Milan Marković
email: milan.markovic@univ-avignon.fr

Elodie Mezzatesta

Stéphanie Porcier

Cathy Vieillescazes

Carole Mathe
email: carole.mathe@univ-avignon.fr

Chemical Characterization of Embalming Materials of Four Ibis Mummies from the

Keywords: Alteration and ageing, Ancient Egypt, Animal Mummies, Infrared spectroscopy, Gas Chromatography coupled to Mass Spectrometry

and research institutions in France or abroad, or from public or private research centers.

Introduction

While anthropogenic body preservation is a phenomenon that could be seen in past communities ranging from today's northern Chile to modern Japan [START_REF] Arriaza | South American mummies: culture and disease, in: Mummies, Disease & Ancient Cultures[END_REF][START_REF] Sakurai | Mummies from Japan and Chine[END_REF], the deliberate mummification of animals appears to be a ritual practice exclusively limited to societies in Ancient Egypt. Thanks to the large amount of data gathered from numerous archaeological excavations it was discovered that Ancient Egyptians mummified millions of animals from the 16th Century BC (New Kingdom) until the 4th Century AD (Roman period) [START_REF] Abdel-Maksoud | A review on the materials used during the mummification processes in ancient Egypt[END_REF][START_REF] Bard | An introduction to the archaeology of ancient Egypt[END_REF][START_REF] Porcier | Datations par le carbone 14 de 63 momies animales du musée des Confluences à Lyon (France)[END_REF][START_REF] Richardin | Cats, Crocodiles, Cattle, and More: Initial Steps Toward Establishing a Chronology of Ancient Egyptian Animal Mummies[END_REF], of which many of them have been classified as "votive mummies" offered to gods and goddesses [START_REF] Ikram | Animals in ancient Egyptian religion: belief, identity, power, and economy[END_REF]. However, ancient writers such as Herodotus, Strabo and Pliny the Elder, indeed mention that animals were subjected to this ritual practice, but in addition, provide scarce information about the organic commodities used during mummification processes (Abdel-Maksoud and El-Amin, 2011; [START_REF] Bard | An introduction to the archaeology of ancient Egypt[END_REF][START_REF] Brettell | Organic residue analysis of Egyptian votive mummies and their research potential[END_REF][START_REF] David | Egyptian mummies: an overview[END_REF][START_REF] Ikram | Animals in ancient Egyptian religion: belief, identity, power, and economy[END_REF] More importantly, up to this date, there are only two scientific articles with published data regarding information, obtained through chromatographic and spectroscopic techniques, about the organic substances used in animal mummification practices [START_REF] Brettell | Organic residue analysis of Egyptian votive mummies and their research potential[END_REF][START_REF] Buckley | Complex organic chemical balms of Pharaonic animal mummies[END_REF].

In this regard, taking into account the importance of the study of mummified animal remains in general, and their vital role in social, economic, religious and political context of Ancient Egyptian discourse, the relevance of this research paper lies in contribution of new comparable dataset to the already existing and narrow corpus of knowledge concerning organic substances used in mummification of animals in Ancient Egypt.

This study dealt with a dual analytical approach based on Fourier Transform Infrared Spectroscopy (FT-IR) and Gas Chromatography coupled to Mass Spectrometry (GC-MS) analysis of the embalming agents used in mummifying four votive ibis mummies from the Egyptology collection of Musée des Confluences in Lyon, France. These mummified remains were already studied in traditional archaeological manner and a calibrated C 14 dating was realized [START_REF] Porcier | Datations par le carbone 14 de 63 momies animales du musée des Confluences à Lyon (France)[END_REF][START_REF] Richardin | Cats, Crocodiles, Cattle, and More: Initial Steps Toward Establishing a Chronology of Ancient Egyptian Animal Mummies[END_REF]. FT-IR allows to identify different materials (both organic and inorganic) on the basis of infrared absorption, so this analytical tool permits initial screening of the samples [START_REF] Font | Fourier transform infrared spectroscopy as a suitable technique in the study of the materials used in waterproofing of archaeological amphorae[END_REF][START_REF] Izzo | The study of pitch via gas chromatography-mass spectrometry and Fourier-transformed infrared spectroscopy: The case of the Roman amphoras from Monte Poro, Calabria (Italy)[END_REF][START_REF] Łucejko | An analytical approach based on X-ray diffraction, Fourier transform infrared spectroscopy and gas chromatography/mass spectrometry to characterize Egyptian embalming materials[END_REF][START_REF] Ménager | Study of Egyptian mummification balms by FT-IR spectroscopy and GC-MS[END_REF]. However, FT-IR analysis is not sufficient for delicate molecular identification of precise ingredients, especially in complex and aged mixtures, present in embalming matter used for mummification of animal mummies. Therefore, GC-MS is often used as a powerful complementary analytical technique [START_REF] Evershed | Chemistry of Archaeological Animal Fats[END_REF][START_REF] Jones | A prehistoric Egyptian mummy: Evidence for an 'embalming recipe' and the evolution of early formative funerary treatments[END_REF], most notably for molecular analysis, thus demonstrating invaluable help in identifying specific compounds called molecular markers which are diagnostic in their nature and can be found in ancient balms or produced during ageing and/or other alteration processes (Łucejko et al., 2012).

Due to their amorphous and chemically complex nature, the primary aim of this paper was to ascertain the chemical composition of the embalming material applied on four votive ibis mummies using FT-IR and GC-MS analysis, as well as to compare the obtained results from these two complementary analytical techniques. Furthermore, more specific aims included comparing the results from this work with those from other published research papers which allowed assessment of the composition of the organic balms, as well as to ascertain possible similarities and/or differences in mummification of ibis mummies from different archaeological sites and time periods.

Materials and methods

Archaeological samples

Wrapping samples from four votive ibis mummies were selected from the collection of the Musée des Confluences in Lyon (France). The specimens (MHNL 90002472, 90002475, 90002486, 90002491) were acquired by the museum in the early 20 th century. However, little is known about the origin of these mummified animals, with the exception of specimen 90002491 which comes from Roda (Upper Egypt). At that time, these mummified remains were studied by Dr. Louis Lortet, director of the Natural History Museum of Lyon, and the naturalist Claude Gaillard [START_REF] Lortet | La Faune Momifiée de l'Ancienne Égypte[END_REF].

Votive mummies under study are in a variable state of conservation. The mummy MHNL 90002472, partially unwrapped a century ago, consists solely of linen textiles in which it was initially wrapped, while the body of the animal itself is absent (Figure 1a). On the other hand, mummy MHNL 90002475 is intact and initial investigation established that the body of the ibis is present (Figure 1b). Finally, two other mummies are in a poor state of conservation (MHNL 90002486, 90002491), partially damaged, some of the original linen textile is missing, the biological tissues are conserved partially, damaged by necrophagous insects, and most bones are visible (Figure 1c and1d). Finally, these four votive mummies were chosen because of their state of preservation, which made it possible to carry out invasive analysis and to collect 50-200 mg of sample in order to characterize the organic matter present in balms. However, high historical value of these archaeological findings had necessitated certain levels of restraint during sampling. Worth mentioning is that one of the four mummies (MHNL 90002491) had been dated to the Greco-Roman period (92 cal BCE-65 cal CE) [START_REF] Porcier | Datations par le carbone 14 de 63 momies animales du musée des Confluences à Lyon (France)[END_REF][START_REF] Richardin | Cats, Crocodiles, Cattle, and More: Initial Steps Toward Establishing a Chronology of Ancient Egyptian Animal Mummies[END_REF]. Sampling of balms, corresponding to black amorphous substances, were realized on ibis referred MHNL 90002475 and MHNL 90002486 and sampling of impregnated textiles were done on mummies MHNL 90002472 and MHNL 90002491.

Solvents and reagents

All solvents and reagents were of analytical grade. Tetrahydrofurane (THF), hexane and N,O-Bis(trimethylsilyl)trifluoroacetamide/Trimethylchlorosilane (BSTFA/TMCS) were supplied by Sigma-Aldrich. Ethanol, dichloromethane (DCM) and diethyl ether were supplied by Merck.

Fourier Transform -Infrared Spectroscopy (FT-IR)

Archaeological samples were mixed and homogenized with 100 mg of KBr (VWR International, USA) and then pressed under 10 T/cm -2 to obtain a KBr pellet. Analyzes were performed with a Thermo-Nicolet iZ10 FT-IR spectrometer in transmission mode with OMNIC software. All FT-IR spectra were collected in the middle infrared (400 to 4000 cm -1 ) recording 32 scans.

