Filippo Cellini

Francesco Lavini

Tengfei Cao

Walt De Heer

Claire Berger

Angelo Bongiorno

Elisa Riedo
email: elisa.riedo@nyu.edu

Epitaxial two-layer graphene under pressure: Diamene stiffer than Diamond

The unprecedented ultrahigh interlayer stiffness of supported two-layer epitaxial graphene on silicon carbide (SiC) has been recently reported by our research group. We found that under localized pressure a two-layer epitaxial graphene behaves as an ultra-hard and ultrastiff coating, showing exceptional mechanical properties that far exceed those of bare SiC. Density functional theory (DFT) calculations indicate that this unique behavior stems from a sp 2 -to-sp 3 reversible phase transition of carbon films under compression, leading to a single-layer diamond-like structure that we called diamene. In this paper, force versus indentation depth curves from high-resolution nanoindentation experiments of CVD diamond and sapphire are carried out and compared to those obtained from two-layer epitaxial graphene on SiC. These new measurements confirm that the stiffness of epitaxial graphene is larger than that exhibited by CVD diamond and sapphire substrates. Our measurements show that areas of the film consisting of buffer layer plus one, or at most two, additional graphene layers are the ones most likely to exhibit phasechanging behaviors and larger-than-diamond stiffness.

INTRODUCTION

The outstanding mechanical properties of graphene have been investigated for more than a decade. Probably the most relevant experimental investigation to date of the nanomechanical properties of graphene was reported in 2008 in Science [START_REF] Lee | Measurement of the elastic properties and intrinsic strength of monolayer graphene[END_REF]. In this experiment, the elastic modulus and strength of mechanically exfoliated monolayer graphene was measured by nanoindentation in an atomic force microscope (AFM). Experimental results demonstrated the extremely high in plane stiffness of monolayer graphene, of the order of 1 TPa, and the outstanding membrane strength of above 100 GPa. These results opened avenues to further investigation of the mechanical properties of exfoliated graphene [START_REF] Scarpa | Effective elastic mechanical properties of single layer graphene sheets[END_REF][START_REF] Zhang | Nanofracture in graphene under complex mechanical stresses[END_REF][START_REF] Zandiatashbar | Effect of defects on the intrinsic strength and stiffness of graphene[END_REF] and graphene oxide [START_REF] Suk | Mechanical Properties of Monolayer Graphene Oxide[END_REF], whereby different studies attempted to dissect the structural characteristics of graphene flakes that are responsible for their incredible mechanical response.

Despite being the most reliable and cost-effective technique for producing high quality crystals, mechanical exfoliation of graphene from graphite produces only sparse isolated flakes, with no precise control on dimensions and thickness distribution. This limitation has hampered application of mechanically exfoliated graphene to large-scale devices and technological platforms. For this reason, epitaxial growth of graphene on hexagonal substrates has gathered the increasing attention of the scientific community as a viable alternative to mechanical exfoliation [START_REF] Tetlow | Growth of epitaxial graphene: theory and experiment[END_REF]. Several production methods have been explored, some of them involving the growth of epitaxial graphene (EG) on transition metal surfaces via chemical vapor deposition (CVD) [START_REF] Ago | Epitaxial chemical vapor deposition growth of single-layer graphene over cobalt film crystallized on sapphire[END_REF], other providing a surface-confined growth through precise control of temperature ramping (temperature programmed growth, or TPG [START_REF] Coraux | Growth of graphene on Ir (111)[END_REF]), or exploiting the carbon solubility on suitable substrates [START_REF] Liu | Segregation growth of graphene on Cu-Ni alloy for precise layer control[END_REF].

In this regards, the preparation of epitaxial graphene by thermal decomposition of silicon carbide substrate (SiC) is considered as a solid route to the controlled synthesis of large scale graphene films for several technological applications [START_REF] Berger | Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics[END_REF]. Recent developments in this technique have led to an accurate control over dimensions and thicknesses of the films, making possible to obtain continuous and homogenous single layer graphene domains up to several tens of micrometers in length and width [START_REF] Emtsev | Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide[END_REF].

Fundamental characteristic of this growth process is the formation of an interfacial layer between the graphene layers and the SiC substrate, which is called buffer layer. Because of the strong covalent bonds with the SiC, the buffer layer presents substantially different properties from graphene. In fact, although maintaining a graphite-like honeycomb structure, the buffer layer does not display the Π bands of graphene [START_REF] Riedl | Structural and electronic properties of epitaxial graphene on SiC (0 0 0 1): a review of growth, characterization, transfer doping and hydrogen intercalation[END_REF], is semiconductive [START_REF] Nair | Band gap opening induced by the structural periodicity in epitaxial graphene buffer layer[END_REF], and is highly charged [START_REF] De Heer | Epitaxial graphene[END_REF]. Layers grown on top of the buffer layer act like few-layer graphene structures, stacking on top of the buffer and presenting the same electronic structure of graphene. Therefore, the presence of the buffer layer is known to play a fundamental role in shaping the properties of few layer epitaxial graphene on SiC.

Very recently, AFM experiments and density functional theory (DFT) calculations explored the mechanical properties of few-layers epitaxial graphene film grown on SiC(0001), particularly focusing on the interlayer response of the material to nanoindentation [START_REF] Gao | Elastic coupling between layers in two-dimensional materials[END_REF][START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF]. By harnessing the sub-ångström-resolution of modulated nano-indentation (MoNI), these experiments demonstrated that at room temperature and under pressure, two-layer (2-L) epitaxial graphene films display stiffness much larger than the SiC substrate. Here, two-layer epitaxial graphene refers to a single layer of graphene grown on top of the interfacial buffer layer. The ultra-high stiffness of these films was explained through a detailed set of DFT calculations showing that 2-L epitaxial graphene under pressure would likely undergo a homogenous phase transition from a sp 2 -hybridized graphitic to a sp 3 -diamond-like structure. These results strongly supported our hypothesis that the ultrahigh stiffness observed in the experiments was indeed associated with the formation of a new material at the interface between SiC and graphene, here-after called diamene.

Our previous study demonstrated for the first time the ultra-high stiffness of diamene. However, in our report, we did not provide an estimation of the effective stiffness of this new diamond-like phase by direct comparison with other stiff materials. In this work, we further explore the properties of diamene, comparing its stiffness with that of two hard substrates, namely CVD diamond and sapphire. These new experimental observations confirm that the stiffness of diamene is indeed comparable or even higher than the stiffness of bulk diamond and is of the order of 1 TPa.

The rest of the paper is organized as follows. In Section 2, we discuss the growth process of epitaxial graphene and the procedure for MoNI (Å-indentation). Furthermore, we analyze the challenges related to the identifications of ultrahigh stiffness regions in few-layer epitaxial graphene samples. In Section 3, we report the topography and frictional properties of an epitaxial graphene sample where the possible formation of diamene was observed. The comparison between indentation curves of diamene, buffer layer, and two other reference materials, CVD diamond and sapphire is also given. In Section 4, we present our conclusions.

MATERIALS and METHODS

Growth and characterization of epitaxial graphene films on SiC

Epitaxial graphene samples employed in these experiments are grown on on-axis 4H-SiC wafer by the confinement-controlled sublimation method [START_REF] De Heer | Large area and structured epitaxial graphene produced by confinement controlled sublimation of silicon carbide[END_REF][START_REF] Berger | Electronic confinement and coherence in patterned epitaxial graphene[END_REF][START_REF] Kelly | Physics of graphite[END_REF]. In its fundamental incarnation, the confined sublimation method is composed of two phases: sample preparation and graphene growth in a high temperature furnace. In the first phase, SiC wafers are initially cut to shape (approximately 5 x 5 mm 2 samples are employed in this work) and polished on the growth face. After that, samples are placed in the furnace under Argon atmosphere for graphene growth. Temperature and time are optimized to produce multilayer graphene layers on the SiC(000-1) face (C-face) and a single graphene layer on the SiC(0001) face (Si-face) [START_REF] Berger | Electronic confinement and coherence in patterned epitaxial graphene[END_REF]. This specific growth process is realized in two steps, a first step around 1450 ºC for 7 minutes and a second step at 1550 ºC for 20 minutes.

