Andrei S Kozlov

Thomas Risler

A J Hudspeth

Coherent motion of stereocilia assures the concerted gating of hair-cell transduction channels

come

Coherent motion of stereocilia assures the concerted gating of hair-cell transduction channels

The high sensitivity of sensory systems requires an efficient use of the energy in stimuli to bias the open probability of ion channels. For a hair cell of the inner ear, mechanical forces directly gate transduction channels atop stereocilia, the rod-like constituents of the mechanosensitive hair bundle [START_REF] Hudspeth | Putting ion channels to work: mechanoelectrical transduction, adaptation, and amplification by hair cells[END_REF] . A hair bundle's sensitivity is determined by the relation between the applied force and the number of channels opened: the narrower the force range over which gating occurs, the greater the sensitivity. The coordinated gating of transduction channels is also thought to underlie active hair-bundle motility, a component of the active process that amplifies and tunes the responses of hair cells [START_REF] Fettiplace | Active hair bundle movements in auditory hair cells[END_REF] .

Because mechanical stimuli are ordinarily applied at the tall edge of a hair bundle, channel gating depends upon the propagation of mechanical force across the array of stereocilia.

Each stereocilium possesses a basal rootlet of actin filaments that tends to hold the process upright; as measured at the hair bundle's tip, the combined stiffness of these stereociliary pivots is about 200 µN•m -1 (ref. [START_REF] Marquis | Effects of extracellular Ca 2+ concentration on hair-bundle stiffness and gating-spring integrity in hair cells[END_REF] ). In addition, the successive stereocilia in each file are joined by tip links that are thought to represent the gating springs attached to transduction channels at one or both ends. For large bundle deflections and in the presence of a physiological concentration of Ca 2+ , the combined stiffness of these gating springs is typically 1000 µN•m -1 (ref. 3). The opening and closing of transduction channels reduces the effective stiffness of the gating springs-the phenomenon of gating compliance-to a value comparable to that of the pivots, or even lower [START_REF] Howard | Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell[END_REF][START_REF] Martin | Negative hair-bundle stiffness betrays a mechanism for mechanical amplification by the hair cell[END_REF] .

The stereocilia of a hair bundle appear at first glance to be connected in a series-parallel configuration such that a force applied to the tallest stereocilium in each file would first deflect that process alone (Fig. 1a). Movement of the tallest stereocilium would then tighten the tip link and perhaps other filaments connecting it to the second, deflecting that process; the second stereocilium would in turn pull on the third, and so on across the hair bundle. If stereocilia were to operate in such a configuration, the magnitude of their deflection would diminish progressively from the tallest to the shortest [START_REF] Silber | Computational models of hair cell bundle mechanics: III. 3-D utricular bundles[END_REF][START_REF] Nam | Mechanical properties and consequences of stereocilia and extracellular links in vestibular hair bundles[END_REF] and the open probability of the transduction channels would therefore vary with their location (Fig. 1b). This arrangement would broaden the relation between force and channel open probability and thereby reduce the sensitivity of mechanoelectrical transduction. The ensemble of mechanosensitive channels would function more efficiently if the stereocilia were instead to adopt a parallel arrangement, in which an applied force is shared equally among them and deflects all to a similar extent (Fig. 1b). This arrangement would prevail if the stereocilia were somehow constrained to remain in close contact during excitation.

Visual observations [START_REF] Hudspeth | polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli[END_REF] and video measurements [START_REF] Crawford | Activation and adaptation of transducer currents in turtle hair cells[END_REF][START_REF] Karavitaki | Hair bundle mechanics at high frequencies: a test of series or parallel transduction[END_REF] have suggested that a hair bundle moves as a unit when subjected to relatively large, low-frequency stimuli. However, a conclusive examination of the propagation of mechanical forces across a bundle requires simultaneous measurements of the positions of two stereocilia with a sub-nanometer spatial and a sub-millisecond temporal resolution, for these are the scales typical of stereociliary movements during hearing. Because interferometry can detect motions with the requisite precision, we constructed a dual-beam, differential laser interferometer and used it to examine the correlations between the thermal motions of individual stereocilia both in quiescent and in spontaneously oscillating hair bundles (Fig. 1c). Our experiments showed that the movements of stereocilia located as far apart as the bundle's opposite edges displayed high coherence and zero phase lag over a wide range of frequencies. This result implies that stereocilia are strongly constrained to move in unison, a feature that promotes the high sensitivity of mechanoelectrical transduction and fosters the coordinated gating that underlies active hair-bundle motility.

RESULTS

The morphological organization of the hair bundle is highly conserved throughout the vertebrates. The experiments reported in this study were therefore performed on hair cells from the bullfrog's sacculus, a preparation whose mechanical and electrical properties have been extensively studied and which was used successfully in earlier experiments employing laser interferometery [START_REF] Denk | Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer[END_REF] . For each hair bundle, we measured the time-dependent positions of stereocilia with three distinct configurations of the dual-beam interferometer.

In the first arrangement, the two laser beams were focused together on one of the bundle's edges, for example at the same point on the tip of the longest stereocilium (Fig. 2a). As expected, the resultant records were closely similar to one another (Fig. 2b). For a quiescent hair bundle, the autocorrelation of each signal declined exponentially from its peak value with a time constant of approximately 1 ms (Fig. 2c). This correlation time represents the quotient of the bundle's drag coefficient, circa 130 nN•s•m -1 (ref. 4,11), and its stiffness, about 150 µN•m -1 including the gating compliance near the resting position [START_REF] Martin | Spontaneous oscillation by hair bundles of the bullfrog's sacculus[END_REF] . In 38 measurements from 18 hair bundles, the peak value of the cross-correlation of the two signals was 0.93 ± 0.04. The difference of 7% between this value and the maximal value of one provides a quantitative indication of the noise level in the illumination and detection systems.

A second experimental configuration provided a control for the presence of drift by the whole epithelium, which might have introduced artifactual correlations between the motions of two different spots on a given hair bundle. In this instance, we acquired 17 measurements with the laser beams focused on two adjacent hair bundles. As expected for signals from independently moving sources, the cross-correlation was randomly distributed in time and displayed an average magnitude of 0.08 ± 0.03, similar to that of the background noise (Fig. 2c).

In the third and critical set of measurements, we estimated the degree of common motion between stereocilia across a hair bundle by positioning the laser beams on its two opposite edges.

The individual records were highly similar in quiescent hair bundles (Fig. 3a ). The autocorrelations and cross-correlation from each cell were almost identical (Fig. 3b). For 29 measurements from 18 quiescent hair bundles, the peak value of the averaged cross-correlation was 0.92 ± 0.03; this value differed by only 1% from the peak cross-correlation obtained with both lasers focused on the same stereocilium.

The cross-correlation commingles information about the components of hair-bundle movement over the full measurable range of frequencies. To assess the degree of common motion as a function of frequency, we characterized the coherency spectrum of the two signals.

The coherency is a dimensionless, complex quantity whose argument represents the estimated phase lag between two signals and whose modulus, called the coherence, represents the quality of this phase estimate [START_REF] Nowak | Rossi X-Ray Timing Explorer observation of Cygnus X-1. II. Timing analysis[END_REF] . For signals of infinite duration, the coherence is bounded at each frequency by zero for uncorrelated signals and by unity for perfectly correlated ones. For 18 quiescent hair bundles, and except for a few deviations caused by laser noise, the average coherence obtained in 29 measurements from opposite hair-bundle edges remained high at all sampled frequencies and exceeded 0.88 between 100 Hz and 5 kHz (Fig. 3c). When the two laser beams were positioned together on one edge of the bundle, the average coherence in 38 measurements was only 2% greater (Fig. 3d). Phase-lag estimates were close to zero over the whole spectrum for all the quiescent hair bundles. Between 100 Hz and 5 kHz, the standard deviation was smaller than 0.23 radian for determinations from the bundles' opposite edges and beneath 0.18 radian for measurements at the same edges. The coherence and phase estimates were limited at low frequencies by independent drifts in the two laser beams and at high frequencies by the diminishing signal power, which eventually approached the background noise level.

The gating compliance of healthy hair bundles lowers their effective stiffness to a value comparable to that of a damaged bundle. To ensure that our data reflected the activity of functional hair bundles, we repeated the measurements with nine oscillatory bundles, whose spontaneous movements required the normal gating of transduction channels by intact tip links (Fig. 4a). In this instance, the average cross-correlation obtained in 29 measurements from opposite hair-bundle edges peaked at a value of 0.92 ± 0.05 (Fig. 4b). The associated coherence exceeded 0.87 between 100 Hz and 5 kHz, (Fig. 4c), as compared to the value of 0.93 obtained in 17 measurements with the lasers focused on the same bundle edge (Fig. 4d ). In every instance, the estimated phase lag was negligible over the whole spectrum: the standard deviation was less than 0.25 radian for measurements at the opposite edges of the oscillating hair bundles, and below 0.12 radian for same-edge measurements.

The striking concordance in the movements of the stereocilia across a hair bundle might reflect the transmission of forces through the tip links or other filamentous connections between stereocilia. Alternatively, the geometrical arrangement of the hair bundle might constrain the stereocilia to move together. To distinguish between these possibilities, we treated cells with 5 mM BAPTA, a procedure known to disrupt tip links and certain other connections [START_REF] Assad | Tip-link integrity and mechanical transduction in vertebrate hair cells[END_REF][START_REF] Bashtanov | The mechanical properties of chick (Gallus domesticus) sensory hair bundles: relative contributions of structures sensitive to calcium chelation and subtilisin treatment[END_REF] . As expected because tip links contribute significantly to hair-bundle stiffness, treated bundles displayed both a greater root-mean-square displacement (10.2 ± 2.1 nm, n = 20 versus 5.5 ± 1.8 nm, n = 67; Fig. 5a) and an increased correlation time (2.2 ± 0.4 ms, n = 20 versus 1.1 ± 0.4 ms, n = 67; Fig. 5b). The coherence between 100 Hz and 5 kHz nonetheless exceeded 0.89 in 11 measurements from the opposite edges of the bundles (Fig. 5c) and 0.96 in nine measurements from the same edges (Fig. 5d). Phase-lag estimates showed standard deviations smaller than 0.14 radians for the opposite bundle edges and 0.08 radians for the same edges.

