Anthony Delalande
email: anthony.delalande@cnrs-orleans.fr

Spiros Kotopoulis
email: spiros.kotopoulis@googlemail.com

Tijs Rovers
email: tijs.rovers@rub.de

Chantal Pichon
email: pichon@cnrs-orleans.fr

Michiel Postema
email: michiel.postema@ift.uib.no

Sonoporation at a low mechanical index

Keywords: Sonoporation, Low mechanical index, Microbubbles, Ultrasound contrast agent, HeLa cells, Cell penetration

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Introduction

Sonoporation is the transient permeabilisation and resealing of a cell membrane with the help of ultrasound and/or an ultrasound contrast agent, allowing for the trans-membrane delivery and cellular uptake of macromolecules between 10 kDa and 3 MDa. 1 Many studies have demonstrated increased drug and gene uptake of sites under sonication. [2][3][4][5][6][7][8][9] These studies presumed, that a physical membrane disruption mechanism, i.e., sonoporation, caused the increased uptake, as opposed to naturally occurring active uptake processes, such as endocytosis, that are controlled by the system biology. [2][3][4][5][6][7][8][9] Although mechanical disruption with the aid of ultrasound has been attributed to violent side effects of inertial cavitation and microbubble fragmentation, most notably, the increased uptake has also been observed at low acoustic amplitudes, i.e., in acoustic regimes where inertial cavitation and microbubble fragmentation are not to be expected. An ultrasound contrast agent microbubble might act as a vehicle to carry a drug or gene load to a perfused region of interest. If the same ultrasound field that has been implicated in the sonoporation process can cause release of the therapeutic load, this load could be delivered into cells. Apart from plainly mixing ultrasound contrast agents with therapeutic agents, several schemes have been proposed to incorporate therapeutic loads to microbubbles. These include loads to the microbubble shell, 10 therapeutic gases inside the microbubble, 11 gas-filled lipospheres containing drugs, 12 and drug-filled antibubbles. 13 To understand and ameliorate ultrasound-assisted drug and gene delivery, the physics of controlled release and of sonoporation have been under investigation. That objective also forms the focus for this paper. Moreover, we studied the behaviour of ultrasound contrast agent microbubbles near cancer cells deliberately at low acoustic amplitudes in in order to probe whether sonoporation in this regime was possible; and if so, to ascertain what the microscopic mechanism might entail; and finally, to assess and scrutinise the safety aspects of ultrasound exposure in this regime.

Mechanical index

The mechanical index (MI) gives an indication of mechanical damage of tissue due to inertial cavitation. It is defined by:

MI = p - √ f c , (1)
where p -is the maximum value of peak negative pressure anywhere in the ultrasound field, measured in water but reduced by an attenuation factor equal to that which would be produced by a medium having an attenuation coefficient of 0.3 dB cm -1 MHz -1 , normalised by 1 MPa, and f c is the centre frequency of the ultrasound normalised by 1 MHz. For MI<0.3, the acoustic amplitude is considered low. For 0.3>MI>0.7, there is a possibility of minor damage to neonatal lung or intestine. [START_REF]Guidelines for the safe use of diagnostic ultrasound equipment[END_REF] These are considered moderate acoustic amplitudes. For MI>0.7, there is a risk of cavitation if an ultrasound contrast agent containing gas microspheres is being used, and there is a theoretical risk of cavitation without the presence of ultrasound contrast agents. [START_REF] Haar | [END_REF] The risk increases with MI values above this threshold. These are considered high acoustic amplitudes.

On commercial scanners, the MI has been limited to 1.9 for medical imaging. 16 At low MI, microbubbles pulsate linearly, whereas at high MI, their greater expansion phase is followed by a violent collapse. During the collapse phase, when the kinetic energy of the bubble surpasses its surface energy, a bubble may fragment into a number of smaller bubbles. Fragmentation has been exclusively observed with contrast agents with thin, elastic shells. Fragmentation is the dominant disruption mechanism for these bubbles. 17 Although the fragmentation of therapeutic load-bearing microbubbles must release their loads, the actual drug or gene delivery is in this case a passive process, dependent on diffusion rate and proximity to the target cells. Fragmenting microbubbles may not create pores in cells, since fragmentation costs energy. However, if a microbubble collapses near a free or a solid boundary, the retardation of the liquid near the boundary may cause an asymmetry. This asymmetry causes differences in acceleration on the bubble surface. During further collapse, a funnel-shaped jet may protrude through the microbubble, shooting liquid to the boundary. 18 The pore size created by a jet has been empirically related to the microbubble expansion. 19 If jets could be directed to cell layers, in case of a microbubble carrying a therapeutic load, the load could be delivered into cells. The jet formation is effected by the cavitation topology, synergistically interacting with local fluid dynamics arising through the bubble's expansion and contraction due to the ultrasound field. However, as the fluid forming the microjet is just the bulk fluid which carries no therapeutic agent, then there is no guarantee that, even with the formation of a sonopore due to jet impact with the cell membrane, therapeutic agent will enter the cell. It needs to be dislodged and mobilised from the bubble first. Furthermore, jetting has not been observed at low or moderate MI, 20 so that fragmentation is likely to occur before any delivery takes place.

By pushing the loaded microbubbles towards the vessel wall using primary radiation forces, 21 release can take place closer to target vessels. In a recent study, Caskey et al. pushed bubbles into tissue-mimicking gels at MI=1.5. 22 We previously studied how microclusters consisting of lipid-encapsulated microbubbles can be formed using primary and secondary radiation forces, and how these clusters can be pushed towards vessel walls. 23 We found that, even at MI<0.15, microbubble clusters can be formed and pushed within seconds.

Sonoporation

There are five non-exclusive hypotheses for explaining the sonoporation phenomenon.

These have been summarised in Figure 1: push, pull, jetting, shear, and translation. [START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF] It has been hypothesised that expanding microbubbles might push the cell membrane inward, and that collapsing bubbles might pull cell membranes outward. [START_REF] Van Wamel | [END_REF] These mechanisms require microbubbles to be present in the close vicinity of cells. A separate release mechanism should then ensure localised delivery. Although jetting only occurs in a high-MI regime, it is very effective in puncturing cell membranes. Jetting has been observed through cells using ultrasound contrast agent microbubbles. However, the acoustic impedance of the solid cell substratum formed the boundary to which the jetting took place, not the cell itself. 26 Also, there has not been any proof yet of cell survival after jetting. In a separate study, we excluded the role of jetting as a dominant mechanism in sonoporation. 27 If a microbubble is fixed to a membrane, the fluid streaming around the oscillating bubbles creates enough shear to rupture the membrane. 28 Here again, separate release mechanism should then ensure localised delivery. Finally, it has been speculated that lipid-encapsulated microbubbles, in compressed phase, translate through cell membranes or channels in the cell membrane.

In case of therapeutic loading, the load would be delivered directly into the target cell.

The main advantage of the latter mechanism is that microbubble translation by means of ultrasonic radiation forces requires very low acoustic pressures. Hence, and potential damaging bioeffects due to inertial cavitation can be ruled out.

Materials and methods

Sonoporation configuration

In previous studies, increased gene uptake was demonstrated at MI<0.3. 29,30 We used a similar sonoporation configuration for our experiments. An overview of the experimental setup is shown in Figure 2. A signal consisting of 50 cycles with a centre frequency of 6.6 MHz and a pulse repetition frequency of 10 kHz, i.e., a duty cycle of 7.5%, was generated by an AFG 3102, dual channel arbitrary function generator (Tektronix, Inc., Beaverton, OR, USA), amplified by a 150A250 radio-frequency (RF) amplifier (Amplifier Research, Souderton, PA, USA) set to maximum gain, and fed to a custom-built 6.6-MHz ultrasound transducer with a hexagonal lithium niobate y-36 o -cut active element with a maximum width of 25 mm. [START_REF] Kotopoulis | Proc. IEEE Ultrason. Symp[END_REF] The peak-negative acoustic pressure was measured to be 0.5 MPa in a separate tank and in the sonication chamber itself. This corresponds to an MI of 0.2. The transducer was placed in a custom-built, 260 × 160 × 150 (mm) 3 Perspex sonication chamber, in which an OptiCell R cell culture chamber (Nunc GmbH & Co. KG, Langenselbold, Germany) was placed. One side of the cell culture chamber contained a monolayer of 1.6×10 was connected to the microscope. The sensor was rotated to make sure that in all recorded movies, the ultrasound is directed from the left to the right of the frame.

Fluorescence configuration

An overview of the setup used for the fluorescence experiments is shown in Figure 3.

It is almost identical to the setup described in the previous section. However, here, the signal consisting of 40 cycles with a centre frequency of 6.6 MHz and a pulse repetition frequency of 10 kHz, i.e., a duty cycle of 6.1%, was amplified using a 2100L, +50-dB RF amplifier (Electronics & Innovation, Rochester, NY, USA) and fed to our custom-built 6.6-MHz ultrasound transducer. [START_REF] Kotopoulis | Proc. IEEE Ultrason. Symp[END_REF] Prior to injection in the OptiCell R , the MicroMarker R contrast agent was labelled using a DiD (DilC Oil DIC M27 objective (Carl Zeiss AG), with automated z-stack functionality.

The peak-negative acoustic pressure was measured at the objective's field of view and corresponded to MI =0.2.

To ensure that the microbubbles were not naturally attracted to the cells, We recorded 23 movies under 6.6-MHz sonication at frame rates between 500 and 2000 frames per second, representing 15 minutes of real-time exposure. Of these, 11 movies were recorded using fluorescence. In addition we recorded 10 control movies, with a total duration of 22 minutes.

Results and discussion

Throughout this section, the optical z-axis is defined from distal-to-focus (negative) to proximal-to-focus (positive), with z = 0 as the focal plane.

Figure 5 shows z-stacks of fluorescence emitted by the DiD dye attached to the membranes of four typical HeLa cells, representing the cell geometry. In total, the thicknesses of 42 cells were measured. The cultured cells were found to be 13 ± 2 µm thick. Clearly, these cells had thicknesses much greater than ultrasound contrast agent microbubble oscillations amplitudes at MI=0.2.

