Numerical response of predators to large variations of grassland vole abundance and long‐term community changes

Abstract Voles can reach high densities with multiannual population fluctuations of large amplitude, and they are at the base of predator communities in Northern Eurasia and Northern America. This status places them at the heart of management conflicts wherein crop protection and health concerns are often raised against conservation issues. Here, a 20‐year survey describes the effects of large variations in grassland vole populations on the densities and the daily theoretical food intakes (TFI) of vole predators based on roadside counts. Our results show how the predator community responded to prey variations of large amplitude and how it reorganized with the increase in a dominant predator, here the red fox, which likely negatively impacted hare, European wildcat, and domestic cat populations. This population increase did not lead to an increase in the average number of predators present in the study area, suggesting compensations among resident species due to intraguild predation or competition. Large variations in vole predator number could be clearly attributed to the temporary increase in the populations of mobile birds of prey in response to grassland vole outbreaks. Our study provides empirical support for more timely and better focused actions in wildlife management and vole population control, and it supports an evidence‐based and constructive dialogue about management targets and options between all stakeholders of such socio‐ecosystems.


| INTRODUC TI ON
The relationship between people and rodents is an old one. Early accounts clearly show that rodents were a destructive agent for crops and a source of disease for many ancient and current societies (Huitu et al., 2009;Krebs, 2013;Villette, 2018). Voles can reach high densities with multiannual population fluctuations of large amplitude, and they are often considered as pests in temperate farmland Jacob et al., 2020). However persecuted for this reason (Delibes-Mateos et al., 2011;Jacob et al., 2020), their effects on biodiversity are crucial. They are at the base of food webs maintaining communities of predators in Northern Eurasia and Northern America, as well as modifying nutrient cycling, soil aeration, micro-organism, and plant assemblages (Giraudoux et al., 2019;Nicod et al., 2020). This status places them at the heart of management conflicts where crop protection and health concerns are often raised against conservation issues (Delibes-Mateos et al., 2011). Moreover, poisoning when using chemicals for rodent pest control can depress populations of predators that are able to contribute to the regulation of rodent populations Jacquot et al., 2013). A better understanding of the links between grassland vole population variations and predator responses will allow more timely and better focused management actions for all stakeholders in multifunctional socio-ecosystems.
Predation has been suggested to be one of the main drivers of rodent population fluctuations. Theory predicts that specialist predators that feed on one or a few kinds of prey can destabilize prey populations because they exert delayed and direct density-dependent mortality on their prey populations, while generalist predators, which feed on a wide variety of prey species, have direct density-dependent mortality and therefore stabilize prey populations (Andersson & Erlinge, 1977). However, experimental tests on this prediction (e.g., predator removal) and observational field studies have provided evidence and indications both supporting and rejecting this hypothesis. The approach principles (experimental versus observational) and the space scale at which they were carried out have led to much controversy still going on (Krebs, 2013). However, studies in the Arctic and Fennoscandia on small mammal population cycles have accumulated support for the predation hypothesis (Hanski et al., 2002). For instance, in Northwest Territories, Canada, predation was manipulated using exclosures, and this study demonstrated that predation depresses peak and minimum densities of the collared lemming, Dicrostonyx groenlandicus, and further shapes the population cycle by extending the duration of the decline (Wilson et al., 1999). In the tundra of Greenland, observational studies indicate that the numerical response of the stoat (Mustela erminea) might drive the population dynamics of the collared lemming by a 1-year delay. These dynamics are concurrently stabilized by strongly density-dependent predation of three generalist predators, the arctic fox (Vulpes lagopus), the snowy owl (Bubo scandiacus), and the long-tailed skua (Stercorarius longicaudus) (Gilg et al., 2003(Gilg et al., , 2006.

