Olivier Pays
email: olivier.pays@univ-angers.fr

Pierrick Blanchard

Simon Chamaillé-Jammes

Marion Valeix

Andrew J Loveridge

David W Macdonald

Stéphanie Périquet

Esther Van Der Meer

Patrick Duncan

Godfrey Mtare

Hervé Fritz

Disentangling the roles of bottom-up and top-down drivers in the trade-off between food acquisition and safety in prey with multiple predators

Keywords: Antipredator response, Feeding rate, Foraging strategy, Herbivore, Patch quality, Risk effect, Savanna, Vigilance

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Limitation of populations under natural conditions is driven by both bottom-up and top-down drivers [START_REF] Sinclair | Testing hypotheses of trophic level interactions: A boreal forest ecosystem[END_REF][START_REF] Shurin | A cross-ecosystem comparison of the strength of trophic cascades[END_REF][START_REF] Hayward | Carrying capacity of large African predators: predictions and tests[END_REF][START_REF] Hopcraft | Herbivores, resources and risks: alternating regulation along primary environmental gradients in savannas[END_REF]. Food abundance and quality have been reported to control herbivore biomass [START_REF] Fritz | On the carrying capacity for large ungulates of African savanna ecosystems[END_REF] as they affect the physical condition of individuals and thus their capacity to survive and breed [START_REF] Mduma | Food regulates the Serengeti wildebeest: a 40-year record[END_REF]. The role of predators in the limitation of prey populations through numerical lethal effects (e.g. direct killing) has been demonstrated in numerous studies [START_REF] Sinclair | Patterns of Predation in a Diverse Predator-Prey System[END_REF][START_REF] Preisser | Scared to death? The effects of intimidation and consumption in predator-prey interactions[END_REF][START_REF] Heithaus | Towards a predictive framework for predator risk effects: the interaction of landscape features and prey escape tactics[END_REF]). In addition, antipredator behaviours of prey, such as changes in habitat use (e.g. [START_REF] Werner | An experimental test of the effects of predation risk on habitat use in fish[END_REF], changes in temporal niches (Valeix et al. 2009a), vigilance (e.g. [START_REF] Dröge | Risky times and risky places interact to affect prey behaviour[END_REF]) and foraging strategies (e.g. [START_REF] Barnier | Diet quality in a wild grazer declines under the threat of an ambush predator[END_REF], may have energetic (e.g. Kotler, [START_REF] Kother | Apprehension and time allocation in gerbils: the effects of predatory risk and energetic state[END_REF]) and physiological consequences (e.g. stress, [START_REF] Boonstra | The impact of predator induced stress on the snowshoe hare cycle[END_REF][START_REF] Creel | Glucocorticoid stress hormones and the effect of predation risk on elk reproduction[END_REF], which can adversely affect prey demography (e.g. [START_REF] Lima | Nonlethal Effects in the Ecology of Predator-Prey Interactions: What are the ecological effects of anti-predator decision-making?[END_REF][START_REF] Creel | Relationships between direct predation and risk effects[END_REF][START_REF] Zanette | Perceived predation risk reduces the number of offspring songbirds produce per year[END_REF].

Although the antipredator responses of prey have been well described [START_REF] Creel | The control of risk hypothesis: reactive vs. proactive antipredator responses and stress-mediated vs. food-mediated costs of response[END_REF], assessments of the costs of these responses are scarce and little is known about the non-lethal effects of the presence of predators on large mammalian prey populations [START_REF] Creel | The relationship between direct predation and antipredator responses: a test with multiple predators and multiple prey[END_REF], Say-Sallaz et al. 2019).

Vigilance is one behaviour that is central to the trade-off between food acquisition and safety, and contributes to the indirect impact of predators on the fitness of prey through its link with fitness-enhancing activities [START_REF] Hopcraft | Herbivores, resources and risks: alternating regulation along primary environmental gradients in savannas[END_REF]. Although maintaining high levels of predator detection allows prey to reduce their probability of being killed, this strategy is likely to reduce food acquisition and thus to incur fitness costs [START_REF] Brown | Hazardous duty pay and the foraging cost of predation[END_REF]. Studies in birds [START_REF] Fritz | The cost of vigilance for intake rate in the mallard (Anas platyrhynchos): An approach through foraging experiments[END_REF] and mammals [START_REF] Fortin | Foraging costs of vigilance in large mammalian herbivores[END_REF]) have reported that an increase of vigilance significantly reduced feeding efficiency (e.g. instantaneous intake rate) of foragers. This trade-off between foraging costs and vigilance may be critical when food resources are of poor nutritional quality, forcing foragers to maximise their foraging effort.

In studies investigating the non-lethal effects of the presence of predators, information on the spatial and temporal variation in food availability for prey is often lacking, particularly in studies of vigilance strategies in free-ranging animals. This makes it difficult or impossible to disentangle the roles played by predation pressure and food quality in shaping the trade-off between food acquisition and predator detection [START_REF] Mcnamara | The effect of a change in foraging options on intake rate and predation rate[END_REF]. When food biomass and quality are not measured, it is uncertain whether vigilance behaviour of prey reduces food intake rate up to the point where it jeopardizes fitness, as intake rates vary with patch quality and biomass [START_REF] Cromsigt | Resource partitioning among savanna grazers mediated by local heterogeneity: an experimental approach[END_REF][START_REF] Owen-Smith | Foraging theory upscaled: the behavioural ecology of herbivore movement[END_REF]. Although the foraging strategies of herbivores have been well studied [START_REF] Spalinger | Mechanisms of foraging in mammalian herbivores: new models of functional response[END_REF][START_REF] Wilmshurst | What constrains daily intake in Thomson's gazelles?[END_REF], the impacts of variations in forage characteristics, particularly when they are seasonally driven, on the foraging costs of vigilance are far from clear [START_REF] Favreau | Food supply fluctuations constrain group sizes of kangaroos and in turn shape their vigilance and feeding strategies[END_REF]. For instance, studies of short-grass grazers have shown that higher grass biomasses are generally less digestible [START_REF] Fryxell | Forage quality and aggregation by large herbivores[END_REF], making the relationship between food intake and the greenness and biomass of food (i.e. two proxies of patch quality) complex to understand. However, an increase in vigilance is likely to affect food acquisition differently if the animals are foraging in patches of different forage characteristics and quality: food acquisition is affected by grass height and density (through their effects on bite sizes and rates), and the chemical composition of grass affects its digestibility. Moreover, during antipredator vigilance, many animals, including birds [START_REF] Baker | Are the costs of routine vigilance avoided by granivorous foragers?[END_REF]) and mammals [START_REF] Blanchard | Induced or routine vigilance while foraging[END_REF], reduce foraging costs by exhibiting vigilance while processing food (e.g. chewing) or moving [START_REF] Illius | Costs of vigilance in foraging ungulates[END_REF][START_REF] Fortin | Foraging costs of vigilance in large mammalian herbivores[END_REF]. Vigilance with chewing contrasts with high-cost vigilance (called exclusive vigilance) during which individuals stop handling food. Thus, the effects of predation risk on food acquisition should be examined with attention to the way these two types of vigilance affect functional adjustments in foraging parameters that influence intake rates (particularly bite rate and step rate) in relation to patch quality.

