Elise Say-Sallaz
email: elise.saysallaz@gmail.com

Simon Chamaillé-Jammes

Stéphanie Périquet

Andrew J Loveridge

David W Macdonald

Antony Antonio

Hervé Fritz

Marion Valeix

Large carnivore dangerousness affects the reactive spatial response of prey

Keywords: African lion, antipredator response, ecology of fear, plains zebra, predator-prey 98 interactions, spotted hyaena. 99

Abstract

Predators differ through different attributes: their body size, sociality, speed, preferred prey size, hunting mode, etc. Altogether these characteristics contribute to shape an overall dangerousness, which is likely to underlie the variations in the nature and strength of a prey anti-predator responses. This link, although somehow intuitive, has been rarely quantified in natural ecosystems.

The goal of this study is to compare the antipredator response of a prey to two predators with contrasting dangerousness in large terrestrial mammals, focusing on the less studied reactive spatial response. We assessed if plains zebras' (Equus quagga) reactive spatial response differed after an encounter with African lions (Panthera leo) or spotted hyaenas (Crocuta crocuta). We expected lions to be perceived as more dangerous and hence to induce a stronger reactive spatial response than hyaenas.

Using data from GPS collars deployed simultaneously on the three species, we studied the reactive spatial responses of zebras after coming into close proximity to either predator.

We found that zebras responded differently, and more strongly to lions than to hyaenas. Indeed, zebras were twice more likely to flee after an encounter with a lion than a hyaena and, immediately after an encounter with a lion, zebras moved on average faster and further than after an encounter with a hyaena.

The results of this study are consistent with a correlation between the predator dangerousness and the strength of the prey anti-predator response. Future studies covering other pairs of large carnivores are needed to rigorously assess the role of the different predator attributes (body size, speed, preferred prey, and hunting mode).

Introduction

Most species alter their behaviour in response to changes in predation risk [START_REF] Lima | Behavioral decisions made under the risk of predation: a review and prospectus[END_REF]. For instance, in ungulates, these responses are as diverse as increased vigilance [START_REF] Hunter | Vigilance behaviour in African ungulates: the role of predation[END_REF], altered grouping strategies [START_REF] Creel | Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves[END_REF], relocation to safer areas [START_REF] Fortin | Wolves influence elk movements: behavior shapes a trophic cascade in Yellowstone National Park[END_REF], changes in diel activity rhythms [START_REF] Valeix | Does the risk of encountering lions influence African herbivore behaviour at waterholes?[END_REF], and combinations of these [START_REF] Creel | Effects of predation risk on group size, vigilance, and foraging behavior in an African ungulate community[END_REF][START_REF] Courbin | Zebra diel migrations reduce encounter risk with lions at night[END_REF]. While prey antipredator behavioural responses have been well described for a variety of predator-prey systems and their interactions theoretically investigated [START_REF] Mitchell | Predator-prey shell games: Large-scale movement and its implications for decision-making by prey[END_REF][START_REF] Patin | Space use and leadership modify dilution effects on optimal vigilance under food-safety trade-offs[END_REF], we know very little about the factors underlying the variations in the nature and strength of these responses in natural ecosystems.

Not all predatory species are the same and understanding how their characteristics may influence prey anti-predator responses may shade light on some of these variations. Indeed, predators differ through their body size, sociality, speed, preferred prey size, and hunting mode, which all have the potential to play a role in predator-prey interactions, with larger, quicker, social forager, and ambush predators perceived as the most dangerous ones [START_REF] Thaker | Minimizing predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates[END_REF][START_REF] Chamaillé-Jammes | Innate threatsensitive foraging: black-tailed deer remain more fearful of wolf than of the less dangerous black bear even after 100 years of wolf absence[END_REF][START_REF] Makin | Herbivores employ a suite of antipredator behaviours to minimize risk from ambush and cursorial predators[END_REF][START_REF] Cuthbert | Influence of intra-and interspecific variation in predator-prey body size ratios on trophic interaction strengths[END_REF][START_REF] Hirt | Rethinking trophic niches: Speed and body mass colimit prey space of mammalian predators[END_REF]. Besides, a response that is efficient toward a predator may not serve as an efficient defence against another one [START_REF] Leblond | Caribou avoiding wolves face increased predation by bears -Caught between Scylla and Charybdis[END_REF]. For all these reasons, prey are unlikely to respond the same way to different predators [START_REF] Relyea | The relationship between predation risk and antipredator responses in larval anurans[END_REF]. Studies assessing the effect of several sympatric predators are lacking [START_REF] Say-Sallaz | Non-consumptive effects of predation in large terrestrial mammals: Mapping our knowledge and revealing the tip of the iceberg[END_REF][START_REF] Montgomery | A tendency to simplify complex systems[END_REF] and needed if we want to understand the role of predator dangerousness in general, and of predator attributes in particular (e.g., body size, speed, hunting mode), on prey anti-predator behaviour.

Our work contributes to fill this gap. Using GPS data acquired simultaneously on plains zebras Equus quagga and their two main predators, lions and spotted hyaenas Crocuta Crocuta, we explored whether the reactive spatial response of zebras is influenced by the predator species encountered. Most studies investigating the role of the predator species on prey responses in large mammals considered proactive responses, i.e., when prey modify their behaviour in response to an a priori assessment of the level of risk based on the cumulative knowledge a prey has of its environment (independently from the actual presence of the predator; e.g., [START_REF] Thaker | Minimizing predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates[END_REF][START_REF] Makin | Herbivores employ a suite of antipredator behaviours to minimize risk from ambush and cursorial predators[END_REF]. In this work, we assessed the much less studied reactive response, i.e., when prey detect the presence of a predator assimilated to an immediate threat (either an attack, an impending attack, or the mere presence of the predator that may decide to launch an attack an any time). Lions are more than twice the body size of hyaenas, and in general the level of threat posed by lions on zebras can intuitively be considered as higher than the level of threat posed by hyaenas. Further lions are ambush predators, whereas hyaenas are cursorial predators. Following the same logic as the one developed in the existing literature on the role of predator cues for proactive responses [START_REF] Preisser | Predator hunting mode and habitat domain alter nonconsumptive effects in predator-prey interactions[END_REF][START_REF] Thaker | Minimizing predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates[END_REF][START_REF] Miller | Fear on the move: predator hunting mode predicts variation in prey mortality and plasticity in prey spatial response[END_REF], we made the assumption that lions, ambush predators, are more likely to stay in a given area than hyaenas, cursorial predators that can chase down their prey over long distances, and hence the detected presence of a lion should be more strongly associated to the probability of presence of this predator in the near future. Consequently, we hypothesized that zebras should display stronger reactive spatial responses to encounters with lions (larger and ambush predators, which are expected to be perceived as more dangerous) than to encounters with hyaenas.

To test this hypothesis, we specifically addressed 4 questions corresponding to different steps in the reactive spatial response of zebras (Fig. 1, see "Materials and Methods" for details): (1) Does a zebra leave an area more often after an encounter with a lion than with a hyaena?; [START_REF] Say-Sallaz | Non-consumptive effects of predation in large terrestrial mammals: Mapping our knowledge and revealing the tip of the iceberg[END_REF] When a zebra leaves an encounter area, does it do so at a higher speed and does it go further away after an encounter with a lion than with a hyaena?; (3) For a zebra leaving an encounter area, does it come back to the same area after a longer interval after an encounter with a lion than with a hyaena?; (4) For a zebra that initially stayed in the encounter area, does it stay longer in this area following an encounter with a hyaena than after one with a lion? with a predator (i.e., zebra and predator simultaneously located less than 500m apart). Once an encounter with a predator has occurred at a specific location, a zebra has two options for its short-term spatial response (<2h) (): either it leaves the encounter area (defined as the area within 900m of the encounter) or it stays. At a longer time scale, a zebra that left the encounter area can move more or less far from the encounter area () and either never return or come back to the encounter area (). For a zebra that initially stayed in the encounter area, it can either stay for a long period () in the encounter area or initiate a delayed departure.

