Alexander Oleinick

Irina Svir

Christian Amatore
email: christian.amatore@ens.fr

A few key theoretical issues of importance in modern molecular electrochemistry

Keywords: Theory at nanoscale, Nanoelectrochemistry, Single molecule electrochemistry, RTILs, Numerical simulation

whether they are published or not. The documents may come

A few key theoretical issues of importance in modern molecular electrochemistry

Introduction

The advent of nanoscale electrochemistry has opened a multitude of problems that could only glimpsed at ca 25 years ago when microelectrodes started to make their way in laboratories for routine experiments [START_REF] Amatore | Electrochemistry at Ultramicroelectrodes[END_REF]. At that time the main theoretical issues seemed mostly be related to the difficulty of treating edge effects under steady and quasi-steady state electrochemical conditions, and to the consequences of having diffusion layers and interfacial diffuse layers merging to the point where electroneutrality cannot be considered anymore to apply over the solution range where concentration gradients of electroactive species develop [START_REF] Amatore | Is Cyclic Voltammetry Above A Few Hundred KiloVolts per Second Still Cyclic Voltammetry?[END_REF][START_REF] Norton | Effect of the electrical double layer on voltammetry at microelectrodes[END_REF][START_REF] Smith | Theory of the voltammetric response of electrodes of submicron dimensions violation of electroneutrality in the presence of excess supporting electrolyte[END_REF]. These problems still keep their important topicality, but many others have been arising that deal more directly with the nano-sizes of electrodes and with the important role played by nanoscale structures forming in electrolytes near electrodes.

The format allowed for this type of perspective does not permit discussing all such theoretical problems even assuming that we could foresee all of them at the present time. So we decided to select three topics that have currently high experimental and technological interest and in which these problems are playing significant roles though it seems to us that this is not so well perceived by experimentalists.

Single molecule electrochemistry in nano-confined dual-electrodes cells

The so-called single molecule electrochemistry [START_REF] Fan | Electrochemical detection of single molecules[END_REF][START_REF] Fan | Single Molecule Electrochemistry[END_REF] term was coined more than 20 years ago. The method is taking advantage of the current amplification created when a feedback mode is established between two close electrodes, e.g., a SECM tip and a conducting substrate [START_REF] Bard | Scanning electrochemical microscopy. 12. Theory and experiment of the feedback mode with finite heterogeneous electron-transfer kinetics and arbitrary substrate size[END_REF]. In fact this elaborates on the well-known principle of redox cycling between two close electrodes [START_REF] Anderson | Thin-layer electrochemistry: steady-state methods of studying rate processes[END_REF], except that the use of nanometric electrodes provides an excellent signal-to-noise ratio allowing the precise measurement of currents ranging from a few picoamperes to a few femtoamperes due to the redox-cycling amplification of only one (to a few) molecules "trapped" within nanometer-sized thin-layer cells formed by nanometric electrodes separated by nanometric gaps [START_REF] Fan | Electrochemical detection of single molecules[END_REF][START_REF] Sun | Electrochemistry of individual molecules in zeptoliter volumes[END_REF]. The possibility of monitoring electrochemically such small numbers of molecules has stimulated a huge interest in expectation of observing and analyzing for the first time fluctuations in electrochemical properties (see a recent review discussing this in deeper depth than here) [START_REF] White | Redox cycling in nanogap electrochemical cells[END_REF]. Indeed, classical electrochemical experiments give access only to statistically averaged values because of the huge numbers of events involved in each single measurement [11,12]. New nanofabrication methods have been recently developed to create nanochannels with interelectrodes gaps of precise dimensions in the tens of nanometers range in hope to evaluate in more details the stochastic properties of a redox molecules [12][START_REF] Kang | Electrochemical singlemolecule detection in aqueous solution using self-aligned nanogap transducers[END_REF][START_REF] Mathwig | Nanoscale methods for single-molecule electrochemistry[END_REF][START_REF] Kang | Single-molecule electrochemistry in nanochannels: probing the time of first passage[END_REF]. More interestingly in view of the subject of this perspective is the fact that such nano-gap electrochemical cells allowed investigating the effect of diffuse layer electrical fields on the meaning of electron transfer (ET) kinetics [START_REF] Xiong | Ion transport within high electric fields in nanogap electrochemical cells[END_REF][START_REF] Cao | Ion transport through ultrathin electrolyte under applied voltages[END_REF][START_REF] Fu | Electrochemistry at single molecule occupancy in nanoporeconfined recessed ring-disk electrode arrays[END_REF][START_REF] Bae | Recessed nanoelectrodes for nanogap voltammetry[END_REF][START_REF] Bae | Diffuse layer effect on electron-transfer kinetics measured by scanning electrochemical microscopy (SECM)[END_REF][START_REF] Fu | Ion selective redox cycling in zero-dimensional nanopore electrode arrays at low ionic strength[END_REF], as well as the consequences of adsorption of one member of the investigated redox couple [START_REF] Chen | Self-Inhibitory electron transfer of the Co(III)/Co(II)-complex redox couple at pristine carbon electrode[END_REF], while these effects are difficultly interpreted when observed under classical electrochemical conditions. However, to the best of our knowledge, none of these studies or many others reported on the topics of single entities electrochemistry [START_REF] White | Redox cycling in nanogap electrochemical cells[END_REF]23] have considered a point that seems to us to have an extreme importance, maybe because one thinks to such events as one is used to do when analyzing classical electrochemical experiments. Indeed, under classical electrochemistry the continuity of the current pathway between the working and auxiliary electrodes is ensured by a sequence of different phenomena that occur almost simultaneously (i.e., within the limit of the speed of light across the electrochemical cell) and that are generally represented as in Figure 1A. The use of the reference electrode allows uncoupling the two active electrodes by relating the current flow across the cell to the potential applied to the working electrode independently of that applied to the auxiliary electrode. However the current intensity flowing through the working electrode must also flow through the auxiliary electrode in order to complete the whole electrical circuit. In other words, one takes advantage that classical electrochemical cells contains a colossal number of redox active molecules (in fact a not so small fraction of the Avogadro number) to ensure that within the duration of an electron transfer event occurring at the working electrode, viz., a few femtoseconds, another one occurs in the opposite direction at the auxiliary electrode. This only enables the ionic current flowing through the solution bulk to be converted into the electronic current that flows through the electrodes and the external equipment. On the other hand this also maintain the global electroneutrality of the bulk solution. Evidently, this cannot occur so easily when the number of molecules contained in a nanoelectrochemical cell becomes extremely small. Pushed to the extreme, in a zeptoliter volume containing a single ferrocene molecule, the one-electron oxidation at the working anode cannot be compensated by a simultaneous one-electron reduction occurring at the auxiliary cathode whenever the potential drop across the cell is maintained over the range of the ferrocene/ferricinium wave. In other words, upon oxidizing the single ferrocene molecule contained in the nano-cell one has created a charge that cannot be immediately compensated by a Faradic process and drastically increases the potential of the formerly electroneutral zeptoliter solution volume [24].

Figure 1

Comparison between the functioning modes of an electrochemical cell under (A) classical conditions for two-or three-electrode operating mode or (B) during "single molecule" operation (two-electrode mode) in a zeptoliter volume cell containing a single redox molecule. The color code indicates the nature of the current flow: red = electronic current towards the working electrode lead (W); blue = electronic current from the auxiliary electrode lead (Aux); green = ionic current in the solution; brown = Faradic impedances. Each double layer capacitor "couples" an electronic contribution to an ionic one of same magnitude (charge/discharge of the capacitance); each Faradic impedance "converts" an electronic current into an ionic one or reciprocally hence the naming "anodic" (B1) or "cathodic" (B2) current flows.

Nonetheless, experimentally [START_REF] Kang | Electrochemical singlemolecule detection in aqueous solution using self-aligned nanogap transducers[END_REF]25], one observes that this is associated to an anti-correlated current flowing at the cathode. This evidences that under such circumstances the electrical circuit is closed by a non-Faradic mean, viz., through charging of the cathode double layer (Figure 1B-1) due to the increase of the electrolyte potential, a known phenomenon usually named "capacitive coupling" [26]. The opposite occurs when the ensuing ferricinium ion reaches the cathode where it is reduced as is sketched in Figure 1B-2, thus relaxing the solution potential increase. In fact, note that by construction, except if a proper accounting of the successive events is made in experiments such as those in Refs [12][START_REF] Kang | Electrochemical singlemolecule detection in aqueous solution using self-aligned nanogap transducers[END_REF][START_REF] Mathwig | Nanoscale methods for single-molecule electrochemistry[END_REF][START_REF] Kang | Single-molecule electrochemistry in nanochannels: probing the time of first passage[END_REF], it is difficult to decide at which electrode an electron transfer is occurring and is compensated by a mirror capacitive current at the other one.

Presumably, this is the source of the uncommon effects related to the composition of the electrolytes cited above [START_REF] Xiong | Ion transport within high electric fields in nanogap electrochemical cells[END_REF][START_REF] Cao | Ion transport through ultrathin electrolyte under applied voltages[END_REF][START_REF] Fu | Electrochemistry at single molecule occupancy in nanoporeconfined recessed ring-disk electrode arrays[END_REF][START_REF] Bae | Recessed nanoelectrodes for nanogap voltammetry[END_REF][START_REF] Bae | Diffuse layer effect on electron-transfer kinetics measured by scanning electrochemical microscopy (SECM)[END_REF][START_REF] Fu | Ion selective redox cycling in zero-dimensional nanopore electrode arrays at low ionic strength[END_REF]. We therefore strongly believe that this problem of single molecule electrochemistry should be precisely investigated theoretically before any hope of using these approaches to unravel electrochemical properties beyond investigations related to the stochastic nature of fundamental electrochemical laws [11,12,27]. The main difficulties in building serious theoretical approaches to the problem is that one is dealing here with a succession of stochastic single events, each one having its own specific features. Hence, no classical formulations such as those implicitly considered for each component in the schematic diagrams in Figure 1 can be used. Brownian molecular dynamics may be useful in this context [24] for transport including migration in the double layers but will require its coupling with DFT (QM/MM) to treat molecular organization at the interfaces [28] as well as electron transfer kinetics and thermodynamics [29,30] since again no classical electron transfer theory such as Marcus' or Nernst's can be used. In our opinion the availability of theoretical contributions on these subjects will be useful not only for fundamental investigations and basic knowledge but also for many practical issues that arise presently in many advances for electrocatalysis in nanoconfined environments, energy conversion and storage in supercapacitors.

Electrochemistry in room temperature ionic liquids (RTILs)

This is a second example of a rather recent experimental electrochemical field that has rapidly expanded owing to the peculiar physical and chemical properties of RTILs and their importance in electrochemistry [31][32][START_REF] Bodin | Biredox ionic liquids: new opportunities toward high performance supercapacitors[END_REF]. However, it is clear that the very structure of RTILs [START_REF] Hayes | Structure and Nanostructure in Ionic Liquids[END_REF] imposes that all classical electrochemical concepts need to be revisited and cannot be applied in these media and carry the same meaning as under classical electrochemical conditions. Indeed, almost all the concepts we use on everyday basis to analyze electrochemical data have been developed for simple electrolytes diluted in non-viscous solvent media. Hence, their very roots appear fully irrelevant to situations in which the medium itself is composed of organic bulky ions in close contact [START_REF] Gehrke | Structure and lifetimes in ionic liquids and their mixtures[END_REF] in which high degrees of order are maintained over mesoscopic spatial scales [START_REF] Russina | New experimental evidence supporting the mesoscopic segregation model in room temperature ionic liquids[END_REF].