We analysed our optical system and compared our results to bubbles and cells that were slightly out of focus, to rule out that the movement of the bubble takes place in a plane different from that of the cell. Figure 6 shows a z-stack of two ultrasound contrast agent microbubbles, similar to Figure 10 of Postema et al. 33 Proximal-to-focus Airy disks can be seen around the bubbles, whereas distal-to-focus the bubble boundaries are blurred. Note that the boundary contrast is maximal just proximal-to-focus. 33 At a centre frequency of 6.6 MHz, we recorded 17 events of microbubbles entering HeLa cells. After entering, the microbubbles were observed to quickly dissolve. As an example, Figure 7 shows an event resampled at 3.4 Hz and 40 Hz, respectively, where two bubbles were pushed to a cell during 11 s of sonication. A microbubble "A" of 4-µm diameter entered the cell and dissolved, whereas a microbubble "B" of 2-µm diameter stuck to the cell membrane.

Figures 8 and9 show two similar events, where fluorescence-coated microbubbles were used. The left panels show a microbubble apparently penetrating through the cell membrane in optical focus. Approximately 70 ms after the ultrasound has been switched on a microbubble is seen to penetrate through the cell membrane in Figure 8. In Figure 9 the microbubble is seen to penetrate through the cell membrane approximately 24 ms after the ultrasound has been switched on. The right panels show a z-stack through the entire cell, to record whether the apparent microbubble entry is actually into the cell.

For both events, Figure 10 shows average fluorescent intensities in two regions of interest, one inside the cell, and one control region. In both events, most fluorescence from apparent microbubble entry can be observed within 5 µm proximal to optical focus, thus well within the cells themselves.

Figure 11 shows frames in optical focus from the events in Figures 8 and9, before sonication and approximately 8 minutes after sonication. Clearly, fluorescence has transferred into the cells and remained inside the cells long after sonication.

At these low acoustic amplitudes, inertial cavitation, fragmentation, and jetting should not occur. Hence, as a mechanism in sonoporation at low MI, these phenomena might justifiably be neglected.

Our observations do not explain why some microbubbles enter a cell and others don't. The quick dissolution after entering suggests that the microbubble loses (part of) its shell whilst entering.

The ζ-potential measurements showed that the microbubble shells had a charge of -43.9±2.4 mV. As cells have a natural negative charge, 34,35 the ultrasound contrast agent should be repelled by the cells, in our recordings we see that, once the ultrasound was turned on, the microbubbles would be attracted to the closest cell, independent of the direction of the sound field. This supports the recent finding that cell membranes can be acoustically active, [START_REF] Krasovitski | Proc. Nat. Acad. Sci[END_REF] and therefore interact with microbubbles.

Other cell types than HeLa cells must be used in follow-up studies, to investigate differences in bubble-cell interaction.

Conclusions

We have demonstrated that lipid-shelled microbubbles can be forced to enter cells at a low MI. Hence, if a therapeutic load is added to the bubble, ultrasound-guided delivery could be facilitated at diagnostic settings.

In addition, these results may have implications for the safety regulations on the use of ultrasound contrast agents for diagnostic imaging. Each frame corresponds to a 76 × 76 (µm) 2 area.

List of Figures

  18 (5)) lipophilic fluorescent probe (Vybrant TM Molecular probes, Invitrogen, San Diego, CA, USA). A ratio of 1 µl of DiD to 40 µl MicroMarker R was homogenised by pipetting and incubating for 5 minutes at room temperature. Figure 4 shows how the DiD fluorescent probe bonded to the phospholipid. 32 Emitted λ=649-703 nm fluorescence was localised on the microbubble shell when exciting at λ=633 nm. A custom-made aluminium sonication chamber with internal dimensions of 130 × 170 × 35 (mm) 3 was locked into to the xy-stage of a 200M inverted confocal microscope (Carl Zeiss AG, Oberkochen, Germany) coupled with a LSM Axiovert 510 scanning device (Carl Zeiss), using an EC Plan-Neofluar 40×/1.30

30 µl

 30 MicroMarker R was diluted into 700 µl of distilled water and tested for electrophoretic mobility (ζ-potential) using a Zetasizer 3000 (Malvern Instruments, Malvern, Worcestershire, United Kingdom). To measure the thickness of the cultured cells 10 5 HeLa cells were seeded into a OptiCell R . The cell plasma membrane was labelled with DiD lipophilic fluorescent probe (Vybrant TM Molecular probes) according to the manufacturers protocol. The membrane fluorescence was measured using a 200M confocal microscope. Cell thickness was calculated from the difference between the upper and lower slices where fluorescence was seen.

1 13 2 14 3 15 4 19 8 20 9 21 10Figure 1 :Figure 2 :

 13141519202112 Figure 1: Possible mechanisms of sonoporation: a) push, b) pull, c) jetting, d) shear, e) translation. Based on Figure 9.2 in Postema et al.[START_REF] Postema | Fundamentals of Medical Ultrasonics[END_REF]

Figure 3 :

 3 Figure 3: Experimental setup (top) and a close-up of the fluorescence configuration (bottom).

Figure 4 :

 4 Figure 4: Schematic representation of DiD (DilC 18 (5)) lipophilic fluorescent probe bonding to phospholipid.32

Figure 5 :Figure 6 :

 56 Figure 5: z-stacks of fluorescence emitted by the DiD dye attached to the membranes of four typical HeLa cells, representing the cell geometry.

Figure 7 :

 7 Figure 7: A sonoporation event including microbubble dissolution during 11 s of sonication (left ) and selected frames of the microbubble entereing a cell (right ). Microbubble "A" entered the cell and dissolved, whereas microbubble "B" stuck to the cell membrane. Each frame corresponds to a 23 × 23 (µm) 2 area.

Figure 8 :

 8 Figure 8: Microbubble of 5-µm diameter apparently penetrating through the cell membrane in optical focus (left ); z-stack through the entire cell, to record whether the apparent microbubble entry is actually into the cell (right ). Areas (A) and (C) are regions of interest inside and outside the cell, respectively.

Figure 9 :Figure 11 :

 911 Figure 9: Microbubble of 4-µm diameter apparently penetrating through the cell membrane in optical focus (left ); z-stack through the entire cell, to record whether the apparent microbubble entry is actually into the cell (right ). Areas (A) and (C) are regions of interest of high fluorescence and low fluorescence, respectively, inside the cell. The white dotted lines in the upper left frame of the right panel indicates the cell membrane. Each frame corresponds to a 52 × 52 (µm) 2 area.

  Several lipid-shelled ultrasound contrast agents were tested in this study. In this paper, we present results of a 3.33% dilution of

	6 HeLa cells that had been cultured in MEM with Earl's salts medium (PAA Laboratories GmbH, Pasching, Austria) supplemented with 10% v/v heat-inactivated fetal calf serum, GlutaMAX TM (Life Technologies Gibco, Paisley, Renfrewshire, UK), 1% v/v of non-essential amino-acids TM (VisualSonics B.V., Amsterdam, Netherlands), a lipid-shelled agent with a mean diameter of 2.5 µm. A customised BXFM-F microscope unit with an LCAch N 20×/0.40 PhC (Olympus Deutschland GmbH, Hamburg, Germany) and a LUMPlanFL 60×/0.90 water-immersion objective (Olympus) was placed on top of the sonication chamber. The colour charge coupled device (CCD) of a PHOTRON FastCam (PAA), penicillin (100 units ml -1 ) and streptomycin (100 µg ml -1 ) (PAA), at 37 MicroMarker MC-2.1 high-speed camera (VKT Video Kommunikation GmbH, Pfullingen, Germany)

o C in a humidified atmosphere containing 5% CO 2 . The cells were used when there was 60-80% confluency. Ultrasound contrast agent was injected into the cell culturing chamber before each experiment.

Acknowledgements

This work has been supported by DFG Emmy Noether Programme Grant 38355133 and EPSRC Grant EP/F037025/1. The authors are grateful to Conseil Regional for A. Delalande's fellowship.


Naoufel Azouz

Khadidja Benzemrane

Gilney Damm

Gilbert Pradel

MODELING AND DEVELOPMENT OF A 4 ROTORS HELICOPTER UAV

Keywords: Unmanned aerial vehicles, robot modelling, embedded systems, robot automatic control

This paper presents the conception and construction of a mini 4 rotors helicopter for indoor and outdoor applications. The proposed UAV, named XSF, has a very maneuverable platform and is indicated to work in inaccessible spaces such as performing inspection tasks under bridges as well as inside pipes or tanks. Its main advantage with respect to classical 4 rotors helicopters is the ability of flipping two motors in order to obtain two more control inputs. This feature allows the XSF to have a better horizontal displacement or to create a yaw movement without translation. In this work we present the XSF's conception and implementation as well as its dynamic model, including the aerodynamic and gyroscopic effects.

INTRODUCTION

Recent development of small Unmanned Aerial Vehicles (UAV), have provided new possibilities for civil tasks such as search and rescue, survey and inspection. For the two last tasks, the rotor based aerial vehicles have an important advantage over conventional fixed wings aircrafts since they can easily hover above the target. In addition, in order to execute some specific tasks, the UAV should also be small and autonomous. With this goal, we discuss in this paper the design, modelling and control of a mini 4 rotors helicopter (quadrotor). This helicopter configuration is well known and there are a number of works dedicated to this subject as [START_REF] Pounds | Design of a four-rotor aerial robot[END_REF] and [START_REF] Castillo | Realtime stabilization and tracking of a four rotor mini-rotorcraft[END_REF]. The main reasons for using this configuration of UAV is its relatively mechanical simplicity in respect to the motors construction, with no need of complex mechanics in order to obtain a directional thrust, in particular for small drones. Furthermore, this con-figuration is highly symmetric, hence control and modeling are simplified. Finally, this UAV is much maneuverable and is mostly indicated to work in inaccessible spaces. The main applications for this configuration are then inspection under bridges and other buildings or structures, specially with non-smooth surfaces. Indoors supervision and inspection such as inside pipes or tanks are another important tasks for this kind of drones.

