Yani Chen

Guy Royal

Emmanuel Flahaut

Saioa Cobo

Vincent Bouchiat

Laëtitia Marty

Nedjma Bendiab
email: nedjma.bendiab@neel.cnrs.fr

Light control of charge transfer and excitonic transitions in a carbon nanotube/porphyrin hybrid

Keywords: Nanotubes, Optoelectronics, Single electron tunneling, Raman enhancement, Porphyrins

Carbon nanotube-chromophore hybrids are promising building blocks in order to obtain a controlled electro-optical transduction effect at the single nano-object level.

In this work, we observe a strong spectral selectivity of the electronic and the phononic response of our chromophore-coated single nanotube transistor for which standard photo-gating cannot account. We investigate how light irradiation strongly modifies the coupling between molecules and nanotube within the hybrid by means of combined Raman diffusion and electron transport measurements. Moreover, we observe a nonconventional Raman enhancement effect when light irradiation is on the absorption range of the grafted molecule. Finally, we show how the dynamics of single electron

tunneling in the device at low temperature is strongly modified by molecular photoexcitation. Both effects will be discussed in terms of photo-induced excitons coupled to electronic levels.

Low dimensional sp 2 carbon nanostructures such as graphene and nanotubes have emerged as ideal platforms for molecular electronics enabling new functional devices such as ultrasensitive molecule detectors, molecular scale logics and quantum devices. 1 In particular, nanotube ambipolar behavior along with direct bandgap allows their use for optoelectronics. 2 However, single wall nanotubes (SWNTs) are sensitive to any non specific and slight fluctuation in their environment, which directly alters their opto-electronic properties. Grafting chromophores onto nanotubes is an hybrid route towards specific functions for nanoelectronics.

It is of great interest and challenging to reach the limit of hybrids at the single nanotube level. In this limit, the number of active molecules is limited by the 1D geometry and a single nano-object can be detected. [3][4][5][6][7][8][9][10] In the particular case of optically active hybrids, Zinc(II) metalloporphyrins coating a SWNT network field effect transistor (FET) device was proposed for light harvesting. 11 Recent applications of porphyrin dyes for dye-sensitized solar cells have shown high yield in light energy harvesting. 12 However, only few studies have demonstrated efficient photo-induced charge transfer in nanotubes/porphyrins hybrid systems by using electrochemical methods, 13 photoluminescence excitation experiments 14 and absorption spectroscopy. 15 These works highlight the importance of energy and/or charge transfers between molecules and nanotubes either in assembly of nanotubes or in isolated nanotubes in solution. Here we investigate how light excitation can be used to tune the signatures of the hybrids related to nanotube/chromophore coupling: the enhancement of the Raman signal from the so-called GERS effect 16,17 and the onset of single charge trapping with molecular traps. 18 These well-known effects should dramatically depend on light exposure in the case of chromophores, which has not been addressed yet.

To investigate the dependence of electronic and phononic response of a chromophorecoated single nanotube transistor under light irradiation, our approach consists in using com-plementary Raman spectroscopy and electron transport measurements on the same samples.

First, we will discuss how grafting chromophores on a single nanotube transistor induces a visible charge transfer in both phononic and electronic response. In a second part, we report on a strongly non conventional vibrational response under light irradiation of the hybrid at different wavelengths. Finally, we will address the possibility to control the dynamics of single charge trapping with light at low temperature.

The chromophore used here is a porphyrin moiety metallated with a Zinc(II) ion in its center named as Zinc(II)-meso-tetraphenylporphyrin (see Figure 1(a), TPPZn in the following).

Porphyrins provide an extremely versatile synthetic plateform for a variety of applications. 19 Their optical properties are very interesting for energy transfer with molecular control 14,20 and for potential applications in optoelectronics. 21 The absorption spectrum of TPPZn in toluene exhibits an intense Soret band at 422 nm and a main Q band at 549 nm (see Figure 1(a)). 22,23 This zinc-based molecule was demonstrated to provide photo-gating on nanowires and nanotubes 11,24 and furthermore presents the advantage of being reversibly charged by using light excitation in an easily accessible visible range. The Raman spectrum of TPPZn powder at 532 nm excitation line presents a huge luminescence which does not allow us to measure the Raman fingerprint of the molecule (not shown) whereas the one at 488 nm presents the two main molecular modes at 1356 cm -1 and 1547 cm -1 corresponding to the C-C bond vibration and to a combined modes of carbon-carbon vibration and carbon-azote vibration 25 (Figure 1(b)).

This study was conducted on 16 double wall carbon nanotube FETs (CNFETs) which exhibit similar behavior under grafting and light irradiation. First step consists in characterizing the double wall nanotube (DWNT) electronic nature by cross-correlating Raman spectra and gate transfer characteristics. On Figure 1(b), one Radial Breathing Like Mode (RBLM) and the G Raman modes of an hybrid DWNT transistor are presented. Since resonance conditions were not completely fulfilled for all FETs, we focus, in the following, on a typically resonant transistor for the sake of clarity in the observed effect. In the G band region, a main peak around 1589 cm -1 is observed along with a metallic-like Breit-Wigner-Fano (BWF) shoulder. The G band shape and the position of the RBLM are compatible with an inner semi-conducting tube and an outer metallic tube (see supplementary information for details). After acquiring the Raman spectra and I-V curves of the pristine device, a solution of TPPZn in tetrahydrofuran (THF) was drop-casted onto DWNT transistors which were then rinsed with THF and dried under nitrogen. AFM characterization (see Supplementary Information) shows that molecules tend to cluster onto the nanotube (cluster size of about 30 nm). At 532 nm, we observe the presence of the TPPZn fingerprint superimposed onto the nanotube one, whereas no peak was observed in the molecule powder at this wavelength. This quenching of TPPZn luminescence by nanotube at this wavelength allow us to detect the molecular Raman modes. It's also an indication of the effective coupling between these two moieties. 7,26,27 Moreover, after the deposition, the nanotubes modes are enhanced by a factor 4 to 7 in intensity and their frequency are downshifted by 3 cm -1 for the G mode (see Figure 1(b)). These signatures indicate a charge transfer between molecules and nanotubes after grafting. Furthermore, such intensity enhancement and luminescence quenching are a signature of chemical enhancement from charge transfer and/or dipolar effect between the nanotube and the molecules. 17,26 Regarding transistor operation at room temperature (see Supplementary Information), the hybrid CNFET exhibits a p-type field effect characteristics which is in agreement with the G band frequency downshift. Moreover, the nanotube hybrid transistor shows a relatively low conductance in the off state (1.3 nS), and an on-to-off ratio of 65, in agreement with previous reports of porphyrin coated SWNT FETs, which was explained as the result of the addition of charged scattering sites distributed randomly along the nanotube. 7 These features are typical of nanotube/molecular hybrids; we will focus in the following on the evolution of these electronic and phononic features under light exposure. This spectral selectivity is also observed on the phononic response. Actually, we record Raman spectra of the devices under white light illumination for both 488 nm and 532 nm Raman laser excitations (see Figure 3). At 532 nm excitation line, only a global enhancement is observed (Figure 2a) whereas at 488nm, a non conventional Raman behavior is observed.

In fact, at 532 nm, a slight reversible frequency upshift of the G band components is measured from the dark to the light on state (see supplementary information for the fitting details), allowing us to conclude that only a small charge transfer occurs. Another general feature that appears under light illumination is the broadening of the G -peak and an increase of the background. These effects are compatible with a weak charge transfer and a partial luminescence from molecules respectively. At 488 nm, the enhancement of the G modes is far different from the 532 nm case. The G mode region exhibits dramatic changes: under light exposure only, two large peaks turn out to be visible, one of them matching the dark state G mode with an upshift of 1 cm -1 and an intensity twice higher, whereas the most intense one at 1587 cm -1 was barely visible in the dark state. When the light is turned off, the new observed intense peak vanishes, while the other mode remains, still shifted by 1 cm -1 and reduced in intensity. Different explanations can be proposed for such a photo-induced signature. The first one is that the nanotube is not fully covered with the molecules, thus some parts of it could sense the optical gating from the molecules whereas some remain unchanged. This would lead to a spectrum featuring superimposed peaks from the two portions, coupled and not to the molecules. In such case we would expect to observe superimposed features also in the dark state which is not the case. Moreover light excitation brings the molecules in a new redox state which is stable for a few hours at room temperature. Such a state can transfer the photo-generated charges to the nanotube as visible by the shift of the G mode. This shift is compatible with surface charges on the nanotube induced by the molecules but it cannot account for the rise of a new peak when light is on.

