Thomas Von Larcher

Uwe Harlander

C Egbers

Thomas Von Larcher

& C Egbers

Multivariate data analysis methods for detecting baroclinic wave interactions in the thermally driven rotating annulus

come

Motivation

Since the pioneering studies by R. Hide in the fifties of the last century [START_REF] Hide | An experimental study of thermal convection in a rotating fluid Phil[END_REF], the elegant laboratory set-up of the differentially heated, rotating cylindrical gap of fluid is used by many authors to study the stability as well as the transition of fully 3D wavy flow patterns. They evolve from the release of potential energy through baroclinic instability that occur due to a radial temperature gradient and rotation. A vertically and horizontally sheared mean flow develops from which regular and complex wave flow patterns of different wave number can then emerge. These wave flows are called baroclinic waves due to the underlying instability mechanism, and the flow regimes, that develop in the annulus, depend mainly on two forcing parameters, i.e. on the temperature difference ∆T and on the angular velocity Ω. Note that the fluid viscosity is also a key parameter (e.g., [START_REF] Fein | An experimental study of the effects of Prandtl number on thermal convection in a rotating, differentially heated cylindrical annulus of fluid[END_REF]), but is kept fix in the experiments.

The rotating annulus, though being subject to detailed investigations since more than four decades, is still of interest not only in recent experimental research with respect to atmospheric sciences but also in the development of new numerical models where it then can be used as reference for the validation of new model concepts. For this purpose, the set-up might be particularly suited due to its relative simple geometry as well as due to the well definable forcing parameters. On the other hand, a rich flow behaviour is found that is either steady or time-dependent (e.g., [START_REF] Früh | Wave interactions and the transition to chaos of baroclinic waves in a thermally driven rotating annulus[END_REF], [START_REF] Read | Quasi-periodic and chaotic flow regimes in a thermaly-driven, rotating fluid annulus[END_REF], [START_REF] Sitte | Higher order dynamics of baroclinc waves[END_REF]). The latter one, for example, undergoes changes in the wave amplitude or shape and also more types of complex flow patterns are known to exist, driven by e.g., wave-wave interactions and wave-mean flow interactions.

Our experimental set-up, described in detail in [START_REF] Larcher | Experiments on transitions of baroclinic waves in a differentially heated rotating annulus[END_REF], is one of only few exclusive reference experiments within the priority program 'Multiple Scales in Fluid Mechanics and Meteorology' (MetStröm), that focus on the development of spatiotemporal, multiple scales numerical model concepts, see http://metstroem.mi.fu-berlin.de.

Data analysis methods

In our experimental study, we make use of non-intrusive measurement techniques of a quite different nature to better understand the transition from the regular wave regime to the quasi-chaotic regime at high rotation rates and to reveal the underlying dynamic processes of complex wave flow patterns. While the high accurate Laser-Doppler-Velocimetry (LDV ) and Particle Image Velocimetry (P IV ) is used for the acquisition of high resolution velocity data, a high sensitive thermographic camera, which resolution allows for resolving fine scale structures, measures time series of temperature distribution at the surface. These techniques allow us to detect the flow dynamics in the subsurface, as well as the dynamics of the surface flow.

Both time series data are analyzed by using multivariate statistical techniques. While the LDV data sets are studied by applying the Multi-Channel Singular Spectrum Analysis (M -SSA), the temperature data sets are analyzed by applying the Empirical Orthogonal Functions (EOF ). In addition, the temperature data are processed in a way to become comparable to the LDV data, i.e. reducing the size of the data set in such a manner that the temperature measurements would imaginary be performed at equidistant azimuthal positions only. This approach initially results per se in a great loss of information. But applying the M -SSA to the reduced temperature data sets enables us not only to compare the different data analysis methods but also to reclassify the results yielded with the LDV data analysis.

Exemplary analysis of a particular data set

An exemplary analysis run of one particular temperature data set is shown in figure 1. The dominating regular wave pattern of azimuthal wave number m=3 has three vortices of lower temperature at the inner (cooler) sidewall and three relative warm regions near the outer (warmer) sidewall, see figure 1a. The narrow jetstream circumventing the eddies transports heat and momentum. Figure 1b shows a spatio-temporal plot of the processed data. The drift rate of the dominating mode m=3 is determined to 0.025 rad /s. That wave mode is also found in the first component of the data reconstruction using the (EOF 1 and 2) of the (M -SSA), see figure 1c. At this parameter point, no higher mode than m=3 is found.

Objectives

Our work presented here is based on a previous experimental study on baroclinic wave interactions by [START_REF] Harlander | PIV-and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus[END_REF] who apply multivariate, statistical data analysis methods to velocity data. In addition, we use temperature data as well as velocity data, which are measured at the same parameter points but -unfortunately-not synchronous. The use of different data acquisition techniques allow us to match not only the information coming from the analysis of temperature and velocity data but also to match the analysis of the surface flow and of subsurface flows. For example, the results of the (EOF ) analysis of velocity and temperature data can be used to calculate the turbulent radial heat flux (v T ), which is a key parameter for understanding the observed flow phenomena (v (T ) denotes the deviation from the mean velocity (temperature)).

With the use of the statistical analysis tools, we gain the knowledge of the variability of the flow regimes particularly in the transition between regular wave modes of different azimuthal wave number as well as in the transition to quasi-chaotic flow. Our work is a continuation of the efforts of the authors and colleagues to reach these goals and it should be regarded as part of an overall operation.

EUROMECH

  Colloquium 525, 21-23 June 2011, Écully, France Instabilities and transition in three-dimensional flows with rotation

Figure 1 :

 1 Figure 1: Exemplary analysis of a regular wave flow of wave number m=3. (a) View of surface temperature distribution, unit [ • C], (b) merge plot of temperature time series processed at 20 equidistant locations on mid radius, the anomaly at t * ≈ 27 results from a malfunction during data acquisition, unit [ • C]. (c) Reconstructed time series using EOF 1 and 2 computed of the temperature data set.


Maurice Rossi

Ivan Delbende

Benjamin Piton

Instabilities and transition in three-dimensional flows with rotation DYNAMICS OF FLOWS WITH HELICAL SYMMETRY

Context and objectives

Rotating devices such as propellers, wind turbines, helicopter rotors are known to develop a system of helical vortices in their wake. These structures result from the rapid roll-up of the vorticity sheet continuously generated at the trailing edge of the rotating blades. Very often, these flows display a helical symmetry, meaning that they are, at least locally, invariant through combined axial translation of distance ∆z and rotation of angle θ = ∆z/L around the same z-axis. The helix pitch 2πL is then a spatial period of the flow. In the literature, the analytical [START_REF] Hardin | The velocity field induced by a helical vortex filament[END_REF][START_REF] Kuibin | Self-induced motion and asymptotic expansion of the velocity field in the vicinity of a helical vortex filament[END_REF] and numerical [START_REF] Lucas | A family of helically symmetric vortex equilibria[END_REF] works describing stationary helical vortices have been mostly restricted to helical vortex filaments and patches in inviscid situations with the vorticity always pointing along helical lines of pitch 2πL. However, wake vortices form through the roll-up of the trailing vorticity sheet, and viscous diffusion eventually leads to continuous distributed vorticity distributions within the vortex cores, such as Gaussian. Moreover, a distribution of axial velocity may also be present, which has always been disregarded in the literature. The objective of the current study is to simulate the viscous dynamics of helical vortex systems without the above restrictions. We present here an original DNS code [START_REF] Delbende | DNS of flows with helical symmetry[END_REF] which solves the incompressible Navier-Stokes equations with enforced helical symmetry at fixed pitch 2πL. The three-dimensional equations are reduced to a modified two-dimensional unsteady problem which can be solved via a generalised vorticity/streamfunction formulation. The code is thus able to take 3D vortex curvature and torsion effects into account while the resolution is of a 2D type, allowing for finer grids, higher Reynolds numbers and longer integration times.

Results

In this framework, we study the long-time (or equivalently far-wake) dynamics of systems with 2 and 3 helical vortices regularly spaced along a cylinder of radius R. Figure 1 shows the time evolution of the distance between two interacting helical vortices (when cut in a plane perpendicular to their common axis) for different values of the reduced pitch L. At high pitch (L/R > 2), one recovers the classical picture of pure 2D vortex merging (L = ∞), yet with larger evolution time scales. At smaller pitch (see L/R = 0.8) a quite different type of vortex merging occurs which involves neighbouring spires, as shown in figures 2 and 3. The conditions on vortex pitch and core size leading to one type of merging or to the other as well as the associated transition are investigated. Helically symmetric flows are also produced by natural instability of axisymmetric jets, wakes and trailing vortices. DNS of the nonlinear saturation of such instabilities are presented here in the case of the Batchelor vortex. We retrieve the different behaviours observed when the swirl parameter is varied [START_REF] Delbende | Nonlinear evolution of a swirling jet instability[END_REF], and we present new results concerning the saturation of viscous centered modes [START_REF] Dizès | Large-Reynolds-number asymptotic analysis of viscous centre modes in vortices[END_REF].

EUROMECHFigure 1 :Figure 2 :

 12 Figure 1: Merging of two helical vortices at Re = Γ/ν = 10000 for different values of the reduced pitch L: time evolution of the distance r max of one of the vortices from the axis. Initially, the helical vortices have circulation Γ = 1, core size a = 0.2 and are on a cylinder of radius R = 1.