That BAPTA neither lowered the coherence nor increased the phase lag implies that the coordination of motion among stereocilia does not depend on tip links.

To compare our findings with those anticipated for a series-parallel configuration of the hair bundle, we modeled the thermal motions expected for stereocilia interconnected by gating springs of various stiffnesses. For the stiffness value estimated in previous experiments on hair bundles from the bullfrog's sacculus [START_REF] Howard | Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell[END_REF][START_REF] Martin | Spontaneous oscillation by hair bundles of the bullfrog's sacculus[END_REF] , the cross-correlation between the movements of stereocilia on opposite edges of the modeled bundle was near zero (Fig. 6a). The coherence of these movements approached the value associated with independent motion at all frequencies; consistent with this result, the phase was essentially random (Fig. 6b). Even when the gatingspring stiffness was increased more than fiftyfold in an effort to foster closer coupling between stereocilia, the cross-correlation failed to attain the values found in actual experiments (Fig. 6a).

In this instance, the coherency spectrum displayed coordinated movements of stereocilia on a bundle's opposite edges only at low frequencies, but essentially independent motion for frequencies in excess of 1 kHz (Fig. 6c ). A simple series-parallel model therefore seems incapable of reproducing the experimental results with values of gating-spring stiffness compatible with the hair bundle's measured stiffness.

DISCUSSION

The present results demonstrate that the stereocilia throughout a hair bundle exhibit strongly correlated motions up to high frequencies. The coherences measured with the two laser beams focused on the same or on opposite edges of hair bundles agree within 2% for frequencies between 100 Hz and 5 kHz. Because quiescent hair bundles display a root-mean-square motion of about 3 nm, these coherence values imply that the average splaying between their successive stereocilia is no more than a few tens of picometers. It follows that stimulus forces exerted on a hair bundle are distributed almost equally among the gating springs. Unlike a simple seriesparallel arrangement, the bundle's actual configuration ensures that most of the stimulus energy is delivered to the gating machinery of transduction channels. The results also validate previous estimates of tip-link stiffness and buttress the model of negative hair-bundle stiffness, both of which rely on the assumption that the tip links are arrayed in parallel [START_REF] Howard | Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell[END_REF][START_REF] Iwasa | Cooperative interaction as the physical basis of the negative stiffness in hair cell stereocilia[END_REF] . Although the present experiments involved a receptor organ sensitive to relatively low frequencies, we have observed similar behaviors in preliminary experiments performed on auditory hair cells in the gecko's cochlea.

What mechanisms might account for the high correlation between the motions of stereocilia at a bundle's opposite extremes? Viscosity could contribute to the phenomenon, for the tendency of any stereocilium to separate from a neighbor during high-frequency stimulation would be opposed by the resultant reduction in the fluid pressure between them [START_REF] Henderson | Propagation of hydrodynamic interactions in colloidal suspensions[END_REF] . Next, the basal and lateral links that conjoin stereocilia [START_REF] Hudspeth | Mechanoelectrical transduction by hair cells in the acousticolateralis sensory system[END_REF] might resist the separation of these processes. It should be noted, however, that the enzymatic digestion used for the present experimental preparation largely removed these attachments [START_REF] Jacobs | Ultrastructural correlates of mechanoelectrical transduction in hair cells of the bullfrog's internal ear[END_REF] . The most intriguing possibility is that stereocilia do not separate because they are forced together, whether at rest or in motion, by the curvature of the cuticular plate into which they insert [START_REF] Hudspeth | Mechanoelectrical transduction by hair cells in the acousticolateralis sensory system[END_REF] . If the stereocilia were prestressed against one another, the deflection of any stereocilium during stimulation would allow each successive stereocilium to relax towards its position of mechanical equilibrium. This movement would compel the hair bundle to move as a unit without imposing the increased stiffness associated with stereociliary cross-linking.

The negative stiffness of a hair bundle is analogous to the negative resistance of a neuron during the rising phase of an action potential: both depend upon the collective action of ion channels that are globally coupled to one another, whether mechanically or through the membrane voltage, and therefore display concerted gating. Such channel interactions resemble those between protein molecules involved in cooperative phenomena. Molecular cooperativity, such as that in hemoglobin and allosterically regulated enzymes, ordinarily involves molecular contacts so intimate that changes in the configuration of one subunit or domain are physically communicated to its neighbors. In a hair bundle, however, the stimulus-induced opening and closing of individual transduction channels-situated micrometers apart on separate stereocilia-alters the balance of forces in the whole structure, in turn affecting the force experienced by the entire channel ensemble.

METHODS

Experimental preparation. Sacculi dissected from adult bullfrogs (Rana catesbeiana)

following a protocol approved by the Institutional Animal Care and Use Committee were maintained in oxygenated saline solution comprising 120 mM NaCl, 2 mM KCl, 1 mM CaCl 2 , 10 mM D-glucose, and 5 mM HEPES at pH 7.3. After a 30-60 min digestion at room temperature in 1 mg•ml -1 collagenase (type XI, Sigma Chemical Co.), each sensory epithelium was separated from the underlying connective tissue [START_REF] Denk | Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer[END_REF] and the otolithic membrane was removed.

The epithelium was then folded in its plane of mirror symmetry [START_REF] Jacobs | Ultrastructural correlates of mechanoelectrical transduction in hair cells of the bullfrog's internal ear[END_REF] so that hair bundles protruded radially from the creased edge and could be imaged in profile. The preparation was secured to the coverslip bottom of an experimental chamber by placing over it a golden, 100-mesh electronmicroscopic grid.

Interferometric recording. The dual-beam laser interferometer incorporated the basic features of a differential interferometer [START_REF] Denk | Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer[END_REF][START_REF] Denk | Optical measurement of picometer displacement of transparent microscopic objects[END_REF] . Two independent illumination pathways were established, one with red light from a 1.8-mW, 633-nm helium-neon laser (117A, Spectra-Physics), the other with green light from a 10-mW, 532-nm diode-pumped solid-state laser (85 GCA 010, Melles Griot Inc.). Each pathway included a Faraday reflection suppressor, a telescopic beam expander, and polarization and steering optics. The two beams were combined and directed into the microscope's differential-interference-contrast optical system, which split each circularly polarized beam into two orthogonally polarized components separated by circa 100 nm. A 40X objective lens of numerical aperture 0.8 acted as a condenser to focus each beam in the specimen plane to a diffraction-limited spot with a full width at half-maximal intensity of about 300 nm.

After traversing the specimen, the light from the two colored beams was collected through a second, identical objective lens and separated with a dichroic mirror into two independent measurement pathways. Each beam impinged on a polarizing beam splitter, which resolved the elliptically polarized light into two components whose magnitudes were measured with independent photodiodes. The amplified outputs were passed through eight-pole Butterworth anti-aliasing filters with a low-pass corner frequency of 20 kHz, then sampled with 16-bit resolution at 10-µs intervals. For each color channel, the ratio of the difference between the signals of orthogonal polarization to their sum was directly related to the phase difference between the two closely spaced optical pathways, and thus to the position of the object intercepted by the beam.

To calibrate each beam of the instrument, the lens forming one end of the associated beam-steering telescope was displaced through a known distance with a piezoelectrical manipulator. This procedure deflected the relevant focal spot in the specimen plane by a fixed amount set by the system's optical parameters. Using video imaging, we measured this shift in the specimen plane and thus determined the relation between the voltage applied to the piezoelectrical manipulator and the ensuing movement. Finally, during an actual experiment, the steering lens was displaced through a known distance and the resultant signal from the photodiodes was measured, thus establishing the calibration factor relating specimen movement to photodiode output.

In the absence of a specimen, each beam displayed a spectrally flat instrument noise of 5•10 -6 nm 2 •Hz -1 over the frequency range from 100 Hz to 20 kHz, corresponding to a root-meansquare sensitivity of 0.3 nm. When directed at one edge of a hair bundle, the interferometer detected thermal motion consistent with previous measurements [START_REF] Denk | Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer[END_REF][START_REF] Denk | Optical measurement of picometer displacement of transparent microscopic objects[END_REF][START_REF] Denk | Forward and reverse transduction at the limit of sensitivity studied by correlating electrical and mechanical fluctuations in frog saccular hair cells[END_REF][START_REF] Denk | Mechanical response of frog saccular hair bundles to the aminoglycoside block of mechanoelectrical transduction[END_REF] : the power-spectral density was approximately 0.03 nm 2 •Hz -1 up to a cutoff frequency near 180 Hz, implying a root-meansquare displacement of 3 nm. When the red and green laser beams were focused at the same point on a hair bundle, there was no detectable cross-talk between the two measurement channels.

Data analysis.

Each measurement consisted of a set of twenty, 100-ms-long records sampled at 10-µs intervals, between which the detection apparatus was calibrated independently for each laser beam. Discrete Fourier analysis of these records was performed after tapering of the data with a Bartlett window. Correlation functions were estimated from Fourier power-spectral amplitudes for which tapered records had previously been padded with 100-ms-long strings of zeros to avoid spurious correlations. Outliers were rejected on the basis of unstable root-meansquare amplitudes, abnormal cross-correlation amplitudes, or pronounced drift in the raw data.