Variations in prey animals' perception of predation risk (such as high vs low risk habitats) affects the time prey allocate to foraging [START_REF] Creel | Sex-specific behavioural responses of elk to spatial and temporal variation in the threat of wolf predation[END_REF]) and food acquisition [START_REF] Sansom | Individual behavior and survival: the roles of predator avoidance, foraging success, and vigilance[END_REF]. Although some studies have investigated responses of prey to a single predator species [START_REF] Chamaillé-Jammes | Innate threat-sensitive 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] Lamanna | Costs of fear: behavioural and life-history responses to risk and their demographic consequences vary across species[END_REF], we know little about the effects of the presence of more than one predator species on vigilance strategies and consequently on food intake rates. Most natural ecological systems are multi-predator systems in which prey can be caught by several predator species [START_REF] Sinclair | Patterns of Predation in a Diverse Predator-Prey System[END_REF][START_REF] Thaker | Minimising predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates[END_REF], Creel et al. 2017, Montgomery et al. 2019). For a complete understanding of the trade-off between vigilance and food acquisition in these multi-predator systems, it is important to determine how prey alter their intake rate in response to specific predator species and the presence of single versus multiple predator species. Finally, it is uncertain for how long after a predator is near the prey, it affects the trade-off between food acquisition and predator detection by prey particularly when they do not encounter their predators every day [START_REF] Middleton | Linking anti-predator behaviour to prey demography reveals limited risk effects of an actively hunting large carnivore[END_REF][START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF].

To examine the role of predators and food quality in shaping the trade-off between food acquisition and predator detection, we studied vigilance and foraging strategies in impala (Aepyceros melampus), a medium-sized herbivore, in Hwange National Park (HNP), Zimbabwe. Over a two-year period, we used an experiment in which patch quality was manipulated by fertilising and mowing plots in a grassland (cutting stimulates regrowth, [START_REF] Leriche | Grass response to clipping in an African savanna: Testing the grazing optimisation hypothesis[END_REF], thus affecting both plant biomass and its quality (the proportion of green plant material). Predation risk was investigated by monitoring the presence of three predators, African lions (Panthera leo), spotted hyaenas (Crocuta crocuta) and African wild dogs (Lycaon pictus) marked with GPS-collars.

We first assessed how impalas adjusted their feeding behaviour to patch quality (biomass and greenness) controlling for the presence of predators and perceived predation risk (visibility around the individual impalas). Three parameters were used to describe impala feeding behaviour: bite rate, i.e. the number of bites per min, step rate, i.e. the number of steps per min, and the ratio between the number of bites and steps (the number of bites per feeding station), which is an indicator of the number of bites per feeding station. Bite rate can be a proxy of intake rate, as it is highly dependent on the rate of bite encounters, i.e. bite density, and on bite size, since bigger bites take longer to chew hence lowering bite rate. In our study, grass biomass was mostly below 50g/m² (see FigS1 Appendix1). Below this value, medium sized antelopes and gazelles are limited in their adjustment of bite size [START_REF] Wilmshurst | What constrains daily intake in Thomson's gazelles?[END_REF][START_REF] Wilmshurst | The allometry of patch selection in ruminants[END_REF].

Thus, bite size can vary but not in relation to patch biomass. Hence, we expected feeding parameters in impalas foraging in our study area to respond more to the proportion of green tissues than variation of grass biomass. This limited possibility to adjust bite size implies that bite rate was a reasonable proxy of intake rate, and this intake rate was more dependent on encounter rate than chewing rate (Process 2 of [START_REF] Spalinger | Mechanisms of foraging in mammalian herbivores: new models of functional response[END_REF]. Step rate while foraging gives an index of the rate of change in feeding stations, with a greater rate of change when grass quality is low. While step rate may affect the bite rates and the local density of acceptable bites, step rate can be influenced by disturbance mechanisms unrelated to food. Thus, one metric that may directly translate the perception of feeding patches giving a better description of the perceived patch quality is the ratio bite rate/step rate (the number of bites per feeding station). If the amount of acceptable bites in a given patch is high, the number of bites per feeding station is high. Thus we predicted that under low predation risk, step rate should decrease with increases in patch quality while bite rate remains stable, resulting in an increase in the number of bites per feeding station with patch quality i.e. in enriched patches of tall grass (Fig 1a).

We tested the effects of perceived predation risk (measured by the level of vigilance) and the recent nearby occurrence of predators on the feeding behaviour of impalas (bite rate) and how impalas perceived and used feeding patches (indicated by the number of bites per feeding station).

We expected to find one or both of two patterns of adjustment to perceived predation risk (Pattern 1.1 and 1.2) and one pattern to the recent nearby occurrence of predators (Pattern 2) which are presented in the Figure 1. Pattern 1.1 and 1.2 result from perceived predation risk that increases the need for low-cost vigilance (while chewing or moving) and causes adjustment of step rate or bite rate, respectively. In Pattern 1.1 the animal maintains selectivity for high quality bites. When the cropping process is interrupted by vigilance before the mouth is full, the individual leaves the partially depleted patch to go to a better patch with higher densities of acceptable bites, thus increasing step rate. It is also consistent with vigilance interruption impairing searching for food items in a partially depleted patch [START_REF] Fritz | The cost of vigilance for intake rate in the mallard (Anas platyrhynchos): An approach through foraging experiments[END_REF]. This would lead to a decrease in the number of bites per feeding station mostly induced by higher step rate (Fig 1b). In Pattern 1.2, the animal broadens the acceptability of bites in a given patch to achieve a full mouth before vigilance interrupts it. This implies more bites per patch and smaller distances between bites, therefore higher bite rates, leading to an increase of the number of bites per feeding station because of this increase of bite rate for a given feeding station (Fig. 1c).

When predators are actually present, the level of vigilance should be higher for both low and high-cost vigilance [START_REF] Favreau | Short-term behavioural responses of impalas in simulated antipredator and social contexts[END_REF]. We expected a different pattern (Pattern 2) in which the increase of high-cost vigilance visually disconnected the individual from its food patch, inducing a greater cost of searching for acceptable bites. Under this scenario, we expected the number of bites per feeding station to decrease because bite rate decreases (Fig 1d), particularly in the tall grass where searching may be more difficult, but mainly because visibility while foraging with head down is poor and thus perceived as risky [START_REF] Pays | Detecting predators and locating competitors while foraging: an experimental study of a medium-sized herbivore in an African savanna[END_REF]. If the costs of resuming searching for remaining bites is high, then stepping to another feeding station would be an alternative option allowing for vigilance while moving. As in Pattern 1, this would cause an increase in step rate.