For example, the very structure and dynamics of electrode/RTIL [START_REF] Reichert | Molecular scale structure and dynamics at an ionic liquid/electrode interface[END_REF] or water/RTIL [START_REF] Kakiuchi | Ionic Liquid | Water Interface: A New Electrified System for Electrochemistry[END_REF] electrified interfaces have been investigated appears to contradict predictions based on the classical Gouy-Chapman-Stern theory. This questions in turn the very notion of reorganization energies and work terms whose roles in ET theories are critical. Similarly, what precise phenomena underlie the experimental values of diffusion coefficients measured in RTILs and justify their Arrhenius-type temperature dependence [39]? All these issues are critical as soon as one wants to use and rationalize electrochemical data [START_REF] Lin | Understanding mass transport influenced electrocatalysis at the nanoscale via numerical simulation[END_REF] in such media. It seems to us that owing to the critical roles of the nanoscale properties (of importance for conditioning local structures as well as for dynamics) that are concerned, any classical modelling based on usual physicochemical laws will not provide any suitable access to understand the real fundamental nature of the parameters involved in the simulations. To be more precise, even if experiments supported by precise simulations based on classical electrochemical laws [START_REF] See | Voltammetry of Oxygen in the Room-Temperature Ionic Liquids 1-Ethyl-3methylimidazolium Bis((trifluoromethyl)sulfonyl)imide and Hexyltriethylammonium Bis((trifluoromethyl)sulfonyl)imide: One-Electron Reduction To Form Superoxide. Steady-State and Transient Behavior in the Same Cyclic Voltammogram Resulting from Widely Different Diffusion Coefficients of Oxygen and Superoxide[END_REF] provide values for the above parameters, such theoretical approaches alone will never be able to rationalize the origin of their distinctiveness compared to their analogs under usual electrochemical conditions. However, owing to the increasing involvement of RTILs in many nanoscale-electrochemical topics such as advanced supercapacitors we believe that a profound understanding of the fundamental phenomena that govern their peculiar behavior is required. In this respect, considering the important role of nanoscale structures and that of the dynamics of their local deformations, we believe that molecular dynamics simulations will certainly provide the needed understanding. Indeed, these approaches have already shown their ability in investigating structural and dynamics problems involved in many RTILs [START_REF] Hayes | Structure and Nanostructure in Ionic Liquids[END_REF][START_REF] Gehrke | Structure and lifetimes in ionic liquids and their mixtures[END_REF] in particular by providing important information on ion pairing and ion cages structures and life-times, i.e., about fundamental issues of interest for understanding electrochemistry in these media. Hence, multiscale theoretical approaches involving molecular dynamics coupled to DFT (QM/MM) [28-30] should provide interesting outcomes to unravel the physicochemical phenomena that underlie electrochemistry in RTILs; see e.g. references [START_REF] Reichert | Molecular scale structure and dynamics at an ionic liquid/electrode interface[END_REF][START_REF] Kakiuchi | Ionic Liquid | Water Interface: A New Electrified System for Electrochemistry[END_REF][39][START_REF] Lin | Understanding mass transport influenced electrocatalysis at the nanoscale via numerical simulation[END_REF][START_REF] See | Voltammetry of Oxygen in the Room-Temperature Ionic Liquids 1-Ethyl-3methylimidazolium Bis((trifluoromethyl)sulfonyl)imide and Hexyltriethylammonium Bis((trifluoromethyl)sulfonyl)imide: One-Electron Reduction To Form Superoxide. Steady-State and Transient Behavior in the Same Cyclic Voltammogram Resulting from Widely Different Diffusion Coefficients of Oxygen and Superoxide[END_REF][START_REF] Lu | Ionic liquid interface at an electrode : Simulations of electrochemical properties using an asymmetric restricted primitive model[END_REF][START_REF] Chen | On the temperature dependence of the double layer capacitance of ionic liquids[END_REF] for recent interesting approaches in such directions.

Simulations of transient voltammetry involving realistic ohmic and capacitive contributions and dynamic adsorption of reactive electroactive species

Transient voltammetry has proven its great advantages over most electrochemical methods for unravelling complex mechanistic features in electrochemistry. Yet, under most circumstances, viz., as soon as the electrochemical mechanism is not straightforward, one cannot rely on the application of analytical relationships between peak potentials or current intensities with scan rates, etc. [44], to characterize the mechanism and extract the relevant kinetic and thermodynamic information. Then a complete theoretical analysis of the voltammetric data based on comparison with simulations is required. Today several user-friendly commercial programs allow simulations of 1D and 2D electrochemical problems involving complex mechanistic sequences in solution (e.g., among the most popular ones: DigiSim © [START_REF] Rudolph | A simulator for cyclic voltammetric responses[END_REF], DigiElec © [START_REF] Rudolph | Digital simulations on unequally spaced grids: Part 2. Using the box method by discretization on a transformed equally spaced grid[END_REF], KISSA © [START_REF] Amatore | A new strategy for simulation of electrochemical mechanisms involving acute reaction fronts in solution: Principle[END_REF][START_REF] Amatore | A new strategy for simulation of electrochemical mechanisms involving acute reaction fronts in solution: Application to model mechanisms[END_REF][49]) and this can be extended by self-programming of multi-purpose programs originally devised for physical problems such as Comsol © . Hence, one may have the impression that the efforts started in the middle of the sixties have reached their final goal. However, today, many problems at hand in molecular electrochemistry are no more limited to situations where the only role of the electrode was to provide or accept electrons while the ensuing chemistry took place in solution. Indeed, many electrocatalytic systems investigated nowadays involve critical dynamic interplays between solution and surface kinetic intermediates. This in turn involve dynamic adsorption/desorption steps and leads to competitive, possibly parallel, reactions of intermediates on the electrode surface and in the solution [START_REF] Klymenko ; Buriez | Uncovering a Missing Link between Molecular Electrochemistry and Electrocatalysis: Mechanism of Benzyl Chloride Reduction at Silver Cathodes[END_REF]51]. Figure 2A represents the general situation expected for a simple reduction pathway in which electron transfers may occur either in solution at the OHP or between adsorbed species of the same redox couple.

This general scheme is contrasted in Figure 2B to that of a solution electron transfer according to the classical Smoluchowski-Debye model. This comparison evidences that interfacial ET may well also occur when the substrate is not at the OHP. Indeed, transposition of the Smoluchowski-Debye equation for rate constants evidences that long range ET may occur. Evidently since in usual media ET rate constant decays exponentially with the distance this is irrelevant at macroor even microelectrodes since anyway the uncertainty on the local ET position does not matter (except for the magnitude of the corresponding rate constant) because the dimension of diffusion layers is excessively large compared to a few angstroms uncertainty on the exact ET positions. This is simply reflected by the extracted ET rate constant value. However, this may become a serious problem at nanoelectrodes or at catalytic nanoparticles [START_REF] Sun | Electrochemistry at a single nanoparticle: from bipolar regime to tunnelling[END_REF]. In this case simulations ought to consider stochastic probabilities accounting for the fact that ETs may occur from/to a point located significantly deep in the diffusion layer that would be predicted on the basis of Fick's laws. This may be extremely important when the nanoelectrode or nanoparticle size are small enough for the distinction between the diffuse layer and the diffusion one to become ambiguous [START_REF] Amatore | Is Cyclic Voltammetry Above A Few Hundred KiloVolts per Second Still Cyclic Voltammetry?[END_REF][START_REF] Norton | Effect of the electrical double layer on voltammetry at microelectrodes[END_REF][START_REF] Smith | Theory of the voltammetric response of electrodes of submicron dimensions violation of electroneutrality in the presence of excess supporting electrolyte[END_REF][START_REF] Bae | Diffuse layer effect on electron-transfer kinetics measured by scanning electrochemical microscopy (SECM)[END_REF] or when partial blocking of the electrode is associated to the electrochemical process [START_REF] Chen | Self-Inhibitory electron transfer of the Co(III)/Co(II)-complex redox couple at pristine carbon electrode[END_REF][START_REF] Amatore | Charge Transfer at Partially Blocked Surfaces. A Model for the Case of Microscopic Active and Inactive Sites[END_REF][START_REF] Sliusarenko | Validating a Central Approximation in Theories of Regular Electrode Electrochemical Arrays of Various Common Geometries[END_REF][START_REF] Sliusarenko | Development and Validation of an Analytical Model for Predicting Chronoamperometric Responses of Random Arrays of Micro-and Nanodisk Electrodes[END_REF][START_REF] Sliusarenko | Importance of Stochastic Limitations in Electrochemistry at Arrays of Nanoelectrodes Functionalized by Redox Self-Assembled Monolayers[END_REF]. Note that this involves a different kind of stochastic problem than those considered in the case of single molecule electrochemistry.

To conclude this section we want to discuss two linked major problems in voltammetric experiments especially when compared with simulations. This concerns the effect of ohmic drop and time constant (or the way of correcting the distortions they induce [57]). Indeed, to simulate the effect of ohmic drop and time constant, commercial simulation programs such as DigiSim © or DigiElec © consider a classical RC series circuit where C is a pure capacitive element featuring the double layer capacitance acting in parallel to the Faradic impedance and R represents the uncompensated solution resistance, i.e., that between the working and reference electrodes (see Figure 1A). However, it is enough to consult the voltammetric literature to understand that, except for a few exploited cases, the assumption of a constant double layer capacitance over a potential range suited to voltammetric investigations is a myth, even when the voltammetric range is set sufficiently far away from the point of zero-charge. This is the main reason why such pseudo-corrections have not been implemented in KISSA © .

In fact under most experimental conditions the double layer capacitance is best represented by a constant phase element (CPE) [START_REF] Charoen-Amornkitt | Ohmic resistance and constant phase element effects on cyclic voltammograms using a combined model of mass transport and equivalent circuits[END_REF][START_REF] Aoki | Effects of the dipolar double layer on elemental electrode processes at micro-and macro-interfaces[END_REF]. Though CPE double layer capacitances are seldom considered in rationalizing voltammetric experiments, CPEs are now widely accepted and used to model electrical equivalent circuits in electrochemical impedance spectroscopy [START_REF] Hirschorn | Determination of effective capacitance and film thickness from constant phase-element parameters[END_REF]. Incorrectly predicted ohmic drop and capacitive background may have severe consequences on the interpretation of transient voltammetric data as soon precise measurements are sought [START_REF] Charoen-Amornkitt | Ohmic resistance and constant phase element effects on cyclic voltammograms using a combined model of mass transport and equivalent circuits[END_REF]. This clearly claims for the integration of CPEs in finite difference numerical simulation programs able to treat any complex mechanistic sequence.