For each set of data in a given experimental condition, power spectra and correlation functions were computed with the remaining independent estimates. The averaged autocorrelation and cross-correlation functions were obtained after normalization of each record by its root-mean-square value. The coherence and phase spectra associated with these measurements represented the modulus and phase of the coherency spectrum defined at a frequency f by

€ γ( f ) = C XY ( f ) / S X ( f ) S Y ( f )
If X(t) and Y(t) represent the signals from the two laser beams for an individual record, C XY (f) denotes the associated cross-spectrum estimate at the frequency f, S X (f) and S Y (f) specify the two power-spectral estimates at that frequency, and ... indicates averaging over several independent records. Modeling. To compare our findings with those expected if the stereocilia were to operate in the series-parallel configuration depicted in Fig. 1b, we simulated the outcome of the principal experiments. The modeled hair bundle consisted of a file of seven stereocilia, each subjected to linear frictional forces from the surrounding solution that included a deterministic component with an effective friction coefficient 20 nN•s•m -1 and a stochastic white noise representing the thermal motion at an ambient temperature of 295 K. Each stereocilium was connected to the cuticular plate by a flexional spring of stiffness 5 µN•m -1 and to each of its immediate neighbors by a gating spring whose stiffness was adjusted to either 1,000 µN•m -1 or 53,000 µN•m -1 . The former value corresponds to previous estimates of gating-spring stiffness in the bullfrog's saccular hair cells [START_REF] Howard | Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell[END_REF][START_REF] Martin | Spontaneous oscillation by hair bundles of the bullfrog's sacculus[END_REF] ; the latter value is tenfold that proposed in a series-parallel model [START_REF] Nam | Mechanical properties and consequences of stereocilia and extracellular links in vestibular hair bundles[END_REF] . To mimic the experimental protocol, we generated data in sets of twenty, 100-ms-long records sampled at 10-µs intervals. We then analyzed the results by the procedures described above and averaged the results of ten independent repetitions. The cross-correlation peaks at 0.97 ± 0.02, which indicates an instrumentation-noise level 3% of the peak signal. The black trace, which represents the cross-correlation averaged over 19 records with the laser beams focused on two adjacent bundles, lies at the system's noise level.

Figure 1

 1 Figure 1 The hair bundle and its possible modes of motion. (a, left) A scanning electron micrograph depicts a saccular hair bundle, which comprises about 60 cylindrical stereocilia and a single kinocilium at its tall edge. (a, right ) A schematic diagram of a slice along the central file of a hair bundle illustrates the geometrical arrangement of the stereocilia. The bundle is about 8 µm in height and each stereocilium is roughly 500 nm in diameter; tip links of exaggerated thickness are depicted between the adjacent stereocilia. Although the stereocilia differ substantially in height, the extensions of the associated tip links are nearly identical over the physiological range of stimulation 19 . The spots at the upper edges of the resting hair bundle represent the diffraction-limited laser beams employed in interferometric measurements, here positioned on the bundle's opposite edges. The calibration bar corresponds to 5 µm. (b, left) Upon application of a stimulus to the bundle (arrow), the force would spread decrementally from the longest to the progressively shorter stereocilia if these were arranged in the series-parallel configuration suggested by the bundle's structure. (b, right ) By contrast, a principally parallel configuration would distribute the stimulus force more-or-less equally among the stereocilia. (c, left) Under thermal motion, the stereocilia would display relatively independent positional fluctuations in the series-parallel arrangement. (c, right) In the more parallel configuration, the stereocilia would be constrained to move together.

Figure 2

 2 Figure 2 Experimental preparation and control measurements (a) The laterally protruding hair bundles are apparent in a micrograph of a folded sensory epithelium secured by an electron-microscopic grid. The hair bundle selected for measurements, designated by a dashed square, is depicted at a higher magnification on the right. Each calibration bar corresponds to 10 µm. (b) When the green and red laser beams are focused at the same point on the tips of the longest stereocilia, the two records of thermal motion are highly similar. (c) The red dashed line represents the averaged

Figure 3

 3 Figure 3 Coherency of stereociliary motion for quiescent hair bundles. (a) When the green and red beams are positioned on the opposite edges of a hair bundle, the two traces are very similar apart from different amplitudes owing to different stereociliary lengths. (b) For this hair bundle, the cross-correlation, averaged over 20 records (blue line) and superimposed on the corresponding autocorrelation (red dashed line), reaches a peak value of 0.95 ± 0.01. (c ) The averaged coherency spectrum for 29 measurements from the opposite edges of 18 hair bundles shows uniformly high values and a negligible phase lag at frequencies up to 10 kHz. The standard deviations for these measurements indicate the degree of variability in the different coherence and phase estimates. The phase spectrum shown at a higher magnification demonstrate a systematic deviation of the mean phase lag from zero at frequencies close to analog filters' cutoff. This deviation occurs in all records and results from non-identical phase delays introduced by the anti-aliassing filters. (d) In 38 measurements from the same cells, the spectrum for the beams focused on the same edge of the hair bundle is highly similar to that in (c).

Figure 4

 4 Figure 4 Coherency of stereociliary motion for oscillating hair bundles. (a) Although the interferometric records from the opposite edges of a spontaneously active hair bundle document displacements substantially larger than those observed in a quiescent bundle, the two traces are again very similar. (b) Averaged over 20 records, the cross-

ACKNOWLEDGMENTS

The authors thank A. J. Hinterwirth for assistance in constructing the interferometer, B. Fabella for programming the experimental software, and O. Ahmad, M.O. Magnasco, K. Purpura, and J.

Victor for useful discussions. The members of our research group provided helpful comments on the manuscript. The research reported in this paper was funded by the U.S. National Institutes of Health. T.R. was supported by funding from the F.M. Kirby Foundation and from the U.S. National Institutes of Health. A.S.K. was supported by Howard Hughes Medical Institute, of which A.J.H. is an Investigator.

AUTHOR CONTRIBUTIONS

A.J.H. conceived the experiments, A.S.K. performed them, and T.R. conducted the data analysis. A.S.K., T.R., and A.J.H. wrote the paper.

COMPETING INTERESTS STATEMENT

The authors declare that they have no competing financial interests. correlation peaks at 0.99 ± 0.01. The time constant of the correlations' decay exceeds that observed in quiescent cells, for example in Fig. 3b, owing to the low-frequency oscillatory movements of the bundles. The negative values of the correlations for times exceeding ±7 ms reflect the bundle's tendency to move in the opposite direction after dwelling at one extreme or the other. As shown on a coarser time scale in the insert, the cross-correlation also illustrates the roughly 70-Hz periodicity associated with the oscillations. (c) In 29 measurements from nine hair bundles, the averaged spectrum obtained with the beams directed at the bundles' opposite edges displays a high coherence and negligible phase lag. (d) The corresponding spectrum for 17 control measurements from the same hair bundles is essentially identical to the foregoing.


Isabelle Tritsch

Damien Arvor

Transition in environmental governance in the Brazilian Amazon: emergence of a new pattern of socio-economic development and deforestation

Keywords:  Brazilian Amazon,  Deforestation,  Socio-economic development,  Environmental Kuznets curve,  Boom-bust cycles,  Environmental governance

come

Transition in environmental governance in the Brazilian Amazon: emergence of a new pattern of socio-economic development and deforestation

Introduction

Socio-economic development across the Brazilian Amazon is a controversial research topic. In the late 2000s, seminal studies evidenced a boom-and-bust development pattern (Rodrigues et al., 2009, Celentano and Veríssimo, 2007and Celentano et al., 2012). That is, timber extraction and the conversion of forests into cropland and pasture generate a boom in incomes and jobs in the first years of land occupation, which is then followed by a collapse as forest resources and soil fertility are depleted (Sears et al., 2007). This scenario recalls the historical pattern of economic development in the Amazon when the cycles of extraction of forest products used to follow a boom-and-bust pattern, characterized either by a rapid rise and decline in market prices or by the depletion of resource stocks. Associated with high deforestation rates over the past four decades, the boom-and-bust pattern may be considered as a lose-lose scenario from a long term perspective since it generates high environmental costs and limited socio-economic benefits (Weinhold et al., 2015).

Yet, the last decade has been marked by a dramatic decrease in deforestation rates in the Brazilian Amazon (Nepstad et al., 2014 andArima et al., 2014) and a significant increase in the Human Development Index (HDI) (Caviglia-Harris et al., 2016). As a consequence, important recent studies reviewed the originally widely accepted boom-and-bust development hypothesis. Weinhold et al. (2015) evidenced that pre-and post-frontier municipalities in 2000 have enjoyed an equal increase in their Human Development Index (HDI) across the Amazon during the last decade. Caviglia-Harris et al. (2016) asserted that socio-economic welfare has become decoupled from environmental factors and is converging to rising national averages.

While these studies provide evidence that deforestation has not been followed by a socioeconomic decline and thus reject the boom-and-bust hypothesis in the Brazilian Amazon, they provide little insight into the current scenario of socio-economic development and deforestation across the Amazon. In this paper, we suggest that the increased socio-economic development associated with a decrease in deforestation activity emphasizes profound changes on the land-use frontier and attests to the emergence of an environmental Kuznets curve (EKC). The EKC hypothesis predicts that environmental degradation may have an inverted U-shaped relationship with development: environmental degradation goes along with development until primary needs are met; then a turning point is reached when concerns for the environment increase and environmental degradation decreases (Dinda, 2004 andPfaff andWalker, 2010).

To validate this assumption, we conducted the first sub-municipal analysis of socio-economic development and deforestation in the Brazilian Amazon with the objective of providing evidence for the transition from a boom-and-bust to an EKC pattern in the Amazon. First, we confirmed the reversal of the boom-and-bust development pattern using different socioeconomic data than Weinhold et al. (2015) and Caviglia-Harris et al. (2016). Second, the fine analysis of the relationship between socio-economic and deforestation variables produced evidence for the emergence of an EKC. Finally, we discussed the policies implications of such evolution of the deforestation and socio-economic development pattern, especially with regard to the recent advancements in environmental governance in Brazil.

