Henri Boutin
email: boutin@lam.jussieu.fr

John Smith

Joe Wolfe

Trombone lip mechanics with inertive and compliant loads ('lipping up and down') Running title: Trombone lip mechanics: 'lipping up/down'

Keywords: work, trombone, lip valve, inertive, compliant, lipping, phase, impedance, sweeping flow

Trombonists normally play at a frequency slightly above a bore resonance. However, they can 'lip up and down' to frequencies further above the resonance (more compliant load) and below (inertive load). This was studied by determining the pressures, flows and acoustic impedance upstream and downstream and by analyzing high speed video of the lips. The range of lipping up and down is roughly symmetrical about the peak in bore impedance, rather than about the normal playing frequency. The acoustic flow into the instrument bore has two components; the flow through the lip aperture and the sweeping flow caused by the moving lips. Variations in the phases of each of these two components with respect to the mouthpiece pressure allow playing regimes loaded by bore impedances varying from compliant to inertive. In a simple model, this sweeping motion also allows the pressure difference across the lips to do work on the lips around a cycle. Its magnitude is typically about 20 times smaller than the work input to the instrument but of the same order as the maximum kinetic energy of the lips. In some cases, this sweeping work may therefore contribute most or all of the energy required for auto-oscillation. [200 words, limit 200]

I. INTRODUCTION

In models of lip oscillation for playing brass (lip-valve) instruments, the phase and magnitude of the acoustic impedance that loads the lips on the downstream side are important, and primarily determine the playing pitch. However, players of brass instruments can 'lip up' and 'lip down': in other words, they can adjust their lips and other playing parameters so as to shift the pitch significantly up or down without changing the configuration of the instrument.

An understanding of how this is done requires knowledge of how the motion of the lips, the flow into the instrument and the pressures up-and downstream vary when lipping up and down. Measurements of these parameters form the basis of this paper. They are then used, in ! 2

conjunction with a simple model, to show how the observed motion can provide the energy for auto-oscillation for both compliant and inertive loads.

The motion of the lips of players of lip-valve instruments has been studied by stroboscopy and high-speed video (e.g. [START_REF] Martin | Lip vibrations in a cornet mouthpiece[END_REF][START_REF] Copley | A stroboscopic study of lip vibrations in trombone[END_REF]Yoshikawa and Muto, 2003;[START_REF] Tarnopolsky | Vocal tract resonances and the sound of the Australian didjeridu (yidaki) I: Experiment[END_REF][START_REF] Newton | Mechanical response measurements of real and artificial brass players lips[END_REF][START_REF] Bromage | Open areas of vibrating lips in trombone playing[END_REF] and hardware lip models (e.g. [START_REF] Gilbert | Artificial buzzing lips and brass instruments: Experimental results[END_REF][START_REF] Cullen | Brass instruments: linear stability analysis and experiments with an artificial mouth[END_REF]. The steady pressure in the player's mouth (upstream) has been related to the downstream acoustic pressure in the instrument [START_REF] Bouhuys | Pressure-flow events during wind instrument playing[END_REF][START_REF] Elliott | Regeneration in brass wind instruments[END_REF][START_REF] Yoshikawa | Acoustical behavior of brass player's lips[END_REF][START_REF] Fletcher | Blowing pressure, power, and spectrum in trumpet playing[END_REF]. The acoustic impedance in the player's mouth has been measured

during playing [START_REF] Tarnopolsky | The vocal tract and the sound of a didgeridoo[END_REF][START_REF] Chen | Do trumpet players tune resonances of the vocal tract?[END_REF]. The acoustic pressures have been measured up-and downstream simultaneously [START_REF] Fréour | Acoustical interaction between vibrating lips, downstream air column, and upstream airways in trombone performance[END_REF]. In a previous paper [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF], we have related lip motion to the up-and downstream impedance spectra, the acoustic and steady pressures and to the flow into the instrument, for playing at normal pitch.

Brass instruments are normally played at frequencies that slightly exceed those of the bore resonances and so the bore impedance ! is compliant: the phase of the flow into the instrument leads that of the pressure in the mouthpiece. This phase is an important constraint in models of self-oscillating valves (e.g. [START_REF] Elliott | Regeneration in brass wind instruments[END_REF][START_REF] Fletcher | Autonomous vibration of simple pressure-controlled valves in gas flows[END_REF]. It is known, however, that the lipping up and down of brass instruments covers a range above and below the peak of ! that lies near the playing pitch [START_REF] Yoshikawa | Acoustical behavior of brass player's lips[END_REF][START_REF] Chen | Nature of the lip reed[END_REF][START_REF] Campbell | Nonlinear dynamics of musical reed and brass wind instruments[END_REF][START_REF] Eveno | The Relationship Between Bore Resonance Frequencies and Playing Frequencies in Trumpets[END_REF]. Consequently, it is interesting to investigate the correlations among lip motion, up-and downstream pressure and flow for notes with either compliant or inertive loads. It is also interesting to know how the range of

Z mouth Z bore Z bore ! 3
lipping up and down is distributed with respect to the frequency of the resonance that sustains the fundamental of a particular note.

In this paper the acoustic impedance upstream and the pressures up-and downstream are measured during playing and related to the flow into the instrument. Analysis of the motion of the lips then allows two components of the acoustic flow to be identified; the aperture flow through the lip aperture and the sweeping flow produced by the lips as they move into and out from the mouthpiece. This is done for normal playing and for lipping up and lipping down, covering a range in which the phase of the bore impedance changes sign and the magnitude changes considerably. These results are discussed in relation to a simple model for the lip motion that quantifies the energy input to auto-oscillation by the sweeping motion over the range of lipping up and down.

II. MATERIALS AND METHODS

A. The instrument.

The trombone (Yamaha YBL 321) and mouthpiece are those used in an earlier study [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF] with the B♭-F 'trigger' in the shorter configuration and the main slide all the way in. (This is called first position by trombonists, and used to play notes in a harmonic series, including the note B ♭2, nominally 116.5 Hz, but which was 'lipped' to frequencies in the range 100 Hz to 125 Hz in this study). The tuning slide was always 18 mm from its shortest position (a typical position for playing at A440).

The original mouthpiece was replaced by a transparent one having the same volume and a similar rim. A shank with the same shape was inserted on the side, rather than the axis of the mouthpiece, so that the lips were visible from in front and from the side through plane glass plates. The previous study showed the pressure throughout the mouthpiece to be ! 4

uniform to a good approximation, so a single pressure transducer (8507C-2, Endevco, CA, USA) measured the mouthpiece pressure near the rim.

B. The trombone input impedance

The input impedance of the trombone bore, was measured using an impedance head mounted in a plane plate that was sealed to the rim of the modified mouthpiece [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF]. An acoustic current source [START_REF] Smith | The acoustic impedance of the Boehm flute: Standard and some non-standard fingerings[END_REF] Measurements were conducted in a lab at temperature of 26.3 ± 0.3 °C and 55 ± 6% relative humidity.

The frequency and magnitudes of the peaks in impedance of the instrument depend on the temperature and composition of the air in the instrument bore. To determine their behavior during playing, the input impedance of the instrument was measured as soon as possible (within 3 s) after the instrument, initially at ambient temperature and flushed with dry air, had played a sustained note for 10 seconds. The impedance head was then connected and impedance measurements started. Each impedance measurement comprised 32 contiguous cycles of the measurement signal, each cycle involving 2 16 samples at the sampling frequency of 44.1 kHz and consequently lasting 1.49 s. The frequency and magnitude of each impedance peak were then calculated for each cycle. The values at the moment when playing ceased (i.e.

3 s before the first cycle of measurement) were determined by linear regression over the following 32 cycles during the measurement period. These were used for the precise

Z bore ( f ), ! 5

C. Measurement of lip motion

The axis of the mouthpiece is horizontal, perpendicular to the face, and defined as the direction; the y direction is also horizontal along the bore of the trombone and at right angles to x. The z direction is vertical, as shown in Fig. 1. A high-speed video camera (X-stream VISION TM XS-4 with Nikon Nikkor 35 mm f1.4 lens) is used to record (x, z) images directly through the window from the side of the lips and (y, z) images opposite the lips via a mirror parallel to and at to . Image acquisition is triggered by input from a pulse generator

Z bore -45 ° x z -45 ° x ! 6
at 11025 frames per second. The exposure time is 62 µs and the maximum length of each movie is 0.2 s.

For experiments, the player started playing a note at normal pitch and then either lipped up, lipped down or maintained the pitch. When satisfied with the stability of the playing frequency, typically after a few seconds, the player pushed a switch to start recording of images. The camera generated a square pulse corresponding to the acquisition of each frame;

this signal was digitally recorded along with the pressure transducer outputs, which allowed the synchronization of images with the measurements of up-and down-stream pressures.

D. The impedance in the mouth and the up and downstream pressures , the impedance in the player's mouth, was measured during playing as described previously [START_REF] Tarnopolsky | The vocal tract and the sound of a didgeridoo[END_REF][START_REF] Chen | Do trumpet players tune resonances of the vocal tract?[END_REF]. Two small parallel cylindrical ducts were glued together to make an impedance head with an oval cross section 4.8 mm 7.8 mm. This was positioned to pass between the lips at the corner of the mouth (see Fig. 1).

Players were asked to position the measurement end of the impedance head at the center of the mouth, between their upper and lower teeth. Players reported no difficulty in playing B ♭2, lipping up and down while doing this. This arrangement locates the impedance measurement close behind the lips. One of the ducts was used to inject the current source and the other led to a pressure transducer (8507C-2, Endevco, CA). The current source is the sum of sine waves from 50 to 1000 Hz with spacing 0.67 Hz. This impedance head is calibrated using an acoustically infinite duct, having diameter 26 mm and length 194 m [START_REF] Dickens | Improved precision in acoustic impedance measurements by using calibration loads without resonances[END_REF].