Figure 3 :

 3 Figure 3: Same as 2 but viewed in a meridian plane.


Instabilities and transition in three-dimensional flows with rotation

AXISYMMETRIC VORTEX BREAKDOWN IN CONSTRICTED PIPES

François GALLAIRE 1 , Philippe MELIGA 2 1 Laboratory of Fluid Mechanics and Instabilities, Ecole Polytechnique Fdrale de Lausanne CH-1015 Lausanne, Switzerland. 2 M2P2, UMR-6181 CNRS IMT, 38, Rue Frdric Joliot-Curie 13451 MARSEILLE Cedex 13, France.

We investigate numerically and theoretically the axisymmetric vortex breakdown occurring in a contracting pipe of finite extension, i.e. the transition from a smooth columnar state to a breakdown state exhibiting a recirculation bubble. Velocity distributions are prescribed at the pipe inlet under the form of Batchelor vortices with uniform axial velocity and variable levels of confinement. A numerical continuation technique is developed to follow the branches of nonlinear steady solutions when varying the swirl parameter. In the most general case, for Re=500, vortex breakdown occurs abruptly owing to a subcritical, global instability of the non-parallel, viscous columnar solution, and results in the coexistence of multiple stable solutions over a finite range of swirl. For highly confined vortices, a second scenario prevails, where the flow transitions smoothly from the columnar to the breakdown state without any instability. These results are reminiscent of those obtained by [START_REF] Lopez | On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe[END_REF] and [START_REF] Beran | The role of non-uniqueness in the development of vortex breakdown in tubes[END_REF] where slip is allowed at the wall. The effect of a low flow rate jet positioned at the pipe wall is then characterized in the perspective of control. Its effectiveness is evaluated in light of three practically meaningful criteria, namely the ability of the control to optimize either the stability domain or the topology of the columnar state, and its ability to alleviate hysteresis. For each criterion, an optimal jet position is determined from nonlinear simulations.

The results are in good agreement with those issuing from an weakly nonlinear asymptotic expansion of the Navier-Stokes equations, which yields two normal forms describing the two saddle-node bifurcations underlying the fold structure of the bifurcation. The open-loop control enters as a forcing term in the resulting amplitude equations.

Figure 1 :

 1 Figure 1: Bifurcation diagram illustrating the onset of vortex breakdown as the swirl is increased. The minimum axial velocity u min is plotted as a function of the swirl -Re = 500.


Dr David M B Christmas
email: david.christmas@nhs.net

M Sam Eljamel

Sharon Butler

Hiral Hazari

Robert J Macvicar

Douglas Steele

Alison Livingstone

Keith Matthews

Sam Eljamel

Consultant Psychiatrist

Long-Term Outcome of Thermal Anterior Capsulotomy for Chronic, Treatment-Refractory Depression

Keywords: Anterior Capsulotomy, Long-term clinical outcome, major depressive disorder, Neurosurgery for Mental Disorder; Voxel-based imaging

come

INTRODUCTION

Chronic depression, defined by DSM-IV as an episode persisting for over two years in duration, occurs in approximately 20% of patients with major depression. [START_REF] Judd | A prospective 12-year study of subsyndromal and syndromal depressive symptoms in unipolar major depressive disorders[END_REF][START_REF] Kennedy | Remission and recurrence of depression in the maintenance era: long-term outcome in a Cambridge cohort[END_REF] Remission rates decline substantially with increasing numbers of failed antidepressant trials, with one-third of individuals not remitting after four antidepressant trials. [START_REF] Rush | Acute and Longer-Term Outcomes in Depressed Outpatients Requiring One or Several Treatment Steps: A STAR*D Report[END_REF] There is limited evidence to support specific interventions for chronic treatment-refractory depression. [START_REF] Stimpson | Randomised controlled trials investigating pharmacological and psychological interventions for treatment-refractory depression. Systematic review[END_REF] In recent years, Vagus Nerve Stimulation (VNS), Deep Brain Stimulation (DBS) and the Cognitive Behavioural Analysis System of Psychotherapy (CBASP) [START_REF] Rush | Effects of 12 months of vagus nerve stimulation in treatment-resistant depression: a naturalistic study[END_REF][START_REF] Keller | A Comparison of Nefazodone, the Cognitive Behavioral-Analysis System of Psychotherapy, and their Combination for the Treatment of Chronic Depression[END_REF] have been reported to confer benefit. However, numbers of patients treated by DBS remain low with limited long term data. Also, efficacy for VNS and CBASP appears modest compared with treatment-as-usual [START_REF] George | A One-Year Comparison of Vagus Nerve Stimulation with Treatment as Usual for Treatment-Resistant Depression[END_REF] and there is no evidence for either of these treatments being effective in chronic, highly treatment-refractory populations such as reported here.

First described by Talairach in 1949, Anterior Capsulotomy (ACAPS) places lesions in the anterior one-third of the anterior limb of the internal capsule, a large whitematter bundle connecting prefrontal and anterior cingulate cortices with the thalamus, hippocampus, and amygdala. ACAPS lesions are generated by the thermal effects of radiofrequency current or focal irradiation. Whilst several published studies report the clinical outcomes of ACAPS for Obsessive-Compulsive Disorder [START_REF] Oliver | Bilateral anterior capsulotomy for refractory obsessivecompulsive disorders[END_REF] and anxiety disorders, [START_REF] Rück | Capsulotomy for refractory anxiety disorders: long-term follow-up of 26 patients[END_REF] there is only one report on the outcome of ACAPS as a treatment for depression. [START_REF] Herner | Treatment of mental disorders with frontal stereotaxic thermo-lesions: A follow-up study of 116 cases[END_REF] described outcomes for 19 patients with a diagnosis of "a depressive state" (not otherwise defined clinically), treated by thermal ACAPS with a maximum follow-up of two years. [START_REF] Herner | Treatment of mental disorders with frontal stereotaxic thermo-lesions: A follow-up study of 116 cases[END_REF] Fourteen (74%) were rated as showing "permanent improvement"; three (16%) showed "temporary improvement"; one (5%) was "unchanged"; and one (5%) was "worse". Fifteen (75%) experienced permanent side effects which were mild in 47%. Additionally, Simpson and colleagues reported "marked" improvements in almost 60% of 24 patients undergoing ACAPS for depression. [START_REF] Simpson | Stereotactic anterior capsulotomy for intractable depression and obsessive compulsive disorder[END_REF] However, details of these outcomes have not been published.

Although ACAPS has now been superseded in our unit (Dundee) by Anterior Cingulotomy, ACAPS remains the only neurosurgical procedure performed in England and Wales for intractable psychiatric illness. Between 2005 and 2009, the Mental Health Commission approved seven procedures which were performed at the University Hospital of Wales in Cardiff. [START_REF]Mental Health Act Commission. Risk, Rights, Recovery. Twelfth Biennial Report 2005-2007[END_REF][START_REF]Mental Health Act Commission. Coercion and consent[END_REF] ACAPS is also offered as a treatment for refractory OCD and Major Depression in several other European countries. The anterior limb of the internal capsule is one of the preferred targets for studies of Deep Brain Stimulation (DBS) for OCD [START_REF] Greenberg | Deep brain stimulation of the ventral internal capsule/ventral striatum for obsessive-compulsive disorder: worldwide experience[END_REF] and remains a target for ablative neurosurgery for OCD. It is also emerging as a DBS target for major depression. [START_REF] Malone | Deep brain stimulation of the ventral capsule/ventral striatum for treatment-resistant depression[END_REF] This anatomical region, therefore, remains very important for neurosurgical interventions for psychiatric illness.

In Dundee, Anterior Cingulotomy became the procedure of choice due to early reports of adverse effects from ACAPS for OCD and anxiety disorders, many of which came from Sweden. We have previously highlighted the possibility of differences in adverse effects depending on the indication, [START_REF] Christmas | Adverse events following neurosurgery[END_REF] but given the similar clinical outcomes reported for Anterior Cingulotomy, [START_REF] Freeman | Neurosurgery for mental disorder. Report from the Neurosurgery Working Group of the Royal College of Psychiatrists[END_REF] a decision was made to change procedures.

METHODS

Subjects

All patients who underwent ACAPS in Dundee from 1992 were considered. The only a priori exclusion criteria were inability to trace a participant, or inability of the participant to provide written informed consent for the study. Ethical approval for this study was provided by the Tayside Medical Research Ethics Committee. Written informed consent was obtained from all patients, and as a requirement of the relevant Scottish Mental Health Acts (1984 and 2003), all patients undergoing neurosurgery were independently assessed pre-operatively by three panel members from the Mental Welfare Commission for Scotland with regard to the suitability of the proposed intervention and capacity to provide sustained informed consent. Diagnosis before surgery was determined according to ICD-10 by the lead psychiatrist for the neurosurgical programme. This diagnosis was subsequently corroborated retrospectively by the current study authors using OPCRIT. [18] Information regarding the number of previous illness episodes and the duration of interillness episode recovery was extracted from detailed case note review, to identify the course of individual episodes according to the ACNP Task Force definitions. [START_REF] Rush | Report by the ACNP Task Force on Response and Remission in Major Depressive Disorder[END_REF]

Clinical assessments

The following rating scales were completed at pre-operative baseline, 12-month followup, and long term follow-up: Hamilton Rating Scale for Depression, 17-item version (HRSD 17 ); [START_REF] Hamilton | A rating scale for depression[END_REF] Montgomery-Åsberg Depression Rating Scale (MADRS); [START_REF] Montgomery | A new depression scale designed to be sensitive to change[END_REF] Clinical Global Impression (CGI); [START_REF]CGI: Clinical Global Impressions[END_REF] Pippard Postoperative Scale; [START_REF] Pippard | Rostral leucotomy: a report on 240 cases personally followed up after one and one half to five years[END_REF] Lancashire Quality of Life Profile (LQoLP); [START_REF] Oliver | Quality of life and mental health services[END_REF] and the Personality Assessment Schedule (PAS). [START_REF] Tyrer | Reliability of a schedule for rating personality disorders[END_REF] In addition, a semi-structured interview for adverse effects was conducted at long-term follow-up. Case notes were reviewed for the occurrence of adverse effects occurring in the first post-operative year that were not recalled at later interview.