Materials and methods

Data processing

We crossed socio-economic data from full-population censuses in 2000 and 2010 provided by the Brazilian Institute of Geography and Statistics at census sector scale (IBGE, 2010) with the PRODES deforestation maps provided by the Brazilian National Institute for Space Research (INPE) (INPE, 2014). As IBGE raw data are produced for 37,295 census sectors covering the entire Amazon, whereas there are only 775 Amazonian municipalities, the census sector data presents a finer spatial scale than the municipal data traditionally used in socio-economic studies (e.g. Rodrigues et al., 2009, Celentano et al., 2012and Weinhold et al., 2015).

Both datasets were projected on a 10x10 km regular grid for two reasons (Tritsch and Le Tourneau, 2016). First, the number of census sectors in the Brazilian Amazon grew rapidly from 11,850 to 37,295 sectors during the study period, thus limiting the relevance of an inter-annual comparison at sector level. Second, while deforestation decreased dramatically in the 2000s, we considered the original sector level of the census was not adequate to capture the spatial variability of deforestation across the Amazon, especially in rural areas where census sectors can be very large. The cell's area (100 km 2 ) was defined to round down the average area of a census sector as observed in 2010 (137 km 2 ).

For each cell in the grid (n = 51,642 cells), we first retrieved the areas of forest, non forest (i.e. mainly Cerrado areas), deforestation (with the corresponding year), water, and cloud from PRODES data. We then discarded cells with large unobserved areas, in other words, a cell was only analyzed if the sum of areas of forest, deforested land and water accounted for more than 70% of the cell's area. Additionally, it is worth mentioning that urban areas were kept in the analysis although they may induce some artifacts due to their high population densities and incomes associated to low deforestation activity. We felt that the bias caused by these urban areas is limited as we applied the same methods on both datasets (2000 and 2010). Overall, discarding urban areas would remove a large part of the Amazonian population and wealth, thus limiting the interest of the study.

The final grid thus contains 30,693 cells for which we computed two deforestation indices also used by Rodrigues et al. (2009):

•Deforestation extent is the cumulative proportion of deforestation in a cell in 2000 and 2010;

•Deforestation activity is the proportion of land area in a cell that has been cleared during the preceding three years, i.e. 1998-2000 and 2008-2010 time periods.

In addition, we computed different measures of socio-economic development by referring to the standard of living (income per household in Brazilian Real, R$), literacy (proportion of literate heads of household) and access to basic services such as sanitation (proportion of households with toilets). To do this, we proportionally shared out the socio-economic data from each sector across all underlying corresponding cells. As an example, a sector of 1000 inhabitants of which 25% of its area covers a cell A and 75% covers a cell B will attribute 250 inhabitants to cell A and 750 inhabitants to cell B. We did not use the HDI as it is only calculated at the municipal scale but not at the census scale. Finally, to avoid any artifact in the socio-economic data, all cells crossing a census sector with No data value were deleted so that the final database contains n = 24,068 cells in 2000 and n = 23,123 cells in 2010.

Boom-and-bust analysis

To ensure continuity with the study of Rodrigues et al. (2009) who evidenced the boom-andbust development pattern in 2000, we classified the cells in the same seven frontier classes (A to G) based on both the extent of deforestation and deforestation activity (Fig. 1). The classes range from pre-frontier classes (A, B) characterized by a limited area of deforestation and low deforestation activity, through active frontier classes (C, D, E) with increasing area of deforestation and high deforestation activity, up to post-frontier classes (F, G) where the extent of deforestation is high but deforestation activity is low. These seven classes represent the different stages of the process of frontier expansion under which wildlands are converted into highly anthropized areas, as conceptualized by DeFries et al. (2004) andFoley (2005). The stabilized cells with a moderate extent of deforestation and low deforestation activity remain unclassified in this conceptualization of frontier expansion. To test the existence of a boom-and-bust development pattern, we plotted the socioeconomic development variables against the frontier classes in 2000 and 2010 and evaluated the statistical differences among the classes using the Kruskal-Wallis test and Tukey's honestly significant difference test. The first test verifies whether samples originate from the same distribution while the second is used in post-hoc analysis to test if mean values of two samples are significantly different.

Environmental Kuznets curve analysis

While the boom-and-bust hypothesis analyses a pattern of socio-economic development depending on deforestation, the EKC explores how socio-economic development acts on deforestation. Its application to tropical deforestation has long been debated and appears to be somewhat controversial (Koop andTole, 1999 andChoumert et al., 2013). There is a disagreement between researchers who consider the EKC relevant and present it as one of the hypothesis explaining the forest transition process (Barbier et al., 2010, Mather et al., 1999, Rudel et al., 2005and Culas, 2012) and others who dismiss the EKC (Stern, 2004). In this regard, the lack of consideration for institutional factors while they play an important role in the implementation of environmental policies and, consequently in the relationship between environmental quality and socio-economic development, has especially been emphasized as a major limitation of EKC analysis (Bhattarai and Hammig, 2001, Bhattarai and Hammig, 2004and Culas, 2007).

From a methodological point-of-view, most critics raised several empirical shortcomings due to the choices made by authors about the statistical properties of the data used, the econometric strategy, the measure of deforestation, the geographical area and the presence of control variables (Stern, 2004 andChoumert et al., 2013). For example, while panel data should be preferred, the EKC is usually analyzed in cross-sectional analysis that fails to account for the wide diversity of physical and social characteristics across countries (Koop and Tole, 1999). In the present study, we considered the Brazilian Amazon cross-sectional data appropriate to analyze the EKC relationship between deforestation and socio-economic development because we compared changes that occurred between two periods in a regional area subject to the same public policies.

Additionally, deforestation is sometimes considered as irrelevant to monitor a decline in environmental degradation since it is usually seen as an irreversible process, as in the PRODES data where forested areas are under continuous degradation since forest regeneration is not taking into account. However, deforestation still represents the main threat to the environment in the Amazon and the major source of greenhouse gas emissions (Baccini et al., 2012). This is why we considered deforestation activity as a relevant indicator of environmental degradation.

In view of these concerns, it is worth noting that the present study is more engaged on a general argument about the evolution of the relationship between deforestation and socio-economic development in the prism of environmental governance than in a detailed discussion of the EKC theory in an empirical approach.

Concretely, we statistically tested the hypothesis of the emergence of an EKC in the Brazilian Amazon by measuring the relationship between deforestation activity and income per household based on a quadratic model (Eq. ( 1)) where DEF is deforestation activity and INC is income per household. Koop and Tole, 1999and Choumert et al., 2013. As suggested by Choumert et al. (2013), we considered that an EKC relationship exists if the coefficient is positive for income (β 1 > 0) and negative for the squared income (β 2 < 0). equation( 1)

DEF=β 0 +β 1 INC+β 2 INC 2 +ϵDEF=β0+β1INC+β2INC2+ϵ
We then attempted to quantify the turning point of the EKC, i.e. the inflection point at which environmental degradation starts declining (Koop andTole, 1999 andDinda, 2004). We thus focused our analysis on the identification of (i) an income threshold above which socioeconomic growth does not appear anymore to be a driver of deforestation and (ii) a deforestation threshold above which new clearings do not appear to be a vehicle for economic growth.

In this regard, the frontier classification proposed by Rodrigues et al. ( 2009) is not appropriate since it is not inclusive. Indeed, cells with a moderate extent of deforestation and low deforestation activity remain unclassified (white cells in Fig. 1). However they are expected to have increased in importance in the 2000s due to the decline of deforestation and thus deserve to be monitored with special care to identify a possible change in the environmental and socio-economic development pattern. For this reason, we chose an inclusive approach including all the cells in the database.

To identify the income threshold, we first sorted all cells according to income per household and grouped them by percentile. We then plotted the deforestation activity (in %) for each group of cells and computed a moving average in order to outline the trends. To ensure the best possible comparison between the 2000 and 2010 periods, we calculated the income per household relative to the Brazilian minimum wage (i.e. 151 R$ in 2000 and 510 R$ in 2010) (Salario minimo, 2016).

Finally, we defined a deforestation extent threshold using the ratio of the income per household in inactive cells (deforestation activity ⩽ 0.5%) to active and very active cells (deforestation activity > 0.5%) for different classes of deforestation extent. With this ratio, we aimed to identify a deforestation extent threshold above which the income per household in inactive areas becomes greater than in areas of active to very active deforestation. We focused the analysis on areas with deforestation extent values ranging from 10 to 90% since we considered that inactive cells are over-represented beyond these thresholds. To define classes in that range, we sorted the deforestation extent values for inactive cells (which are less represented in the database) and grouped them by percentile so that each class is represented by a fix number of at least N inactive cells and a variable number of K active and very active cells (K being usually greater than N). We then calculated the ratio between the median income per household in inactive cells and active + very active cells and outlined the trends with a moving average. Additionally, we also computed the ratio between the median income per household in inactive cells with the median income of the N richest and N poorest active cells (in terms of income per household) in order to (i) limit any bias related to over-representation of a class (in cases where K >> N) and (ii) define the full range of ratio values for each class of deforestation extent and thus provide a confidence interval to the results.