Materials & Methods

Study area

The study area is Hwange National Park, a large unfenced protected area (~15 000 km²) located in western Zimbabwe (19°00'S, 26°30'E). This ecosystem is characterized by a dystrophic (low nutrient soil) semi-arid savanna where the vegetation is dominated by bushlands and woodlands with small patches of grasslands [START_REF] Arraut | The 2013-2014 vegetation structure map of Hwange National Park, Zimbabwe, produced using free satellite images and software[END_REF]. The main woody plant species are Baikiaea plurijuga, Colophospermum mopane, Terminalia sericea, Acacia spp. and Combretum spp. [START_REF] Arraut | The 2013-2014 vegetation structure map of Hwange National Park, Zimbabwe, produced using free satellite images and software[END_REF]. The long-term mean annual rainfall is 600mm (± 30% CV), with most rains falling between November and April. The surface water available to animals is found in natural waterholes, which dry up as the dry season progresses, as well as in artificially supplied waterholes pumped throughout the dry season. The study was conducted in the Main Camp region of the Park (~1 200 km²). There, zebra density is estimated to be around 1 indiv./km² [START_REF] Grange | Demography of plains zebras (Equus quagga) under heavy predation[END_REF], lion density around 4 indiv./100 km 2 [START_REF] Loveridge | Conservation of large predator populations: Demographic and spatial responses of African lions to the intensity of trophy hunting[END_REF], and hyaena density around 9 indiv./100 km 2 [START_REF] Périquet | Sharing The Top. How Do Spotted Hyaenas Cope With Lions?[END_REF].

Zebras are predated by both predators, accounting for 8-9% of lion kill sites [START_REF] Davidson | Seasonal Diet and Prey Preference of the African Lion in a Waterhole-Driven Semi-Arid Savanna[END_REF] and 11% of hyaena scat samples [START_REF] Périquet | Spotted hyaenas switch their foraging strategy as a response to changes in intraguild interactions with lions[END_REF]. Predation has been suggested as the main ecological process causing low survival in this zebra population [START_REF] Grange | Demography of plains zebras (Equus quagga) under heavy predation[END_REF].

Data

Thirty-two female adult zebras from different harems were equipped with GPS collars, which recorded a location every hour or 30 minutes (we used only one location per hour for the analyses) between August 2009 and July 2015. Zebras were equipped for a mean of 387 (± 256 SD) days. During this 6-year period, in the area used by the studied zebras, 14 lions (from 9 different prides/coalitions) and 7 hyaenas (from 3 different clans) were also equipped with GPS collars recording hourly locations. Lions were equipped for a mean of 492 (± 580 SD) days, and hyaenas for a mean of 453 (± 370 SD) days. The capture and collaring of zebras, lions and hyaenas were performed by qualified personnel, under permits from Zimbabwe Parks and Wildlife Management Authority, using standard protocols for these species (see Ethical notes for details).

Ethical note

The collaring exercises on the three species were part of three separate long-term monitoring projects. Animals from different species were captured neither at the same location nor at the same time. Permissions were provided by the appropriate agencies (Zimbabwe Parks and Wildlife Management Authority, Wildlife Drugs Sub-committee of the Drugs Control Council of Zimbabwe and Zimbabwe Veterinary Association, Wildlife Group, and licenses to acquire, possess and administer game capture drugs/dangerous drugs) and permits were issued for each monitoring protocol (lions' monitoring permits: REF:DM/Gen/(T) 23(1)(c)(ii):713/12/01, 03/2002, 07/2003, 20/2004, 01/2005, 01/2007, 03/2008, 03/2009, 25/2010, 06/2011, 12/2012, 08/2013, 51/2014, 10/2015 /2010, 25/2010, 05/2011, 06/2011, 12/2012, 15/2012, 08/2013). Relevant animal care protocols were followed during capture and collaring of all the animals, which were under chemical immobilization/anesthesia during the collaring. Drugs were administered by trained project personnel who attended and successfully passed the Zimbabwe wildlife capture and handling course, and who held a dangerous drug license (renewed annually through the Wildlife Veterinary Association and administered by Medicines Control Authority, Zimbabwe). Also, animal capture and collaring followed the ASAB/ABS guidelines for the Use of Animals in Research.

Lions were equipped with GPS collars from Televilt/Followit Positioning (AB, Lindesberg, Sweden, or African Wildlife Tracking, Pretoria, South Africa) or Sirtrack Ltd. (Havelock North, New Zealand), the GPS collars weighed between 600 and 900 g, which represent 0.6 and 0.9%, respectively, of the smallest individual captured (100 kg). Spotted hyaenas were equipped with GPS radio-collars with UHF download and VHF transmitter from African Wildlife Tracking (model: UHF 407). The GPS collars fitted weighed 1kg, which represents 1.2%, of adult female hyaena body weight (60kg). Zebras were equipped with GPS radio-collars with UHF download and VHF transmitter from Africa Wildlife Tracking or Vectronics (Vectronics Aerospace GmbH, Berlin, Germany). Fitted collars always weighted less than 1kg, which would be less than 0.5% of the body weight of a 200kg adult female zebra.

All the animals were immobilized by chemicals, they were darted from the ground using Dan Inject J.M.SP.25 CO2 powered dart guns, hence drugs were administered by intramuscular injection (shoulder or rump) and were species specific. For lions and hyaenas, a bait was used to attract the targeted individuals and to be in a position to dart them, hence there was no pursuit of the animal before the immobilization. Zebras were darted once sighted from a vehicle. Lions received the dissociative anaesthetic Zoletil; dosage: 0.83-0.32 (range 0.53e1.38) mg/kg; manufacturer: Virbac RSA, Halfway house, South Africa, and sedative (Medetomidine (Zalopine/Domitor); dosage 1⁄4 0.05 0.01 (range 0.04e0.06); manufacturer: Novartis, Isando, South Africa or Orion Pharma, Turku, Finland), Hyaenas received a standard mix of 500 mg Ketamine (Kyron laboratories Pvt. Ltd, Benrose, RSA) and 200 mg Xylazine (Rompun; Bayer, Leverkusen, Germany) or of 80 mg Zoletil (Virbac RSA, Halfway House, RSA) and 4 mg Medetomidine (Zalopine, Wildlife Pharmaceuticals, Karino, RSA). Zebras received a standard mix of 6mg of Etorphine (Captivon®, Wildlife pharmaceuticals (Pty) Ltd., Mpumalanga, South Africa) and 48 mg of Azaperone (Wildlife pharmaceuticals (Pty) Ltd., Mpumalanga, South Africa). It took about 7-8 minutes for the animals to be immobilized after the drugs were administered, then the eyes were covered and ear plugs fitted to reduce stimuli and stress and the collars were fitted. For lions, an additional safety measure was taken by using a light leg restraint in case of unexpected arousal of the animal. While animals were immobilized, blood and hair samples were collected for hyaenas and lions (not for the purpose of this specific study but to optimize the immobilization and prevent the need for other animals to be captured to answer different scientific questions). Scat sample (when possible) were collected on hyaenas. The complete procedure could take up to one hour maximum for all species. Then, immobilization drugs were reversed, for lions drugs were reversed with Atipamezole (dosage 1⁄4 0.18 0.07 (range 0.01e0.28) mg/kg; manufacturer: Farmos, Orion Corp., Finland or Novartis, Isando, South Africa), for hyaenas drugs were reversed with 16 mg of Yohimbine (Rx drug, Kyron Labs, Benrose, RSA), and for zebras drugs were reversed using 18mg of Diprenorphine (Wildlife pharmaceuticals (Pty) Ltd., Mpumalanga, South Africa). Once drugs reversal were injected animals were monitored until their full recovery (meaning walking away normally and joining back their group especially their harem for zebras), it took on average 20 minutes post drug reversal injections for the individuals to fully recover, zebras were even standing up within seconds after the drug reversal injections. No adverse effect has been recorded for any of the three species. For all the species, fully grown adult were preferentially collared and when subadults were collared, sufficient space was allowed to ensure that the collar did not become tight as the neck grew.

Non-pregnant females were preferably collared, early-stage pregnancy cannot be determined visually but the immobilization drugs used have no known effect on unborn fetuses, are extremely safe and widely used on wildlife.