We rather consider that under light irradiation, the Soret and Q states of the porphyrin are populated so that energy is transferred from these molecular states to the nanotube excitonic state as already observed in SWNT photoluminescence experiments. 28 Excitonic states can have a major influence on the Raman intensity: if the Raman diffusion process involves a transition between a vibronic state of the nanotube that is close to an excitonic one, the coupling between these states allows the enhancement of the Raman cross section as described by Islam et al . 29 They observed such an enhancement for a phonon mode of CdSe quantum dots coupled to pyridine molecules where the laser excitation energy is in resonance with a charge transfer state and an excitonic state of the hybrid. In our case, we thus attribute the enhancement of one intrinsic mode of the nanotube G band to a Raman process promoted by charge transfer resonance and an excitonic resonance in our hybrid device. Since the two optical phonons G + and G -present different symmetries, they will be enhanced differently depending on the dipolar influence of the excitons in the system.

Regarding the different enhancement factors between the Raman spectra at 532 nm and at 488 nm, only laser line at 488 nm exhibits a dramatic enhancement of optical phonons, while 532 nm line is resonant with the nanotube (RBLM modes are visible meaning the laser matches an electronic transition) but do not show so strong enhancement. These two observations strongly suggest that this enhancement arises from a resonance of the 488 nm line with the molecular charged state (after illumination) and with the excitonic state of the nanotube. Indeed, energy separation between the two laser lines (210 meV) is compatible with the energy of excitons in a nanotube.

Interestingly, the redox state reached by the molecule under light irradiation is stable for hours after illumination whereas the non conventional Raman effect disappears as the light is turned off. In order to get more insights into the underlying dynamics of these phenomena, we recorded the time evolution of the electrical and vibrational response of the hybrid device.

Figure 4 shows the resistance of an hybrid CNFET during a dark/light-on/light-off cycle as shown on the timeline. The gate voltage is set at a constant value of 22 V so that the CNFET is in the threshold regime and not fully saturated in order to gain electrostatic field sensitivity. When switching on the light, we observe a resistance decrease from 20 to 17 kΩ (-15%) which, according to the transfer characteristics shown in Figure 2, corresponds to an effective p-doping. The time needed to reach a new steady state is of about 100 s. When switching off the light after 80 s, we observe no significant change in the resistance of the device. We tested over 16 samples, among which only one went back to the previous state after 2 days in ambient condition. However, by applying a gate voltage about -40 V on the backgate, we observe that within 150 s the resistance reaches a new steady state. In order to avoid the influence of the hysteresis, we then apply +30 V backgate voltage. When the backgate is tuned from 30 V to 22 V, the resistance goes back to 22 kΩ, which is similar (-15%)) to the dark state of the CNFET (not shown). Thus, we can use the back-gate voltage to control and reset the illumination effect on the molecule in the hybrid in order to perform repeated operation of the optical switching of the device. Similar behavior is observed in the vibrational response in burst mode Raman spectroscopy: a short accumulation time (1s) was used so as to record one spectrum every five seconds, and cycles of 100 s illumination followed by off states of 100 s were applied. For the first cycle, there is a clear doubling of the RBM intensity (x 2) when switching the light on, with a constant time of about 50 s, followed at the switching off by a decrease to a lower value than finally to the dark state (-25%) with a constant time of about 60 s. Almost the same behavior is observed on the G band (a lowering of -22% with a time constant around 40 s, not shown). Similar measurements were performed for non functionalized devices which showed no effect at all. Both Raman and transport measurements show that two different dynamics come into play. First, a relatively fast process with a constant time of 50 s reveals the weak capacitive coupling between the nanotube and the molecules. The second process involves long characteristics time constants up to hours corresponding to the relaxation time of charges trapped around the nanotube either in the substrate or in molecules around.

From room temperature experiments we conclude that the dramatic enhancement of the phonon signature of the hybrid is due to the possibility of resonantly transferred excitons from the charged state of porphyrins to the nanotube under light exposure. Furthermore, the persistence of the light induced doping is strongly dependent on charge trapping in the nanotube vicinity. Charge trapping in nanotube transistors is related to adsorbates, defects or trapping sites in the oxide layer or at interfaces and is known to strongly modify effective doping. [30][31][32][33] Charge trapping is thermally activated, in order to get insights into trapping mechanisms, we record single charge trapping/detrapping in the nanotube vicinity at low temperature depending on the light irradiation.

At low temperature (10K), the transfer characteristics is similar to that observed at room temperature but exhibits additional features superimposed on the regular field effect response. These features are hysteretic conductance steps regularly spaced both in gate voltage and in the logarithm of the conductivity (Figure 5(a)). This behavior is assigned to single charge transfer between a trap and the nanotube as already observed in single electron memories 18 and CNFETs decorated with nanoparticles. 3,6 In the hybrid system, single charge tunneling between molecular cluster and nanotube, the latter being also a single charge electrometer. Considering the nanometer range of the nanotube diameter, electric field lines are concentrated at the nanotube surface which promote charge tunneling with the environment and detection through field effect of the transistor. Such features are not observed on non-functionalized nanotubes and are assigned to the presence of the deposited molecules. From the voltage change between two steps, one can infer the capacitance C T between the trap T and the nanotube channel as:

C T = e ∆V G ( 1
)
where ∆ V G = 0.56 V which gives C T = 0.3 aF. AFM performed on our devices shows that the molecular grains are larger than the nanotube diameter and about 30 nm (see Supplementary Information), so we can approximate C T with a simple cylinder-plane capacitance model:

C T = 2π 0 r d T ln( h+ √ h 2 -d 2 N T d N T ) (2)
where d N T is the nanotube diameter (2 nm), d T is the trap size and h is the tunneling distance between the trap and the nanotube. We then obtain a distance of about 30 nm which allows to observe signatures of charge tunneling. Since the steps are regularly spaced in gate voltage, we conclude that the associated trap is not a single molecule which would rather exhibit molecular orbital spectrum. We thus attribute these regular peaks to a cluster of molecules in the Coulomb blockade regime. Furthermore, the presence of hysteresis between the up and down ramps of gate voltage is a signature of irreversibility in the charge tunneling (Figure 5(a)). Such irreversibility cannot occur in a single tunneling junction, but requires junctions in series implementing a so-called multiple tunneling junction (MTJ). 18 In such junctions, charges tunnel one by one along a series of potential wells which could be due in our case to tunneling from one molecule to another within the cluster before tunneling to the nanotube.

When exposing the device to light illumination, the power is low on the sample to prevent heating. For red light illumination (Figure 5 b), we observe very little changes on the transfer characteristics: steps are still visible with the same spacing and shifted by only 0.1 V. Neither smoothing nor resistance change which discard any eventual heating from the light. Dramatic changes occur when using a blue filter including the absorption range of the molecule. First we observe a global shift of the transfer characteristics by +1,5 V corresponding to an effective p-doping similar to the room temperature case. Moreover, we still detect quantized features which are regularly spaced with the same gate steps as without light, meaning that the trap self capacitance is still the same as without light. We attribute these features to the single charge transfers from the same molecular trap observed without light. This result is similar to what has been observed in porphyrins embedded in silica: 34 optical switching of tunneling effect was performed in molecule-based tunneling junctions.

However this group observed a similar global shift at any wavelength which discarded the absorption by the molecules. In our case, the occurence of a global shift for a wavelength matching the absorption peak of the molecule shows that the molecular optical transition is involved in the optical switching process. Furthermore, the most intriguing modification we observe, is the shape of these features which, from a staircase-like in darkness, turn to sharp peaks under blue illumination. If heating was involved, such features would have turned even less sharp. This is associated with a modification of the hysteresis in the trappingdetrapping event: when extracting the hysteresis area for the first step, we obtain an area A dark = 3.4.10 -6 S.V while under blue light exposure A blue =1.6.10 -6 S.V which corresponds to a reduction of the hysteresis of 53%. According to Nakazato et al., 18 this area is a function of the trap charging energy, the temperature and the ratio v s /v s0 where v s is the gate voltage sweep rate and v s0 = e/τ C T is characteristic of the MTJ and provides a time constant τ related to the charge tunneling dynamics. In our experiment, temperature and gate sweep rate are kept constant. We observe an overall shift of the characteristics upon blue light but the quantized steps exhibit same spacing as in the dark state. This spacing is directly proportional to the charging energy which we conclude to be constant upon illumination.