Results

The stabilization of the frontier and the end of the boom-and-bust development pattern

We first mapped the frontier classes (A-G) defined in Fig. 1 according to deforestation activity and deforestation extent (Fig. 2). These maps illustrate the stabilization of the frontier between 2000 and 2010. The active frontier areas (classes C, D and E) decreased dramatically from 4310 to 1268 cells (i.e. a 70% decrease). In 2010, most of the active cells were located in Pará state along the Cuiabá-Santarém (BR-163) and Belém-Brasília roads. Other smaller active frontiers are located to the east of Rondônia (along the BR-364 road), in Roraima and Mato Grosso states. The decrease in active frontier areas corresponds to an increase in post-frontier areas (from 1425 to 3010 cells for F and G classes) and stabilized areas (from 3530 to 7265 unclassified cells). Actually, most of the active frontier areas of the "arc of deforestation" in 2000 became stabilized or post-frontier areas in 2010. 2009) from a cross sectional perspective (Fig. 3). Although all socio-economic measures increased significantly at each frontier stage between the two dates, the development pattern changed dramatically. In 2000, a boom-and-bust trend can be observed for all variables. The post-frontier class (G) presents a lower level of socio-economic development than the active frontier classes (C, D, E) and a similar level to that of the B pre-frontier class. This was statistically confirmed by the Tukey's honestly significant test and thus confirms the results obtained by Rodrigues et al. ( 2009) at municipal level, as it also validates our approach based on a regular grid and census sector data. Conversely, in 2010, the post-frontier areas (F, G) had better levels of socio-economic development than the pre-frontier (A, B) and active frontier (C, D, E) areas, indicating that the last decade was marked by the end of the boom-and-bust socio-economic development pattern in the Brazilian Amazon. The results we obtained with socio-economic data at census sector level thus confirm the analysis of Weinhold et al. (2015) and Caviglia-Harris et al. ( 2016) at municipal level. Nonetheless, while Tukey's honestly significant test logically does not evidence any boom-and-bust pattern (G differs significantly from classes A and B), neither does it confirm a boom pattern, since class G does not significantly differ from class C, for example.

These results question the reasons for the reversal of the boom-and-bust development pattern. Actually, Weinhold et al. (2015) recently suggested that the bust observed in 2000 could be due to a spatial bias. Our maps of the frontier stages in 2000 and 2010 (Fig. 2) tend to support this hypothesis. Indeed, 44% of post-frontier cells in 2000 were spatially clustered in the state of Maranhão, which had a significantly lower level of development than other states in the Amazon and thus pulled the average socio-economic measures of post-frontier areas downwards. In contrast, ten years later, post-frontier areas expanded to other states, mainly Rondônia (11% of total G cells), Mato Grosso (22%) and Pará (30%) and better represented the spatial variability of socio-economic conditions across the entire arc of deforestation. However, it also increased the within-class variance and decreased the between-class separability, explaining why the Tukey's test was not conclusive for 2010. In this regard, the end of the boom-and-bust development pattern observed in the cross sectional analysis may appear to be the result of a "business as usual" expansion of the deforestation frontier.

Emergence of an environmental Kuznets curve in the Brazilian Amazon

A priori, a scenario with a higher level of socio-economic development in post-frontier areas (highly deforested cells) may encourage new clearings in the pre-and active-frontier areas and thus result in a deforestation boom. Nonetheless, the last decade has been characterized by an unprecedented decline in deforestation (Nepstad et al., 2009) suggesting that enhanced socio-economic development may actually be related to improved environmental preservation. Such a scenario has long been theorized by the environmental Kuznets curve (EKC) hypothesis, which states that environmental degradation increases in the early stages of socio-economic development until primary needs are met and decreases in later stages as the economy develops and create wealth for populations (Dinda, 2004 andPfaff andWalker, 2010).

We measured the relationship between deforestation activity and income with Eq. ( 1). The results confirmed the hypothesis of a significant EKC relationship between income and deforestation (Table 1). Actually, we found an EKC for both 2000 and 2010, indicating that the transition to an inverted U-shaped relationship between deforestation and socioeconomic development was already underway at the end of the 1990s, i.e. before the deforestation decline observed from the mid-2000s. Significance at the 0.1% level. We considered that an EKC relationship exists if the coefficient is positive for income (β 1 > 0) and negative for the squared income (β 2 < 0) Choumert et al. (2013).

The emergence of the EKC relationship in the Brazilian Amazon implies the existence of a turning point above which environmental degradation starts declining. Koop andTole, 1999 andDinda, 2004. In this context, we attempted to identify thresholds in both income per household and extent of deforestation.

Income threshold above which deforestation activity starts declining

Fig. 4 depicts the deforestation activity as a function of income, and hence the EKC. It emphasizes a positive relationship between deforestation and income in low income areas. In the case of high incomes, the relationship is stable in 2000 and negative in 2010. For 2000, the curve does not illustrate the EKC hypothesis but the plateau explains why we statistically identified an EKC trend in 2000 (Table 1). In 2010, the inverted U-shaped curve is typical of an EKC and illustrates a decoupling between deforestation and socio-economic development in the Brazilian Amazon as also expressed by Caviglia-Harris et al. (2016). Concerning the income threshold, in 2000, our results (Fig. 4) indicate an inflection point over an income per household equal to 2.5 times the Brazilian minimum wage, above which the relationship between income and deforestation reaches a plateau at high levels of deforestation activity. In 2010, the turning point is observed around one minimum wage per household. Above this income value, deforestation activity decreased significantly.

These results raise important issues about the relative responsibility of low and high income populations in explaining deforestation. Actually, whereas 85.3% of the total deforested area in the Amazon in the 1998-2000 period was carried out in cells where the mean income per household was higher than one minimum wage, this proportion fell to 48.9% in the period 2008-2010. The growing importance of low income populations in total deforestation is first explained by the rapid increase (from 33.9% to 56.7% between 2000 and 2010) in the number of cells with low income values (< one minimum wage) due to the fact that the minimum wage evolved faster than inflation in the 2000s (Cornia, 2014). However, the increase in average deforestation activity (from 0.61% to 0.85% during the same period) in low income cells should not be overlooked, since it is evidence of profound changes in the drivers and actors of deforestation in the Brazilian Amazon, as also evidenced by Godar et al. (2014).

Deforestation extent threshold above which incomes in inactive areas become higher than in areas subjected to active deforestation

To define a threshold of deforestation extent, we analyzed the ratio between the median income in inactive cells (deforestation activity ⩽ 0.5%) and active or very active cells (deforestation activity > 0.5%) for different ranges of deforestation extent ( Fig. 5). In 2000, low values (≃1) indicated no significant difference in income per household in areas undergoing active deforestation when compared with inactive ones, independently of deforestation extent. In contrast, in 2010, high ratios (>1) appeared for every range of deforestation extent so that the incomes per household were always higher in inactive areas than in areas undergoing active deforestation. So we cannot identify a deforestation extent threshold above which incomes in inactive areas become higher than in active areas. This assertion is even true when the ratio is computed comparing the income of all inactive cells with the richest active and very active cells only.

This result is very important as it puts an end to the assumption that active deforestation is necessary to ensure socio-economic development in the Brazilian Amazon. Actually, it also emphasizes the importance of active deforestation as an indicator of a precarious economic situation what corroborates our previous conclusions.

Discussion: emergence of the EKC as a result of a transition in environmental governance

The emergence of the EKC inverted U-shaped relationship between deforestation and socioeconomic development in the Brazilian Amazon is the result of a transition in environmental governance that occurred over the last decade to ensure a move toward land use sustainability (Culas, 2007 andGalford et al., 2013). Ambitious and effective policies at national, state and local levels to (i) contain deforestation (e.g. the Soy and Beef Moratorium or the Action Plan for Prevention and Control of the Legal Amazon Deforestation, PPCDAm) (Rudorff et al., 2011, Gibbs et al., 2015and Le Tourneau, 2015) and (ii) support socioeconomic development (e.g. different nationwide social policies such as the Bolsa Familia, Fome zero, Luz para todos and rural retirement programs ( Fenwick, 2009) have shaped a new environmental and socio-economic development pattern in the Amazon.

Here we discuss the different dimensions of this transition and policy implications that deserve to be put into perspective with regard to the emergence of an EKC for the specific case of deforestation in the Brazilian Amazon.

Increased investments in environmental preservation

The EKC is linked to effective policies that imply sufficient direct investment in environmental preservation (Culas, 2007 andDinda, 2004). In the case of deforestation in the Brazilian Amazon, efforts have primarily been oriented toward the reinforcement of command-and-control policies. These efforts required the investment of considerable capital stock, which was made available after the expansion of the commodity-oriented agricultural model. The rapid economic growth in Brazil since the 1990s made it possible to bank ambitious programs to ensure secure property rights and private property registration, to implement an efficient remote sensing-based deforestation monitoring system, to establish restrictions on access to credit and to support the expansion of a network of protected areas (Nepstad et al., 2014). It also enabled the introduction of environmental taxes such as the Ecological Tax over Merchandise and Services Circulation (ICMS-Ecológico, Imposto sobre Circulação de Mercadorias e Serviços), which can be conceptualized as a system of compensation for municipalities where land use is restricted in specific areas for environmental reasons. In this regard, rents resulting from past deforestation were reinvested in physical, human and natural capital so that forest resources were replaced by these other inputs to sustain economic growth ( Caviglia-Harris et al., 2016).

Nonetheless, environmental preservation efforts to date were mainly directed towards reducing deforestation. One should keep in mind that despite the spectacular decrease in deforestation, others forms of environmental degradation still persist in the Brazilian Amazon. In this regard, we suggest that particular attention should be paid to the forest degradation process in future EKC studies, because of its critical magnitude in the Brazilian Amazon (Souza et al., 2013, Aragão and Shimabukuro, 2010, Chaplin-Kramer et al., 2015and Bustamante et al., 2016). Similarly, forest regeneration should also be taken into account since it partially counteracts the deforestation effect, especially with regards to greenhouse gas emissions. Furthermore, forest regeneration can mark the beginning of a forest transition dynamic (Rudel et al., 2010, Rudel et al., 2005and Barbier et al., 2010) which may represents the next path towards environmental preservation after the emergence of the EKC (Pfaff andWalker, 2010 andCulas, 2012).