Gas Chromatography -Mass Spectrometry (GC-MS)

GC-MS analyses were performed with a Thermo Scientific Focus gas chromatographic system composed of a Thermo Scientific Al 3000 auto-sampler coupled with an ITQ 700 ion trap mass spectrometer (Thermo Fisher Scientific). A GC fused silica capillary column Thermo trace GOLD TG-5MS (5% diphenyl / 95% dimethylpolysiloxane, 30 m length × 0.25 mm i.d.

× 0.25 μm film thickness) was used. The carrier gas was helium with a constant flow of 1 mL.min -1 . 1μL of each sample was injected in splitless mode. Mass spectra were recorded in electron impact mode with an electron ionization voltage of 70 eV, an ionization time of 25,000 μs and a mass range of 40-650 m/z, while the temperature of the injector was set at 250 °C.

Transfer line, ion trap and manifold temperatures were respectively set at 300 °C, 200 °C and 50 °C The separation was achieved with the following temperature program: 50 °C with a 2 min hold, increased at 10°C.min-1 to 200 °C, then increased at 2.5 °C.min-1 to 310 °C, then increased at 8°C.min-1 to 330 °C and held isothermally for 3 min. All of the injections were realized in triplicate. Peak identification was implemented following established protocol in the form of comparison with mass spectra and retention times of pure standard compounds, as well as using NIST database (NIST MS Search 2.0) 2.4. Preparation of samples 10 mg of sample was extracted with 1 mL of dichloromethane and ultrasound was applied during time period of 10 min. Then the solution was centrifuged at 6000 rpm for 10 min. The supernatant was set aside to extract the solid pellet again. This step was repeated 2 times. The three fractions were collected, combined and evaporated to dryness under a stream of nitrogen. All of the extractives were trimethylsilyled with 200 μL of BSTFA/TMCS (99/1 v/v) and heated at 70°C for 30 min, the mixture was again evaporated to dryness and then dissolved in 0.2 to 1 mL of a hexane/DCM mixture (1/1, v/v) and filtered on a polytetrafluoroethylene cartridge (PTFE, 0.45 μm, VWR) (Mezzatesta et al., 2020a). 1 μL of the solution was injected in GC-MS apparatus.

Saponification

10 mg of sample was extracted with 3 x 1 mL of THF aided by sonification (5 min) and then centrifuged at 6000 rpm (5 min). The supernatant was set aside to extract the solid pellet again. The solvent extracts were combined and then 2 mL of a solution of potassium hydroxide KOH 10% in MeOH/H2O (9/1, v/v) were added. The mixture was magnetically stirred and heated at 65°C during 1 hour. After evaporation 3 mL of pure water was added with 1 mL of HCl 5 M. The aqueous phase was washed with 3 x 5 mL of diethyl ether. The organic phases were combined and dried with anhydrous sodium sulphate, then filtered on filter paper. Excess reagent was evaporated to dryness under a stream of nitrogen. Trimethylsilylation was applied.

After evaporation, the derivatized sample was solubilized in hexane/DCM mixture (2/1, v/v) and filtered on PTFE cartridge before injection in GC-MS (Mezzatesta et al., 2020a).

2.6. Solid-Phase Extraction (SPE) 10 mg of sample was extracted with 1 mL of hexane/THF (1/1; v/v) aided by ultrasound for 5 min and then centrifuged at 6000 rpm for 5 min. The supernatant was set aside in order to extract the solid pellet again and these steps were repeated 3 times. The three fractions were combined and evaporated to dryness under a stream of nitrogen, then redissolved with 500 μL of hexane/THF (1/1; v/v). This solution is called charging. In parallel, a Strata® 200 mg / 3 mL SPE cartridge (Phenomenex) is calibrated with 4 mL of hexane. The initial 500 μL charge is deposited on the cartridge, then a first elution is carried out with 4 mL of hexane and collected in a hemolysis tube (fraction 1 for presence or absence of markers for bitumen, such as hopanes and steranes). A second elution is carried out with 4 mL of EtOH and then collected in another tube (fraction 2 for presence of resins). Finally, a final elution is carried out with 4 mL of DEE and 2% AcOH (fraction 3 for presence of fatty acids). Each fraction is evaporated to dryness under a stream of nitrogen. After trimethylsilylation with, fractions 1 and 2 were solubilized with 60 μL of a hexane/DCM mixture (2/1; v/v) while fraction 3 was solubilized with 1.5 mL of hexane/DCM (2/1; v/v). The three fractions were then filtered on a PTFE cartridge (0.45 μm) before respective injections in GC-MS apparatus (Mezzatesta et al., 2020b).

Results

FT-IR results

According to identified diagnostic and specific infrared bands (Table 1) such as hydroxyl (~3400 cm -1 ), methylene (~2960-2850 cm -1 ) and carbonyl (~1750-1650 cm -1 ) functional groups [START_REF] Bellamy | The infrared spectra of complex molecules[END_REF], all analyzed spectra of samples 90002472, 90002475, 90002486 and 90002491, unambiguously indicated the presence of organic material corresponding to terpenic compounds and fatty matter (plant oil and/or animal fat). The resulting FT-IR spectra of the four analyzed samples have shown a similar standard transmittance profile specific for diterpenic resins extracted from Pinaceae family [START_REF] Scalarone | Ageing behaviour and pyrolytic characterisation of diterpenic resins used as art materials: Colophony and Venice turpentine[END_REF]. Presence of diterpenic resin has been confirmed according to the several infrared signals specific to these compounds (Figure 2). Namely, hydrocarbon skeleton structures, present in tricyclic structures in diterpenoids, emit strong stretching C-H vibrations modes of =CH2 and CH3 groups displayed at ~2957-2872 cm -1 and ~2920-2850 cm -1 [START_REF] Font | Fourier transform infrared spectroscopy as a suitable technique in the study of the materials used in waterproofing of archaeological amphorae[END_REF][START_REF] Izzo | The study of pitch via gas chromatography-mass spectrometry and Fourier-transformed infrared spectroscopy: The case of the Roman amphoras from Monte Poro, Calabria (Italy)[END_REF]. Regarding the specific carbonyl C=O stretching band occurring between ~1720-1710cm -1 , the absorption frequency also suggests the presence of a plant resin in all analyzed samples (Łucejko et al., 2012). In terms of further assessments (presence of either diterpenic and/or triterpenic compounds), several spectroscopic studies on fresh resins have shown that absorption band of C=O carbonyl group produces its maximum in range between 1705-1690 cm -1 depending on terpenic resin type [START_REF] Ménager | Study of Egyptian mummification balms by FT-IR spectroscopy and GC-MS[END_REF]. Notably, as a diagnostic marker, location of the carbonyl band is used to distinguish between different types of terpenic compounds, in a way that C=O band for diterpenoids is always located below 1700cm -1 , and for triterpenoids it lies above this frequency [START_REF] Bruni | Identification of archaeological triterpenic resins by the nonseparative techniques FTIR and 13C NMR: The case of Pistacia resin (mastic) in comparison with frankincense[END_REF].

However, it is important to note that this "artificial border" can shift in degraded archaeological objects, especially in complex aged mixtures such as balms used for mummification [START_REF] Ménager | Study of Egyptian mummification balms by FT-IR spectroscopy and GC-MS[END_REF]. Furthermore, in samples 90002486 and 90002491, shoulder band around ~1740-1735 cm -1 (serving as diagnostic frequency for presence of methyl esters) together with methylene (=CH2) and methyl (CH3) groups bending at respectively 1463-1454 cm -1 and 1384-1373cm -1 (diagnostic frequencies for diterpenic pine resins present in all four samples) as well as with bending vibrations from COOH at ~1173 cm -1 , suggest the presence of a mixture of exceedingly oxidized and dehydrogenated molecules [START_REF] Font | Fourier transform infrared spectroscopy as a suitable technique in the study of the materials used in waterproofing of archaeological amphorae[END_REF]. These molecules are normally found in coniferous pine resins and they have been detected in the studied balms. On the other hand, the occurrence of fatty matter in the samples referred 9002475, 90002486 and 9002491 was confirmed through the presence of rocking C-H band at ∼720 cm -1 and stretching C-O band between ∼1170-1160 cm -1 . In all four samples these signals are valuable because they indicate the presence of the characteristic long linear molecular chains of fatty acids present in plant oils and animal fats [START_REF] Font | Fourier transform infrared spectroscopy as a suitable technique in the study of the materials used in waterproofing of archaeological amphorae[END_REF][START_REF] Ménager | Study of Egyptian mummification balms by FT-IR spectroscopy and GC-MS[END_REF].