In boreal areas, experimental studies based on predator removal
have demonstrated that only the reduction of all main predators was sufficient to prevent the summer decline of the field vole, Microtus agrestis, the sibling vole, M. rossiaemeridionalis, and the bank vole, Myodes glareolus (Korpimaki & Norrdahl, 1998). This also increased the autumn density of voles fourfold in the low phase, accelerated the increase twofold, increased the autumn density of voles twofold in the peak phase, and retarded the initiation of decline of the vole cycle (Korpimaki et al., 2002).
Population dynamic patterns of the common vole (Microtus arvalis) in intensive agricultural landscapes of southwest France are largely consistent with five of six patterns that characterize rodent cycles in Fennoscandia and can be explained by the predation hypothesis (Lambin et al., 2006). Hence, it is likely that predation, in combination with other factors, plays a role in regulating small mammal population dynamics also in temperate ecosystems like in boreal and the arctic. However, in such ecosystems the multiplicity of prey resources and the large number of predator species combined with landscape diversity (e.g., the spatial arrangements of optimal and suboptimal habitats for prey and predators) (Lidicker, 1995;Lidicker, 2000) make the disentangling of the detailed processes and the role of each species and factors involved a challenge (Krebs, 2013). For instance, based on a 20-year survey of the effects of an epidemic of sarcoptic mange that decreased fox populations in Scandinavia, Lindström et al. (1994) revealed that red fox (Vulpes vulpes) predation was a crucial factor in conveying the 3-to 4-year fluctuations of voles (both bank and field voles (Myodes glareolus and Microtus agrestis)) to small game, for example, periodically limiting the populations of hare (Lepus europeus), tetraonids (Tetrao urogallus, Tetrao tetrix, Bonasia bonasia), and rowdeer fawns (Capreolus capreolus). The importance of such prey switchings on prey population dynamics has also been reported for a long period in Newfoundland, where lynx (Lynx lynx), prey on snowshoe hares (Lepus americanus), until the hare population crashes. Then, lynx switch to caribou calves (Rangifer tarandus), and the cycle continues (Bergerud, 1983). As a whole, those multiple and complex interactions can hardly be investigated in depth by simple modeling (Baudrot et al., 2016) or by small-scale experiments that cannot technically take into account all the relevant space-time scales and species communities involved in the real world and, thus, be generalized.
However, stakeholders in such systems are often protagonists of endless debates about regulation adoption and management decisions, which each of them advocating the control of one among many possible population targets and subsequent options for management. This debating is the case in the Jura mountains where massive outbreaks of a grassland vole species, the montane water vole, Arvicola amphibius (formerly A. terrestris (Chevret et al., 2020)), occur with 5-to 6-year cycles and population densities exceeding 500-1,000 ind.ha −1 . High-density peaks propagate over grasslands under the form of a traveling wave (Berthier et al., 2014;Giraudoux, 1997).
In the same area, outbreaks of the common vole (>1,000 ind.ha −1 ), another grassland vole, also occur; however, they are noncyclic in this area (Giraudoux et al., 2019). Previous studies have shown that the population dynamics of the two species are shaped by landscape features, with hedgerow networks and wood patches dampening the population dynamics and by contrast open grassland landscapes amplifying the outbreaks (Delattre et al., 1996;Duhamel et al., 2000;Foltête et al., 2016;Foltête & Giraudoux, 2012;Giraudoux et al., 1997;Morilhat et al., 2008). Those outbreaks provide regularly massive quantities (up to >80 kg.ha −1 ) of prey for many species of carnivorous mammals and birds in grassland and by contrast low densities of secondary prey resources that are less accessible (vegetation and/or antipredation behavior) such as forest, marsh and fallow small mammals (maximum about 3 kg.ha −1 ) (e.g., bank vole, wood mice, Apodemus sp., field vole, etc.), with periodic (5-6 years) concomitant low densities in every habitats.
The variation in this predator community structure over the time span of large fluctuations of prey abundance has not been documented yet in this system, limiting both comparisons with ecosystems described in other part of the world where small mammal outbreaks occur (Jacob et al., 2020) or with more simple food webs of northern ecosystems. Moreover, a large-scale inadvertent experiment was offered by chemical control of vole populations in the 1990s, leading to a dramatic decrease in the fox population due to secondary poisoning, and its gradual recovery the following years after a shift in vole control practices (Jacquot et al., 2013).
The aim of this 20-year study is to describe the effects of large variations of grassland vole populations on their predator communities and of the long-term increase in the fox population in such system. The aims were to (a) describe how a predator community responds to prey variations of large amplitude, (b) describe how this community reorganizes over the long term with increases in a dominant predator, here the red fox, (c) attempt to quantify the prey consumption of this predator community.