The acoustic pressure in the mouthpiece and that in the mouth measured by the pressure transducers in those locations were also recorded digitally. The mouth pressure signal was electronically modulated so that information on its slowly varying or DC component was not

Z mouth × ! 7
removed by the high-pass filtering in the audio interface. This signal was later demodulated during signal processing.

E. The players

Seven players participated in the experiment: four (called advanced players) had more than six years of experience in bands and orchestra. Of the other three (called beginners): two had orchestral and band experience on brass but had not played for several years. The last is the first author, who started playing the trombone for the purposes of this research project, 3 years before the measurements presented in this paper.

They were asked to play for as long as was necessary to become comfortable and to familiarise themselves with the apparatus. Then they were asked to play at normal pitch, for several repetitions. They were then asked to play a sharp, stable note (lipping up), raising the pitch as far as they could while sustaining a stable note, without 'jumping' to the next resonance. Then they played flat (lipping down) at different pitches. Between each set, the instrument was dried with compressed air at laboratory temperature.

F. Acoustic and steady flows and components

The flow into the bore of the instrument is the sum of two components; one is the flow through the lip aperture the other is the sweeping flow produced by the motion of the lips, i.e. The acoustic flow into the bore, , is calculated by dividing the spectrum of the

U bore U ap , U sw U bore U ap + U sw Ūap u ap U sw Ūsw U bore = Ūbore + u bore Ūap + u ap + u sw u bore ! 8
mouthpiece pressure by the bore impedance spectrum measured in the mouthpiece under playing conditions (both quantities complex), a technique described previously by [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF] To calculate the sweeping flow , the vertical cross-sectional area A of the lips inside the mouthpiece cup is calculated from the side view of each video image. The volume V is then given by V = A L, where L is the effective width of the lips (assumed constant) in the horizontal (y) direction. (There are some similarities to the sweeping flow due to the motion of a reed [START_REF] Dalmont | Some aspects of tuning and clean intonation in reed instruments[END_REF].)

During the phase when the lips are closed, there can be no aperture flow ( ) and then = -see eqn 1. Consequently, it is possible to determine the effective lip width L and the value of , neither of which were measured directly. This involved a linear least-squares fit between the waveforms of (= and during the period when the lips are closed. (The average value of L was 13 mm which is 0.56 times the inner width of the mouthpiece). The acoustic aperture flow (the component of the acoustic flow passing between the lips) is simply the difference between and .

G. Longitudinal sweeping flow

According to a simple model discussed later, the work done on the lips by , the pressure difference across the lips, depends on the longitudinal sweeping flow, i.e. the component of sweeping flow in the x direction. The displacement of the inner surface of the lips is not available, so the calculations of longitudinal sweeping flow must be regarded only as estimates. The upper and lower edges of the aperture and are used in a definition of the effective upper and lower heights of the aperture with respect to the position of the aperture at the first frame of lip opening: these are given by . The component of volume

p bore Z bore u sw U ap = 0 U bore u sw Ūbore u sw L d A /dt) U bore ( = Ūbore + u bore ) u ap u bore u sw PV ∆ P z upper( y, t ) z lower( y, t ) z = 0 z top (t) = ∫ z upper( y, t ) d y/L and z bottom (t) = ∫ z lower( y, t ) d y/L ! 9
displaced by the lips in the x or longitudinal direction during is then

(2)

where the upper and lower limits are the top and bottom of the image. Then, the longitudinal sweeping flow is defined as .

III. RESULTS AND DISCUSSION

A. Up-and downstream impedance, pressure and flow

The acoustic pressure difference across the lips is given by , where is the acoustic flow out of the mouth and into the bore and where and are the acoustic pressures and impedances measured in the mouth and mouthpiece (subscripts mouth and bore) (Elliot and Bowsher, 1982;Benade, 1985). The magnitudes of the impedance peaks measured in the mouths of brass players are typically ~10 times smaller than those of the bore of the instrument, and the players do not tune these to the playing pitch [START_REF] Chen | Do trumpet players tune resonances of the vocal tract?[END_REF][START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF]. [START_REF] Fréour | Acoustical interaction between vibrating lips, downstream air column, and upstream airways in trombone performance[END_REF] find that can exceed one at the playing frequency, but mainly for high notes, where becomes small. Consequently, in normal playing for the notes studied here, contributes little to the series impedance and thus little to . For lipping up and lipping down by more than 10% in frequency, however, players are well away from the bore resonance so is a somewhat larger fraction of the series impedance at the playing frequency. Figures 2a andb show that is still several times smaller than for playing frequencies around B ♭2.

has a larger contribution for the next higher notes of the harmonic series: F3 The normal playing range is always on the upper (compliant) side of the impedance

dt d V x (t) = L ∫ z upper lim it z top (t) ( x(z, t) -x ( z, t -dt ) ) d z + ∫ z bottom (t) z lower lim it ( x(z, t) -x ( z, t -dt ) ) d z U x = d V x /dt Δp = p mouth -p bore -(Z mouth + Z bore )u bore u bore p Z | p mouth | / | p bore | Z bore Z mouth (Z mouth + Z bore ) Δp Z mouth Z mouth Z bore Z mouth ! 10
Z mouth / | Z mouth + Z bore | Z bore | (Z mouth /(Z mouth + Z bore ) | ! 11
peak. However, players can lip up a little way from the normal range and can lip down over a rather larger pitch range. Thus, the range of lipping up and down is not symmetrical with respect to the normal playing frequency. Rather, Fig. 2 indicates that the lipping range is roughly symmetrical with respect to the frequency of the (nearly symmetrical) impedance peak.

! 12 ! 15

In Fig. 3d, and show the effective -components of the displacement of the lips on the sagittal plane (the vertical plane of symmetry), estimated from the area of the lips in the side view, divided by their heights; is the distance between the highest and the lowest points of the aperture. The plots of and in Fig. 3d and the images in Fig. 4 show that the longitudinal (x) motion leads the transverse (z) motion in phase, so that the lips begin to move forward into the mouthpiece while still closed, open while displaced forward, retract from the mouthpiece while open, and close when the lips are substantially retracted towards the teeth. For the same reason, the volume of lip tissue in the mouthpiece leads the area of the aperture between the lips. Similar observations about the motion of brass players' lips for normal playing were made by [START_REF] Copley | A stroboscopic study of lip vibrations in trombone[END_REF] and Yoshikawa and Muto (2003). A quantitative analysis of this behavior and its contribution to maintaining auto-oscillation is given below.

In the present study, players produce auto-oscillation with loads varying from compliant (flow leads pressure) to inertive (pressure leads flow), and the phase difference by which flow leads pressure in the bore varies from about +69° to -75°. How is this range of phase difference between flow and pressure related to the motion and the mechanics of the lips? We begin with qualitative explanations of the data presented in Figs. 3 and4 for one player; later in Fig. 5 the average data for the fundamental frequency is shown as a phasor diagram for all measurements and players.

For the notes studied here, the impedance magnitude of the vocal tract is small compared with that of the bore, so (especially for normal playing, which is close to a bore impedance peak). So, because is small, the acoustic component of the pressure difference acting across the lips in the longitudinal direction, , is proportionally little different from (this is quantified below). Figure 3b shows that the relatively short minimum in the mouthpiece (bore) pressure (corresponding to a maximum in ) coincides roughly with the period when the lips are closed, i.e. is roughly in phase with the lip aperture, which means that the pressure difference across the lips is large only while the lips are closed. (This is not as trivial as it might seem: the Bernoulli effect and the inertance and viscosity of the air between the lips could contribute to a pressure difference but, for this frequency and an aperture this large, these effects are small.)

Comparing Figs 3b and3c shows that the interval between extrema in and varies considerably between lipping up and down. (Later we show that the average phase varies from +59° (up) to -55° (down) at the fundamental frequency of the note.) Equation ( 1)

shows that is the sum of two different flows; the sweeping flow which alternates between positive and negative, and the (always) positive aperture flow . The phase difference between and will depend upon the detailed behaviour of aperture.

The contribution of to makes a significant difference. In general, once the lips start to move forward into the mouthpiece, will start to make a positive contribution to , but remains zero until the lip aperture opens; at that moment starts to make a positive contribution. Eventually the lips will start to retract and then becomes negative.

The relative timing of the events, lip advancing, lip opening, lip retraction and lip closing, can shift the relative phase of with respect to .

Thus, if the lips open whilst is increasing or near its maximum, will add to and bring the maximum in forward.

If the lips open whilst is decreasing, the maximum in can be delayed; this effect will be much greater when is negative. The relative magnitudes of and will also be important in determining how their sum behaves.

Δp

C. Phases and amplitudes of the fundamental components

Comparison between the acoustic waveforms and the constraints imposed by the impedance of the bore can be improved by considering only their fundamental components.