A TEM micrograph of few graphene layers grown on the Si-face is displayed in Figure 1(a). A schematic and molecular model of the epitaxial graphene structure is displayed in Figure 1(b). Atomically thin epitaxial graphene films up to 5 atomic layers, and buffer layer, are generally grown on the SiC(0001) face (Si-face) of the SiC, while films with more than ten layers are grown on the carbon face of SiC(000-1). The first grown carbon layer on Si-face is known as the buffer layer. The buffer layer is characterized by a graphene-like honeycomb atomic structure with about 30% of its carbon atoms bonding to the Si atoms of the SiC(0001) face. This particular structure gives the buffer layer a unique set of properties, such as semiconducting electronic properties due to its interaction with SiC(0001) surface.

Stiffness measurements by Å-indentation MoNI

MoNI is an Atomic Force Microscopy (AFM)-based force spectroscopy technique which allows for sub-ångström resolution indentation measurements. We specifically select MoNI for our experiments to overcome limitations in the study of atomically thin two-dimensional (2D) materials that are introduced by other nanoindentation methods [START_REF] Oliver | An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments[END_REF][START_REF] Li | A review of nanoindentation continuous stiffness measurement technique and its applications[END_REF]. Traditional nanoindentation measurements usually employ indentation depths of the order of few hundred nanometers, whereby small residual deformations are likely to be produced on the surface of the test sample. In the case of few layer graphene films in Figure 1(a) and (b), these indentation depths substantially exceed the thickness of the film, compromising the accuracy and reliability of the measured stiffness, which is not characteristic of the thin film, but arises from the predominant contribution of the substrate.

Different from traditional techniques, MoNI employs extremely small (sub-ångström) vertical oscillations to probe the surface of the sample (see Figure 2(a)). The oscillatory displacement (Δzpiezo) is imposed to the cantilever-tip system by using a small sinusoidal voltage (<0.4 mv) applied to the piezotube of the AFM (Agilent PicoPlus AFM) by a lock-in amplifier (Stanford Research Systems, SR830), while the contact force (Fz) between tip and sample is maintained constant by the feedback loop of the AFM. In further details, the tip is first brought in contact with the surface. Once the contact force has reached Fz ~10 2 nN, the tip is slowly retracted (0.01 nm/s) from the surface while oscillating with amplitude Δzpiezo (<1 Å). The variation in the normal force (ΔF(Fz)) induced by the imposed oscillation is measured while reducing Fz, until the tip loses contact with the surface.

The stiffness of the contact kcont(Fz)=(Δzpiezo/ΔF(Fz) -1/klev) -1 is recorded at different decreasing loads (klev being the spring constant of the AFM cantilever), allowing high-resolution force(Fz)indentation(zindent) curves to be constructed by computing the following integral:

𝑧 indent = 𝑧 P0 + ∫ 𝑑𝐹 𝑧 ′ 𝑘 cont (𝐹 𝑧 ′ ) 𝐹 𝑧 𝐹 𝑃0 (1)
where 𝐹 𝑃0 is the pull-out force measured by the AFM when the tip loses contact with the sample's surface at 𝑧 P0 .

The stiffness of the contact between the tip and the sample can be identified by fitting the indentation curve with the classical Hertz model:

𝐹 𝑧 = 4𝐸 * √𝑅 3 𝑧 𝑖𝑛𝑑𝑒𝑛𝑡 3/2 (2)
where R is the tip radius and E * = ((1-ν 2 tip)/Etip + (1-ν 2 )/E ) -1 is the effective Young modulus of the tip/sample contact, dependent on the Poisson's ratios and elastic modulus of both tip (νtip, Etip) and sample (ν, E). Despite its simplicity, the Hertz equation turns out to be accurate in matching the experimental data [START_REF] Lee | Measurement of the elastic properties and intrinsic strength of monolayer graphene[END_REF]. Indentation curves measured on 2-L and 10-layer epitaxial graphene are reported in Figure 2(b), together with the indentation curve obtained for a bare SiC substrate employed for graphene growth. According to the Hertz formula in equation ( 2), when tip properties (νtip, Etip) and shape (contact radius, R) are maintained constant across different experiments, the slope of the indentation curves is directly proportional to the stiffness of the surface, with a steeper indentation curve indicating a stiffer surface. Therefore, the substantially steeper slope of the 2-L graphene curve indicates that this film is much stiffer than SiC. As discussed in our former work [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF], we associate this surprising result to the non-permanent transformation of 2-L graphene into an ultrastiff diamene layer due to the pressure of the AFM tip.

In [START_REF] Gao | Elastic coupling between layers in two-dimensional materials[END_REF], direct quantification of multi-layer (10-layer) graphene stiffness (E~33 GPa) was successfully performed using equation [START_REF] Scarpa | Effective elastic mechanical properties of single layer graphene sheets[END_REF], by comparing the stiffness of the film to the stiffness of the bare SiC substrate. However, a similar identification performed on 2-L graphene indentation curves in Figure 2(b) would give a stiffness of diamene substantially higher than that of diamond [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF], which is one of the stiffest material known to mankind. For this reason, we report herein diamene indentation curves measured in parallel to indentation curves of other ultrastiff materials, namely CVD diamond and a sapphire crystal. Through direct comparison, accurate estimation of diamene indentation modulus can be performed.

In what follows, sub-ångström resolved nanoindentation curves of 2-L graphene are obtained through MoNI. In these experiments, a diamond-coated Si tip (Nanosensor DT-NHCR) is brought into hard contact with the surface of the sample, reaching normal loads up to 300nN, corresponding to pressure of around 10 GPa, considering the contact area between the spherical tip and the flat surface (see Figure 2(a)). We use the MoNI technique at room temperature to probe the transverse mechanical response of 2-L epitaxial graphene and compare it with those of bulk (0001) sapphire (Al2O3) and a thin film of CVD (111) diamond (2.2 µm on Si substrate). The indentation is performed in 5-6 different positions on each sample, to have an estimation of the uncertainty of the data acquired.

Identification of graphene/diamene structures and their mechanical response

Although thermally induced growth of the epitaxial graphene on SiC substrate has been widely investigated [START_REF] Berger | Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics[END_REF][START_REF] Emtsev | Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide[END_REF], the perfect control of thickness distribution of graphene structure is still very challenging, involving complex dynamics and requiring precise recipes. Therefore, it is difficult to obtain homogeneous and uniformly covered samples of epitaxial graphene, in particular when few layer graphene samples are fabricated. Due to rapid growth rates in the initial stages of the process, large few-layer graphene regions usually coexist with multilayer regions, as well as uncovered buffer layers domains [START_REF] Riedl | Structural and electronic properties of epitaxial graphene on SiC (0 0 0 1): a review of growth, characterization, transfer doping and hydrogen intercalation[END_REF].

From a nanomechanical standpoint, these regions have very different properties. As discussed in the previous section, multilayer epitaxial graphene (10 layers or more) presents mechanical stiffness similar to the interlayer stiffness of graphite (approximately 30 GPa). On the other hand, the buffer layer has an indentation modulus that is almost the same as SiC (approximately 440 GPa) [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF], which can be explained with the partial graphitization of the buffer layer and its strong covalent bonding to the underlying SiC structure. The formation of diamene is observed only in few-layer graphene regions. However, this ultrahigh stiffness is not systematically observed at each point of the sample, which led us believe that only specific graphene structures/number of layers can lead to the formation of ultrastiff diamene.