Conclusion

The increasing availability of nanoscale technologies or of new electrolytes has allowed precise and accurate experimental investigations of electrochemical systems under conditions that would have been unthinkable two decades ago. However, these experiments are most often rationalized using theoretical concepts that were invented and refined for making sense of situations corresponding to much larger time and space scales and involving much larger numbers of molecules or ions. Ironically, the outcomes of such discordant views produces results that look perfectly adequate, at least up to the moment one starts to interrogate the meaning of the values extracted for the usual electrochemical parameters. In this short opinion paper we illustrated three typical cases in which, despite the huge number of published experimental data, new theoretical concepts need to be implemented. This paper validated the use of Brownian dynamics simulations for investigating double layer relaxation after electron transfer as well as the importance of capacitive coupling. 25 Compare for example the anti-correlated current traces in Figures 1 and4 in reference [START_REF] Kang | Electrochemical singlemolecule detection in aqueous solution using self-aligned nanogap transducers[END_REF],

in Figures 1d, 2 and 3 in reference [START_REF] Kang | Single-molecule electrochemistry in nanochannels: probing the time of first passage[END_REF] or in Figure 6 • This paper provides a first and elegant analytical approach to the problem discussed in this section based on analytical probabilities when the potential difference E between the two electrodes is kept constant. Interestingly, it establishes that (i) the average time duration of a complete redox cycle (i.e., forward electron transfer followed by its backward one at the second electrode) is given by the classical result L 2 /D (where L is the electrodes distance and D is the diffusion coefficient), and (ii) that an average limiting current is reached at large │E│ values and whose expression is the same as for a generator-collector macrodevice.

Figure 2 (

 2 Figure 2

  27 Kätelhön E, Wolfrum B: Simulation-based investigations on noise characteristics of redoxcycling sensors. Phys. Status Solidi A 2012, 209: 881-884. 28 See e.g.: Balme S, Picaud F, Lepoitevin M, Bechelany M, Balanzatc E, Janota JM: Unexpected ionic transport behavior in hydrophobic and uncharged conical nanopores. Faraday Discuss. 2018, Advance Article (DOI: 10.1039/c8fd00008e). 29 • Nazmutdinov RR, Bronshtein MD, Zinkicheva TT, Glukhov DV: Modeling of electron transfer across electrochemical interfaces: State-of-the art and challenges for quantum and computational chemistry. Int. J. Quantum Chem. 2016, 116: 189-201. 30 • Futera Z, Sodeyama K, Burda JV, Einaga Y, Tateyama Y: A double-QM/MM method for investigating donor-acceptor electron-transfer reactions in solution. Phys. Chem. Chem. Phys. 2014, 16: 19530-19539. • These two papers propose interesting elements for possible solutions to the problems discussed in the text. 31 For an early review, see e.g.: Silvester DS, Compton RG: Electrochemistry in room temperature ionic liquids: a review and some possible applications. Zeitschrift für Physikalische Chemie 2006, 220: 1247-1274. 32 Simon P, Gogotsi Y: Materials for electrochemical capacitors. Nat. Mater. 2008, 7: 845-854.

Relaxation of the electrical double layer after an electron transfer approached by Brownian dynamics simulation

  23 One excellent volume of Faraday Discussions has been devoted to this topics (FaradayDiscuss. 2016, 193); see a summary of the various topics discussed in: Crooks RM:

	Concluding remarks: single entity electrochemistry one step at a time. Faraday Discuss.
	2016, 193: 533-547.
	24 • Grün F, Jardat M, Turq P, Amatore C: . J. Chem. Phys. 2004, 120:
	9648-9655.

Current Response for a Single Redox Moiety Trapped in a Closed Generator-Collector System: The Role of Capacitive Coupling

	in: Kostiuchenko ZA, Glazer PJ, Mendes
	E, Lemay SG: Chemical physics of electroactive materials -the oft-overlooked faces of
	electrochemistry. Faraday Discuss. 2017, 199: 9-28.
	26 •• Feldberg SW, Edwards MA:

. Anal. Chem. 2015, 87: 3778-3783.

Acknowledgments

This work was supported in parts by CNRS, ENS, Sorbonne University and PSL University (UMR 8640 PASTEUR). CA acknowledges Xiamen University for his position of Distinguished Professor.


Xin-Wei Zhang

Alexander Oleinick

Hong Jiang

Quan-Lan Liao

Quan-Fa Qiu

Irina Svir

Yan-Ling Liu

Christian Amatore
email: christian.amatore@ens.fr

Wei-Hua Huang
email: whhuang@whu.edu.cn

Electrochemical Monitoring of ROS/RNS Homeostasis Within Individual Phagolysosomes Inside Single Macrophages

Reactive Oxygen/Nitrogen Species (ROS/RNS) produced by macrophages inside their phagolysosomes are closely related to immunity and inflammation by being involved in the removal of pathogens, altered cells, etc. The existence of a homeostatic mechanism regulating the ROS/RNS amounts inside phagolysosomes has been invoked to account for the efficiency of this crucial process but this could never be unambiguously documented. In this work, intracellular electrochemical analysis with platinized nanowires electrodes (Pt-NWEs) allowed monitoring ROS/RNS effluxes with sub-millisecond resolution from individual phagolysosomes randomly impacting onto the electrode inserted inside a living macrophage. This evidenced for the first time that the consumption of ROS/RNS by their oxidation at the nanoelectrode surface stimulates the production of significant ROS/RNS amounts inside phagolysosomes. These results established the existence of the long-time postulated ROS/RNS homeostasis and allowed quantifying its kinetics and efficiency. ROS/RNS concentrations may then be maintained at sufficiently high levels for sustaining proper pathogen digestion rates without endangering the macrophage internal structures.

Macrophages are essential in protecting our body against bacteria, viruses and mutant or abnormal cells. [1] They detect and internalize such pathogens within endocytotic vesicles named phagosomes. These are carried inside the macrophages cytoplasm where they merge with lysosomes, another kind of vesicle, whose membranes host a panoply of enzymes including NADPH oxidase 2 (NOX2) and inducible nitric oxide synthase (iNOS) prone to release reactive oxygen/nitrogen species (ROS/RNS) inside the resulting phagolysosomes. This allows the biological cargoes carried by the initial phagosomes to be broken down to the molecular level. [2] To ensure a complete digestion of these pathogens the quantities of ROS/RNS present inside phagolysosomes must be sufficient without being excessively high to prevent their leakage and accumulation inside macrophages cytoplasm. [3] This dual requirement suggested the presence of some feedback mechanism operating inside phagolysosomes in order to ensure a ROS/RNS homeostasis. [4] . Such hypothesis was recently shown to be coherent with the outcome of long-time (minutes) electrochemical monitoring of ROS/RNS fluxes produced inside phagolysosomes of RAW 264.7 murine macrophages stimulated by Lipopolysaccharides (LPS) and Interferon-γ (IFN-γ). [5] However, to the best of our knowledge, the monitoring of ROS/RNS production inside phagolysosomes with the sub-millisecond time resolution required to establish the very existence of a fast homeostatic regulation could never be achieved before the present work.

Nanoelectrochemical monitoring of intracellular ROS/RNS at the single cell level is a very efficient and quantitative method that has been applied in cancer cells, [6] macrophages [4,5,7] and neurons. [8] We recently reported the fabrication of a novel kind of platinized nanowire SiC@C electrodes (Pt-NWEs) and demonstrated their perfect suitability to analyze ROS/RNS inside single phagolysosomes of living macrophages. [9] Phagolysosomes may then randomly collide onto the surface of a Pt-NWE inserted into a macrophage cytoplasm (Figure 1A). This situation is identical to that which operates during vesicle impact electrochemical cytometry (VIEC), a method initially introduced for quantifying neurotransmitters amounts in liposomes and exocytotic vesicles. [10] The high electric field prevailing at the electrode surface over nanometric distances is more than enough for electroporating bilipidic membranes. [10] ROS/RNS contained in phagolysosomes may then spill onto the Pt surface through the ensuing pore and be oxidized giving rise to individual amperometric spikes (Figure 1B).

By analogy to the release of neurotransmitters [11,12] it is expected that in the absence of any ROS/RNS homeostasis all recorded spikes display three main features: (i) a small pre-spike feature evidencing the initial opening of the pore followed by (ii) a rapid increase of the current due to the rapid expansion of the pore up to its maximum size, and (iii) finally an exponentially decaying branch (Figure 1D) representing the diffusion-limited emptying of the initial ROS/RNS content. However, only 25% of the events (N = 1040) presented this expected pattern [10,11,12] (Figures 1D,2C). The large majority (75%) of spikes displayed the anticipated behavior only up to a given point (t < texp in Figure 2A, S2A, C) located on their descending branch. The current then significantly deviated from their expected exponential falloff.

In VIEC experiments exocytotic vesicles or liposomes may only release their initial load of electroactive molecules. [10,11,12] However, phagolysosomes are not inert containers. Their membranes are equipped with pre-assembled NOX2 and iNOS enzymes that are likely to be activated to swiftly produce ROS/RNS at least while phagolysosomes keep their functionality after being electroporated. In other words, the unexpected behavior displayed by 75% of the events could be the first quantitative evidence of the long-time purported homeostatic activity, provided it is established that the current shoulders correspond to ROS/RNS oxidation. This is fully consistent with a recent report by some of us showing that intact phagolysosomes could produce NO and O2 •-under near steady-state conditions over time durations exceeding tens of minutes. [5] However, if the present Pt-NWEs provided an exceptional time resolution in vivo compared to those used in ref. [5], they could not allow a complete chemical characterization of the efflux giving rise to the current shoulders during the short time life of electroporated phagolysosomes. [13] Instead, a biochemical approach was implemented by taking advantage that NOX2 and iNOS enzymes may be selectively inhibited by diphenylene-iodonium chloride (DPI) or N G -monomethyl-L-arginine monoacetate salt (L-NMMA) respectively. Macrophages treated with DPI and L-NMMA immediately before the intracellular insertion of a Pt-NWE afforded much fewer and smaller spikes per unit of time. More importantly, their spikes displayed perfect exponential decay branches (Figure 2C). This confirmed that the species responsible for the current shoulders of spikes observed in absence of inhibitors (Figure 2A,B) consisted in freshly produced ROS/RNS. Together with the observations reported in ref. [5] this brings strong evidences that phagolysosomes are equipped with efficient means of regulating their intravesicular ROS/RNS content at optimum levels.

For quantitatively investigating the kinetics and intensity of the underlying mechanism we adapted a previous theoretical model [10i, 11f, 12] developed for rationalizing the kinetics of neurotransmitters release. This allows assessing the ROS/RNS quantities present inside one phagolysosome of released by it in terms of the electrical charge that they deliver upon oxidation at the Pt-NWE surface rather than in moles. The two quantities are proportional through the Faraday law. Herein, the time-dependent quantity of ROS/RNS, [14] Qin(t), present at time t inside the phagolysosome is then formulated as: [12c] 𝑘 𝑄 𝑡 1 where 𝑄 t is a time-dependent kinetic term accounting for the ROS/RNS production inside the phagolysosome during release; 𝑘 is a pseudo-rate constant featuring the diffusion-controlled release out of the phagolysosome pore of time-dependent radius (t). [12c] The current, i(t), featuring the ROS/RNS oxidation at the Pt-NWE surface is then: [12c] 𝑖 t 𝑘 𝑄 t 2

Introducing Eqn (2) into Eqn ( 1) and integrating affords Eqn (3):

𝑄 t 𝑄 t 𝑄 𝑖 τ dτ ( 3
)
where Q0 is the initial ROS/RNS content, i.e., that contained in the phagolysosome just before it is electroporated. [10h,i,j] 𝑄 ∞ , the limit achieved by 𝑄 t at the end of the spike represents the total ROS/RNS quantity that has been produced by the phagolysosome while it could maintain its functions after being electroporated (Figure 2B). Q0 and 𝑘 are intrinsic characteristics of each individual phagolysosome so they are not known a priory. Even so, they can be determined from the theoretical reconstruction of the variations of the spike current when Qprod(t) is negligible, i.e., for t < texp (Figure 2A). Indeed, the theoretical procedure previously developed to account for the treatment of vesicular exocytosis is then readily applicable based on Eqns (1,2). [12c] The outcome of this procedure is evidenced by the orange curves reconstructed and extrapolated in Figures 2A,C. (see more detailed description in SI and Figure S1 in SI for the extracted 𝑘 time-variations for the spikes shown in Figures 2A,C). Q0 and 𝑘 being then known, Eqn (3) immediately affords the time variations of Qprod(t) (Figures 2B,D) whose time derivative gives (Figures 2A,C). This evidenced that for all 75% spikes exhibiting shoulder signals the homeostatic process was activated less than 1 ms after the beginning of release and led to 𝑄 ∞ values ranging between ca. one third and one half of the initial content Q0 (Table S2, Figure 2B). Conversely, for the remaining 25% spikes Qprod(t) resulted negligible compared to background current fluctuations (Fig. 1D; compare Figs. 2C,D).