From Nakazato's model, we conclude that the hysteresis area change is then directly due to a modification of the time constant τ , pointing out to a modification in the dynamics of charge transfer through the MTJ, which is consistent with the work of Holloway et al. 35 Upon light exposure, the molecules involved in the MTJ turn excited which modifies the potential profile of the multiple barriers involved in the charge transfer to the nanotube. Indeed, Gruneis et al. have observed sharp features in the case of a trap being very well coupled to a nanotube. 6 In our case, we conclude that from a weak nanotube-trap coupling in darkness, light allows Ω Ω

Figure 2

 2 Figure2shows the influence of light illumination on a typical CNFET. We compare the

Figure 1 :

 1 Figure 1: a) UV-visible absorption spectrum of TPPZn (inset: Raman spectrum of TPPZn powder with and without extra white light illumination. The Raman spectra are measured at excitation wavelengths of 488 nm), b) Raman spectrum of isolated DWNT-TPPZn hybrid transistor at 532 nm (inset: chemical structure of the zinc(II) metalloporphyrin derivative(TPPZn)).

Figure 2 :Figure 3 :

 23 Figure 2: Light effect on hybrid CNFET. a) Transfer characteristics at room temperature in dark (black) and under 2 mW laser excitation at a) 475 nm (green) and b) 555 nm (blue) (inset: SEM image of an isolated DWNT transistor, scale bar is 1 µm).

Figure 4 :

 4 Figure 4: a) Differential resistance at V g = 22 V and b) RBLM peak intensity evolution under a cycle of white light ON and OFF cycle.

Figure 5 :

 5 Figure 5: a) Transfer characteristics of DWNT/TPPZn hybrid transistor at 10 K. The curve is plotted at V ds = 1 mV (AC) for opposite gate sweeps of ± 0.1 V/s (Inset shows the position of each step). b) Full hysteresis cycle of transfer characteristics of a DWNT/TPPZn hybrid transistor measured in dark (black curve), under red light illumination (red curve) and blue light (blue curve) at V ds = 1 mV (AC). c) Gate voltage position of the steps shown in b). d) Same curves in dark and blue light for decreasing gate sweep and horizontally shifted for the sake of clarity (inset: Light power dependence of the observed gate shift obtained using neutral densities).

Acknowledgement

The authors wish to thank B. Soula, E. Anglaret, V. Jourdain, M. Holzinger and R. Martel for fruitful discussions, V. Reita, D. Jegouso, T. Crozes for technical support. This work is supported by TRICO ANR, LANEF program (Cryoptics) and the Chinese Scholarship Council.


Julie C Aleman

A Fayolle

C Favier

A C Staver

K G Dexter

C M Ryan

A F Azihou

D Bauman

M Te Beest

E N Chidumayo

J A Comiskey

J P G M Cromsigt

H Dessard

J-L Doucet

M Finckh

J-F Gillet

S Gourlet-Fleury

G P Hempson

R M Holdo

B Kirunda

F N Kouame

G Mahy

F Maiato

P Gonçalves

I Mcnicol

P Nieto Quintano

A J Plumptre

R C Pritchard

R Revermann

C B Schmitt

A M Swemmer

H Talila

E Woollen

M. D Swaine

Floristic evidence for alternative biome states in tropical Africa

Keywords: Alternative stable states, Tropical biomes, Tree species composition, Precipitation and seasonality, Fire, Paleo-ecological data

whether they are published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Tree cover and canopy openness are commonly used to differentiate tropical forests and savannas, but the difference between the two biomes is not just a matter of structure [START_REF] Ratnam | When is a 'forest' a savanna, and why does it matter?[END_REF]. Whereas tropical moist forests form a closed canopy with a complex vertical structure, savannas are more open, allowing fire-and drought-adapted grasses to grow in the understory. Typically, forest dominates in wetter areas while savannas occur in drier, seasonal areas [START_REF] Ratnam | When is a 'forest' a savanna, and why does it matter?[END_REF][START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF], although transitions between forest and savanna are not rigidly determined by climate [START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF][START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Silva De Miranda | Using tree species inventories to map biomes and assess their climatic overlaps in lowland tropical South America[END_REF]. Soils and topography can be locally and regionally important, but at intermediate rainfall (between 1,000-2,500 mm globally), forest and savanna, both widespread, potentially represent alternative stable states maintained by feedbacks between tree cover and disturbances -specifically fire [START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Hirota | Global Resilience of Tropical Forest and Savanna to Critical Transitions[END_REF][START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF][START_REF] Favier | Abrupt shifts in African savanna tree cover along a climatic gradient[END_REF] and chronic herbivory [START_REF] Hempson | Alternate Grassy Ecosystem States Are Determined by Palatability-Flammability Trade-Offs[END_REF]. As a result, forest and savanna tree species show contrasting adaptations [START_REF] Hoffmann | Ecological thresholds at the savanna-forest boundary: how plant traits, resources and fire govern the distribution of tropical biomes[END_REF][START_REF] Charles-Dominique | Functional differentiation of biomes in an African savanna/forest mosaic[END_REF], and transitions across the forest-savanna boundary are characterized by high species turnover [START_REF] Charles-Dominique | Functional differentiation of biomes in an African savanna/forest mosaic[END_REF][START_REF] Swaine | The forest-savanna boundary in west-central Ghana[END_REF].

Despite these functional and floristic differences, most recent efforts devoted to understanding forest-savanna transitions have relied solely on information about the canopy structure, whether using satellite-based maps of percent tree cover [START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Hirota | Global Resilience of Tropical Forest and Savanna to Critical Transitions[END_REF][START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF][START_REF] Aleman | Spatial patterns in the global distributions of savanna and forest[END_REF], canopy height [START_REF] Xu | Remotely sensed canopy height reveals three pantropical ecosystem states[END_REF], or using field data on tree basal area [START_REF] V. De L. Dantas | Disturbance maintains alternative biome states[END_REF]. However, these studies have two types of shortcomings. The first type is linked to the use of remote sensing products which are ill-suited to capture the structural difference between savanna and forest. Most tree cover products are parameterized to identify trees greater than 5 m in height [START_REF] Hansen | Towards an operational MODIS continuous field of percent tree cover algorithm: examples using AVHRR and MODIS data[END_REF][START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF] and their spatial resolution is not sufficient to correctly characterize vegetation structure. Even though Landsat-based tree cover is available at 30 m resolution and MODIS tree cover at 250 m, the accuracy of these products is low in open systems [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF], and although it increases with spatial aggregation, it then fails to represent the fine-scale heterogeneity characteristic of savanna. Moreover, the tree cover threshold used to differentiate forest from savanna seems to depend strongly on calibration, with higher thresholds (75%) for Landsat tree cover [START_REF] Aleman | Spatial patterns in the global distributions of savanna and forest[END_REF] and lower (55-65%) for MODIS tree cover [START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Aleman | Land-use change outweighs projected effects of changing rainfall on tree cover in sub-Saharan Africa[END_REF]. The second type of shortcomings is even more important since defining forest and savanna using only canopy structure misses key aspects of forest vs savanna function tied to differences in the structure of the grass layer and in the tree species composition [START_REF] Ratnam | When is a 'forest' a savanna, and why does it matter?[END_REF]. The relatively open canopies of drier forests can be structurally similar to those of wetter savannas [START_REF] Torello-Raventos | On the delineation of tropical vegetation types with an emphasis on forest/savanna transitions[END_REF] but are not separable with a structural approach, even though the two differ dramatically in terms of species composition and ecosystem function [START_REF] Veldman | Clarifying the confusion: old-growth savannahs and tropical ecosystem degradation[END_REF]. Also, systems with similar physiognomies can have different histories, reflecting human land-use practices and recent disturbances [START_REF] Aleman | Spatial patterns in the global distributions of savanna and forest[END_REF]. For instance, forests subjected to human disturbances (such as clearing) can appear more like savannas, while some practices (particularly fire suppression) can make savannas appear more like forests [START_REF] Veldman | Clarifying the confusion: old-growth savannahs and tropical ecosystem degradation[END_REF][START_REF] Osborne | Human impacts in African savannas are mediated by plant functional traits[END_REF].