Figure 5 shows the amplitudes of the fundamental components of measured acoustic waveforms and the lip motion and their phase differences for 40 measurements on the seven players. They are gathered into three categories depending on whether players were asked to "lip down" (flat), to play at "normal pitch" (normal) or to "lip up" (sharp). The upper diagrams correspond to the averaged measurements for playing frequencies between 100 Hz and 112 Hz (Fig. 5a), between 112 Hz and 118.0 Hz (Fig. 5b), and between 116 Hz and 126

Hz (Fig. 5c). For each magnitude, the angle of the line corresponds to the phase difference relative to the mouthpiece pressure , chosen as the reference. The phase difference between the mouthpiece pressure and the flow into the bore has large variations over all players and frequencies: averaged over all data, the mouthpiece pressure leads the flow by 55° while lipping down (inertive load), it lags the flow by 35° at normal pitch and 59° while lipping up (compliant loads). Some of this wide range of phase angles can be explained by altered timing of the lip aperture with respect to the lips moving forward. Here we will take the upper lip as the reference because the upper lip leads the lower

u bore ∆ p = p mouth -

D. Work done on the lips

In order to investigate how , the lip motion and their phase difference contribute to the lip oscillation, one component of the work done on the lips is estimated using a simple model to explain aspects of the auto-oscillation [START_REF] Boutin | Lipping down on the trombone: phases of lip motion and pressures[END_REF]. It has been argued [START_REF] Cullen | Brass instruments: linear stability analysis and experiments with an artificial mouth[END_REF] that models with a single degree of freedom ('one mass one spring') cannot reproduce important features of the observed behavior of the lip-bore interaction.

x Although the lip-bore-airflow interaction has strongly non-linear elements, some insights may be gained using a linear model for the lip, with two degrees of freedom (as demonstrated by [START_REF] Velut | How Well Can Linear Stability Analysis Predict the Behaviour of an Outward-Striking Valve Brass Instrument Model?[END_REF].

Following [START_REF] Strong | Simulation of a player-trumpet system[END_REF] and Adachi and Sato (1996), the lips are treated here as plates that swing in the plane and contract and expand along their vertical length. The motion of the top lip in that model is sketched in Fig. 6 for four instants in a cycle in which the bottom right corner executes sinusoidal oscillations in the x and z directions. Approximately uniform pressures and are assumed to act on the up-and downstream sides of the lips respectively. Making the approximation that the kinetic energy of the jet is completely lost in turbulence, there is no pressure recovery: the pressure is the same between the lips as downstream (Elliot and Bowsher, 1982;[START_REF] Cullen | Brass instruments: linear stability analysis and experiments with an artificial mouth[END_REF]. [START_REF] Giordano | Force on the lips of a trumpet player[END_REF] calculates the pressure distribution for a partly similar model, though for much higher pressure and frequency.) With this approximation, is also the pressure in the channel, as indicated. (The pressure falls from to as the air is accelerated to its highest speed between the lips; it then loses all its kinetic energy in turbulence.) Hence, negligible work is done on the lips by during the lip contraction (ii to iii) and extension (iv to i). Further, these two small contributions tend to cancel each other out around a cycle.

(x,
(In other words, because the channel pressure equals the downstream pressure, negligible work is required for the represented by the dotted areas in Fig. 6.) It is therefore important to distinguish between the volume of air displaced by motions in the x and z directions.

This model does not include surface waves or independent motion of multiple masses in the z direction, mechanisms that allow to do work on the lips due to their z motion.

Omitting it here does not imply that such work is negligible. Rather, this work is something that cannot be easily estimated from the measurements reported here, because they do not reveal such motion.

In the model used here, with pressure between the lips equal to , the nett sweeping work done around a cycle can be positive for two reasons. First, if (the acoustic component of ) and the forward velocity had roughly the same phase, then would do positive work on the lips in both directions. The second reason comes from the observation that the lip aperture is smaller when moving forward in the x direction than when returning.

For this behavior, even if were constant ( ) around a complete cycle, then the work done on the lips would be positive, because the closed lips sweep more volume in the x direction during the forward motion than the open lips do in returning. Thus always does work on the lips for the motion observed here, while the sign of the work done by changes, depending on the relative phase of and the longitudinal lip motion .

is the longitudinal component of the flow due to the sweeping action of the lips, calculated as described in section IIG. The work done on the lips by the pressure difference over each time step, according to the simple model, is then calculated as

∆ P ∆ V ∆ P P bore ∆ p ∆ P ∆ p ∆ P ∆ p = 0 ∆ P PV PV Δp ∆ p x(t) U x d W x ! 22
. Note that the longitudinal sweeping flow has a non-zero average, because the lips are taller as they move forwards and shorter when they retreat. This Figure 8 shows the sweeping work done on the lips during one cycle. Overall, increases from lipping down to normal to lipping up (frequency ranging from 100 to 126 Hz). There is considerable scatter. For 39 of the 51 measurements and for 20 of the 23 notes played by advanced players, is positive and its average value is 39 µJ

u x ∆ p ∆ p u x W x W x = ∫ ΔP . U x dt W x W x ! 24
overall, and 46 µJ for advanced players. For 12 of the measurements, it is negative (median value equal to -22 µJ).

The negative values in are interesting. How is auto-oscillation possible when does negative sweeping work? Note that nearly all of the negative cases are for two particular players (beginners) when lipping down. It is possible that another effect, such as the surface wave effect mentioned above, provides the positive work in such situations. The experiments conducted here do not allow estimates of work from these other effects, so the following discussion quantifies only the longitudinal sweeping work.

In the simple model discussed above, two different effects provide driving force on the lips. First, the oscillatory pressure difference acts to accelerate them in the x direction. If the phase of this pressure term is within about π/2 of that of (and thus if Δp is between about zero and π ahead of x), Δp does positive work on the lips round each cycle. In lipping down, the phase of Δp leads x by nearly π, but the angle decreases for normal and lipping up.

Thus this term delivers little power for regeneration when lipping down, but successively more regenerative power for normal and for lipping up and contributes to the positive correlation evident in Fig. 8.

A second effect is that does work on the lips around a whole cycle because of the non-zero longitudinal sweeping flow; this term delivers power , in phase with , as explained above. The longitudinal term arises because the lips are longer coming forward than going backwards, so is expected to be in phase with or π/2 ahead of x. This provides a regenerative work term that is largely independent of the phase of other variables.

E. Energy considerations

Figure 8 includes estimations of energies made using the average values for each of the three gestures. The sweeping work done on the lips is estimated using for one

W x ∆ P Δp v x ΔP ΔPU x u x u x ΔPU x v x ∫ ΔPU x dt ! 25
cycle using the simple model. The sweeping work is divided in two terms:

and . The first term (first bar) is positive on average, since and are positive, while the second term (second bar) can be positive or negative, depending on the phase difference between and . Any work done in the transverse direction according to vertical motion and to other effects and models is not included.

To obtain a rough estimate of the kinetic energy of the lips, the maximum of the effective -velocity, , is given by the peak of the time derivative of lip volume inside the mouthpiece cup, divided by 4.2 cm 2 , the area inside the mouthpiece rim. The andcomponents of the lip motion have comparable amplitude, so they are arbitrarily set equal. If the measured phase difference between the two is , then the maximum kinetic energy is . The values in Fig. 8 assume an effective thickness of 5 mm (so a mass of 2 g bounded by the mouthpiece rim). Consequently, even if the lip-lip or lip-teeth collision is wholly or substantially inelastic, the sweeping work done by can usually replace it. Note that these energy terms are all much smaller than the energy input by the player's breath, , which is typically ~1 mJ for one cycle (an input power of about 100 mW).

As discussed earlier, the lip regeneration via the sweeping motion in normal playing involves one or both of two effects: a positive and an x motion that leads the z motion, or a similar phase of Δp and . In the absence of the downstream resonator, and well away from resonances of the vocal tract, only the first effect is available. If a player could buzz the lips using the lip motion measured for normal playing but with a constant value of kPa, equal to that for normal playing, then the sweeping work would be ~20 µJ, (as in Fig. 8).

F. The range of lipping up and down

∆ P ∫ U x dt ∫ ΔpU x dt ∆ P ∫ U x dt ∆ p u x x v xeff x z α mv 2 xeff cos 2 (α /2) m ∆ P ∫ P mouth U bore dt ∆ P v x ∆ P ~1.3 ! 26
To the question of what limits the range of lipping, many brass players would give a simple pragmatic answer: in practice, players who try to lip up a long way end up 'jumping'

to the instrument's next register. In many cases, this is what happened in this study when players tried to extend the range of lipping up. In the other direction (lipping down from B ♭2), the only bore resonance with a lower frequency (at about 38 Hz) is difficult to play because its harmonics do not coincide with resonances. Instead, experienced players can play what is called a pedal note, B ♭1, for which the second and higher harmonics fall close to the second and higher resonances, but the first does not fall near a resonance. In this study, the lower limit did not involve 'jumping' to a lower register, but instead, players ceased to make a periodic sound. (It should be remembered that the limits discussed here only apply to stable notes: many good players can, without using the slide, perform a 'lip glissando' (strictly a lip The negative value of for lipping down contributes to the low value of sweeping work in Fig. 8. This may contribute to the lower limit of lipping down, but not to the upper limit.

IV. CONCLUSIONS

Players normally play a little above the frequency of the bore impedance peak; they are capable of 'lipping up' roughly half a semitone and 'lipping down' roughly a tone. The upper and lower limits of the range have similar values of the impedance magnitude, being about 15% of the magnitude at resonance, and relative phases ranging from about -69° to +75°.

In order to lip up and down, players must alter the phase between and so it matches the requirements of at the desired frequency. This adjustment is possible in part Yoshikawa, S., and Muto, Y. (2003). "Lip-wave generation in horn players and the estimation of lip-tissue elasticity," Acta Acust. United Ac. 89, 145-162.

! 32

  was located in the plane next to a microphone (4944A, Brüel & Kjaer, Denmark) connected to a preamplifier and a FireWire audio interface (MOTU 828, Cambridge, MA). The impedance head was calibrated by measuring the impedance of an acoustically infinite duct, 142 m long and 7.8 mm diameter. The broadband signals used for calibration and measurement were sums of sine waves between 50 Hz and 1.0 kHz, with a spacing of 0.67 Hz (44.1 kHz/2 16 ).