| Study area
The study was carried out around the Pissenavache hamlet (46.95°N, 6.29°E) in Franche-Comté, France, in an area of 3,425 ha (2,646 ha of farmland, 1,094 ha of forest, 167 ha of buildings), at an average altitude of 850-900 m above sea level (Figures 1 and 2). There, 100% of the farmland was permanent grassland used for pasture and (high grass) meadow for cattle feeding in winter (minimum of 5 months, November-March), with a productivity ranging from 5 to 6.5 tons of dry matter.ha −1 .year −1 under the specifications of the European Protected Geographical Indication of the locally produced Comté cheese. A KML file with the bounding box of the study area is provided with the data.

| Roadside counts
Predator and hare (Lepus europeus) populations have been monitored from June 1999 to September 2018 (20 years) using night and day roadside counts. Each sampling event consisted of driving a car with 4 people (the driver, a data recorder, and two observers) along a fixed track at less than 20 km/h. The length of the track was 18.6 km from 1999 to 2009 and then 19.6 km due to a slight variation in the itinerary (trail blocked by mud, see Figure 1). Observations were performed using 100-W spotlights at night and binoculars for species identification. Distinction between domestic cats (Felis silvestris catus) and European wildcats (Felis silvestris silvestris) was made visually considering phenotypic criteria (relative to pelage and morphology) with-

| Daily food intake
Theoretical daily food intakes (TFI) per predator species were computed following Crocker et al.'s method (2002) with small mammals considered as prey. The average body mass of predators, when missing in (Crocker et al., 2002), was estimated based on the Encyclopédie des carnivores de France (Artois et al., 2001;Henri et al., 1988;Le et al., 1989;Stahl et al., 1992), the Handbook of Birds of Europe, the Middle East and North Africa (Cramp, 1994), and the Encyclopedia of Life (https://eol.org).

| Transects
Small mammal (A. amphibius, M. arvalis, and Talpa europea) relative abundance was assessed using a transect method adapted from (Delattre et al., 1990;Giraudoux et al., 1995;Quéré et al., 2000); a 5-m-wide transect across the study area was divided into 10-m-long intervals and the proportion of intervals positive for fresh indices (tumuli, molehill, runway, feces, cut grass in holes) was considered an index of abundance. The total transect length was 11.6 km

| A. amphibius communal scores
To obtain abundance assessments on a larger space-time scale, abundance was also assessed at the commune-scale by technicians of the FREDON of Bourgogne Franche-Comté (a technical organization for plant pest prevention and control contracted by the Ministry of Agriculture (Légifrance, 2014), in the 7 communes crossed by the roadside count itinerary (Figure 1). Assessments were made in autumn since 1989. The FREDON assessment uses a ranking system that ranges from 0 to 5:0-no A. amphibius sign in any parcel within the commune; 1-low or no A. amphibius tumuli, voles and moles (T. europea) cohabiting the same tunnel systems; 2-A. amphibius tumuli present in some parcels within the commune and mole burrow systems still present in some parcels; 3-A. amphibius tumuli present in some parcels within the commune, few, or no mole burrow systems present in the commune; 4-A. amphibius colonies established in the majority of meadows and within pastures; 5-all of the commune colonized by A. amphibius. The FREDON index not directly translates to transect-based indices, partly because it is applied at the commune-scale and not the parcel scale, but Giraudoux F I G U R E 2 General views of the study area. Top, from the roadside count road at P1 (see Figure 1); bottom, from P2 with the Pissenavache hamlet, a segment of the roadside count road can be seen in the background (photos PG, 20/02/2020) et al. (1995) found that levels 0-1 correspond to densities < 100 voles.ha −1 , level 2 to 100-200 voles.ha −1 , and levels 3-5 to >200 voles.ha −1 . For a given year, the median score of the 7 communes was taken as a score of abundance.