Biodiversity data available for sub-Saharan Africa [START_REF] Linder | The partitioning of Africa: statistically defined biogeographical regions in sub-Saharan Africa[END_REF][START_REF] Linder | The evolution of African plant diversity[END_REF][START_REF] Hempson | A continent-wide assessment of the form and intensity of large mammal herbivory in Africa[END_REF] and for tropical Africa [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF][START_REF] Fayolle | Patterns of tree species composition across tropical African forests[END_REF][START_REF] Fayolle | A sharp floristic discontinuity revealed by the biogeographic regionalization of African savannas[END_REF], offer new opportunities to differentiating and mapping the tropical forest and savanna biomes at continental scale. Here, we delineate the distribution of forest and savanna, and test for forestsavanna bistability, using a biogeographic approach, which reflects the evolutionary history and ecology of each biome, and does not rely on any structural metrics. We combined data on native tree species for sites identified earlier as forest (ref 26, n=455) and savanna (ref 27, n=298) and covering the full extent of these biomes in Africa [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF]. Each site consists of a species list assigned to either forest or savanna by the original authors or by the data contributors who conducted the floristic surveys according to vegetation structure, species composition and/or ecosystem functioning (see Materials and methods). We used tree species composition from these 753 floristic surveys to determine the climatic envelopes of the forest and savanna biomes (and their overlap) and to analyze the differences in tree species composition between them. We then used georeferenced herbarium collections [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF] to expand the floristic information spatially and describe the complete distribution of forest and savanna across Africa, and to identify the determinants of their present day distribution.

Extensive climatic overlap of forest and savanna in Africa

Alongside the expected patterns of forest in wetter areas and savanna in drier and more seasonal ones [START_REF] Ratnam | When is a 'forest' a savanna, and why does it matter?[END_REF][START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF], also retrieved here (Fig. 1A and SI Appendix, Fig. S1), we found an extensive climatic area (Fig. 1B-C, S2) within which both forest and savanna sites are widespread, which we term the 'bistable' region. Mean Annual Precipitation (MAP) partly differentiates the forest, the bistable region, and the savanna; although the climatic gradient used to determine and map them is more complex and integrates precipitation and seasonality (see Materials and methods for the details of the Principal Component Analysis on gridded climate data). We find a large extent of forest, 1.8 million km², covering almost the whole Guineo-Congolian Region (Fig. 1D), in line with the stability of forest in Lower Guinea suggested over the last two millennia by pollen records [START_REF] Vincens | Forest response to climate changes in Atlantic Equatorial Africa during the last 4000 years BP and inheritance on the modern landscapes[END_REF], but challenging previous findings of bistability across the entire Congo basin (3). Savanna was found to occupy the majority of the areas north, east and south of the Congo Basin, under drier and more seasonal conditions, and totaling almost 8.4 million km². The savanna notably includes the west coast of southern Africa (Fig. 1D), which contrasts with description of this area as thicket, scrub or bush land [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF]. This is due to the presence of northern (Sahel) and eastern (Horn) savanna sites with extremely arid climate in the floristic surveys, which extended the climatic envelope of savanna this far, and also because northern and western savannas are not completely analogous climatically to southern and eastern ones [START_REF] Fayolle | A sharp floristic discontinuity revealed by the biogeographic regionalization of African savannas[END_REF]. Meanwhile, the bistable region covers a vast area of more than 7.5 million km², often described as woodland [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF] and spans a broad MAP range (700-1900 mm, SI Appendix, Fig. S2). The bistable region was previously proposed to span a 1,000-2,000 mm MAP range in Africa [START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF] or, alternately, to extend to drier sites (> 650 mm) in a study restricted to savannas [START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF] and to wetter sites (1,000-2,500 mm) in the global tropics [START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Aleman | Spatial patterns in the global distributions of savanna and forest[END_REF]. Our bistable region can be separated into two sub-regions: a wetter region more likely to be forest (hereafter, bistable forest) and a drier and more seasonal one more likely to be savanna (hereafter, bistable savanna). Bistable forest is located in the periphery of the Guineo-Congolian Region, but also includes the Congolese Batéké Plateau and the Dahomey gap, which are currently dominated by savanna. This stresses the importance of factors other than climate in the outcome of forest-savanna bistability. The Batéké Plateau corresponds to the northern limit of the hyper-well-drained relict dunes of the Kalahari sands, while the Dahomey gap is well known to have shifted to savanna between 4,500 and 3,400 years ago following an abrupt climatic change [START_REF] Salzmann | The Dahomey Gap: an abrupt climatically induced rain forest fragmentation in West Africa during the late Holocene[END_REF]. Thus, the predominance of savanna in areas more likely to be forest has arisen either because of soil characteristics (i.e., sandy soils, 30) or the legacy of past climatic changes [START_REF] Vincens | Forest response to climate changes in Atlantic Equatorial Africa during the last 4000 years BP and inheritance on the modern landscapes[END_REF] and/or past disturbances [START_REF] Salzmann | The Dahomey Gap: an abrupt climatically induced rain forest fragmentation in West Africa during the late Holocene[END_REF][START_REF] Aleman | Palaeo-trajectories of forest savannization in the southern Congo[END_REF].

Paleo-ecological evidence

Long-term paleo-ecological data (from lacustrine and soil cores) around the Gulf of Guinea largely corroborates these areas of biome transition and stability (inset, Fig. 1D). For the bistable region, forest-to-savanna transitions were predominant with 16 transitional vs nine stable sites, while for the forest, stable biome identity was retrieved for ten out of 13 paleo-sites. For the savanna, the stability of savanna vegetation has been demonstrated around Lake Tilla (#21 on the map) in Nigeria [START_REF] Salzmann | Are modern savannas degraded forests?-A Holocene pollen record from the Sudanian vagetation zone of NE Nigeria[END_REF].

Current fire regime is also an important determinant of savanna distribution worldwide [START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF][START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF], specifically in relatively wetter areas [START_REF] Osborne | Human impacts in African savannas are mediated by plant functional traits[END_REF][START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF], and here we found that bistable savanna is more likely to burn than either forest or bistable forest, and also than savanna (SI Appendix, Fig. S3). The latter is explained by the lower productivity of drier savannas [START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF], but could also be linked to the presence of semi-desert grasslands [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF] in our study area (Sahel, Namib, Kalahari), where the discontinuous grass layer prevent the spread of fires.

African forests and savannas have distinct floristic composition

We found a marked dissimilarity in tree species composition between forest and savanna sites, based on floristic surveys. Pairwise comparisons showed a mean species turnover of 98% between forest and savanna sites, much higher than the turnover within the same biome (SI Appendix, Fig. S4). This result confirms the divergence of the forest and savanna floras [START_REF] Linder | The evolution of African plant diversity[END_REF] and is consistent with the results of plot-based studies of forest-savanna transition in South Africa [START_REF] Charles-Dominique | Functional differentiation of biomes in an African savanna/forest mosaic[END_REF], Ghana [START_REF] Swaine | The forest-savanna boundary in west-central Ghana[END_REF], and across the tropics [START_REF] Torello-Raventos | On the delineation of tropical vegetation types with an emphasis on forest/savanna transitions[END_REF]. Because forest and savanna represent alternative compositional states, we were confident in categorizing tree species into significant indicators of forest, or forest specialists (n=825 species, 48%), and significant indicators of savanna, or savanna specialists (n=523, 31%). Species that were not a significant indicator of either forest or savanna were interpreted as generalists (n=359, 21%). Our group of generalists included true generalists but also rare species or those otherwise rarely represented in the floristic surveys (Fig. 2). Evidence for biome specialization was even stronger when only common species were analyzed (i.e., those present at ≥ 10 sites), with only 8% of common species classified as generalists. It is worth noting that our results for 1,707 tree species represent only a fraction of the c. 45,000 flowering plant species reported for sub-Saharan Africa [START_REF] Klopper | Floristics of the angiosperm flora of sub-Saharan Africa: an analysis of the African Plant Checklist and Database[END_REF]. The specificity of the forest and the savanna flora is therefore likely underestimated, since grasses and forbs were not included, despite being a highly distinctive component of the savanna flora [START_REF] Linder | The evolution of African plant diversity[END_REF]. Functionally, though, these results are demonstrative, since the tree flora already captures some functional differences between the forest and savanna biomes [START_REF] Charles-Dominique | Functional differentiation of biomes in an African savanna/forest mosaic[END_REF] but it would be of great interest to extend the analyses to other growth forms to test the patterns observed for trees.

The regions described above based on climate (Fig. 1) have distinct compositions (SI Appendix, Fig. S5), assessed using an independent occurrence dataset (Fig. 2; see Materials and methods) derived from georeferenced herbarium records [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF]. Forest and bistable forest are composed mainly of forest specialists, and savanna and bistable savanna are composed mainly of savanna specialists. Indeed, forest specialists were found to dominate the Guineo-Congolian Region and its periphery, and to be abundant in East African Mountains (Fig. 2A). Within the Guineo-Congolian Region, Upper and Lower Guinea were better sampled than Congolia, for which herbarium records are sparse, and Upper Guinea includes the warm and wet forest sheltered by the Guinean Highlands in Sierra Leone and Guinea (Conakry). The latter were not included in our mapped extent of forest (Fig. 1D) likely because the floristic surveys we used do not cover this climate zone (positive scores on PC1 and PC2, Fig. 1A). Savanna specialists dominate in the north and west of Africa, including the Dahomey gap, and in the east and south (Fig. 2C). Interestingly, generalist species were found to be widespread and present within each region, and while they are more frequent in the bistable region, the difference is small (SI Appendix, Fig. S5B) and generalists almost never dominate (Fig. 2B and SI Appendix, Fig. S6).