Mixtures of oils, resins and beeswax are difficult to separate solely based on FT-IR analysis due to the overlapping of these signals. The characteristic bands of beeswax at 2920 cm -1 , 2850 cm -1 , 1740 cm -1 and 1173 cm -1 reflecting respectively the C-H bonds, as well as C=O and C-O bonds of the ester function were observed in samples 90002486 and 90002491 [START_REF] Cuní | Characterization of the binding medium used in Roman encaustic paintings on wall and wood[END_REF][START_REF] Svečnjak | An approach for routine analytical detection of beeswax adulteration using ftir-atr spectroscopy[END_REF]. As already discussed in previous lines, all of these bands could be also coming either from plant oils, or resinous substances.

The presence of proteins was possible in the samples 90002475 and 90002486 most notably due to FT-IR bands centered at ~1635 cm -1 (Amide I group) and 1540 cm -1 (Amide II group). Nevertheless, it is essential to underline here that GC-MS analysis was performed in order to target fatty matter and resinous compounds and therefore possible presence of proteins was not further assessed.

GC-MS results

The results of the gas chromatography-mass spectrometry analysis are summarized in Table 2. Analyzed data showed that primary commodities present in all four extracts from the embalming substance of ibis mummies are of organic nature originating most certainly from mixture of plant oils and/or animal fats, plant resins and beeswax.

Presence of beeswax

Fresh beeswax found in nature is defined as a complex mixture of different chemical compounds. This product made from the genus Apis is composed of long-chain fatty acids (C24-C34), n-alkanes (C23-C33) and mono-, di-and tri-esters, as well as some hydroxy-polyesters which are highly diagnostic of the presence of this substance [START_REF] Clark | Tracing the Evolution of Organic Balm use in Egyptian Mummification via Molecular and Isotopic Signatures[END_REF][START_REF] Ikram | Animals in ancient Egyptian religion: belief, identity, power, and economy[END_REF].

However, when compared to fresh beeswax, in archaeological beeswax several differences are observed which can occur due to the human processing of this material in the past, microbial action or any other processes occurring over time which could alter the original chemical structure of this substance. It is important to mention that in archaeological samples beeswax can undergo oxidation thus yielding monocarboxylic acids and long chain alcohols.

Furthermore, these long chain alcohols can undergo through process of oxidation, hence forming long chain fatty acids.

In this study presence of beeswax was observed in samples 90002486 and 90002491 without saponification preliminary step (Figure 3) through detection of several long-chain monocarboxylic fatty acids, while in samples 90002472 and 90002475, diagnostic markers essential for this substance were not identified in any of the analyzed chromatograms.

The characteristic fatty acid profile of beeswax [START_REF] Buckley | Organic chemistry of embalming agents in Pharaonic and Graeco-Roman mummies[END_REF][START_REF] Heron | The Chemistry of Neolithic Beeswax[END_REF], observed in samples 90002486 and 90002491, consisted of several fatty acids (FA)

ranging from C22 to C32, with lignoceric acid (C24, tetracosanoic acid) as the most abundant type, followed by cerotic (C26, hexacosanoic acid), montanic (C28, octacosanoic acid), melissic (C30, triacontanoic acid) and lacceroic (C32, dotriacontanoic acid) acids. n-Alkanes were not detected in chromatograms of samples 90002486 and 90002491 and a possible explanation for this particular phenomenon could be that the loss of alkanes happened due to extensive heating [START_REF] Heron | The Chemistry of Neolithic Beeswax[END_REF] of the embalming material (in support of this hypothesis the presence of retene have been also detected, see the below section). With the purpose of confirming either presence or absence of beeswax, saponification was performed as a preliminary step. Results obtained through saponification are in accordance with aforementioned data, that being the presence of beeswax was confirmed in samples 90002486 and 90002491, and absent in 90002472 and 90002475.

Identification of resins in balms

In this study, chemical markers of diterpenic carbon-structures diagnostic for resins coming from coniferous trees were identified in all analyzed ibis' mummies (Figures 3). 3). These oxidized and dehydrogenated abietane structures serve as markers for presence of coniferous diterpenic resins obtained from trees belonging to the Pinaceae family [START_REF] Brettell | Organic residue analysis of Egyptian votive mummies and their research potential[END_REF][START_REF] Buckley | Organic chemistry of embalming agents in Pharaonic and Graeco-Roman mummies[END_REF][START_REF] Colombini | Characterization of the Balm of an Egyptian Mummy from the Seventh Century B[END_REF][START_REF] Degano | Multi-analytical techniques for the study of pre-Columbian mummies and related funerary materials[END_REF]. Normally, in fresh diterpenic resins of coniferous trees, dehydroabietic acid is present but as a minor constituent unlike abietic acid which acts as a primary and most abundant component. However, with natural alteration processes (ageing), abundance of dehydroabietic acid starts to decrease and, other compounds are starting to appear like already mentioned 7-oxo-dehydroabietic acid which is the major oxidized diterpenoid, after dehydroabietic acid, present in the analyzed ibis' samples. These highly oxidized compounds indicate an advanced state of oxidation of conifer resin.

In addition to these results it is important to note that in all samples methyl esters derivatives were detected such as 7-oxo-dehydroabietic methyl ester (M •+ 328 and fragment ion of m/z 253 B + ) and 15-hydroxy-7-oxodehydroabietic methyl ester. These methylated derivatives occur during the preparation of wood tar with releasing of methanol during pyrolysis of the resinous wood [START_REF] Colombini | Characterisation of organic residues in pottery vessels of the Roman age from Antinoe ( Egypt )[END_REF][START_REF] Izzo | The study of pitch via gas chromatography-mass spectrometry and Fourier-transformed infrared spectroscopy: The case of the Roman amphoras from Monte Poro, Calabria (Italy)[END_REF]. Retene (M •+ 234 and fragment ion of m/z 219 B + ) was also identified in samples 90002486 and 90002491. This last compound is considered as a marker for pine pitch because when the resin is heated to high temperatures or distilled in a low oxygen environment to obtain a pitch, aromatisation, demethylation, and defunctionalisation reactions occur in the abietadiene and pimaradiene acids [START_REF] Colombini | Characterisation of organic residues in pottery vessels of the Roman age from Antinoe ( Egypt )[END_REF]. These phenomena lead to the formation of a series of products as norabietatrienes and tetrahydroretene, with retene as the final stable product of all these transformations.

Furthermore, we can argue that in samples 90002486 and 90002491 combined abundance of methyl esters with presence of retene indicated that a high-temperature pre-application processing of this resin was applied [START_REF] Brettell | Organic residue analysis of Egyptian votive mummies and their research potential[END_REF][START_REF] Jones | A prehistoric Egyptian mummy: Evidence for an 'embalming recipe' and the evolution of early formative funerary treatments[END_REF]. On the contrary, presence of retene was not confirmed in samples 90002472 and 90002475, meaning that resinous material employed for mummification was subjected to low-temperature preapplication heating. Additionally, we can argue that this particular ingredient used for mummification of these mummies, had to be imported from outside of the territory of Ancient Egypt and such claims are already reported in ancient texts from mid-first century AD [START_REF] Chapman | The embalming ritual of late period through Ptolemaic Egypt[END_REF].

Presence of plant oil and/or animal fat

Thanks to the written historical sources (great number of ancient Egyptian texts identifying oils and fats as fundamental components of perfumes, cosmetics and medicines) [START_REF] Clark | Tracing the Evolution of Organic Balm use in Egyptian Mummification via Molecular and Isotopic Signatures[END_REF][START_REF] Ikram | Animals in ancient Egyptian religion: belief, identity, power, and economy[END_REF] associated with archaeological data (lipids preserved in canopic pottery jars used during mummification), researchers were able to recognize to importance of these substances in mummification process [START_REF] Łucejko | Chemical analyses of Egyptian mummification balms and organic residues from storage jars dated from the Old Kingdom to the Copto-Byzantine period[END_REF][START_REF] Ménager | Study of Egyptian mummification balms by FT-IR spectroscopy and GC-MS[END_REF]. Based on these data, it was observed that certain plant oils and animal fats were convenient as a foundation for applying and/or mixing other ingredients, while others were most likely used due to their hydrophobic and drying properties [START_REF] Clark | Tracing the Evolution of Organic Balm use in Egyptian Mummification via Molecular and Isotopic Signatures[END_REF].

With regard to the presence of markers for plant oils and/or animal fats in the ibis mummies, analyzed data revealed a great number of linear saturated monocarboxylic fatty acids in the C6-C32 range, with myristic (C14:0, M •+ 300 and diagnostic fragment ions of m/z 75, 117, 285), palmitic (C16:0, M •+ 328 and diagnostic fragment ions of m/z 75, 117, 313) and stearic (C18:0, M •+ 356 and diagnostic fragment ions of m/z 75, 117, 341) acids as the most abundant acidic components in obtained chromatograms. A general approach in differencing between both fresh and degraded remains of oils and fats, in archaeological samples, is to calculate the ratio of C16:0 and C18:0 fatty acids [START_REF] Eerkens | GC-MS analysis and fatty acid ratios of archaeolological potsherds from the western Great Basin of North America[END_REF][START_REF] Evershed | Organic residue analysis in archaeology: The archaeological biomarker revolution[END_REF][START_REF] Evershed | Chemistry of Archaeological Animal Fats[END_REF].