| Grassland prey resource relative abundance
The dynamics of prey resource abundance in grassland have been estimated (a) over the time span when transects were carried out, summing the relative abundance of A. amphibius and M. arvalis divided by four, divided by the maximum of this sum over the series and (b) before this time span, when no transect was present, by dividing the FREDON score by the highest score recorded during the study . This process took into account that the M. arvalis body mass is four times smaller than A. amphibius's on average (Quéré & Le Louarn, 2011) and helped to better visualize grassland rodent populations variation on the same scale and fill the gap when transect data were lacking. The amplitude of the high-density phase is biased to an unknown extent with this method (e.g., arbitrarily summing weighted relative abundances, chained with standardized FREDON scores), but not the time locations of the low-density phases. Thus, the alternation between high-density and low-density phases, which are always very large (ranging from 0 to 1,000 voles.ha −1 ), was robustly and correctly represented over the time series as an abundance index, in the best possible way given the data, for further comparisons.

| Rodenticide use
In France, bromadiolone, an anticoagulant rodenticide, has been used to control water vole populations since the 1980s, with deleterious effects on nontarget wildlife including vole predators . In the early 2000s, the development of an integrated pest management (IPM) approach  led to a dramatic decrease in the quantity of bromadiolone applied by farmers and their nonintentional effects Jacquot et al., 2013). By law, the delivery of bromadiolone baits for vole control to farmers is under strict FREDON supervision and compulsory usage declaration to ensure traceability (Legifrance, 2014). Data on bromadiolone quantities used in the 7 communes of the study area were provided by the FREDON of Bourgogne Franche-Comté.
Grassland small mammal abundance. The standard errors of small mammal relative abundances assessed from transects were computed across 1,000 bootstrap replicates (Efron & Tibshirani, 1994).
The grassland prey resource index corresponding to each roadside count was linearly interpolated over time between the two bracketing abundance index estimates.
Response of predators to prey abundance. We used generalized linear models with a Poisson error distribution of the form: n = a 0 + a 1 ln(x 1 ) + a 2 x 2 + a 3 x 3 + a 4 x 4 + ε, with n, the number of observations of a given species, x 1 , the length of the itinerary, x 2 , the time, x 3 , the season, x 4 , the prey abundance index, a i, the model coefficients, and ε, the residuals. The linear trend on time was not kept if not found statistically significant. Interactions between seasons and prey abundance had been preliminarily explored but were not statistically significant. To avoid overestimation of the degrees of freedom from time series data (here irregular and intrinsically autocorrelated), statistical inference was computed using permutation tests.
Predator and hare spatial distribution. The shortest distance of observations to the roadside count itinerary, to the nearest forest, and to the nearest building was computed (Bivand et al., 2019a(Bivand et al., , 2019b and their distribution examined. To test whether the proximity of some habitats might explain the observed distributions and their variations, the mean distance to forest and buildings was compared to the mean distances obtained from 1,000 simulations of the same number of random positions as the number of observations in the strip observed along the itinerary. Predator and hare population density estimates. To obtain density estimates, the distance to the itinerary data was analyzed using conventional distance sampling with a truncation distance (Buckland et al., 2001(Buckland et al., , 2015Thomas et al., 2010) including 90% of the observations for each species at the minimum. As avoidance behavior along the road was detected for most species, we used hazard-rate detection functions fitted to the data. This function type has a more pronounced shoulder that compensates for the bias due to avoidance (Thomas et al., 2010). Models with a seasonal effect as a covariate were compared with concurrent models with no covariate using the Akaike index criterion (Burnham & Anderson, 2002). periods could be identified (1999, 2007, 2010-2011, 2014 and 2017) alternating with four populations peaks reaching thousands of voles. ha −1 in our area (Figure 3c). F I G U R E 3 Small mammal population dynamics. Numbers with arrows indicate high-density peaks in the communes including the study area; a, dotted gray line,A. amphibiusFREDON scores; red line and red scale, quantity of bromadiolone (g) applied forA. amphibiuscontrol in the communes of the study; (b) abundance index based on transects, vertical bars are 95% confidence intervals (gray scale and dotted line are related to the A. amphibius FREDON scores for comparison); (c) estimated variations of the grassland prey resource, the rug on thex-axis represents roadside count events F I G U R E 4 Day roadside counts. Black circles at the bar top identify autumn counts. The gray line in the background shows the variations of grassland prey abundance (the scale is the same in every plot). The letters above identify the sessions available and selected to estimate densities based on distance sampling during high (^) or low (o) abundance period 3.2 | Numerical responses to grassland prey variation, and hare relative abundance