Most literature in the field of designing quadrotor helicopters is based on the development of indoor prototypes, see [START_REF] Altug | Control of a quadrotor helicopter using visual feedback[END_REF], [START_REF] Castillo | Realtime stabilization and tracking of a four rotor mini-rotorcraft[END_REF], [START_REF] Guenard | Dynamic modelling and intuitive control strategy for an x4-flyer[END_REF] and [START_REF] Marti | The zero g eye: Towards a free hovering camera[END_REF]. However, the main problem associated with this concept is the instability of these prototypes face to atmospheric disturbances especially when maneuvering. In fact, quadrotors displacement is done in a quasi static attitude caused, in addition to physical reasons, by the difficulty of controlling such an aircraft. The main reasons of this difficulty are: the quite complex non-linear behavior of the quadrotor; the impossibility, in the general case, of measuring its internal state; the underactuated nature of the system. The first difficulty may be overcome by an improvement in the modeling phase. Actually, better understanding the system allow the development of improved robust and possible nonlinear controllers to ensure its stability. The second point will be discussed in section 3.1. Measurement or estimation of internal state is an important problem for small aerial vehicles, for which it is not possible to rely on the standard sensors as GPS. Finally, the third point is the underactuated nature of quadrotors which is the main motivation for the proposed structure. In fact, the addition of two control inputs is capital for the simplification of the control design step.

Fig. 1. The XSF and its test bed.

DESIGN AND CONSTRUCTION

The XSF drone (Figure 1)is a quadrotor with 0.68m × 0.68m. It is designed in the shape of a cross and was built in carbon fiber. Each end of the cross has a rotor including an electric brushless motor Flyware LRK-350/10, a motor speed controller Flyware rated 60A at 12V and a twoblade Graupner ducted propeller. Rotors (1) and (2) turn clockwise, while rotors (3) and (4) turn counterclockwise in order to maintain equilibrium and even be a control input in yaw motion. The main characteristic of the XSF compared to the existing quadrotors, is the swivelling of the supports of motors (1) and (4) around their pitching axis in a close manner of VTOL (Vertical Take-Off and Landing) planes. This allows an adequate horizontal flight and a supplementary control input for yaw motion.

In the center of the XSF, it is located a main cylinder enclosing the embedded sensors and microcontroler, namely an Inertial Measurement Unit, a GPS, ultrasound sensors and the 12V LI-POLY battery cells. The embedded electronics is built around an ARM family processor running a realtime e-Cos operating system. In addition, a camera is used to provide image to a possible human pilot at a remote land-base. This pilot may give higher order tasks to the robot, waypoints or completely control it to better positioning of the camera in inspection tasks. The radio link connecting the embedded system to the remote base is made by a 2.4 GHz RF transmiter.

Fig. 2. Representation of the UAV

Dynamic model

The XSF drone is modelled first as a rigid flying object. We use here an eulerian approach, while a lagrangian approach can be seen in [START_REF] Beji | Modelling, motion planning and control of the drones with revolving airfoils: an outline of the xsf[END_REF] and [START_REF] Castillo | Realtime stabilization and tracking of a four rotor mini-rotorcraft[END_REF]:

We can first state:

d(mV ) dt = τ 1 d( ĪΩ) dt = τ 2 (1)
where m represents the mass of the UAV, Ī its inertia tensor, V the linear speed in the center of gravity G, Ω the angular velocity of the local reference frame (RL) ≡ (x, y, z) (figure 2) and τ 1 τ 2 the applied forces and moments, such as weight, aerodynamic forces and torques. Expressing the equation in the local reference frame obtains:

m d(V ) dt + Ω ∧ V = τ 1 Ī d(Ω) dt + Ω ∧ ĪΩ = τ 2 (2)
R 1 = (x 1 , y 1 , z 1 ),
that is parallel to the inertial reference frame R 0 = (x 0 , y 0 , z 0 ). We have used the Euler angles ψ, θ and φ in order to express the relation betwen these different reference frames as: The angular speed is given by:

r = R T r 1 (3)
Ω = ψ • e z1 + θ • e y2 + φ • e z3
with e y2 an unitary vector resulting from the rotation ψ of (x 1 , y 1 , z 1 ) around e z1 ; e x3 an unitary vector resulting from the rotation θ of (x 2 , y 2 , z 1 ) around e y2 . The angular speed may then be expressed as:

Ω =    p q r    =    φ -sθ. ψ sφ.cθ. ψ + cφ. θ cφ.cθ. ψ -sφ. θ    (4)
In terms of the Euler angular velocities:

η =   φ θ ψ   =   1 sφ.tgθ cφ.tgθ 0 cφ -sφ 0 sφ/cθ cφ/cθ     p q r   (5)
We may then introduce u, v and w the linear speeds on the three axes of the local reference frame, such that V = u v w

T , and then we obtain:

m( u + qw -rv) = X -m.g.sθ m( v + ru -pw) = Y + m.g.sφcθ m( ẇ + pv -qu) = Z + m.g.cφcθ (6)
with X, Y and Z the aerodynamic forces applied to the UAV.

We also introduce:

I xx ṗ + (I zz -I yy )qr + ( ṙ + pq)I xz + (q 2 -r 2 )I yz +( q -pr)I xy = L I yy q + (I xx -I zz )rp + ( ṗ + rq)I xy + (r 2 -p 2 )I zx +( ṙ -pq)I yz = M I zz ṙ + (I yy -I xx )pq + ( q + rp)I yz + (p 2 -q 2 )I xy +( ṗ -qr)I zx = N (7)
L, M and N being the aerodynamic torques.

Taking into account that the plan xz and yz are symmetry plans of the XSF, we may conclude that the inertia products I xy , I xz and I yz are void. This fact allow us to simplify the previous system:

I xx ṗ = L -(I zz -I yy )qr I yy q = M -(I xx -I zz )rp I zz ṙ = N -(I yy -I xx )pq (8)
The linear speed expressed in the fixed reference frame ṙ = ( ẋ0 ẏ0 ż0 )

T may be expressed by the equation:

ẋ0 = cθcψu + (sφsθcψ -cφsψ)v + (cφsθcψ + sφsψ)w ẏ0 = cθsψu + (sφsθsψ + cφcψ)v + (cφsθsψ -sφcψ)w ż0 = -sθu + sφcθv + cφcθw (9)

Gyroscopic torques

The gyroscopic effects of the rotating elements are introduced in the model as follows. Let's denote ĪR ω i the kinetic moment of the rotor (i), such as

ĪR ω i △ = h i x h i y h i z T
, then to incorporate these effects on the dynamic model it is rewritten as:

i=1 h i z + r 4 i=1 h i y I yy q = M -(I xx -I zz )rp -r 4 i=1 h i x + p 4 i=1 h i z I zz ṙ = N -(I yy -I xx )pq -p 4 i=1 h i y + q 4 i=1 h i x ( 10
)
where we have used I R the inertia moment of the rotating elements in the rotors.

Aerodynamic forces and torques

In this section, we define the characteristics of the aerodynamic forces and torques issued from the blade theory. The blade behaves as a rotating wing. Each element of the blade dr is in contact with the airflow. The local dynamic pressure at the blade element is : q = 1 2 ρ(ωr) 2 and each elementary section of the blade of width dr creates a lift dL such as (see [START_REF] Prouty | Helicopter Performance, Stability and Control[END_REF]):

dL = 1 2 ρ(ωr) 2 C Lα c.α.dr ( 11
)
where ρ is the air density, C Lα represents an adimensional coefficient of the gradient of lift, and the attack angle α is such that α = γ -Φ.

Furthermore, γ is the geometric pitch of the blade, Φ the local inflow angle, and finally c is the aerodynamic chord that were assumed constant here.

Since the inflow angle Φ is small, we have assumed

that tanΦ = V z ωr Φ = V z ωR r R = Φ tip r R
We denote here Φ tip = Vz ωR , with R the length of the blade and V z the induced velocity. Similarly we suppose that the geometric pitch γ varies related to its value in the tip of the blade such as:

γ = γ tip r/R .
Relation (11) becomes then:

dL = 1 2 ρ(ωr) 2 C Lα c. γ tip -Φ tip r/R .dr = 1 2 ρω 2 C Lα c. γ tip -Φ tip R r.dr (12)
And integrating this last equation for the whole blade, one obtain:

L blade = R 0 dL = k 1 ω 2 (γ tip -Φ tip ) ( 13
)
With k 1 = 1 4 ρR 3 C Lα c. For a rotor with B blades, the total thrust of the rotor is then given by:

F = Bk 1 ω 2 (γ tip -Φ tip ) (14)
In the other hand, during hovering, the induced velocity is given by (see [START_REF] Padfield | Helicopter Flight Dynamics[END_REF]): V z = F 2ρA with A the area of the rotor disc. This induces that:

Φ tip = V z ωR = k 2 F 1/2 ω ( 15
)
Here

k 2 = 1 R √ 2ρA .
Equation ( 14) can be written as:

F = Bk 1 ω 2 γ tip - k 2 F 1/2 ω ( 16
)
that can be transformed in a second order equation in F 1/2 , resulting in:

F = -k 4 + (k 4 ) 2 04k 3 2 2 .ω 2 (17) with k 3 = Bk 1 γ tip k 4 = Bk 1 k 2
Equation ( 17) can be re-defined simpler as:

F △ = k T ω 2 (18)
The computation of the lift coefficient is often complex. Moreover marginal swirls at the tip of the blade can modify significantly the lift in this area.

It was thus essential to elaborate an experimental process which would enable to determine the coefficient kT as well as the limits of validity of the relation (18).

Drag is defined similarly to lift, and produces a torque defined as

M D = k M ω 2 (19)
The compensation of this torque in the center of gravity is done using the counter-rotating rotors 1-3 and 2-4. Recalling that by assumption we have ω 3 , ω 4 < 0, these last two rotors having propellers with reversed pitch.

Swivelling of rotors 1 and 3

To allow a better horizontal displacement of the XSF without banking, we give the driving supports 1 and 3 an additional degree of freedom represented by their rotation around the y axis.