  FIG. 1. Schematic diagram (not to scale) showing how the mouth and mouthpiece pressure,

  the DC components will be indicated by a capital letter with an overhead bar or macron, and the acoustic component by lower case). The sweeping flow is equal to the time derivative of the volume V of the lips inside the mouthpiece cup;

  FIG. 2. a: (left) Impedance ratios at the playing frequencies near

  FIG. 3. <color online> Pressures, flow and lip motion for an expert player lipping down (left

  = p mouthp bore -p bore ! 16

FIG. 5

 5 FIG. 5 Top: the phases of the AC components:

  FIG. 6. Black lines show four instants during a cycle of a simplistic model for the motion of

  FIG. 7. Amplitude of the acoustic pressure difference across the lips (a), of the acoustic

  Figure2indicates that the lipping range is roughly symmetrical around the nearly

  because has two distinct components. One is the flow through the lip aperture, , which is always positive and starts when the lip aperture opens. The other is the sweeping flow, , that is a consequence of the changing volume of the lips inside the mouthpiece; this flow is initially positive when the lip volume increases and becomes negative as the lips begin to contract. The relative timing of these four events, lip forward motion, lip aperture opening, lip retraction and lip closing, can shift the relative phase of with respect to . (Other subtleties are discussed above.) Because the lips move forward before they open, non-zero work would be done on them by the pressure difference across the lips even if that pressure difference were constant. If it varies and has phase overlap with the longitudinal velocity of the lips, the work done per cycle is greater. The work from these two terms is available to compensate for internal mechanical and other losses associated with vibration. This sweeping work is about 20 times smaller than the work it modulates, i.e. the work input to the instrument by pressure and air mouth. The sweeping work is, however, of the same order as the maximum kinetic energy of the lips. It is thus capable of replacing the energy lost per cycle in lip-lip and lip-teeth collisions. This makes sweeping work a likely source of much or perhaps all of the energy required for auto-oscillation.

ACKNOWLEDGMENTS

We thank the Australian Research Council for support and our volunteer subjects. Adachi, S., and Sato, M. (1996). "Trumpet sound simulation using a two-dimensional lip vibration model," J. Acoust. Soc. Am. 99, 1200-1209. Benade, A. H. (1985). "Air column, reed, and player's windway interaction in musical instruments" in Vocal Fold Physiology, Biomechanics, Acoustics and Phonatory


Malory Randon
email: randon@chasseurs-drome.fr

Christophe Bonenfant

Jacques Michallet

Thierry Chevrier

Carole Toïgo

Jean- Michel Gaillard

Marion Valeix

Population responses of roe deer to the recolonization of the French Vercors by wolves

Keywords: body mass, Canis lupus, Capreolus capreolus, population abundance, predation

In a context of changing carnivore populations worldwide, it is crucial to understand the consequences of these changes for prey populations. The recolonization by wolves of the French Vercors mountain range and the long-term monitoring (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017) of roe deer in this area provided a unique opportunity to assess the effects of wolves on this prey. Roe deer was the main prey of wolves in the west Vercors mountain range during this recolonization. We compared roe deer abundance and fawn body mass in two contrasted areas of a wolf pack territory: a central area (core of the territory characterized by an intense use by wolves) and a peripheral area (used more occasionally). Roe deer population growth rates were lower in the central area between 2001 and 2006, resulting in a decline in roe deer abundance. Roe deer abundance substantially dropped in the two study areas after an extremely severe winter but the abundance of roe deer in the central area facing with wolves was slower to recover and remained at lower abundance levels for 6 years. Fawn body mass was consistently lower in the central area, varied similarly as roe deer abundance, and was not influenced by weather conditions or red deer population abundance. Altogether, the effects of wolves on roe deer in the central area occurred during a 10-year period following the establishment of wolves, through the interplay between wolf predation (before wolves started preying on red deer), harsh winter conditions and possibly naivety of prey to this recolonizing predator.

Introduction

For large herbivores, the main drivers of population dynamics have been studied in great detail over the last few decades (e.g. [START_REF] Coulson | Age, sex, density, winter weather, and population crashes in Soay sheep[END_REF][START_REF] Gaillard | How does climate change influence demographic processes of widespread species? Lessons from the comparative analysis of contrasted populations of roe deer[END_REF] for case studies). The consequences of density, weather, habitat quality or hunting on age-specific survival and reproduction are well documented in many species, with increasing empirical evidence of interactions among these factors [START_REF] Bonenfant | Empirical evidence of density-dependence in populations of large herbivores[END_REF][START_REF] Hone | Climate, food, density and wildlife population growth rate[END_REF]. Predation is clearly a major driver of evolution and population dynamics of prey [START_REF] Reznick | Effect of extrinsic mortality on the evolution of senescence in guppies[END_REF][START_REF] Volterra | Leçons sur la théorie mathématique de la lutte pour la vie[END_REF]. Understanding and measuring the consequences of predation on the population dynamics of large herbivores is, however, much more complex than for most other environmental variables.

Consequently, important ecological questions such as whether large herbivores are undergoing bottom-up or top-down limitation are still debated [START_REF] Hopcraft | Herbivores, resources and risks: alternating regulation along primary environmental gradients in savannas[END_REF][START_REF] Laundré | The landscape of fear: the missing link to understand top-down and bottom-up controls of prey abundance?[END_REF].

By increasing mortality, predators are strongly expected to limit the population growth rate of their prey. However, there are several arguments suggesting that prey populations can withstand strong predation pressure. If predation is compensatory because of density-dependence, prey population dynamics may remain little affected until attack rates become really high and predation becomes additive to other sources of mortality [START_REF] Errington | Predation and vertebrate populations[END_REF]. Similarly, the difference in spatial scale between the ranging behaviour of large carnivores and herbivores leads to differences in densities of several orders of magnitude between predators and prey [START_REF] Skogland | What are the effects of predators on large ungulate populations?[END_REF]. Consequently, large predators may have limited consequences for population growth rate of prey. This is particularly the case if predators are generalists and can switch between different prey species [START_REF] Murdoch | Switching in general predators: experiments on predator specificity and stability of prey populations[END_REF]. This is also the case if predators select juvenile or senescent individuals because the population growth rate of large herbivores is most sensitive to variation in the survival of prime-aged adults [START_REF] Gaillard | Temporal variation in fitness components and population dynamics of large herbivores[END_REF]. However, highly specialized predator species or individuals can clearly reduce population growth rate and the abundance of large herbivores (Bourbeau-Lémieux et al. 2011;[START_REF] Festa-Bianchet | Stochastic predation events and population persistence in bighorn sheep[END_REF]. For instance, roe deer Capreolus capreolus dynamics are markedly affected by lynx Lynx lynx predation [START_REF] Andrén | Large impacts of Eurasian lynx predation on roe deer population dynamics[END_REF][START_REF] Heurich | Survival and causes of death of European roe deer before and after Eurasian lynx reintroduction in the Bavarian Forest National Park[END_REF] particularly so in winter when snow depth is thick, which greatly limits roe deer mobility [START_REF] Heurich | Survival and causes of death of European roe deer before and after Eurasian lynx reintroduction in the Bavarian Forest National Park[END_REF].

Evidence has also accumulated in the past decades about the numerous anti-predation behaviours that prey have evolved such as grouping [START_REF] Fortin | Group-size-mediated habitat selection and group fusion-fission dynamics of bison under predation risk[END_REF], vigilance [START_REF] Creel | Effects of predation risk on group size, vigilance and foraging behaviour in an African ungulate community[END_REF], habitat shift [START_REF] Courbin | Reactive response of zebras to lion encounters shape their predator-prey space game at large scale[END_REF], and temporal niche shift (Valeix et al. 2009a) that may affect foraging behaviour [START_REF] Barnier | Diet quality in a wild grazer declines under the threat of an ambush predator[END_REF]). However little is known about the consequences of these behaviours in large mammals and on the overall non-lethal effects of predators on their prey, that is the decrease of prey performance generated by the presence of a predator and hence, not involving killing and prey consumption [START_REF] Creel | Predation risk affects reproductive physiology and demography of elk[END_REF][START_REF] Middleton | Linking anti-predator behaviour to prey demography reveals limited effects of an actively hunting large carnivore[END_REF]; review in Say-Sallaz et al.