Assessment of Treatment Resistance

Ratings of the adequacy of previous antidepressant trials were made according to the Antidepressant Treatment History Form (ATHF). [START_REF] Sackeim | The definition and meaning of treatment-resistant depression[END_REF] Each treatment had to score ≥ 3 on the Antidepressant Resistance Rating (ARR) to be defined as 'adequate'. Treatment resistance was also rated according to the Massachusetts' General Hospital Scoring Method (MGH-S), [START_REF] Fava | Diagnosis and definition of treatment-resistant depression[END_REF] and classified using the Thase & Rush Treatment-Resistant Depression Staging (TR-S) method. [START_REF] Thase | When at first you don't succeed: sequential strategies for antidepressant nonresponders[END_REF] Definitions of response 'Response' and 'remission' were defined a priori. Using the HRSD-17, 'response' was ≥ 50% reduction in baseline score, with 'remission' being a score of ≤ 7. For the MADRS, 'response' was ≥ 50% reduction in baseline score and 'remission' was a score of ≤ 10.

On the clinician-rated CGI-I, 'response' was a score of 1 or 2. Participants were deemed to meet criteria for clinical response if they met 'response' criteria on the HRSD-17, MADRS, or the CGI ratings. Similarly, 'remission' was deemed present if criteria were met on either the HRSD-17 or MADRS scales. Categorical outcomes were also defined by CGI-I and the Pippard Postoperative Scale. 'Improved' was defined as a score of 1 or 2 on the CGI-I or I or II on the Pippard Scale. 'Unchanged' was defined as a score of 3 or 4 on the CGI-I or III or IV on the Pippard Scale. 'Worse' was a score of 5, 6, or 7 on the CGI-I or V on the Pippard Scale. Since statistically significant changes may not necessarily reflect meaningful benefit to a particular individual, 'clinically significant change' (CSC) was calculated for each participant. These methods are described in detail by Jacobson & Truax.[29]

Clinical Neuropsychological Assessment

The following tests were performed at baseline and long-term follow-up: National Adult Reading Test (NART); [START_REF] Nelson | The Revised National Adult Reading Test (Part II) Manual[END_REF] Information/Orientation, Word Lists, Paired Associates Learning, Logical Memory, Visual Reproduction and Digit Span tasks taken from the Wechsler Memory Scale -Revised (WMS-R) [START_REF] Wechsler | Memory Scale -Revised[END_REF] and subsequently the WMS-III; [START_REF] Wechsler | Wechsler Memory Scale -Third Edition[END_REF] Arithmetic, Comprehension, Block Design, Digit Symbol and Similarities tasks from the Wechsler Adult Intelligence Scale -Revised (WAIS-R) [START_REF] Wechsler | Wechsler Adult Intelligence Scale -Revised[END_REF] and more latterly the WAIS-III ; [START_REF] Wechsler | Wechsler Adult Intelligence Scale -Third Edition[END_REF] '6 elements' test from the Behavioral Assessment of the Dysexecutive Syndrome (BADS); [START_REF] Wilson | The Development of an Ecologically Valid Test for Assessing Patients with a Dysexecutive Syndrome[END_REF] the Verbal Fluency Test/ Controlled Oral Word Association Test (COWAT); [START_REF] Ruff | Benton controlled oral word association test: Reliability and updated norms[END_REF] Stroop Neuropsychological Screening Test; [START_REF] Trenerry | The Stroop Neuropsychological Screening Test[END_REF] and Trail-Making Test (TMT). [START_REF] Reitan | The Halstead-Reitan neuropsychological test battery: Theory and clinical interpretation[END_REF] Individuals who had been tested on a version of the WMS or WAIS prior to revision were tested again on the same version, with each new patient being tested on the most current version. Data at 12 months post-op were available for some patients.

Cambridge Neuropsychological Test Automated Battery (CANTAB)

CANTAB was used to assess a variety of cognitive domains (attention; memory; nonstrategic learning; and 'executive' functions). These tests are sensitive to the effects of a range of neuropsychiatric disorders including major depression. [START_REF] Elliott | Neuropsychological impairments in unipolar depression: the influence of perceived failure on subsequent performance[END_REF][START_REF] Porter | Neurocognitive impairment in drug-free patients with major depressive disorder[END_REF][START_REF] Purcell | Neuropsychological function in young patients with unipolar major depression[END_REF] Surgical procedure Surgical procedures were conducted under general anaesthesia. Volumetric CT and MRI images were obtained parallel to the intercommisural plane for each patient and merged using the FrameLink Stereotactic Linking System (Medtronic Inc., Minneapolis, MN, USA). The bilateral target volume was 19-21mm anterior to the Anterior Commissure.

Two small scalp incisions and two burr holes were made at the entry points. A 3 mm wide, 6 mm long radiofrequency probe was sited within the target such that its tip was at the inferior aspect of the target volume. Single lesions were made in each hemisphere by heating the probe to 70º Celsius for 90 seconds using a Radionics radiofrequency lesion generator. Additional bilateral lesions were similarly made such that the initial lesion was extended caudally to produce a total lesion within each capsule of approximately 18-20mm height and 8mm width. Individual lesion volumes were therefore predicted to range from 670mm 3 (ellipsoid) to 1000mm 3 (cylinder) depending on shape.

Statistical Methods

Where data were normally distributed, summary data were reported using the mean ± standard deviation (SD). Where data were not normally-distributed, the median and range were chosen as measures of central tendency. Differences between two normallydistributed variables were assessed using t-tests. Comparison between groups was performed with independent samples t-tests and comparison between two time points was performed with paired samples t-tests. Corresponding non-parametric tests were the Mann-Whitney U-test.

Incomplete HRSD-17 scores

Pre-operative HRSD-17 scores were unavailable for 30% of participants but preoperative MADRS scores were available. To test the validity of inferring HRSD-17 scores from MADRS scores, MADRS-imputed HRSD-17 scores for all participants at long-term follow-up were compared to actual clinician-rated scores (completed for all participants) completed at the same time. The correlation between the two scores was highly significant (Pearson Correlation Coefficient, r = 0.963, p<0.001). Consequently, pre-operative MADRS scores were used to infer pre-operative HRSD-17 scores.

Incomplete MADRS scores

Baseline MADRS scores were not available for one participant, and missing at 12-months for eight (40%). To determine if there were differences between those with complete data and those with missing data at 12-months, groups were compared on a number of demographic variables (gender, age at surgery) and indices of severity (duration of presenting episode, number of previous episodes, number of adequate treatment trials, and baseline MADRS scores). The only significant difference was a greater number of pre-operative hospital admissions in those with missing data.

Neuroimaging assessment

Magnetic Resonance (MR) imaging was obtained for 14 patients 6.5 ± 3.6 years after ACAPS using a Siemens 1.5T scanner (Magnetom Avanto and Symphony models). T2weighted images were obtained with a matrix of 512x512 and a slice thickness of 4.5-5mm. Using SPM2 (http://www.fil.ion.ucl.ac.uk/spm), images were spatially normalised to the SPM2 template, which conforms to Montreal Neurological Institute (MNI) anatomical space, then resliced to form 1mm 3 isotropic voxels. Each spatially normalised image was then segmented to form separate grey matter, white matter, and cerebrospinal fluid (CSF) images. ACAPS lesions appear as CSF density structures. For each scan, the outline of each lesion was highlighted as a 'region of interest' (ROI) on each slice using MRIcro (http://www.sph.sc.edu/comd/rorden/) independently by two raters (DC and JDS). The former based the estimation on the spatially normalised T2 image; the latter used the CSF images. The ratings made by both assessors were averaged. The centres of mass of the lesions were calculated by averaging the voxel coordinates in the ROIs in each dimension, and the volumes were calculated from the sum of all voxels within the ROIs (each being 1 mm 3 ).

At long-term follow-up, seven participants had undergone subsequent procedures: Since data were available to determine 'response' at 12-months, lesion coordinates for ACAPS were compared between responders (n=4) and non-responders (n=6) at 12months post-op. Differences between groups were examined using Mann-Whitney Utests (recognising the low power of this comparison to reject the null hypothesis of no difference). In order to visualise possible differences in lesions between responders and non-responders, the ROI for each participant was plotted on the same spatially normalised MRI.

RESULTS

Participant sample

Twenty-three patients were identified as suitable for inclusion. Three subjects were excluded (one had died; one was untraceable; and one had a previous subcaudate tractotomy), leaving a study sample of 20 patients. Long-term follow-up assessments were completed 7.0 ± 3.4 years (range, 47.4 -662.2 weeks) after ACAPS. These data represent outcomes from the initial ACAPS only. Seven participants went on to have a second procedure (ACAPS=1; Anterior Cingulotomy=6) due to inadequate clinical response. One individual subsequently had a Vagus Nerve Stimulator implanted (outwith the Dundee service). The second procedure was performed after a mean interval of 154.5 ± 55.2 weeks. For two participants, this interval was less than 120 weeks and the longest follow-up reported below represents the assessment prior to the second procedure. Longterm outcome data, therefore, represent outcomes from the first ACAPS only.