However, this common method is not exactly best suited when it comes to analysis of balms applied in Ancient Egypt mummification processes [START_REF] Ménager | Study of Egyptian mummification balms by FT-IR spectroscopy and GC-MS[END_REF]. The ratio between these two fatty acids can be altered due to lipid thermal degradation and what is more likely, embalmers could have using a mixture of different oils and/or fats, thus "contaminating"

proportion between these essential compounds. Moreover, C16:0/C18:0 ratio could be influenced by the presence of beeswax which contains high levels of palmitic acid.

Unsaturated fatty acid profile was observed only in sample 90002475 through the presence of C18:1 (oleic acid). In the case of C18:1, as it is most common in plant sources, specifically in large quantities in vegetable oils (e.g. olive oil), it can also be constitutive part of animal fats, hence this particular unsaturated fatty acid does not provide enough information for precise determination of the origin of this compound [START_REF] Clark | Tracing the Evolution of Organic Balm use in Egyptian Mummification via Molecular and Isotopic Signatures[END_REF][START_REF] Evershed | Organic residue analysis in archaeology: The archaeological biomarker revolution[END_REF][START_REF] Evershed | Chemistry of Archaeological Animal Fats[END_REF], as it is possible for instance with erucic and gondoic acids (biomarkers for radish oil) [START_REF] Copley | Gas chromatographic, mass spectrometric and stable carbon isotopic investigations of organic residues of plant oils and animal fats employed as illuminants in archaeological lamps from Egypt[END_REF].

Furthermore, the presence of odd chain fatty acids in archaeological samples, should also be taken into particular consideration. Namely, non-negligible quantities of C15:0 (M 90002475, 90002486 and 90002491 (Donato et al., 2013;[START_REF] Eerkens | GC-MS analysis and fatty acid ratios of archaeolological potsherds from the western Great Basin of North America[END_REF][START_REF] Lantos | Exploring the culinary uses of Santa María and Belén painted vessels from the Late Intermediate Period in Catamarca, Argentina[END_REF][START_REF] Lantos | Preliminary molecular evidence of feasting in the Inca site of Fuerte Quemado-Intihuatana, Catamarca, Argentina[END_REF][START_REF] Łucejko | Chemical analyses of Egyptian mummification balms and organic residues from storage jars dated from the Old Kingdom to the Copto-Byzantine period[END_REF]. In an extensive and extremely comprehensive study conducted by [START_REF] Eerkens | GC-MS analysis and fatty acid ratios of archaeolological potsherds from the western Great Basin of North America[END_REF], it was strongly suggested that quantifying the ratios between odd (C15:0 + C17:0) and even chain fatty acids (C12:0 + C14:0 + C16:0 + C18:0) could provide insights whether we can denote or deny the presence of ruminant fat in studied samples. In the aforementioned research, it was pointed out that the calculated values that are higher than 0.04 are distinctive for ruminant animals, which was the case in all four analyzed samples of ibis mummies (~0.05).

Nevertheless, we should be careful with this, given the fact that the presence of C15:0 and C17:0 could result from soil bacterial degradation of lipids within the body of the animals. Indeed, contamination from body fluids of animal mummies is often an issue in this type of analyses.

In the light of the foregoing discussion, it would seem difficult to achieve a more precise plant oil or animal fat origin assessment, present in studied balms, based exclusively on presence of the fatty acid profile in the analyzed samples. Embalmers could have been using a mixture of different plant oils and animal fats, and more importantly, due to degradation pathways of major diagnostic unsaturated components, which is confirmed by the presence of short chain dicarboxylic acids in the studied samples. Regarding the presence of the aforementioned dicarboxylic acids it was clearly observed in gas chromatograms of every sample that they represent the second most abundant components in the acidic profile. Further assessment of data identified presence of α, ω -dicarboxylic acids ("diacids") in the C4 to C12 carbon chain length range, with azelaic (diC9, nonanedioic acid) as the most abundant one together with suberic and sebacic diacids. Dicarboxylic acids are naturally not present in plant oils, resins, waxes and animal fat; they are formed as a result of several different oxidative degradation mechanisms of the double bond(s) in mono-, or poly-unsaturated fatty acids. Thus, the position of the double bond is directly related to the carbon chain length of the diacids formed. Therefore, the presence and the amount of diC9 (azelaic acid, originating from C18 fatty acid with double bond between carbons 9 and 10 like linoleic and linolenic acids) combined with presence of diC8 (suberic acid) and diC7 (pimelic acid) acids are indicators of degraded vegetable oils, thus suggesting that a siccative or semi-siccative plant oil high in oleic acid was used during mummification of all four samples that are the subject of this study [START_REF] Brettell | Organic residue analysis of Egyptian votive mummies and their research potential[END_REF][START_REF] Colombini | Characterisation of organic residues in pottery vessels of the Roman age from Antinoe ( Egypt )[END_REF][START_REF] Copley | Gas chromatographic, mass spectrometric and stable carbon isotopic investigations of organic residues of plant oils and animal fats employed as illuminants in archaeological lamps from Egypt[END_REF][START_REF] Degano | Multi-analytical techniques for the study of pre-Columbian mummies and related funerary materials[END_REF][START_REF] Jones | A prehistoric Egyptian mummy: Evidence for an 'embalming recipe' and the evolution of early formative funerary treatments[END_REF][START_REF] Russa | A scientific approach to the characterisation of the painting technique of an author: The case of Raffaele Rinaldi[END_REF][START_REF] Łucejko | Chemical analyses of Egyptian mummification balms and organic residues from storage jars dated from the Old Kingdom to the Copto-Byzantine period[END_REF], 2012;[START_REF] Tchapla | Characterisation of embalming materials of a mummy of the ptolemaic era. Comparison with balms from mummies of different eras[END_REF].

Additionally, the presence of ricinoleic acid (12-hydroxy-9-cis-octadecenoic acid) acting as a diagnostic compound of castor oil was identified only in sample 90002491 (M •+ 442 and fragment ion of m/z 187 B + ). However, the fatty acids distribution in this sample is not dominated by this chemical marker, which in this case acts as a minor constituent (Figure 4).

The explanation for this phenomenon can be explained through interpretation of the resulting fatty acid profile which originates most probably from a mixture with other plant oils and/or animal fats that were included in the formulation of this specific balm applied in mummification of mummy 90002491 [START_REF] Tchapla | Characterisation of embalming materials of a mummy of the ptolemaic era. Comparison with balms from mummies of different eras[END_REF].

Discussion

Up to this date, only few scientific articles dealing with animal mummification are available to the scientific community [START_REF] Brettell | Organic residue analysis of Egyptian votive mummies and their research potential[END_REF][START_REF] Buckley | Complex organic chemical balms of Pharaonic animal mummies[END_REF]) and total number of four balms from other votive ibis mummies were chemically characterized.

Therefore, it is important to realize a comparison between the ibis balms of this study and those described in the specialized literature. Unlike the ibis mummies that are the subject of this study, in article published by [START_REF] Buckley | Complex organic chemical balms of Pharaonic animal mummies[END_REF] it was argued that embalming agents consisted, mainly, of hydrolyzed plant sugar gum used for securing the mummy wrappings. Additionally, only trace quantities of fatty acids were detected with high amounts of C16 to C18 ratios, which, according to authors of that paper, indicated oil of plant origin [START_REF] Buckley | Complex organic chemical balms of Pharaonic animal mummies[END_REF][START_REF] Buckley | Organic chemistry of embalming agents in Pharaonic and Graeco-Roman mummies[END_REF]. However, it is important to emphasize the fact that the mummy from Buckley et al. study originate from XXVI-XXX dynasty period (664-343 BC) as opposed to sample 90002491 (Roda) which was dated to the very end of the Ptolemaic period (92-65 cal BC) [START_REF] Richardin | Cats, Crocodiles, Cattle, and More: Initial Steps Toward Establishing a Chronology of Ancient Egyptian Animal Mummies[END_REF]. Given the fact that both of these samples originate from archaeological sites in Lower Egypt it is possible to consider the difference in their embalming strategy. According to numerous research papers, it is argued that the increase in use of conifer resin exudates in everyday and religious life of Egyptian societies started with Ptolemaic and Roman periods possibly due to relative abundance and ease of extraction [START_REF] Colombini | Characterization of the Balm of an Egyptian Mummy from the Seventh Century B[END_REF]. Number of research works, dealing with human mummification practices, demonstrated that in majority of cases, presence of conifer resins acts in a certain way as indispensable part of embalming material that were applied during mummification due to their highly valued antimicrobial properties [START_REF] Buckley | Organic chemistry of embalming agents in Pharaonic and Graeco-Roman mummies[END_REF][START_REF] Colombini | Characterization of the Balm of an Egyptian Mummy from the Seventh Century B[END_REF][START_REF] Degano | Multi-analytical techniques for the study of pre-Columbian mummies and related funerary materials[END_REF][START_REF] Ikram | Animals in ancient Egyptian religion: belief, identity, power, and economy[END_REF].