Previous observations in HNP reported that zebras, Equus quagga, encountered lions at night every 35 days on average [START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF]). Thus observations with predators in the vicinity of impalas may be rare compared to the ones without predators. From a statistical standpoint, this may lead to failure to detect an effect of the recent nearby occurrence of collared predators on the behaviours of the impalas. To avoid missing an effect of predation on the trade-off between food acquisition and vigilance, we compared vigilance and bite rates and step rates of focal impalas on days when collared predators had been in the vicinity during the previous 24 hours with observations on days before their arrival (i.e. the preceding 24 hours). We also investigated whether behavioural adjustments were more extreme when more than one predator species was present.

Materials and methods

Study site

Hwange National Park (HNP) hosts an exceptional diversity of mammals including most of the small to large herbivores and carnivores observed in Southern African savannas [START_REF] Fritz | A food web perspective on large herbivore community limitation[END_REF] The density (± SD) of impalas around Main Camp was 1.43 impalas/km² (± 0.63) [START_REF] Chamaillé-Jammes | Seasonal density estimates of common large herbivores in Hwange National Park, Zimbabwe[END_REF]. Impalas are expected to be top-down limited [START_REF] Hopcraft | Herbivores, resources and risks: alternating regulation along primary environmental gradients in savannas[END_REF] as their body mass averages 45 kg [START_REF] Cumming | Ungulate community structure and ecological processes: body size, hoof area and trampling in African savannas[END_REF], i.e. below the 180-200kg threshold under which population dynamics of prey should be controlled by predation [START_REF] Sinclair | Patterns of Predation in a Diverse Predator-Prey System[END_REF]. Impalas are preferred by African wild dogs, cheetahs (Acynonyx jubatus), and leopards (Panthera pardus) [START_REF] Hayward | Prey preferences and dietary overlap amongst Africa's large predators[END_REF] and other large carnivores such as spotted hyaenas and lions also feed on impalas (e.g. impalas represent 17% and 8% of the total number of prey found in lion and hyaena scats respectively in HNP [START_REF] Davidson | Seasonal diet and prey preference of the African lion in a waterhole-driven semi-arid savanna[END_REF]Périquet et al. 2015 respectively)). Impalas are mixed feeders and their feeding strategy varies seasonally [START_REF] Jarman | The social organisation of antelope in relation to their ecology[END_REF]: they are predominantly grazers while grasses are green and growing, and browsers of foliage, forbs, shoots and seedpods at other times. Here, we studied behavioural responses of impalas when they were grazing. Focals when impalas browsed short bushes or trees were excluded from this analysis.

From 50 to 150 impalas (mainly adult females and juveniles) foraged each day at the study site. All adult females in the study site formed a single herd (as described in [START_REF] Jarman | Daily activity of impala[END_REF] which divided into a variable number of groups with marked fusion-fission dynamics. It was not possible to capture and mark all individuals in the study population. However, since the year 2000 newborn fawns have been captured and tagged on an annual basis, it was possible to regularly observe about 30 ear-tagged adult females. Ear-tagged individuals allowed us to confirm that individuals randomly selected for observations (called 'focals' here) were rarely resampled and the effect of potential pseudo-replication is therefore negligible.

Ethical Statement

The experiments complied with the laws (including animal welfare ethics) of Zimbabwe. They were

Experimental design

We manipulated the impalas' food resources by spreading common fertiliser for pasture (N: 3.5%, P 2 O 5 , 24.4%, S: 11.0% and Zn: 0.5%, at 70kg/ha) and by mowing (cutting) grass to increase both the biomass and the proportion of grass that was green (and thus high quality) since herbivores select for green tissues (e.g. [START_REF] Murray | Resource-ratio theory applied to large herbivores[END_REF]. Four enriched and four control plots (60 × 120m), all including strips of cut and uncut grass, were created at different distances from cover (Fig 2).

Fertilisation and mowing were performed in January 2009 and 2010, two weeks before the beginning of the behavioural studies. We confirmed that fertilisation and mowing changed grass availability and quality by measuring grass biomass, greenness and bare soil in all plots (192 samples in 2009 and 353 in 2010 for the three cited variables). Grass biomass was measured using a previously calibrated diskpasture meter and the proportion of green tissues and the average grass cover were estimated visually by using photographs (as in [START_REF] Vanha-Majamaa | Digitized photographs in vegetation analysis-a comparison of cover estimates[END_REF], see Pays et al. 2012 for details, and see Appendix 1 for statistical details and variations among seasons and between years and the effects on patch quality). On average, during the 2-year experiment, biomass was 30% higher in enriched plots compared to control plots in uncut strips while we did not detect any significant difference in cut strips. The proportion of green tissues was 25 % higher in enriched plots than in control plots in cut strips and 13% higher in uncut strips. In cut and uncut strips, the proportion of bare soil was on average 17% lower in enriched plots compared to control plots.

Recording behaviour

We studied vigilance and foraging behaviours of impalas by videotaping focal adult females only (hence avoiding adding sex-age effects), for 5-min periods chosen at random during the daytime from February to August. Juveniles were present in all groups; it was not possible to say at which female each juvenile belonged to. We filmed individuals in groups whose predominant activity during the video sequence was grazing. 5-min focals were sufficient to obtain sequences during which both foraging and vigilance behaviours could be studied. In total we recorded 740 sequences: 532 in 2009 and 208 in 2010.

Observations were made from vehicles, maintaining a minimum distance of 100m between the focal group and the observer to minimize disturbance. When several individuals were filmed during the same day, the observer took care to avoid filming the same individuals to ensure independence between observations. Finally, it was crucial that animals did not move long distances (i.e. stayed in the same ecological conditions) during the 5-min video sequences to ensure that food biomass and quality remained approximately stable during the focal. So we rejected focals during which the individual left the plot and did not forage in the same mowed or uncut strips during the 5 min video sequence. We sampled 163 impalas foraging inside enriched plots, 58 in control plots and 519 outside plots (Fig 2c). We considered data collected outside plots as uncut controls.