Emergence of market-oriented forms of regulation

An EKC also appears when command-and-control policies are associated with marketoriented forms of regulation (Dinda, 2004). The implementation of the Soy and Beef Moratorium through which traders agreed not to purchase soy and cattle from newly deforested lands in the Brazilian Amazon (Rudorff et al., 2011, Nepstad et al., 2014and Gibbs et al., 2015) is a concrete example of the way civil society managed to establish market-oriented policies to put pressure on an agro-industrial sector to satisfy society's increased consideration of the environment.

A way to encourage new market-oriented forms of regulation consists in assigning an economic value to natural resources, which can then foster the emergence of the EKC (Dinda, 2004). In this sense, the initiatives from REDD (Reducing Emissions from Deforestation and forest Degradation) could provide financial incentives to avoid deforestation and so flatten the inverted U-shaped curve of the EKC (Culas, 2012).

Different initiatives of payments for ecosystem services (PES) have already been implemented in the Brazilian Amazon, for example the Bolsa-Floresta program in humanoccupied protected areas of the State of Amazonas and the REDD+ pilot program PAS (Projeto Assentamentos Sustentaveis na Amazonia) in the Trans-Amazonian Highway. A wider implementation of such initiatives should be encouraged in order to mix "carrot and stick" policies to promote forest conservation ( Börner et al., 2014).

Emergence of an intensive agricultural model

In neoclassical growth theory, long-term growth rates depend on technical progress (Caviglia-Harris et al., 2016). This may combine with environmental preservation and the emergence of the EKC if investments are made to promote technological progress and replace obsolete technologies by upgraded new and cleaner ones (Dinda, 2004). This is especially true for large-scale agriculture in the Brazilian Amazon that underwent a rapid shift towards the adoption of intensive practices. In the state of Mato Grosso, the generalization of double-cropping systems is a major driver of the decoupling of deforestation and crop production (Macedo et al., 2012, Arvor et al., 2012and Arvor et al., 2013). This is because it became more profitable for producers to invest in new technologies for use in already opened areas than to finance new forest clearings. This situation emerged for three reasons: (i) efficient command-and-control and market-oriented policies discouraged producers from investing their capital in the acquisition of new areas to be cleared, (ii) the economic situation marked by very high oil prices at the end of the 2000s did not stimulate crop expansion (Richards et al., 2012) and (iii) the scarcity of high quality remaining agricultural land available for agricultural expansion, especially at the southern Amazon's agricultural frontier (Spera et al., 2014).

However, although the intensification process may have reduced pressure on forests, it is also connected with social and environmental degradation, linked to increased inequality in land ownership (Lapola et al., 2014) and greenhouse gas emissions, soil degradation and water pollution. On the one hand, in relation to the environmental aspects of agriculture, the recent launch of the ABC plan ("Plano para uma Agricultura de Baixo Carbono") demonstrates a willingness to ensure a transition toward a more environmental friendly agricultural model. It has the following objectives: restoration of degraded pastures, promotion of integrated crop-pasture-forest systems, generalization of no-tillage practices, improvement of biological nitrogen fixation, increase in forest plantation, recycling of animal waste and adaptation to climate change. But by now, how this ambitious program will effectively be implemented remains a challenging question ( Galford et al., 2013). On the other hand, in relation to the social aspects of agriculture, the policies to resolve land tenure problems and to support smallholder agriculture -yet responsible for the major part of the food consumed in Brazil -are still too weak. They should be reinforced if Brazil wants to go ahead towards a social and environmental friendly agricultural model. For example, more agro-ecological programs promoting alternative ways of sustainable production for smallholders, such as agroforestry systems, should be supported (Tremblay et al., 2014).

Forthcoming challenges for environmental governance

The current context of political and economic crisis could weaken the Brazilian institutional and financial capacities to ensure environmental preservation in the Amazon. On the one hand, recent statistics provided by INPE already indicate that deforestation rates get in a plateau with small variations up and down which could be exacerbated by the political instability caused by Presidential impeachment process (Rodrigues-Filho et al., 2015) and the revision of the forest code (Soares-Filho et al., 2014 andVerburg et al., 2014). On the other hand, current very low oil prices and high exchange rates between US$ and R$ could encourage agricultural expansion by reducing the costs for forest clearing and crop production. Moreover, maintaining and strengthening the costly command-and-control environmental policies may become challenging in an unfavorable economic context.

In this regard, it is worth mentioning that, in their seminal paper about EKC, Grossman and Krueger (1995) estimated that the EKC turning point where environmental degradation starts declining usually comes when a country reaches a per capita GDP of US$ 8000. After a rapid increase of the GDP in the 2000s, Brazil has reached this threshold in 2008 (TWB Group, 2016), i.e. approximately (but maybe coincidentally) at the same time period we identified the emergence of the EKC. As a consequence, considering how the more recent decline of the Brazilian GDP per capita (from US$13,000 in 2013 to US$8540 in 2015) may affect the transition in environmental governance is a worrying issue.

Additionally, even though the structure of production of the agricultural model is changing rapidly, it is not being accompanied by equivalent changes in the structure of consumption. In this case, "EKC may actually record displacement of dirty industries from developed economies to less developed economies" ( Dinda, 2004). Indeed, although Brazilian efforts to contain deforestation in the Amazon have produced promising results, these were not achieved at the expense of the growth of the Brazilian agricultural sector. This sector continues to expand in other Brazilian regions: the soybean agricultural frontier has now reached the Cerrado areas of MATOPIBA (i.e. Maranhão, Tocantins, Piaui, Bahia states) (Eloy et al., 2015, Macedo et al., 2012and Richards et al., 2014) which is targeted by investors from Brazil and abroad ( Ofstehage, 2015 andEMBRAPA, 2016). So particular attention should be paid to deforestation of the Cerrado biome when defining future environmental policies. Recent studies also evoked the emergence of a new soybean frontier in Southern Africa, where Brazil is reinforcing its economic presence ( Gasparri et al., 2015, Clements and Fernandes, 2013, Seibert, 2011, Oliveira, 2015and Shankland and Gonalves, 2016).

Environmental governance fosters the emergence of the EKC

In the Brazilian Amazon, despite the recent political crisis, the governance structures have improved and become much more solid than a few decades ago. As we have seen, it has significantly affected the Brazilian Amazon deforestation process and the path toward land use sustainability while the social policies and cash transfer programs have enabled several millions of Brazilians to leave poverty behind (Barrientos, 2013 andFenwick, 2009).

For these reasons, besides the traditional mechanisms of causality normally claimed in the EKC literature such as the transformation of the structure of the economy (e.g. agricultural intensification and the substitution of forest products by alternative sources (Cropper and Griffiths, 1994)) or the greater emphasis that the society places on environmental value of forest resources (biodiversity, wildlife conservation, aesthetic value, and carbon sequestration, all yet still little merchantable) (Bhattarai and Hammig, 2001), the Brazilian Amazon case emphasizes the special attention that should be paid to the environmental governance efforts, especially through the reinforcement of institutions, to explain the EKC for deforestation.

In fact, institutional factors and macroeconomic policies can reduce the amplitude of the EKC and consequently the environmental price of economic growth (Culas, 2007, Bhattarai and Hammig, 2001and Bhattarai and Hammig, 2004). Factors such as improved literacy, secure property rights, better enforcement of law and contracts, and citizen participation in decision-making can weaken the income effect on the EKC hypothesis and so flatten the EKC curve. Thus the society can avoid potential environmental catastrophes while achieving sustainable growth (Torras and Boyce, 1998, Panayotou, 1997, Bhattarai and Hammig, 2001and Bhattarai and Hammig, 2004). So, the EKC literature for tropical deforestation should definitely pay more attention to the governance and institutions which can directly foster the emergence and flattening of the EKC.

Conclusion

The historical Amazonian pattern of boom-and-bust development was reversed between 2000 and 2010. The depletion of the Amazonian forest is no longer linked with a socioeconomic collapse as predicted by the boom-and-bust scenario. In all cases, post-frontier regions present better socio-economic indicators than pre-frontier and frontier regions. This sounds consistent as today the economic activities of the post-frontier regions are dominated by intensive agricultural production of commodities including soybean. Yet, the soy cultivation is associated with increased household incomes but also increased inequality among producers (Weinhold et al., 2013 andLapola et al., 2014). This modern economy is fully integrated, with national and international investments, markets and improvement programs, and has enabled an efficient transition to intensive agriculture. Although these post-frontier areas remain vulnerable to international (commodity prices) and national (exchange rates) economic conditions, they now have a sufficiently strong economic base to avoid a future economic collapse. So the re-emergence of a boom-and-bust development pattern is very unlikely.

Our data shows profound changes in the Brazilian Amazon since we evidenced the emergence of an environmental Kuznets curve as a new environmental and socio-economic development pattern in the Amazon. It bears witness to a rupture in the traditional frontier expansion cycle related to increased consideration for environmental preservation and implementation of several innovative governance measures. To date, regions subjected to active deforestation present lower socio-economic indicators than inactive (stabilized) regions, even in areas that still have a high forest cover. This is the result of the establishment of an effective environmental governance aimed at controlling deforestation and the expansion of large-scale commodity-oriented agriculture. The continuing deforestation despite environmental legislation today appears to be a sign of socioeconomic precariousness. This sounds consistent with the results from de Souza et al. (2013) who showed that areas where agriculture and livestock have low level of agrarian technology coincide with the areas of highest deforestation in the Amazon on the 2005-2009 period. So future social and environmental policies should concentrate more on areas where deforestation is still active, by supporting low income farmers in the improvement of their agrarian and economic situation, while achieving legal compliance (Coudel et al., 2012).