DFT calculations suggest that the formation of diamene is possible in the case of one graphene layer over the buffer layer and two graphene layers over the buffer layer, but it is highly unlikely when the number of layers exceed four [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF]. Indentation data presented in this work are obtained for 2-L epitaxial graphene films. Nevertheless, we are currently working on determining if similar results are found in a three-layer epitaxial graphene film, by developing a methodology to clearly identify in-situ the exact number of layers while performing the MoNI experiments.

In the case of epitaxial graphene, differently from mechanically exfoliated graphene, topographic information is not sufficient to distinguish graphene regions of different thickness. During the growth process, the surface of SiC substrate undergoes substantial changes, resulting from the sublimation of Si atoms and consequent rearrangement of C atoms into a graphitic structure. Additional graphene layers after the first one grow underneath it [START_REF] Nair | Band gap opening induced by the structural periodicity in epitaxial graphene buffer layer[END_REF], with the buffer layer being essentially a moving interface between the graphene layers and the SiC substrate. This characteristic of the growth process heavily reflects on the topography, in the sense that the surface height profile does not necessarily follow the effective changes of the graphene thickness.

Friction force microscopy (FFM) can prove to be very useful towards the characterization of the sample structure. It has been demonstrated that friction response varies in epitaxial graphene as a function of thickness and that the friction of the buffer layer far exceeds that of few layers graphene [START_REF] Filleter | Friction and Dissipation in Epitaxial Graphene Films[END_REF]. Mapping the friction response from the surface of the sample can help distinguishing between different graphene domains, opening new avenues for understanding how the number of layers correlates with the formation of diamene and the mechanical properties of the surface.

RESULTS and DISCUSSION

Topography of the EG sample and identification of two-layer graphene regions

Figure 3 shows a typical atomic force microscopy (AFM) topographic image of the 2-L epitaxial graphene sample studied in this work, together with its corresponding friction force map 1 . Figure 3(a) displays the topography of the epitaxial graphene sample. The structure of the sample displays several vertical terraces resulting from the annealing of SiC, each terrace being separated from the others by clear vertical steps. Graphene growth is known to start at the edges of these steps, and gradually distribute on the SiC terraces. For this reason, regions close to the step edges usually show lower topography, which is associated to the formation of a multilayer graphene structure (Si atoms sublimate faster near the step edges). Moving from the edges into the terraces, two different regions can be identified: i) regions at higher topography, which we identify as exposed buffer layer in areas where slower sublimation has not allowed the formation of a complete graphene layer; ii) regions at lower topography, which can be identified as the 2-L graphene regions on which we found the ultrastiff diamene. In the friction map, it is possible to clearly identify the buffer layer as the high-friction areas being surrounded by the low-friction 2-L epitaxial graphene. Analyzing the values obtained from the two distinct domains, we find that the buffer layer shows a friction force around 9 times larger than the one displayed by 2-L epitaxial graphene. Overall, this ratio agrees with results found in the literature [START_REF] Filleter | Friction and Dissipation in Epitaxial Graphene Films[END_REF]. As expected, higher topographic domains match the bright spots in the friction map, univocally identifying the buffer layer and allowing us to recognize the exposed epitaxial graphene and select suitable areas to perform nanoindentation measurements.

Nanoindentation of Diamene, Diamond and Sapphire

The ultra-high stiffness of 2-L graphene on SiC has been already established in our previous experiments, but a clear comparison with other ultrastiff materials has not been performed to date. For this purpose, indentation curves are simultaneously acquired on two ultrastiff materials as sapphire (0001) and CVD (111) diamond, and the results are compared with the indentation data of buffer layer and 2-L graphene.

Figure 4(a) displays MoNI indentation curves measured on 2-L epitaxial graphene (diamene) and buffer layer, together with indentation curves of sapphire and CVD diamond. Notably, the slope of the indentation curve of the buffer layer is comparable to the slope of the curve measured on sapphire. On the other hand, a much higher contact force is recorded on regions of the sample with 2-L graphene, leading to a slope of the indentation curve steeper than that of CVD diamond. We associate the ultra-high stiffness of the 2-L graphene regions with the formation of the new ultrastiff diamene phase. We remark that ultra-high stiffness is not observed uniformly everywhere on the sample, and results for mechanical properties can change from region to region. Further investigation is now ongoing to understand which features exactly reveal the presence of diameneforming graphene in different regions of the sample.

Quantitative evaluation of the stiffness of the different materials is performed by fitting the experimental data in Figure 4(a) with Equation (2) using a non-linear regression procedure in Python 2 . Sapphire, taken as the reference material, shows a value of stiffness very close to the expected one [START_REF] Oliver | An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments[END_REF], with an indentation modulus of 412 ± 36 GPa. For the buffer layer, we compute a stiffness of 498 ± 26 GPa, which is comparable but slightly higher than the expected stiffness of 1 Both topography and friction measurements are performed in contact mode with a Bruker Multimode 8 AFM, using a silicon AFM tip (PPT-CONT Nanosensor) with normal spring constant of 17 N/m. 2 For these calculations, we assume for the diamond coated tip Etip =1050 and νtip = 0.115. SiC (440 GPa). Fitting of the CVD diamond data yields a stiffness of 923 ± 78 GPa. Finally, the stiffness obtained for the diamene film is 1079 ± 69 GPa.

From our analysis, it is clear that diamene structures present a transverse stiffness higher than CVD diamond. This finding agrees with previous micro-hardness experiments [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF], where 2-L epitaxial graphene on SiC proved to be resistant to perforation by a diamond indenter. Upon applying pressure above 17 GPa with a diamond Berkovich indenter, permanent plastic deformation was induced on bare SiC substrate, while no residual indentation mark was found on the 2-L epitaxial graphene grown on the same substrate. In addition, when applying larger loads on 2-L graphene on SiC, the tip broke.

Density functional theory (DFT) calculations have been carried out to shed light on this surprising experimental observation [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF]. In Figure 4(b), we report a schematic of one of possible phase transitions from graphene to diamene, explaining the remarkable hardening effect of the 2-L graphene on SiC. A fundamental result of this analysis is that the sp 2 -to-sp 3 phase transition occurs in 2-L graphene surface under localized pressure, while the rest of the thin film would maintain the graphitic-flexible state. DFT calculations show also that the mechanism depicted in Figure 4(b) is fully reversible and that this transition is possible only for specific number of atomic layers and stacking patterns. Experiments have indeed verified the absence of this stiffening transition in the case of the sole buffer layer, where the stiffness of the graphitic film matches that of SiC substrate, or in the case of epitaxial graphene with 5 layers or thicker grown on SiC [START_REF] Scarpa | Effective elastic mechanical properties of single layer graphene sheets[END_REF]. The phase transformation seems thus to require a specific topology and stacking of the graphene film as well as a mechanism to saturate a critical fraction of the surface dangling bonds at the interfaces, in particular the one between diamene and substrate. In view of this, the presence of the buckled buffer layer in direct contact with incommensurable and reactive Si-face of the SiC substrate may play a key role in the evolution of the phase transition.

CONCLUSION

In conclusion, sub-ångström resolution indentation experiments show that, at room temperature, under the pressure of about 10 GPa, a 2-L epitaxial graphene film grown on SiC(0001) behaves as a diamond-stiff coating, exhibiting mechanical stiffness higher than CVD diamond. DFT simulations show that, being independent on stacking patterns, a homogeneous reversible phase transition of 2-L epitaxial graphene is achievable under pressures of experimental indentation. However, in multilayer graphene films, this transformation process is prohibited by stacking constraints [START_REF] Gao | Ultrahard carbon film from epitaxial two-layer graphene[END_REF].