An impala was considered vigilant when it raised its head above the horizontal, scanning its surroundings, without moving its feet. Previous studies have shown that impala often chew when vigilant, but it is assumed that this multitasking might reduce their ability to hear approaching predators. Impalas have indeed been observed to stop chewing when hearing a threatening stimulus [START_REF] Blanchard | Induced or routine vigilance while foraging[END_REF][START_REF] Favreau | Short-term behavioural responses of impalas in simulated antipredator and social contexts[END_REF]. Thus, we extracted the total time an individual spent in vigilance, distinguishing high-cost vigilance when impalas stopped chewing their bites while vigilant and low-cost vigilance when they continued chewing. From each focal, we also recorded when individuals moved their left front leg to calculate the step rate and when they took a bite (easily recognizable by jerky head movements) to calculate the bite rate. We then calculated the number of bites per feeding station.

The observer recorded date, time of day and the location of the focal females on a field map.

Visibility around foraging individuals was categorized based on the height of the grass (Grass height), which was visually estimated and classified in four classes: short when grass height was not above the focal impala's hooves distinguishing between cut (short cut) and uncut (short uncut) strips, medium when it was below the upper part of the impala's metacarpals, and high when it reached the impala's tibia. In tall grass, how easily the focal impala could see the potential predators was assumed to be strongly limited. The position of the individuals within a group (i.e. peripheral or central) was impossible to determine during the video sampling because the animals moved constantly when foraging. Although distance to cover was assessed through three classes: ≤50, 50-100, and >100m, we did not detect any effect of this variable on any of the vigilance and foraging behaviours of impalas (Chi-square tests, all P > 0.54), probably because we included plot identity as a random factor and plots were set up at different distances to cover. Moreover, although group size was assessed during video sampling, we did not detect any effect of the log-transformed group size, considering the two way interactions on any feeding parameters (Chi-square tests, all P > 0.080) and vigilance activities (Chi-square tests, all P > 0.071), probably because the range of group size was not great enough since we avoided small group sizes (the mean group size (± SD) = 41.74 ± 32.70, range from 10 to 108 individuals). Thus, we did not consider these two variables in the final analyses.

Carnivore data

Long-term GPS-tracking studies of large carnivores in HNP allowed us to investigate how the presence of carnivores influenced impala foraging behaviour. During the study period, 7 lions in different groups (2 female adults from 2 different prides and 5 male adults from 5 different coalitions), 5 spotted hyaenas distributed in 2 clans, and 2 wild dogs representative of 2 clans of 5 and 7 individuals were tracked around the study site, which they did use. Given the size of the different predator groups, this leads to the following proportions of collared individuals for the local populations of lions, wild dogs and hyaenas respectively: 0.50, 0.20, and 0.17. Collared individuals visited the study site in 2009 and 2010 occasionally or regularly. We assumed that these individuals were representative of the movements of their groups at least for lions (Valeix et al. 2009b) and wild dogs (van der Meer 2011) (see Appendix 2 for more details). Although other predator species were not collared, visits of cheetah and leopard were rarely observed during the study. We therefore assumed that predation pressure at the study site was mainly driven by the three monitored predator species. Because lions and hyaenas are active mainly at night and move little during the day, GPS locations were acquired every hour from 18h to 6h hours, plus two fixes during the day. For wild dogs, GPS locations were acquired every 100 minutes day and night (see van der Meer 2011; [START_REF] Benhamou | Movement-based analysis of interactions in African lions[END_REF][START_REF] Périquet | Spotted hyaenas switch their foraging strategy as a response to changes in intraguild interactions with lions[END_REF] for details on captures and GPS-collars of wild dogs, lions and hyaenas respectively). From GPS coordinates of collared predators, we determined whether predators occurred in the vicinity of the focal impalas (i.e. within a radius of 2 km centred around the focal impala) in the 24 hours preceding the focal. A previous study in the same area reported that vigilance of prey including impala was affected by predators at this 2 km threshold [START_REF] Périquet | Influence of immediate predation risk by lions on the vigilance of prey of different body size[END_REF]. Predators were present within 2 km of the focal impalas in 127 of the 740 video sequences, including 97 sequences with lion only, 19 with wild dog only and 11 with both lion and hyaena. As we observed only hyaenas only once, and the combination wild dog with lions only once, we discarded these two sequences for the analyses.

Data analysis

Functional adjustment of foraging

We fitted linear mixed effect models to test for the effect of food quality or quantity on the variations in bite rate. We included plot enrichment (whether the impala foraged on control or enriched plots), grass height (contrasting the four classes, i.e. high, medium, short uncut, short cut), predator within 2 km (whether GPS-collared predators were present in the 2 surrounding km in the preceding 24 hours, i.e. no or yes) and two two-way interactions as independent variables: w(x) = β 0 + β 1 (Plot enrichment) + β 2 (Predator within 2 km) + β 3 (Grass height) + β 4 (Plot enrichment × Predator within 2km) + β 5 (Predator within 2km × Grass height) (1) With w(x), the response variable (e.g. bite rate), β 0 , the intercept and β k the coefficient estimated for each predictor x k . Because of the mowing of the grass, the two-way interaction Plot enrichment × Grass height could not be considered in the models. We included year (contrasting 2009 and 2010), season (contrasting three periods i.e. Feb.-March, April-May or July-Aug.) and plot identity as nested random factors to control for time and spatial correlations that might occur in the data set. To capture the sequential structure of the data set, we converted the dates of focals to Julian days cumulated over the two years and applied an autocorrelation function of order 1 using the function corAR1. We tested the effect of each variable using likelihood ratio tests (i.e. χ²). We used post-hoc Tukey tests for multiple comparisons when necessary. The same procedure was applied to the logtransformed step rate and the number of bites per feeding station. We paid special attention to check the normality of residuals, the distribution of residuals against fitted values and the lack of sequential autocorrelation in residuals (see Appendix 4).

Trade-offs between bite rate, the number of bites per feeding station and vigilant behaviour To investigate how investment in vigilance affected bite rate in these impalas, we fitted linear mixedeffect models including total time in vigilance as the predictor and bite rate as the dependent variable. We log-transformed the total time spent in vigilance to achieve statistical requirements on model's residuals:

w(x) = β 0 + β 1 (Log(Total vigilance)) (2)
With w(x), the response variable (e.g. bite rate), β 0 , the intercept and β 1 , the coefficient derived for the predictor. Year, season and plot identity were included as nested random factors and an autocorrelation function of order 1 on Julian day as described earlier. The same procedure was used to test the effect of vigilance on the number of bites per feeding station and the effect of low and high-cost vigilance on bite rate and the number of bites per feeding station.