We denote by β i this swing angle. The two driving supports can either swivel in the same direction to create an horizontal component propelling the XSF in translation, or swivel in opposite directions to create a yaw movement without translation. The angles β 1 and β 3 are limited to 20 degrees, where this value was chosen because it maximazes energy in our application. The intensity lost on the vertical component of the force is about 6%, while the horizontal component of the force represents 33% . This component is big enough to thrust the XSF with the maximum desired speed (10m/s). Finally we should note that the swivelling of the driving supports has a negligible influence on the inertia terms. We assume then that the inertia terms are constant during the swivelling maneuver. .

Complete Model

We may now introduce the total dynamic model of the XSF taken into account the aerodynamic and gyroscopic effects, but not considering the effect of atmospheric wind (u G and l b are physical lenghts):

ẋ0 = cθcψu + (sφsθcψ -cφsψ)v + (cφsθcψ + sφsψ)w ẏ0 = cθsψu + (sφsθsψ + cφcψ)v + (cφsθsψ -sφcψ)w ż0 = -sθu + sφcθv + cφcθw (20) m u = m(-qw + rv -g.sθ) -k T (ω 2 1 .sinβ 1 + ω 2 3 .sinβ 3 ) m v = m(-ru + pw + g.sφcθ) m ẇ = m(-pv + qu + g.cφcθ) -k T (ω 2 1 cosβ 1 + ω 2 2 + ω 2 3 cosβ 3 + ω 2 4 ) (21) η =   φ θ ψ   =   1 sφ.tgθ cφ.tgθ 0 cφ -sφ 0 sφ/cθ cφ/cθ     p q r   (22)
and

I xx ṗ = -l b k T (ω 2 1 .cosβ 1 -ω 2 3 .cosβ 3 ) -(I zz -I yy )rq -qI R (ω 1 cosβ 1 + ω 2 + ω 3 cosβ 3 + ω 4 ) I yy q = l b k T (ω 2 2 -ω 2 4 ) -(I xx -I zz )rp -rI R (ω 1 sinβ 1 + ω 3 sinβ 3 ) + pI R (ω 1 cosβ 1 + ω 2 + ω 3 cosβ 3 + ω 4 ) + k M (ω 2 3 sinβ 3 -ω 2 1 sinβ 1 ) + u G k T (ω 2 1 .sinβ 1 + ω 2 3 .sinβ 3 ) I zz ṙ = -l b k T (ω 2 1 .sinβ 1 -ω 2 3 .sinβ 3 ) -(I yy -I xx )pq + qI R (ω 1 sinβ 1 + ω 3 sinβ 3 ) + k M (ω 2 3 sinβ 3 + ω 2 4 -ω 2 1 sinβ 1 -ω 2 2 )
(23) This model's parameters have been identified on our test bed as:

m = 2.500Kg kt = 1e -5 N.s 2 l b = 0.23m I R = 100e -7 Kgm 2 Ixx = 224931e -7 Kgm 2 Iyy = 222611e -7 Kgm 2 Izz = 325130e -7 Kgm 2 k M = 9e -5 N s 2 m u G = 0.032m
where l b is the length of each arm of the drone while u G represents the distance between the center of gravity and the geometric center of the drone.

CONTROL STRATEGY

The foreseen applications for the XSF are based on a remote human operator that gives high level orders to the UAV, without needing to completely pilot it. A wireless link between a base-station and the UAV allows the operator to send navigation orders. Neverthless, the link can be cut if the UAV goes behind an obstacle and is hidden to the base. For this reason, the stabilizing controller must be on-board and not in the base-station. This stabilizing controller is based on classical robust control techniques. In the future, we intend to include pre-defined trajectories such that the drone may chose a behavior (fly higher, fly lower) to recover the link to the base. If this link is not recover after a pre-defined delay, an emergency procedure is chosen to drive the XSF to a soft descent to land. Another problem we are currently working on is optimazing the energy consumption as well as the measurement of the remaining energy in the battery cells. At any time this measurement is made to inform both the basestation and the on-board system. When a low level is reached, the on-board controller has to land the UAV.

Observers

Most control algorithms for quadrotors (see [START_REF] Guenard | Dynamic modelling and intuitive control strategy for an x4-flyer[END_REF], [START_REF] Lozano | Global stabilization of the pvtol : Real-time application to a mini-aircraft[END_REF]) need the drone's internal states. While the angles and angular velocities are readily available, position and linear velocities may be delicate to obtain. The standard solution is to use GPS sensors which may present a large error depending in the environment of the drone. These errors are usually small compared to the size of the vehicle and the distance to obstacles. Unfortunately, these techniques are not applyable for small drones, less than 1 meter wide, flying at low speed. This is even more relevant in indoors, or just urban applications. In these cases, the errors produced by a GPS system may reach many meters. This is a classical problem that was dealt with by the application of Kalman filters, which are not very effectible in the case of small drones. Recently, many works (see for instance [START_REF] Zhao | Discrete nonlinear observers for inertial navigation[END_REF] and [START_REF] Vik | A nonlinear observer for gps and ins integration[END_REF]) were consecrated to the development of observers in order to dynamically estimate at least part of the state vector. We have followed this direction and we have recently proposed an robust nonlinear adaptive observer [START_REF] Benzemrane | Unmanned aerial vehicle speed estimation via nonlinear adaptive observers[END_REF] that will be implemented on the embedded microprocessor, in order to be coupled in the robot's stabilization control algorithm. This observer was designed based on the techniques presented in [START_REF] Benzemrane | Systeme observateur pour un drone helicoptere[END_REF], [START_REF] Marino | Robust adaptive observers for nonlinear systems with bounded disturbances[END_REF] and [START_REF] Marino | Robust adaptive state-feedback tracking for nonlinear systems[END_REF]) and its first results even in the presence of noise are very interesting.

CONCLUSION

We have presented the XSF drone, a novel 4 rotors flying robot which presents a new design compared to the classical quadrotor version. This small drone is semi-autonomous and may perform different tasks of supervision and inspection following high level commands from a remote human operator. We have presented its physical model, its mechanical construction, and its control strategy. For the moment, the proposed drone has only flown on a test bed, and future steps will be flying tests on outdoors, the coupling of the observer algorithm to the controller, and the human-machine interface in order to close the loop.

Fig. 3 .

 3 Fig. 3. Definition of the reference frames

  .cψcφ.sψ sφ.sθ.sψ + cφ.cψ sφ.cθ cφ.sθ.cψ + sφ.sψ cφ.sθ.sψsφ.cψ cφ.cθ   where r is the position of a point in the local reference frame, and r 1 its position in the bodyfixed frame. Let's note cφ = cosφ and sφ = sinφ.

Fig. 4 .

 4 Fig. 4. Description of forces applied on the blade.


Josefa Bleu
email: josefa.bleu@gmail.com

Manuel Massot

Claudy Haussy

Sandrine Meylan

An experimental study of the gestation costs in a viviparous lizard: a hormonal manipulation

Keywords: arginine vasotocin, AVT-induced parturition, endurance, maternal effects, phenotypic engineering, reproductive costs, trade-offs, viviparity

The trade-offs between reproduction and survival or future reproduction represent the costs of reproduction, which are central to the theory of life history traits evolution. In particular, different stages of the reproductive cycle may be associated with different costs and thus explain the evolution of alternative reproductive strategies. Viviparity (live-bearing) has evolved from oviparity (egg-laying) several times independently in vertebrates. To better understand these transitions, we aimed to specifically investigate gestation costs in a squamate reptile with a new experimental procedure. We reduced litter size during gestation in the common lizard (Zootoca vivipara) with a hormonal injection of arginin vasotocin. This method is less invasive than a surgical method and does not reduce the number of offspring of future reproductive events. We monitored body mass change, immune response, endurance capacity, thermoregulatory behavior, offspring characteristic at birth, female and offspring survival, female body mass gain after parturition, and offspring growth rate after birth. Maternal treatment did not significantly change the offspring characteristics measured. Thus, litter size reduction did not change offspring development during gestation. For the females, there is evidence that endurance capacity during gestation is modified because of the physical burden of the litter and because of physiological changes. With respect to gestation costs, we did not observe a trade-off between the investment during gestation and females' resources postparturition (female body mass) or survival, but there was a facultative trade-off with the immune response. It will be interesting to replicate this study to increase the robustness of these results and to confirm the effects on the endurance capacity and the immune response.

Gestation costs seem to be limited in this species and they should be studied in more detail to evaluate their influence on the evolution of viviparity.

INTRODUCTION

Costs of reproduction are the trade-offs that exist between reproductive investment and survival and/or future reproduction [START_REF] Stearns | Trade-offs in life-history evolution[END_REF][START_REF] Roff | Life History Evolution[END_REF]. A simple energetic link may explain such costs [START_REF] Roff | Life History Evolution[END_REF]: females that used more energy have fewer resources to invest in the following reproductive event. Moreover, carrying eggs may constitute a physical burden and directly reduce females' locomotor abilities and thus survival (e.g. [START_REF] Shaffer | A cost of viviparity and parental care in scorpions: reduced sprint speed and behavioural compensation[END_REF][START_REF] Lee | Reduction in escape performance as a cost of reproduction in gravid starlings, Sturnus vulgaris[END_REF][START_REF] Veasey | Flight muscle atrophy and predation risk in breeding birds[END_REF][START_REF] Miles | Reproductive burden, locomotor performance, and the cost of reproduction in free ranging lizards[END_REF]. However, indirect effects may also exist, and the physiological basis of reproductive costs are increasingly studied [START_REF] Zera | The physiology of life history trade-offs in animals[END_REF][START_REF] Harshman | The cost of reproduction: the devil in the details[END_REF].