2019).By

In a context of rapidly changing abundance and distribution of large carnivore populations worldwide [START_REF] Chapron | Recovery of large carnivores in Europe's modern human-dominated landscapes[END_REF][START_REF] Ripple | Status and ecological effects of the world's largest carnivores[END_REF], it is important to understand the consequences of these changes for prey populations and ultimately for ecosystem functioning. Even though studies on these consequences have accumulated over the past decades, most of our current knowledge comes from studies in North American National Parks, and particularly from the grey wolf Canis lupus and elk Cervus canadensis of the Greater Yellowstone Ecosystem [START_REF] Kuijper | Paws without claws? Ecological effects of large carnivores in anthropogenic landscapes[END_REF][START_REF] Say-Sallaz | Non-consumptive effects of predation in large terrestrial mammals: mapping our knowledge and revealing the tip of the iceberg[END_REF]. There is thus a need for studies from different contexts, particularly in Europe where large carnivores live in or are recolonizing anthropogenic landscapes [START_REF] Chapron | Recovery of large carnivores in Europe's modern human-dominated landscapes[END_REF]. Further, whether prey have continuously co-evolved with their predator or have evolved in a predator-free environment for several generations due to predator extirpation from some ecosystems may ultimately influence the extent to which prey are vulnerable to predators [START_REF] Berger | Recolonizing carnivores and naïve prey: conservation lessons from Pleistocene extinctions[END_REF][START_REF] Byers | American pronghorns: social adaptations and ghosts of predators past[END_REF]. Indeed, naive prey may fail to recognise the cues of a novel predator (but see [START_REF] Chamaillé-Jammes | Innate threat-sensitive foraging: blacktailed deer remain more fearful of wolves than of the less dangerous black bear even after 100 years of wolf absence[END_REF] or may fail to respond appropriately and effectively to the risk of predation by this predator due to the lack of experience [START_REF] Banks | Alien predation and the effects of multiple levels of prey naiveté[END_REF][START_REF] Carthey | Naïveté in novel ecological interactions: lessons from theory and experimental evidence[END_REF]. For instance, along brown bear Ursus arctos recolonization fronts, brown bears killed adult moose Alces alces at disproportionately high rates compared to sites where brown bears have always been present [START_REF] Berger | Recolonizing carnivores and naïve prey: conservation lessons from Pleistocene extinctions[END_REF]). However, very little is known on how naive prey respond to recolonizing predators and how quickly they become effective at efficiently escaping these predators.

In 1992, wolves crossed the Italian border to recolonize eastern France from where this predator had been missing for ca. 100 years [START_REF] Valière | Longdistance wolf recolonization of France and Switzerland inferred from non-invasive genetic sampling over a period of 10 years[END_REF]Supporting Information 1). In this work, we preliminarily checked that roe deer is an important prey for wolves during this recolonization. We then used the long-term monitoring (17 years) of roe deer in the west Vercors mountain range covering contrasting areas in terms on wolf occupancy to assess the effects of wolves on roe deer. If predation by wolves and the associated predation risk affect roe deer, we expect a decrease in the roe deer population abundance and growth rate, and a decrease in roe deer fawn body mass, following the return of wolves.

Materials and Methods

Study area

The study was carried out between 2001 and 2017 over a study area of 30 776 ha encompassing six neighbouring counties (Bouvante (8 431 ha), La Chapelle-en-Vercors (4 562 ha), Vassieux-en-Vercors (4 798 ha), Saint-Julien-en-Vercors (1 867 ha), Saint-Martin-en-Vercors (2 700 ha), Saint-Agnan-en-Vercors (8418 ha)) in the French department of Drôme, in the west Vercors mountain range (Fig. 1).

The west Vercors mountain range is characterized by an Alpine climate (identical to the Northern Alps) with a forest dominated by beech Fagus sylvatica and silver fir Albies alba. The large herbivore community is composed of roe deer, red deer Cervus elaphus, chamois Rupicapra rupicapra, mouflon Ovis gmelini, and wild boar Sus scrofa. The six counties are used by people for agriculture, livestock breeding, forestry, hunting, and outdoor recreational activities (see Supporting Information 2(a) for detail on land use type). The mean altitude is 1,110m (range: 305m-1,729m; see Supporting Information 2(b) for detail by county).

History of wolf presence in the west Vercors mountain range

Wolves were extirpated from the Drôme department in 1901 [START_REF] Faton | Mammifères (Mammalia) drômois : ongulés et carnivores. DDA, FDC[END_REF]. In 1998, the first field evidence from prey carcasses, tracks and faeces suggesting the return of wolves from the Italian Alps to the west Vercors mountain range were found [START_REF] Valière | Longdistance wolf recolonization of France and Switzerland inferred from non-invasive genetic sampling over a period of 10 years[END_REF]. The ONCFS (French National Hunting and Wildlife Agency) network "Grands Prédateurs" later confirmed the permanent occupancy (3 individuals identified based on DNA analyses) and reproduction of wolves in the west Vercors mountain range in [START_REF] Plummer | JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling[END_REF]/2004[START_REF] Oncfs | Quoi de neuf n°15 -Juin 2006[END_REF]. At this early stage of the recolonization, only lone wolves or single pairs were observed. Since 2007/2008, wolves form packs of a minimum of five individuals. In this study, we contrasted two main study areas based on the intensity of use by wolves. The central area is the core of the west Vercors wolf pack territory (central area hereafter), and encompasses the counties of Bouvante, Vassieux-en-Vercors and the western sector of La Chapelle-en-Vercors (Fig. 1). The central area is characterized by an intensive use of the area by wolves where sightings of wolves, wolf tracks, and wild prey carcasses are frequently reported. In contrast, the peripheral area is used by wolves more occasionally, and encompasses the eastern sector of La Chapelle-en-Vercors, Saint-Julien-en-Vercors, Saint-Martin-en-Vercors, and Saint-Agnanen-Vercors (Fig. 1). We extracted data on land use type from the Corine Land Cover 2006 database (Table 1 for summarized information for the 2 study areas; Supporting Information 2(a) for detailed information by county). The central and peripheral areas differ in terms of land use type (²=4711.1; p = 0.0005) but the main change is that the central area mostly includes broad-leaved forests, whereas the peripheral area is dominated by coniferous forests (Table 1). Agricultural lands represent a low proportion of land use types in both study areas (Table 1).

Weather data

We obtained weather data (daily rainfall and mean daily temperature) from Météo France for the weather station La Chapelle-en-Vercors. It is the only existing weather station in the two study areas as they are very close geographically (see scale on Fig. 1) and the weather is not likely to differ between the two study areas. The weather indices calculated below are therefore average weather indices considered to be representative of the weather of the west Vercors mountain range, and hence they are the same for the two study areas. We calculated the Gaussen index (i.e. the amount of precipitation minus twice the mean temperature) to measure the water deficit of plants in spring (April-June) and summer (July-August) (e.g. [START_REF] Gaillard | Early survival in roe deer: causes and consequences of cohort variation in two contrasted populations[END_REF][START_REF] Garel | The effects of a severe drought on mouflon lamb survival[END_REF]) to which roe deer are particularly susceptible [START_REF] Pettorelli | The response of fawn survival to changes in habitat quality varies according to cohort quality and spatial scale[END_REF]. The Gaussen index is a proxy of the balance between rainfall and evapo-transpiration of plants [START_REF] Gaussen | Les climats biologiques et leur classification[END_REF]. High values of the Gaussen index mean positive water balance, higher plant growth, and hence better foraging conditions for large herbivores, and conversely [START_REF] Toïgo | How does environmental variation influence body mass, body size, and body condition? Roe deer as a case study[END_REF]). Winter can be very long in the west Vercors mountain range so this season was defined from October to March. To characterize winter conditions, we collected information on snow-fall, snow depth, and number of days with snow cover from the local skiing resorts in Bouvante. Because of the strong correlation existing among winter variables, we performed a Principal Component Analysis (PCA) on these standardized variables. The first principal component (PC1) accounted for 62% of the overall variance, so we used the point projections on PC1 as a winter harshness index. Low values of this index were associated with severe winters and hence more difficult conditions for roe deer as harsh winters are generally associated with a lower survival of fawns [START_REF] Gaillard | Roe deer survival patterns: a comparative analysis of contrasting populations[END_REF]), especially at high latitude/elevation, and costly movements for large herbivores [START_REF] Parker | Energy expenditures for locomotion by mule deer and elk[END_REF], which, in turn, could increase predation rates [START_REF] Mech | Winter severity and wolf predation on a formerly wolf-free elk herd[END_REF].

Predation by wolves

Large herbivore carcasses due to predation by wolf were recorded in the study areas between 1998, when the first carcass was attributed to wolf predation, and 2010, when predation by wolf was common and not reported any more. Carcass report only took place in the winter months (October to March) when snow allowed easier detection of carcasses. Because the return of the wolf was of high concern to local people (most of them being hunters), any wildlife carcass found during that period was reported to the "Fédération Départementale des Chasseurs de la Drôme" (local hunting agency in charge of game management in the study area). Qualified staff then performed autopsy of the carcasses, identifying species and confirming whether they were due to wolf predation.

Roe deer abundance

We monitored the abundance of roe deer after winter, in March-April, when vegetation flush has not started yet, along roads known to be practicable at that time of the year. This monitoring was carried out in 5 of the 6 study counties because deep snow cover made most roads in Bouvante county inaccessible at the time of surveys in all years. We drove along 3 transects located in the central area (1 transect in the western sector of La Chapelle-en-Vercors and 2 transects in Vassieux-en-Vercors) and 3 transects in the peripheral area (1 transect in Saint-Agnan-en-Vercors, 1 transect across St-Julien-en-Vercors and St-Martin-en-Vercors, and 1 transect in the eastern sector of La Chapelle-en-Vercors -see Fig. 1). Ninety percent of the total transect length included departmental roads, which were regularly snow-cleared and intensively used by cars. The remaining 10% was forest roads.

Previous works suggest that wolves select trails and low-use roads, but avoid highly used roads (Fahrig and Rytwinski 2009;[START_REF] Theuerkauf | Spatiotemporal segregation of wolves from humans in the Bialoweza Forest (Poland)[END_REF]Whittington et al. 2009). It is thus unlikely that wolves preferentially used transects we sampled for monitoring roe deer abundance. We carried out counts at night with a powerful spotlight reflecting animals' eyes. We drove transects at low speed (10-15 km/h) with one driver, two observers who spotted and identified all animals seen, and one person who recorded the observations. Spatial information was not available for the observations for the whole study period so habitat covariates could not be taken into account in the subsequent analyses. However, transects sampled similar habitats in the two study areas (central area: 80% of forests, 15% of pastures or agricultural lands, and 5% of natural open areas; peripheral area: 84% of forests, 15% of pastures or agricultural lands, and 1% of natural open areas). We repeated counts twice a year between 2001 and 2004, three times a year between 2005 and 2012, and four times a year since 2013. For the central and peripheral areas, we obtained an abundance index of roe deer population (AI) by calculating the mean number of roe deer seen per kilometre (see [START_REF] Pellerin | Saving time and money by using diurnal vehicle counts to monitor roe deer abundance[END_REF] for a similar approach applied to diurnal car counts). Although spotlight counts do not allow accurate assessment of roe deer population size and are unlikely to detect small changes in population abundance [START_REF] Cederlund | Managing roe deer and their impact on the environment: maximising the net benefits to society[END_REF], this method can still be used to detect marked changes in population abundance.