On the other hand, results of three ibis mummies published by Brettel et al. (2017) Namely, in this study no hydrocarbon diagnostic biomarkers characteristic for bitumen were observed. The absence of diagnostic markers such as steranes and hopanes was confirmed in all chromatograms obtained by complementary experiments using Solid-Phase Extraction protocol (Mezzatesta et al, 2020b). This SPE protocol was performed on all of the samples and it permitted to clearly confirm the occurrence or the absence of bitumen in the studied archaeological samples.

Beeswax was detected through presence of several long chain monocarboxylic saturated fatty acids (C26, C28, C30, C32). In contrast to this, in Brettel et al. paper, presence of bitumen was observed in samples 165 and 471, while beeswax was absent in the analyzed chromatograms.

Conclusion

The chemical analysis of organic embalming material employed in Late Ptolemaic/Early Roman Egyptian mummification of ibis animals from the Collection of the Musée des Confluences in Lyon (France) was performed. A dual analytical approach was employed in order to characterize the organic matter present in balms and impregnated textile of four votive ibis mummies.

In first step, the resulting FT-IR spectra have shown the presence of mixture of terpenic compounds and fatty matter (plant oil and/or animal fat). A standard transmittance profile of diterpenic resins extracted from Pinaceae family was more particularly observed.

In a second step, the GC-MS technique has confirmed and clarified certain results.

Beeswax was observed in samples 90002486 and 90002491. Concerning these two samples, the combined abundance of methyl esters with presence of retene indicated that hightemperature pre-application processing of the resinous matter was applied, while in samples 90002472 and 90002475 resin was subjected to lower temperature, which is in accordance with the corresponding FT-IR results of these archaeological samples.

Moreover, some indicators of degraded plant oils suggested that a siccative or semisiccative plant oil was used in the preparation of these balms. At last, a diagnostic marker of castor oil was identified only in sample 90002491. According to FT-IR results, proteins were present in samples 90002475 and 90002486. GC-MS analysis was performed in order to target lipid/resinous compounds and therefore the presence of proteins was not further assessed.

Additionally, the origin of proteinous sources are complicated because they could be a contaminant originating from the body fluids.

Results of this study showed that applied balms were complex mixtures, consisting of plant oils and/or animal fats, conifer resins and beeswax in certain cases, which when compared to other animal and human mummies confirm that similar range of substances were used for mummification during Late Ptolemaic and early Roman period, but with possibility of different approach in methodology of embalming the body of the animal.

  Further chemical analysis focused on interpretation of these diterpenic markers revealed clearly the presence of dehydroabietic acid (molecular peak M •+ 372 and base peak fragment ion of m/z 239 B + ), 7-oxodehydroabietic acid (M •+ 386 and fragment ion of m/z 253 B + ), 15-hydroxy-7oxo-dehydroabietic acid (M •+ 460 and fragment ion of m/z 445 B + ), 3-hydroxydehydroabietic acid and 7-hydroxydehydroabietic acid in the sample 90002491 (Figure

605R:Figure 1 .

 1 Figure 1. Photographs of the 4 ibis mummies of the Musée des Confluences: (a) MHNL 90002472; (b) MHNL 90002475; (c) MHNL 90002486; (d) MHNL 90002491 (© Program MAHES).

Figure 2 .Figure 3 .

 23 Figure 2. FT-IR spectra of samples 90002472, 90002475, 90002486 and 90002491

  , are more similar with those obtained in this study. For two mummies it was determined that they belong to Ptolemaic (Inv. Num. 165, Sakkara site) and Roman period (Inv. Num.162). As in this study, paper from Brettel et al. showed that the main component of the analyzed balm contained either plant oil or animal fat, or combination of both. Also, the diterpenoids were confirmed through presence of Pinaceae resin in sample 471, while in sample 162 triterpenoids were observed through presence of Pistacia spp. resin which contrasts results obtained in this study with the absence of triterpenoids in all of the samples. In this study the presence of retene, observed in samples 90002486 and 90002491 which acts as a diagnostic marker for extensive heating, was not detected in any of the samples studied by Brettel et al. This difference begs the question of how they then mixed and process the various material needed for embalming the bodies of the animal? Furthermore, through additional comparison of data between these two research works, we can clearly notice another thing that implies the possibility of different approach in embalming strategy through presence or absence of either bitumen or beeswax.

Table 1 598

 1 FT-IR data and interpretation of the obtained results

	To conclude, this research study offers a new comparative dataset in a still evolving
	field, thus contributing to the development of scientific work of Egyptian votive animal
	mummies.

Table 2 .

 2 List of identified compounds obtained from GC-MS analysis of embalming substances 604 from ibis' mummies (D: dicarboxylic acids; S: Saturated fatty acids; U: Unsaturated fatty acids;

Acknowledgements

This research was financially supported by Marie Skłodowska-Curie Innovative Training Network, The ED-ARCHMAT European Joint Doctorate, H2020-MSCA-ITN-EJD ED-ARCHMAT Joint Doctorate (Project ESR10, grant agreement no 766311) and it was carried out in connection with MAHES Program supported by the Agence Nationale de la Recherche from the « Investissement d'Avenir » program ANR-11-LABX-0032-01 LabEx ARCHIMEDE. The authors of this work are grateful to Dr. Didier Berthet, curator at the Musée des Confluences in Lyon (France) for giving us the opportunity to work on samples which are part of the collection of animal mummies. The authors acknowledge the anonymous reviewers

for their careful reading of our manuscript and their many insightful comments and suggestions.

Conflict of interest

The authors declare that they have no conflict of interest.


Jade Lopez

Natacha Nikolic

Martin Riethmuller

Jérôme Dubos

Patrick Pinet

Patxi Souharce

François-Xavier Couzi

Matthieu Le Corre

Audrey Jaeger

Laurence Humeau

High genetic diversity despite drastic bottleneck in a critically endangered, long-lived seabird, the Mascarene Petrel Pseudobulweria aterrima

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

the universal M13 forward primer to enable fragment analysis multiplexing. Simplex PCR amplifications, tar geting one locus at a time, were performed using a Gen eAmp PCR System 9700 (Applied Biosystems) in a 10 lL reaction volume containing 5 lL of MasterMix Applied 2x (Applied Biosystems), 0.025 lM of the for ward primer with M13 5' tail, 0.25 lM of the reverse primer, 0.25 lM of dyes and 2 lL of genomic DNA (15 ng/lL). PCR amplifications were carried out under the following conditions: an initial denaturing step at 95 °C for 5 min, followed by 40 cycles of 95 °C for 30 s, annealing temperature for 30 s (Table S1) and 72 °C for 30 s, and a final elongation at 72 °C for 20 min. Two different simplex PCR plates, each with a different dye, were mixed and PCR product sizes were determined using a 3730XL DNA analyser (Applied Biosystems) and sized with a LIZ (500) standard using GeneMapper (Applied Biosystems).

For each locus, evidence for null alleles, large allele dropout and stutter peaks were examined using Micro Checker (Van Oosterhout et al. 2004). The test for link age disequilibrium among loci was conducted with GENEPOP (Rousset 2008) using a Benjamini and Yeku tieli correction (Benjamini & Yekutieli 2001, Narum 2006). Diversity indices were calculated with GenAlex (Peakall & Smouse 2012). Hardy Weinberg Equilibrium (HWE) was examined with GENEPOP (Rousset 2008) using an exact test with 100 batches and 1000 iterations per batch for each locus and a Chi square test for global HWE. Contemporary genetic effective population size (Ne) was estimated using the VarEff 1.2 R package (https://forge dga.jouy.inra.fr/). In addition, past changes in effective population size from microsatellite data (Nikolic & Chevalet 2014) were estimated with the approximate likelihood Markov chain Monte Carlo (MCMC) approach in the VarEff 1.2 R package (https://forge dga.jouy.inra.fr/). The mutation rate of microsatellite markers used in theVarEff 1.2 R package was calculated according to the method of Storz and Beaumont (2002) demographic and environmental stochasticity that pre vail (Lynch & Gabriel 1990, Lynch & Lande 1998, Masel 2012). Species life history traits may influence the rate of genetic variability decrease (Lipp e et al. 2006). For example, the loss of genetic diversity could be slo wed down in monogamous species (Kuo & Janzen 2004, Weiser et al. 2013). Monogamous breeding will retain genetic diversity more effectively than situations that allow mate choice or intrasexual competition (Gooley et al. 2018). Long generation time and overlapping gen erations could also reduce genetic loss. Multiple repro ductive outputs in long lived species result in higher genetic contribution to subsequent generations com pared with one or few reproductive outputs. When a population passes through a bottleneck, reduction of genetic diversity depends on population size and time, measured in number of generations (Hailer et al. 2006). Overlapping generations, often associated with a long generation time, thus reduce the loss of genetic diversity by allowing multiple cohorts simultaneously to be part of a genetic pool.