| Time variations
Twenty-seven species for the day roadside counts and 24 for the night were observed, corresponding to 19,010 and 7,355 individual observations, respectively, and to 58 sessions for each count type (≈348 night or day counts in total). Among them, the following species were both observed frequently enough over time and considered of interest for this study: for day roadside counts, the carrion crow (Corvus corone), the common buzzard (Buteo buteo), the red kite (Milvus milvus), the kestrel (Falco tinnunculus), the domestic cat  For instance, common buzzard KAI was highly significantly correlated to grassland prey index, with KAI 2.2 times higher in autumn than that in spring. In spring, during the breeding season, KAI was 4.3 times larger in the peak phase than that in the low-density phase of grassland vole populations. Red kite's correlation p-value was equal to and kestrel's above but not far from the critical threshold generally accepted of p(H o ) ≤ .05. This lack of significance for the kestrel held from one outlier, when prey estimates were derived from the FREDON scores on a communal scale only. Dropping this observation from the data set would lead to reject H o at p = .02 and to conclude formally on a correlation between the number of observations of this species and grassland prey abundance. Figure 6 shows the dynamics of nocturnal species. We did not detect statistically significant correlation between red fox, badger, and long-eared owl abundance and grassland prey index and seasons. Domestic cat did not correlate to grassland prey index but to seasons, with lower counts in winter. Hare and wildcat KAIs were significantly correlated to grassland prey index but seasonal variations could not be detected (Table 1 and Figure 7). Fox and hare KAIs were highly and negatively correlated to each other (p < .001). Furthermore, a model of hare abundance as response variable including grassland prey index and fox KAI as independent variables showed that controlling for grassland prey, hare abundance did not significantly correlate to fox KAI at a probability ≤ 0.05 (however with an observed p-value of .07).
Red fox and badger showed significantly higher abundance in average in the last half of the time series, and hare, wild and domestic cat, long-eared owl, and hen harrier significantly lower (one-tailed permutation tests on mean, p < .001) (Figures 4 and 6).

| Spatial variations
Observations were truncated at a distance of 300 m and 350 m from the track for night and day roadside counts, respectively, accounting for 92% and 93% of their total number. Among all species in the open grassland strip along the itinerary, only the common buzzard with regard to forest and buildings, and the red fox with regard to buildings were randomly distributed. Carrion crow, red kite, kestrel, and hare were observed at a greater distance to forest than expected from a random distribution; hen harrier, red fox, wildcat, long-eared owl, badger at a smaller distance; wildcat, long-eared owl, and badger at a  Table A2 for details).
Seventy-five percent of the observations of domestic cat were made at less than 500 m of buildings by night and at less than 250 m by day (Figure 8). No change in any of those patterns was observed between the first and the second half of the time series.
F I G U R E 6 Night roadside counts. Black circles at the bar top identify autumn counts. The gray line in the background shows the variations of grassland prey abundance (the scale is the same in every plot). The letters above identify the sessions available and selected to estimate densities based on distance sampling during high (^) or low (o) abundance period