Demographic details for participants (n=20) are shown in Table 1, diagnoses are given in Table 2. All were Caucasian and six (30%) were subject to compulsory detention at the time of neurosurgery.

INSERT Table 1 INSERT Table 2

Treatment resistance

Indices of treatment resistance are shown in Table 3. All participants had at least two lifetime courses of ECT. Fifty-percent of participants had four or more courses of ECT during the presenting Major Depressive Episode (MDE) and only one participant (5%) had not had ECT in the presenting MDE due to previous non-response.

INSERT Table 3

Clinical outcomes

At 12-months, five (25%) participants met criteria for 'Response' and two (10%) also met criteria for 'Remission'. At long-term follow-up, 10 (50%) met criteria for 'Response' with eight (40%) also meeting criteria for 'Remission'. These categories are not mutually exclusive and remitters also met criteria for response. According to categorical rating scales, at long-term follow-up, 11 (55%) were 'Improved', seven (35%) were 'Unchanged', and two (10%) were 'Worse'. Categorical scores were also obtained from participants and next-of-kin. Correlations between raters were highly significant and ranged from p=0.025 to p<0.001. Changes in scores are shown in Table 4. At 12-months, 4/20 (20%) participants had achieved CSC, and at long-term follow-up, nine (45%) met criteria for CSC. Correlations between rates of CSC and clinical definitions of 'response' at 12-months were highly significant using Spearman's rank correlation [r=0.909, p<0.001], and remained significant for 'remission' at 12-months [r=0.592, p=0.002], and for both 'response' [r=0.761, p<0.001] and 'remission' [r=0.757, p<0.001] at long-term follow-up.

INSERT Table 4

Neuropsychological outcomes

A summary of changes in score on a variety of neuropsychological measures is presented in Table 5. The median duration of follow-up for clinical neuropsychological assessment was 396.0 (range 117.8 -625.8) weeks, and for CANTAB testing the median was 401.1 (48.4 -662.2) weeks. There were non-significant improvements in the majority of tests of general intelligence, memory, and executive function.

INSERT Table 5

Personality Assessments

Scores on the PAS were available at baseline for 11 (55%) participants, long-term followup for 11 (55%), and at both time points for six (30%) participants. At baseline, 2/11 had either personality difficulties or disorder, and at long-term follow-up, 1/6 of those with scores at both time points had moved from the 'personality difficulties' to 'no personality disorder' category. Clinical interview at long-term follow-up did not identify features that were suggestive of significant personality dysfunction. The IIP-PD, a self-report scale reflecting "personality dysfunction" [START_REF] Kim | Confirmatory factor analysis of the personality disorder subscales from the Inventory of Interpersonal Problems[END_REF] was completed by 14 participants at long-term follow-up, seven (50%) of whom had scores suggestive of personality disorder (Cluster C = 6, Cluster B = 1). Four of the seven had undergone a subsequent anterior cingulotomy (ACING) and only one had a score suggestive of personality disorder (Cluster C) at longterm follow-up.

The study team did consider that some subtle deficits in reciprocal social communication may have been evident for a small number of participants (n=4) during informal interactions, but it is not known if these were present prior to surgery. Despite these subjective perceptions, it is worth noting these patients seemed to function with considerable social competence and did not show significant deteriorations in neurocognitive functioning on the clinical or computerised batteries. Gross frontal-lobe symptoms or signs were not detected in any of the participants at clinical interview.

Adverse effects

There were no deaths by suicide. One patient died prior to study completion at the age of 70 years. This occurred 12 years after ACAPS and was considered attributable to causes unrelated to neurosurgery. One individual developed a left-sided temporal haematoma approximately 6 years after ACAPS. Smoking and hypertension were considered key aetiological factors. The most common adverse effects reported are shown in Table 6.

Adverse effects were typically transient and there were no adverse effects present at long-term follow-up that could be reliably attributed to ACAPS, with the exception of disturbance of bladder control (n=2) which was mild in both cases. All but one participant were taking prophylactic antidepressant medication at long-term follow-up.

Vulnerability to addiction was difficult to assess. One participant had given up smoking four years after ACAPS, whilst another participant developed alcohol dependence following a period of psychosocial stress. A possible relationship with surgery was unclear in both cases. There were self-reported weight gains made by many of the study participants over the follow-up period. Although this could not be attributed definitively to the procedure, such findings are consistent with other reports of ACAPS in the literature. Similarly, reduced motivation was reported by a number of participants and it was not possible to fully distinguish between amotivation consistent with frontal lobe impairment and lack of motivation caused by depression and/ or medication. A classic frontal lobe syndrome was not observed in any participants.

INSERT Table 6

Neuroimaging Results

Lesion coordinates and volumes are shown in Table 7. The measured lesion volumes for both hemispheres lay within the surgically expected range. The results are depicted in Figure 1. Although the differences are not statistically significant, which is unsurprising given the small numbers in each group, there is a suggestion of a trend for 'responder' lesions to be placed more inferiorly within the internal capsule. There were no significant differences between groups in x, y, or z planes.

INSERT Table 7

INSERT Figure 1

A colour version of the figure is included as a supplemental file (description under 'Figure Legends' below).

DISCUSSION

This is the largest follow-up study of ACAPS for chronic, refractory Major Depression and the first since 1961. These data represent the most complete and the most detailed assessment of the clinical outcomes of ACAPS for treatment-refractory Major Depression. In our study, we found that 10/20 (50%) patients met criteria to be described as responders approximately 7 years after surgery, with 8/20 (40%) meeting criteria for clinical remission (categories not mutually exclusive). The population described in our study is drawn from the extreme end of the treatment-refractory depressive spectrum.

Recent reports of the outcomes for Vagus Nerve Stimulation and electrical Deep Brain

Stimulation for chronic, refractory depression describe populations that are less chronic and refractory than our cohort. [START_REF] George | A One-Year Comparison of Vagus Nerve Stimulation with Treatment as Usual for Treatment-Resistant Depression[END_REF][START_REF] Rush | Vagus Nerve Stimulation for Treatment-Resistant Depression: A Randomized, Controlled Acute Phase Trial[END_REF][START_REF] Sackeim | Vagus nerve stimulation (VNS) for treatmentresistant depression: efficacy, side effects, and predictors of outcome[END_REF] Detailed, prospective testing of neuropsychological function failed to demonstrate consistent deteriorations over time in any cognitive domain. Indeed, there was a general trend towards improvement on many measures of executive function. We believe this may be mediated indirectly by reduced global symptom burden. However, it could be argued that the neuropsychological battery used in this study was insufficient to detect all potential sequelae of ACAPS. Previously, we have reported that patients treated with Anterior Cingulotomy and ACAPS exhibited a general impairment of accuracy of recognition of dynamic emotional displays compared to healthy controls. [START_REF] Ridout | Emotion recognition from dynamic emotional displays following anterior cingulotomy and anterior capsulotomy for chronic depression[END_REF] This study differs from recent reports from ACAPS for OCD and anxiety disorders [START_REF] Rück | Capsulotomy for refractory anxiety disorders: long-term follow-up of 26 patients[END_REF][START_REF] Rück | Capsulotomy for Obsessive-Compulsive Disorder: Longterm Follow-up of 25 Patients[END_REF] in a number of important respects: data on both clinical and neuropsychological measures for our cohort was collected prospectively and we used modern quantitative voxel-based methods (VBM) to examine lesion characteristics.

Importantly, VBM overcomes the problems inherent with traditional radiological subjective descriptive methods which do not correct for individual differences in brain size and differences in brain orientation at the time of scanning. Whilst attempts have been made to describe the optimal target for OCD or anxiety disorders, [START_REF] Lippitz | Lesion topography and outcome after thermocapsulotomy or gamma knife capsulotomy for obsessive-compulsive disorder: relevance of the right hemisphere[END_REF][START_REF] Amat | Medial prefrontal cortex determines how stressor controllability affects behavior and dorsal raphe nucleus[END_REF] almost nothing is known about optimal ACAPS lesion characteristics for treating depressive illness. Based on our current work, [START_REF] Steele | Anterior Cingulotomy for Major Depression: Clinical Outcome and Relationship to Lesion Characteristics[END_REF] we suggest that the reporting of lesion coordinates in MNI space and the use of VBM should be generally adopted.

There are several limitations to our study. First, the dataset is incomplete. However, full data on symptom severity were available for 95% of participants at long-term followup. Second, the timing of the assessments (12-months and long-term follow-up) can provide only a snapshot of an individual's level of functioning over time and the results should be viewed within the context of a chronic and relapsing-remitting illness. Third, this study, like many others, suffers from a lack of validated psychometric tools for assessing personality before and after intervention. There are, to our knowledge, no validated scales that are designed for repeated testing, that are insensitive to changes in depressive symptoms, and which have sufficient sensitivity to detect potentially subtle alterations in personality characteristics. We currently use the Iowa Scales of Personality Change, [START_REF] Barrash | Acquired personality disturbances associated with bilateral damage to the ventromedial prefrontal region[END_REF] an informant-rated tool, in addition to other assessments to rate personality post-operatively. Finally, the absence of a control group is common to all reports of interventions of this type. Available data would suggest that response rates to 'treatmentas-usual' in much less refractory populations are low, [START_REF] George | A One-Year Comparison of Vagus Nerve Stimulation with Treatment as Usual for Treatment-Resistant Depression[END_REF] and in a more refractory cohort 'spontaneous' remission is unlikely to account for the improvements seen.