Red deer abundance

Roe deer suffer competition from red deer [START_REF] Richard | High red deer density depresses body mass of roe deer fawns[END_REF]. Red deer observations were also recorded during the roe deer spotlight counts described above. Hence, for the central and peripheral areas, we were able to obtain an abundance index of red deer population (AI) by calculating the mean number of red deer seen per kilometre. Contrary to the roe deer case, spotlight counts have been shown to be a reliable method to monitor population abundance of red deer [START_REF] Garel | Are abundance indices derived from spotlight counts reliable to monitor red deer Cervus elaphus populations?[END_REF].

Roe deer fawn body mass

Twenty local hunting associations (which encompass 500 hunters) contributed to this study and were equipped with a digital scale with an accuracy of 100 grams to weigh hunted roe deer. Between 2002 and 2007, hunters measured the full body mass of harvested roe deer, but have switched to dressed body mass (i.e. guts, liver, heart and lungs removed) since 2007. Between 2007and 2009, 43 local , 43 local hunting associations in the whole Drôme department were asked to measure both full and dressed body masses. From a sample of 170 roe deer with the two measurements, we checked that a close relationship existed between dressed and full body masses (dressed body mass = (0.837 x full body mass) -1.054; R² = 0.92) and used this relationship to estimate dressed body mass of roe deer harvested during 2002-2007. We used dressed body mass in all subsequent analyses. Because roe deer are income breeders with limited fat reserves [START_REF] Andersen | Factors affecting maternal care in an income breeder, the European roe deer[END_REF], and variation in adult body mass is mainly caused by early-life conditions [START_REF] Pettorelli | Variations in adult body mass in roe deer: the effects of population density at birth and of habitat quality[END_REF], we analyzed body mass of roe deer fawns (individuals < 1 year when shot). We excluded body mass data from la Chapelle-en-Vercors because the exact locations of where animals were shot were not recorded, which prevented us from assigning the hunted roe deer of this county to the central vs. peripheral area.

Analyses Predation by wolves

We calculated the percentage that roe deer represented in the large herbivore carcasses attributed to predation by wolves. We then compared if the distribution of the carcasses differed in terms of large herbivore species between the early stage of the recolonization, when only lone wolves or single pairs were observed, and the later stage of the recolonization, when wolves formed a pack of a minimum of five individuals, using a ² test with bootstrap p-value calculation.

Roe deer population abundance and growth rate

We analysed variation in roe deer abundance (assessed using the AI) in time with a state-space model to tease apart sampling from process variances (also known as Kalman filter; de Valpine and Hastings 2002) in its Bayesian formulation [START_REF] Kéry | Bayesian population analysis using WinBUGS: a hierarchical perspective[END_REF]. We built a Generalised Linear Models (GLMs) setting a logarithmic link function and a negative binomial distribution. We opted for a negative binomial distribution because the model with a Poisson distribution did not fit the data well (goodness-of-fit test: χ² = 1 451.71, df = 287, P < 0.001) resulting from over-dispersed count data (ver Hoef and Boveng 2007). Even if we did our best not to change the road count protocol, transect length did vary among years and across transects. We included an offset variable (log-transformed number of kilometres) to account for this heterogeneity in the length of the driven transects. Our observation process equation hence was:

where AI z,t is the number of observed roe deer in each transect per year, µ is the intercept, B t are the t-1 coefficients of the variable 'year' (a categorical variable with 16 levels), B z is the effect of the variable 'wolf area' (a 2-level categorical variable: "central area" vs. "peripheral area"), and B i are the coefficients for the interaction between 'time' and 'wolf area'. Corresponding to the state process of our model, the predicted number of roe deer seen per km was then linked to the unobserved variable D z,t by the following equation:

where D z,t is a normally distributed random variable of mean and variance . This baseline state-space model hence returns D z,t the predicted roe deer abundance per km, accounting for the sampling variance of the counts.

We first investigated differences in roe deer abundance in time and between the central and peripheral areas by modelling D z,t as a function of 'year', 'wolf area', and the interaction term between the effects of 'year' and 'wolf area'. We selected the best model describing the spatiotemporal variation of D z,t with the Widely Applicable Information Criterion (WAIC; [START_REF] Vehtari | Practical Bayesian model evaluation using leave-one-out crossvalidation and WAIC[END_REF];

Watanabe 2010). The lower the WAIC is, the better the compromise between the relative fit of the model and the number of parameters entered to describe the data is. We calculated 95% credible intervals for predicted abundance without any attempt to model spatial autocorrelation of observations because the exact location of seen roe deer was not recorded during the protocol. We then assessed whether there were contrasted periods in terms of roe deer population abundance by modelling and D z,t as a function of 'year', 'wolf area', and the interaction term between 'wolf area' We derived the annual population growth rate in each wolf area (r z,t ) from our baseline statespace model with a simple exponential demographic model linking roe deer abundance at t and t+1

(see [START_REF] Knape | On observation distributions for state space models of population survey data[END_REF] for a similar approach). This was achieved by adding the following constrains on D z,t :

where the annual growth rate r z,t is a normally distributed random variable with mean and variance

. Note that we ended up with t-1 estimates of annual growth rates in each area. We first tested whether roe deer population growth rates differed among periods, once the yearly variation was accounted for, by fitting the following model: whereby B t are the coefficients of the variable 'year', B z the coefficients of the variable 'wolf area', and B i the coefficients for the interaction between 'wolf area' and 'period'. We then tested the association between an ecological variable and r z,t with an additional level of analysis in the statespace model:

where and are the intercept and slope of the effect of variable E on the annual population growth rate, respectively. The four different ecological variables E we considered were winter harshness index, spring and summer Gaussen indices, and the red deer abundance. We concluded to the statistical significance of the different ecological variables on r z,t if the 95% credible interval of the posterior MCMC (Monte Carlo Markov Chains) distribution of the corresponding excluded 0. Modelling the interaction between 'wolf area' and the environmental variable is straightforward and we proceeded the same way to test its statistical significance.

We implemented the Bayesian state-space model on roe deer abundance using JAGS [START_REF] Plummer | JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling[END_REF]. We ran all models with 50 000 iterations, 3 MCMC, and a burn-in stage of 30 000

iterations. With a thinning factor of 5, we estimated the posterior distributions of model parameters from a 5 000 MCMC samples and report the mean and its associated 95% credible intervals. We checked model convergence graphically, looking for a good mixing of MCMC chains, in combination with the Rhat statistic [START_REF] Brooks | General methods for monitoring convergence of iterative simulations[END_REF], which should read 1 at convergence for all estimated parameters. All distributions for priors were flat and non-informative. The JAGS code of our baseline model is provided in Supporting Information (Supporting Information 3).

Fawn body mass

We analysed fawn body mass of roe deer using Gaussian linear models. All models consistently included both sex (a 2-level categorical variable) and date of harvest (the number of days elapsed since June 1 st of the year of birth) as explanatory variables to account for sex differences and fawn body growth over the hunting season. In a first model, we tested for temporal variation in average body mass of fawns and whether the temporal dynamics of roe deer fawn body mass differed between the central and peripheral areas by modelling fawn body mass depending on 'year' (a categorical variable with 16 levels), wolf area (a 2-level categorical variable: "central area" vs.

"peripheral area"), and the interaction term between the effects of 'year' and 'wolf area'. We then quantified and tested for the effects of five environmental variables: spring Gaussen index at year t,

summer Gaussen index at year t, winter harshness index for the winter season covering years t and t+1, roe deer population abundance at year t (to test for density-dependence) and red deer population at year t (to test for interspecific competition) on fawn body mass from the hunting season covering years t and t+1 by replacing 'year' in the model described above with the corresponding environmental variable , one at a time (i.e. 5 different models for the 5 environmental covariates). For example, to test for the effect of the spring Gaussen index, we modelled fawn body mass depending on 'spring Gaussen index', 'wolf area', and the interaction term between the effects of 'spring Gaussen index' and 'wolf area'. For our model selection, we sequentially removed nonstatistically significant variables starting from the most complex model. We tested for the effect of sex, date of harvest and year using LRT. For the effect of environmental covariates, we tested their significance using an analysis of deviance (ANODEV) [START_REF] Grosbois | Assessing the impact of climate variation on survival in vertebrate populations[END_REF][START_REF] Skalski | Regression of abundance estimates from mark-recapture surveys against environmental covariates[END_REF].

We performed the analyses with the statistical software R 3.4 (R Core Team 2018) extended with the MASS package [START_REF] Venables | -## theta ~ dunif(0, 50) beta ~ dmnorm(mu.beta, tau.beta) for[END_REF]. We set the significance level to α = 0.05 and reported estimates as mean ± 95% confidence interval unless otherwise stated.

Results

Weather variables (i.e. winter harshness index, spring and summer Gaussen indices) during the study period are provided in Supporting Information (Supporting Information 4). Winter 2004/2005 was the harshest of the time series, with a record of snow-fall (total snow-fall = 498 mm, max snow depth = 140 mm) and snow duration (number of days with snow cover = 110).