Savanna-forest co-existence is possible, but restricted spatially

Based on a biome index, indicating the relative dominance of savanna (-1) and forest (1) specialists (see Materials and methods), we find that forest-savanna coexistence is limited (Fig. 3) even though the climate envelope where it is possible is large (42.4% of the study area and 25% of the African continent, Fig. 1D). Vast and continuous areas are dominated by the extremes of the biome index, representing either strict savanna or strict forest (SI Appendix, Fig. S7), and these extremes of the biome index correspond to recognized centers of endemism [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF], i.e., the Guineo-Congolian Region where forests are predominant, and the Sudanian and Zambezian Regions where savannas and woodlands are predominant, and both have specific floras and faunas (21-Figure 2. Distribution of forest specialist, generalist, and savanna specialist tree species. To test for specialization toward the forest and savanna biomes by individual tree species, we applied the IndVal procedure (50) to the presence matrix of the 1,707 species in the 753 sites (455 forest and 298 savanna sites), and obtained a classification of species into forest specialists (n=825 species) and savanna specialists (n=523), with non-significant indicators resulting in species being interpreted as generalists (n=359). For each 0.5° pixel containing herbarium records for at least 5 of our 1,707 species, we computed and mapped the percentage of (A) forest specialists, (B) generalists and (C) savanna specialists. White pixels thus correspond to a paucity of georeferenced herbarium records for our classified tree species. Major waterbodies are shown in blue. The frequency distribution of the number of sites in which (A) forest specialists, (B) generalists, and (C) savanna specialists occurred in the original floristic surveys is given on the bottom of each panel, illustrating the higher frequency of extremely infrequent species in the group of generalist species, in comparison to the specialists. 24). In contrast, intermediate values of the biome index, which correspond to the third mode in the frequency distribution (inset, Fig. 3), appear spatially restricted (SI Appendix, Fig. S7). The zones of intermediate biome index, which arise either from frequent generalists (as in East Africa) or from a mixture of forest and savanna specialists elsewhere (Fig. 2B and SI Appendix, Fig. S6), correspond to long recognized transition zones, forest-savanna mosaics [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF], and to recently deforested areas [START_REF] Aleman | Forest extent and deforestation in tropical Africa since 1900[END_REF]. A deeper investigation shows however that the possible intermediate state mostly corresponds to data-deficient areas since the tri-modal signal shifted towards a bi-modal signal when including only pixels with at least five or ten of our classified tree species (SI Appendix, Fig. S8). Thus, the floristic surveys (26, 27) combined with georeferenced herbarium records [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF] suggest that there are two floristic states in the intact tropical African vegetation.

Finally, we provide estimates of the current distribution of the forest and savanna biomes across the African continent combining both floristic and environmental information (Fig. 4). First, we re-computed the biome index on interpolated species distributions derived from ordinary kriging (SI Appendix, Fig. S9), while accounting for spatial autocorrelation (inset, Fig. 4A). This shows that there is a strong spatial structure for specialist species-whether forest or savanna-while generalist species do not show any spatial structure, suggesting that they do not correspond to an ecologically meaningful third group. We additionally include principle components of climate (PC1 and PC2 from Fig. 1) and soil information (sand percentage and cation exchange capacity), as well as data on fire and herbivory (see Materials and methods for the source of the datasets) as potential determinants of the biome index in a random forest regression (Fig. 4B). Topographic and hydrologic factors (e.g., seasonal flooding, topographically mediated frost occurrence or toxic heavy metal concentrations in soils) that are important determinant of mosaic landscapes locally [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF] were not included at this continental scale. The predictions of our random forest model on a validation subset of 10% of data pixels were accurate (R²=0.81 with a non-significant intercept and a predicted vs observed slope of 0.82 ± 0.03). This analysis of the joint determinants of both forest and savanna showed that precipitation and seasonality (PC1) are the main determinants of the biome index. Fire and, to a lesser extent, temperature (PC2, which is related to altitude) were also important drivers. Herbivory (including livestock and wild herbivore biomass) and sandy soils were found to have an equivalent and moderate impact, at this continental scale. The environmental model notably predicts a smaller forest area than the interpolated species distribution data (Fig. 4A) and than the raw data (Fig. 2,3). The latter possibly results from preferential sampling of forest trees in herbarium collections. More importantly, our results support the primary role of precipitation (1, 2), precipitation seasonality [START_REF] Vincens | Influence of rainfall seasonality on African lowland vegetation during the Late Quaternary: pollen evidence from Lake Masoko, Tanzania[END_REF], and fire [START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF][START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF][START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF] in the distribution of both forest and savanna in Africa, while most analyses of the determinants of savanna distribution have so far ignored forest [START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF][START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF]. Therefore, the predictions of the random forest (Fig. 4B) should be considered as our best estimate of the current distribution of the forest and savanna biomes across the African continent. We predicted the distribution of the biome index across the climatic space covered by the floristic surveys using (A) spatial information only vs (B) a random forest approach based on environmental determinants. For the spatial predictions, we interpolated the distribution of the percentage of forest specialists, generalists and savanna specialists using ordinary kriging, and recomputed the biome index. The empirical semi-variogram (points) and the spherical semi-variogram model (lines) used for kriging and shown as inset in (A) indicate that the spatial structure of generalist species is weaker and more homogeneous than that of forest and savanna specialists. For the environmental predictions of the biome index, we used climate (described by PC1 and PC2, Fig. 1A), fire, herbivory (total biomass of both livestock and wild herbivores), and soil factors (described by the percentage of sand and CEC in the first 0-5 cm). The relative importance of each environmental determinant is shown as inset in (B). The importance (% increase in MSE) tests how the accuracy of the results is affected if the input variable is randomly permuted. White pixels in (A) correspond to areas outside the geographical extent and the environmental range covered by the floristic surveys. White pixels in (B) additionally contain pixels for which herbivory data were not available (coastal edge and edge of inland waterbodies). Major waterbodies are shown in blue.

Conclusions and practical implications

In this study, we provided evidence for two compositional states across the African continent, alternatively dominated by forest and savanna species. These two states can coexist in a wide range of climates, but our biome index showed that current day spatial co-existence is spatially restricted, with one state or the other dominating over vast areas. This supports the notion that the two biomes are stable alternatives, and, consistent with the predictions of alternative stable state theory, suggests the potential for abrupt shifts in composition under external perturbations such as climate change, or altered fire regimes, as demonstrated by paleoecological evidence. With our correlative approach, we were not able to determine the ecological mechanisms allowing savanna persistence, but the facts that fire is more frequent in the bistable savanna area, and that fire is the second determinant of the biome index after the precipitation and seasonality gradient, support the hypothesis of fire acting as a major feedback mechanism, allowing savanna under climates favorable to forest.

These results are important for the ongoing efforts to restore African ecosystems, which depend on accurate biome maps to set appropriate targets for the restored states. This will help avoid, for example, inappropriate planting of forest trees, or attempts to "restore" forest in savanna areas. Up to now, because of the wide climatic zone where forest and savanna are both widespread, savanna has often been mischaracterized as degraded forest [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF][START_REF] Laestadius | Opportunities for forest landscape restoration[END_REF] and has been seen as a target for higher carbon storage via afforestation [START_REF] Laestadius | Opportunities for forest landscape restoration[END_REF][START_REF] Greve | Spatial optimization of carbon-stocking projects across Africa integrating stocking potential with co-benefits and feasibility[END_REF]. This viewpoint neglects several features of savannas, including their substantial belowground carbon storage [START_REF] Abreu | The biodiversity cost of carbon sequestration in tropical savanna[END_REF], their high biodiversity and endemism [START_REF] Murphy | The underestimated biodiversity of tropical grassy biomes[END_REF], and their socio-economic value [START_REF] Ryan | Ecosystem services from southern African woodlands and their future under global change[END_REF]. Our biome index map therefore is a useful tool for restoration, as it could help set appropriate species targets, and to identify degraded forest and encroached savanna areas which should be restored using forest and savanna specialists, if needed. Indeed, the current trend within bistable savannas is toward woody encroachment [START_REF] Stevens | Savanna woody encroachment is widespread across three continents[END_REF] and in this case restoration strategies mainly involve tree-cutting and prescribed fire to restore biodiversity and ecosystem services [START_REF] Buisson | Resilience and restoration of tropical and subtropical grasslands, savannas, and grassy woodlands[END_REF]. Conversely, restoring arid savannas to prevent desertification might involve tree and shrub planting [START_REF] Kaptué | On regreening and degradation in Sahelian watersheds[END_REF], and in this case using savanna specialists is and has been warranted. In the spatial extent where both biomes currently coexist, potentially both may be restored but a deeper investigation is needed, for example using long-term data, to determine the baseline biome [START_REF] Gillson | From myopia to clarity: sharpening the focus of ecosystem management through the lens of palaeoecology[END_REF], and human preference should also be considered.