All the collared individuals were monitored by being tracked from a vehicle. Collared lions were located weekly to bimonthly from a vehicle or microlight aircraft. Positional data from the GPS radio-collars were downloaded, and observations made of group composition. Collared hyaenas and zebras were tracked from a vehicle using a four-element yagi antenna and VHF (Very High Frequency) receiver (Icom IC-R20). Data from GPS collars were downloaded using a downloading console and a USB UHF modem on a monthly basis whenever possible, either directly by the observer or retrieved from automatic downloading stations (African Wildlife Tracking, range of download: ~300 m) located at waterholes. Collars were removed when batteries where flat, when collars were malfunctioning, or deteriorations happened to ensure the safety of animals. For one zebra, the collar had slipped over the ears of the animals and so was removed the day after the observation. Also, sometimes collars would fall off due to the deterioration. If the collar did not fell off by itself (or with the help of a drop-off systems that were controlled using UHF signals for certain zebras' collars) collars were removed using the same immobilization procedure as described before.

Analyses

Definition of encounters -We assumed that a zebra encountered a predator when they were simultaneously located less than 500m apart (as in [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF] this distance threshold appears a good balance between a biologically meaningful threshold for this work and a cut-off point that allows reasonable sample sizes; we preliminarily checked that the results of this work were qualitatively robust if we would have used a shorter distance, and that there was no effect of the distance between the zebra and its predator on the results). For consecutive pairs of simultaneous locations less than 500m apart, the first pair was considered as the encounter. We only considered night encounters (between 6pm and 6am) since this is when lions and hyaenas are active and likely to be hunting [START_REF] Hayward | Temporal Partitioning of Activity in Large African Carnivores: Tests of Multiple Hypotheses[END_REF]. In the subsequent analyses, we included only individual zebras that encountered both predators during the period they were tracked. This was the case for 15 zebras. We identified 68 encounters between a zebra and a lion, and 90 encounters between a zebra and a hyaena.

Definition of controls -For each encounter between a zebra and a predator, we randomly selected 10 locations of the same zebra that occurred at the same time but at a different date.

We made sure that these randomly selected locations were not from a night during which an encounter with another GPS-collared predator occurred. The effect of undetected predators should mainly reduce our capacity to detect differences in zebra spatial response between encounters and controls.

Description of environmental variables -For each encounter and control location, we extracted:

(1) the distance to the closest waterhole. Waterhole areas are considered hotspots of predator-prey interactions in the Hwange ecosystem [START_REF] Valeix | Does the risk of encountering lions influence African herbivore behaviour at waterholes?[END_REF][START_REF] Périquet | Sharing The Top. How Do Spotted Hyaenas Cope With Lions?[END_REF]). We were interested in contrasting zebra responses in the vicinity or away from waterholes, and thus used a simple dichotomy for the variable 'distance to water' (referred as 'water' in the equations below): 'close' (≤1km from a waterhole) vs "distant" (> 1km from a waterhole).

(2) the vegetation type (referred as 'vegetation' in the equations). Based on the vegetation structure map by [START_REF] Arraut | The 2013-2014 vegetation structure map of Hwange National Park, Zimbabwe, produced using free satellite images and software[END_REF], we contrasted two types of vegetation: 'open vegetation' (corresponding to the class 'grassland' in the original map) and 'dense vegetation' (corresponding to the classes 'bushed grassland', 'bushland', 'woodland', 'mopane woodland', and 'woodland evergreen' in the original map).

(3) the period of the night (referred as 'night' in the equations), classified as either the 'beginning' (between 6pm and midnight) or 'end' (between midnight and 6am) of the night.

At the 'beginning' of the night, prey, if not responding, will have to cope with the presence of the predator for most of the night. In contrast, at the 'end' of the night prey only have to deal with the presence of the predator for a few hours before it becomes much less dangerous after dawn, as both predators are mainly active at night [START_REF] Hayward | Temporal Partitioning of Activity in Large African Carnivores: Tests of Multiple Hypotheses[END_REF]. We therefore predicted that prey would be more likely to leave an encounter area at the 'beginning' of the night than at the 'end'.

We preliminarily assessed if encounters occurred in a specific subset of circumstances (environmental conditions or time), compared to those generally experienced by zebras during the night in order to assess if characteristics of the encounters varied between the two predators. We detected no major difference. Details on the analyses and the results are available in Appendix A.

Describing the variability of the reactive spatial response -For each encounter with a predator (a lion or a hyaena) and for each control, we calculated the distance between these locations and each zebra's location during the next 24h. Plotting the data revealed a high variability of how zebras moved away from the locations with time (Appendix B), which led us to decompose the spatial response of zebras to understand this variability (Fig. 1). Building upon [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF], who performed an unsupervised model-based clustering analysis to classify the immediate response of zebras after an encounter with lions and found that the best model was a two-cluster model (superior to the model with only one model), we first identified two types of immediate spatial responses depending on whether zebras were further than 900m from the encounter location 2 hours after the encounter ('immediate flight') or not ('initial stay'). This 900m threshold distance defines the 'encounter area' hereafter, and was the distance that best discriminated the two types of immediate responses in [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF]. To assess whether the choice of the 2-hour time window affected the results, we ran the subsequent analyses with a 1-hour and a 3-hour time window to preliminarily check that the results were qualitatively the same. As this was the case, we present the results for the 2hour window only. This corresponds to step (1) in Fig. 1. We assessed whether this immediate response was influenced by the predator species and the environmental variables. We then investigated whether there were longer-term spatial responses. We specifically calculated, for zebras that left the encounter area, the speed with which they left the area and at which distance they moved away over 24 hours (step (2) in Fig. 1), and compared whether this dynamic of the flight was influenced by the predator species. We further assessed how long it took zebras that initially displayed a flight response to come back to an encounter area (step (3) in Fig. 1). For zebras that initially stayed in the encounter area, we assessed whether predator species or environmental variables influenced the time zebras spent ultimately in the encounter area after the encounter (step (4) in Fig. 1).

Statistical analyses

1. Short-term spatial response of zebras after a predator encounter -We used a mixed logistic regression to assess the probability that an encounter led to an 'immediate flight' response (coded 1) vs. an 'initial stay' response (coded 0) and if this probability was affected by the predator species and the environmental variables (step (1) in Fig. 1):

(1)

Where

is the probability of an 'immediate flight', i being the i th observation and j the j th zebra. is the intercept, is the estimated coefficient for the explanatory variable 'predator species encountered' (abbreviated 'predator'; a categorical variable with three levels: hyaena, lion, and control), the others are the estimated fixed regression coefficients for the environmental variables, and is the random effect on the intercept for zebra j.

Temporal dynamics of the spatial response for zebras that performed an 'immediate flight'

-For 'immediate flight' responses (n=19 after an encounter with a hyaena and n=31 after an encounter with a lion), we assessed if the predator species encountered influenced (i) the speed with which the zebra left the encounter area, and (ii) how far the zebra went following the 'immediate flight' response (step (2) in Fig. 1). The controls included in this analysis (and the next one) are controls when zebras moved further than 900m in 2 hours, i.e., comparable to an "immediate flight". For each encounter or control location, we calculated, for each hourly interval from 5h before to 24h after the location, the speed (meters/hour) of the zebra.

To assess how far zebras moved after a predator encounter, we calculated the net displacement from the encounter or control location for each location over the same period (5h before to 24h after the encounter or control location). We then compared the mean difference of speed over each hourly interval (for all the encounters) and the mean difference of net displacement between situations corresponding to encounters with a lion, encounters with a hyaena and controls by using multiple means comparisons [START_REF] Herberich | A robust procedure for comparing multiple means under heteroscedasticity in unbalanced designs[END_REF].

Including data 5 hours before the encounter allowed comparing zebras' trajectories before and after the encounter.