The Mascarene Petrel is a primarily monogamous and long lived species with delayed sexual maturity (Schreiber & Burger 2001) and an estimated genera tion time of 17.7 years according to Birdlife Interna tional. Thus, we can expect that the loss of genetic diversity is less important than expected in this species even if it has a small population size. The objective of this study was to conduct a first assessment of the evolutionary potential of Mascarene Petrels, thereby informing future conservation measures and to see whether the results support the hypothesis that life history traits could preserve allelic diversity in small populations. We identified and characterized polymor phic microsatellite loci in order to investigate: (1) genetic diversity and inbreeding, (2) contemporary effective population size and (3) a potential popula tion bottleneck in this species.

METHODS

Total genomic DNA was extracted from whole blood samples of 22 Mascarene Petrels found grounded during the seabird rescue campaign on Reunion Island from 2008 to 2018. Blood samples were stored in 70% etha nol, and DNA was then extracted with the QIAmp Blood & Tissue kit (Qiagen).

A genomic library was constructed using DNA of one bird. Fifteen microsatellite sequences were isolated by Ecogenics GmbH (Zurich, Switzerland; Data S1).

A 3 primer PCR approach using an M13 tail (5' CACGACGTTGTAAAACGAC 3') for the forward pri mer was used for microsatellite loci amplification of DNA from all 22 birds, following Schuelke (2000). Four different dyes (6 FAM, PET, VIC, NED) were used for

RESULTS

Only one locus (Pseate 7805) had null alleles. Analyses were performed without this locus and these did not dif fer from analyses with all markers, so it was kept in this study. No large allele dropout and no stutter peaks were detected for any of the loci. No significant linkage dise quilibrium was observed among the loci (P > 0.05). The number of alleles per locus (Na) ranged from 3 to 16, with an average of 7.27 (Table 1). The mean number of effective alleles (Nef) (from Kimura & Crow 1964) was 4.01 per locus and was always lower than Na, highlight ing the presence of rare alleles. The observed (Ho) and expected (He) heterozygosities had means of 0.68 and 0.67, respectively. Ho reached 1 for locus Pseate 5563, which is 100% heterozygous for this locus. No signifi cant deviation from HWE was found in the population and the mean Fis was negative ( 0.051) and non signifi cant (P 0.213). With regard to loci, only locus Pse ate 7805 showed significant deviation from HWE (P 0.001).

The 15 microsatellite markers shared a similar range of mutation rate of around 3 x 10 -4 (sd 0.0004) with MSVAR estimates. The estimate of contemporary effec tive population size (Ne) from 22 stranded individuals was 1211 individuals in harmonic mean (95% confi dence interval (CI) 489 7999) from VarEff analysis. Estimates of the posterior distribution of past effective population sizes revealed a relatively large ancestral pop ulation size, three times larger than the current estimate (current theta index 4.405, past theta index 12.886). Analysis of the posterior distribution of the TMRCA showed a clear peak about 10 000 genera tions ago and confirmed a decrease in population size in the past, with a smaller peak at about 500 generations (Figure S1). The two bottlenecks detected had high con fidence intervals of 94% but the beginning of the oldest peak interval (10 000 generations) was unclear due to the mixed signals of overlapping peaks. Bottleneck anal ysis based on expected heterozygosity excess also showed clear support for a recent population contrac tion. Both TMP and SSM models were consistent with the scenario of a bottleneck according to the results of Wilcoxon sign rank test, sign test and standard differ ence test (TPM: P 0.041, 0.002 and 0.073, respec tively; SMM: P 0.011, 0.000 and 0.030, respectively).

DISCUSSION

These results show the importance of understanding genetic diversity in rare and critically endangered spe cies. Indeed, our results suggest that an assumption of low genetic diversity in very rare species is not always supported and that conservation of the Mascarene Petrel may be successful despite a very small population size. It is interesting to note that Mascarene Petrels have a relatively high genetic diversity (highlighted by the anal ysis of Na and Nef values) for a rare and threatened spe cies that appears to have suffered a recent bottleneck (Ardern & Lambert 1997, Spielman et al. 2004) (2007) simulations on Wandering and Amsterdam alba trosses (Diomedea exulans and Diomedea amsterdamen sis), which have respectively a large and small population size, support the hypothesis that genetic diversity in these two long lived species was already depleted prior to their divergence. Amsterdam Albatross would be able to maintain its genetic variation over a very long period of time, due to its life history traits: long life span, high reproductive success, inbreeding avoidance behaviours (e.g. Amos & Balmford 2001) and odour based individual recognition (e.g. Bonadona & Nevitt 2004). Although there are some limitations in comparing genetic diversity across microsatellite studies, our study adds to a body of work that suggests that long lived species may be able to maintain their genetic variability, a key factor enabling survival of a natural population (Frankham 2005).

Our results suggest that there is still high genetic diversity in the Mascarene Petrel, supporting the argu ment that conservation efforts are not too late for this species. Further studies of diversity and genetic structur ing, associated with other markers such as single nucleotide polymorphisms (SNPs), and of additional individuals sampled from the newly discovered breeding sites could help to better understand this species and contribute to more informed conservation planning.

This study is a production of the European project LIFE + Petrels (grant number: LIFE13 BIO/FR/000075) co led by Le Parc national de La R eunion, l'Universit e de La R eunion, La Soci et e d'Etudes Ornithologiques de La R eunion (SEOR) and l'Office National de la Chasse et de la Faune Sauvage, with financial support from the European Union, La Direction de l'Environnement l'Am enagement et du Logement (DEAL) and Le Conseil D epartemental of Reunion Island. We thank all of the people who have participated in the SEOR rescue cam paign of Mascarene Petrels, especially Fabien Jan, Julie Tour metz and Samantha Renault. Thanks to M. Goron, M. Manoury and D. Da Silva for their help in the laboratory. We are very grateful to Claude Chevalet for improving the VarEff package and allowing us to calculate confidence intervals around detected bottlenecks. We also thank P. Hodum for values are also lower than Na values, which may suggest the presence of rare alleles in this population. Inbreeding and substructuring (Wahlund effect) have not been detected in the population, as indicated by the absence of a significant deviation from HWE (Wright 1969, Gar nier G ere & Chikhi 2001).

Assuming an average generation length of 17.7 years for this species (Birdlife International 2018), the two peaks observed with the VarEff package would then indicate two population bottlenecks about 8850 and 177 000 years ago. The first event was consistent with the tests for heterozygosity excess in the Bottleneck pro gram, which is detectable over a relative short period 2Ne 4Ne generations in the past (Cornuet & Luikart 1996), and both analyses (VarEff package and Bottle neck) converged towards a reduction in population size.

Despite these findings, we interpret our results with caution because our sample size is small and estimates of the time of the demographic event could be more biased and subject to higher error than are estimates of Ne (Cabrera & Palsbøll 2017). Cornuet et al. (2008) suggested that the poor estimation performance in time of the demographic event is caused by insufficient data. Moreover, the signal for a population decrease could also be due to population structure, which is known to generate spurious signals of bottlenecks (Nikolic & Che valet 2014, Mazet et al. 2015). VarEff can be used to detect the effect of structure by varying the sampling strategy (Nikolic & Chevalet 2014, Salmona et al. 2017) but we were limited in this study by the small number of individuals sampled.

High genetic diversity has already been observed in some vulnerable procellariiform species. Hale et al. (2015) reported high genetic diversity in two relict Hut ton's Shearwater Puffinus huttoni breeding populations. They found an average of 6.89 alleles/locus with an average Ho (observed heterozygosity) of 0.49 in the first population (n 39), and 7.33 alleles/locus with Ho 0.45 for the second population (n 30). Gravley et al. (2019) also found high genetic diversity in two subspecies of Northern Fulmar (Fulmarus glacialis rodger sii and Fulmarus glacialis auduboni). They found an aver age of 5.0 alleles/locus with an average Ho of 0.40 (n 39) for the first species (F. g. rodgersii), and an average of 6.1 alleles/locus with an average Ho of 0.45 for the second (F. g. auduboni)(n 30). Loss of genetic diversity should occur whenever a population goes through a bottleneck (Nei et al. 1975) and relatively high genetic diversity in a rare species can indicate that decline in population size is recent (Moritz 2002).