| Predator population density variations and daily food intake
Comparing detection models with 'season' as covariate with models with no covariates led us to reject the hypothesis of a seasonal effect on the detection function for every species (detection functions are presented in Figures A1 and A2). Based on the visual examination of KAI dynamics, for each species, we identified periods when the indices could be considered similarly high or similarly low with regard to the amplitude of variations and categorize them as subsamples of 'low' or 'high' densities (see Figures 4 and 6). Table 2 shows conversion coefficients from KAI to densities, presents the maximum density values observed, and summarizes the estimations obtained using distance sampling by density categories ('low' or 'high'). Considering the relative aggregation of the domestic cat close to buildings, we provide one density estimate for the entire study area, and another for a buffer of 300 m (night) or 250 m (day) around buildings. (3.8-4.2) kg.km −2 .day −1 . The largest predator densities were reached during the high-density peaks of grassland vole populations, with a maximum observed in autumn 2008, with 60 ind.km −2 (carrion crow making 48% of this total) and a daily TFI of 10.7 kg.km −2 .day −1 (39.3% from carrion crow).  Table 3 also shows that the TFI ranged from 1.5 to 2.7 kg.km −2 .day −1 in the low-density phases and from 6.9 to 10.7 kg.km −2 .day −1 in the high-density peaks. Thus, the TFI was multiplied by 7.1 at the maximum, while the grassland small mammal population biomass was multiplied by thousands.

| Response to grassland vole population variations
Among the 11 species monitored, 4 (maybe 5, if the kestrel is in-  (Leclercq et al., 1997). This response was interpreted as being the result of predation switches during the decline phase of the voles, with a supposed relaxation of the predation pressure on the capercaillie during the high-density peak, that is well documented, for example, in Scandinavian ecosystems (Angelstam et al., 1985;Lindström et al., 1994;Marcström et al., 1988).
The variations in the populations of other species were independent of the grassland vole populations over the study time span. ticide, here bromadiolone, is known for its deleterious side effects on vole predators , with a canid sensitivity that is more than 3 times higher than that of felids (Erickson & Urban, 2004). This effect has been proven to have drastically decreased the fox population in the area at the end of the 1990s (Raoul et al., 2003) until the beginning of our study. This difference in sensitivity might explain simultaneously relatively large cat populations due to extremely limited effects of poisoning.

| Long-term changes in the predator community structure
Furthermore, Jacquot et al. (2013) have shown how the fox population has recovered on a regional scale after the change in rodent control practices. In our study, the predator community shifted from a very low fox density of 0.1 ind.km −2 (CI 95% 0.01-0.3) foraging in grassland up to a much larger fox abundance of 2.6 ind.km −2 (CI 95% 2.2-3.2), with a peak at 4.9 ind.km −2 in autumn 2012 (followed by a stabilization or a slight decrease with an epidemic of sarcoptic mange, which is still ongoing). This value is one of the highest population densities reported in rural landscapes of Europe (Demirbaş, 2015;Ruette et al., 2015). This increase was concomitant with a sudden and dramatic decrease in the hare population during a low-density phase of the vole populations, and TA B L E 2 Comparison of density estimates (n.km −2 ) derived from all species data and distance sampling Note: Lower and upper densities correspond to estimations during low-or high-density period (see Figures 4 and 6).
with a decrease in wild and domestic cats. This result strongly suggests that those declines might be the consequences of the increase in the fox population, possibly by direct predation or by creating a 'landscape of fear' (Bleicher, 2017;Laundre et al., 2010), thus limiting the distribution of the prey species to shelter areas where they could not be detected by roadside counts (houses, forest, etc), or both. In Australia, fox removal experiments showed in one study that cats foraged more in open habitats where foxes were removed (Molsher et al., 2017) and in two others that they were more abundant (Marlow et al., 2015;Read & Bowen, 2001).
Furthermore, in western Poland, the hare population during the same year had 1.7 times higher density in response to fox removal (Panek et al., 2006), and responded positively to sarcoptic mange epidemics that depressed the fox population in Scandinavia (Lindström et al., 1994). We did not observe changes in the spatial distribution of species between the first and second half of the study, making the 'landscape of fear' hypothesis less likely herein, thus suggesting a major role for direct predation.