Avoidance of the encounter area by zebras that performed an 'immediate flight' -For

'immediate flight' responses, we calculated the time elapsed before coming back to the encounter area (Appendix C, step (3) in Fig. 1). We chose to study this response only within a 72h-window following the encounter, to ensure that we were studying the actual prey antipredator response. Indeed, the larger the time gap since the encounter is, the less likely it is that zebras' trajectories are influenced by the predator encounter. For returns within 72 hours (which happened for 92% of the 'immediate flight' responses, Appendix C), we further studied the drivers of this temporal dynamics of avoidance of the encounter area by using a

Poisson regression:

(2)

4. Time spent in the encounter area for zebras that initially stayed -For 'initial stay' responses (n=71 after an encounter with a hyaena and n=36 after an encounter with a lion, one lion encounter was removed from the analysis as it was lethal), and for controls where zebras initially stayed in the encounter area, we calculated the time spent in the encounter area (Appendix D; step (4) in Fig. 1) and investigated if some factors influenced it using a mixed negative binomial regression as it fitted the data better than the Poisson regression model:

(3)

The goodness of fit of every model was assessed using the Hosmer-Lemeshow test [START_REF] Hosmer | Applied Logistic Regression[END_REF]; see gof p-value in the results). All the statistical analyses were performed with the R software (version 3.6. 1, Team, R core, 2021). We considered explanatory variables with p-value lower than 0.05 statistically significant.

Results

Short-term spatial response of zebras after a predator encounter

The probability of observing an "immediate flight" response was higher after an encounter with a lion (0.48 on average) than after an encounter with a hyaena (0.21 on average), both being higher than for control situations (0.14 on average, Table 1, Fig. 2). After an encounter with a predator, zebras went mostly in the direction opposite from the predator location during the encounter (Appendix E). The probability of an 'immediate flight' response was lower at the end of the night (Table 1, Fig. 2), but was not significantly affected by distance to water or the vegetation type where the encounter occurred (Table 1, gof p-value = 0.07).

Table 1: Estimates of the variables explaining the probability for a zebra to engage in an 'immediate flight' response within the 2 hours following an encounter with a predator (hyaena being the reference level for the predator variable). Significant values are in bold.

Estimates

Temporal dynamics of the spatial response for zebras that performed an 'immediate flight'

Zebras that fled immediately after an encounter with a hyaena did not move on average faster than during control situations as no mean speed difference at any time period is significant (mean speed ± SD = 1010 ± 838 m/h and 854±741 m/h respectively; p-value=0.87; Fig. 3 a).

After an encounter with a lion, zebras immediately moved on average faster (mean speed ± SD =1544 ± 1198 m/h) than after a control (mean speed ± SD =854 ± 741 m/h, Fig. 3 b, p-value = 0.4e-05), or than after an encounter with a hyaena (mean speed ± SD =1010 ± 838 m/h, Fig. 3 c, p-value=0.03). We also detected a significant mean speed difference for the hour preceding the encounter (Fig. 3b,c). This is most probably because an encounter is defined from simultaneous hourly GPS fixes and the actual encounter may have occurred within the hour preceding the acquisition of these fixes. Afterwards, mean speed differences between lion encounters and hyaena encounters or controls were not significant, indicating that a higher mean speed characterized only the hour following the encounter (Fig. 3).

Avoidance of the encounter area by zebras that performed an 'immediate flight'

Zebras returned sooner to an encounter area after an encounter with a hyaena (mean =7.17h;

CI=3.74-13.74) or after a control (mean=10.81; CI=3.10-37.71) than after a lion encounter (mean = 14.90h; CI=4.22-52.46, Table 2 Appendix F, gof p-value=0.99).

Time spent in the encounter area for zebras that initially stayed

The duration of zebra stay in the encounter area did not differ between encounters with lions or hyaenas (Table 3, Fig. 5, gof p-value=1.00) and was ~10 hours on average (CI=8.25:12.31), but was a couple of hours shorter than under control situations (mean = 12h;

CI=8.01-17.29, Table 3, Fig. 5). Zebras stayed longer (2 hours more on average) in the encounter area when it was close to a waterhole (Table 3, Fig. 5).

Table 3: Estimates of the variables explaining the time spent by a zebra in the encounter area before leaving the encounter area for zebras that performed an 'initial stay' response (hyaena being the reference level for the predator variable).

Discussion

Zebras' immediate spatial response to predation risk differs according to the dangerousness of the predator species encountered -Overall, our study shows that zebras were more likely to leave an area after an encounter with a lion than after an encounter with a hyaena, and fled faster when it happened. The spatial response of zebras to predation risk by lions depicted in Hwange (this study; [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF] was also demonstrated in Kruger National Park, South Africa, where GPS data from simultaneously collared zebras, wildebeests

Connochaetes taurinus and lions showed that zebras leave an encounter area more often than wildebeests (Martin & Owen-Smith, 2016). However, both herbivores were more active near lions, particularly during new moon [START_REF] Traill | Lion proximity, not moon phase, affects the nocturnal movement behaviour of zebra and wildebeest[END_REF]. No study, to our knowledge, has been conducted on the spatial response of zebras to predation risk by hyaenas.

Overall, our results are consistent with prey anti-predator responses strengthening as the dangerousness of the predator increases. The differences observed in the zebra reactive spatial response between encounters with both predators can be intuitively explained by the difference in body size between lions and hyaenas, as the larger body size of lions gives this predator an obvious advantage over hyaenas to capture zebras. More originally, our results are also consistent with the hypothesis originating from the invertebrate literature that prey exposed to cues from sit-and-pursue predators (equivalent to ambush predators) should display stronger anti-predator responses than prey exposed to cues from actively hunting predators [START_REF] Preisser | Predator hunting mode and habitat domain alter nonconsumptive effects in predator-prey interactions[END_REF][START_REF] Miller | Fear on the move: predator hunting mode predicts variation in prey mortality and plasticity in prey spatial response[END_REF]. The underlying mechanism would be that sit-and-pursue predators tend to spend longer periods in the same area, and hence cues of their presence should be more indicative of imminent predation risk, and therefore evoke stronger prey responses. The idea that predator hunting mode can affect prey antipredator responses this way has started to become present in the literature on large mammals, with support for the above hypothesis at the scale of the proactive responses of prey [START_REF] Thaker | Minimizing predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates[END_REF][START_REF] Moll | Spatial patterns of African ungulate aggregation reveal complex but limited risk effects from reintroduced carnivores[END_REF][START_REF] Makin | Herbivores employ a suite of antipredator behaviours to minimize risk from ambush and cursorial predators[END_REF]. Furthermore, the hunting success of ambush predators, such as lions, benefits from a surprise effect, as they can run at a very high speed but over short distances. Hence, once a prey has detected an ambush predator and leaves the encounter area, the probability that it will be pursued is low. This is different for cursorial predators, such as hyaenas, which can chase down prey over long distances and thus remain dangerous once detected. Hence, upon an encounter with a cursorial predator, leaving the area might not decrease the probability that the predator will pursue the prey. It has been shown that cursorial predators, such as hyaenas or wild dogs, are often more successful hunters when prey flee right after the encounter [START_REF] Mills | Kalahari Hyaenas: comparative behavioural ecology of two species[END_REF][START_REF] Creel | The African wild dog: behaviour, ecology, and conservation[END_REF]. It is therefore possible that zebras do not leave the area immediately after encountering a hyaena, as this may be the most effective antipredator response, in particular if they increase their vigilance level. Our findings thus complement the other studies that found that lions elicited stronger proactive antipredator responses in African herbivores than hyaenas [START_REF] Thaker | Minimizing predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates[END_REF][START_REF] Moll | Spatial patterns of African ungulate aggregation reveal complex but limited risk effects from reintroduced carnivores[END_REF][START_REF] Makin | Herbivores employ a suite of antipredator behaviours to minimize risk from ambush and cursorial predators[END_REF], and suggest that this may hold for reactive antipredator spatial responses too. However, more studies covering other pairs of large carnivores are clearly needed to rigorously assess the role of the predator hunting mode.

Our study focused on the reactive spatial response, but prey can invest in other types of reactive responses, such as exclusive vigilance [START_REF] Creel | The relationship between direct predation and antipredator responses: a test with multiple predators and multiple prey[END_REF], resistance display such as bunching [START_REF] Dannock | Assessing blue wildebeests' vigilance, grouping and foraging responses to perceived predation risk using playback experiments[END_REF] or fighting behaviours [START_REF] Lingle | Fight or flight? Antipredator behavior and the escalation of coyote encounters with deer[END_REF]. This illustrates the limits of studies based on GPS data only, for which detailed information on prey non-spatial behaviour is missing. Furthermore, GPS data that records hourly locations miss spatial response at a finer time scale, as zebras might also move away for a few minutes only. Tackling the full complexity of the role of behaviour in predator-prey interactions will likely require a suite of data that new technologies can now provide [START_REF] Suraci | Beyond spatial overlap: harnessing new technologies to resolve the complexities of predator-prey interactions[END_REF].