The target of ACAPS is the horizontally-oriented fibres in the inferior part of the capsule which connect the frontal lobes with the thalamus. [START_REF] Spiegelmann | CT target selection in stereotactic anterior capsulotomy: anatomical considerations[END_REF] The orbitofrontal cortex (OFC) has rich connections with limbic structures including the subgenual cingulate cortex, the insular cortex, and the hippocampus. [START_REF] Cavada | The Anatomical Connections of the Macaque Monkey Orbitofrontal Cortex. A Review[END_REF] Fibres within the anterior limb of the internal capsule constitute three distinct fibre tracts [START_REF] Axer | Morphological asymmetry in anterior limb of human internal capsule revealed by confocal laser and polarized light microscopy[END_REF]: 1) Fibres originating in the anterior thalamic peduncle, which connects to the cingulum bundle, [START_REF] Mufson | Some observations on the course and composition of the cingulum bundle in the rhesus monkey[END_REF] the target of Anterior Cingulotomy; 2) A deeper system of fibres made up of frontopontine fibres; 3) A third set which does not run in bundles and connects the caudate nucleus and the lentiform nucleus. A recent neuroimaging study demonstrated neuronal degeneration within these three pathways in five patients after ACAPS. [START_REF] Hurwitz | Tract Identification by Novel MRI Signal Changes following Stereotactic Anterior Capsulotomy[END_REF] A mechanism of action for ACAPS is, as yet, unknown. Dalgleish et al suggested that the therapeutic effects of a different ablative neurosurgical procedure, subcaudate tractotomy, might be effected by a relative insensitivity to negative feedback information. [START_REF] Dalgleish | Neuropsychological Processing Associated With Recovery From Depression After Stereotactic Subcaudate Tractotomy[END_REF] However, prospective data were not available to confirm whether such changes were, indeed, acquired.

One persisting criticism of psychiatric neurosurgery is that the benefits occur in a minority and that the risk of neuropsychological and/ or personality dysfunction is high. This ignores varying surgical techniques and patient selection criteria at different centres.

We have not been able to find empirical support for either of these statements, for the technique and criteria used in Dundee. More broadly, ACAPS remains a treatment option for patients with chronic, treatment-refractory Major Depression and is offered by a number of centres performing psychiatric neurosurgery. The ACAPS lesion target is of active interest in trials of DBS for OCD and depression, and patients are often offered ablative ACAPS should their trial of DBS prove unsuccessful. Therefore, the clinical outcomes of ACAPS remain of importance for contemporary clinical practice. In our series, the ACAPS procedure was associated with significant long-term clinical improvements for almost half of all patients. In addition, the adverse effect burden does not appear to be as great as described in the literature, at least with our selection criteria and neurosurgical procedure. ACAPS, as defined here, remains a viable treatment option for highly selected patients with chronic, refractory depression. A colour version of the figure is included as a supplemental file, and the description of this file is:

TABLES

:

  Comparison of lesions (overlaid as Regions of Interest) for responders (n=4) and non-responders (n=6). Lighter shades represent greater frequency of overlap in responders. Darker shades represent regions more commonly lesioned in non-responders. The regions of interest in the coronal section are enlarged to show a trend towards more inferior lesions in responders.

Figure 1 :

 1 Figure 1: Comparison of lesions (overlaid as Regions of Interest) for responders (n=4)

Figure 1 (

 1 Figure 1 (Supplemental): Comparison of lesions (overlaid as Regions of Interest) for

Table 1 . Participant characteristics (n=20)

 1

	Values are mean ± SD or median (range)
	Gender (M:F)	5:15
	Median age at time of ACAPS	40.4 (30.2 -64.2)
	Mean age of first episode of major depression	30.1 ± 11.0
	Mean age of onset of current MDE	37.8 ± 11.6
	Median number of previous episodes †	1.5 (1 -6)
	Median duration of all lifetime episodes (months)	89.0 (35.5 -289.1)
	Median duration of current MDE at time of surgery (months) 78.0 (31.3 -238.2)
	Mean number of previous admissions to hospital (lifetime)	7.0 ± 4.5
	Median duration (months) of hospital admissions (lifetime)	26.4 (1.3 -108.2)
	Mean number of suicide attempts (lifetime) ‡	4.6 ± 2.6

†

Recovery from episode defined as ≥ 6 months of remission

[57]

‡ This information was reliable in only 10 (50%) cases

Table 2 . Participant Diagnoses

 2

	Diagnosis

Table 3 . Indices of treatment resistance (n=20)

 3 Values are mean ± SD or median (range).

	Mean number of failed antidepressant treatments in presenting MDE †	8.1 ± 2.8
	Median number of failed antidepressant treatments from different	4.0 (3 -6)
	classes †
	Median number of courses of ECT (presenting MDE)	3.5 (0 -10)
	Median number of courses of ECT (lifetime)	4.0 (2 -10)
	Median Thase and Rush staging score (TR-S)	5.0 (3 -5)
	Mean MGH Staging Score (MGH-S)	13.1 ± 2.2
	† Includes ECT; measured using the Antidepressant Treatment History Form [26]

Table 4 . Changes in Rating Scales following ACAPS (n=20)

 4 Hamilton Rating Scale for Depression; MADRS Montgomery Asperg Depression Rating Scale; LQoLP Lancashire Quality of Life Profile; HADS Hospital Anxiety and Depression Scale. Paired samples t-test used to calculate P values.

	Rating Scale	Baseline	Post-Op	12-	Long-	Percentage	P
				months	term	change at	(baseline
					follow-up	long-term	to long-
							term)
	HRSD-17	26.8 ± 3.9	20.8 ±	15.3 ±	13.3 ±	-50.7%	0.101
	(actual	(n=6)	10.6	10.7	12.0		(n=6)
	scores)		(n=4)	(n=6)	(n=18)
	HRSD-17	23.3 ± 4.6	15.8 ± 7.0	16.2 ± 7.0	13.8 ±	-44.2%	0.004
	(imputed	(n=18)	(n=16)	(n=12)	11.6		(n=18)
	scores)				(n=20) †
	MADRS	39.6 ± 6.5	24.2 ±	24.1 ±	22.6 ±	-42.9%	0.001
	(not imputed)	(n=18)	11.6	12.2	16.4		(n=18)
			(n=16)	(n=12)	(n=20)
	LqoLP	3.9 ± 1.1	N/A	4.5 ± 0.92	4.9 ± 0.9	+25.6%	0.049
	(mean	(n=12)		(n=7)	(n=17)		(n=11)
	satisfaction
	scores)
	HADS	14.7 ± 5.0	8.5 ± 6.9	8.4 ± 8.0	10.4 ± 4.9	-29.3%	0.132
	(anxiety	(n=10)	(n=6)	(n=5)	(n=17)		(n=9)
	subscale)
	HRSD-17

†

Data not imputed at long-term follow-up.

Table 5 : Neuropsychological test test scores at baseline and long-term follow-up. Positive scores indicate improvement. CANTAB tests are italicised.

 5 DMS = Delayed Matching to Sample; SRM = Spatial Recognition Memory; PRM = Pattern Recognition Memory; PAL = Paired Associate Learning; SSP = Spatial Span; SWM = Spatial Working Memory; ID/ED

	N	Change in	P
		Performance

= Intradimensional/ Extradimensional Shift; SOC = Stockings of Cambridge. All tests paired-samples t-test, unless specified ( † =Mann-Whitney U-test)

Table 7 : Summary of lesion characteristics (n=14) MNI Coordinate (mean ± SD) Volume (mm 3 )

 7

	Left

Acknowledgements

The Dundee psychiatric neurosurgical programme was conceived and established by George Fenton, Professor of Psychiatry, and T.K. Varma, Consultant Neurosurgeon. We wish to thank Craig Adam, Alex Bell, and Dr June Gilchrist for assistance with the conduct of neuropsychological testing and video recording of assessments and Eleanor Sorrell for the conduct of Personality Assessments.

Funding

The study was funded by the Chief Scientist Office of the Scottish Executive Health Department; grant number CZG/2/223. The funding body had no influence on the design of the study, collection, or interpretation of the data.

Licence for Publication:

The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non exclusive for government employees) on a worldwide basis to the BMJ Publishing Group Ltd to permit this article (if accepted) to be published in JNNP and any other BMJPGL products and sublicences such use and exploit all subsidiary rights, as set out in our licence.

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Àlex Rollan
email: alexrollan@gmail.com

Joan Real
email: jreal@ub.edu

Effect of wildfires and post-fire forest treatments on rabbit abundance

Keywords: Oryctolagus cuniculus, Forest fires, Mediterranean scrubland, Management, Burnt branches

One of the main factors involved in the decline in the European wild rabbit in the Iberian Peninsula is the loss of suitable habitats caused by abandonment of agricultural and grazing activities. Nowadays, Mediterranean landscapes suffer from wildfires that affect extensive areas and produce considerable habitat changes. However, little is known about the influence of wildfires and post-fire treatments on rabbit abundance to address policies to recover their populations. To do so, we studied abundances of this species in four types of plots during three consecutive years after a wildfire in Catalonia (NE Spain): (A) unburnt forests, (B) burnt forests with removal of burnt trees but with branches left, (C) burnt forests with removal of burnt trees and branches, and (D) non-forested burnt plots. Rabbits progressively colonised burnt plots, where their abundance increased for at least 5 years after the fire, but decreased or even disappeared in unburnt ones, indicating that forest fires have a positive effect on rabbit populations. Although abundances did not differ between the three burnt plot types, plots with removal of burnt branches had the highest increase in abundance. In addition, soil covered by branches or by dense vegetation appeared negatively correlated with abundance, indicating that this could hinder rabbit movements, while some plant species could benefit rabbits by providing high quality food. Thus, post-fire treatments favourable to rabbit populations might therefore be a good way of increasing the conservation and economic value of areas affected by forest fires.