Population contraction over a large number of gener ations may be required for loss of genetic diversity but this effect could be influenced by a species' life history traits, such as long generation times, delayed sexual maturity and/or the rate of demographic fluctuation (Kuo & Janzen 2004). This phenomenon has been improving the English text. We thank Genoscreen GmbH (Zur ich, Switzerland) for the development of microsatellite markers and the Gentyane platform (Clermont Ferrand, France) for determination of the PCR product sizes. Finally, we are grateful for the efforts of the reviewers to improve the manuscript.

  implemented in the MSVAR 1.3 pro gram. The likelihood frequency of bottleneck events from the time to the most recent common ancestor (TMRCA) detected has been estimated with a new function source (BTLIKE, with free access and help sup port on the website https://forge dga.jouy.inra.fr/).

	Finally, we used Bottleneck 1.2.02 (Piry et al. 1999) to
	test for recent changes in Ne using three different tests
	based on expected heterozygosity excess: Wilcoxon sign
	rank test (two tailed for heterozygosity excess or defi
	ciency), sign test and standard difference test (100 000
	iterations; Cornuet & Luikart 1996), and under two
	mutation models: a two phase (TPM; non step
	wise 5%, variance 12; typical values for many
	microsatellite markers; Busch et al. 2007) and a stepwise
	mutation model (SMM).

Table 1 .

 1 . Nef Results of initial microsatellite primer screening for Mascarene Petrels. in other bottlenecked populations (Hailer et al. 2006, Pickles et al. 2012) and supports the hypothesis that monogamy and long generation time could slow genetic diversity loss after the detected bottleneck in the Mascarene Petrel population. For example, Hailer et al.

	Locus	n	Na	Nef	Ho	He	Fis	HWE test
	Pseate 143	20	9	2.996	0.600	0.666	0.099	0.052
	Pseate 255	22	8	5.469	0.864	0.817	0.057	0.647
	Pseate 321	22	6	3.025	0.773	0.669	0.154	0.926
	Pseate 1317	22	7	3.546	0.591	0.718	0.177	0.453
	Pseate 1500	22	3	1.865	0.500	0.464	0.078	1.000
	Pseate 1594	22	5	3.315	0.727	0.698	0.041	0.748
	Pseate 1603	22	12	4.914	0.773	0.796	0.030	0.050
	Pseate 1837	22	4	1.537	0.409	0.349	0.172	1.000
	Pseate 3421	22	4	1.624	0.455	0.384	0.183	1.000
	Pseate 3689	22	4	2.127	0.636	0.530	0.201	0.702
	Pseate 5557	22	3	2.451	0.727	0.592	0.229	0.611
	Pseate 5563	22	16	12.253	1.000	0.918	0.089	0.966
	Pseate 7441	22	13	6.127	0.909	0.837	0.086	0.133
	Pseate 7805	22	9	5.319	0.636	0.812	0.216	0.001
	Pseate 8002	22	6	3.639	0.727	0.725	0.003	0.437
	All loci
	Mean	21.867	7.267	4.014	0.688	0.665	0.051	0.213
	se	0.133	1.012	0.698	0.043	0.044	0.035	--

Fis coefficient of consanguinity (Wright 1931); He expected heterozygosity; Ho observed heterozygosity; n number of individuals; Na total number of alleles per locus; Nef number of effective alleles per locus; HWE test P-values of the Hardy Weinberg equilibrium exact test (significant values in bold, P < 0.05).

observed

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are pre sent in Table S2


Wenhui Pang

Kazuki Nishino

Tsuyoshi Ogikubo

Masaaki Araidai

Masashi Nakatake

Guy Le Lay

Junji Yuhara

Epitaxial growth of honeycomb-like stanene on Au(111)

Stanene, which is predicted to be a quantum spin Hall topological insulator with tunable topological state, seems to be the most promising candidate of the post-graphene elemental two-dimensional (2D) materials. Here, we prepared epitaxial honeycomb-like stanene on gold (111) substrates and investigated its superstructure by Low Energy Electron Diffraction and Scanning Tunneling Microscopy. Angle-Resolved PhotoEmission Spectroscopy was applied to explore the electronic structures, further confirmed by first principles calculations. The stanene-like sheet forms a nearly planar structure on the Au(111) surface with a "2×√3" superstructure in large surface areas. Core-level spectroscopy reveals that the stanene-like sheet lays almost directly on the Au(111) surface. This is consistent with DFT calculations of the atomic structure. A characteristic 2D band with parabolic dis-persion is observed.

Introduction

The success of graphene has driven extensive attention to other two-dimensional (2D) materials, due to outstanding properties, such as to-pological insulating character [START_REF] Pesin | Spintronics and pseudospintronics in graphene and to-pological insulators[END_REF], Quantum Spin Hall (QSH) effect [START_REF] Kane | Quantum spin hall effect in graphene[END_REF][START_REF] Xu | Large-gap quantum spin hall insulators in tin films[END_REF], and enhanced thermoelectricity [START_REF] Ouyang | A theoretical study on thermoelectric properties of graphene nanoribbons[END_REF]. Unfortunately, however, most available materials with such properties are until now often based on multicomponent materials with different sublattices or complex alloys. These are still challenging to fabricate in terms of large-scale production. Among various post-graphene elemental 2D materials [START_REF] Yuhara | Graphene's latest cousin: plumbene epitaxial growth on a "Nano WaterCube[END_REF], one of them, stanene, the tin-based analog, attracted special attention due to its Dirac cone-like energy dispersion and large spin-orbit strength, permitting to envision exciting emerging properties. Typi-cally, it has been predicted that stanene with a large gap 2D QSH state can enable dissipationless electric conduction at room temperature (RT) [START_REF] Ezawa | Monolayer topological insulators: silicene, germanene, and stanene[END_REF][START_REF] Ni | Germanene and stanene on two-dimensional substrates: Dirac cone and Z 2 invariant[END_REF][START_REF] Rachel | Giant magnetoresistance and perfect spin filter in silicene, germanene, and stanene[END_REF]. Several theoretical and experimental efforts have been carried out on stanene [START_REF] Rojas-Sánchez | Spin to charge conversion at room temperature by spin into a new type of topological insulator: α -Sn Films[END_REF][START_REF] Mortazavi | Firstprinciples investigation of mechanical properties of silicene, germanene and sta-nene[END_REF][START_REF] Zheng | Epitaxial growth and electronic properties of few-layer stanene on InSb (111)[END_REF], e.g., stanene with a 0.44 eV band gap, has been grown on InSb(111) recently [START_REF] Xu | Gapped electronic structure of epitaxial stanene on InSb(111)[END_REF].

The first realization of a highly buckled stanene-like overlayer has been achieved on a Bi2Te3 topological insulator substrate [START_REF] Zhu | Epitaxial growth of two-dimensional stanene[END_REF]. Then further researches have been devoted to exploring the distinct elec-tronic properties of stanene formed on different substrates, such as semiconducting InSb(111), SiC(0001) and MoS2 [START_REF] Zheng | Epitaxial growth and electronic properties of few-layer stanene on InSb (111)[END_REF][START_REF] Li | Stanene on a SiC(0001) surface: a candidate for realizing quantum anomalous Hall effect[END_REF][START_REF] Chen | Multi-layer elemental 2D materials: antimonene, germanene and stanene grown directly on molybdenum disulfides[END_REF], semimetals Sb(111) [START_REF] Gou | Strain-induced band engineering in monolayer stanene on Sb(111)[END_REF], and metallic Ag(111) [START_REF] Yuhara | Large area planar stanene epitaxially grown on Ag(111)[END_REF], Cu(111) [START_REF] Ahmed | Structure determination of ultra-flat stanene on Cu(111) using low energy electron diffraction[END_REF]; for interesting reviews, see Refs. [START_REF] Vishnoi | 2D Elemental Nanomaterials Beyond Graphene[END_REF] and [START_REF] Lyu | Stanene: A Promising Material for New Electronic and Spintronic Applications[END_REF]. Searching for alternative substrate materials, recent theoretical works especially predicted interesting possibilities with the Au(111) surface [START_REF] Nigam | Evidence of a graphene-like Snsheet on a Au(111) substrate: electronic structure and transport properties from first principles calculations[END_REF], while density functional theory (DFT) calculations indicate that low-buckled stanene is more stable than highly buckled stanene [START_REF] Xu | Large-gap quantum spin hall insulators in tin films[END_REF].