The behavioural ecology of predator-prey interactions is context-dependent -One important finding from our work is the high variability in the zebra spatial responses, as zebras did not always leave an encounter area after a predator encounter and there was a high variability in the speed of the movement following the encounter. In some cases, it is possible that predation risk was wrongly assessed, or assessed as not warranting a response, or that another antipredator response was more appropriate. The ecology of predator-prey interactions is context-dependent and influenced by attributes of the predator, the prey and the environment [START_REF] Wirsing | The context dependence of non-consumptive predator effects[END_REF]. First, the behaviour of the predator, its group size and its hunger state can influence prey antipredator behaviour. For instance, an 'immediate flight' response might be the most appropriate to a hunting predator with a thin belly, likely hungry, while an 'initial stay' response might be the most appropriate to a walking predator with a fully distended belly that suggests that the predator is satiated. For instance, gerbils adjust their foraging behaviour to the hunger state of owls [START_REF] Berger-Tal | Complex state-dependent games between owls and gerbils[END_REF]. Prey attributes may affect the perception of predation risk and the associated antipredator responses such as group size [START_REF] Childress | Predation risk, gender and the group size effect: does elk vigilance depend upon the behaviour of conspecifics[END_REF], presence of young [START_REF] Gochfeld | Vigilance in African Mammals: Differences Among Mothers, Other Females, and Males[END_REF], hunger state [START_REF] Berger-Tal | Complex state-dependent games between owls and gerbils[END_REF], and personality [START_REF] Belgrad | Predator-prey interactions mediated by prey personality and predator hunting mode[END_REF]. Another prey attribute is diet and more precisely the importance of their diet in their habitat selection. For instance, by having a selective diet for patches of short grass, blue wildebeests are less likely to leave a short grass patch after an encounter with a lion, while zebras, which are generalists, are less constrained and thus more likely to leave (Martin & Owen-Smith, 2016). Finally, the assessment of predation risk and the associated antipredator response may be influenced by the habitat configuration at the landscape level with an important role of the relative abundance and distribution of safe and risky areas [START_REF] Laundré | The landscape of fear: the missing link to understand top-down and bottom-up controls of prey abundance[END_REF][START_REF] Smith | Habitat complexity mediates the predator-prey space race[END_REF].

In our study, habitat (vegetation structure and distance to water) at the encounter location did not play an important role in zebra immediate spatial response. The probability of a zebra initiating an 'immediate flight' response increased at the beginning of the night, suggesting that encounters occurring at that time are riskier or that the costs associated to staying in the same area as their predator is too high when they need to monitor the predator for the whole night ('risky times' and 'risky place' hypotheses - [START_REF] Dröge | Risky times and risky places interact to affect prey behaviour[END_REF].

Predator influence on prey space use at the landscape level and on a longer temporal scale -

In our study, we further explored how far a zebra went after an encounter with a predator and how long it avoided an encounter area (already studied for encounters with lions in [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF]. We believe such results provide useful insights into the predator-prey space game at the landscape scale [START_REF] Sih | Predator-Prey Space Use as an Emergent Outcome of a Behavioral Response Race[END_REF]. Our results show that lions influenced zebra space use over larger spatial scales than hyaenas. Indeed, zebras performed an "immediate flight" more often after an encounter with a lion, they also moved further away when they encountered a lion (> 6 km away on average 24h after the encounter) than a hyaena (~ 4 km on average). The immediate flight response is therefore associated to a missed opportunity cost in terms of foraging, as zebras forage a lot at night (unpublished data), and prematurely leave their foraging patch for 'immediate flight' responses; but also to travelling costs (higher when zebras encounter lions because of higher speed immediately after the encounter and longer distances covered). Additionally, our results mirror previous findings on lions leaving a kill area, probably because of prey behavioural depression after prey have located the lions and moving to a different area (> 5km away [START_REF] Valeix | Understanding Patch Departure Rules for Large Carnivores: Lion Movements Support a Patch-Disturbance Hypothesis[END_REF]. This illustrates the predatorprey space game at the landscape scale. However, it is noteworthy that zebras that performed an "immediate flight", often came back in the encounter area by the next night, which may indicate a strong but non-lasting avoidance.

Zebras that initially stayed in the encounter area stayed longer in control situation than when they encounter a predator, especially when close to water. Waterholes are important drivers of zebra habitat selection, as zebras are water dependant and need to drink daily [START_REF] Redfern | Surface water constraints on herbivore foraging in the Kruger National Park, South Africa[END_REF]. Furthermore, open grassland areas where zebras mainly forage are scarce and often associated with waterhole areas in the study ecosystem [START_REF] Arraut | The 2013-2014 vegetation structure map of Hwange National Park, Zimbabwe, produced using free satellite images and software[END_REF].

This result is consistent with a scenario whereby zebras in control conditions left the area because they had finished exploiting the resource patch [START_REF] Searle | Should I stay or should I go? Patch departure decisions by herbivores at multiple scales[END_REF], whereas zebras disturbed by a predator likely had to leave prematurely their resource patch. Zebras that had left immediately returned sooner to an encounter area after a hyaena encounter than after a lion encounter. This result suggests that zebras may perceive the environment risky for a longer period after a lion encounter and is again consistent with the hypothesis that ambush predators induce stronger antipredator response.

Emergent multiple predator effects? -Different predators may affect prey's landscape of fear in complex ways [START_REF] Sih | Emergent impacts of multiple predators on prey[END_REF]. They can interfere directly by chasing each other [START_REF] Périquet | Dynamic interactions between apex predators reveal contrasting seasonal attraction patterns[END_REF]. They can interfere indirectly by reducing their hunting efficiency leading to risk reduction for the prey [START_REF] Hoset | Multiple predators induce risk reduction in coexisting vole species[END_REF]. They can also facilitate each other if the prey response to one predator makes the prey more vulnerable to the other [START_REF] Leblond | Caribou avoiding wolves face increased predation by bears -Caught between Scylla and Charybdis[END_REF].

At a small spatial scale (the encounter area), our results suggest that lion presence may lead to a prey depression for hyaenas, while at a larger spatial scale, hyaenas may benefit from lions that force zebras to move across the landscape at night. Indeed, in Hwange National Park, hyaena density is high, hyaenas show no strong habitat selection pattern [START_REF] Périquet | Sharing The Top. How Do Spotted Hyaenas Cope With Lions?[END_REF], and hyaena distribution is rather homogeneous across the landscape (unpublished camera-trap data). Therefore, hyaenas are likely to represent a uniform risk of predation over the landscape and lions may increase the probability that a zebra will encounter a hyaena by increasing zebra movements at night.

Our study builds upon and completes the study on the reactive spatial response of zebras to encounters with lions by [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF]. The controlled comparison with the reactive spatial response to encounters with hyaenas is a first step towards a better understanding of the role of the predator identity and overall dangerousness on the nature and strength of this antipredator response. Our work further emphasizes that the immediate flight response is not that frequent, even after an encounter with a lion. It also highlights the limits of knowledge exclusively based on GPS information regarding the biological context of the encounter (predator behaviour, predator group size, prey context). Our study calls for further

Figure 1 Figure 1 :

 11 Figure 1

  ; Spotted hyaenas' monitoring permit: [ZPWMA, 23(1)(c)(ii)15/2012-2013)]; zebras' monitoring permit: REF:DM/Gen/(T) 23(1) (c)(ii): 03/2009, 01

Figure 2 :

 2 Figure 2: Probability (calculated from the model estimates, with error bars representing the

Figure 3 Figure 3 :

 33 Figure 3

Figure 4 :

 4 Figure 4: Difference of mean net displacement between pairs of situations a) hyaena

Figure 5 Figure 5 :

 55 Figure 5

Table 2 :

 2 Estimates of the variables explaining the time spent by a zebra that performed an 'immediate flight' response before returning to the encounter area (hyaena being the reference level for the predator variable) within 72 hours. Significant values are in bold.