The same procedure was used to compare the homeostatic performances of different phenotypes of RAW 264.7 murine macrophages, i.e., in the resting stage (M0 type) or after their 24h incubation (M1 type) with LPS/IFN-γ. [4,5,15,16] Both phenotypes exhibited extremely different morphologies and diverse mean intracellular ROS/RNS concentrations as revealed, respectively, by bright-field microscopy and DCFH-DA fluorescent staining (see insets in Figure 3A). [START_REF]cytoplasm of M0 (N=9) and M1 (N=11) were twice larger in M1 cells. These data were obtaind from different series of experiments, and the cell numbers are not the same as listed in Figure 3B, C. Based on the results in refs[END_REF] S2). S2 evidenced that the mean Q0 value for M1 cells (18 fC) was nearly double that (9.1 fC) for M0 cells. [START_REF]The "mean" values reported in the text correspond to the mean values of the logarithmic charges values since all quantities (Imax, Qspike, Q0 and Q ∞ ) obeyed log-normal distributions[END_REF] The same occurred for the homeostatic efficiency as indicated by 𝑄 ∞ values (6.1 fC for M1 cells versus 3.1 fC for M0 ones). [START_REF]The "mean" values reported in the text correspond to the mean values of the logarithmic charges values since all quantities (Imax, Qspike, Q0 and Q ∞ ) obeyed log-normal distributions[END_REF] These quantitative differences confirm that LPS/IFN-γ activated macrophages contain phagolysosomes generating higher initial level of ROS/RNS (Q0) and equipped with more efficient biological means for maintaining their homeostasis ( 𝑄

Figures 3B, C and Table

∞

). This may be tentatively ascribed to an up-regulation of enzymes due to the LPS/IFN-γ treatment. [19] In conclusion, this work reported an easily implemented and very efficient experimental and theoretical strategy for quantitative monitoring of ROS/RNS content and production by individual phagolysosomes over sub-millisecond time-scales. This unambiguously unraveled for the first time the existence of a fast ROS/RNS homeostasis and allowed characterizing quantitatively its efficiency under different conditions. We believe that this electrochemical strategy will allow deeper quantitative understanding of phagocytosis.

Figure 1 .

 1 Figure 1. A) Schematic principle of electrochemical detection of ROS/RNS spilling out individual phagolysosomes with a platinized SiC@C nanowire electrode (Pt-NWE) inserted into the cytoplasm of a single macrophage (the pink-colored area at the tip of the NWE symbolizes the black-Pt electroactive coating). B) Typical amperometric trace recorded in a RAW 264.7 murine macrophages. C, D) Magnified resolution of the two representative spikes marked by the dashed rectangles in B. C) spike displaying a clear shoulder superimposed onto its exponential decay branch (75% of events); D) spike displaying a characteristic exponential decay branch (25% of events) as expected in the absence of ROS/RNS homeostatic mechanism. The orange hatched areas in (C, D) represent the contributions of the expected releasing behavior in absence of homeostasis while the green hatched one in (C) represents the superimposed homeostatic contribution (see text and Fig. 2).

Figure 2 .

 2 Figure 2. Typical spikes recorded at Pt-NWEs from phagolysosomes (RAW 264.7 murine macrophages) displaying an efficient ROS/RNS homeostasis (A, and two more examples are shown in Figure S2) or after inhibition by DPI and L-NMMA (C), some quantitative data are listed in TableS1. The corresponding charges are displayed in B) for (A), and D) for (C). In all figures the untreated experimental data are shown in black circles. The orange dashed curves in A) and C) are the reconstructed spikes assuming no homeostasis. The green dashed curves provide the computed rates of ROS/RNS homeostatic production in A) and C) or the corresponding charges in B) and D) respectively. The dashed vertical line in A) marks the instant, texp, at which an efficient production of fresh ROS/RNS began.

Figure 3 .

 3 Figure 3. A) Typical amperometric traces recorded inside M0 (upper) or M1 (lower) RAW 264.7 murine macrophages; the same scale bar applies to the two amperometric traces; the arrows indicate the moments of insertion of Pt-NWEs. Insets: optical microphotographs of macrophages (BF: bright field; FL: fluorescence after staining with DCFH-DA); scale bars: 25 μm. B, C) Distribution of the logarithms of initial, Q0 (B) and freshly produced, 𝑄 ∞ (C) charges recorded for the M0 (black, 909 spikes from 15 cells) and M1 (red, 127 spikes from 5 cells) phenotypes; arrows indicate the average values (see quantitative details in TableS2).

Acknowledgements

In China, this work was supported by the National Natural Science Foundation of China (Grants 21725504, 21675121, and 21721005), the University of Xiamen and the State Key Laboratory of Physical Chemistry of Solid Surfaces (PCOSS, University of Xiamen, China) through a Distinguished Scientist Chair awarded to C.A. In France, it was supported in part by PSL University, École Normale Supérieure, CNRS, and Sorbonne University (UMR 8640). Both teams gratefully acknowledge the CNRS Sino-French support (LIA "NanoBioCatEchem").

Keywords: nanoelectrode amperometry • phagolysosomes • ROS/RNS production • homeostasis


Alain ; Dejean
email: alain.dejean@wanadoo.fr

Arthur Compin

Jacques H C Delabie

Frédéric Azemar

Bruno Corbara

Maurice Leponce

Frédéric Azémar

Biotic and abiotic determinants of the formation of ant mosaics in primary Neotropical rainforests

Keywords: ant mosaics, connections on the ground, host tree attractiveness, indicators of disturbance, primary Neotropical rainforest, territoriality ant mosaics, connections on the ground, host tree attractiveness, indicators of disturbance, primary Neotropical rainforest, territoriality

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Introduction

Ants dominate the fauna of tropical rainforest canopies both in terms of biomass and number of individuals, an ecological success possible thanks to their entirely or partially herbivorous diet as they feed on extrafloral nectar, food bodies and hemipteran honeydew [START_REF] Blüthgen | Bottom-up control and co-occurrence in complex communities: honeydew and nectar determine a rainforest ant mosaic[END_REF][START_REF] Davidson | Explaining the abundance of ants in lowland tropical rainforest canopies[END_REF]. Yet, only a limited number of ant species with large colonies are concerned, something corresponding to the notion of 'numerical dominance' (the predominance of a species in frequency of occurrence in the ant community). When combined with 'behavioral dominance' (dominance in interspecific competition due to superior fighting and/or recruitment abilities) this results in 'ecological dominance' (see [START_REF] Davidson | Resource discovery versus resource domination in ants: a functional mechanism for breaking the trade-off[END_REF].

Certain canopy ants correspond rather to the latter case as they are characterized by very populous colonies of up to several million workers, large and/or polydomous nests (see Fig. 1), and an absolute intra-and interspecific territoriality so that they are called 'territorially dominant arboreal ant species' (TDAAs) [START_REF] Majer | Comparison of the arboreal ant mosaic in Ghana, Brazil, Papua New Guinea and Australia: its structure and influence of ant diversity. Hymenoptera and Biodiversity[END_REF].

Two TDAAs can share the same territory (i.e., 'co-dominance') when they have complementary rhythms of activity (i.e., one is diurnal, the other is nocturnal), when their workers avoid each other with only occasional conflicts for food, or during "parabiosis" (i.e., two species share the same territories and nests, but lodge in different cavities of these nests) [START_REF] Majer | Comparison of the arboreal ant mosaic in Ghana, Brazil, Papua New Guinea and Australia: its structure and influence of ant diversity. Hymenoptera and Biodiversity[END_REF][START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF][START_REF] Dejean | The ecology and feeding habits of the arboreal trap-jawed ant Daceton armigerum[END_REF][START_REF] Vicente | Defining habitat use by the parabiotic ants Camponotus femoratus (Fabricius, 1804) and Crematogaster levior Longino[END_REF]Yusha et al., 2017). TDAAs tolerate within their territories the presence of 'non-dominant' species with small colonies that represent only ≈5% of the ant biomass and individuals, but are species-rich (e.g., 43 species on one tree; 85 species on two trees) [START_REF] Hölldobler | Journey to the ants: a story of scientific exploration[END_REF][START_REF] Tobin | Competition and coexistence of ants in a small patch of rainforest canopy in Peruvian Amazonia[END_REF].