Effect of the presence of collared predators in the surroundings Although Eq. 1 allowed us to examine whether predator presence affected foraging and vigilance over the whole period, we ran the same model (Eq. 1) comparing focals when collared predators were in the surroundings in the 24h preceding the focals (N = 127) with focals the day before their arrivals (N = 69). We used linear mixed-effect models including year and season as nested random factors. To compare focals belonging to the same event, we created a variable called predator event identity allowing focals during which a collared predator was present to be linked to focals collected the day before their arrival and included it as a random factor nested into year and season. We applied the same autocorrelation function of order 1 on the Julian day as described earlier. We tested the effect of each variable using likelihood ratio tests (i.e. χ²). The residuals of the model were analysed and they fulfilled statistical requirements (see Appendix 4). The same procedure was applied on bite rate, the log-transformed step rate and the number of bites per feeding station.

Finally, we tested for differences in vigilance including high and low-cost vigilance (logtransformed), bite rate, the log-transformed step rate and the number of bites per feeding station between different categories of predation risk within the surrounding 2km (lion only, wild dog only vs lion with hyaena) using linear mixed effects models including predator species within 2 km and grass height and including year, season and predator event identity as nested random factors: w(x) = β 0 + β 1 (Predator species within 2 km) + β 3 (Grass height) (3)

With w(x) as bite rate, the log-transformed step rate and number of bites per feeding station, β 0 , the intercept and β k the coefficient derived for each predictor x k . The size of the data set did not allow us to test for the effect of two-way interactions with each type of collared predator on foraging parameters and vigilance, as each type of predator was not observed in each class of grass height.

We applied the same autocorrelation function of order 1 on the Julian day as described earlier. The residuals of the model were analysed and they fulfilled statistical requirements.

Statistical analyses were performed using R 3.6.2 (R Development Core Team 2019). Models were performed with the nlme package [START_REF] Pinheiro | nlme: Linear and Nonlinear Mixed Effects Models[END_REF]) and multiple comparisons with the lsmeans package [START_REF] Lenth | Least-Squares Means: The R Package lsmeans[END_REF].

Results

Functional adjustments of foraging parameters

On average, bite rate, step rate and the number of bites per feeding station (mean ± SD) in impalas foraging in our study area were 30 ± 9.60, 4.5 ± 3.60, and 15 ± 20 respectively. Plot enrichment and grass height affected certain foraging parameters of these impalas. As expected, bite rate declined in taller grass (22% reduction between tall and short cut grass, Fig. 3a), with the highest values when impalas foraged in short cut strips (Table 1). We did not detect any significant effect of plot enrichment on bite rate (Table 1), but step rate was lower by 27% and the number of bites per feeding station higher by 18% in enriched than in control plots (Fig. 3b,d). On average, step rate declined in the tall grass by 12% (Table 1, Fig. 3c) although we did not detect any difference between medium and short-grass height for step rate (Appendix 3 for multiple comparisons). Contrary to step rate, the number of bites per feeding station increased in tall grass by 53% (Table 1, Fig. 3e) with no difference between medium and short grass height (Appendix 3). To conclude, when plot enrichment increased patch quality (see Appendix 1), impalas reduced their step rate by 1 step per minute on average and gained 3 bites per feeding station.

Trade-offs between bite rate, the number of bites per feeding station and vigilance

The impalas spent on average (± SD) 15% (± 13) of their foraging time in vigilance with 22% (± 20) of their total vigilance spent in high-cost vigilance. Thus, while vigilant, individuals mostly continue chewing and processing their food. Bite rate decreased with the log-transformed time spent in vigilance (β ± SE = -11.213 ± 0.611, χ² = 273.044, df = 1, P < 0.001, pseudo R² = 0.35), high-cost vigilance (β ± SE = -3.450 ± 0.289, χ² = 131.586, df = 1, P < 0.001, pseudo R² = 0.16) and low-cost vigilance (β ± SE = -6.788 ± 0.631, χ² = 100.988, df = 1, P < 0.001, pseudo R² = 0.18). Figure 4 shows that when individuals invested a lot in vigilance to detect predators (for instance 66% of their foraging time, i.e. log(2.4)), impalas could lose up to 20 bites per minute, falling from 40 to 20.

The number of bites per feeding station also decreased with the log-transformed time spent in vigilance (β ± SE = -0.134 ± 0.033, χ² = 16.045, df = 1, P = 0.001, pseudo R² = 0.01) and high-cost vigilance (β ± SE = -3.450 ± 0.289, χ² = 42.007, df = 1, P < 0.001, pseudo R² = 0.05) whereas low-cost vigilance had no effect (χ² = 0.725, df = 1, P = 0.394). Despite the significant patterns, the pseudo R² were low and the investment in vigilance was not a good predictor of the number of bites per feeding station.

Effect of the presence of collared predators in the surroundings

Collared predators were present in the surroundings (within 2km) during 18 days of the 114 days of data collection. Contrasting focals during these 18 days with the ones from the day before the predator's arrival (controls) and controlling for the effects of grass height, showed that the presence of collared predators (regardless of species) affected bite rate but did not affect step rate or the number of bites per feeding station (Table 2). On average, impalas lost about 4 bites per minute when predators were in the surroundings (14% reduction) with no difference of bite rate between a single predator species or multi-predator species (χ² = 1.999, df = 2, P = 0.368). Finally, the presence of collared predators affected both the total time spent in vigilance and high-cost vigilance (Table 3) but did not affect low-cost vigilance (χ² = 1.986, df = 2, P = 0.370). Compared to days before the predator's arrival (controls), impalas were more vigilant and increased their high-cost vigilance when wild dogs were in surroundings by 101% and 167% respectively and when both lions and hyaenas were present by 116% and 355% respectively although we did not detect any significant difference when only lions were present (Table 4, Fig. 5).

Discussion

Functional adjustment of foraging parameters

As reported in other species of herbivores including warthog (Phacochoerus aethiopicus) and white rhinoceros (Ceratotherium simum) [START_REF] Cromsigt | Resource partitioning among savanna grazers mediated by local heterogeneity: an experimental approach[END_REF], our study shows that local patch quality shapes the feeding strategy of impalas. In enriched plots, impalas reduced their step rate, the rate of change in feeding stations, and increased their number of bites per feeding station while bite rate was not affected. The main adjustment parameter for the intake rate is therefore step rate. By adjusting step rate to maintain bite rate, hence presumably intake rate, impala decreased the number of bites per feeding station in control plots (for enrichment, Fig. 3d) i.e. in places where there was a smaller proportions of green material. This analysis of feeding parameters from the experimental plots suggests that intake rate is limited by the encounter rate of acceptable bites, as occurs in the Process 2 in the theoretical framework of [START_REF] Spalinger | Mechanisms of foraging in mammalian herbivores: new models of functional response[END_REF]. This result is consistent with both our prediction of the selective feeding strategy in such medium-sized ruminants (see Fig. 1a) and other studies in the same species [START_REF] Fritz | Foraging in a social antelope: effects of group size on foraging choices and resource perception in impala[END_REF]. Our results suggest that for medium-sized and large herbivores that use step rate as an adjusting parameter of intake rate, individuals may use low-cost vigilance (i.e. vigilance while chewing or moving) to minimise cost of predator detection [START_REF] Blanchard | Induced or routine vigilance while foraging[END_REF]).