Materials and methods

To delineate the distribution of forest and savanna across the African continent and to identify their underlying determinants, we developed a biogeographic approach consisting of four steps, each testing a specific hypothesis. First, we used the location of specific sites originally classified as forest [START_REF] Fayolle | Patterns of tree species composition across tropical African forests[END_REF] or savanna [START_REF] Fayolle | A sharp floristic discontinuity revealed by the biogeographic regionalization of African savannas[END_REF] to test the forest-savanna bistability, i.e., whether forest and savanna can both occur in areas with similar climates, earlier identified via remote-sensing products at the global (3, 5) and landscape [START_REF] Favier | Abrupt shifts in African savanna tree cover along a climatic gradient[END_REF] scales. In addition, for a selected area around the Gulf of Guinea with good paleo-ecological data, we tested for historical biome transitions to confirm forest-savanna bistability. Second, we used tree species lists for the same forest and savanna sites to test the biome specialization of the tree species, and to evaluate the overall distinctiveness of forest and savanna tree floras [START_REF] Linder | The evolution of African plant diversity[END_REF]. Third, we gridded the geo-referenced herbarium records available for tropical Africa [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF], and tested the degree of biome specialization characterizing each pixel, thereby testing the forest-savanna bistability from a floristic perspective. Finally, we used spatial and environmental predictions to delineate the distribution of the forest and savanna biomes at the continental scale and to test the relative influence of climate, fire, herbivory, and soils on the forest and savanna distributions [START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF][START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF].

Datasets

(i) Floristic data. We combined native tree species lists for 455 forest [START_REF] Fayolle | Patterns of tree species composition across tropical African forests[END_REF] and 298 savanna sites [START_REF] Fayolle | A sharp floristic discontinuity revealed by the biogeographic regionalization of African savannas[END_REF] across sub-Saharan Africa (Fig. 1D, Dataset S1). Each site consists of a species list assigned to either forest (excluding 'montane forest', and 'thicket') or savanna (including 'woodland') by the original authors or by the data contributors who conducted the floristic surveys. Forest sites corresponded to moist broadleaved forest, though restricted to lowland and terra firme, while savanna sites both included wooded grasslands and woodlands. Indeed, several southern African woodland types, such as Miombo, mopane and Baikiaea woodlands [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF], are considered as savannas since they burn regularly and have a relatively continuous grass layer [START_REF] Ratnam | When is a 'forest' a savanna, and why does it matter?[END_REF][START_REF] Osborne | Human impacts in African savannas are mediated by plant functional traits[END_REF]. Inclusion of a species list corresponding to either forest or savanna was first based on the definition given in the source according to vegetation structure (savannas do not show closed canopy and have a grass layer) and/or on clear indications of species composition and ecosystem functioning. The combined floristic dataset analyzed consisted of a total of 1,707 species occurring in more than five of our combined forest and savanna sites, belonging to 590 genera and 110 families (Dataset S1). The majority of the species were trees, but some shrubs were included in the savanna sites. The taxonomy was standardized according to the African Plant Database (http://www.villege.ch/musinfo/bd/cjb/africa/recherche.php?langue=an) in January 2018.

To spatially extrapolate the floristic information from our forest and savanna sites, we used independent data of plant species occurrence available online (https://gdauby.shinyapps.io/rainbio/) and assembled in the RAINBIO project (http://rainbio.cesab.org/). These represent the largest ever collation of georeferenced herbarium records for tropical Africa [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF].

We additionally gathered information on past vegetation for 42 paleo-ecological sites located around the Gulf of Guinea (Dataset S2) from published records of lacustrine fossil pollen (n=24), lacustrine phytoliths (n=1), and phytoliths (n=4) and δ 13 C of soil organic matter (n=14) from soil profiles. We selected records with at least 2,000 years of vegetation history. From the original studies, we identified 20 paleo-sites with stable vegetation during the Holocene, either forest or savanna, and 22 which experienced a biome transition, always from forest to savanna. Two sites, Lakes Bosumtwi and Barombi Mbo, date back to the Last Glacial Maximum (~21,000 years BP), during which the vegetation was probably a mosaic of savanna (identified by an increase in Poaceae) and forest elements.

(ii) Environmental drivers. Our study area corresponded to the geographical extent covered by the floristic surveys, but excluding two extreme sites in the very south (Fort Hare, South Africa) and east (Ogo, Somalia), ending up with latitudes ranging from 28°S to 17.5°N, and longitudes from 17°W to 42.5°E.

To characterize the climatic conditions across the study area, we used the bioclimatic variables from Worldclim version 2 at 0.5° resolution [START_REF] Fick | WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas[END_REF], which consist of 19 variables describing precipitation and temperature, and including mean annual temperature (MAT), mean diurnal range (mdrT), isothermality (isoT), temperature seasonality (Tsea), maximum temperature of the warmest month (Twm), minimum temperature of the coldest month (Tcm), temperature annual range (Tar), mean temperature of the wettest quarter (Tweq), mean temperature of the driest quarter (Tdq), mean temperature of the warmest quarter (Twaq), mean temperature of the coldest quarter (Tcq), mean annual precipitation (MAP), precipitation of the wettest month (Pwm), precipitation of the driest month (Pdm), precipitation seasonality (Psea), precipitation of the wettest quarter (Pweq), precipitation of the driest quarter (Pdq), precipitation of the warmest quarter (Pwaq), and precipitation of the coldest quarter (Pcq).

Beyond climate, we also considered disturbance, specifically fire and chronic herbivory (herbivore biomass), and soils (sand percentage and cation exchange capacity) because they have been identified as determinants of savanna distribution [START_REF] Lehmann | Deciphering the distribution of the savanna biome[END_REF][START_REF] Sankaran | Determinants of woody cover in African savannas[END_REF]. Estimates of fire frequency were derived from the burned area product from Moderate Resolution Imaging Spectroradiometer Active Fire (MODIS) data at 1-km resolution (47) over the 2003-2012 period. Current-day estimates of herbivore biomass at 0.5° resolution across the African continent included livestock and also historical wild herbivore biomass filtered by landscape change indices [START_REF] Hempson | The consequences of replacing wildlife with livestock in Africa[END_REF]. In this map, originally developed at 1° resolution excluding grid cells with > 50 % in inland water bodies, and then later refined at 0.5° resolution, there is no information for a large edge along the coast and around inland waterbodies. Among available soil variables at 250-m resolution for sub-Saharan Africa (https://soilgrids.org/), we retained the percentage of sand and the cation exchange capacity in the top layer (0-5 cm) of soil [START_REF] Hengl | Mapping soil properties of Africa at 250 m resolution: Random forests significantly improve current predictions[END_REF]. Soil variables were first projected and resampled to fit the 0.5° resolution.

The Global Lakes and Wetlands Database (GLWD, https://www.worldwildlife.org/pages/global-lakes-and-wetlands-database) was used to map major waterbodies, including lakes (GLWD-1) and rivers (GLWD-2).

Data analyses (i) Climatic envelope of forest and savanna. To detect the major climatic gradients over the entire study area, we performed a Principal Components Analysis (PCA) on the matrix of climate variables at 0.5° resolution (Fig. 1 and SI Appendix, Fig. S1). On the factorial plane defined by the first two Principal Components (PC1 and PC2), the pixels containing floristic surveys were colored and the climatic space they cover was defined by a convex hull (Fig. 1A). The first climatic gradient (PC1, describing 42.3% of the total variance) is characterized primarily by variation in precipitation, and by seasonality of precipitation and of temperature (Fig. 1A and SI Appendix, Fig. S1), and differentiates forest and savanna sites. The second climatic gradient (PC2, 31.1% of variance) is driven by temperature (Fig. 1A), and differentiates northern and western savannas from southern and eastern savannas and woodlands (SI Appendix, Fig. S1C), which are generally found at higher altitudes [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF] and thereby exposed to colder climates [START_REF] Fayolle | A sharp floristic discontinuity revealed by the biogeographic regionalization of African savannas[END_REF], except for coastal plains (e.g., in Mozambique).