Exceptionally, colonies of non-dominant ants can become large enough to occupy and defend the crown of a tree; they are then called 'subdominants' [START_REF] Majer | Comparison of the arboreal ant mosaic in Ghana, Brazil, Papua New Guinea and Australia: its structure and influence of ant diversity. Hymenoptera and Biodiversity[END_REF][START_REF] Majer | Arboreal ant community patterns in Brazilian cocoa farms[END_REF]. 4 When the tree crowns are contiguous or interconnected by liana, the TDAAs' territories are distributed in a mosaic pattern creating what has become known as 'arboreal ant mosaics' [START_REF] Majer | The ant mosaic in Ghana cocoa farms[END_REF][START_REF] Majer | Comparison of the arboreal ant mosaic in Ghana, Brazil, Papua New Guinea and Australia: its structure and influence of ant diversity. Hymenoptera and Biodiversity[END_REF]. Ant mosaics have been noted in the upper canopies of tropical African, Asian, Bornean, New Guinean and Neotropical rainforests and tree crop plantations [START_REF] Majer | Comparison of the arboreal ant mosaic in Ghana, Brazil, Papua New Guinea and Australia: its structure and influence of ant diversity. Hymenoptera and Biodiversity[END_REF][START_REF] Adams | Territory defense by the ant Azteca trigona: maintenance of an arboreal ant mosaic[END_REF][START_REF] Armbrecht | An ant mosaic in the Colombian rain forest of Chocó (Hymenoptera: Formicidae)[END_REF][START_REF] Blüthgen | Ant mosaics in a tropical rainforest in Australia and elsewhere: a critical review[END_REF][START_REF] Davidson | Tropical ant mosaic in a primary Bornean Rain Forest[END_REF][START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF][START_REF] Dejean | Spatial distribution of dominant arboreal ants in a Malagasy coastal rainforest: gaps and presence of an invasive species[END_REF][START_REF] Dejean | How territoriality and host-tree taxa determine the structure of ant mosaics[END_REF]Dejean et al., , 2018;;[START_REF] Pfeiffer | Exploring arboreal ant community composition and cooccurrence patterns in plantations of oil palm (Elaeis guineensis) in Borneo and Peninsular Malaysia[END_REF][START_REF] Fayle | Ant mosaics occur in SE Asian oil palm plantation but not rain forest and are influenced by the presence of nest-sites and non-native species[END_REF][START_REF] Ribeiro | Competition, resources and the ant (Hymenoptera: Formicidae) mosaic: a comparison of upper and lower canopy[END_REF][START_REF] Klimes | Diversity and specificity of ant-plant interactions in canopy communities: insights from primary and secondary tropical forests in New Guinea. Ant-plant interactions: impacts of humans on terrestrial ecosystems[END_REF][START_REF] Yusah | Lecythidaceae Eschweilera grandiflora 11M103 Daceton armigerum Boraginaceae Cordia sp. 11M104 Crematogaster stollii, Ectatomma tuberculatum Cecropiaceae Cecropia obtusa (LD) 11M105 Azteca ovaticeps Cecropiaceae Pourouma sp. (LD) 11M106 Crematogaster stollii, Ectatomma tuberculatum Mimosoideae Inga melinonis (LD) 11M107 Dolichoderus bidens Lecythidaceae Eschweilera grandiflora 11M108 Dolichoderus bidens Lecythidaceae Eschweilera grandiflora 11M109 Crematogaster stollii Malvaceae Sterculia sp. (LD) 11M110 Daceton armigerum Caesalpinioideae Pseudopiptadenia suaveolens 11M111 Da. armigerum, Az. instabilis, Cre. levior, Para. clavata, Cre. stollii Sapotaceae Micropholis guyanensis 11M112 Camponotus femoratus, Crematogaster levior Malvaceae Sterculia sp. (LD) 11M113 Camponotus femoratus, Crematogaster levior Malvaceae Sterculia sp. (LD) 11M114 Crematogaster stollii Lecythidaceae Couratari guianensis 11M115 Crematogaster stollii Cecropiaceae Cecropia obtusa (LD) 11M116 Azteca ovaticeps Cecropiaceae Cecropia obtusa (LD) 11M117 Azteca ovaticeps Meliaceae Carapa sp. 11M118 Camponotus femoratus, Crematogaster levior, Paraponera clavata Lauraceae sp. 11M119 Camponotus femoratus, Crematogaster levior Caesalpinioideae Parkia nitida 11M120 Camponotus femoratus, Crematogaster stollii Boraginaceae Cordia sp. 11M121 Crematogaster stollii, Ectatomma tuberculatum Sapotaceae Pouteria eugeniifolia 11M124 Camponotus femoratus, Crematogaster levior Apocynaceae Aspidosperma marcgravianum 11M125 Camponotus femoratus, Crematogaster levior, Paraponera clavata Caesalpinioideae Vouacapoua americana 11M126 Azteca jelskii, Crematogaster levior, Ectatomma tuberculatum Caesalpinioideae Vouacapoua americana 11M128 Azteca instabilis, Crematogaster levior, Daceton armigerum Mimosoideae Inga capitata (LD) 11M129 Crematogaster levior Mimosoideae Inga flagelliformis (LD) 11M130 Camponotus femoratus, Crematogaster levior References[END_REF][START_REF] Leponce | Tree-dwelling ant survey (Hymenoptera, Formicidae) in Mitaraka, French Guiana[END_REF]. Nevertheless, ant mosaics are often absent from the 'sub-canopy' likely due to the scarcity of hemipterans whose honeydew is necessary to fuel the TDAA colonies [START_REF] Floren | Do ant mosaics exist in pristine lowland rain forests?[END_REF][START_REF] Blüthgen | Ant mosaics in a tropical rainforest in Australia and elsewhere: a critical review[END_REF][START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF]Dejean et al., , 2018;;[START_REF] Ribeiro | Competition, resources and the ant (Hymenoptera: Formicidae) mosaic: a comparison of upper and lower canopy[END_REF]. Yet, very large TDAAs colonies can occupy vast spaces involving all canopy growth stages [START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF][START_REF] Klimes | Disentangling the diversity of arboreal ant communities in tropical forest trees[END_REF].

Founding queens do not install their colony by chance in tree crowns as selective plant attractiveness has been shown experimentally for both plant-ants and TDAAs (Djiéto-Lordon & Dejean, 1999a,b). Although tempered by the extension of the territories over adjacent trees (of different species) with the increasing size of the TDAAs' colonies, this effect remains perceptible [START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF][START_REF] Dejean | How territoriality and host-tree taxa determine the structure of ant mosaics[END_REF](Dejean et al., , 2018;;[START_REF] Fayle | Experimentally testing and assessing the predictive power of species assembly rules for tropical canopy ants[END_REF]. Also, an ontogenetic succession of ant species follows the sequence of stages in tree and vegetal formation development [START_REF] Watt | The diversity and abundance of ants in relation to forest disturbance and plantation establishment in southern Cameroon[END_REF][START_REF] Kenne | Influence of insecticide treatments on ant-hemiptera associations in tropical plantations[END_REF]da Conceição et al., 2015;[START_REF] Dejean | The dynamics of ant mosaics in tropical rainforests characterized using the Self-Organizing Map algorithm[END_REF]. Finally, the forest structure plays a role in the formation of ant mosaics. For example, tropical African rainforests have proportionately more 'large' trees (i.e., tall with a wide trunk and a large crown) than do the tropical forests of other continents, likely due to fewer disturbances over recent decades [START_REF] Lewis | Above-ground biomass and structure of 260 African tropical forests[END_REF]; see projections of African trees in Fig. 2). This explains why the Neotropical rainforest canopies are frequently irregular with tree crowns at different heights likely resulting from treefall gaps, breaking the continuity of the territories of the TDAAs [START_REF] Ribeiro | Competition, resources and the ant (Hymenoptera: Formicidae) mosaic: a comparison of upper and lower canopy[END_REF].

F o r R e v i e w O n l y
5 Studying ant mosaics is important because TDAAs prevent attended hemipterans from proliferating [START_REF] Styrsky | Ecological consequences of interactions between ants and honeydew-producing insects[END_REF] and protect their host trees from defoliating insects through their predatory behavior or by deterring them either actively or simply through the presence of their long-lasting landmarks [START_REF] Majer | Comparison of the arboreal ant mosaic in Ghana, Brazil, Papua New Guinea and Australia: its structure and influence of ant diversity. Hymenoptera and Biodiversity[END_REF][START_REF] Dyer | A quantification of predation rates, indirect positive effects on plants, and foraging variation of the giant tropical ant, Paraponera clavata[END_REF][START_REF] Floren | Arboreal ants as key predators in tropical lowland rainforest trees[END_REF][START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF]Offenberg et al., 2007).

Ant mosaics can be impacted by canopy gaps created by the death of a tree or the fall of trees by snapping or uprooting due to strong winds that are considered small-scale natural

disturbances. An indirect impact also occurs during the formation of large gaps as they permit light-demanding tree species with low wood density (e.g., pioneer trees) to develop quickly from seeds [START_REF] Schnitzer | Treefall gaps and the maintenance of plant species diversity in tropical forests[END_REF].

In this study, conducted in a primary moist Neotropical rainforest situated in French Guiana, we aimed to determine: (1) if an ant mosaic exists in the upper canopy, (2) if TDAA workers follow trails on the ground that interconnect neighboring trees to compensate the irregularity of the canopy or if they use underground galleries, (3) if the host tree taxa influence the TDAAs' distribution and (4) if locally strong winds due to the neighboring presence of an inselberg affect the distribution of the TDAAs, favoring certain of them.

Materials and methods

Study site, tree mapping and identification

The Nouragues Ecological Research Station (4°05' N -52°41'W), dominated by a partly denuded Inselberg (430 asl), is located within the Montagnes Balenfois massif typical of the Guiana Shield. The radiocarbon dating of charcoal and pollen coring suggest that the forest cover has remained intact over at least 3000 years, but with fires occurring ≈500 years ago. A variety of vegetal formations occur within a radius of 1.5 km, including: (1) the inselberg's

F o r R e v i e w O n l y 6 summit,
(2) a low transition forest, (3) a wide, forested plateau, and (4) a liana forest whose origin might be due to strong winds or a microtornado. The climate is moist tropical, with a mean annual rainfall of 3000 mm distributed over ≈280 days; the daily mean temperature ranges from 20.3°C to 33.5°C [START_REF] Grimaldi | Geography and climate. Nouragues. Dynamics and plant-animal interactions in a Neotropical Rainforest[END_REF][START_REF] Tymen | Evidence for arrested succession in a liana-infested Amazonian forest[END_REF].

In the Nouragues area, strong winds, likely due to the vicinity of the Inselberg, generated on the plateau the formation of a liana forest and large gaps. Liana forests, caused by windthrow events resulting in > 1ha gaps, generally persist for a long time, blocking the forest succession (van der Meer & Bonger, 1996;[START_REF] Stefan | Lianas suppress tree regeneration and diversity in treefall gaps[END_REF][START_REF] Tymen | Evidence for arrested succession in a liana-infested Amazonian forest[END_REF]. Field studies were conducted on the plateau (2006)(2007)(2008)(2009)(2010) where the staff of the Nouragues Ecological Research Station has established grid trails every 100 m, creating 1 ha forest plots over 70 ha; the trees have been mapped, measured, tagged and identified [START_REF] Poncy | The lowland high rainforest. Structure and tree species diversity. Nouragues. Dynamics and plant-animal interactions in a Neotropical Rainforest[END_REF].

Canopy access, gathering TDAA samples and mapping the ant mosaic

We used the single rope technique to reach the upper canopy tree crowns, permitting us to gather samples from 157 trees. To collect ant samples, we cut off two to four branches (10-15 cm in diameter) from each tree. Because arboreal ants mark these branches as part of their territories (i.e., the workers deposit ''landmarks'' that can last for more than 1 year; Beugnon [START_REF] Beugnon | Adaptive properties of the chemical trail system of the African weaver ant[END_REF]Offenberg, 2007), several dozen to thousands of workers remained on them for more than 1 hour after the sectioning of the branches [START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF][START_REF] Dejean | Spatial distribution of dominant arboreal ants in a Malagasy coastal rainforest: gaps and presence of an invasive species[END_REF][START_REF] Dejean | How territoriality and host-tree taxa determine the structure of ant mosaics[END_REF].

Using entomological aspirators, we were thus able to collect samples of the ants crawling on the fallen branches or hidden in hollow twigs.

In contrast to trapping methods permitting large numbers of species to be collected, this branch clipping method allows us to sample numerically dominant ants and obtain information on the co-occurrence of these species on the same branches, and so interspecific 1).

F o r R e v i
The presence of arboreal ant trails on the ground was noted during a sampling of litterdwelling ants in the area studied [START_REF] Groc | Leaf-litter ant communities in a pristine Guianese rainforest: stable functional structure versus high species turnover[END_REF]. We therefore verified if the trails interconnected the bases of different trees and if certain workers transported brood and nestmates from one tree to another (see [START_REF] Orivel | Ant activity rhythm in a pioneer vegetal formation of French Guiana[END_REF]. As most of the TDAAs in the area are diurnal, each hour between 8:00 and 18:00 during five non-consecutive sunny days, we walked along the same path that was chosen because it passed between trees whose canopies were not in contact whereas they share the same TDAAs. Because E. tuberculatum and Crematogaster stollii use underground galleries to connect trees (Table 1) when one or the other species was noted on groups of trees we sought to determine if these trees belonged to the same colony. We thus sprayed paint on workers from one nest (from ≈60 cm so that each ant had only some spots) and verified during the three next days if ants with spots of paint were present on the adjacent trees. For E. tuberculatum, we unearthed a nest from the base of a tree and sprayed blue paint as the workers are yellowish. For Cr. stollii, we opened galleries at the base of a tree and sprayed yellow paint as the workers are black; the verification required opening galleries of adjacent trees. All these techniques permitted us to pinpoint the exact limits of the TDAAs' territories, allowing the precise mapping of these territories (Fig. 2). Ant samples were preserved in 70% ethanol for later identification; voucher specimens were deposited in the Laboratório de Mirmecologia, UESC/CEPLAC, Ilhéus, Bahia, Brazil and in the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.