Up to now the microscopic details of the graphene-diamene structural transition remain elusive. But this discovery opens up a series of possibilities in the field of mechanical technologies, including, in particular, applications in ultra-hard and ultra-light coatings and composites. A phasechanging 2D carbon films can have great potential as an entirely new class of ultra-light protective coatings and armors for military and law enforcement personnel, vehicles, and devices. But in order to step into the applicability of such technology, a deeper understanding of the mechanisms behind the phase transition, as well as a broader characterization of the mechanical properties of this novel carbon forms, are absolutely necessary. This can be achieved, for example, by studying different type of graphene films and substrates, including different growth processes, or by exploring other types of mechanical experiments, such as dynamic high-strain rate and ballistic testing. Finally, both experiments and mechanical modeling studies are also necessary to understand whether the same stiffening effect can be exhibited by 2D atomically thin films other

Figure 3 (

 3 Figure 3(b) displays the friction force map corresponding to the topographic image in Figure 3(a).In the friction map, it is possible to clearly identify the buffer layer as the high-friction areas being surrounded by the low-friction 2-L epitaxial graphene. Analyzing the values obtained from the two distinct domains, we find that the buffer layer shows a friction force around 9 times larger than the one displayed by 2-L epitaxial graphene. Overall, this ratio agrees with results found in the literature[START_REF] Filleter | Friction and Dissipation in Epitaxial Graphene Films[END_REF]. As expected, higher topographic domains match the bright spots in the friction map, univocally identifying the buffer layer and allowing us to recognize the exposed epitaxial graphene and select suitable areas to perform nanoindentation measurements.

Fig. 1 .

 1 Fig. 1. (a) TEM image and (b) schematic illustration of few-layers epitaxial graphene grown on SiC (0001) substrate by Si sublimation at high temperatures.In the 3D lattice model, it is possible to distinguish the interfacial carbon buffer layer, which is directly bonded to the SiC substrate, and the graphene layers grown on top of it.

Fig. 2 .

 2 Fig. 2. (a) Schematic illustration of the contact model assumed in the Modulated Nanoindentation (MoNI) technique. The AFM tip can be represented as a sphere indenting locally the 2D film surface, assimilated, together with the substrate, to an elastic half-space. (b) Force versus indentation depths curves obtained from high-resolution Modulated Nanoindentation (MoNI) measurements, showing the mechanical responses of epitaxial graphene films of different thicknesses, compared to that of the SiC substrate.

Fig. 3 .

 3 Fig. 3. (a) Contact-mode AFM topographic image (vertical scale: 10 nm) of the 2-L epitaxial graphene sample studied in this work. Higher domains represent the buffer layer. (b) Corresponding friction force image (vertical scale: 50 nN). Thanks to the large difference in their friction response, from the friction map it is possible to clearly distinguish the exposed 2-L epitaxial graphene (low friction-dark contrast) form the buffer layer domains (high friction-brighter contrast). Friction force map has been acquired scanning the sample at 5nN normal load.

Fig. 4 .

 4 Fig. 4. (a) Force versus indentation depth curves obtained from MoNI experiments on 2-L epitaxial graphene on SiC(0001) and on different hard materials. The curves plotted are the result of an averaging process of data extracted from different positions on the surface of each sample. Shaded areas represent the respective standard deviations from the mean value. All the measurements are performed using the same diamond tip. The reported experiment clearly shows that the diamene/SiC structure (green line) exhibits a stiffness larger than that of CVD bulk diamond (magenta line). (b) Illustration of a 2-L epitaxial graphene film on SiC (represented by the bottom green atomic plane), undergoing the phase transition to a diamond-like structure (diamene) under the effect of compression exerted by the AFM tip (upper green atomic plane).

ACKNOWLEDGMENTS

We acknowledge the support from the Office of Basic Energy Sciences of the US Department of Energy (grant no. DE-SC0016204).

than graphene.


Vanessa Robitzch

Natalia Arakaki

Stéphane Mauger

José Carlos

Zapata Rojas

Marie-Laure Guillemin
email: marielaure.guillemin@gmail.com

Stranded alone: The first reported Peruvian population of Agarophyton chilensis is a single-male's clone

Keywords: Agarophyte, Colonization, Microsatellite, Population genetic, Range expansion, Red alga

Gracilariales, a red macroalgal order, is considered one of the top ten most invasive algal taxa. While Agarophyton vermiculophyllum is a well know example of an algal invader worldwide, its congeneric species A. chilensis has mainly remained within its original distribution range for thousands of years, and was only engaged in a few dispersal journeys to arrive from New Zealand to Chile over 19 000 years ago. Nowadays, A. chilensis is intensively farmed along the Chilean coast and the establishment of new populations has mostly been due to intentional/planned cultivation practices. No other source of range expansion has ever been reported, since its first description. However, in 2014 it was sighted for the first time at the docking of a small artisanal port in Peru, which nowadays represents its northernmost population. We genetically assessed 60 specimens taken from Peru in 2015 and 2017, using two different types of molecular markers (the ribosomal Internal Transcribed Spacer 2, ITS2 and six nuclear microsatellites). Altogether, our results suggest the population in Perú to be an unattached, vegetative, single male's clonal population. This population has sustained itself successfully, reproducing asexually through fragmentation, for at least four consecutive years and seems to have expanded in the area. The ITS2 sequences from these individuals corresponds all to one haplotype, the one ubiquitous among populations from Chile, the eastern coast of New Zealand and the Chatham Islands, not allowing to narrow down the potential area of origin of the Peruvian population. Based on first the allelic frequencies of six microsatellite loci estimated for 28 Chilean and five loci for seven New Zealander populations and second the analyses of Bayesian clustering, we propose the natural or unintentional anthropogenic introduction of a single male's thallus from Chile to be the source of the Peruvian population.

Introduction

Algal colonizers have previously been reported to successfully expand their original distribution range by spreading their reproductive propagules (spores or zygotes) or thallus fragments, either through: oceanic current systems[1-3], rafting on floating substrata [START_REF] Ingólfsson | Floating clumps of seaweed around Iceland: natural microcosms and a means of dispersal for shore fauna[END_REF][START_REF] Wares | Phylogeography and historical ecology of the North Atlantic intertidal[END_REF][START_REF] Thiel | The ecology of rafting in the marine environment: II. The rafting organisms and community[END_REF][START_REF] Muhlin | The influence of coastal topography, circulation patterns, and rafting in structuring populations of an intertidal alga[END_REF][START_REF] Fraser | Genetic affinities between trans-oceanic populations of nonbuoyant macroalgae in the high latitudes of the southern hemisphere[END_REF][START_REF] Thiel | The Humboldt Current system of northerncentral Chile: oceanographic processes, ecological interactions and socioeconomic feedback[END_REF][START_REF] Macaya | Float and raft: role of buoyant seaweeds in the phylogeography and genetic structure of nonbuoyant associated flora[END_REF], attached to ship hulls, in ballast waters, or as a result of other anthropogenic activities such as aquaculture and the aquarium trade [START_REF] Williams | A global review of the distribution, taxonomy, and impacts of introduced seaweeds[END_REF][START_REF] Neiva | Climate oscillations, range shifts and phylogeographic patterns of North Atlantic Fucaceae[END_REF]. It is thought that at least 346 algal taxa have successfully expanded their original biogeographic range and formed new populations worldwide [START_REF] Neiva | Climate oscillations, range shifts and phylogeographic patterns of North Atlantic Fucaceae[END_REF].

Amongst these, at least 17 non-buoyant seaweeds have colonized new transoceanic territories across vast distances of open ocean [START_REF] Macaya | Float and raft: role of buoyant seaweeds in the phylogeography and genetic structure of nonbuoyant associated flora[END_REF][START_REF] Smith | Rare long-distance dispersal of a marine angiosperm across the Pacific Ocean[END_REF]. Species of the red macroalgal order Gracilariales are recognized among the top ten invasive algal taxa and Agarophyton vermiculophyllum (previously known as Gracilaria vermiculophylla [START_REF] Gurgel | Systematics of the Gracilariales (Rhodophyta) including new subfamilies, tribes, subgenera, and two new genera, Agarophyton gen. nov. and Crassa gen. nov[END_REF]) is a well know example of an algal invader worldwide [START_REF] Williams | A global review of the distribution, taxonomy, and impacts of introduced seaweeds[END_REF].