F I G U R E 9
Variations in densities for each species (n.km −2 ). Variations in biomass (kg.km −2 ) and theoretical daily food intake (kg.km −2 . day −1 ) are presented in Figures A3andA4 However, the long-term increase in the European badger population since the rabies vaccination in the early 1980s has been well documented in Europe (Holmala & Kauhala, 2006;Macdonald & Newman, 2002;Sobrino et al., 2009). In our study, the sudden increase since summer 2013 remains unexplained.
Excluding the stability of the carrion crow population in large numbers, a striking feature of our system is the change in predator community structure over the study period. In the early led to least weasel density increase (Norrdahl & Korpimaki, 1995).
In our study, the lack of data regarding Mustela sp. and Martes sp.
does not permit us to determine whether those compensations observed in a community subset extend to the whole community of vole predators. TA B L E 3 Density (ind.km −2 ) and theoretical daily food intake, TFI (kg.km −2 .day −1 ) in the low (LD)-and high (HD)-density phases of grassland vole populations. Numbers between parentheses are percentages Total without crow 1.8 5.5 1.5 6.5 2.7 5.8 2.8

| Food consumption by predators
This is the first study, to our knowledge, to provide data on the vari-

| Dietary issues
The carrion crow is mostly opportunistic and feeds principally on invertebrates, cereal grain but also small vertebrates, bird eggs, and carrion, in various proportions according to the place and season. At the extreme, vertebrates and eggs in particular can reach 86.6% of the dry weight of pellets in winter, for example, in southern Spain, and they are often observed to cooperate when killing small vertebrates in pairs or small groups, also commonly forcing other birds including raptors to drop prey (Cramp, 1994). Their behavior has not been systematically studied in our area, and the importance of small mammals in the diet is not yet known; however, all the behaviors mentioned above, including scavenging on dead animals, hunting voles, and forcing raptors, have been occasionally observed (Montaz et al., 2014). Thus, one can hardly infer conclusions about the impact of such an opportunistic species in this ecosystem, for example, on vole regulation. Mechanically, however, their number might have a chronic impact on species that are vulnerable to predation such as small game and bird nests.
The other species are more specialized toward small mammal prey. The detailed diet of the domestic cat is unknown in our area.
However, in a similarly rural area of the Ardennes, rodents made up 55.9% of the dietary items found in 267 domestic cat feces (6% birds, 36.7% human-linked food), with little difference between outdoor cats (owned by people other than farmers) and farm cats (Forin-Wiart, 2014). Rodents (Murids and Cricetids) constitute the main prey of wildcats, and they can account for 97% of the diet composition (Condé et al., 1972), while lagomorphs and birds generally appear as alternative prey. However, when the availability of lagomorphs increases, wildcats can substantially shift their diet toward them (Malo et al., 2004).
In the area, the dietary response of the red fox to variations of grassland vole relative densities differed between M. arvalis (no response) and A. amphibius (Holling's type III-like) .
M. arvalis could make up to 60% of prey items in feces even at very low densities (range from 0%-80% of prey items over the whole range of vole densities), and A. amphibius showed a sigmoid increase that quickly reached a plateau (at 15% of the positive intervals of a transect -see material and methods) where it made up 40% of the dietary items on average (range from 0%-80% of prey items). The description of the dietary response in this context where the two main prey abundances varied among several other alternative food resources is quite complex (Bernard et al., 2010;Dupuy et al., 2009;Giraudoux, 1991;Weber & Aubry, 1993). Comparisons of multispecies functional response (MSFR) models with empirical data on the red fox and barn owl showed that switching between prey depends on the proportion of the prey available among other prey (frequency dependence), as commonly thought, but also on the total amount of prey (density dependence), with a nonlinear frequency and density-dependent interactions (Baudrot et al., 2016).