F o r R e v i e w O n l y 8
Rarefaction curves of tree and ant assemblages Diversity statistics were calculated using EstimateS 9.1 software [START_REF] Colwell | EstimateS: statistical estimation of species richness and shared species from samples[END_REF] with 100 randomizations of the sampling order without replacement. To estimate sampling completeness, the Chao1 (tree data, abundance-based) and Chao2 (ant data, occurrence-based) non-parametric estimators of total species richness were calculated [START_REF] Colwell | Interpolating, extrapolating, and comparing incidencebased species accumulation curves[END_REF].

Because ant mosaics correspond to non-random patterns of co-occurrence related to the mutual exclusion of TDAAs, we used a fixed-equiprobable null model and the C-score cooccurrence index with the sequential swap algorithm and 5, 000 iterations available in the EcoSim software [START_REF] Gotelli | EcoSim: Null models software for ecology. Version 7. Acquired Intelligence Inc. & Kesey-Bear[END_REF][START_REF] Blüthgen | Ant mosaics in a tropical rainforest in Australia and elsewhere: a critical review[END_REF][START_REF] Fayle | Ant mosaics occur in SE Asian oil palm plantation but not rain forest and are influenced by the presence of nest-sites and non-native species[END_REF].

The fixed-equiprobable algorithm maintains the species occurrence frequencies and considers all sites (trees) equiprobable [START_REF] Gotelli | Null model analysis of species co-occurrence patterns[END_REF]. The C-score index used in combination with the fixed-equiprobable algorithm generally has good statistical properties and is not prone to false positives [START_REF] Gotelli | Null model analysis of species co-occurrence patterns[END_REF]. Specific associations between the most frequent ant species (i.e., present on more than 10% of the 157 trees sampled) were tested using Chi-square tests with Yates' correction. When field observations revealed that a single tree crown belonged to two different territories (n= 7 cases), the species involved were encoded separately in the cooccurrences matrix (the whole results in a matrix of 6 ant species x 164 sampling units).

Testing the relationships between tree family (or subfamily) and ant species

To determine the influence of host trees in shaping the ant mosaic, the TDAAs recorded for each tree family (or subfamily for the Fabaceae) allowed us to build a '10 ant species x 31 tree families' matrix. TDAAs found only occasionally were eliminated to avoid the effect of outliers as were the 11 cases for which the trees were not identified, so that this study was conducted on 144 out of the 157 trees sampled.

F o r R e v i e w O n l y
9 To ordinate the host tree families based on the TDAAs they sheltered, we conducted a nonmetric multidimensional scaling (NMDS) on a matrix of dissimilarity based on the Bray-Curtis dissimilarity index using 100 random starts. The final stress value of 0.06 < 0.1 can be acknowledged as providing a good representation for a 2-D configuration. A hierarchical clustering using the 'complete' agglomeration method (NbClust package) on the dissimilarity matrix resulted in eight clusters of ant species; this was the best clustering scheme obtained using the 'majority rule' (24 indices computed). These analyses were conducted using the Vegan and NbClust packages in R software (R Development Core Team, 2015).

Identifying different degrees of 'small-scale disturbance' between five Guianese rainforests

Because the parabiotic, ant-garden ants Camponotus femoratus (Formicinae) and

Crematogaster levior (Myrmicinae) are characteristic of pioneer formations (Dejean et al., 2000) but are also present in rainforest canopies, particularly around treefall gaps [START_REF] Vicente | Defining habitat use by the parabiotic ants Camponotus femoratus (Fabricius, 1804) and Crematogaster levior Longino[END_REF], they can serve as a basis for comparison to establish different degrees of 'smallscale natural disturbances' between rainforests. This needs to be distinguished from major disturbances such as those caused by hurricanes or by humans. Thus, we compared the number of trees sheltering these ant garden ants versus those sheltering the other dominant ants between five Guianese rainforests (data from the present study, Dejean et al. 2018, and[START_REF] Leponce | Tree-dwelling ant survey (Hymenoptera, Formicidae) in Mitaraka, French Guiana[END_REF]. A set of Fisher's exact-tests was used for pairwise comparisons; simultaneous comparisons were adjusted using the false discovery rate, BH correction [START_REF] Pike | Using false discovery rates for multiple comparisons in ecology and evolution[END_REF]. We also compared the number of tree crowns sheltering these ant-garden ants between light-demanding and other types of trees on the Nouragues plateau as well as the frequency of light-demanding trees between the Nouragues plateau and Paracou, two terra firme rainforests (see data in Appendix S1A, B).

F o r R e v i e w O n l y 10

Results

General points

The 157 trees sampled represented 77 species belonging to 29 families, the Lecythidaceae (30 trees) being the most frequent followed by the Fabaceae (28 trees) (Appendix S1), but we noted the incompleteness of the tree survey (Fig. 3a). The projected on-ground crown map (Fig. 2) corresponds to the location of individual trees in more or less circular horizontal projected crown areas whose diameters varied from 5-6 m to, exceptionally, 14-15 m (see tree #11M11); one can note the presence of numerous gaps between these tall canopy trees.

A representative part of the dominant ant assemblage was inventoried (Fig. 3b). Among the 16 ant species recorded (nine genera from six subfamilies), only Camponotus rapax is a non-dominant species, here in the situation of sub-dominant on one tree: #11L447. The most frequent species, Cr. levior, noted on 43.95% of the tree crowns, generally nests in parabiosis with Ca. femoratus, both sharing ant gardens (Table 1; Figs. 1, 2; Appendix S1).

Mapping the territorially dominant ant territories

Despite the absence of direct contact between certain tree crowns or their connection via lianas in many cases, the cohesion of these territories is possible thanks to the presence of trails on the ground that interconnect the trees. These trails are used during the warmest hours of the day (11:00-15:00), the workers walking in both directions transporting larvae, nymphs and nestmates. This was noted for Az. jelskii (connections between trees #11L403, #11L399 instabilis and Daceton armigerum (tree #11M128) or Dolichoderus bispinosus (tree #11L408) (Fig. 2; Appendix S1).

The null model analysis confirmed the existence of a mosaic by revealing less species cooccurrence than expected by chance between the six most common ant species, indicating a competitively structured assemblage (observed C-score = 912.9; simulated C-score = 614.6; P<0.001). The pairwise approach showed that Crematogaster levior and Ca. femoratus were positively associated with each other but negatively associated with all four other frequent species, while Cr. stollii was positively associated with E. tuberculatum (Table 2).

Influence of tree family (or subfamily) on the ant species distribution

The NMDS ordination of Bray-Curtis distances and the complete agglomeration method showed a strong host tree selectivity by the 10 most frequent dominant ant species as eight clusters were delimited with, as expected, the two parabiotic, ant-garden ants, Cr. levior and Ca. femoratus, grouped together. Azteca jelskii was associated with D. bispinosus, whereas all other ant species were related to a specific set of tree taxa (Fig. 4). Thus, the sampling size

F o r R e v i e w O n l y
12 was large enough to obtain evidence that the formation of ant mosaics depends to some extent on the host trees.

Identifying different degrees of small-scale disturbances between five Guianese rainforests

The rate of presence of the ant-garden ants Ca. femoratus and Cr. levior on the Nouragues plateau (present study) and the Mitaraka swamp forest was not significant, but significantly higher than the three other forests (Table 3). Among the latter, the difference between the forest of Paracou and the Mitaraka plateau was not significant, but was significant between them and the Petit Saut forest (ant-garden ants absent there) (Table 3).

The number of tree crowns sheltering Ca. femoratus and/or Cr. levior on the Nouragues plateau was not significant between light-demanding and other types of trees (8 cases out of 20; 40% versus 59 out of 120; 49.17%; Fisher's exact-test: P = 0.48). Also, the comparison between the Guianese terra firme rainforests of the Nouragues plateau and Paracou resulted in non-significant differences in the relative numbers of light-demanding tree species (26 out 146 trees identified versus 22 out of 109; Fisher's exact-test: P = 0.87) (see Appendix S1).

Discussion

Ant mosaic characteristics and traits related to ant species dominance Although Neotropical rainforest canopies are reputed to be irregular, breaking the continuity of the territories of TDAAs [START_REF] Ribeiro | Competition, resources and the ant (Hymenoptera: Formicidae) mosaic: a comparison of upper and lower canopy[END_REF], we show the existence of an ant mosaic. This was demonstrated by mapping the spatial segregation of the numerically dominant ants in the upper canopy (Fig. 2), the use of a null model co-occurrence and a pairwise approach. TDAAs, co-dominance and even a colony of the non-dominant species Ca. rapax in the position of sub-dominance (small Ca. rapax colonies nest in old branches of trees; Table 1).

In addition to the parabiosis between Cr. levior and Ca. femoratus, most cases of codominance involved Cr. stollii whose workers moreover defend territories vis-à-vis other TDAAs even though they mostly move inside carton galleries [START_REF] Longino | A taxonomic review of the genus Azteca in Costa Rica and a global revision of the aurita group[END_REF][START_REF] Schmidt | A dolichoderine ant that constructs traps to collectively ambush prey: convergent evolution with a myrmicine genus[END_REF]. They were frequently associated with E. tuberculatum (Table 2). Some other cases of co-dominance correspond to tolerance between TDAA foraging workers (Fig. 2, Appendix S1).

A representative part of these dominant arboreal ants was inventoried in the upper canopy (Fig. 3), whereas this was not the case for trees for which a very large sampling effort might be necessary due to the hyperdiverse Amazonian rainforests (see [START_REF] Poncy | The lowland high rainforest. Structure and tree species diversity. Nouragues. Dynamics and plant-animal interactions in a Neotropical Rainforest[END_REF]. Importantly, although the TDAA territories frequently spread over several tree crowns, some tree crowns were divided into two or more separate territories (Fig. 2; [START_REF] Ribeiro | Competition, resources and the ant (Hymenoptera: Formicidae) mosaic: a comparison of upper and lower canopy[END_REF]Dejean et al., 2018). This situation needs to be handled with care to avoid confusing it with cases of co-dominance causing wrong data to be used in the statistical analyses leading to erroneous interpretations. A complementary survey conducted at ground level is necessary because it will allow trees whose crowns are not interconnected by contact or via lianas to be grouped in the same territory and, here too, avoid misinterpretations. Indeed, we showed that the workers of five TDAAs use trails on the ground or the low vegetation to interconnect trees whose crowns are not in contact, permitting them to exchange brood and workers and thus to maintain the colony odor as is known for two ground-nesting ant species [START_REF] Beugnon | Colony structure and foraging behavior in the tropical formicine ant Gigantiops destructor[END_REF][START_REF] Orivel | Ant activity rhythm in a pioneer vegetal formation of French Guiana[END_REF]. Furthermore, we confirmed that the colonies of Cr. stollii and E. tuberculatum [START_REF] Hölldobler | Journey to the ants: a story of scientific exploration[END_REF][START_REF] Tobin | Competition and coexistence of ants in a small patch of rainforest canopy in Peruvian Amazonia[END_REF].

interconnect

Roles of host trees and small-scale disturbances on the distribution of dominant ants

Host tree specificity due to attractive chemicals acting on founding queens and workers, well known for myrmecophyte-ant relationships, was generalized to include TDAAs during ethological experiments showing the basis of nest-site selection by these arboreal ants (Djiéto-Lordon & Dejean, 1999a,b). This was also shown via the distribution of the dominant ants' territories even though the latter expand as the colonies age (i.e., they occupy neighboring trees whose taxa are distributed by chance) [START_REF] Dejean | Rainforest canopy ants: the implications of territoriality and predatory behavior[END_REF][START_REF] Dejean | How territoriality and host-tree taxa determine the structure of ant mosaics[END_REF][START_REF] Bolton | Species: Cephalotes atratus[END_REF] this study). Our approach was valid as we indeed noted that the two ant-garden ants shared the same cluster and that the plant-ant Az. ovaticeps was associated with its mutualist host mymecophyte, Cecropia obtusa (Cecropiaceae) (Fig. 4). Cr. levior in the ant mosaic studied, two species typical of pioneer formations that are also frequent around treefall gaps and in plantations (Dejean et al., 2000;[START_REF] Vicente | Defining habitat use by the parabiotic ants Camponotus femoratus (Fabricius, 1804) and Crematogaster levior Longino[END_REF].