		Estimates	Std. Error	z	pr(>|z|)	Confidence Interval 2.5% 97.5%
	Intercept	1.97	0.33	6.00	2.00e-09	1.32	2.62
	Control (predator)	0.41	0.30	1.35	0.18	-0.19	1.01
	Lion (predator)	0.73	0.31	2.39	0.02	0.12	1.34
	End (night period)	0.21	0.17	1.23	0.22	-0.13	0.54
	Open (vegetation type)	0.14	0.24	0.57	0.57	-0.34	0.61
	Distant (distance to water)	0.27	0.23	1.19	0.24	-0.18	0.73

Acknowledgements

We deeply thank Nicholas Elliot, Jane Hunt and Brent Stapelkamp for the collection of lion GPS data. We thank Scott Creel, Camilla Wikenros, Elsa Bonnaud, Nadège Bonnot and Anne Loison for helpful comments on the manuscript and fruitful discussions. We thank Salomé Bourg for the drawings in figure 1.

'Agence Nationale de la Recherche' through grants ANR-08-BLAN-0022, 11-CEPS-003 and 16-CE02-0001-01, the Zone Atelier programme of the CNRS, the RP-PCP platform, and for the Hwange Lion Project supported by grants from The Darwin Initiative for Biodiversity Grant 162/09/015, The Eppley Foundation, Disney Foundation, Marwell Preservation Trust, Regina B. Frankenburg Foundation, The Rufford Maurice Laing Foundation, Panthera Foundation, and the generosity of Joan and Riv Winant. Elise Say-Sallaz benefited from a grant from the French "Ministère de la recherche" through the "Ecole Doctorale E2M2" of Claude Bernard Lyon 1 University for this research.

Funding statement

This study was supported by the HERD project (Hwange Environmental Research Development, today Zone Atelier Hwange -Hwange LTSER), and funded by the French

Data archiving statement

The data used in this study is archived and available from a dryad repository.

Conflict of interest

The authors declare that they have no conflict of interest.

Authors' contributions

Elise Say-Sallaz: Formal analysis (lead); Investigation (equal); Methodology (equal); Writing original draft (lead); Writingreview and editing (equal). Simon Chamaillé-Jammes: We detected no significant difference between mean net displacements after an encounter with a hyaena and after a control (Fig. 4 a,. Zebras moved further away after an encounter with a lion (mean net displacement ± SD = 6.2 ± 4.4 km 24 hours after; Fig. 4 b) than after a control (mean net displacement ± SD = 4.1 ± 3.8 kilometres 24 hours after; p-value=0.004; Fig. 4 b). However, in the 3 hours following an encounter, zebras moved further away after a lion encounter (mean net displacement ± SD = 4.8 ± 2.5 km 3 hours after; Fig. 4 c) than after a hyaena encounter (mean net displacement ± SD = 3.2 ± 2.4 km 3 hours after p-value=0.004; Fig. 4c).

Conceptualization

Figure 4

studies on other pairs of large mammalian predator species to be able to draw general conclusions on the impact of different predator attributes (e.g., body size, hunting mode) on prey antipredator response.

Highlights

 Zebras reactive response is stronger after encountering a lion than a hyaena.

 Zebras were twice more likely to flee after an encounter with a lion than a hyaena.

 Zebras moved on average faster and further than after an encounter with a hyaena.

 Large mammal predators hunting mode may affect the reactive response of prey.


Patrick Rozier
email: rozier@chimie.ups-tlse.fr

Mariyappan Sathiya

Alagar-Raj Paulraj

Dominique Foix

Thomas Desaunay

Pierre-Louis Taberna

Patrice Simon

Jean-Marie Tarascon
email: jean-marie.tarascon@college-de-france.fr

Anionic redox chemistry in Na-rich Na 2 Ru 1 -y Sn y O 3 positive electrode material for Na-ion batteries

Keywords:

The synthesis and Na-electrochemical activity of Na-rich layered Na 2 Ru 1-y Sn y O 3 compounds is reported. Like their Li-analogue, Na 2 Ru 1-y Sn y O 3 shows capacities that exceed theoretical capacity calculated from the cationic redox species. The high capacity was found, by means of XPS analysis, to be associated to the accumulation of both cationic (Ru 4+ /Ru 5+ ) and anionic (O 2-/O 2 n-) redox processes. The structural evolutions during cycling have been followed and found to be associated with the cation disordering and loss of crystallinity on cycling.

Introduction

Na-ion batteries promise to be an inexpensive and sustainable alternative to their Li counterpart since Na is abundant and widely spread over the world. However, performances of Na-based materials are hindered by the relatively higher atomic weight of Na and its larger atomic radius which limits the variety of materials where sodium can be reversibly extracted and inserted. Most research efforts have been focused on layered Na x MO 2 [START_REF] Kim | Enabling sodium batteries using lithium-substituted sodium layered transition metal oxide cathodes[END_REF][START_REF] Yabuuchi | P2-type Nax[Fe 1 / 2 Mn 1 /2]O 2 made from earth-abundant elements for rechargeable Na batteries[END_REF] or NASICON [START_REF] Saravanan | First report on excellent cycling stability and superior rate capability of Na 3 V 2 (PO 4 ) 3 for sodium ion batteries[END_REF] type structure that mimic Li-ion batteries positive electrode materials. Recently alkali-rich materials Li 2 MO 3 have shown promising properties [START_REF] Lu | Synthesis, structure, and electrochemical behavior of Li[END_REF][START_REF] Johnson | The significance of the Li 2 MnO 3 component in 'composite' xLi 2 MnO 3 • (1 -x)LiMn 0.5 Ni 0.5 O 2 electrodes[END_REF][START_REF] Armstrong | Demonstrating oxygen loss and associated structural reorganization in the lithium battery cathode Li[END_REF][START_REF] Sathiya | High performance Li 2 Ru 1-y Mn y O 3 (0.2 ≤ y ≤ 0.8) cathode materials for rechargeable lithium-ion batteries: their understanding[END_REF][START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF] as their experimental capacities exceed the theoretical value calculated according to the oxidation of the metallic species [START_REF] Armstrong | Demonstrating oxygen loss and associated structural reorganization in the lithium battery cathode Li[END_REF][START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF]. This extra capacity is associated, as shown in the case of Li 2 Ru 1-x Sn x O 3 , to the high voltage redox activity of the anionic species [START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF]. To our knowledge only the study of Na 2 RuO 3 analogous Na-rich oxide is reported [START_REF] Tamaru | Layered Na 2 RuO 3 as a cathode material for Na-ion batteries[END_REF]. It presents a layered structure [10] and electrochemical properties similar to that of Li-based analogue, however with an extra capacity of only 7% of the theoretical capacity [START_REF] Tamaru | Layered Na 2 RuO 3 as a cathode material for Na-ion batteries[END_REF].

In this work, we studied the electrochemical behavior of Na ) redox couple.

Experimental

Stoichiometric amounts of RuO 2 , SnO 2 and 10% excess of Na 2 CO 3 (99.9% Sigma Aldrich) were mixed for the syntheses of Na 2 Ru 1 - y Sn y O 3 (y = 0; 0.25; 0.5; 0.75; 1) samples. The reactants, hand grinded, are placed in a platinum crucible and introduced into a quartz tube. The sample is heated at 900 °C for 10 h under a flow of Argon, cooled down to room temperature and stored in an Argon-filled glove box. X-rays diffraction (XRD) patterns were recorded using a Bruker D8 diffractometer (λ CuKα = 1.5418 Å). Electrochemical tests were performed versus metallic Na in Swagelok-type cells. The active material is mixed with 20 wt.% carbon black. As all obtained results are independent of the salt NaClO 4 or NaPF 6 we used, we report only those obtained with a 1M NaClO 4 solution in a mixture of ethylene carbonate, propylene carbonate and dimethyl carbonate (9:9:2 weight ratio). Electrochemical tests were conducted at 20 °C using a Mac-pile or a VMP system operating in galvanostatic mode in the 1.5-4.2 V voltage range and with a C/20 rate (C = exchange of one mole of electron per mole of active material in 1 h). The in situ XRD study is conducted using a Swagelok-type cell equipped with a Beryllium window protected by an aluminum foil acting as current collector. The patterns are collected every 0.1 Na exchanged during electrochemical relaxation time and analyzed using the Rietveld method as implemented in the FullProf suite. XPS measurements were carried out using a Kratos Axis Ultra spectrometer. The data are collected using Al Kα radiation (1486.6 eV) and a 5.10 -9 mbar pressure in the analysis chamber. The stability of the samples was analyzed using short acquisition time before normal collection condition with constant pass energy of 20 eV. The binding energy scale was calibrated using the C1s peak at 285.0 eV and the peak positions and areas were optimized by a weighted least-squares fitting method using 70% Gaussian, 30% Lorentzian line shapes. Quantification was performed on the basis of Scofield's relative sensitivity factors.