| Predation and vole population abundance
In our study area, the population of the main prey species varied between 0 and approximately 1,000 ind.ha −1 on a scale of tens of km 2 (Berthier et al., 2014;Giraudoux et al., 1997) and an amplitude 5-100 times larger than those observed on a similar scale in different areas worldwide (Dupuy et al., 2009;Erlinge, 1983;Gilg et al., 2006;Lambin et al., 2000). A similar amplitude has been reported locally for M. arvalis in alfalfa semi-permanent plots of some ha in an intensive agriculture matrix of plowed fields of western France (50-1,500 ind.ha −1 ) (Pinot et al., 2016). In our study area, in grassland, to a large number of predator species, but the TFI was multiplied by 7.1 at its maximum, while the grassland small mammal population biomass was multiplied by thousands. Although we have been unable to monitor mustelids and some species of owls such as the barn owl, Tyto alba (but see (Bernard et al., 2010)) and the tawny owl, Strix aluco, these numbers prompt the question of the magnitude of the impact of this subset of the predator community on the vole population declines.
Furthermore, our study documented that domestic cat populations could reach much higher densities of 2.4-9.1 ind.km −2 up to more than 18 ind.km −2 around villages within a 250-500 m radius, except during winter nights when they likely prefer to stay warmly at home. This can cause spatial heterogeneity in predation pressure.
For instance, during small mammal low-density phases, their proportion varied between 5.9% (autumn 2010) and 23.4% (spring 2007) of the total number of predators counted. In south-central Sweden, Hansson (1988) observed that domestic cats, supplied with continuous alternate food, were able to dampen the population fluctuations of the field vole, compared to more or less cat-free areas. In villages at some kilometers from our study area, Delattre et al. (1996Delattre et al. ( , 1999 reported

| CON CLUS ION
Overall, our results indicate that in such ecosystem with large variations of grassland prey, the structure of the predator community can change over the long term without changing its overall TFI variation pattern over a rodent cycle. Although the role of small and medium mustelid populations remains unknown, the higher predator densities observed during the grassland rodent peak were mostly due to mobile birds of prey that followed the rodent population increase. In such a system, the carrion crow was numerically the largest population with the largest TFI, but its impacts on the ecosystem could not be clearly assessed due to its eclectic diet. After a shift in rodent control practices and a much more moderate usage of anticoagulant rodenticides, the red fox population recovered and then stabilized at much larger densities, which likely negatively impacted hare, wildcat, and domestic cat populations. The domestic cat population was aggregated close to buildings, with a 400 m buffer where the vole population was generally lower.
From an applied viewpoint, in such a highly productive and connective grassland system favorable to grassland voles, it is believed that any means aiming at increasing the populations of predators during the low-density phase (e.g., hedgerow networks, roosts, cats around villages, etc.) should lead to better control of grassland small mammal populations (slowing down the increase phase) (Paz et al., 2013). However, the impacts of a management with large densities of cats around human settlements on other wildlife (Loss et al., 2013;Woods et al., 2003) and pathogen organ-

CO N FLI C T O F I NTE R E S T S
The authors declare to have no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data are available as a zip file at https://doi.org/10.5061/dryad. qz612 jmd3. It includes: S1 kml file. Location of the study area (can be dropped in a Google Earth window or read from a GIS). S2 Excel file. Road-side counts (sheet 1) and list of species observed (sheet 2).

TA B L E A 1 (Continued)
TA B L E A 2 Mean distance (in meters) of observations to forest and buildings; random locations is the mean distance obtained from 1,000 random replicates of the same number of geographical coordinates as the observations in the observation strip; the permutation test being one-tailed, p(Ho) is the number of random mean distance equal or above, or equal or below, the observed mean distance, divided by 1,000