Indeed, some functions may be downregulated as a consequence of a high reproductive investment which may affect female survival or future reproduction. Major functions that can be downregulated are the immune system (e.g. [START_REF] Hanssen | Cost of reproduction in a long-lived bird: incubation effort reduces immune function and future reproduction[END_REF][START_REF] French | Trade-offs between the reproductive and immune systems: facultative responses to resources or obligate responses to reproduction[END_REF][START_REF] Cox | Experimental evidence for physiological costs underlying the trade-off between reproduction and survival[END_REF], the oxidative defence (e.g. [START_REF] Dowling | Reactive oxygen species as universal constraints in life-history evolution[END_REF][START_REF] Garratt | Is oxidative stress a physiological cost of reproduction? An experimental test in house mice[END_REF] and growth (e.g. [START_REF] Berglund | Reproductive costs in the prawn Palaemon adspersus: effects on growth and predator vulnerability[END_REF][START_REF] Landwer | Manipulation of egg production reveals costs of reproduction in the tree lizard (Urosaurus ornatus)[END_REF][START_REF] Cox | A test of the reproductive cost hypothesis for sexual size dimorphism in Yarrow's spiny lizard Sceloporus jarrovii[END_REF]). Most experimental studies on reproductive costs are based on phenotypic engineering [START_REF] Sinervo | Allometric engineering: an experimental test of the causes of interpopulational differences in performance[END_REF][START_REF] Sinervo | Allometric engineering: a causal analysis of natural selection on offspring size[END_REF]) and more precisely on clutch/litter size manipulation. The strength of these studies is that the experimental approach allows causal conclusions to be drawn as opposed to correlations.

Different stages of the reproductive cycle may be associated with different costs, and thus the timing of litter size manipulation is important. For example, in birds clutch size is usually manipulated after laying (to study the costs of chick rearing), however egg production and incubation also incur fitness costs [START_REF] Reid | Resource allocation between reproductive phases: the importance of thermal conditions in determining the cost of incubation[END_REF][START_REF] Visser | The costs of egg production and incubation in great tits (Parus major)[END_REF].

In mammals, lactation is more costly than gestation (e.g. [START_REF] Clutton-Brock | Fitness costs of gestation and lactation in wild mammals[END_REF][START_REF] Michener | Reproductive effort during gestation and lactation by Richardson's ground squirrels[END_REF][START_REF] Dufour | Comparative and evolutionary dimensions of the energetics of human pregnancy and lactation[END_REF]. Disentangling the relative importance of each stage may be important to assess the costs and benefits of different reproductive strategies.

Viviparity (live bearing) has evolved from oviparity (egg laying) several times independently in vertebrates (Blackburn 1999a;[START_REF] Sinervo | Mechanistic analysis of natural selection and a refinement of Lack's and Williams's principles[END_REF]. In squamates (lizards and snakes) in particular, viviparity has evolved more than 100 times (Blackburn 1999a). To better understand these transitions we aimed to specifically investigate gestation costs in a squamate reptile. The main advantage of squamates is that, in most species, most nutrients for embryonic development are provided in the egg yolk (lecithotrophic viviparity (Blackburn 1999a)). This means that the period of egg formation (i.e. vitellogenesis) can be costly for females as in oviparous species and that few nutrients are transferred during gestation. The energy needed during gestation thus represents the costs to maintain and carry the developing embryos (gestation costs). In other words, the energetic cost in terms of egg formation (vitellogenesis cost) and the costs of gestation can be decoupled.

Clutch or litter size can be manipulated before egg laying by a surgical or hormonal manipulation. The removal of follicles (yolkectomy) (e.g. [START_REF] Sinervo | Hormonal and physiological control of clutch size, egg size, and egg shape in side-blotched lizards (Uta sansburiana): constraints on the evolution of lizard life histories[END_REF] or ovaries (e.g. [START_REF] Cox | A test of the reproductive cost hypothesis for sexual size dimorphism in Yarrow's spiny lizard Sceloporus jarrovii[END_REF][START_REF] Cox | Experimental evidence for physiological costs underlying the trade-off between reproduction and survival[END_REF] decreases or even suppresses the reproductive effort. An injection of the follicle stimulating hormone (FSH) increases the number of follicles and thus the reproductive effort (e.g. [START_REF] Sinervo | Hormonal and physiological control of clutch size, egg size, and egg shape in side-blotched lizards (Uta sansburiana): constraints on the evolution of lizard life histories[END_REF][START_REF] Sinervo | Costs of reproduction in the wild: path analysis of natural selection and experimental tests of causation[END_REF][START_REF] Swain | Facultative placentotrophy: half-way house or strategic solution?[END_REF][START_REF] Oksanen | Hormonal manipulation of offspring number: maternal effort and reproductive costs[END_REF][START_REF] French | Trade-offs between the reproductive and immune systems: facultative responses to resources or obligate responses to reproduction[END_REF]. These manipulations are a very powerful way to study reproductive costs but do not allow the researcher to quantify gestation costs per se: we need to manipulate litter size during gestation. Previous studies in squamates used a surgical procedure to decrease litter size during gestation: removal of one of the two oviducts containing developing embryos ("halfhysterectomy"). This method allows to study the development of the remaining embryos [START_REF] Sangha | The effect of surgical removal of oviductal eggs on placental function and size of neonates in the viviparous snake Virginia striatula[END_REF][START_REF] Swain | Facultative placentotrophy: half-way house or strategic solution?[END_REF] and also gestation costs (Bleu et al. 2012b).

However, such a procedure is invasive and permanent for the females. Thus it would be interesting to develop a relatively non-invasive hormonal method to reduce litter size. The hormones oxytocin in mammals and the arginine vasotocin (AVT) in Reptilia are appropriate for these types of experiments because they induce early parturition or oviposition when injected into pregnant/gravid females [START_REF] Guillette | Further observations on arginine vasotocin-induced oviposition and parturition in lizards[END_REF][START_REF] Guillette | Prostaglandins, oviducal function, and parturient behavior in nonmammalian vertebrates[END_REF][START_REF] Feldman | Some options to induce oviposition in turtles[END_REF]. Depending on species, on concentrations and on the timing of the injection, AVT induce partial or full parturition (oviposition) in viviparous (oviparous) squamates (e.g. [START_REF] Guillette | Stimulation of parturition in a viviparous lizard (Sceloporus jarrovi) by arginine vasotocin[END_REF][START_REF] Summers | Induction of oviposition in cycling Anolis carolinensis requires a beta-adrenoreceptor blocker and a high dosage of arginine vasotocin[END_REF]Atkins, Jones & Guillette 2006).

The aim of this study is to use AVT to manipulate litter size during gestation with a relatively noninvasive method and to assess the behavioral, physiological and survival gestation costs of large litters. To this end, we used the common lizard, Zootoca vivipara, and measured shortterm effects of the manipulation: body mass change, immune response, endurance capacity, thermoregulatory behavior, offspring characteristics at birth and also long-term effects: female and offspring survival, offspring growth rate after birth and female body mass gain after parturition. An effect of the treatment on these traits would reveal gestation costs of large litters, whereas an effect of the initial litter size (litter size before the hormonal treatment) would suggest vitellogenesis costs (i.e. a correlation with the initial investment of the female). We also compared the results with previous ones from a study where litter size was surgically reduced during gestation in Z. vivipara (half-hysterectomy) (Bleu et al. 2012b).

Thus we measured the same variables as in Bleu et al. (2012b) and we also measured the endurance capacity of the females (this measure is possible because this hormonal manipulation is less invasive than the surgical one). This study also aims to better understand the physiological control of parturition in a squamate.

MATERIALS AND METHODS

Model species, capture and rearing conditions

Zootoca vivipara is a small (adult snout-vent length 45-70 mm) ground-dwelling lizard, widely distributed across Eurasia. It includes both oviparous and viviparous reproductive forms in allopatric populations [START_REF] Surget-Groba | Intraspecific phylogeography of Lacerta vivipara and the evolution of viviparity[END_REF]. We studied viviparous populations located in the Massif Central mountain range (South-eastern France). In this area, adults start to become active around mid-April (males) or early May (females). Mating may occur as early as 0-3 days after emergence and reproductive investment (vitellogenesis) occurs on average during the first three weeks after emergence [START_REF] Bauwens | The timing of reproduction in the lizard Lacerta vivipara: differences between individual females[END_REF]. During gestation, placentas formed from the chorioallantois and yolk sac allow respiratory, aqueous and mineral exchanges between mother and embryos [START_REF] Panigel | Contribution à l'étude de l'ovoviviparité chez les reptiles: gestation et parturition chez le lézard vivipare Zootoca vivipara[END_REF][START_REF] Stewart | Extraembryonic membrane development in a reproductively bimodal lizard, Lacerta (Zootoca) vivipara[END_REF][START_REF] Stewart | Calcium provision to oviparous and viviparous embryos of the reproductively bimodal lizard Lacerta (Zootoca) vivipara[END_REF]. Parturition occurs after an average gestation period of 2 months. Mean litter size is five (range 1-12). Live offspring hatch immediately after parturition from their soft-shelled eggs and are thereafter autonomous.

Lizards gradually enter into hibernation in September.

We captured 46 pregnant females in mid-June 2010 at Mont-Lozère (44°22'16''N, 03°47'47''E, 1260 m a.s.l.). The study site is ca. 5500 m 2 and is covered with a mixture of grass, heath, trees and rocks. Females were marked by toe-clipping, and brought to a field laboratory until parturition (July 14-24). Females were kept in individual terraria (18 cm x 12 cm x 12 cm) with a shelter and with damp soil as substrate. A 25-W spotlight provided opportunities for thermoregulation for 6 hours daily (from 9:00 to 12:00 and from 14:00 to 17:00), creating a thermal gradient from 24.7°C to 39.4°C in the terrarium. Water was provided ad libitum and 1 Pyralis sp. larva was offered per week. Immediately after parturition, mothers and their offspring were separated and measured. Within 4 days, the females were released at their capture point and offspring were released randomly at 10 different points on the site. Offspring from the same family were released at the same point.