Predation by wolves

Overall, we recorded 178 large herbivore carcasses attributed to predation by wolves during the period 1998-2010 in the west Vercors mountain range. Roe deer represented the main prey of wolves (37% of these carcasses), together with red deer (36 % of the carcasses). Additionally, the contribution of the different prey species changed between the early stage of the recolonization (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005), when only lone wolves or single pairs were observed, and the later stage of the recolonization (2006-2010), when wolves formed a pack of a minimum of five individuals (²=10.56; p = 0.019). This change is mainly characterized by a decrease of the contribution of roe deer and an increase in the contribution of red deer (Fig. 2).

Roe deer population abundance and growth rate

The negative binomial model fitted the data satisfactorily (goodness-of-fit test: χ² = 292.55, df = 287, P = 0.40). According WAIC, the roe deer population abundance varied between years, with different patterns between the central and peripheral areas (Table 2; Fig. 3A). Roe deer AI decreased continuously between 2001 and 2006 in the central area (Fig. 3A), and roe deer AI decreased dramatically in both areas in 2005 (Fig. 3A), coinciding with the most severe winter of the study period (2004)(2005). Between 2005 and 2010, roe deer AI remained low in the central area while it increased in the peripheral area (Fig. 3A). Since 2011, the annual variation in roe deer AI was synchronous in the two areas (Fig. 3A). Overall, roe deer AIs were significantly lower in the central area in the period 2005-2010 only (mean difference in AI = -0.400 [CI: -0.677; -0.119]; see the horizontal grey bar in Fig. 3A).

Roe deer population growth rates were lower in the central area in the period 2001-2005 only (mean difference in growth rates = -0.124 [CI: -0.327; 0.070]; see the horizontal grey bar in Fig. 3B). This explains the decline in AIs in the central area during that period. It further shows that the difference in roe deer AI between the two areas for the period 2005-2010 did not result from lower growth rates in the central area these years but resulted from the combined lower growth rates in the central area between 2001 and 2005. After 2006, the annual growth rates were rather similar in the two study areas (Fig. 3B). Despite the lowest growth rate occurring between 2004 and 2005 henceforth including the harshest winter, we did not detect an effect of the winter harshness index on roe deer population growth rate (Table 3). Only the Gaussen index in spring at year t had a significant positive effect on the population growth between year t and t+1 (Table 3). The differences in mean fawn body mass among years and between areas were, however, rather low (≤ 1 kg). Of the five environmental covariates (i.e. the 3 weather indices, the roe deer population abundance index, and the red deer population index), none accounted for annual variation in fawn body mass (Table 4), but the positive relationship between roe deer abundance and roe deer fawn body mass approached significance.

Roe deer fawn body mass

Discussion

At the early stage of the recolonization of the west Vercors mountain range by wolves (before 2005), roe deer was one of the main prey killed by wolves (with red deer). This result is in line with a previous analysis of wolf diet from 41 wolf scats carried out during the same period in the same area, which showed that roe deer represented 43.8% of the scats found and was the main prey of wolves (ONCFS network "Grands Prédateurs", unpublished data; Fluhr 2011). In parallel, roe deer abundance dropped in the central area, which corresponds to the core of a wolf pack territory and is characterized by an intense use of the area by wolves, with lower population growth rates in the central area than in the peripheral area between 2001 and 2005. The abundance of roe deer strongly dropped between 2004 and 2005 in both the central and the peripheral areas most likely because of the extreme severity of the winter 2004-2005, which was the harshest winter throughout the 17-year study period. This is consistent with several previous studies that showed that severe winters decrease survival of young and old individuals in populations of large herbivores (e.g. [START_REF] Gaillard | Temporal variation in fitness components and population dynamics of large herbivores[END_REF][START_REF] Saether | Environmental stochasticity and population dynamics of large herbivores: a search for mechanisms[END_REF] for reviews). Wolf predation is expected to increase with snow depth. For instance, on the Isle Royale, wolves hunted in larger packs and tripled the number of moose they killed per day in the snowiest years [START_REF] Post | Ecosystem consequences of wolf behavioural response to climate[END_REF]. Likewise, the relative importance of wolf predation on white-tailed deer Odocoileus virginianus mortality increased with winter severity in Minnesota (DelGiudice et al. 2002). Such higher susceptibility of ungulates to wolf predation during severe winters is associated with costlier and less efficient movements of ungulates in deep snow [START_REF] Parker | Energy expenditures for locomotion by mule deer and elk[END_REF]. Between 2006 and 2010, roe deer abundance remained lower in the central area. This difference in population abundance results from the consistent lower growth rates reported in the AI between 2001 and 2005. Additionally, our findings are in line with previous studies that showed that the presence of established wolves suppress the recovery of prey populations after a stochastic density-independent event, such as a severe winter [START_REF] Hebblewhite | Elk population dynamics in areas with and without predation by recolonizing wolves in Banff National Park, Alberta[END_REF].

The predator species, (ii) resource limitation, and (iii) disease. Regarding (i), no other large carnivore is present in the study areas. Since roe deer are hunted in both study areas, it is important to note that the yearly variation in roe deer harvest bags was similar in the two areas (Supporting Information 6).

Regarding (ii), differences in forest species composition obviously affect the resource availability in the two areas and differences in resource availability between the two areas may exist and affect roe deer population abundance. However, no change in forest management occurred, so we can discard big changes in resource availability within an area to account for the difference observed. Likewise, possible competition with red deer [START_REF] Richard | High red deer density depresses body mass of roe deer fawns[END_REF]) seems unlikely because we did not find any effect of red deer population abundance on roe deer population growth rate and fawn body mass (supported by the lack of increase of the browsing index -see Supporting Information 7). The two wolf areas being very close geographically, differences in local weather conditions can also be excluded. Regarding (iii), no disease outbreak was reported over the study period. Predation by wolves is thus the most likely factor to explain the difference we reported in population dynamics between the central and peripheral areas. However, the changes in the roe deer abundance we detected based on spotlight counts correspond to local changes in the areas close to the transects sampled and can thus arise from either true changes in the study areas' roe deer population abundance or changes in roe deer space use and habitat selection that would affect the detection probability of roe deer on the driven transects. A change in the foraging behaviour of roe deer with an increased use of suboptimal habitats may have occurred (as shown in other systems, e.g. [START_REF] Creel | Elk alter habitat selection as an anti-predator response to wolves[END_REF]Valeix et al. 2009b). However, future studies involving detailed GPS monitoring of individual roe deer are needed to investigate whether roe deer alter their habitat use and selection as a response to predation risk by wolves. Unfortunately our data did not allow us to disentangle between the lethal and non-lethal effects of wolves. Wolves clearly killed roe deer but we cannot assess whether this mortality was additive or compensatory.

The sample sizes of roe deer fawn body mass were rather low but still allowed us to depict that body mass was lower in the central area than in the peripheral area. It is noteworthy that the difference in fawn body mass between the two areas was low (~1kg) compared to differences previously reported in roe deer in response to changes in density (about 2 kg in response to spatial variation in resources, [START_REF] Pettorelli | Spatial variations in springtime food resources influences the winter body mass of roe deer fawns[END_REF]> 3kg in response to population density, [START_REF] Douhard | Variation in adult body mass of roe deer: early environmental conditions influence early and late body growth of females[END_REF]. This difference could arise from non-lethal effects of predation risk through stress-mediated and food-mediated costs, which occur even at a low density of predators [START_REF] Ramler | Crying wolves? A spatial analysis of wolf location and depredations on calf weight[END_REF][START_REF] Creel | The control of risk hypothesis: reactive vs. proactive antipredator responses and stress-mediated vs. food-mediated costs of response[END_REF][START_REF] Macleod | Fear and lethality in snowshoe hares: the deadly effects of non-consumptive predation risk[END_REF]), but because the temporal dynamics of changes in roe deer fawn body mass were similar in the two study areas, it is more likely that an unmeasured/unknown variable predation on red deer instead of roe deer (Fig. 2) with increasing pack size. This second explanation is supported by the fact that the attack success of wolves on red deer increases with larger pack size between 1 and 5 wolves [START_REF] Macnulty | Nonlinear effects of group size on the success of wolves hunting elk[END_REF].

Altogether, our findings suggest that the settlement of a wolf pack in an area from where the predator was absent for a very long time leads to a 10-year period of impact of the predator on the naive prey living in this area. Our study highlights the importance of long-term studies as different phases were detected in this work after the arrival of wolves. Indeed, after a first period when differences in roe population growth rates between the two study areas were detected, we detected a 6-year period when differences in roe deer abundance between the two areas were detected, and after no long-lasting detectable effect of wolves on roe deer populations could be detected. Our study further shows the difficulty of disentangling the lethal versus non-lethal effects of predators on their prey and encourage future studies to study (i) the spatial distribution of prey before and after the settlement of the predator, and (ii) the population dynamics of prey using capture-markrecapture monitoring whenever possible. Finally, from a management or conservation perspective, our results suggest that a new equilibrium has been reached between wolves and the roe deer in the west Vercors mountain range. study would not have been possible. We thank Simon Chamaillé-Jammes for fruitful discussions about the interpretation of the results of this study, and Eric Marboutin and Maryline Pellerin for comments on the manuscript. Finally, we thank Jean-Pierre Fermond ("Bubu"), Jérôme Guilloud and Christophe Randon who have supported this study since the beginning, provided guidance throughout and commented earlier versions of this draft. We thank two anonymous reviewers for their helpful suggestions that improved the quality of this manuscript. Effects of ecological variables on the annual population growth rate of roe deer in the west Vercors mountain range between 2001 and 2017, France. We computed annual population growth rates from roe deer abundance accounting for sampling variance with a Bayesian state-space model. We considered the additive and interactive effects of 4 ecological variables on annual population growth rates and present the estimated slope (estimates) along with its 95% credible intervals (95 CI_low; 95 CI_up). We standardized all ecological variables to ease comparison of relative effects. Effects of the five ecological variables tested on dressed body mass of roe deer fawns (n = 422) harvested during the autumn-winter of years 2002 to 2016 in the west Vercors mountain range (both the central and peripheral areas of the wolf pack territory). We present the standardized coefficients (and their 95% confidence limits) and the analysis of deviance (ANODEV) of the effect of environmental covariates on roe deer fawn body mass, accounting for the harvest date and the sex.