Finally, our results raise important conceptual issues about the relationship between socioeconomic development and the environment in the tropics. First, it questions if economic growth is a mandatory stage before environmental preservation. If so, one should carefully consider the environmental benefits of the effective social policies and cash transfer programs (Barrientos, 2013 andTritsch et al., 2015) led at federal level to enable several millions of Brazilians to leave poverty behind. Although improving socio-economic conditions led to a slight increase in deforestation activity by low income populations, it also helped them rapidly reach the turning point of the EKC. This point is of critical importance when considering the willingness of Brazil to export its environmental leadership (Ferreira et al., 2014) and its expertise in tropical agriculture to other countries that would not previously have had the necessary conditions to establish effective socio-economic programs.

The second issue refers to the role of environmental preservation as a source of economic development. To date, the efforts led by the Brazilian authorities to control deforestation have mainly been based on command-and-control punitive measures (Nepstad et al., 2014). The decoupling between deforestation and income is evidence of the capacity of farmers to rapidly adapt their economic strategies to the newly established rules. However, these strategies remain mainly oriented toward the production of raw commodities and the potential of environmental preservation as a source of income is still undervalued. It is thus necessary to support more voluntary market-oriented forms of regulations such as payments for environmental services (PES) to take advantage of the remarkable adaptability of local actors and thus achieve the ambitious objectives of environmental preservation in the Amazon.

Fig. 1 .

 1 Fig. 1. Definition of frontier classes based on the extent of deforestation and deforestation activity used to classify cells (inspired by Rodrigues et al., 2009).

Fig. 2 .

 2 Fig. 2. Maps of frontier classes in 2000 and 2010. Classes range from pre-frontier (A, B) to active frontier (C, D, E) and post-frontier (F, G) classes. Non forest areas are represented in dark grey.

Fig. 3 .

 3 Fig. 3. Variation in income per household, literacy and access to basic sanitation services in 2000 (in red) and 2010 (in blue) across the frontier classes. Dots indicate median values and bars indicate first and third quartiles. Dashed lines represent extreme values. All variables present significant variation across the frontier classes (Kruskal-Wallis: P< 0.0001); classes that do not have a letter (u, v, w, x, y, z) in common differ significantly (Tukey's honestly significant difference test: P< 0.05).

Fig. 4 .

 4 Fig. 4. Deforestation activity as a function of mean income per household in 2000 and 2010. In 2000, the curve illustrates a positive relationship between income and deforestation activity. In 2010, this relationship follows an inverted U-shaped, evidence of the emergence of the EKC: beyond a income threshold of one minimum wage per household, deforestation activity begins to decrease.

Fig. 5 .

 5 Fig. 5. Ratio between the median income in inactive cells (deforestation activity ≤ = 0.5%) and active + very active cells (deforestation activity > 0.5%) for different ranges of deforestation extent. High ratio values (>1) indicate that income per household in inactive cells is greater than in active + very active cells. Dashed lines represent the ratio between the median income per household in inactive cells with the median income of the n richest and n poorest active + very active cells. Lower diagrams indicate the number of inactive or active + very active cells for each class of deforestation extent. The minimum number of cells by class of deforestation extent is n = 14 and n = 33 for 2000 and 2010 respectively.

Table 1 .

 1 Coefficients of the quadratic regression model between deforestation activity and income for 2000 and 2010.

	2000	2010
	β1 0.985437*** 0.322695***
	β2 -0.029710*** -0.040279***
	***

Acknowledgements

The authors wish to thank the French National Agency for Research (ANR) which funded the DURAMAZ2 project (grant agreement ANR-11-BSH1-0003), the University Sorbonne-Nouvelle Paris 3 for Post-doctoral Fellowship and the European Union which funded the H2020-MSCA-RISE-2015 ODYSSEA project (Project Reference: 691053). They are also grateful to the two anonymous reviewers for their constructive comments, which helped to improve the manuscript.


PALAEOBOTANY

A tree without leaves Brigitte Meyer-Berthaud and Anne-Laure Decombeix

The puzzle presented by the famous stumps of Gilboa, New York, finds a solution in the discovery of two fossil specimens that allow the entire structure of these early trees to be reconstructed.

The Middle Devonian (397-385 million years ago) was a notable time for the evolution of early land plants: the diversification of reproductive strategies, the advent of leaf-precursors, and a tendency to increasing height all led to the rise of plants of modern appearance. One of the best locations for studying these processes is Gilboa, New York, which is internationally renowned for its wide range of terrestrial organisms from the late Middle Devonian. These organisms include a rich variety of arthropods, for example, but also large, enigmatic stumps that in life formed extensive stands and were fossilized where they grew.

Since the discovery of these Eospermatopteris stumps in the nineteenth century, questions about their affinities and what kind of trees they supported have exercised generations of palaeobotanists. Evidence presented by Stein et al. 1 on page 000 of this issue not only answers these questions but also provides a new glimpse of the requirements necessary to make a tree.

Reconstructing entire fossil plants is an important step in assessing the patterns of plant diversification through time, and the roles that plants played in past environments. This task is challenging because plants naturally shed parts of their body during their lifetime, and it is rarely achieved for structures such as trees that have a complex architecture and extended lifespan. However, the two exceptionally well-preserved specimens collected by Stein et al. 1 were sufficient to reconstruct the kind of tree that made the Gilboa forest (Fig. 1a).

The two specimens partly overlap in size and morphology. One consists of a slender trunk exceeding 6 m in length, exhibiting an enlarged Eospermatopteris-type base, and covered with branch scars at the top. Slender 'coalified' strands extending downwards from the bottom of the stump are interpreted as roots. The other specimen is the top part of a trunk terminated by a crown of short and erect branches, and with branch scars at the bottom.

Branches of the crown were divided digitately -that is, they produced several closely spaced branchlets flattened in a plane. The terminal appendages were three-dimensional and do not resemble leaves (organs with a flat blade of photosynthetic tissue). In the Devonian, this branching pattern characterizes the Pseudosporochnales, an extinct group traditionally considered to be closer to the ferns than to the seed plants and known to have included 3 meter tall organisms about 392 million years ago 2 . This group was successful and occurred worldwide during the Middle Devonian 3 .

One consequence of Stein and colleagues' discovery is that Archaeopteris, a close relative of seed plants that flourished in the Late Devonian (385-359 million years ago), is no longer the oldest known modern tree (Fig. 1b). The conifer-like reconstruction of this 'progymnosperm' appears in most botany textbooks and many of us are familiar with its woody stump measuring up to 1.5 m in diameter, which is suspected to have reached 40 m in height and was deeply anchored into the soil by an extensive root system [START_REF] Beck | Origin and Evolution of Gymnosperms[END_REF][START_REF] Scheckler | Palaeobiology II[END_REF] . Archaeopteris had large, perennial (long-lived) branches that were essential components of its architecture [START_REF] Meyer-Berthaud | [END_REF] . As it grew, Archaeopteris added more of these branches to its trunk, a process that contributed to its three-dimensional increase in size. Short-lived branches produced at the periphery were leafy.

The Gilboa tree differs from Archaeopteris in having a trunk of more moderate size, in lacking perennial branches, and in possessing a limited root system that apparently consisted of many roots of similar size. The short, disposable branches of the crown were shed when senescent and were continuously replaced by new branches at the top of the trunk. Unlike Archaeopteris, the root and branch systems in the Gilboa tree did not increase much in extent during growth. In this, the tree resembles the tree-ferns, and the cycads and palms with single trunks that occur today; but unlike these, it was unable to make planate leaves. Instead it seems that photosynthesis was carried out by the periodically shed branches of the crown and, more specifically, by their three-dimensional terminal appendages.

One benefit often assumed for taller plants is their enhanced ability to capture light. Ten years ago, Niklas 7 simulated the architecture of early land plants and tested their efficiency in performing several essential functions. The Gilboa tree fits closely with the morphology that optimizes two functions, mechanical stability and reproduction. But the reduced surface area of its crown was not optimal for light interception.

Two contrasting ways of making trees evolved during the Devonian (Figs 1a,b; Fig. 2). That represented by Archaeopteris, and by most extant trees of temperate and tropical areas, requires a complex machinery of tissues and organs to achieve growth in all spatial directions and build the larger body sizes recorded in the plant kingdom. The Gilboa tree represents an economical alternative where, beyond the necessary investment in spores to ensure reproduction, the products of photosynthesis were mainly devoted to vertical growth of the trunk. The new specimens from New York 1 show that the first giants in the history of the land plants achieved the tree habit and significant biomass despite their inability to construct optimal photosynthetic structures, such as leaves or horizontal branches, and despite not building an extensive root system. Brigitte Meyer-Berthaud (CNRS) and Anne-Laure Decombeix (Université Montpellier 2) are in the Unité Mixte de Recherche Botanique et Bioinformatique de l'Architecture des Plantes (AMAP), CIRAD, 34398 Montpellier Cedex 5, France. e-mails: meyerberthaud@cirad.fr; anne-laure.decombeix@cirad.fr Gilboa tree is a member of the extinct group, Pseudosporochnales. Archaeopteris is a progymnosperm, a close relative of the seed plants [START_REF] Meyer-Berthaud | [END_REF]8 that is also extinct. Time scale is millions of years ago. Many representatives of ferns and seed plants exist today, the latter being by far the main constituent of the world's current terrestrial flora.

Figure 1

 1 Figure 1 Two types of Devonian tree. a, The newly described Gilboa tree 1 , a member of the

Figure 2

 2 Figure 2 Trees in time. Two contrasting ways of making trees, evident in the fossils of the


D Paboeuf
email: david.paboeuf@institutoptique.fr

G Lucas-Leclin

P Georges

B Sumpf

G Erbert

C Varona

P Loiseau

G Aka

B Ferrand

900 nm Emission of a Nd:ASL Laser Pumped by an Extended-Cavity Tapered Laser Diode

We describe here the use of a 798-nm-stabilized high-brightness tapered laser diode to pump a Nd:ASL crystal for 900 nm laser operation. An output power of 150 mW is obtained.