Experimental procedure

Litter size reduction during gestation,

The experimental reduction of litter size during gestation was achieved by an injection of AVT (Sigma-Aldrich, V0130). Previous studies on reptiles have successfully used this drug to induced parturition in viviparous lizards, at very different concentrations across species [START_REF] Guillette | Prostaglandins, oviducal function, and parturient behavior in nonmammalian vertebrates[END_REF][START_REF] Girling | Induction of parturition in snow skinks: can low temperatures inhibit the actions of AVT[END_REF]Atkins, Jones & Guillette 2006;Bleu et al. 2012a). Females were randomly allocated to each treatment group: AVTinjected females (n = 25) and unmanipulated control females (n = 21). These two experimental groups did not differ in snout-vent length (SVL), body condition (i.e. body mass with SVL as a covariate in the statistical model) and litter size (fecundity) at the beginning of the experiment (all P > 0.40). On the July 5 or 6, females from the AVT-injected group received an intraperitoneal injection (20 μL) of 0.02μg/μL AVT diluted in sterile phosphatebuffered saline (PBS, Sigma-Aldrich, reference D 5773). After the injection, 13 females gave birth to a partial litter and 12 females did not. In some of the females that did not give birth, we nonetheless saw contractions indicating that the AVT was active also in these females.

There are no differences in initial SVL, body condition or fecundity between the females that reacted to the AVT injection and the females that did not (all P > 0.60). The manipulation was performed in the last third of gestation (embryos removed were at stages 34 to 37 [START_REF] Dufaure | Table de développement du lézard vivipare: Lacerta (Zootoca) vivipara Jacquin[END_REF]) because this drug is thought to be more efficient in late gestation (e.g.

Guillette, Dubois & Cree 1991).

The experimental treatment resulted in three different groups: control females (hereafter called C, n = 21); females that received an AVT injection but did not react, i.e. they did not lay following the injection (hereafter called AC, n = 12); females that reacted to the injection and laid a partial litter (hereafter called ALR, n = 13). The females that did not react to the AVT injection (AC) may allow us to control for the effects of AVT that are not related to parturition, if the AVT was nonetheless active in these females. These three groups did not differ in initial SVL, body condition or fecundity (all P > 0.69).

Short term effects of litter size reduction on female's performances, Endurance was measured once on July 8 or 9. After warming up to approximately 27°C (natural activity temperature) for at least 30 min, we induced the females to run at the pace of the belt (0.5 km/h) by gently tapping on the hind leg (Le [START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF][START_REF] Miles | Corticosterone, locomotor performance, and metabolism in side-blotched lizards (Uta stansburiana)[END_REF]. A lamp suspended above the belt was used to maintain the body temperature of lizards. Our measure of endurance was the amount of time the lizards maintained their position on the treadmill until exhaustion. A lizard was determined to be exhausted if it failed to maintain its position on the belt after three attempts.

After the measure of endurance, the behavior of each lizard was measured seven times over 5 days, 1 or 2 times per day between 10:00-11:00 and/or 15:00-16:00, by an observer who did not know the treatment of the lizards. The observer noted whether the lizard was sheltering (under the shelter or the substrate), full basking or half-basking (the head under the light and the rest of the body hidden; as described elsewhere [START_REF] Cote | Food deprivation modifies corticosterone-dependent behavioural shifts in the common lizard[END_REF]Bleu et al. 2012a;[START_REF] Sinervo | Mechanistic analysis of natural selection and a refinement of Lack's and Williams's principles[END_REF]).

We distinguished half-basking from full basking, as the behaviors may differ in thermoregulatory efficiency (female body temperature) or predation risk.

After parturition (2.29 days, SE = 0.12 days), immunocompetence was estimated with the phytohaemagglutinin (PHA)-induced skin-swelling test as described by Bleu et al. (2012b).

Briefly, we injected subcutaneously 0.04 mL of a solution of phosphate-buffered saline (PBS, Sigma-Aldrich, reference D5773) containing 2.5 mg/mL of PHA (Sigma-Aldrich, reference L8754) in the right posterior leg and measured the swelling response 12h later. We measured thickness of the leg to the nearest 0.01 mm with a spessimeter (ID-C Absolute digimatic, Mitutoyo, France, reference 547-301). Although PHA swelling response is complex, including both innate and adaptive components of the immune system [START_REF] Tella | The PHA test reflects acquired T-Cell mediated immunocompetence in birds[END_REF][START_REF] Vinkler | Functional analysis of the skin-swelling response to phytohaemagglutinin[END_REF], it evaluates the general ability of an individual to mount an inflammatory response [START_REF] Vinkler | Functional analysis of the skin-swelling response to phytohaemagglutinin[END_REF].

Parturition date, realized fecundity (litter size at parturition) and litter success (i.e. the presence or absence of non-viable embryos) were recorded. Initial fecundity was also calculated as the sum of the realized fecundity and the number of eggs removed by the AVT treatment. Offspring were marked by toe clipping, measured for SVL (to the nearest mm), weighed (to the nearest mg) and sexed by ventral scale count [START_REF] Lecomte | Sex identification in juveniles of Lacerta vivipara[END_REF]. Females were weighed after parturition.

Delayed effect of litter size reduction on growth and survival, We recaptured the offspring and the adult females in late August of the year of release and in late May of the following year (Table 1). At each recapture, we weighed and measured SVL of all individuals. Juvenile growth rates before hibernation were calculated as the change in SVL (SVL at recapture -SVL at birth) divided by the time interval (date of recapturedate of birth). Adult body mass gain before hibernation was calculated as the change in body mass (body mass at recapturepostpartum body mass) divided by the time interval (date of recaptureparturition date).

Statistical analyses

All models were implemented in R 2.15.0 statistical software (http://cran.r-project.org/). They included the following additive fixed effects: (i) treatment (C, AC, ALR); (ii) female SVL;

(iii) standardized initial fecundity (residuals from a regression between initial fecundity and female SVL, R 2 = 0.32, P < 0.0001), which represents the effect of the initial investment of females; and (iv) the first-order interactions with treatment. Models were simplified using backward elimination of the non-significant terms (P > 0.10). For the behavior, we first analyzed the proportion of time spent basking (half-or full basking), and then we analyzed the proportion of time spent full basking when the lizard was basking. These analyses were conducted using generalized linear models with a quasibinomial family (to correct for overdispersion) and a logit function link (glm procedure). Since there was overdispersion, fixed effects were tested with F-tests [START_REF] Venables | Modern Applied Statistics with S[END_REF]. Litter success was analyzed as a binomial variable (litters with all viable offspring vs. litters with at least one failure) using the same glm procedure with a binomial family. In this case, fixed effects were tested with chi-square tests. Endurance (log transformed to achieve normality), postpartum body condition, PHA response and parturition date were analyzed with linear models (lm procedure and type III F-tests [START_REF] Quinn | Experimental Design and Data Analysis for Biologists[END_REF]). SVL and body condition at birth of offspring were analyzed with linear mixed effects models (lme procedure and marginal F-tests [START_REF] Pinheiro | Mixed-effects Models in S and S-PLUS[END_REF]). The random part of the models was maternal identity to account for a family effect. SVL of offspring at birth also included an effect of offspring sex. Offspring body condition at birth also included an effect of offspring sex and of offspring SVL.

Juvenile growth rates and female adult body mass gain before hibernation were analyzed with linear mixed effects models (lme procedure) and linear models (lm procedure) respectively.

We tested the effects of the experimental treatment and the standardized initial fecundity. For the analysis of juvenile growth rate, we also included juvenile sex and initial SVL to control for decelerating growth curves (Andrews 1982). The random effect was maternal identity. For the analysis of female body mass gain, we also included female SVL and postpartum body condition (residuals from a regression between postpartum body mass and female SVL).

The assumptions of normality and homogeneity of variances were checked for all initial and final models. The values presented in the results section are the means for each group or the estimates of the models ± the SEs.

Survival analyses

We tested the effect of the treatment on the probability of survival for adult females, juvenile males and juvenile females. Survival estimates were obtained independently of capture probabilities, using a capture-mark-recapture method based on the open population model of Cormack-Jolly-Seber. This model produces apparent survival estimates resulting from mortality and emigration. We used the program MARK version 6.0 to fit models [START_REF] White | Program MARK: survival estimation from populations of marked animals[END_REF], and models were compared with Akaike Information Criterion corrected for small sample size (AICc [START_REF] White | Program MARK: survival estimation from populations of marked animals[END_REF]). The best model is the most consistent with the data while using the fewest number of parameters, i.e. giving the lowest AICc. It is considered that two models differ when their difference of AICc is higher than 2 [START_REF] Burnham | Model Selection and Inference: a Practical Information-theoretical Approach[END_REF]. The goodness-of-fit of the time-dependent Cormack-Jolly-Seber models were tested with the bootstrap procedure (1,000 simulations) provided by the program MARK [START_REF] White | Program MARK: survival estimation from populations of marked animals[END_REF]), and we did not find significant over-dispersion in the data (all P > 0.18).

RESULTS

Reproductive traits

The treatment affected the realized fecundity (F 2,42 = 15.12, P < 0.001, see Figure 1). Post hoc comparisons show that on average ALR females gave birth to 2.90 ± 0.55 fewer offspring compared to C females (t = -5.32, P < 0.001) and to 2.52 ± 0.62 fewer offspring compared to AC females (t = -4.07, P < 0.001). Litter sizes of C and AC females were not significantly different (t = -0.68, P = 0.499). In the ALR group, the AVT injection reduced litter size by 52.34 ± 22.35 % (range = 14%-83 %, see Figure 1). The treatment had no effect on litter success (χ 2 = 3.85, df = 2, P = 0.146). However, the AVT injection affected parturition dates of both ALR and AC females (F 2,43 = 3.68, P = 0.034, Figure 2). All females gave birth in a 10-day period and post hoc comparisons show that ALR females gave birth on average on the same day as AC females (t = -0.61, P = 0.547) but 2.51 ± 0.99 days earlier than C females (t = -2.55, P = 0.015). The difference between C and AC females approached significance (t = 1.81, P = 0.077, Figure 2).

Concerning juvenile characteristics at birth, body condition (body mass statistically corrected by size) was not affected by the treatment (F 2,34 = 0.28, P = 0.754, Table 2). As typical in Z. vivipara, male offspring were more corpulent than females (F 1,135 = 13.34, P < 0.001). Also, offspring body condition was not significantly correlated to female standardized initial fecundity (F 1,36 = 2.03, P = 0.163). The interactions and other variables tested were not significant (all P > 0.29). We observed the same pattern for offspring size at birth: there was no effect of the treatment (F 2,34 = 0.02, P = 0.984, Table 2), but a significant effect of sex (F 1,136 = 52.46, P < 0.001). Offspring size was not significantly correlated to female standardized initial fecundity (F 1,36 = 2.36, P = 0.133).