Results and discussion

Na 2 RuO 3 [10] and Na 2 SnO 3 [11] adopt the Na-rich layered structure corresponding to the stacking of alternating Na + and [NaMO 3 ] -layers (Fig. 1). The examination of the XRD patterns of the compounds (Fig. 1) shows that they can be indexed using the conventional hexagonal system. Extra peaks (close to 2θ = 20°) with intensity increasing with Sn content are indexed using monoclinic distortion of the cell. They show [START_REF] Viciu | Crystal structure and elementary properties of Na x CoO 2 (x = 0.32, 0.51, 0.6, 0.75, and 0.92) in the three-layer NaCoO 2 family[END_REF] that Sn is responsible for the ordering of the Na-Sn-Ru distribution in the layer. This relationship being beyond the scope of this study, for conciseness, the average description is kept. The cell parameters refinement, in agreement with the larger radius of Sn 4+ (0.69 Å) than Ru 4+ one (0.62 Å), indicate that the Sn 4+ to Ru 4+ substitution operates via a solid solution mechanism.

The electrochemical reactivity of Na 2 Ru 1-y Sn y O 3 series analyzed in Na-half cells shows that the first charge (Fig. 2a), despite similar with Li analogues, present a few differences. For the Sn free sample, there are three successive plateaus on charge which are less pronounced on the subsequent discharge (Fig. 2b) and progressively vanish upon long cycling. For the y = 0.25 sample, the three plateaus on charge exhibit a faster disappearance upon cycling (not observed during the second charge). For greater Sn concentration first charge exhibits only two plateaus which convert to S-like shape during discharge and subsequent cycles. This shows that a greater Sn content (N0.25) is needed for the Na-system, as compared to the Li-system (b0.25), to fully depart from the structural behavior of the parent A 2 RuO 3 phases. The voltage of the two plateaus, respectively 2.8 V and 3.8 V vs Na + /Na, is consistent with the voltage 3. contradiction is explained by the high sensitivity to moisture and spontaneous oxidation of the Sn free Na 2 RuO 3 sample which hampered the accurate investigation of the extra-capacity phenomenon as recently confirmed [START_REF] Tamaru | Corrigendum to "Layered Na2RuO3 as a cathode material for Na-ion batteries[END_REF]. The increase of Sn content leads to an increase of the high voltage plateau capacity up to 1 and 1.3 Na + together with a larger Na lost between the first charge and discharge which reaches nearly 0.46 and 0.56 Na + for the y = 0.5 and 0.75 samples respectively. The investigation of the cycling behavior of Na 2 Ru 0.75 Sn 0.25 O 3 shows (Fig. 3) that a voltage cut-off limited to the charging of Ru 4+ /Ru 5+ alone leads to ~100% capacity retention even after 50 cycles while increasing the charging voltage to 4.2 V reduces the capacity from 140 mAh/g to 100 mAh/g on cycling to 50 cycles. This confirms that the irreversible capacity is associated to the high voltage phenomenon which was already observed in some analogous Li-rich phases. Effectively, whatever the value of y in the Li 2 Ru 1-y Sn y O 3 system, the amplitude of the first and second plateau were nearly equal as expected according to the proposed dual cationic-redox anionic processes [START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF]. Deviation from the above relation (increase of the high voltage plateau correlated to an increase in the irreversibility), already observed with the Li 2 Ru 1-y Mn y O 3 systems, was assigned to the irreversible release of O 2 from the sample [START_REF] Sathiya | High performance Li 2 Ru 1-y Mn y O 3 (0.2 ≤ y ≤ 0.8) cathode materials for rechargeable lithium-ion batteries: their understanding[END_REF]. This implies that for the Na 2 Ru 1-y Sn y O 3 system, the y = 0.5 and y = 0.75 samples show the formation of oxygenated species prior to reach a potential domain over which the samples loose irreversibly O 2 , hence rendering such compositions poorly attractive. For such a reason, Na 2 Ru 0.75 Sn 0.25 O 3 sample is selected to further structural and XPS characterizations.

In situ XRD performed on Na x Ru 0.75 Sn 0.25 O 3 sample (Fig. 4a) shows that the charge starts via a solid solution mechanism indicating that the voltage-composition curve should be considered as a flat S-shaped curve instead of a real 2.8 V plateau as previously suggested. Cell parameters refinement shows that the removal of Na ions is associated with an increase of the interlayer space in agreement with an increase of repulsive effects between layers and a decrease of the layer length in agreement with the diminution of Ru ion radius during oxidation. This indicates that in the first part of the charge Na is removed from the interlayer space thus reducing the screening effect and that the Ru redox couple is active. Further charging below x = 1.3 is associated with the extraction of Na from the mixed Na 1/3 M 2/3 layers and corresponds to the growth of a second phase at the expense of the pristine one which becomes a single phase for x = 1.0. Despite a poor quality of XRD pattern, all peaks can be assigned using the cell setting of pristine one. Cell parameters refinements indicate a brutal change between the pristine phase (a = 3.09 Å c = 16.52 Å) and the second phase (a = 3.04 Å c = 15.88 Å) which results in a decrease of the cell volume from 137 Å 3 to 127 Å 3 . On subsequent discharge, this two steps process is reversible, as witnessed by the shift back of lattice parameters to those of the pristine phase. Nevertheless, the XRD profile show broader Bragg peaks with the absence of superstructure peaks indicating the onset of a Na-driven disorder through the first charge-discharge cycle.

This solid solution-biphasic-solid solution process is exactly the opposite of the one reported for Li analogues [START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF] (biphasic domain then solid solution operating on the second phase) confirming, as widely reported, the drastically different room temperature Li(Na)-driven phase diagrams associated, among others, to both the size and polarity differences between Li and Na ions.

XPS analyses have been carried out on pristine, charged to 2.8 V and 4.3 V, and charge-discharged to 1.5 V electrode materials and valence state evolution confirmed by EPR analysis as previously reported for Li based compounds. They indicate that Sn is not active and Ru 4+ is oxidized up Ru +5 during the 2.8 V process (not shown). Characterization of the O1s band (Fig. 4c) confirms that O is not affected by the charge on the 2.8 V plateau while an extra band observed at higher bending energy is observed for the fully charged sample. These phenomena, fully reversible on discharge, and compared with Li based compound investigation [START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF], are in perfect agreement with the presence of oxygenated (O 2 ) n-species and confirm that the redox activity of anion is effective and responsible for the extra capacity observed for these samples.

Conclusion

We have reported the structural-electrochemical study of Na-rich Na 2 Ru 1-y Sn y O 3 compounds and show that, like their Li analogues, they present large capacities resulting from both cationic (Ru 4+ → Ru 5+ ) and anionic (O 2-→ O 2 n-) redox processes as deduced from XPS spectroscopy. Therefore, in contrast to the Li series, such a formation of oxygen species is followed, for the Sn rich samples, by the irreversible loss of O 2 . The differences in both the size and polarity of Na + as compared to Li + , which lead to different Na-driven structural changes, are most likely at the origin of the increasing instability of the oxygenated species towards the release of O 2 . Scanning transmission electron microscopy imaging methods and electron energy loss spectroscopy for simultaneous mapping of the oxidation state and coordination number of the transition metal cations, are presently being conducted to assess not only the local structure, but also the local chemistry of these Na electrodes. This work which shows for the first time the feasibility of the Na-rich layered phases to have high capacities due the anionic redox activity contribution opens the way to design new positive electrode materials for Na-ion batteries with the possibility to exchange at high voltage more than 1 electron per transition metal. It now remains to chemically manipulate these Na-rich based layered compounds to enhance their cycling behavior and stability against moisture so that they could be handled in air.

Fig. 2 .