Thus, their presence in primary rainforests (Dejean et al., 2018;[START_REF] Leponce | Tree-dwelling ant survey (Hymenoptera, Formicidae) in Mitaraka, French Guiana[END_REF] this study) might indicate some degrees of past disturbances or of frequent disturbances. The comparison between Guianese rainforests showed that the rate of presence of these two ant species was significantly higher on the Nouragues plateau than in other terra firme Guianese rainforests, but similar to that of a swamp forest (Table 3). Note that the characteristics of Neotropical swamp forests are similar to that of young, secondary forests and treefall gaps in old-growth forests [START_REF] Souza | Spatial variation and dynamics of flooding, canopy openness, and structure in a Neotropical swamp forest[END_REF]. Furthermore, the presence of the typical pioneer species Ce. obtusa shows that canopy gaps existed in the past; later these trees reached the canopy and so were recorded in this survey (Appendix S1; Fig. 2).

Relationships between small-scale natural disturbances and the presence of ant-garden ants

Because the comparison of the frequency of the ant-garden ants on the Nouragues plateau and the comparison of the numbers of light-demanding tree species between the Nouragues plateau and Paracou resulted in non-significant differences, we failed to show that these ants select 'light-demanding tree taxa' rather than others. Thus, the neighboring presence of canopy gaps seems enough to favor the presence of these ants in the situation studied (i.e., whether the host trees are light-demanding or not). Therefore, the abiotic disturbances represented by frequent strong winds and the formation of large canopy gaps are likely the main cause of the abundance of the ant-garden ants Ca.

femoratus and Cr. levior that withstand these effects better than do competitive TDAAs (see

F o r R e v i e w O n l y 16
Vicente & Izzo, 2017). Because they build conspicuous ant gardens easy to locate (Fig. 1), they might serve as indicators of different degrees of small-scale natural disturbances.

In conclusion, ant mosaics exist in Neotropical rainforests despite the frequent small-scale natural disturbances and absence of contact between tree crowns due to the structure of the trees. This is due to the TDAAs' territoriality, host tree taxa selection, contact between tree crowns and interconnection via liana, plus the ability of certain TDAAs to interconnect trees belonging to their territories using trails on the ground or underground galleries, whereas an abiotic influence plays a role in the form of strong winds and the formation of large canopy gaps. correction). Symbols indicate the nature of the association: "+" positive, "-" negative, "0" not significant.

F

Frequency 1 2 3 4 5 The discrimination of light-demanding tree species was based on [START_REF] Newbery | Herbivory and defense in pioneer, gap and understory trees of tropical rain forests in French Guiana[END_REF], [START_REF] Roggy | Nitrogen-fixing legumes and sylvigenesis in a rain forest in French Guiana: a taxonomic and ecological approach[END_REF] and [START_REF] Gourlet-Fleury | Ecology and management of a Neotropical Rainforest. Lessons drawn from Paracou, a long-term experimental research site in French Guiana[END_REF]; we would like to acknowledge Dr. Jérôme Chave for verifying our list of tree species.

1 Crematogaster levior 44% 2 Camponotus femoratus 39% + 3 Crematogaster stolli 18% - - 4 Azteca instabilis 14% - - 0 5 Ectatomma tuberculatum 12% - - + 0 6 Azteca jelskii 10% - - 0 0 0 F o r R e v i e w O n l y

  cases of arboreal ant dominance were recorded including classical

Fig. 1 .

 1 Fig. 1. (a) A large carton nest of Azteca chartifex. (b) A conspicuous ant garden resulting from the

Fig. 3 .

 3 Fig. 3. (a) Individual-based rarefaction (Mao-Tau with 95 % CI, solid lines) illustrating the

Fig. 4 .

 4 Fig. 4. Non-metric multidimensional scaling (NMDS) ordination plot showing the ant species (black

Fig. 1 .

 1 Fig. 1. (a) A large carton nest of Azteca chartifex. (b) A conspicuous ant garden resulting from the association between Camponotus femoratus and Crematogaster levior. The scale bar represents 50cm.

Fig. 2 .

 2 Fig. 2. Overhead view of the distribution of the trees and their associated territorially dominant ant species in the area studied in the Nouragues Ecological Field Station, French Guiana. The codes correspond to the trees listed in Appendix S1 (see also examples of the projection of African tree crowns for comparison).128x239mm (600 x 600 DPI)

  Cr. stollii workers confirmed that via underground galleries neighboring trees sheltering these ant species belonged to the territory of one colony (e.g., for Cr. stollii see groups #11M104, In addition to the cases of parabiosis between Ca. femoratus and Cr. levior noted on 56 tree crowns, co-dominance was frequent when involving Cr. stollii which was often associated with E. tuberculatum (i.e., on 16 trees out of 28 sheltering Cr. stollii; Table2; Fig.

	11
	#11M135 and #11N136; #11L556, #11L458 and #11M106; Fig. 2).
	We also noted tree crowns divided into separate territories (e.g., #11L408, #11L411,
	#11L522, #11L403, #11M126, #11M128, #11M111; Fig. 2).
	F
	o r
	R
	e v i e w
	O
	n l
	y
	and #11L402), Az. instabilis (trees #11M77 and #11M66), Ca. femoratus and Cr. levior
	(group of trees whose limits are #11M53, #11M37, #11M93 and #11M90; trees #11M111 and

#11M128; Fig.

2

). The nests of Dolichoderus bidens are interconnected by constantly-used trails passing through low understory vegetation. Also, spraying paint on E. tuberculatum or 2; Appendix S1). Other cases of co-dominance concerned Cr. levior and Cephalotes atratus (tree #11L495), Azteca instabilis and Az. jelskii (trees #11L411 and #11M79), and Az.

Table 1 .

 1 List of dominant ant species collected from 157 trees in the Nouragues Ecological Research Station (the total of the percentages is greater than 100% because one tree crown can shelter several dominant ant species due to cases of co-dominance).

	Ant species	Occurrences	Frequency on trees	Nesting habits
	Crematogaster levior	69	43.95 % Carton nests, ant gardens, polydomous, parabiosis with Camponotus femoratus.	Dejean et al. (2000); Vicente & Izzo (2017)
	Camponotus femoratus	61	38.85 %	Semi-spherical carton nests, ant gardens, polydomous, parabiosis with Crematogaster levior.	Dejean et al. (2000); Vicente & Izzo (2017)
	Crematogaster stollii	28	17.83 %	Carton nests in cavities; galleries on tree interconnecting trees. trunks and branches; continue underground,	Longino (2003)
				Hemispherical carton nests against tree
	Azteca instabilis	22	14.01 %	trunks or base of main branches,	De la Mora et al. (2008)
				polydomous.
	Ectatomma tuberculatum	19	12.10 %	Ground-nesting at the base of trees, polydomous; galleries underground interconnecting trees.	Delabie (1990); Hora et al. (2005)
	Azteca jelskii	16	10.19 % Carton nests in cavities, polydomous.	Longino (2007)
	Dolichoderus bidens	6	3.82 %	Numerous small carton nests under the leaves, polydomous.	MacKay (1993); Delabie et al. (1991) Corbara et al. (2018)
	Dolichoderus bispinosus	6	3.82 % Nests in cavities, polydomous.	MacKay (1993)
	Daceton armigerum	4	2.55 %	Cavities in old branches of trees, polydomous.	Dejean et al. (2012)
	Azteca ovaticeps	4	2.55 %	Nests in hollow trunks and branches of Cecropia spp. trees.	Longino, 2007
	Odontomachus hastatus	4	2.55 %	Nests in trash baskets formed by palm trees or Philodendron.	Gibernau et al. (2007); Camargo & Oliveira (2012)
	Paraponera clavata	4	2.55 % Ground-nesting at the base of trees.	Elahi (2015)
	Azteca chartifex	3	1.91 % Large, triangular carton nests, polydomous.	Delabie et al. (1991); Longino (2007)
	Cephalotes atratus	2	1.27 %	Large cavities in old branches of trees, polydomous.	Bolton (2018)
	Azteca brevis	1	0.63 %	Carton nests in cavities; galleries on tree trunks and branches; continue underground, interconnecting trees	Longino, 2007; Schmidt & Dejean, 2018)
	Camponotus rapax	1	0.63 %	Small colonies nesting in cavities in old branches of trees.

Table 2 .

 2 Associations between the most frequent species (frequency on the 157 trees sampled >10%) by decreasing rank of occurrence and tested using Chi-square tests (1 d.f., Yates'

Table 3 .

 3 Comparison of the parabiotic, ant-garden ants Camponotus femoratus and Crematogaster levior and all other territorially dominant arboreal ant species (TDAAs) between five Guianese rainforests. Statistical comparison: Fisher's exact-tests and false discovery rate (FDR; BH correction) adjustment for simultaneous comparisons.

		A-	B-	C-	D-	E-
		Nouragues	Paracou	Mitaraka	Mitaraka	Petit Saut
		(plateau)		(plateau)	(swamp)
	Ant-garden ants	69 (45.7%)	27 (20.15%)	6 (20%)	15 (50%)	0 (0%)
	All other TDAAs	82 (54.3%)	107 (79.85%)	24 (80%)	15 (50%)	45 (100%)
	Total	151	134	30	30	45
		AxB	AxC	AxD	AxE	BxC
	Fisher's exact-test	P <0.001	P = 0.0088	P = 0.693	P = 0.0001	P = 1
	FDR adjustment	P<0.05	P<0.05	NS	P<0.05	NS
		BxD	BxE	CxD	CxE	DxE
	Fisher's exact-test	P = 0.002	P = 0.001	P = 0.0292	P = 0.0029	P < 0.0001
	FDR adjustment	P<0.05	P<0.05	P<0.05	P<0.05	P<0.05

  The myrmecophytic Cecropia obtusa was not considered in the statistics because it is specifically associated with Azteca ovaticeps. B. For comparison, selection of light-demanding tree species in the forest of Paracou, French Guiana (seeDejean et al., 2018).