Introduction

Neodymium-doped laser materials, operating on the 4 F 3/2  4 I 9/2 laser transition around 900 nm, have a great interest for blue laser generation by frequency doubling in a quadratic non-linear optical crystal. Efficient quasithree-level emission has been obtained in various laser materials, such as Nd:YAG (946 nm), Nd:YVO 4 (914 nm), Nd:GdVO 4 (912 nm) [START_REF] Fan | Continuous-wave operation of a room-temperature, diode-laser-pumped, 946-nm Nd:YAG laser[END_REF][START_REF] Zeller | Efficient, multiwatt, continuous-wave laser operation on the 4 F3/2-4 I9/2 transitions of Nd:YVO4 and Nd:YAG[END_REF][START_REF] Czeranowsky | Continuous wave diode pumped intracavity doubled Nd:GdVO4 laser with 840 mW output power at 456 nm[END_REF]. However, the blue wavelength obtained by frequency doubling of these lasers is not short enough for some applications.

The Nd-doped strontium-lanthanum aluminate crystal: Nd 0.05 Sr 0.7 La 0.25 Mg 0.3 Al 11.7 O 19 , called Nd:ASL, could be a solution since its 4 F 3/2  4 I 9/2 transition correspond to a laser line at 900 nm. Unfortunately, the absorption transitions of Nd:ASL are narrowband and located at 792 nm and 798 nm where no commercial high power laser diodes are available. Then, Nd:ASL laser operation at 900 nm has only been obtained under Ti:Sa pumping at 792 nm [START_REF] Varona | CW blue laser emission by second harmonic generation of 900 nm oscillation of Nd-doped strontium and lanthanum aluminate (ASL)[END_REF]. Moreover, the quasi-three-level operation of this laser requires a high-brightness pump source to exceed the transparency intensity all along the crystal. Thus we propose a novel external-cavity design based on a high-brightness tapered amplifier diode. This laser diode was wavelength stabilized at 798 nm, closer to the maximum-gain wavelength of the tapered amplifier, by use of a volume Bragg grating (VBG) in a simple and compact set-up.

We report here the design and the characteristics of our extended-cavity pump source and the use of this high-brightness and narrow laser source to pump a crystal of Nd:ASL for laser operation at 900 nm.

Description and Characterization of the pumping source

Tapered laser diode is a promising design for high-brightness emission in the 1 to 5 W power range. It consists in a single-mode ridge acting as a spatial filter and a tapered amplifier section [START_REF] Wenzel | High Brightness diodes lasers[END_REF]. The one we used had an emission centered around 800 nm and was designed and grown at Ferdinand Braun Institut für Höchsfrequenztechnick. The active region was composed of a tensile-strained GaAsP single quantum well embedded in a 3-µm thick Al 0.45 Ga 0.55 As waveguide and highly doped Al 0.7 Ga 0.3 As cladding layers [START_REF] Dittmar | High-Power 808-nm Tapered Diode Lasers With Nearly Diffraction-Limited Beam Quality of M 2 =1.9 at P=4.4 W[END_REF]. The index-guided straight ridge section is 2-mm-long and the gain-guided tapered section is characterized by a Volume Bragg Grating (VBG) tapered angle of 4° and a length of 2 mm. The front facet of the tapered laser has a reflectivity of 0.5 %, whereas the rear facet reflectivity was about 0.1%. A passivation coating has been added prior to the antireflection one for improved facet stability. We mounted the tapered amplifier in an extended cavity with a volume Bragg grating acting as a back mirror. The grating is characterized by a Bragg wavelength λ B = 798 nm, a reflectivity of 20% and a spectral selectivity of 0.2 nm. The emission from the ridge side is focused on the grating by a high-numerical-aperture aspheric lenses pair (Fig. 1). This configuration result in a lower sensitivity to misalignements compared to the collimated-on-the-grating standard one and also in a better control of the emitted wavelength [START_REF] Lucas-Leclin | Wavelength Stabilization of Extended-Cavity Tapered Lasers with Volume Bragg Gratings[END_REF].

Tapered amplifier R r <0,1% R t 0,5%  B = 798 nm   0.20 nm R  20% L ext  25 mm aspheric lenses pair L ridge  taper Volume Bragg Grating (VBG) Tapered amplifier R r <0,1% R t 0,5%  B = 798 nm   0.20 nm R  20% L ext  25 mm aspheric lenses pair L ridge  taper L ridge  taper
Without any feedback from the grating, no laser emission has been observed but only amplified spontaneous emission centered around 800 nm and covering a large band of spectrum. In the extended cavity, the laser emission is locked on the Bragg wavelength whatever the operating current or the temperature (Fig. 3) with a very low wavelength shift (< 200 pm). The side-mode suppression ratio is higher than 40 dB. The laser FWHM-linewidth remains lower than 80 pm (OSA-limited). The threshold of the laser diode was as low as 1 A and the slope efficiency reached 0.9W.A -1 . We obtained a maximum output power of 1.4 W for an operating current of 2.5 A (Fig. 2), with no evidence of roll-over. These results are very close to those obtained with a tapered laser based on the same layer design but with a high reflective coating on the back facet [START_REF] Dittmar | High-Power 808-nm Tapered Diode Lasers With Nearly Diffraction-Limited Beam Quality of M 2 =1.9 at P=4.4 W[END_REF], which proves that our extended cavity design doesn't limit the intrinsic performance of the tapered amplifier.

The output laser beam was collimated in the fast axis with an aspheric lens (f'=8 mm). The strong astigmatism of the tapered laser was easily corrected with a cylindrical lens. The focal length of the cylindrical lens (f'=300 mm) was chosen to circularize the output beam. We measured a beam quality parameter M 2 as good as 1.2 in both directions for an operating current of 2 A, which degrades to ~3 at higher operating current. The maximum brightness value is evaluated to 110 MW.cm -2 sr -1 .

Laser operation of Nd:ASL at 900 nm

The CW 900 nm laser emission was investigated by using an end-pumped plane-concave resonator with a Nd:ASL crystal grown by the Czochralski pulling technique. The crystal was mounted on a copper block and maintained at a temperature of approximately 14° C by a water-cooling device. The input mirror was deposited on the first face of the crystal (high transmission at the pump wavelength and 1050 nm, high reflection at 900 nm). The 100-mm-curvature concave output mirror had a high reflectivity at 900 nm and a high transmission at 1050 nm to prevent laser emission from the intense 4 F 3/2  4 I 11/2 4 level transition. For maximum absorption, the polarization of the pump beam was set perpendicular to the c-axis of the crystal by a half-wave plate. We also used an isolator in order to protect the tapered laser from parasitic back-reflections. The pump beam was focused inside the crystal by a lens. input mirror HR@900 nm HT@798 nm HT@ 1050 nm output mirror R=97% @900 nm HT@ 1050 nm R c =100 mm Extended cavity tapered laser diode

collimation lens f'=8 mm cylindrical lens f'=300 mm isolator f'=200 mm Nd:ASL crystal /2
f'=200 mm focusing lens f=50 mm input mirror HR@900 nm HT@798 nm HT@ 1050 nm output mirror R=97% @900 nm HT@ 1050 nm R c =100 mm Several output mirrors with different transmissions at 900 nm have been tested. The optimum pump waist diameter has also been investigated by changing the focal length of the focusing lens. The highest power has been obtained with a T=3% output mirror and a pump waist diameter of 20 µm. A maximum output power of 150 mW for a 1.1 W incident pump power (560 mW absorbed) has been obtained with a 3-mm-long crystal (Fig. 5). The laser threshold is observed at the incident power of 200 mW, corresponding to an absorbed pump power of 120 mW. This leads to an efficiency of 34% with the absorbed power. The laser emission is centered at 900.3 nm with a linewidth of 1 nm. With a 5-mm-long crystal, lower output powers have been obtained. The crystal being longer, the pump intensity at the end of the crystal is lower than transparency intensity, resulting in an increased reabsorption at the laser wavelength. The degradation of the pump beam quality at high powers enhanced this effect.

Under Ti:Sa pumping, an absorbed pump power of 560 mW permitted to reach a power as high as 200 mW with a 5-mm-long crystal [START_REF] Varona | CW blue laser emission by second harmonic generation of 900 nm oscillation of Nd-doped strontium and lanthanum aluminate (ASL)[END_REF]. Our performance is then lower. The main reason is the degradation of the pump beam quality for high operating currents. This fact is confirmed by the beam quality factor M 2 of the laser beam being 1.5 at maximum output power.

Conclusion

We have demonstrated what is, to our knowledge, the first diode-pumped Nd:ASL continuous-wave laser operating at 900 nm. This is a great step on the way to a compact design for Nd:ASL-based blue lasers. A highbrightness tapered laser diode has been stabilized at 798 nm using a volume Bragg grating in a very compact extended cavity. Furthermore, This laser source has a high brightness and a narrow line, which makes it fully suitable for the pumping of Nd:ASL. A power of 1.5W has been reached with this diode. We have used the tapered diode to pump a Nd:ASL crystal to obtain a maximum power of 150 mW at 900 nm. Experiments of intracavity doubling will now be performed with a non-linear optical crystal in order to obtain a blue laser emission at 450 nm.

Figure 1 :

 1 Figure 1 : Design of the extended-cavity tapered laser with a Bragg grating.

Figure 2 :Figure 3 :Figure 4

 234 Figure 2 : Output power vs operating current; operating temperature = 25° C

Acknowledgment: this work has been partially supported by the European Community under the www.BRIGHT.eu integrated project. (IP511722)