Introduction

The European wild rabbit (Oryctolagus cuniculus) has undergone a steep decline in the Iberian Peninsula since the 1950s due to viral diseases (myxomatosis and rabbit hemorrhagic disease), loss of suitable habitat and unfavourable game management [START_REF] Villafuerte | Incidence of viral haemorrhagic disease in wild rabbit populations in Spain[END_REF][START_REF] Calvete | Epidemiology of viral haemorragic disease and myxomatosis in free-living population of wild rabbits[END_REF]Calvete et al. 2004;[START_REF] Virgós | Is the wild rabbit (Oryctolagus cuniculus) a threatened species in Spain? Sociological constraints in the conservation of species[END_REF][START_REF] Williams | Hunting for answers: rabbit (Oryctolagus cuniculus) population trends in northeastern Spain[END_REF]Delibes Mateos et al. 2008). This decrease has been considered as a serious conservation problem because the rabbit is a keystone species in Iberian Mediterranean ecosystems, being the staple prey of several predators [START_REF] Delibes | The rabbit as prey in the Iberian Mediterranean ecosystem[END_REF][START_REF] Delibes Mateos | Rabbits as a keystone species in southern Europe[END_REF], 2008a) such as the endangered Iberian lynx (Lynx pardinus), the Spanish imperial eagle (Aquila adalberti) and Bonelli's eagle (Aquila fasciata). In addition, it is also the primary small game hunting species and is an important source of income for rural areas [START_REF] Angulo | Modelling hunting strategies for the conservation of wild rabbit populations[END_REF]Calvete and Estrada 2004;[START_REF] Monzón | Vegetation structure descriptors regulating the presence of wild rabbit in the national park of peneda-gerês, portugal[END_REF].

Rabbits live in a wide variety of habitats, from agricultural landscapes to woodlands. However, they prefer open areas of grassland, farmland and Mediterranean scrubland [START_REF] Rogers | Ecology of the European wild rabbit, Oryctolagus cuniculus L., in Mediterranean habitats. I. distribution in the landscape of the Coto Doñana, S. Spain[END_REF][START_REF] Moreno | Cover is safe during the day but dangerous at night: the use of vegetation by European wild rabbits[END_REF][START_REF] Palomares | Predation upon European rabbits and their use of open and closed patches in Mediterranean habitats[END_REF][START_REF] Villafuerte | Predation risk, cover type and group size in European rabbits in Doñana (SW Spain)[END_REF][START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Lombardi | Habitatrelated differences in rabbit (Oryctolagus cuniculus) abundance, distribution, and activity[END_REF][START_REF] Virgós | Factors shaping European rabbit abundance in continuous and fragmented populations of central Spain[END_REF]Calvete et al. 2004). The abundance of this lagomorph in scrublands is mainly determined by the vertical vegetation structure and composition and seems to be favoured by a trade-off between abundant low herbaceous vegetation providing high quality food and a certain amount of tall vegetation offering cover but without hindering movement [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Beja | Rabbit Oryctolagus cuniculus habitats in Mediterranean scrubland: the role of scrub structure and composition[END_REF][START_REF] Ferreira | Influence of habitat management on the abundance and diet of wild rabbit (Oryctolagus cuniculus algirus) populations in Mediterranean ecosystems[END_REF].

Forest fires have played an important role in the landscape structure of the Mediterranean Basin [START_REF] Moreno | The role of fire in Mediterranean-type ecosystems[END_REF][START_REF] Rundel | Lanscape disturbance and biodiversity in Mediterranean-type ecosystems[END_REF]), one of the world's biodiversity hotspots [START_REF] Myers | Biodiversity hotspots for conservation priorities[END_REF]. After a wildfire, there is a change in vegetation structure and composition over large areas. It is known that early stages of post-fire successional development, which are dominated by herbaceous plants, are favourable to the animal species typical of open habitats [START_REF] Prodon | L'impact du feu sur la végétation, les oiseaux et les Micromammifères dans diverses formations méditerranéennes des Pyrénées-Orientales: premiers résultats[END_REF][START_REF] Prodon | Fire, bird conservation and land management in the North-Mediterranean area[END_REF][START_REF] Fons | Incendie et cicatrisation des écosystèmes Méditerranéens. Dynamique du repeuplement en micromammifères[END_REF][START_REF] Arrizabalaga | Post-fire succession in small mammall communities in the Montserrat massif (Catalonia, Spain)[END_REF][START_REF] Pons | Short-term temporal patterns in Mediterranean shrubland bird community after wildfire[END_REF][START_REF] Herrando | Bird community succession after fire in a dry Mediterranean shrubland[END_REF][START_REF] Herrando | Does fire increase the spatial heterogeneity of bird communities in Mediterranean landscapes?[END_REF]. Therefore, it is to be expected that wildfires will benefit rabbit populations in the same way as they do other species with similar habitat requirements.

Information on the effects of fire on rabbit populations is restricted to one study of prescribed fires in small experimental areas (300×200 m) of Mediterranean scrubland in the Doñana National Park [START_REF] Moreno | Traditional management of scrubland for the conservation of rabbits Oryctolagus cuniculus and their predators in Doñana National Park, Spain[END_REF]. This study showed an increase of pellet counts in burnt areas compared to unburnt ones, which was attributed to an increase in nutritious forage after fires in the first sample plots. However, the effects of wildfires on rabbit populations are to some extent unknown. In contrast to prescribed fires, wildfires occurred unexpectedly as a result of particular climatic circumstances in specific seasons [START_REF] Chandler | Fire in forestry, Vol I. Forest fire behaviour and effects[END_REF] and their characteristics (such as heterogeneity and intensity) and consequences differed from prescribed fires [START_REF] Wade | A guide for prescribed fire in Southern forests[END_REF][START_REF] Fernandes | A review of prescribed burning effectiveness in fire hazard reduction[END_REF].

One of the most generalised post-fire forest treatments consists of the clear cutting and removal of burnt trees, and then leaving of branches on the ground. This treatment is frequently subsidised by environmental institutions, whose main objective is forest regeneration. During this kind of management, burnt branches are left on the ground, mainly for economic reasons but also to prevent soil erosion [START_REF] Bautista | El tratamiento de la madera quemada tras los incendios forestales[END_REF]). However, the non-forestry consequences of this practice for biodiversity or ecology are poorly known [START_REF] Bautista | El tratamiento de la madera quemada tras los incendios forestales[END_REF]). Since rabbits seem to be favoured by scrublands with open access at ground level [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Beja | Rabbit Oryctolagus cuniculus habitats in Mediterranean scrubland: the role of scrub structure and composition[END_REF]), it might be expected that leaving burnt branches on the ground would have a negative effect on this species' abundance.

In light of the serious decline in rabbit populations in recent decades, the ecological and economic value of this species and the high frequency and extension of wildfires in the Mediterranean Basin, we aimed to assess the effect of wildfires and post-fire forest treatments on rabbit abundance. To do so, we used data on rabbit abundance in different plot types during three consecutive years after a forest fire in north-eastern Spain. Our results were then used to provide management guidelines for improving rabbit populations in Mediterranean habitats after wildfires.

Materials and methods

Study area

The study area was located in the massif of Sant Llorenç del Munt (Catalonia, NE Spain), affected in summer 2003 by a high intensity forest fire that burnt 4,600 ha (Fig. 1). The climate of this area is Mediterranean, with an average annual temperature of 13°C and annual rainfall of 700 mm, mainly concentrated in autumn and spring. Landscape had two different areas depending on the pre-fire dominant vegetation and soils. Whereas the Southern burnt area was dominated by Pinus halepensis forests in conglomerateclay soils, the Northern area was dominated by Pinus nigra ssp. salzmanii and Pinus sylvestris, all with a dense undergrowth of shrubs and Quercus ilex beneath the pines in loam-sandstone soils.

The study of rabbit abundance was focused on the Southern burnt area, which had a characteristic Mediterranean habitat for rabbits [START_REF] Palomares | Predation upon European rabbits and their use of open and closed patches in Mediterranean habitats[END_REF][START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Virgós | Factors shaping European rabbit abundance in continuous and fragmented populations of central Spain[END_REF]Calvete et al. 2004), in order to avoid landscape heterogeneity, and also excluding rugged terrain, urban areas or other elements such as roads or streams. Within the area, 50 plots of 100×100 m were randomly established on gentle slopes at altitudes ranging from 440 m to 655 m a.s.l. The surface of plots corresponded to the area commonly used by an individual rabbit [START_REF] Gibb | Sociality, time and space in a sparse population of rabbits (Oryctolagus cuniculus)[END_REF][START_REF] Lombardi | Habitat use and spatial behaviour in the European rabbit in three Mediterranean environments[END_REF][START_REF] Devillard | Home range of the European rabbit (Oryctolagus cuniculus) in three contrasting French populations[END_REF] and the average distance (±SD) between plots was 2,412±1,256 m, ranging from 200 to 6,615 m (n=2,450 pairs of plots). Thus, distance between plots was at least 200 m, as cited by [START_REF] Richardson | Social structures, genetic structures and dispersal strategies in Australian rabbit (Oryctolagus cuniculus) populations[END_REF] for rabbit dispersal distances. Taking into account forest types and the different post-fire treatments (Fig. 1), four types of plots were considered: (A) unburnt forests, considered as control plot of the pre-fire vegetation (n=10); (B) burnt forests with clear cutting and the removal of burnt trees during 2004, but with branches left on the ground (n=20); (C) burnt forests with clear-cutting and the removal of burnt trees during 2004, but with branches left on the ground that were subsequently shredded outside the plots in spring 2006 (n= 10); due to the high initial cover of burnt branches in these plots (average=33.4%;SD=5.7%), some branches were piled up and were left in the plots (average cover=10.8%; SD=5.1%; <5 piles/ha); (D) burnt shrublands and bare rocks, which had a high percentage of bare ground and no tree cover before the fire (n=10).