	Clusiaceae Caesalpinioideae Vouacapoua americana Symphonia globulifera Sapotaceae Chrysophyllum lucentifolium Malvaceae Sterculia sp.	11L478 Azteca instabilis 11M80 Dolichoderus bidens 11M131 Camponotus femoratus, Crematogaster levior 163 Camponotus femoratus, Crematogaster levior
	Caesalpinioideae Vouacapoua americana Faboideae Swartzia benthamiana Cardiopteridaceae Dendrobangia boliviana Malvaceae Sterculia sp.	11L479 Azteca instabilis 11M81 Camponotus femoratus, Crematogaster levior 11M132 Camponotus femoratus, Crematogaster levior 164 Camponotus femoratus, Crematogaster levior
	Lecythidaceae Malvaceae Rubiaceae Malvaceae	Eschweilera grandiflora Sterculia sp. (LD) Guettarda acreana Sterculia sp.	11L480 Camponotus femoratus, Crematogaster levior 11M82 Azteca brevis 11M133 Camponotus femoratus, Crematogaster levior, Crematogaster stollii 168 Camponotus femoratus, Crematogaster levior
	Lecythidaceae Cardiopteridaceae Dendrobangia boliviana Lecythis persistens Tiliaceae Apeiba glabra (LD) Malvaceae Sterculia sp.	11L481 Camponotus femoratus, Crematogaster levior 11M83 Camponotus femoratus, Crematogaster levior 11M134 Crematogaster stollii, Ectatomma tuberculatum 162 Neoponera goeldii
	Arecaceae Lecythidaceae Not identified Malvaceae	Astrocaryum sciophilum Eschweilera coriacea Sterculia sp.	11L489 Odontomachus hastatus 11M84 Camponotus femoratus, Crematogaster levior 11M135 Camponotus femoratus, Crematogaster levior, Crematogaster stollii 138 Crematogaster levior
	Vochysiaceae Apocynaceae Not identified Malvaceae	Erisma floribundum Aspidosperma helstonei Sterculia sp.	11L491 Dolichoderus bispinosus 11M85 Camponotus femoratus, Crematogaster levior 11N115 Camponotus femoratus, Crematogaster levior 172 Azteca jelskii
	Sapotaceae Phyllanthaceae Not identified Malvaceae	Manilkara bidentata Hyeronima alchorneoides Sterculia sp.	11L492 Dolichoderus bispinosus 11M86 Crematogaster levior 11N116 Crematogaster stollii, Ectatomma tuberculatum 178 Azteca gnava
	Sapotaceae Cecropiaceae Not identified Moraceae	Chrysophyllum lucentifolium Cecropia obtusa (LD) Brosimum guianense	11L494 Dolichoderus bispinosus 11M88 Azteca ovaticeps 11N133 Crematogaster stollii, Ectatomma tuberculatum 39 Dolichoderus quadridenticulatus
	Lecythidaceae Sapotaceae Not identified Moraceae	Eschweilera coriacea Chrysophyllum lucentifolium Brosimum rubescens	11L495 Crematogaster levior, Cephalotes atratus 11M89 Crematogaster stollii 11N134 Crematogaster stollii 123 Azteca jelskii
	Mimosoideae Lecythidaceae Mimosoideae Moraceae	Inga huberi (LD) Lecythis persistens Inga rubiginosa (LD) Heliocostylis pedunculata	11L497 Azteca instabilis 11M90 Crematogaster levior, Paraponera clavata 11N135 Crematogaster stollii, Ectatomma tuberculatum 19 Azteca instabilis
	Vochysiaceae Vochysiaceae Not identified Moraceae	Qualea rosea Qualea rosea Heliocostylis pedunculata	11L506 Crematogaster stollii, Ectatomma tuberculatum 11M91 Dolichoderus bidens 11N136 Crematogaster stollii, Ectatomma tuberculatum 80 Dolichoderus quadridenticulatus
	Sapotaceae Myristicaceae Mimosoideae 22 light-demanding trees out of 131 identified; 16.79%; 134 trees monitored in total Pouteria guianensis 11L507 Crematogaster stollii Iryanthera sp. 11M93 Camponotus femoratus, Crematogaster levior Inga leiocalycina (LD) 11N137 Crematogaster stollii, Ectatomma tuberculatum
	Bombacaceae Apocynaceae Not identified	Quararibea duckei Geissospermum sp.	11L522 Azteca instabilis, Crematogaster levior 11M94 Camponotus femoratus, Crematogaster levior 11N138 Camponotus femoratus, Crematogaster levior
	Tiliaceae Chrysobalanaceae Licania majuscula Apeiba glabra (LD) Caesalpinioideae Vouacapoua americana	11L523 Azteca instabilis 11M95 Camponotus femoratus, Crematogaster levior 11N145 Camponotus femoratus, Crematogaster levior
	Lecythidaceae Caesalpinioideae Sclerolobium melinonii Couratari multiflora Not identified	11L524 Azteca instabilis 11M96 Crematogaster levior 11N152 Camponotus femoratus, Crematogaster levior
	F o r F o r Pouteria guianensis 11L525 Azteca instabilis Chrysobalanaceae Licania canescens Sapotaceae 11L532 Camponotus femoratus, Crematogaster levior Malvaceae Sterculia sp. (LD) 11L533 Camponotus femoratus, Crematogaster levior Lecythidaceae Eschweilera grandiflora 11L556 Crematogaster stollii, Ectatomma tuberculatum F o r Myrtaceae Guettarda acreana 11M97 Camponotus femoratus, Crematogaster levior Not identified 11MM98 Camponotus femoratus, Crematogaster levior Malvaceae Sterculia sp. (LD) 11M99 Camponotus femoratus, Crematogaster levior Myrtaceae Guettarda acreana 11M100 Camponotus femoratus, Crematogaster levior F o r Not identified 11N152b Camponotus femoratus, Crematogaster levior Not identified F 11N152c Camponotus femoratus, Crematogaster levior Lecythidaceae Eschweilera coriacea 12M6 Camponotus femoratus, Crematogaster levior Mimosoideae Inga stipularis (LD) 12M7 Daceton armigerum o r
	Lecythidaceae Cardiopteridaceae Dendrobangia boliviana Lecythis persistens Cardiopteridaceae Dendrobangia boliviana Lauraceae Ocotea sp. Sapotaceae Chrysophyllum sp. Caesalpinioideae Vouacapoua americana Myristicaceae Virola kwatae Mimosoideae Inga alba (LD) Myrtaceae Guettarda acreana Metteniusaceae Poraqueiba guianensis Lecythidaceae Lecythis persistens Mimosoideae Inga thibaudiana (LD) Lecythidaceae Eschweilera coriacea Caesalpinioideae Vouacapoua americana Lecythidaceae Eschweilera coriacea 157 TREES	189x88mm (300 x 300 DPI) R e v i e w R e v i e w 11L558 Crematogaster stollii, Ectatomma tuberculatum 11L560 Crematogaster stollii, Ectatomma tuberculatum 11L561 Crematogaster stollii, Ectatomma tuberculatum 11L562 Crematogaster stollii, Ectatomma tuberculatum 11M32 Camponotus femoratus, Crematogaster levior 11M33 Camponotus femoratus, Crematogaster levior 11M34 Camponotus femoratus, Crematogaster levior R e v i e w 11M101 Camponotus femoratus, Crematogaster levior 11M102 Camponotus femoratus, Crematogaster levior, Ectatomma tuberculatum R e v i e w 12M136 Camponotus femoratus, Crematogaster levior R 12M137 Dolichoderus bidens 12M139 Dolichoderus bidens 12M18 Azteca chartifex 12M23 Azteca chartifex (very large nest) 12M26 Azteca chartifex e v i e w
	O O 11M35 Odontomachus hastatus 11M37 Camponotus femoratus, Crematogaster levior O O 26 light-demanding tree species out of 146 trees identified; 17.8% Caesalpinioideae Vouacapoua americana Lecythidaceae Eschweilera coriacea O
	Sapotaceae Sapotaceae	Chrysophyllum lucentifolium Chrysophyllum lucentifolium	n l n l 11M53 Camponotus femoratus, Crematogaster levior 11M54 Camponotus femoratus, Crematogaster levior n l n l n l
	Myristicaceae	Virola kwatae	y y 11M55 Camponotus femoratus, Crematogaster levior y y y
	Lecythidaceae	Eschweilera coriacea	11M56 Camponotus femoratus, Crematogaster levior
	Sapotaceae	Pouteria oblanceolata	11M57 Camponotus femoratus, Crematogaster levior
	Meliaceae	Carapa sp.	11M58 Camponotus femoratus, Crematogaster levior
	Sapotaceae Tree family	Micropholis guyanensis Tree species	11M59 Crematogaster levior CODE Territorially dominant arboreal species
	Sapotaceae Anacardiaceae	Chrysophyllum sp. Tapirira sp.	11M63 Azteca instabilis 139 Crematogaster levior
	Lecythidaceae Cecropiaceae	sp. Coussapoa sp.	11M64 Azteca instabilis 151 Azteca instabilis
	Moraceae Celastraceae	sp. Goupia glabra	11M65 Azteca instabilis 85 Azteca chartifex
	Lecythidaceae Celastraceae	Lecythis persistens Goupia glabra	11M66 Azteca instabilis 15 Azteca chartifex
	Sapotaceae Celastraceae	sp. Goupia glabra	11M67 Camponotus femoratus 159 Camponotus femoratus
	Lecythidaceae Faboideae	Eschweilera coriacea Swartzia panacoco	11M68 Camponotus femoratus 91 Azteca instabilis
	Lecythidaceae Faboideae	Eschweilera coriacea Swartzia panacoco	11M70 Camponotus femoratus, Crematogaster levior, Ectatomma tuberculatum 92 Azteca instabilis
	Caesalpinioideae Vouacapoua americana Faboideae Swartzia panacoco	11M71 Camponotus femoratus 153 Azteca instabilis
	Sapotaceae Mimosoideae	Pradosia ptychandra Inga alba	11M77 Azteca instabilis 40 Azteca chartifex
	Myristicaceae Mimosoideae	Virola micheliil Inga alba	11M78 Camponotus femoratus 34 Azteca instabilis
	Caesalpinioideae Vouacapoua americana Mimosoideae Inga huberi	11M79 Azteca instabilis, Azteca jelskii 25 Azteca jelskii

Acknowledgements

We would like to thank Jérôme Chave for furnishing us the maps of the area studied, the identification of the trees and information on tree functional traits, the staff of the Nouragues Ecological Research Station for logistical assistance, Lannick Rerat for sampling ants from the canopy using the singlerope technique, Eleonore Compin for technical help and Andrea Yockey for proofreading the manuscript. Financial support for this study was provided by the ''Investissement d'Avenir'' grants managed by the French Agence Nationale de la Recherche (CEBA, ref. ANR-10-LABX-25-01) and a research grant from the Brazilian Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for JHCD. AD, BC and ML designed the experiments; AD and ML conducted the field study;

JHCD identified the ants; AC and ML analyzed the data; FA prepared the illustrations; AD wrote the paper, and all authors made significant contributions in terms of ideas and revisions. All authors have approved the manuscript and there are no conflicts of interest.

Supporting Information

Additional Supporting Information may be found in the online version of this article under the DOI reference: 10.1111/een.?????? Appendix S1. A. Identification of the 157 trees studied in the Nouragues Ecological Research Station and the dominant ant species they sheltered in their crowns (the codes are nailed to the trunks of the trees at ≈1.60 m in height). (LD): light-demanding tree species including pioneer tree species (26 species out of 120 taxa identified). B. For comparison, selection of light-demanding tree species in the forest of Paracou, French Guiana (see Dejean et al., 2018).

dominant ant species they sheltered in their crowns (the codes are nailed to the trunks of the trees at ≈1.60 m in height). (LD): light-demanding tree species including pioneer tree species (26 species out of 120 taxa identified).

Tree family

Tree