Agarophyton chilensis [START_REF] Bird | Gracilaria chilensis sp. nov. (Rhodophyta, Gigartinales), from the Pacific South America, Can[END_REF], despite its name, is originally from New Zealand and it is considered most likely that recurrent colonizers naturally expanded the species distribution range to the Chatham Islands and to the southern part of the Pacific coasts of South America dating back at least 19 000 years ago [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF][START_REF] Cohen | Molecular identification of two sibling species under the name Gracilaria chilensis (Rhodophyta, Gracilariales)[END_REF].

In late February 2014, the presence of A. chilensis at the Grau Port in Morro Sama, Tacna, Peru, was reported for the first time. First specimens were collected in May of the same year and were morphologically and genetically (based on the ribulose 1,5-bisphosphate carboxylase/oxygenase gene, rbcL, plastid) coherently identified [START_REF] Arakaki | First occurrence of Gracilaria chilensis, and distribution of Gracilariopsis lemaneiformis (Gracilariaceae, Gracilariales) in Peru on the basis of rbcL sequence analysis[END_REF]. Agarophyton chilensis is a red alga commonly found and cultivated along the shores of Chile. Here, it is found from Raul Marin, in the South (43°S), all the way up to the Bahia Mejillones (23°S) in northern Chile [START_REF] Bird | Gracilaria chilensis sp. nov. (Rhodophyta, Gigartinales), from the Pacific South America, Can[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF][START_REF] Santelices | Ecological differences among Chilean populations of commercial Gracilaria[END_REF]. At its currently northernmost distribution, in Coquimbo (29°S) and Caldera (27°S, an introduced population likely originating from Coquimbo), A. chilensis is intensively farmed and harvested for the production of agar [START_REF] Bird | Gracilaria chilensis sp. nov. (Rhodophyta, Gigartinales), from the Pacific South America, Can[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF].

All northern populations, north of Coquimbo, at 29°S, are populations introduced by fishermen for cultivation purposes and were not part of the historical natural distribution range of the species [START_REF] Bird | Gracilaria chilensis sp. nov. (Rhodophyta, Gigartinales), from the Pacific South America, Can[END_REF][START_REF] Buschmann | Seaweed farming in Chile: a review[END_REF]. Some of these northern farms have already disappeared probably due to poor management choices (Wilkomirsky, personal communication). Among these farms, La Herradura Bay, Coquimbo (29°S), remains the oldest reported and established population, dating back to at least the 1950s. In Peru, A. chilensis is not farmed, which indicates that the new Peruvian population was not intentionally introduced, and it has been hypothesized to have rather come from a nearby farm in northern Chile.

However, since the rbcL genetic marker studied in the Morro Sama locality is not variable at the species level (i.e., same sequence across the entire Pacific range [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF]) for A. chilensis, the origin of the new Peruvian population remained unsolved [START_REF] Arakaki | First occurrence of Gracilaria chilensis, and distribution of Gracilariopsis lemaneiformis (Gracilariaceae, Gracilariales) in Peru on the basis of rbcL sequence analysis[END_REF]. Two scenarios could have led to the colonization of the Peruvian coasts: (1) a direct transoceanic colonization from New Zealand to Peru, or (2) a natural or anthropogenic range expansion from Chilean populations to the North.

Agarophyton chilensis, has a complex reproductive life cycle with an alternation between haploid (male and female gametophytes) and diploid (tetrasporophytes) individuals. The species can reproduce sexually through the production of spores or asexually by fragmentation of its thallus. The latter resulting in individuals unattached to the substrata (lacking attachment discs) and forming populations of thalli drifting over, or embedded in sandy/muddy seabeds, which are commonly found in estuaries and bays [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. Farmers also take advantage of fragmentation to seed their farms with cuttings of thalli and grow new algae [START_REF] Buschmann | Intertidal cultivation of Gracilaria chilensis (Rhodophyta) in southern Chile: long term invertebrate abundance patterns[END_REF]. In this process of induced asexual reproduction in farms, a loss in fertility of the farmed unattached population (which also mainly comprises vegetative tetrasporophytes) has further been recorded [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. In contrast, sexually reproducing natural populations are composed of individuals growing anchored to pebbles, shells or the rocky substratum by attachment discs [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. Most individuals in natural populations are fertile, and the populations typically comprise a mixture of males, females, and tetrasporophytes [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. In the case of Peru, the first collected individuals were reported to be infertile and growing buried in sand [START_REF] Arakaki | First occurrence of Gracilaria chilensis, and distribution of Gracilariopsis lemaneiformis (Gracilariaceae, Gracilariales) in Peru on the basis of rbcL sequence analysis[END_REF], and thus, so far, rather resembling a farmed Chilean population. Yet, there is little knowledge on the demographics of the Peruvian population since an assessment of population dynamics and genetics is still needed.

This study seeks to comprehensively assess the putative origin as well as the phase and sex ratio of the Peruvian population of A. chilensis, combining knowledge on the biology of the species, metadata of the site, and phenotypic and genotypic data. Using population genetics including a large genetic data base of the ribotype of the Internal Transcribed Spacer 2 (ITS2) and microsatellite nuclear DNA markers of A. chilensis specimens collected along its entire distribution range (seven locations from New Zealand, including Chatham Islands, and 28 in Chile [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]), we verify whether or not the newly found Peruvian population is representative of another case of transoceanic colonization from New Zealand or rather a range expansion from the Chilean coast. Additionally, Peruvian samples were taken in 2015 and 2017 to assess potential temporally recent genetic and demographic changes within the population of Morro Sama.

Materials and Methods

Sampling location, direct thalli examinations, and DNA extraction

The 12 th of September of 2015, 30 samples of Agarophyton chilensis were collected under the structure of a small dock for artisanal fishers' boats [START_REF] Arakaki | First occurrence of Gracilaria chilensis, and distribution of Gracilariopsis lemaneiformis (Gracilariaceae, Gracilariales) in Peru on the basis of rbcL sequence analysis[END_REF], at the Grau Port, in Morro Sama, Tacna, Peru (17° 59' 39.7" S and 70° 52' 59.1" W; Fig. 1). Another 30 specimens were sampled on the 31 st of august, 2017. During both samplings, a brief field evaluation of the A. chilensis population was carried out and basic environmental parameters were measured using a field thermometer (for temperature in °C), a WTW Multiparameter (Multi 3630, for pH), and an Atago Master Refractometer (for salinity).

Both collections were evaluated under a stereoscope in search for reproductive structures as well as attachment discs. For further genetic analyses, a fragment of each of the 60 samples was kept in dry silica gel prior DNA extraction following the protocol in [START_REF] Cohen | Molecular identification of two sibling species under the name Gracilaria chilensis (Rhodophyta, Gracilariales)[END_REF] [START_REF] Cohen | Molecular identification of two sibling species under the name Gracilaria chilensis (Rhodophyta, Gracilariales)[END_REF].

Genetic Data acquisition

The ploidy level and sex of the vegetative Peruvian individuals were determined using the genetic sex markers published by [START_REF] Guillemin | Characterization of genetic markers linked to sex determination in the haploid-diploid red alga Gracilaria chilensis[END_REF] [START_REF] Guillemin | Characterization of genetic markers linked to sex determination in the haploid-diploid red alga Gracilaria chilensis[END_REF]. Ploidy level given by genetic sex markers was cross-checked with microsatellite genotypes (i.e., haploid gametophytes should not present more than one allele for each microsatellite locus).