Females' behavior and performance

Before parturition, ALR, AC and C females had different endurance capacity depending on their initial standardized fecundity (Table 3). In C females, there was a negative relationship between the endurance capacity and the initial standardized fecundity (Figure 3, t=-2.47, P=0.018). This relationship was not observed in AC and ALR females (t=1.87, P=0.070 and t=-0.44, P=0.663 respectively). Moreover, ALR females showed highest endurance (Figure 3). Concerning the thermoregulatory behavior, ALR, AC and C females were not significantly different (Tables 2 and3): the proportion of time spent basking and the proportion of time spent full basking when the female was basking were not significantly affected by the treatment. After parturition, the response to PHA was dependent on the treatment and female size (Table 3, Figure 4). The response to PHA was positively correlated to female size only in ALR females such that longer ALR females had a stronger response than AC and C females (Figure 4). The postpartum body condition of the females (body mass statistically corrected by size) was not significantly different between the experimental treatments (Tables 2 and3).

Females and offspring growth rates and survival

We recaptured the adult females and the juveniles on two recapture sessions (see sample sizes in Table 1). None of our variables significantly explained female body mass gain between parturition and hibernation, and in particular it was not dependent on the treatment (F 2,21 = 0.99, P = 0.388). The probability of female survival was not significantly affected by the treatment or by the time of recapture (best AICc for model Φ constant and p constant , Table A1).

Juveniles' growth before hibernation was not dependent on the treatment of their mother (Tables 2 and4). The probability of survival of juvenile females before hibernation was independent of the maternal treatment (best AICc for model Φ constant and p treatment , Tables 2 andA2 A). This best model and the other comparable models (ΔAICc < 2, see Table A2 A) suggest that juvenile females had different capture probabilities depending on the maternal treatment (C = 0.376 ± 0.087, AC = 0.364 ± 0.116, ALR = 1.00 ± 0.01). For juvenile males, the best model suggests that the probabilities of survival and capture were not dependent on the maternal treatment (best AICc for model Φ time and p time and model Φ constant and p time , Tables 2 andA2 B). However, other models have comparable AICc, including a model where capture probabilities and survival probabilities are dependent on the maternal treatment (Table A2 B).

DISCUSSION

Viviparity and oviparity are two reproductive strategies which entails specific costs and benefits. The main cost of viviparity is supposed to be the existence of higher reproductive cost due to gestation costs and the lower probability to produce several litters per season [START_REF] Tinkle | The distribution and evolution of viviparity in reptiles[END_REF]Blackburn 1999a). Gestation costs in viviparous squamates may be attributed to an increase in metabolism, a shift in thermal preference and locomotor impairment [START_REF] De Marco | Physiological cost of pregnancy in a viviparous lizard (Sceloporus jarrovi)[END_REF][START_REF] Olsson | Locomotor impairment of gravid lizards: is the burden physical or physiological[END_REF][START_REF] Ladyman | Gestation, thermoregulation, and metabolism in a viviparous snake, Vipera aspis: evidence for fecundity-independent costs[END_REF][START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF][START_REF] Lin | Influence of pregnancy on locomotor and feeding performances of the skink, Mabuya multifasciata: Why do females shift thermal preferences when pregnant[END_REF]. However above-cited studies are based on comparisons between reproductive and nonreproductive females, or between reproductive and postreproductive females. Thus, they do not allow causal conclusions. In the first kind of comparison, females may differ according to other variables than their reproductive state: for example, in squamates, nonreproductive females often have lower body condition than reproductive females (e.g. [START_REF] Naulleau | Body condition threshold for breeding in a viviparous snake[END_REF]. And when comparing performances of the same female before and after parturition, other confounding effects arise, such as seasonal variation in traits (e.g. [START_REF] Qualls | Costs of reproduction in conspecific oviparous and viviparous lizards, Lerista bougainvillii[END_REF].

In this article, we report an experimental study that is complementary to a previous study where litter size of Z. vivipara females was reduced by half-hysterectomy (Bleu et al. 2012b).

Concerning short term effects, we found no effect of the litter size reduction on offspring characteristics at birth, in line with results of the first study (Bleu et al. 2012b). It further supports the hypothesis that offspring development during gestation is not limited by maternal nutrient transfer or by the space available [START_REF] Du | Does body volume constrain reproductive output in lizards?[END_REF]Bleu et al. 2012b). We did not observe a trade-off between initial litter size and offspring mass or size. The detection of trade-offs in natural populations is difficult because it is obscured by the natural variability between females (e.g. variability in food acquisition) [START_REF] Van Noordwijk | Acquisition and allocation of resources: their influence on variation in life history tactics[END_REF]. In particular in the common lizard, it has been shown that the litter size-offspring mass trade-off is not observed every year [START_REF] Bleu | Reproductive allocation strategies: a long-term study on proximate factors and temporal adjustments in a viviparous lizard[END_REF]. We also found different results compared to the previous study (Bleu et al. 2012b): there was no effect of the litter size manipulation on the thermoregulatory behavior and on female postpartum body mass. Previously we showed that females with a reduced litter size spent more time half-basking and had a higher postpartum body mass (Bleu et al. 2012b). Metabolic rates increase with temperature, thus females which have higher daily energetic demands may bask more and therefore lose a greater proportion of body mass after parturition compared to females with lower daily energetic demands. In this case, thermoregulatory behavior would reflect the energetic needs and thus reproductive costs (Bleu et al. 2012a;[START_REF] Sinervo | Mechanistic analysis of natural selection and a refinement of Lack's and Williams's principles[END_REF]. However in this study we did not detect different reproductive costs (energetic needs) between females with a reduced or an unmanipulated litter size (no difference in body mass), which may explain that there was no differences in the thermoregulatory behavior. The immune response was increased in females with a reduced litter although it was not affected in the previous study (Bleu et al. 2012b). This suggests a trade-off between reproductive investment and the immune function. However this effect was size dependent: only the longer females had a higher immunocompetence. This shows that it is not an obligatory response to gestation [START_REF] French | Trade-offs between the reproductive and immune systems: facultative responses to resources or obligate responses to reproduction[END_REF]. Larger females can store more resources [START_REF] Avery | Storage lipids in the lizard Lacerta vivipara: a quantitative study[END_REF]) and may thus be able to invest more in their immune response contrary to smaller females. It should be noted that the level of significance of this effect is not very strong (p-value = 0.018) and that, if we corrected the statistical analysis for multiple testing, this p-value would not be considered significant. Thus, it will be necessary to replicate this study on more individuals and different populations to confirm this effect.

This study highlights some differences with the previous study of experimental litter size manipulation in Z. vivipara (Bleu et al. 2012b). We cannot exclude that this reflects annual (different years) or geographic (different populations) variations in reproductive costs (e.g. [START_REF] Qualls | Geographic variation in "costs of reproduction" in the scincid lizard Lampropholis guichenoti[END_REF]. Also, we performed the manipulation of litter size slightly later during gestation (stages 34-37 compared to stages 29-34). However, the hormonal treatment itself might explain some of these differences. Indeed, AVT can induce parturition but it has also other effects. Most importantly, AVT affects sexual, social and aggressive behaviors [START_REF] Goodson | Social behavior functions and related anatomical characteristics of vasotocin/vasopressin systems in vertebrates[END_REF][START_REF] Godwin | Nonapeptides and social behavior in fishes[END_REF], thermoregulatory behavior [START_REF] Bradshaw | Effect of hypernatraemia and the neurohypophysial peptide, arginine vasotocin (AVT) on behavioural thermoregulation in the agamid lizard, Ctenophorus ornatus[END_REF]) and the salt and water balance [START_REF] Bradshaw | Arginine vasotocin: site and mode of action in the reptilian kidney[END_REF]. The AC females should allow us to detect these other effects, but we do not know why these females did not lay eggs in response to the AVT injection. The fact that parturition dates and endurance capacity of these females differed from control females is an indication that the AVT had some effects. However, we do not know to what extent the effects of AVT are similar in AC and ALR females and thus to what extent AC females are a relevant control group. For example, a change of the thermoregulatory behavior due to the AVT but only in the ALR females may counterbalance the effect of reproductive costs and result in the absence of differences between the females of the different experimental groups. This experiment shows that there is a need to increase our understanding of the actions of AVT in squamates, besides its classical effect on parturition.

