were partly produced through the technical facilities of the Centre Méditerranéen Environnement Biodiversité. LC was partly funded by the LABEX (Laboratoire d'Excellence) entitled TULIP (vers une Théorie Unifiée des Interactions biotiques: rôle des Perturbations environnementales; ANR-10-LABX-41) and the LIA BEEG-B (Laboratoire International Associé -Bioinformatics, Ecology, Evolution, Genomics and Behaviour; CNRS). The authors declare no conflict of interest.

DATA ACCESSIBILITY

Simulated and empirical data: DRYAD entry http://dx.doi. org/10.5061/dryad.j2v6q [START_REF] Prunier | Data from: Contribution of spatial heterogeneity in effective population sizes to the variance in pairwise measures of genetic differentiation[END_REF].