Microsatellite data were generated according to [START_REF] Guillemin | Development of microsatellites DNA markers in the cultivated seaweed, Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF] with the following codes for each of the six microsatellite loci: Grc-8B2, Grc-7F12, Grc-2B2, Grc-6C7, Grc-7D3, and Grc-AC/CT23) [START_REF] Guillemin | Development of microsatellites DNA markers in the cultivated seaweed, Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF] [START_REF] Cohen | Molecular identification of two sibling species under the name Gracilaria chilensis (Rhodophyta, Gracilariales)[END_REF] and were performed on an ABI 3100 Sequencer (Applied Biosystem, Foster City, CA). Sequences were edited using CHROMAS [25] and multiple sequence alignments were constructed with BIOEDIT [START_REF] Hall | BioEdit: a user-friendly biological sequence alignment editor and analysis program for Windows 95/98/NT[END_REF].

Microsatellites and ITS data analyses

First, allelic frequencies and probabilities to generate the Peruvian genotypes under the null hypothesis of free recombination [START_REF] Tibayrenc | A clonal theory of parasitic protozoa: The population structures of Entamoeba, Giardia, Leishmania, Naegleria, Trichomonas, and Trypanosoma and their medical and taxonomical consequences[END_REF] were estimated in various populations and regions. Allele frequencies were estimated using GenoDive v.2.0b27 [START_REF] Meirmans | GENOTYPE and GENODIVE: Two programs for the analysis of genetic diversity of asexual organisms[END_REF], for each microsatellite locus, for every single sampling location in 1). Within each location or region, the likelihood of producing a Peruvian genotype was estimated using the product of the frequency of each allele characterizing the genotype (i.e., two per locus for diploid genotypes, one per locus for haploid genotypes). Since only five microsatellites were available for most populations from New Zealand (including Chatham Islands) these calculations were done (1) using five microsatellite loci among samples from all available locations (in South America and New Zealand), and (2) using six microsatellite loci among samples from South America.

Second, using allele frequencies estimated above, genic differentiation between the population of Morro Sama and all the other populations sampled was calculated using the Fisher's exact probability test and 1,000 permutations, in GENEPOP v.4.2 [START_REF] Raymond | GENEPOP (version 1.2): population genetics software for exact tests and ecumenicism[END_REF][START_REF] Rousset | GENEPOP'007: A complete re-implementation of the GENEPOP software for Windows and Linux[END_REF]. Genic differentiation was estimated using the five microsatellite loci available in all populations.

Third, Bayesian clustering assuming genetic admixture and correlated allele frequencies was performed in STRUCTURE v.2.3.4 [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF][START_REF] Falush | Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies[END_REF] with a burn-in of 50,000 and a run-length of 100,000 iterations, making 10 runs for each K from 1 to 15 and without any prior population assignment, to evaluate with which individuals of the 35 total sampling locations, the Peruvian samples were more likely to cluster with. In order to achieve this, two different datasets were consecutively run: (1) using all sampling sites and all available microsatellite markers (six loci among South American samples and two sites in New Zealand, and five loci for the remaining sites in New Zealand and Chatham Island, with the sixth locus coded as missing data), (2) using only those sampling sites with which the Peruvian samples clustered within the first data set and all six available microsatellite markers. For STRUCTURE analyses, haploids were artificially diploidized as homozygotes at every locus. The most likely number of K was determined using the Evanno method implemented in STRUCTURE HARVESTER v.0.6.94 [START_REF] Earl | STRUCTURE HARVESTER : a website and program for visualizing STRUCTURE output and implementing the Evanno method[END_REF].

To assess ribotype diversity present in Peru, the ITS2 sequences obtained were compared to the sequences available from Chile and New Zealand (108 sequences from Chile and 93 from New Zealand, Guillemin et al. 2014 [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF]) using MEGA7 [START_REF] Kumar | MEGA7: Molecular Evolutionary Genetics Analysis version 7.0 for bigger datasets[END_REF].

Results

Characteristics of the Morro Sama Agarophyton chilensis population

In 2015 the Peruvian A. chilensis population covered only an area of about 18 m in diameter. During the field evaluation in 2017, the site was described as sheltered, without currents, turbid with 10 m visibility, depths ranging from 1-4 m, sea surface temperature of 16-17°C, pH of 7.65, 34.7 salinity, and a total A.

chilensis population of about 100 m x 25 m consisting of isolated patches separated by approximately 1 meter between patches. The substratum was described as mostly muddy-sandy, with a couple of rocks and some boulders.

The evaluation of the population further reported estimates of a 1:9 ratio of fixed to buried or entangled (loose) specimens or fragments.

None of the specimens collected in 2015 or 2017 showed presence of reproductive structures and they were categorized as vegetative samples. No fixation discs were observed, suggesting that the entire population was composed of loose thalli.

Among all 60 samples, the sex marker only amplified PCR products representative to the male marker [START_REF] Guillemin | Characterization of genetic markers linked to sex determination in the haploid-diploid red alga Gracilaria chilensis[END_REF]. The results of the sex markers' amplifications were coherent with the single, unique genotype obtained in Peru (see below; with no more than one allele at each microsatellite locus).

From Peru, 29 individuals collected in 2015 and 28 in 2017 were successfully genotyped at all six microsatellite loci. All 57 Peruvian samples corresponded to one single genotype: 357bp for locus Grc-8B2, 192bp for locus Grc-7F12, 318bp

for locus Grc-2B2; 201bp for locus Grc-6C7; 297bp for locus Grc-7D3 and 220bp

for locus Grc-AC/CT23 (the genotype is given as allele lengths of each of the six microsatellite loci, in base-pairs (bp) following Guillemin et al. 2005) [START_REF] Guillemin | Development of microsatellites DNA markers in the cultivated seaweed, Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF]. All allele lengths found in Peru had already been recorded in Chile [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF][START_REF] Guillemin | Development of microsatellites DNA markers in the cultivated seaweed, Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF] ( [START_REF] Guillemin | Development of microsatellites DNA markers in the cultivated seaweed, Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. Further, we found one single ribotype among all Peruvian sequenced ITS2 fragments (480 bp) generated for 22 samples collected in 2015 (corresponding to "r1", after Guillemin et al. 2014 [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF]).

Altogether, our results suggest the population in Peru to be an unattached, vegetative, single male's clonal population.

Possible origins of Morro Sama' male clone

The ribotype r1 corresponds to the one ubiquitous among Chilean populations and to the most common ribotype on the eastern coast of New Zealand and the Chatham Islands [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF]. Therefore, based on this genetic marker it is only possible to discard the western coast of New Zealand as possible origin for the Peruvian population.

For the data set of five microsatellites, the likelihood to produce the Peruvian genotype was 0.00 in all populations and regions of New Zealand, 0.03 in the region of Coquimbo (north Chile), and 0.23 in the region of the Channel of Chacao (south Chile; see suppl. Table S1 for further details). For the complete data set of six microsatellites, the likelihood to produce de Peruvian genotype was the highest in the region of the Channel of Chacao followed by the region of Coquimbo (0.14 and 0.02, respectively; suppl. Table S1). Among the 28 Chilean sampling locations (no grouping into regions), the most likely to produce the Peruvian genotype was the location of Chaitén (in the continental Chiloé region, p = 0.10), followed by the location of Maullín (in the Channel of Chacao region, p = 0.05). Amongst the northern locations, the most likely source of the Peruvian genotype was Playa Changas (in the region of Coquimbo, p = 0.01). Please note that our values of likelihood to produce the Peruvian genotype within a Chilean population are comparable to ones already estimated for A. chilensis in Chile using the same molecular markers. Indeed, the probability of a given multilocus genotype to be observed in the N samples genotyped from its own sampling site as a consequence of different events of sexual reproduction was estimated to be in between 3.3E-06 and 0.125 for diploid samples and between 4.5E-04 and 0.586 for haploid samples within our Chilean data set (see Supplementary Online Material from Guillemin et al. 2008[19]).