Grass height commonly shapes feeding parameters (e.g. bite size), and hence food intake rate in grazing herbivores [START_REF] Arsenault | Resource partitioning by grass height among grazing ungulates does not follow body size relation[END_REF]. Our results show that in tall grass bite rate and step rate were low and the number of bites per feeding station was high indicating that the amount of acceptable bites was high in patches of tall grass. For a selective herbivore like impala, the difficulty in finding high quality green blades in tall grass may lead individuals to reduce their speed when they forage in tall patches when predators are absent.

However, as visibility around them is low, individuals may also reduce speed as the perception of predation risk is high, investing more in vigilance [START_REF] Pays | Detecting predators and locating competitors while foraging: an experimental study of a medium-sized herbivore in an African savanna[END_REF]. Thus more studies are needed to clarify the functional adjustments with grass height in the trade-off between feeding and detection of predators.

To improve patch quality, besides fertilization, we mowed grass to stimulate regrowth and thus increase the availability of green leaves. Our results show that bite rate, step rate and the number of bites per feeding station did not change significantly between short mown and naturally short grasses. The impalas responded clearly to fertilisation particularly when they foraged in tall grass. However, the effect of mowing on their feeding behaviour was not significant. Indeed, although the percentage of green material was higher in cut strips, the difference in biomass between cut (mown) and uncut strips was small, particularly in 2010, even in fertilised plots (Appendix 1) and might have therefore limited the opportunity to detect an effect of mowing on foraging.

Trade-offs between bite rate, the number of bites per feeding station and vigilance Both high and low-cost vigilance have been examined here, and the total time spent in vigilance was the best predictor of the variation in bite rate. Vigilance altered bite rate (and potentially intake rates) as reported in previous studies [START_REF] Fortin | Foraging costs of vigilance in large mammalian herbivores[END_REF]), although it had no effect on the number of bites per feeding station. When at a feeding station, impalas reduced the relative costs of vigilance by continuing chewing and processing their food [START_REF] Pays | Detecting predators and locating competitors while foraging: an experimental study of a medium-sized herbivore in an African savanna[END_REF]. Our results show that impalas spent around 80% of their vigilance time in low-cost vigilance, indicating how individuals can considerably reduce the potential costs of predator detection when they are foraging.

Feeding with larger bites could mitigate foraging costs of vigilance in grazing herbivores (see [START_REF] Spalinger | Mechanisms of foraging in mammalian herbivores: new models of functional response[END_REF][START_REF] Spalinger | Mechanisms of foraging in mammalian herbivores: new models of functional response[END_REF][START_REF] Wilmshurst | What constrains daily intake in Thomson's gazelles?[END_REF] for an example in gazelles). Larger bites would induce longer chewing bouts, increase spare time and allow individuals to use low-cost vigilance for longer periods. However, in our study, grass biomass was mostly below the optimal value for impala (see Introduction) and it is unlikely that patch biomasses on this site allowed individuals to take larger bite sizes. Our results suggest that step rate was the adjusting parameter of intake rate, so we expect impalas to increase their step rate between two feeding stations to improve bite quality (i.e. to detect patches with more green tissues) and to increase encounter rates [START_REF] Spalinger | Mechanisms of foraging in mammalian herbivores: new models of functional response[END_REF]. Finally, although we did not detect a group-size effect on foraging and vigilance activities (as we mostly sampled individuals in large groups), it has been commonly reported in gregarious species [START_REF] Jarman | The social organisation of antelope in relation to their ecology[END_REF], including impalas [START_REF] Pays | Detecting predators and locating competitors while foraging: an experimental study of a medium-sized herbivore in an African savanna[END_REF], that individuals forage in large groups to reduce foraging costs of vigilance and reallocate the time for predator detection to foraging [START_REF] Fitzgibbon | Cost to individuals with reduced vigilance in groups of Thomson's Gazelles hunted by cheetahs[END_REF][START_REF] Fitzgibbon | Why do hunting cheetahs prefer male gazelles?[END_REF].

Effects of the presence of predators and perceived predation risk [START_REF] Creel | Effects of predation risk on group size, vigilance and foraging behavior in an African ungulate community[END_REF] analysed the variation of antipredator behaviours and their foraging costs in five ungulates (zebra, Equus quagga, Grant's gazelle, Nanger granti, wildebeest, Connochaetes taurinus, impala and giraffe, Giraffa camelopardalis) in response to the presence of lions and spotted hyaenas in the surroundings. They found that the increase of vigilance in response to the presence of predators triggered a large reduction in time spent foraging in four species including impala but not in wildebeest. In our study, we show that in response to the presence of collared predators, impalas 1) were more vigilant, increasing their exclusive (i.e. high-cost) vigilance and 2) on average they reduced bite rate while maintaining their step rate and the number of bites per feeding station. These results suggest that the presence of predators leads individuals to use more vigilance, which visually disconnects foragers from their food and leads to lower bite rates (Fig. 1d). Thus our results may apply to other herbivore prey species in which an increase in vigilance is likely to affect food acquisition. This is particularly expected in tall grass where both bite rate and visibility are low for individuals foraging head down. However, in tall grass bite rate and step rate were low while the number of bites per feeding station was high, our results therefore fully support the expected Pattern 2 as the decrease in bite rate did not lead to a decrease of the number of bites per feeding station when predation risk was high. Finally, our results did not support the hypothesis under which perceived predation risk would increase the need for low-cost vigilance hence reduce the number of bites per feeding station (Pattern 1.1,Fig 1b) or broaden the acceptability of bites in a given patch, leading to an increase of the number of bites per feeding station (particularly in short grass) (Pattern 1.2,Fig 1c).