 2 Fig. 2. Na 2 Ru 1-y Sn y O 3 electrochemical behavior a) voltage composition curve and b) derivative plots.

Fig. 1 .

 1 Fig. 1. XRD patterns for the Na 2 Ru 1-y Sn y O 3 solid solution. Inset shows a projection of the layered structure.

Fig. 4 .Fig. 3 .

 43 Fig. 4. Characterization of Na 2 Ru 0.75 Sn 0.25 O 3 sample a) insitu XRD patterns; b) voltage profile; and c) O1s XPS spectra.

  2 Ru 1- y Sn y O 3 solid solution and report a large extra capacity in contradiction to what was reported for Na 2 RuO 3 . The replacement of active Ru 4+ ion by the non-electrochemically active Sn 4+ helps in isolating the contribution of conventional Ru 4+ /Ru 5+ redox mechanism and preliminary results indicate that the extra capacity is also associated to the anionic (O 2-/O 2

	n-

Conflict of interest

There is no conflict of interest.


domain: info chim

text:
Yassine M Mejri

Mehdi A Beniddir

Olivier Cailloux

Meltem Öztürk

Experimental evaluation of similarity indices about the MIA molecular family

The purpose of this article is to evaluate the performance of the Morgan/Tanimoto, modified cosine similarity, Spec2Vec and MS2Deep Score similarity indices that aim at measuring structural and spectral similarities between molecules. To illustrate this evaluation, we used a spectral database containing about a hundred of the emblematic monoterpene indole alkaloids (MIADB).

Introduction

Comparing two molecules in order to see how similar they are is an important issue for chemists. Such comparisons are used in order to detect new molecules, classify known molecules with respect to their potential use, etc. Overall, two types of information may be used in order to compute similarities between molecules: information on their atomic structures or information obtained from their analytical read-out such as their tandem mass spectrometyr (MS/MS) and NMR spectra, to name a few.

There exist different way to compare such information. In this article we analyse the performance of four similarity indices (generally denoted by σ): one based on their atomic structure and three based on their MS/MS spectra.

• Structure-based indices: we use the Morgan/Tanimoto index [START_REF] Morgan | The generation of a unique machine description for chemical structures-a technique developed at chemical abstracts service[END_REF] that we denote by σT . • MS/MS spectra-based indices: this category includes the rule-based index called modified cosine (denoted by σC ) and two machine-learning-based indices: Spec2Vec(σS) [Huber et al., 2021a] and MS2Deep score (σD) [START_REF] Huber | Ms2deepscore: a novel deep learning similarity measure to compare tandem mass spectra[END_REF].

We use these indices as implemented in the Python library MatchMS [START_REF] Huber | Spec2vec: Improved mass spectral similarity scoring through learning of structural relationships[END_REF] and RDkit [START_REF] Landrum | Rdkit documentation[END_REF].

Only a few articles analyse these indices in the literature [START_REF] Bittremieux | Comparison of cosine, modified cosine, and neutral loss based spectral alignment for discovery of structurally related molecules. bioRxiv[END_REF][START_REF] Huber | Ms2deepscore: a novel deep learning similarity measure to compare tandem mass spectra[END_REF]. Our study is novel on two aspects: the type of molecules that we use in our experiments and the way that we evaluate the indices.

MIAs are known for their various biological activities and isomeric possibilities leading to analytical intricacies with respect to their annotation. To the best of our knowledge, our experiments are the only ones which are specially designed for this family.

In chemistry, molecular families are usually divided into several skeletons classification, according to their C-C bond connectivities. For MIAs, chemists have defined 42 skeletons [Buckingham et al., 2010]. In our experiments, we compare the similarities provided by the four indices with the skeleton classification, proposed by natural product chemists.

We denote by M the set of molecules in our database, by n = |M | = 110 their number, by S the set of skeletons and by s : M → S the function assigning each molecule to its skeleton. Our database spans |s(M )| = 28 of the 42 known MIA skeletons.

Similarity index vs skeleton

A similarity index is a function σ : M × M → [0, 1] (the higher the number σ(m1, m2), the most similar the index σ considers the molecules m1, m2). Apart from the four indices σT , σC , σS and σD introduced here above, we let k = 1 [s(m 1 )=s(m 2 )] , the "ground truth" index, denote the function that returns 1 if m1 and m2 have the same skeletons, 0 otherwise.

We define the average difference between two similarity indices σ1 and σ2 as

ϵσ 1 ,σ 2 = 1 n(n+1) 2 n i=1 n j=i |σ1(mi, mj) -σ2(mi, mj)|.
We use this indicator in order to compare the four indices to the skeleton classification. We also analyse the difference between the structure-based index σT with the three MS/MS spectra-based indices. We see that the structure-based similarity index σT has the lowest average difference with the k index. This is expected as σT uses the atomic structure of the molecules, an information more directly relevant to the structure of the molecule than MS/MS spectrum. However, the three other indices are the ones that are generally useable in practice, as chemists who are trying to discover new molecules generally do not know their atomic structure (but may learn about their mass spectra thanks to specific devices). We also see that both machine learning-based indices currently existing are further away from correct skeleton classification than the commonly used modified cosine index, an observation that suggests promising directions for future work.

One can observe that the computation of ϵ σ,k for σ ∈ {σT , σC , σS, σD}, as displayed in the first column of Table 1, mixes two kinds of indices since the codomain of σ is the interval [0, 1] while the codomain of k is the set {0, 1}. In practice chemists often consider two molecules as similar if the similarity index is greater than 0.6. For this reason, we also use this threshold in order to discretize our similarity indices and thus define σ0.6 = 1 [σ(m 1 ,m 2 )>0.6] , thus, σ0.6(mi, mj) = 1 if σ(mi, mj) > 0.6 and σ0.6(mi, mj) = 0 otherwise. We observe, again, that σT performs best and that σC achieve the best performance among the similarity indices that do not require atomic structural information.

Ongoing work

We are currently investigating clustering methods using the four similarity indices and comparing these clusters to the correct skeletons.

Another research direction that we are currently exploiting is the comparison of MS/MS spectra-based similarities with knowledge given by chemical experts. Instead of considering binary success or failure depending on whether a pair of molecules is correctly considered by some similarity index to belong to the same skeleton, a much richer information, and closer to actual practice, consists in considering how far away skeletons are from each other: different skeletons may be very close or very far away in terms of structure. To this respect, our chemist expert has specified distances between different skeletons. This information can then be used to further evaluate similarity indices, according to whether they tend to consider molecules that belong to similar skeletons as being similar.

Discussion

The starting point of our study was our desire to investigate the reliability of MS/MS spectra-based indices. Such indices are systematically implemented in the discovery process of new molecules. During this analysis based mainly on MS/MS spectra data, information about a large number of molecules is obtained without knowing their atomic structure. For that reason, an automated similarity analysis is needed. Our current results suggest that modified cosine provides the most accurate predictions on the similarities that would be obtained if the atomic structures of molecules were known. It is also the one closest to the skeleton classification of MIAs. However, interpretation of the performance results shown here has to take into account the high proportion of negative pairs (5673 out of 6105) in our sample.

As future work, we will pursue the just described research paths. The second and most important step of our study will be the use of such index for the discovery of new MIA molecules.

Table 1 :

 1 Table 1 shows our results. difference between index measures and skeleton classification and Structure-based index.

	σ	ϵ σ,k	ϵσ,σ T
	σ T	0.22	0
	σ C	0.25	0.18
	σ S	0.39	0.21
	σ D	0.72	0.54

Table 2 :

 2 Table 2 shows these supplementary results. Number of True positive, False positive, False negative and True negative comparisons. Note that ϵ σ 0.6 ,k is the proportion of (False positive + False negative).

	σ	True + False + False -True -	ϵ σ 0.6 ,k
	σ T	155	0	277	5673	0.045
	σ C	248	617	184	5056	0.13
	σ S	230	1082	202	4591	0.21
	σ D	410	5026	22	647	0.84

mohamed-yassine.mejri@dauphine.eu

mehdi.beniddir@universite-paris-saclay.fr

olivier.cailloux@dauphine.fr

meltem.ozturk@dauphine.fr

Acknowledgment

This project has received financial support from the CNRS through the MITI interdisciplinary programs.