Tropical forest and savanna have been shown to co-occur within the same MAP range [START_REF] Staver | The global extent and determinants of savanna and forest as alternative biome states[END_REF][START_REF] Hirota | Global Resilience of Tropical Forest and Savanna to Critical Transitions[END_REF][START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF], which was also apparent along PC1, the more complex climatic gradient integrating precipitation and seasonality (Fig. 1A,C). We defined this climatic space as the region of potential bistability, or 'bistable' region, because forest and savanna are both widespread, and because the stability over time has been previously demonstrated through mechanistic modelling [START_REF] Staver | Tree cover in sub-Saharan Africa: Rainfall and fire constrain forest and savanna as alternative stable states[END_REF]. Because of the non-uniform distribution of sites along PC1, we sub-sampled the sites with a stratified random sampling by taking, with replacement, 20 sites for each bin of 0.1 units PC1 (i.e., 20 samples with PC1 between -4 and -3.9, and so on). Numerically, the bistable region was defined as the region over which the slope in the frequency of the two biomes at each point over PC1 exceeded the mean of the slope averaged over the entire range (SI Appendix, Fig. S2A). In practice, we plotted the frequency of forest and savanna sites along PC1, and computed the slope of these curves for each PC1 bin. The slopes were averaged for the entire PC1 range. The bistable region was then defined as the area of the plot for which individual slopes are above the average. We found that forest and savanna sites coexist between PC1 values of 0.141 and 4.235 (Fig. 1C), and that their frequency distribution is equal to 0.5 for a PC1 value of 1.943, such that below this value, the probability of savanna occurring is higher than the probability of forest, and vice versa.

After defining these thresholds, we mapped the potential biomes based on gridded climatic variables, but we restricted our spatial predictions to the geographic extent and to the climate space covered by the floristic surveys. The latter was defined with a convex hull on the site scores along PC1 and PC2 (Fig. 1A). Predictions were thus not possible for some mountain areas in eastern Africa and for a large area in southern Africa corresponding to (semi-desert) grasslands [START_REF] White | The vegetation of Africa: A descriptive memoir to accompany the UNESCO/AETFAT/UNSO vegetation map of Africa[END_REF]. First, savanna, is defined as having values of PC1 < 0.141, and forest is defined as having PC1 ≥ 4.235 (Fig. 1C and SI Appendix, Fig. S2A). Then, within the bistable region, bistable savanna, which corresponds to a greater probability of savanna in the climatic space of co-occurrence (Fig. 1C), is defined by 0.141 ≤ PC1 < 1.943 and bistable forest, which corresponds to a greater probability of forest in the climatic space of co-occurrence, is defined by 1.943 ≤ PC1 < 4.235. Finally, for clarity and comparison with earlier results, we conducted the same analysis with MAP, sampling 20 sites for each MAP bin of 50 mm (SI Appendix, Fig. S2B), and found a range of 700-1900 mm for the bistable region (SI Appendix, Fig. S2C).

To confirm the forest-savanna bistability we mapped the paleo-ecological evidence of biome transitions (Dataset S2). To specifically test whether the bistable region is more likely to burn than the other potential biomes, we computed mean fire frequency for each potential biome (SI Appendix, Fig. S3). The latter analysis was performed both at the pixel-and at the site-scale.

(ii) Floristics of forest and savanna. We first computed the overall dissimilarity in tree species composition between all pairs of forest and savanna sites (SI Appendix, Fig. S4), using the Simpson index of beta-diversity (βsim), which is known to be richness-independent. We then performed the IndVal procedure (50) on the presence matrix of the 1,707 native tree species encountered in the 455 forest sites and the 298 savanna sites. This allowed us to identify significant indicators for categorizing species as forest or savanna specialists, or generalists (= no significant indicators, Dataset S3). We further applied this classification of our 1,707 tree species on an independent dataset of species occurrence derived from georeferenced herbarium records [START_REF] Droissart | Beyond trees: Biogeographical regionalization of tropical Africa[END_REF][START_REF] Sosef | Exploring the floristic diversity of tropical Africa[END_REF]. We computed the number (and percentage) of forest specialists, generalists, and savanna specialists per pixel of the 0.5° resolution grid representing our study area (Fig. 2).

We verified the concordance between the potential biomes derived from climate, and the species composition in terms of percentage of forest specialists, generalists, and savanna specialists (SI Appendix, Fig. S5). We used Kruskal-Wallis tests to compare each pair of potential biomes (forest and bistable forest, bistable savanna and savanna), and specifically test whether the bistable region is more composed of generalist species, or is a mix of forest and savanna specialist species.

(iii) Spatial distribution of the biome index. The spatial distributions of our forest specialists, generalists, and savanna specialists were then integrated into a biome index at the scale of 0.5° pixel (Fig. 3), with the following formula: biome index =

#𝑠𝑝 𝑓𝑜𝑟 -#𝑠𝑝 𝑠𝑎𝑣 #𝑠𝑝 𝑓𝑜𝑟 + #𝑠𝑝 𝑠𝑎𝑣 + #𝑠𝑝 𝑔𝑒𝑛
where #sp for is the number of forest specialists, #sp sav the number of savanna specialists, and #sp gen the number of generalist species in each pixel. The biome index tracks the specialization of each pixel, with values toward -1 representing the dominance of savanna specialists, and values toward +1 representing the dominance of forest specialists.

To further examine the underlying composition of the biome index, and to specifically test whether the intermediate values of the biome index rather correspond to more generalist species or to a mix of forest and savanna specialists, we used spline regressions between the percentage of each of the three species groups and the biome index (SI Appendix, Fig. S6). Since the frequency distribution of the biome index was found to be slightly tri-modal (inset, Fig. 3), we mapped the three states: the savanna state, the intermediate state, and the forest state, using different thresholds on the biome index (SI Appendix, Fig. S7). Finally, to examine the effect of herbarium record availability, we constructed the map of the biome index for pixels containing at least five or ten of our species and showed the associated frequency distribution (SI Appendix, Fig. S8).

(iv) Spatial and environmental predictions of the biome index. Because species occurrences were missing in remote and/or undersampled areas (Fig. 3), we re-computed our biome index (Fig. 4A) from spatially interpolated values of the percentage of forest specialists, generalists and savanna Figure S2. Climatic overlap. The putative bistable region where forest and savanna may represent alternative stable states was defined as the region of climatic overlap between forest and savanna sites. Slopes of both forest (green) and savanna (orange) frequency distributions are shown with respect to PC1, the complex climatic gradient integrating precipitation and seasonality (Fig. 1A and SI Appendix, Fig. S1). The climate space for which forest and savanna are both widespread (0.141 -4.235 on PC1) is represented in grey, this is the bistable region (Fig. 1C). The black lines correspond to the mean of the rate of change for each distribution (dashed for forest, and dotted for savanna) over the entire PC1 axis. The same analysis was conducted along an axis of (B) Mean Annual Precipitation (MAP, in mm) for comparison with other studies and leads to (C) a MAP range of circa 700-1900 mm for the bistable region. The distribution of forest specialists, generalists, and savanna specialists derived from georeferenced herbarium records was used to devise a biome index based on tree species composition and computed at 0.5° resolution, and here, pixels containing at least (A) five and (B) ten of our 1,707 tree species are solely shown. White pixels correspond to a lack of georeferenced herbarium records for our species. Major waterbodies are shown in blue. The frequency distributions of the biome index given in inset demonstrated that the tri-modal signal observed with all pixels (Fig. 3) gradually disappears under increased sampling (A and B), giving only a savanna (-1) and a forest (+1) mode.

Figure S9

. Interpolated distributions and associated uncertainty. The percentage of (A) forest specialist, (B) generalist and (C) savanna specialist species was spatially interpolated at 0.5° resolution using ordinary kriging. Associated uncertainty was also computed for (D) forest specialist, (E) generalist and of (F) savanna specialist species, using the confidence interval of the spatial predictions. White pixels in the maps (A-C) are outside the geographical extent and/or the environmental range covered by the floristic surveys. White pixels in the maps (D-F) also include the training data (pixels containing georeferenced herbarium records for at least 5 of our 1,707 species) for which there is no uncertainty. Major waterbodies are shown in blue.

Figure 1 .