Genic differentiation assessed between the Peruvian population and the rest of the populations sampled were in all case highly significant (all p<0.0001)

Using the Evanno method in the Bayesian clustering analysis of STRUCTURE, K=2 and K=4 were suggested as the most likely total number of genetic groups in our data set, differing slightly from the results in Guillemin et al. ( 2014) [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF] where K=5 was estimated for the whole A. chilensis distribution area. Results of K=2 can be found in Figure S1 and clustering results for K=4 are given for each population in Figure 2. For K = 2, the Peruvian genetic cluster (P-MSA, in red, S1). The assigned regions are given in underlined bold letters (see also suppl. Table S1). Pie charts indicate the proportion of the population's individuals belonging to a total of four (K=4) possible genetic clusters as assigned by STRUCTURE v.2.3.4 [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF][START_REF] Falush | Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies[END_REF]. Each of these K-clusters is coded by a different color.

Discussion

This study infers the putative origin of the newly found Peruvian population of Agarophyton chilensis, and describes the phase and sex ratios of this population using genetic data available for specimens across the species' entire, currently known distribution [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF][START_REF] Arakaki | First occurrence of Gracilaria chilensis, and distribution of Gracilariopsis lemaneiformis (Gracilariaceae, Gracilariales) in Peru on the basis of rbcL sequence analysis[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. In brief, the Peruvian population was found to comprise clones of one single vegetative male of A. chilensis, which seemingly has been reproducing asexually through fragmentation of its thallus, forming a small, patchy population. This population has sustained itself successfully for at least four consecutive years and appears to have grown in area (2014 [START_REF] Arakaki | First occurrence of Gracilaria chilensis, and distribution of Gracilariopsis lemaneiformis (Gracilariaceae, Gracilariales) in Peru on the basis of rbcL sequence analysis[END_REF]; and from this study for 2015 and 2017). While the ITS2 nuclear DNA marker could not discard New Zealand as a possible transoceanic source, based on allele frequencies of microsatellite markers, our study strongly suggests Chile as possible source of the Peruvian male, whereas all New Zealand locations were discarded. Limited dispersion of Gracilariales spores [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF] suggests that the Peruvian population rather originated from a single stranded fragment of the thallus of a male specimen than from one haploid spore. Further, all the samples analyzed during both sampling periods were vegetative indicating that the population has not been reproducing sexually in recent years. The reasons for this remain undetermined but may be due to the recent (and singular) arrival of the species to Peru or the lack of favorable environmental conditions.

Similarly, in a study on A. vermiculophyllum, newly arrived thalli seemed to rather reproduce vegetatively through fragmentation, forming a vegetative unattached population [START_REF] Krueger-Hadfield | New record of the non-native seaweed Gracilaria parvispora in Baja California -A note on Vergara-Rodarte et al[END_REF].

To date, invasion and expansion of geographic ranges among Agarophyton have been proposed to rely on the arrival of one or a few floating tetrasporophytes, which increase the initial population density and algal biomass via vegetative reproduction through fragmentation, after which the production of a few reproductive structures by these long-standing unattached populations may lead to the production of haploid spores and the fixation of male and female gametophytes on nearby hard substrata, finally recovering the sexual life cycle of the species [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF][START_REF] Krueger-Hadfield | New record of the non-native seaweed Gracilaria parvispora in Baja California -A note on Vergara-Rodarte et al[END_REF][START_REF] Krueger-Hadfield | When invaders go unnoticed: the case of Gracilaria vermiculophylla in the British Isles[END_REF]. In the case of the Morro Sama population, even if the male clone developed functional reproductive structures (i.e., male gametangia), due to the absence of close-by reproductive females, the sexual life cycle cannot be restored. Indeed, in Gracilariales, the male gametes are short-lived (<6h) [START_REF] Destombe | Viability and dissemination of spermatia of Gracilaria verrucosa (Gracilariales, Rhodophyta)[END_REF] and fecundation occurs at a few meters at most [START_REF] Engel | Non-random mating in controlled multiple-donor crosses in Gracilaria gracilis (Gracilariaceae, Rhodophyta)[END_REF][START_REF] Engel | Mating system and gene flow in the red seaweed Gracilaria gracilis: Effect of haploid-diploid life history and intertidal rocky shore landscape on fine-scale genetic structure[END_REF].

The nearest known locality where A. chilensis females have been reported is located in the region of Caldera, almost 1000 km away from Morro Sama [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]). Additionally, most surveyed farms and/or sandy unattached populations have been described to be highly dominated by vegetative tetrasporophytes (in A. chilensis [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF][START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF] and in A. vermiculophyllum [START_REF] Krueger-Hadfield | When invaders go unnoticed: the case of Gracilaria vermiculophylla in the British Isles[END_REF][START_REF] Krueger-Hadfield | Invasion of novel habitats uncouples haplo-diplontic life cycles[END_REF]). In Chile, only one A. chilensis farm mostly contained female gametophytes, the rest being only or mostly tetrasporophytes [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF], with commonly complete absence of male gametophytes. Ecological differences between phases may be one explanation for the dominance of vegetative tetrasporophytes in unattached populations [START_REF] Guillemin | Differential ecological responses to environmental stress in the life history phases of the isomorphic red alga Gracilaria chilensis (Rhodophyta)[END_REF][START_REF] Guillemin | Evidence of reproductive cost in the triphasic life history of the red alga Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF][START_REF] Lees | Nonnative Gracilaria vermiculophylla tetrasporophytes are more difficult to debranch and are less nutritious than gametophytes[END_REF]. For instance, in A. chilensis, vegetative tetrasporophytes have enhanced growth when compared to gametophytes, with the male's growth rate being slowest in this species [START_REF] Guillemin | Differential ecological responses to environmental stress in the life history phases of the isomorphic red alga Gracilaria chilensis (Rhodophyta)[END_REF][START_REF] Guillemin | Evidence of reproductive cost in the triphasic life history of the red alga Gracilaria chilensis (Gracilariales, Rhodophyta)[END_REF].

Altogether, Morro Sama is a unique case among unattached, recently described

Agarophyton populations, and the first asexually reproducing population dominated by male thalli ever reported.

Agarophyton chilensis is negatively buoyant, however, fragments of thalli could either be transported (1) entangled on marine vessels [START_REF] Thomsen | Alien macroalgae in Denmark -a broad-scale national perspective[END_REF][START_REF] Ruiz | Spread of the invasive alga Caulerpa racemosa var. cylindracea (Caulerpales, Chlorophyta) along the Mediterranean coast of the Murcia region (SE Spain)[END_REF], (2) on other positively buoyant rafts like tree trunks or other large floating seaweeds [START_REF] Macaya | Float and raft: role of buoyant seaweeds in the phylogeography and genetic structure of nonbuoyant associated flora[END_REF][START_REF] Fraser | Oceanic rafting by a coastal community[END_REF][START_REF] Fraser | Algal parasite Herpodiscus durvillaeae (Phaeophyceae: Sphacelariales) inferred to have traversed the Pacific Ocean with its buoyant host[END_REF], (3) carried by birds (e.g., in A. vermiculophyllum by either migrating birds [START_REF] Nyberg | Long-term survival of an introduced red alga in adverse conditions[END_REF], or as nesting material of local birds, [START_REF] Arnold | The sea-beach at ebb tide: A guide to the study of the seaweeds and the lower animal life found between tide-marks, The Century Co[END_REF]), or (4) attached to other imported marine goods such as oysters, shells, or clams (e.g., in A.

vermiculophyllum [START_REF] Krueger-Hadfield | Genetic identification of source and likely vector of a widespread marine invader[END_REF][START_REF] Sfriso | First record of Gracilaria vermiculophylla (Gracilariales, Rhodophyta) in the Po Delta lagoons, Mediterranean Sea (Italy)[END_REF][START_REF] Thomsen | Gracilaria vermiculophylla (Rhodophyta, Gracilariales) in Hog Island Bay, Virginia: A cryptic alien and invasive macroalga and taxonomic correction[END_REF]). In terms of geographic distance and likelihood of drift through natural currents or anthropogenically induced transport, northern Chilean populations could be regarded as the more likely source for the arrival of male propagules in southern Peru. Morro Sama is located directly on the path of the Humboldt Current that flows north from 42°S (i.e., North of the Chiloé Island) [START_REF] Thiel | The Humboldt Current system of northerncentral Chile: oceanographic processes, ecological interactions and socioeconomic feedback[END_REF] and is found only 600 km away from Bahia Mejillones, the northernmost point where A. chilensis was transported to be cultivated in Chile. The farm of Bahia Mejillones seems to have disappeared nowadays due to poor management choices (Wilkomirsky, personal communication) but Morro Sama is still located only 980 km north of the region of Caldera (27°S) and 1,170 km north of the region of Coquimbo (29°S), the oldest established farm in northern