Several studies have reported that prey exhibit a large range of proactive behavioural strategies including adjustment of space use, group size and time spent in risky habitat to decrease overall predation risk and to invest in fitness-enhancing activities such as foraging (Valeix et al. 2009b[START_REF] Basille | Plastic response of fearful prey to the spatio-temporal dynamics of predator distribution[END_REF][START_REF] Courbin | Zebra diel migrations reduce encounter risk with lions at night[END_REF]. The interaction between vigilance and proactive space use is complex and might make applying predictions to other systems difficult [START_REF] Fortin | Space Use and Leadership Modify Dilution Effects on Optimal Vigilance under Food-Safety Trade-Offs[END_REF]). In addition, other studies have shown that prey can reactively adjust their space use [START_REF] Middleton | Linking anti-predator behaviour to prey demography reveals limited risk effects of an actively hunting large carnivore[END_REF][START_REF] Courbin | Reactive responses of zebras to lion encounters shape their predator-prey space game at large scale[END_REF] or increase their time allocated to vigilance in response to cues of predation risk [START_REF] Pays | Foraging in groups allows collective predator detection in a mammal species without alarm calls[END_REF], Dannock et al. 2018), as was the case when impalas were stimulated by lion roars [START_REF] Favreau | Short-term behavioural responses of impalas in simulated antipredator and social contexts[END_REF] or faeces of wild dogs (van der Meer, [START_REF] Van Der Meer | Anti predator behaviour of kudu and impala in response to mimicked African wild dogs presence: do age and sex matter?[END_REF]. We show here that impalas increased their vigilance by increasing their high-cost vigilance when two predators (i.e. lion with hyaena) or when wild dogs were in the surroundings. Although our data on hyaenas did not allow us to examine focals with only hyaenas in the surroundings, our results show that the largest increase of high-cost vigilance in impalas was observed when two predators (lions and hyaenas) were present at the same time in the surroundings. As the increase of vigilance with lions only in the surroundings was small, we might expect that the presence of hyaenas affected the vigilance of impalas. Overall, our results suggest that although impala is the main prey of African wild dogs [START_REF] Hayward | Prey preferences and dietary overlap amongst Africa's large predators[END_REF][START_REF] Van Der Meer | Ecological trap in the buffer zone of a protected area: effects of indirect anthropogenic mortality on the African wild dog Lycaon pictus[END_REF], the presence of two predators at the same time may be perceived as the most important threat. Although our data did not allow us to investigate finer time and spatial scales (due to sample size constraints), it would be very interesting to test for behavioural adjustments to predation risk at other time lags.

Analyses over the whole study show that patch quality is the main determinant of feeding parameters (step rate and bite rate). However, these impalas do respond to predators in their vicinity by increasing their vigilance, and this reduced bite rate. This effect was clear only when we compared focal samples from the 24 hour periods when predators were nearby with focals from the days before. Although our experimental design focused on a large herd of impalas (up to 150 individuals) foraging in one grassland area where many predators were collared, some individual impalas may have been affected by uncollared predators. Our study highlights the need to conduct fine scale analyses in order to understand the effect of patch quality and predators on the trade-off between food acquisition and predator detection. In this context, an important aspect of understanding the effect of the predators on feeding

  . The fieldwork was conducted near Main Camp in the north of HNP (19°00'S, 26°30'E). The study site is an open grassland area of 64 ha surrounded by Acacia and Combretum bushes, typical of the mixed bushed grassland on nutrient-poor soils of the eastern Kalahari sands. Bushes form a natural and visually obstructive boundary of the grassland. The long-term mean annual rainfall is 600 mm and the rainy season occurs between October and April (Chamaillé-Jammes, Fritz & Murindagomo 2006). The fieldwork was conducted from January to August in 2009 and 2010, which received 823.6 mm and 935.4 mm of rainfall respectively.

  approved and conducted under permits from the Director General of the Zimbabwe Parks and Wildlife Management Authority (Ref: DM/Gen/ (T), Permit numbers: 23(l) (c) (ii): 01/2009 and 01/2010 for the impala behavioural study and hyaena collaring, 03/2009 and 25/2010 for lion collaring, and 09/2009 and 07/2010 for wild dog collaring). The long-term individual-based study on impala population dynamics in HNP started in 2000 under permits from the same authorities cited above.

FIGURE 1

 1 FIGURE 1 Expected variations of functional parameters of feeding behaviour in impala with patch

FIGURE 2 FIGURE 3

 23 FIGURE 2 Experimental design for manipulating the quality of feeding patches for free-ranging

  Figure 1

Fig. S2 .

 S2 Fig. S2. Variation of the proportion of green tissues and bare soil between enriched and control plots,

Table 1 .

 1 Factors influencing the bite rate (bite per minute), step rate (step per minute, logtransformed) and number of bite per step (Log-transformed) of impalas over the 2-year period β ± SE are indicated for significant variables. Plot enrichment indicated whether the impala foraged on control or enriched plots, Predator within 2 km indicated whether GPS collared predators were present within 2km (no and yes), grass height contrasted 4 classes (High, medium, short, short cut) and Log Group Size was the log-transformed group size in which the focal impala was studied with classes in italics that were considered as references in the linear mixed-effects model including Year, Season and Plot ID as nested random factors.

	Dependant Variables	Predictors	χ²	Df	P	β ± SE (P)
						(intercept: 30.944 ± 1.392)
		Plot enrichment	0.023 1	0.878
		Predator within 2km	1.190 8	1	0.167
	Bite rate	Grass height	14.10 6	3	0.003	Medium: 1.461 ± 0.789 (0.065) Short: 4.060 ± 1.409 (0.005) Short cut: 3.073 ± 1.327 (0.021)
		Plot enrichment × Predator within 2km 1.025 1	0.599
		Predator within 2km × Grass height	6.079 3	0.108
						(intercept: 0.429 ± 0.061)
		Plot enrichment	2.709 1	0.033	Enriched plot: -0.080 ± 0.035
		Predator within 2km	0.003 1	0.957
	Log (Step rate)	Grass height	23.52 2	3	<0.001	Medium: 0.104 ± 0.032 (0.001) Short: 0.195 ± 0.054 (<0.001) Short cut: 0.186 ± 0.053 (<0.001)
		Plot enrichment × Predator within 2km 3.732 1	0.155
		Predator within 2km × Grass height	5.170 3	0.160
						(intercept: 1.028 ± 0.053)
		Plot enrichment	4.234 1	0.039	Enriched: 0.128 ± 0.054
		Predator within 2km	0.279 1	0.598
	Log (Bites per feeding station)	Grass height	12.77 6	3	0.005	Medium: -0.117 ± 0.037 (0.002) Short: -0.116 ± 0.062 (0.060) Short cut: -0.147 ± 0.058 (0.013)
		Plot enrichment × Predator within 2km 5.119 1	0.078
		Predator within 2km × Grass height	6.346 3	0.096

Table 2 .

 2 Factors influencing the bite rate (bites per minute, BR), step rate (steps per minute, log-transformed, SR) and number of bites per step (log-transformed, B/S) of impalas when comparing the behaviour of focals when GPS collared predators were present and the day before the arrival of the predators. β ± SE are indicated for significant variables. Plot enrichment indicates whether the impala foraged on control or enriched plots, predator within 2 km indicates whether GPS collared predators were present within 2km of the impalas (no and yes), grass height contrasts 4 classes (High, medium, short, short cut) and Log Group size is the log-transformed group size in which the focal impala was studied with classes in italics that were considered as references in the linear mixed-effects model including Year, Season and Predator event ID as nested random factors.