 1 Figure 1. Climatic envelope of the forest and savanna biomes in Africa. To determine the climatic envelopes of the two tropical biomes, the dominant climatic gradients were first identified with a Principal Component Analysis of gridded climatic variables. (A) Each point corresponds to the center of a 0.5° pixel, with pixels containing floristic surveys in forest (green) and savanna (orange) sites indicated. Red and blue arrows indicate the influence of temperature and precipitation variables, respectively. (B) Distribution of forest (green) and savanna (orange) sites along an axis of mean annual precipitation (MAP, in mm). (C) Frequency distribution of forest (green) and savanna (orange) sites along a complex precipitation and seasonality gradient (PC1, A), with the climatic area where savanna and forest both occur plotted in light orange (where savanna is more common) and light green (where forest is more common). The dashed line corresponds to an equal probability of savanna and forest. (D) Map of forest and bistable forest, bistable savanna and savanna, with the locations of floristic surveys in forest (green) and savanna (orange) sites. White pixels are outside the geographic extent and/or the environmental range covered by the floristic surveys. The latter was defined by a convex hull on the site scores on PC1 and PC2 (dashed line in A). Major waterbodies and rivers are shown in blue. The paleoecological data available around the Gulf of Guinea retrieved from published records of lacustrine fossil pollen (n=24), lacustrine phytoliths (n=1), phytoliths (n=4) and δ 13 C of soil organic matter (n=14) from soil profiles are shown in inset. The paleo-sites provided information on stable (black) and transitional (grey) sites during the Holocene (see Dataset S2 for the code correspondence of paleo-sites).

Figure 3 .

 3 Figure 3. Spatial distribution of the biome index across Africa. The distributions of forest specialists, generalists, and savanna specialists derived from georeferenced herbarium records were used to devise a biome index based on tree species composition and computed at 0.5° resolution. The biome index tracks the biome specialization of each pixel, with values toward -1 representing the dominance of savanna specialists and values toward +1 representing the dominance of forest specialists. White pixels correspond to a lack of georeferenced herbarium records for our species. Major waterbodies are shown in blue. The frequency distribution of the biome index is given in inset.

Figure 4 .

 4 Figure 4. Spatial and environmental predictions of the biome index.We predicted the distribution of the biome index across the climatic space covered by the floristic surveys using (A) spatial information only vs (B) a random forest approach based on environmental determinants. For the spatial predictions, we interpolated the distribution of the percentage of forest specialists, generalists and savanna specialists using ordinary kriging, and recomputed the biome index. The empirical semi-variogram (points) and the spherical semi-variogram model (lines) used for kriging and shown as inset in (A) indicate that the spatial structure of generalist species is weaker and more homogeneous than that of forest and savanna specialists. For the environmental predictions of the biome index, we used climate (described by PC1 and PC2, Fig.1A), fire, herbivory (total biomass of both livestock and wild herbivores), and soil factors (described by the percentage of sand and CEC in the first 0-5 cm). The relative importance of each environmental determinant is shown as inset in (B). The importance (% increase in MSE) tests how the accuracy of the results is affected if the input variable is randomly permuted. White pixels in (A) correspond to areas outside the geographical extent and the environmental range covered by the floristic surveys. White pixels in (B) additionally contain pixels for which herbivory data were not available (coastal edge and edge of inland waterbodies). Major waterbodies are shown in blue.

Figure S3 .

 S3 Figure S3. Fire frequency. (A) A map of fire frequency over 2003-2012 was derived from MODIS Active Fire burned area. White pixels in the map are outside the geographic extent and/or the environmental range covered by the floristic surveys. Major waterbodies are shown in blue. Fire frequency was examined according to the potential biomes, forest, bistable forest, bistable savanna, and savanna as defined in Fig. 1C-D, (B) for the entire study area, and (C) for the pixels containing floristic surveys.

Figure S5 .

 S5 Figure S5. Composition of the bistable region.Relationships between potential biomes derived from climate and floristic composition derived from georeferenced herbarium records were examined. The boxplots depict for each potential biome (Fig. 1) the percentage of (A) forest specialist species, (B) generalist species, and (C) savanna specialist species, for pixels containing at least 5 of our 1,707 species. The letters (a, b, c and d) in these panels show the results of Kruskal-Wallis tests applied for each pair of potential biomes, with different letters indicating a significant statistical difference at p < 0.05.

Figure S6 .

 S6 Figure S6. Composition of the biome index. The underlying composition in terms of percentage of forest specialist (green), generalist (grey) and savanna specialist (orange) species was examined for the biome index computed with distribution data derived from georeferenced herbarium records. The thick lines represent a spline regression of the data points, illustrating a continuous increase/decrease of the percentage of forest /savanna specialists with the biome index, and a relatively stable and low (< 20) percentage of generalist species across the whole range of biome index, that, however, tended to show a slight peak for intermediate biome index.

Figure S7 .

 S7 Figure S7. Intermediate biome index. Since the frequency distribution of the biome index was found to be slightly tri-modal (inset, Fig.3), we used different threshold to map the intermediate state: (A) |biome index| < 0.6, (B) |biome index| < 0.7, (C) |biome index| < 0.8 and (D) |biome index| < 0.9. The percentage of pixels belonging to the forest state (in green), to the intermediate state (in grey), and to the savanna state (in orange), is given for each threshold. Blue pixels are dominated by waterbodies. In West and Central Africa, intermediate values of the biome index correspond to long recognized transition zones between major floristic regions (1), to savanna areas such as the Dahomey gap that were forested during the Holocene (2), and where forest-savanna mosaics are common, and to recently deforested areas (3). In East Africa, intermediate values of the biome index also correspond to the high elevation forest of Ethiopia, much of which are not included in our species lists, and to densely-populated areas, such as the coastal forest and the Lake Victoria mosaic (1).

Figure S8 .

 S8 Figure S8. Biome index and availability of herbarium records. The distribution of forest specialists, generalists, and savanna specialists derived from georeferenced herbarium records was used to devise a biome index based on tree species composition and computed at 0.5° resolution, and here, pixels containing at least (A) five and (B) ten of our 1,707 tree species are solely shown. White pixels correspond to a lack of georeferenced herbarium records for our species. Major waterbodies are shown in blue. The frequency distributions of the biome index given in inset demonstrated that the tri-modal signal observed with all pixels (Fig.3) gradually disappears under increased sampling (A and B), giving only a savanna (-1) and a forest (+1) mode.

Acknowledgments:

We warmly thank all the members of the Tropical Forestry group in Gembloux Agro-Bio Tech, University of Liège, not listed as co-authors of the study. This work was funded by the Belgian Science Policy (BR/143/A3/HERBAXYLAREDD, A.F) and the Natural Environment Research Council (NE/P008755/1, C.M.R. and K.G.D.). D.B. received support from Fondation Wiener-Anspach.

specialists using ordinary kriging (SI Appendix, Fig. S9A-C). The spherical autocorrelation function provided a good fit to the experimental variograms (inset, Fig. 4A). We evaluated the spatial accuracy of the kriged map outside the pixels containing herbarium records of our study species by computing confidence intervals from the variance of the predictions (SI Appendix, Fig. S9D-F).

We also used a random forest approach to identify the environmental determinants of the biome index, and to map the biome index according to climate (described by PC1 and PC2, Fig. 1A, S1), fire (SI Appendix, Fig. S3), herbivory, and soil factors (described by the percentage of sand and CEC in the top 0-5 cm). For the random forest, our dataset corresponded to the pixels containing at least 5 of our 1,707 species and with available data for all environmental determinants. We kept 10% of the dataset for validation (n=169 pixels) and fit the random forest model on a calibration dataset (n=1,523 pixels). We also examined the importance of each environmental determinant, which measures how the accuracy of the results is affected if the input variable is randomly permuted.

All the analyses were performed within the open source R environment (51) using the raster package (52) for raster constructions and most spatial analyses. The ade4 package (53) was used for the PCA and the dismo package [START_REF] Hijmans | dismo: Species Distribution Modeling[END_REF] for the convex hull. The vegan package (55) was used for the dissimilarity analysis and the labdsv package (56) for computing species indicator values (and significance) for each biome. The gstat package (57) was used for the spatial interpolation by ordinary kriging, while the RandomForest package (58) for the Random Forest regression used to identify the environmental determinants and to provide environmental predictions. List of 42 paleo-sites for which at least 2,000 years of vegetation history is available. Dataset S3. Indicator species. List of forest specialist, generalist and savanna specialist species among the 1,707 tree species present in the 455 forest and 298 savanna sites and retained for analyses.

Supporting Information Appendix for: Floristic evidence for alternative biome states in tropical Africa

Contains