Chile [START_REF] Bird | Gracilaria chilensis sp. nov. (Rhodophyta, Gigartinales), from the Pacific South America, Can[END_REF]. However, at its northern distribution in Chile, A. chilensis populations are farms mostly or even entirely composed of vegetative tetrasporophytes [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF] and our genetic investigation did not refer to a northern population as the most likely source of the Peruvian male. Nonetheless, even if barely reproductive, farmed tetrasporophytes along Chile's northern coasts are still able to produce haploid gametophytes via sexual reproduction every once in a while and these spores can attach and grow on pebbles and shells scattered close to the farms (few fixed males recorded up to 27°S, SP-BAI, region of Caldera [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]). Thus, it is still possible that the male thallus fragment from Morro Sama originated from a rare male specimen in northern Chile in the Coquimbo or the Caldera region. Our genetic data, however, suggest the region of the Channel of Chacao to be the most likely source of the Peruvian genotype (see our results from STRUCTURE;

Channel of Chacao is located more than 2,600km south of Morro Sama). In the region of the Channel of Chacao and around the Island of Chiloé, large natural populations of A. chilensis are established at the opening of estuaries and rivers growing from spores and fixed on small pebbles, shells, or in rock pools.

Agarophyton thalli seem highly resistant and resilient to physiological stress and are able to survive long trips while drifting [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF][START_REF] Krueger-Hadfield | Invasion of novel habitats uncouples haplo-diplontic life cycles[END_REF][START_REF] Krueger-Hadfield | Genetic identification of source and likely vector of a widespread marine invader[END_REF]. Supporting this idea, ecophysiological studies have demonstrated that Agarophyton thalli have the ability to withstand a wide range of physico-chemical conditions (in A.

chilensis [START_REF] Gómez | Photosynthesis of the red alga Gracilaria chilensis under natural solar radiation in an estuary in southern Chile[END_REF]; in A. vermiculophyllum [START_REF] Nyberg | Long-term survival of an introduced red alga in adverse conditions[END_REF][START_REF] Lyons | Range expansion by invasive marine algae: rates and patterns of spread at a regional scale[END_REF]). Furthermore, it has been shown that rapid evolution can occur during range expansion by sieving advantageous genotypes during transport, which for example allows for successful establishment in new environments [START_REF] Lee | Evolutionary genetics of invasive species[END_REF]. In A. vermiculophyllum, adaptation to new environmental conditions during colonization has been proposed due to higher tolerance to extreme heat, cold, or low-salinity [START_REF] Sotka | Combining niche shift and population genetic analyses predicts rapid phenotypic evolution during invasion[END_REF] observed in nonnative populations compared to native ones. Hence, the mere distance between

Channel of Chacao and Morro Sama, and their contrasting latitudinal position (i.e., the two locations are separated by 25°) does not represent a sufficient impediment as to reject South Chile as a possible source of the Peruvian clone.

Indeed, A. chilensis has already undertaken and survived the much longer journey from New Zealand to Chile and was able to colonize most of Chile's coast [START_REF] Guillemin | Tracing the trans-pacific evolutionary history of a domesticated seaweed (Gracilaria chilensis) with archaeological and genetic data[END_REF] and long-distance dispersal has been suggested as an important factor for the distribution of marine macrophytes in the southern Pacific Ocean [START_REF] Smith | Rare long-distance dispersal of a marine angiosperm across the Pacific Ocean[END_REF].

Regardless of the exact Chilean source population, natural colonization by rafting thalli was possibly fostered by the strong northward-flowing Humboldt Current [START_REF] Thiel | The Humboldt Current system of northerncentral Chile: oceanographic processes, ecological interactions and socioeconomic feedback[END_REF][START_REF] Macaya | Float and raft: role of buoyant seaweeds in the phylogeography and genetic structure of nonbuoyant associated flora[END_REF]. Yet introduction linked to anthropogenic activities is not to be discarded, especially since the traffic of boats from Morro Sama has been reported in the northern parts of Chile [START_REF] Emol | Detenidas 6 naves peruanas en aguas chilenas[END_REF][START_REF] Redacción | Ahora son cinco las embarcaciones retenidas por la armada chilena[END_REF][START_REF] Aqua | Armada: Crece ingreso ilegal de embarcaciones pesqueras peruanas, AQUA -Acuacultura y Pesca[END_REF]; and the Peruvian population of A.

chilensis is actually found right at the landing pier for artisanal fisheries (Desembarcadero de Pesca Artesanal, DPA) of the Grau Port (Sama District, Tacna Province), a very small port built in 1995, with the capacity of mooring up to 15 artisanal fishing boats, which daily provide a wide variety of marine products.

Fig. 1 :

 1 Fig. 1: Description of the Peruvian population of Agarophyton chilensis,

Figure S1) also included 12 Fig. 2 :

 122 Figure S1) also included 12 Chilean populations (SP-BAI, F-CMA, F-PCH, F-LHE,

Acknowledgements:

For logistic and financial support in sample collections in Perú, we thank G. Montecinos, S. Faugeron, P.L. Gil Kodaka, and the FONDECYT Regular Grant #1170541 awarded to M.-L. Guillemin. Sampling was made with the help of the FONDECYT Regular Grant #1160930 awarded to S.

Faugeron.

V.R. did data analysis, prepared the figure and table; V.R. and M-L.G. wrote the main manuscript text; S.M. generated molecular data; J.C.Z.R and N.A. collected and analyzed samples as well as site descriptive information. All authors critically reviewed and approved the manuscript's final version prior submission.

Funding: This work was supported by the by the FONDECYT Regular Grant #1170541 awarded to M-L. Guillemin. and #1160930 awarded to S. Faugeron.

Despite the high numbers of samples and locations included in this study, the source of the Peruvian male thallus still remains elusive, especially because of the anthropogenic farming activities in Chile [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF]. Indeed, fresh thalli are commonly exchanged between fishermen's and southern populations were used to seed the artificially introduced farms in the North [START_REF] Guillemin | Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: how farming practices favor asexual reproduction and heterozygosity[END_REF], potentially blurring accurate genetic signature for single geographic sites/regions. Agarophyton chilensis, because of its economic interest, is relatively well known in Chile where most of the natural and farmed populations have been mapped. However, some recognized populations (unattached in the seawater lagoon of Puerto Saavedra, region of Araucanía, 38°S; attached on rocks at Punta Curaumilla or buried in sand in Quintero, region of Valparaíso, 33°S and 32°S, respectively) have not yet been genotyped. It could be interesting to add these populations to the Chilean data set in order to better infer the origin of the Moro Sama population.

Potentially, the utilization of next generation sequencing techniques and the acquirement of much higher numbers of genetic markers, such as SNPs, for population genetics may give a better resolution of the colonization pathways and sources of Agarophyton populations. Until then, the Peruvian A. chilensis population does not seem to be an ecological threat nor is the species categorized as invasive but it will be interesting to keep on monitoring the further development and proliferation of this isolated and unique clonal male.

[1] E. Rothaeusler, I. Gomez, I.A. Hinojosa, U. Karsten, L. Miranda, F. Tala, M.

Thiel, Kelp rafts in the Humboldt Current: Interplay of abiotic and biotic

Author Contributions Statement

Competing interests: The authors declare no competing interests.

Supplementary Information 00

Suppl. Table S1