	Dependant Variables	Predictors	χ²	Df	P	β ± SE (P)
						(intercept: 30.610 ± 1.281)
		Plot enrichment	1.354	1	0.245
		Predator within 2km	7.080	1	0.008	Yes: -3.559 ± 1.177
	Bite rate	Grass height	11.904	3	0.008	Medium: 1.860 ± 1.321 (0.161) Short: 6.252 ± 2.430 (0.011)
						Short cut: 9.258 ± 2.232 (<0.001)
		Plot enrichment × Predator within 2km 0.147	1	0.701
		Predator within 2km × Grass height	6.221	1	0.101
						(intercept: 0.548 ± 0.084)
		Plot enrichment	2.013	1	0.154
	Log (Step rate)	Predator within 2km Grass height	0.596 0.618	1 3	0.440 0.893
		Plot enrichment × Predator within 2km 0.009	1	0.925
		Predator within 2km × Grass height	4.836	1	0.180
						(intercept: 0.929 ± 0.110)
		Plot enrichment	0.574	1	0.449
	Log (Bites per	Predator within 2km	0.181	1	0.671
	feeding station)	Grass height	1.601	3	0.659
		Plot enrichment × Predator within 2km 0.013	1	0.910
		Predator within 2km × Grass height	4.797	1	0.187

Table 3 .

 3 Effect of the presence of a GPS-collared predator within the 2km surroundings when comparing focals on days when collared predators had been in the vicinity during the previous 24 hours with observations on days before their arrival on the log-transformed total time spent in vigilance (Total vigilance) and exclusive (high-cost) vigilance of impalas considering the effects of grass height (High, medium, short, short cut). We contrasted 4 classes (days before predators had been in the vicinity, lion only, wild dog only, lion with hyaena) with in italics, classes that were considered as references. Year, Season and Predator event ID were included as nested random factors. β ± SE are indicated for significant variables.

	Dependent variables Predictors	χ²	Df	P	β ± SE (P)
						(intercept: 1.603 ± 0.119)
	Log total vigilance	Predator within 2 km	7.192	2	0.027 See table 4 for multiple comparison
		Grass height	5.245	3	0.157
						(intercept: 0.188 ± 0.122)
	Log exclusive vigilance	Predator within 2 km	7.180	2	0.028 See table 4 for multiple comparison
		Grass height	1.605	3	0.658

Table 4 .

 4 Post-hoc Tukey test on the effect of the presence of GPS-collared predators within 2km, contrasting 4 classes (days before the predators' arrival, lion only, wild dog only vs lion with hyaena) on the log-transformed total time spent in vigilance (Log Total Vigilance) and high-cost vigilance (Log Exclusive Vigilance). The data on hyaenas were too sparse to allow the effect of this species to be analysed alone.

	Contrast	Log(Total vigilance) Β SE	P	Log(Exclusive vigilance) β SE	P
	Lion only -Days before	0.131	0.071	0.070	0.377 0.253	0.138
	Wild dog only -Days before	0.332	0.118	0.005	0.960 0.558	0.046
	Lion with hyaena -Days before	0.476	0.148	0.002	1.023 0.317	0.001
	Wild dog only -Lion only	0.220	0.114	0.041	0.261 0.245	0.288
	Lion with hyaena -Lion only	0.344	0.145	0.018	0.908 0.311	0.004
	Lion with hyaena -Wild dog only	0.144	0.172	0.404	0.647 0.370	0.082

Acknowledgements

This work was funded by the CNRS INEE ("Institut Ecologie et Environnement"); the "Zones Ateliers" network LTSER France; the Agence Nationale de la Recherche (FEAR project ANR-08-BLAN-0022); the CIRAD; the French "Ministère des Affaires Etrangères" and the "Ambassade de France au Zimbabwe".

The Director General of the Zimbabwe Parks and Wildlife Management Authority is acknowledged for providing the opportunity to carry out this research: we are particularly grateful to Dr. H. Madzikanda for his long term support and friendship and our warm thanks also go to Mr. A.

Musakwa, the then Area Manager, for his support. This study is part of the HERD program (Hwange Environmental Research Development), now Hwange LTSER (Zone Atelier Hwange): we would like to thank the whole HERD team including Martin Muzamba, Marion Lombard, Tawanda Tarakini, Gugulethu Ncube, Stéphane Sourice and François-René Favreau for their insight in the fertilisation

parameters and ultimately the foraging costs of vigilance in prey is the frequency of encounters of the prey with the predator. We suggest that this time scale issue merits specific attention in future studies.

Appendix 1

We tested for differences of biomass and proportions of green tissues and bare soil between enriched and control plots, cut and uncut strips controlling for season and year.

In the uncut strips, biomass was on average higher in enriched plots compared to control plots In the cut and uncut strips in 2009, the proportion of green tissues was higher in enriched plots compared to control plots in April (β enriched in cut ± SE = 0.078 ± 0.036, P = 0.032, β enriched in uncut ± SE = 0.131 ± 0.041; P = 0.002) as well as in July 2010 (β enriched in cut ± SE = 0.032 ± 0.014, P = 0.019) while we did not detect any difference in green tissues among the uncut strips (P = 0.456) (Fig S2). The

Appendix 2

Lions are known to live in a fusion-fission society but the frequency of pride fission increases with increase in pride size (Mbizah et al. 2019. Applying the resource dispersion hypothesis to a fission-fusion society: a case study of the African lion (Panthera leo) Ecology and Evolution 9: 9111-9119). In the Main Camp area, where the study site is located, prides are rather small and composed of up to 4 female adults and previous work has revealed that lionesses from the same pride stay together most of the time, with females from a pride sighted together in 89.2% of sightings (Valeix et al. 2009. article in Ecology cited in the manuscript). Therefore, for lions, we can be rather confident that the movements of the collared individuals are quite representative of the movements of almost all lions around the study site (only dispersing individuals were missed). Regarding wild dogs, members from a pack always stay together except during the denning period when some individuals become helpers at the den. So overall, the individuals that have been GPS collared per pack were representative of the movements of all individuals in their pack around the study site. Regarding spotted hyaenas, because clans are characterized by a very high level of fissionfusion, we have to acknowledge that the movements of the collared individuals cannot be considered representative of the members of the monitored clans. Hence, the results about hyaenas must be interpreted with caution, as it is very likely that the movements of uncollared individuals were missed. However, we believe that the effect of undetected hyaenas should mainly reduce our capacity to detect differences.

Appendix 3

Post-hoc Tukey tests on the effect of grass height on bite rate (bites per minute), step rate (steps per minute) and number of bites per step (Log-transformed) over the 2-year period (a) and when comparing focals when equipped predators were present with the days before their arrival (b) .

Contrast