In squamates, much attention has focused on the decrease of locomotor capacities of reproducing oviparous and viviparous females: a decrease of endurance [START_REF] Cooper | Locomotor impairment and defense in gravid lizards (Eumeces laticeps): behavioral shift in activity may offset costs of reproduction in an active forager[END_REF][START_REF] Miles | Reproductive burden, locomotor performance, and the cost of reproduction in free ranging lizards[END_REF][START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF][START_REF] Zani | Effects of reproductive burden on endurance performance in side-blotched lizards (Uta Stansburiana)[END_REF] and/or sprint speed (Van Damme, [START_REF] Van Damme | Effect of relative clutch mass on sprint speed in the lizard Lacerta vivipara[END_REF][START_REF] Cooper | Locomotor impairment and defense in gravid lizards (Eumeces laticeps): behavioral shift in activity may offset costs of reproduction in an active forager[END_REF][START_REF] Sinervo | Decreased sprint speed as a cost of reproduction in the lizard Sceloporus occidentalis: variation among populations[END_REF][START_REF] Qualls | Geographic variation in "costs of reproduction" in the scincid lizard Lampropholis guichenoti[END_REF][START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF]Shine 2003b) have been documented. Only in some rare cases, locomotor capacities are not affected or are even increased during reproduction [START_REF] Qualls | Geographic variation in "costs of reproduction" in the scincid lizard Lampropholis guichenoti[END_REF], 1998). Despite the interest in quantifying the changes of locomotor performance during reproduction, the underlying causes of these changes are not well understood. Experimental studies suggest that this cost may be both physical and physiological and may be species specific (oviparous: [START_REF] Miles | Reproductive burden, locomotor performance, and the cost of reproduction in free ranging lizards[END_REF]viviparous: Olsson, Shine & Bak-Olsson 2000;Shine 2003a). In Z. vivipara, litter size may be correlated with the decrease of locomotor performances (Van Damme, [START_REF] Van Damme | Effect of relative clutch mass on sprint speed in the lizard Lacerta vivipara[END_REF][START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF], which suggest that it may be driven by the physical burden of reproduction. Moreover, the recovery of endurance capacity is quick (one week). However, the recovery of sprint speed is slower which suggests physiological effects of gestation (Le [START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF]. In control females there is a clear negative correlation between endurance and litter size, and females with reduced litters have a higher performance than control females. This confirms the importance of litter size and the physical burden on endurance capacity. However, AC females also show different endurance capacity than control females. In these females, the endurance capacity is not anymore correlated to litter size. This shows that a hormonal change (AVT injection) can affect endurance capacity despite a physical burden. AVT has been shown to increase activity in some species [START_REF] Boyd | Effect of vasotocin on locomotor activity in bullfrogs varies with developmental stage and sex[END_REF] but also to decrease activity in others [START_REF] Thompson | Vasotocin stimulates appetitive responses to the visual and pheromonal stimuli used by male roughskin newts during courtship[END_REF][START_REF] Nephew | Effects of arginine vasotocin (AVT) on the behavioral, cardiovascular, and corticosterone responses of starlings (Sturnus vulgaris) to crowding[END_REF]. This experiment suggests that it may increase endurance capacity in Z. vivipara. This may explain the quick recovery of endurance capacity after parturition (Le [START_REF] Galliard | Timing of locomotor impairment and shift in thermal preferences during gravidity in a viviparous lizard[END_REF] since AVT is secreted before parturition [START_REF] Guillette | Prostaglandins, oviducal function, and parturient behavior in nonmammalian vertebrates[END_REF]. Thus the physiological changes associated with gestation may also be important to shape locomotor impairment during this period. It will be interesting to confirm this result with additional studies because it is not robust to a correction for multiple testing (p-value = 0.028).

Finally, we also measured long-term effects of litter size reduction. There was no effect of the treatment on female characteristics before hibernation (survival, body mass gain). It seems that there is no important cost of gestation in terms of survival, as observed previously (Bleu et al. 2012b). However, it should be noted that our sample size for the survival analyses would not have allowed us to detect small effects on survival. We also measured offspring characteristics because reproductive effort can have intergenerational effects: offspring quality may decrease when reproductive investment increases, due to a trade-off between offspring number and quality [START_REF] Roff | Life History Evolution[END_REF]. Experiments have shown the existence of such a trade-off: for example, offspring from enlarged litters have been shown to have a lower survival [START_REF] Sinervo | Mechanistic analysis of natural selection and a refinement of Lack's and Williams's principles[END_REF][START_REF] Oksanen | The cost of reproduction induced by body size at birth and breeding density[END_REF], and offspring from reduced litters have been shown to grow faster after birth (in Z. vivipara: Bleu et al. 2012b). In this study, there was no clear effect of the maternal treatment on offspring growth or offspring survival. Offspring growth is very plastic and is influenced by parasite load [START_REF] Uller | Prenatal exposure to testosterone increases ectoparasite susceptibility in the common lizard (Lacerta vivipara)[END_REF], weather conditions [START_REF] Lorenzon | Effect of water constraint on growth rate, activity and body temperature of yearling common lizard (Lacerta vivipara)[END_REF] or food availability (Le [START_REF] Galliard | Juvenile growth and survival under dietary restriction: are males and females equal?[END_REF].

These factors may help explain why we did not find an effect on growth contrary to a previous study (Bleu et al. 2012b). Again, we cannot exclude that the AVT treatment per se had an influence on juvenile growth (in juveniles from ALR or AC females). This hormonal manipulation can have effects beyond the effects on parturition. These effects need to be investigated further to better understand all the actions of AVT and to be able to develop this promising experimental method. In conclusion, with regard to gestation costs, we did not observe a trade-off between the investment during gestation and females' resources postparturition (female body mass) or survival. (AVT-treated females with a reduced litter). There was a significant interaction between the treatment and the standardized initial fecundity (see Table 3 for statistics). In this figure, we distinguished the female with a negative standardized initial fecundity (minus sign) and with a positive standardized initial fecundity (plus sign). (AVT-treated females with no litter size reduction), and the black triangles and the black dashed line represent ALR females (AVT-treated females with a reduced litter). There was a significant interaction between the treatment and the PHA response (see Table 3 for statistics). The slopes were estimated from the statistical model presented in Table 3. 3 We had three experimental groups (treatment): ALR females (AVT-treated females with a reduced litter), AC females (AVT-treated females with no litter size reduction) and C females (control females). The full-models included an effect of the treatment (TRT), of female body length (SVL) and of standardized initial fecundity (FEC). Models were simplified using backward elimination of the non-significant terms (P > 0.10) and only the final models are presented. Measures of endurance were logtransformed to achieve normality. We have three missing values (2 AC and 1 ALR) for this measure. We analyzed the proportion of time spent basking (full basking + half basking) during the observations and also the proportion of time spent full basking when basking. Two females (1 C and 1 ALR) were always sheltering and were thus not included in the last analysis. Female body condition was analyzed as female body mass with female SVL as a covariate in the model. The PHA response was measured after parturition. We have two missing values (1 C and 1 AC) for this measure.

ACKNOWLEDGEMENTS

  We are grateful to the Parc National des Cévennes and the Office National des Forêts for providing facilities during field work. We thank the students who helped collecting data, especially Nastasia Wisniewski and Lucille Billon, and Donald Miles for the treadmill. All experiments complied with the current laws of France. This work was supported by the Agence Nationale de la Recherche [07-BLAN-0217 to M.M.] and the Ministère de l'Enseignement Supérieur et de la Recherche [PhD grant and post-doctoral grant to J.B.]. LITERATURE CITED Andrews, R.M. (1982) Patterns of growth in reptiles. Biology of reptilia (eds C. Gans & F.H. Pough), pp. 273-320. Academic Press, New-York, NY. Atkins, N., Jones, S.M. & Guillette, L.J. (2006) Timing of parturition in two species of viviparous lizard: influences of beta-adrenergic stimulation and temperature upon uterine responses to arginine vasotocin (AVT). Journal of Comparative Physiology B: Biochemical Systemic and Environmental Physiology, 176, 783-792.

  FIGURE LEGENDSFigure1. A. Litter size after the AVT injection (experimental parturition) and at the end of the gestation period (normal parturition). In order to reduce litter size during gestation, we intraperitoneally injected 25 females with AVT (0.02μg/μL). After the injection, 13 females gave birth to a partial litter (ALR females) and 12 females did not (AC females). We also had 21 control females (C females). The graph shows two values for each experimental group: on the left-hand side, the number of eggs laid after the injection (mean ± SE), and, on the right-hand side, the number of offspring delivered on term (mean ± SE). B. Percentage of eggs laid in response to the AVT-injection in ALR females. To calculate a percentage, the total litter size was calculated as the sum of the number of eggs laid at the moment of the injection and the number of offspring delivered at parturition.

Figure 2 .

 2 Figure 2. Parturition dates. Females gave birth to their offspring between July 14 and July 24. The mean ± SE is represented for each experimental group: C females (control females), AC females (AVT-treated females with no litter size reduction) and the ALR females (AVTtreated females with a reduced litter).

Figure 3 .

 3 Figure 3. Endurance. Endurance was measured before parturition as the time (s) spent running on a treadmill (0.5 km/h). The mean ± SE is represented for C females (control females), AC females (AVT-treated females with no litter size reduction) and ALR females

Figure 4 .

 4 Figure 4. PHA swelling response. We measured thickness of the leg before and 12 h after the injection of PHA. PHA swelling response was calculated as the change in thickness of the leg between the two measurements. The white circles and the gray solid line represent C females (control females), the gray squares and the gray dashed line represent AC females

  FIGURESFigure1

Table 1 . Sample sizes during the experiment and the recapture sessions 1

 1

			Adult females			Offspring
			July 2010	Aug. 2010	May 2011	July 2010	Aug. 2010	May 2011
			(release)	(recapture)	(recapture)	(release)	(recapture)	(recapture)
	C	females	21	10	8	54	14	12
		males				46	14	14
	AC	females	12	7	7	27	6	6
		males				30	8	10
	ALR	females	13	7	6	7	4	3
		males				10	3	2
	Total		46	24	21	174	49	47

Table 2 .

 2 Descriptive statistics of the parameters measured 2

	ALR females	AC females	C females

Table 3 . Short term effects of the litter size manipulation 3 Log(endurance) Time spent basking Time spent full basking when the female was basking

 3

	Body mass	PHA response

We had three experimental groups: ALR females (AVT-treated females with a reduced litter), AC females (AVT-treated females with no litter size reduction) and C females (control females). Adult females and their offspring were released shortly after parturition (July

2010) and recaptured at two different times: at the end of August of the same year (before hibernation) and in May of the following year (after emergence from hibernation).

The results are shown as mean ± se. For the offspring characteristics at birth M represents male offspring and F female offspring. Concerning the estimates of survival probabilities, they were obtained from the most parsimonious best models (see TablesA1 and A2), these models did not include an effect of the experimental group on survival. We also measured litter size, endurance capacity and immune response but these data are presented in figures.

4 Growth rates before hibernation were calculated as the change in SVL (SVL at recapture -SVL at birth) divided by the time interval (date of recapturedate of birth). Sample sizes were 28 juveniles from control females (C juveniles), 14 juveniles from AC females (AC juveniles) and 7 juveniles from ALR females (ALR juveniles) as presented in Table 1. The full model included an effect of the maternal treatment, standardized initial fecundity, offspring sex and offspring SVL at birth (initial SVL). Maternal identity is included as a random effect. Models were simplified using backward elimination of the nonsignificant terms (P > 0.10) and only the final model is presented.