Hunting was not allowed within the study area from 2003 to 2008 so as not to affect the results.

Estimation of rabbit abundance

In order to estimate rabbit abundance, plots were sampled once a year during 2006, 2007 and 2008 at peak rabbit abundance in June at the end of the breeding season [START_REF] Cabezas | An experimental study of translocation success and habitat improvement in wild rabbits[END_REF][START_REF] Catalán | Is habitat management an effective tool for wild rabbit (Oryctolagus cuniculus) population reinforcement?[END_REF].

Rabbit abundances in each plot were estimated by counting the number of latrines within 2 m on either side of a 500-m itinerary (500×2 m). Three classes of latrines were defined in terms of the number of pellets (1=5-50 pellets; 2=51-150 pellets; 3>150 pellets), as in [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF]. After a number of trials, we decided to classify latrine classes in terms of their diameter (1<10 cm; 2=10-30 cm; 3>30 cm). Every 25 individual pellets found outside a latrine were classed as belonging to a class 1 latrine. Relative rabbit abundance (number of pellets) was estimated by multiplying the number of pellets within each latrine class by the midpoint of that latrine class, i.e. class 1, ×27 pellets; class 2, ×100 pellets; class 3, ×300 pellets. We considered rabbits were absent on a plot when latrines or pellets were not found.

Independent variables

The independent variables shown in Table 1 were determined for each burnt plot every year (2006, 2007 and 2008) in July. In order to compare the initial soil area covered by burnt branches (%) in each burnt plot type, the C plots were surveyed in February before the burnt branches were shredded in spring 2006. Variables were extracted from the measurements made along two 100 m-long transects (N-S and E-W) intercepting at the centre of each plot using the Point Intercept Method [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF]), a GPS receiver and a tape measure. At sampling points distributed every 1 m along the itineraries (200 points per plot), the presence of burnt branches and the plant species (as well as maximum height of the plants) were recorded and computed in one or more variables shown in Table 1.

Since hard soils hamper warren building and thus might be a limiting factor for rabbit abundance [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Virgós | Factors shaping European rabbit abundance in continuous and fragmented populations of central Spain[END_REF]Calvete et al. 2004;Delibes-Mateos et al. 2008b), soil hardness was determined for each plot as the percentage of the sampling points with soft soils (mostly clays) or hard soils (mostly conglomerates).

Statistical analyses

To assess the effect of wildfires and post-fire forest treatments on rabbit abundance, we used the Kruskal-Wallis and Mann-Whitney U tests [START_REF] Zar | Biostatistical analysis[END_REF]) to compare To assess the effect of burnt branches, vegetation and other ecological factors (see Table 1) on rabbit abundance, we performed a covariance analysis (ANCOVA) using data from 30 burnt plots (types B and D) from the years 2006, 2007 and 2008. The number of pellets was normalised by using the square root transformation; independent variables were normalised with the arcsin transformation [START_REF] Zar | Biostatistical analysis[END_REF]. We only considered the percentages of soil covered by the ten mosy common plant species (Brachypodium phoenicoides, B. retusum, Cistus albidus, Coriaria myrtifolia, Dorycnium pentaphyllum, Psoralea bituminosa, Q. ilex, Rosmarinus officinalis, Rubia peregrina and Rubus ulmifolius) as they were the only species common enough to be normalised. To assess the individual effect of each independent variable on rabbit abundance, we performed an ANCOVA model for each variable including the year as a factor. To determine which group of variables most affected rabbit abundance, we performed a model to explain the maximum variance of rabbit abundance. In this case, we only used groups of variables fully independent between them in order to avoid collinearity. We checked for ANCOVA assumptions as independence of variance estimates, normal distribution of errors, homogeneity of variance and homogeneity of linear regression [START_REF] Zar | Biostatistical analysis[END_REF]). The significance level was set at 0.05. All data analyses were run using SPSS v. 14.0 for Windows.

Results

Effect of wildfires and post-fire forest treatments on rabbit abundance

During the course of this study from 2006 to 2008, the presence of rabbits increased in all types of burnt plots (from 18 to 19 in the B plots, from 6 to 10 in the C plots and from 8 to 10 in the D plots). However, rabbit presence dropped in the unburnt A plots from 9 to 7.

Rabbit abundances did not differ between the plot types in years 2006 (x Kruskal-Wallis 2 =6.328; d.f.=3; p=0.097) and 2007 (x 2 =3.065; d.f. = 3; p=0.382), but did in 2008 (x Kruskal-Wallis 2 =17.397; d.f.=3; p<0.001). When we excluded the unburnt A plots from our analysis of year 2008, abundances between burnt plots B, C and D did not differ (x Kruskal-Wallis 2 =4.839; d.f.=2; p=0.089), indicating that the differences between plot types were caused by differences between the unburnt and burnt plots.

While average rabbit abundance increased from 2006 to 2008 in all burnt plot types, they did not in unburnt

Effect of burnt branches on rabbit abundance

We only found four independent variables that had an individual effect on rabbit abundance (see ANCOVA models a, b, c and d in Table 2). Bare ground surface area (%) and soil covered by P. bituminosa (%) were positively correlated with rabbit abundance, whereas soil covered by vegetation (%) or covered with burnt branches (%) was found to be negatively correlated with rabbit abundances. Despite appearing negatively correlated (F 1, 86 =3.624; p= 0.06), burnt branches did not appear to have a significant individual effect on rabbit abundance.

The ANCOVA model that explains the maximum variance in rabbit abundance (up to 55.2%; see model e in Table 2) includes soil covered (%) by burnt branches, B. phoenicoides, B. retusum, P. bituminosa, Q. ilex, R. officinalis and R. peregrina. Soil covered (%) by burnt branches, B. phoenicoides, B. retusum and Q. ilex appeared negatively correlated with rabbit abundance, whereas soil covered (%) by P. bituminosa, R. officinalis and R. peregrina was positively correlated with rabbit abundance.

Discussion

The progressive appearance of rabbits in burnt plots where they had previously been absent indicates that this species will colonise burnt areas after wildfires. Moreover, in burnt plots, rabbits progressively increased their abundance to the extent that their numbers probably exceeded those from before the wildfire. In 2001, rabbit abundances were very low in this area (0.006-0.030 rabbits/km, KAI with car at dusk; [START_REF] Ballesteros | Dieta de la guineu (Vulpes vulpes) al Parc Natural de Sant Llorenç del Munt i l'Obac. V Trobada[END_REF], in comparison to the 0.5-2 rabbits/km found in other Mediterranean areas [START_REF] Moreno | Long-term decline of the European wild rabbit (Oryctolagus cuniculus) in south-western Spain[END_REF]. Furthermore, the greater rabbit abundance in burnt plots, as well as the maintenance of rabbits in or even disappearance from unburnt plots, indicates that wildfires may favour the presence and abundance of rabbits, a finding which agrees with the situation of other Mediterranean vertebrates typical of open habitats [START_REF] Prodon | L'impact du feu sur la végétation, les oiseaux et les Micromammifères dans diverses formations méditerranéennes des Pyrénées-Orientales: premiers résultats[END_REF][START_REF] Prodon | Fire, bird conservation and land management in the North-Mediterranean area[END_REF][START_REF] Fons | Incendie et cicatrisation des écosystèmes Méditerranéens. Dynamique du repeuplement en micromammifères[END_REF][START_REF] Arrizabalaga | Post-fire succession in small mammall communities in the Montserrat massif (Catalonia, Spain)[END_REF][START_REF] Pons | Short-term temporal patterns in Mediterranean shrubland bird community after wildfire[END_REF][START_REF] Herrando | Bird community succession after fire in a dry Mediterranean shrubland[END_REF][START_REF] Herrando | Does fire increase the spatial heterogeneity of bird communities in Mediterranean landscapes?[END_REF].