Tested ecological variable

The ANODEV quantifies the proportion of temporal variability in the yearly average body mass of roe deer fawns accounted for by the cohort-specific ecological variable. No interaction term between 'wolf area' and an ecological variable was found significant so that only the additive effect is presented. sigma.r = runif(2, 0, 2), fit.tild = c(0.5, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.5, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA) )} # Parameters monitored parameters <-c("fit", "fit.tild", "r", "mean.r", "sigma.r", "sigma.proc")#, "Lik") # MCMC settings ni <-20000 nt <-5 nb <-15000 nc <-3 # Call JAGS jagsmodel <-jags(forJags, inits, parameters, "pois.bug", n.chains = nc, n.thin = nt, n.iter = ni, n.burnin = nb, working.directory = getwd() ) jagsmodel #save(jagsmodel, file = "jagsmodel.RData") #load("jagsmodel.RData")

Environmental variable

  and 'period', with 'period' (a three-level categorical variable with 'period 2001-2005' the beginning of wolf settlement when they were either alone or in pairs and preyed mainly on roe deer (see results), 'period 2006-2010' the establishment of wolf packs and the increase in red deer consumption (see results), and 'period 2011-2016' the period with wolf packs of a minimum of 5 individuals clearly established and preying mainly on red deer).

  Overall, we collected dressed body mass measurements for n = 422 roe deer fawns in the study area from 2002 to 2016, both in the central (Vassieux-en-Vercors, Bouvante; n = 243) and the peripheral (Saint-Julien-en-Vercors, Saint-Martin-en-Vercors, Saint-Agnan-en-Vercors; n = 179) areas. The mean difference in fawn body mass between sexes was 0.30 ± 0.24 kg (males heavier, as expected;[START_REF] Douhard | The cost of growing large: costs of post-weaning growth on body mass senescence in a wild mammal[END_REF], and fawns gained on average 0.29 ± 0.09 kg per month over the hunting season from September to the following March. Mean body mass of fawns varied among years (F = 1.80, df = (14, 404), P = 0.03; see Supporting Information 5 for detailed coefficients per year) but not differently between the central and peripheral wolf areas (interaction term between 'year' and 'wolf area' (F = 1.51, df = (14, 390), P = 0.10)). Fawn body mass was on average lower in the central than in the peripheral wolf area (F = 9.19, df =(1, 404), P = 0.02; 0.79 ± 0.26 kg; Fig.4). The first years of the study were characterized by a high variability due to lower sample sizes in those years. Between 2006 and 2008, roe deer fawn body mass decreased in the two areas and has increased since 2008.

  decrease of roe deer AI in the central area between 2001 and 2005 combined with the slower recovery of the roe deer population in the central area after the severe winter reveals that something different occurred between the two study areas during the period 2001-2010. When studying the effect of a carnivore on a prey, it is important to consider alternative hypotheses that could underline the patterns observed in prey (see fig. 2 in Ford and Goheen 2015): (i) alternative

Figure 1 :

 1 Figure legends

Figure 2 :

 2 Figure 2: Changes in the contribution of large herbivore species to the diet of wolves in the west

Figure 3 :

 3 Figure 3: (A) Changes in the roe deer population abundance index (AI; small circles) and in the

Figure 4 :

 4 Figure 4: Changes in the roe deer fawn body mass (small circles: corrected dressed body mass -see

Figure 1 Figure 2 Figure 1 :

 121 Figure 1

Table 1

 1 Composition of the study areas in terms of land use type (data from the Corine Land Cover 2006 database). Numbers in brackets show the proportion each land use type represent.

	732
	733
	734
	735
	736
	737
	738
	739
	740
	741

Table 2

 2 Model selection with Widely Application Information Criterion (WAIC) for the state-space Bayesian models used to describe the spatio-temporal variation in roe deer abundance in the west Vercors mountain range, France, between 2001 and 2017. We compared here the temporal variation in roe deer abundance between the central and peripheral wolf areas.

	Model description

Table 3

 3

Table 4

 4

	Estimate	95 CI_low	95 CI_up

Acknowledgements

We sincerely thank the successive Presidents of the "Fédération Départementale des Chasseurs de la Drôme" (Alain Golin, Alain Hurtevent, Rémi Gandy), the Director of the "Fédération Départementale des Chasseurs de la Drôme" (Denis Rix) and all board members of the "Fédération Départementale des Chasseurs de la Drôme" for providing all means (technical, funding, staff) to carry out this research. We also thank the ONF technicians of the Vercors and Lente-Léoncel for their invaluable help with data collection and our fruitful discussions, particularly Jean-Pierre Lacour, Eric Rousset, Yves Pesenti, Gaël Gauthier, Franck Millat Carus, Philippe Joanin and Thierry Rozand. We are indebted to all the hunters, and particularly to all the Presidents of the ACCA, without whom this

explains this body mass difference. The positive relationship between roe deer fawn body mass and roe deer AI we reported is opposite to what was expected in presence of density-dependence [START_REF] Bonenfant | Empirical evidence of density-dependence in populations of large herbivores[END_REF]. Indeed, fawn body masses were lower in 2006-2010 when roe deer AI was low abundance in the central area. Such positive relationship has already been demonstrated in a study whereby bighorn sheep Ovis canadensis lambs suffered mortality through reduced growth during years of high predation by cougars Puma concolor, contributing a third of the total impact of predation on lamb survival (Bourbeau-Lémieux et al. 2011); a study that illustrated a case of nonconsumptive effects of predation on a prey population. While our results may suggest such a mechanism, the alternative of a delayed effect of the extremely rigorous winter 2004/2005 that led several consecutive cohorts to be light, and hence prevented any relationship between average fawn body mass and population AI cannot be discarded. Overall, our results do not provide strong support for non-lethal effects of wolves on roe deer fawn body mass. This result aligns with some existing evidence in the literature about weak to non-existent non-lethal effects of wolf predation on prey because behavioural responses of prey are not strong or frequent enough to lead to major changes in individual performance (White et al. 2011[START_REF] Middleton | Linking anti-predator behaviour to prey demography reveals limited effects of an actively hunting large carnivore[END_REF]. However, the two study areas were characterized by wolf presence with different levels of utilization by wolves. Because non-lethal effects may occur even at a low density of predators, it is also possible that they have occurred in both study areas and future studies will need to focus on areas with strictly no wolf before firm conclusions on the existence of non-lethal effects can be drawn.

Roe deer populations in the central and peripheral areas had similar patterns of temporal variation of AI and growth rates after 2011. This suggests that the effects of wolves on the roe deer population in the central area occurred mainly during a 10-year period following the establishment of the pack, with effects at the population level detected during a 6-pear period only (2005)(2006)(2007)(2008)(2009)(2010).

The little difference we reported between the central and peripheral areas after 2011 may be explained by (i) a learning process to recognize wolf cues allowing roe deer to escape from wolf predation (end of naive period), and/or (ii) a predation shift by wolves, which targeted their ------------------------------------# 2 0 0 0 -2 0 0 1 2 0 0 1 -2 0 0 2 2 0 0 2 -2 0 0 3 2 0 0 3 -2 0 0 4 2 0 0 4 -2 0 0 5 2 0 0 5 -2 0 0 6 2 0 0 6 -2 0 0 7 2 0 0 7 -2 0 0 8 2 0 0 8 -2 0 0 9 2 0 0 9 -2 0 1 0

Winter harshness index

Supporting Information 7

Herbivore pressure on the woody vegetation

Because changes in browsing pressure correlate with changes in the abundance of populations of large herbivores [START_REF] Chevrier | The oak browsing index correlates linearly with roe deer density: a new indicator for deer management[END_REF][START_REF] Morellet | The browsing index: new tool uses browsing pressure to monitor deer populations[END_REF], we monitored the browsing pressure in the forest habitats of the central area of the wolf pack territory (Bouvante, Vassieux-en-Vercors, and the western sector of La Chapelle-en-Vercors) from 2001 to 2014. Unfortunately, such monitoring did not take place in the peripheral area. One limit of such index is that it encompasses the browsing pressure from all herbivore species. In the study system, this index encompasses the browsing pressure from both roe deer and red deer. For this monitoring, we focused on the four main woody plant species of the west Vercors mountain range (beech, silver fir, Norway spruce Picea abies, and sycamore Acer pseudoplatanus). Every year in April-May, between snow melt and spring vegetation flush, we monitored 86 quadrats (1 m²) distributed in the central area. In each quadrat, we recorded whether one of these four species was present and whether these plants had been browsed in the past growing season. Following [START_REF] Morellet | The browsing index: new tool uses browsing pressure to monitor deer populations[END_REF], the browsing index was defined as B = (n c + 1)/(n p + 2) where n p is the number of plots where at least one of the monitored species was present, and n c is the number of plots with at least one species consumed.