Observed rabbit colonisation and the increase in rabbit abundance in burnt areas could be related to the appearance of open habitats with a significant surface area occupied by bare ground and a high diversity of low herbaceous, mostly gramineous and leguminous vegetation (Martínez-Sánchez and Herranz 1999; De las [START_REF] Las Heras | Effects of silviculture treatments on vegetation after fire in Pinus halepensis Mill. woodlands (SE Spain)[END_REF]), which coincides with known habitat preferences for rabbits [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Beja | Rabbit Oryctolagus cuniculus habitats in Mediterranean scrubland: the role of scrub structure and composition[END_REF][START_REF] Ferreira | Influence of habitat management on the abundance and diet of wild rabbit (Oryctolagus cuniculus algirus) populations in Mediterranean ecosystems[END_REF]. Our study shows an increase in rabbit abundance for at least 5 years after the fire indicating that in the mid-term, forest fires have a relatively positive effect on rabbit abundance. This agrees with results obtained with prescribed fires in Mediterranean shrublands, where higher pellet counts were obtained in burnt plots in comparison to unburnt plots for at least 3 years after fires [START_REF] Moreno | Traditional management of scrubland for the conservation of rabbits Oryctolagus cuniculus and their predators in Doñana National Park, Spain[END_REF]. However, the long-term effect of wildfires on rabbit abundance is still unknown, although it is expected that rabbit abundance decreases or even disappears as the soil area covered by vegetation increases (and especially by woody species) during plant succession after fire [START_REF] Pausas | Post-fire regeneration patterns in the eastern Iberian Peninsula[END_REF][START_REF] Kazanis | Long-term post-fire vegetation dynamics in Pinus halepensis forests of Central Greece: a functional group approach[END_REF], as occurs in other species with similar requirements [START_REF] Prodon | L'impact du feu sur la végétation, les oiseaux et les Micromammifères dans diverses formations méditerranéennes des Pyrénées-Orientales: premiers résultats[END_REF][START_REF] Prodon | Fire, bird conservation and land management in the North-Mediterranean area[END_REF][START_REF] Fons | Incendie et cicatrisation des écosystèmes Méditerranéens. Dynamique du repeuplement en micromammifères[END_REF][START_REF] Arrizabalaga | Post-fire succession in small mammall communities in the Montserrat massif (Catalonia, Spain)[END_REF][START_REF] Pons | Short-term temporal patterns in Mediterranean shrubland bird community after wildfire[END_REF][START_REF] Herrando | Bird community succession after fire in a dry Mediterranean shrubland[END_REF][START_REF] Herrando | Does fire increase the spatial heterogeneity of bird communities in Mediterranean landscapes?[END_REF].

In regard to different post-fire forest treatments, the greater rate of change in rabbit abundance in C plots seems to indicate that reducing the soil area covered by burnt branches, but as well creating piles with these branches that might be used by rabbits as refuges, has a positive effect on the colonisation and the increase in rabbit numbers. The fact that C plots did not have the highest rabbit abundance can probably be attributed to the lower initial rabbit numbers in C, due possibly to the significantly higher initial soil area covered by burnt branches (33.4±5.7% in the C plots and 25.3±6.1% and 3.1±2.9% in the B and D plots, respectively, expressed as average±SD) (x Kruskal-Wallis 2 =27.070; d.f.= 2; p<0.001). On the other hand, rabbit abundance in the C plots might have been conditioned by the general extent of the post-fire treatment, which included clear cutting and the removal of burnt trees and branches left on the ground (as in the B plots). Furthermore, the C plots probably had lower initial rabbit abundance because they were more forested before the fire, as shown by the higher soil area covered by burnt branches. Thus, these factors might have conditioned the effects of the post-fire treatment in the C plots and mitigated the effect of reducing the amount of soil covered by branches.

The negative correlation between rabbit abundance and the soil area covered by burnt branches or by dense vegetation might be due to the fact that woody cover hinders rabbit movement, an idea reinforced by the positive correlation between the percentage of bare ground and rabbit numbers [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Beja | Rabbit Oryctolagus cuniculus habitats in Mediterranean scrubland: the role of scrub structure and composition[END_REF]. Plant species such as B. phoenicoides, B. retusum, and Q. ilex that form dense soil cover appeared negatively correlated with rabbit abundance. On the other hand, rabbits were positively correlated with other plant species such as R. officinalis that had low soil coverage and do not hinder rabbit movements.

Other plant species might also determine rabbit abundance as a result of their nutritional value [START_REF] Boyd | Factors controlling the length of the breeding season in wild rabbits[END_REF][START_REF] Boyd | Seasonal changes in condition, reproduction and fecundity in the wild European rabbit Oryctolagus cunniculus[END_REF][START_REF] Moreno | Traditional management of scrubland for the conservation of rabbits Oryctolagus cuniculus and their predators in Doñana National Park, Spain[END_REF][START_REF] Ferreira | Influence of habitat management on the abundance and diet of wild rabbit (Oryctolagus cuniculus algirus) populations in Mediterranean ecosystems[END_REF]. For instance, it is known that P. bituminosa, which is very common during the first years after fires (Martínez-Sánchez and Herranz 1999; De las [START_REF] Las Heras | Effects of silviculture treatments on vegetation after fire in Pinus halepensis Mill. woodlands (SE Spain)[END_REF]) and R. peregrina (both positively correlated with the abundance of rabbits), are commonly favoured by other herbivores due to their high nutritive value [START_REF] Chapuis | Utilisation des ressources trophiques par le lapin de garenne (Oryctolagus cuniculus) en garrigue sèche aménagée[END_REF][START_REF] Bartolomé | Diet selection by sheep and goats on Mediterranean heath-woodland Range[END_REF][START_REF] Sternberg | Vegetation response to grazing management in a Mediterranean herbaceous community: a functional group approach[END_REF][START_REF] Ventura | Energy and protein content of Tedera (Bituminaria bituminosa)[END_REF][START_REF] Sternberg | Effects of grazing on Bituminaria bituminosa (L) Stirton: a potential forage crop in Mediterranean grasslands[END_REF].

Although it is known that hard soils hinder warren building and might be a limiting factor on rabbit abundance [START_REF] Elzinga | Habitat correlates of European rabbit (Oryctolagus cuniculus) distribution after the spread of RVHD in Cadiz Province, Spain[END_REF][START_REF] Virgós | Factors shaping European rabbit abundance in continuous and fragmented populations of central Spain[END_REF]Calvete et al. 2004;Delibes-Mateos et al. 2008b), our study found no effects of soil hardness on rabbit abundance; this might be because in our study area there was enough vegetation cover to provide protection and breeding refuges [START_REF] Kolb | The use of cover and burrows by a population of rabbits (Mammalia: Oryctolagus cuniculus) in eastern Scotland[END_REF][START_REF] Moreno | Cover is safe during the day but dangerous at night: the use of vegetation by European wild rabbits[END_REF] and possibly due to the scale of the study as soils may have a role at a regional scale.

In conclusion, taking into account the rate of increase of rabbit abundance in the C plots and the overall negative correlation in burnt plots between burnt branches and rabbit abundance, it is suggested that a reduction in the coverage of burnt branches will have a positive effect on rabbit abundance.

Conservation implications

In recent years, forest fires have become more frequent in Mediterranean areas due to the increase in the forested surface area and the biomass therein resulting from rural abandonment [START_REF] Moreno | The role of fire in Mediterranean-type ecosystems[END_REF][START_REF] Rundel | Lanscape disturbance and biodiversity in Mediterranean-type ecosystems[END_REF]). Fires create open areas which could benefit rabbit populations and other significant species found in Mediterranean ecosystems.

The main objective of one of the most generalised postfire treatments-the clear cutting and removal of burnt trees but with branches left on the ground-is forest regeneration. However, most Mediterranean forest areas are usually quite unproductive [START_REF] Merlos | Valuing Mediterranean forests: towards total economic value[END_REF], although they are of great ecological value and harbour significant levels of biodiversity [START_REF] Myers | Biodiversity hotspots for conservation priorities[END_REF]. Post-fire treatments favourable to rabbit populations might increase the economic and conservation value of areas affected by forest fires. Branches should be removed at the same time as burnt trees, as soil covered by burnt branches appears to have a negative effect on rabbit abundance and colonisation. In areas where burnt branches cannot be totally removed or where there is little vegetation to provide cover for breeding, refuges for rabbits could be built with burnt branches [START_REF] Miguel | Manual para la gestión del hábitat del lince ibérico (Lynx pardinus) y su presa principal, el conejo de monte (Oryctolagus cuniculus)[END_REF]. As well, prescribed fires or livestock could be used to keep vegetation in early succession stadiums that are favourable for rabbit populations [START_REF] Mayor | Biodiversity and sustainable development in the silvopastoral systems of the Cantabrian mountains[END_REF][START_REF] Casals | Silvopastoral Systems in the Northeastern Iberian Peninsula: a multifunctional perspective[END_REF]. Such measures should be accompanied by other actions such as the imposition of sustainable hunting strategies. Long-term monitoring of rabbit populations would also improve knowledge of the effects of wildfires and post-fire treatments on rabbit populations.

The increase in rabbit populations would benefit predators [START_REF] Delibes | The rabbit as prey in the Iberian Mediterranean ecosystem[END_REF][START_REF] Delibes Mateos | Rabbits as a keystone species in southern Europe[END_REF], 2008a) such as the endangered Iberian lynx (L. pardinus), the Spanish imperial eagle (A. adalberti) and Bonelli's eagle (A. fasciata). In addition, hunting would also provide an important source of income in rural areas affected by forest fires [START_REF] Bota | La gestión cinegética como alternativa para la restauración de la zona afectada por el incendio de la Catalunya central de 1998[END_REF].

Fig. 1

 1 Fig.1Location of the study area in the western Mediterranean and location of sampled plots (A unburnt forest, B burnt forests with the removal of burnt trees and branches left on the ground, C burnt forests with the removal of burnt trees and a reduction in the soil area covered by branches, D burnt shrublands and bare rocks) within the study area

Eur J Wildl Res (2011) 57:201-209

Acknowledgements This study was commissioned by the project "Conveni de Col•laboració entre la Caixa d'Estalvis i Pensions i la Diputació de Barcelona per al desenvolupament del Pla de gestió integral per a la conservació dels sistemes naturals de la xarxa de Parcs Naturals de la Diputació de Barcelona". We are deeply indebted to Carles Castell, Martí Doménech, Ramon Espinach, Daniel Guinart, Feliu Madaula, Àngel Miño and Jordi Riera, from "Àrea d'Espais Naturals de la Diputació de Barcelona". Francesc Parés made a huge contribution during the fieldwork. Two anonymous referees provided very helpful comments on earlier drafts of the manuscript.