A few groups have studied the growth of tin on gold (111) surfaces by different methods [START_REF] Barthès | A low energy electron diffraction-Auger electron spec-troscopy study of alloy formation during the adsorption of tin on (100) and (111) Au[END_REF][START_REF] Maniraj | A case study for the formation of stanene on a metal surface[END_REF][START_REF] Liu | Realization of strained stanene by interface engineering[END_REF][START_REF] Sadhukhan | Electronic structure and morphology of thin surface alloy layers formed by deposition of Sn on Au(111)[END_REF][START_REF] Sadhukhan | Electronic structure of Au-Sn compounds grown on Au(111)[END_REF][START_REF] Zhou | Interfacial effects on the growth of atomically thin film: Group VA elements on Au(111)[END_REF]. However, the experimental realization of stanene remains challenging. To the best of our knowledge planar honeycomb-like tin with a "2×√3" superstructure on the Au(111) surface, as will be shown here, has never been reported; hence, we will describe its realization and properties in this paper. This novel tin overlayer features a low-buckled lattice with even-tually three Sn atoms per unit cell arranged in a honeycomb-like structure, as derived from scanning tunneling microscopy (STM), low-energy electron diffraction (LEED) and synchrotron radiation core-level spectroscopy (CLS), along with DFT calculations of the atomic geo-metry. The electronic properties were explored by angle-resolved photoemission spectroscopy (ARPES), and compared to DFT band structure calculations.

Experiment and calculations

We performed our experiments in two different ultra-high vacuum vessels. The first one at Nagoya University, is equipped with a LEED apparatus operating with a LaB6 filament and a UHV Omicron STM-1 system. The second one used for the CLS and ARPES experiments, is at the Aichi synchrotron radiation center. It hosts a MCP-LEED system and a hemispherical analyzer with a 200 mm radius (MB Scientific AB A-1) and wide-angle electron lens. Both vessels consist of a preparation chamber and an analysis chamber with base pressure lower than 10 -10 mbar.

After sputtering the Au(111) surfaces by 700 eV Ar + ions at RT, an annealing at around 600 °C was performed. Temperatures were mon-itored with a radiation thermometer and a type K thermocouple fixed on the base plate of the sample holder. After annealing, Auger electron spectroscopy (AES) was performed at RT to check for surface cleanli-ness. Then the LEED patterns showed sharp reconstruction spots of the well-known Au(111)22×√3 herringbone clean superstructure. Tin was deposited onto the Au(111) surfaces at RT in either UHV vessel with a deposition rate of approximately 0.13 monolayer (ML) min -1 (the rate was measured by using a quartz crystal monitor). The atomic density of a Au(111) plane is 1.391×10 15 atoms cm -2 ; we use this value to define 1 ML Sn coverage. The deposition rate had been calibrated by Rutherford backscattering spectroscopy (RBS); the methodology has been published in Refs. [START_REF] Yuhara | Phase transition of the Si(111)-Au surface from √3×√3 to 5×1 structure studied by means of the low-energy electron diffraction, Auger electron spectroscopy, and Rutherford backscattering spectroscopy techniques[END_REF] and [START_REF] Yuhara | Characterization ofGe δdoped Si(111) with RBS channeling[END_REF]. The amount of deposited Sn is 0.6 ML; errors are less than 10% in mentioned coverage ratios.

In each vessel, the LEED and STM observations were performed at RT. Sharp LEED patterns were obtained with 46-70 eV primary beam energies. All STM images were acquired with W tips. The CL and ARPES spectra were recorded at about 10 K, as the gold specimen was mounted on a liquid-helium-cooled cryostat with 4-axis pulse motor control.

The DFT calculations were performed by the QuantumATK [30], in which wave functions are expressed by the linear combination of pseudo atomic orbitals. The interactions between ionic core and va-lence electrons were described by ONCV-type pseudopotentials of the PseudoDojo project [START_REF] Van Setten | The PseudoDojo: Training and grading a 85 element optimized normconserving pseudopotential table[END_REF]32] and PBE-type exchange-correlation energy functional was also employed [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF]. The lateral size of the Au(111) si-mulation cell was (a,b) = (5.768, 4.995) in unit of A; periodic boundary conditions were imposed along both directions. In the c di-rection, one side of the Au(111) slab consisting of 14 atomic layers was coupled to the semi-infinite Au(111) electrode as the boundary condi-tion by the Green's function technique [START_REF] Brandbyge | Density-functional method for nonequilibrium electron transport[END_REF], and the opposite side had a vacuum region of 15 A. The atomic configuration except for three layers close to the electrode was relaxed until the forces acting on atoms be-came smaller than 10 meV/A. The cutoff energy for space discretization was taken to be 2721.14 eV. The Brillouin zone of the unit cell was sampled with a 5×6×1 Γ-center k-point grid.

Results and discussion

In order to study the growth of tin on the Au(111) surface, at first LEED and STM observations have been carried out. Fig. 1 This is why we name the superstructure as "2×√3", since it is in reality incommensurate. This may be related to the uniaxial compression of the gold surface atoms along the [11 0] direction [START_REF] Barth | Scanning tunneling microscopy observa-tions on the reconstructed Au(111) surface: Atomic structure, long-range super-structure, rotational domains, and surface defects[END_REF].

In Fig. 1(d), the smooth terraces no longer show any signature of the herringbone reconstruction and no 3D islands are observed. Locally, bare Au(111) is recognized as black holes. These terraces are separated by steps with a uniform height of 0.23 nm as shown in Fig. 1(g), indicating a Au(111) step below the tin overlayer. Clearly the Sn atoms form an adlayer wetting the Au(111) surface; the overlayer film is uniform over hundred nanometers with just some second layer patches, as displayed in Fig. 1(h).

The high-resolution STM image displayed in Fig. 2(a) reveals the atomic arrangement of the "2×√3" superstructure. It points to two different local arrangements, namely chain-like within the yellow rec-tangles and honeycomb-like (hexagonal motifs are aligned only in one direction) within the black squares, as illustrated in Fig. 2(b) and (e), respectively, with possibly three equivalent orientations. In the black square areas, the protrusions appear denser than in the yellow rectangle ones, where they look like zigzag chains. As shown in Fig. 3, we further performed high-resolution synchro-tron radiation core-level (CL) spectroscopy of the shallow Sn 4d and Au 4f CL's in highly surface sensitive conditions. A spectrum recorded from the clean Au(111) surface fitted with two components (bulk: B at 84.02 eV binding energy (BE) and surface: S at 83.69 eV BE ones), in excellent agreement with the literature [START_REF] Heister | Adsorption of Alkanethiols and Biphenylthiols on Au and Ag Substrates: A High-Resolution X-ray photoelectron spectroscopy study[END_REF]) is shown in Fig. 3(a). After the deposition of 0.6 ML Sn giving the "2×√3" superstructure, the corresponding Au 4f7/2 photoemission spectrum is presented in Fig. 3(b). The S surface component has vanished, but new components, located at the higher binding energy side of the bulk component, have appeared. There are three components labelled C1, C2 and C3 at 84.29, 84.57 and 84.78 eV BEs, respectively. The bulk component B has markedly decreased, which is the expected behavior for a substrate core-level peak. Component C3 may be related to Au atoms that diffuse through the Sn layer forming the Au-Sn alloy [START_REF] Sadhukhan | Electronic structure of Au-Sn compounds grown on Au(111)[END_REF]. We relate compo-nents C1 and C2 to the interface top Au(111) layer beneath Sn atoms, either in the chain-like or the honeycomb-like local arrangements.

As for the corresponding Sn 4d broad spectrum, displayed in Fig. 3(c), we fit it with three distinct components, S1, S2, and S3, re-spectively at 24.31 (Sn 4d5/2), 24.01 and 24.50 eV BEs. The S3 com-ponent is of comparable intensity and appears at the same binding energy as for the Au-Sn alloy investigated in ref. [START_REF] Sadhukhan | Electronic structure of Au-Sn compounds grown on Au(111)[END_REF], hence, it is in correspondence with C3 discussed above. The main component S2 is about twice the intensity of S1, indicating high and low Sn coverages, respectively. Therefore, we relate components S1 and S2 to the chain-like and the honeycomb-like local arrangements, respectively. This is in correspondence to the previous C1 and C2 Au 4f7/2 components in the interface region.

We have further investigated the electronic band structure of the "2×√3" phase by ARPES measurements at a photon energy of 70 eV. The corresponding data are shown in Fig. 4. A scheme of the Au(111) and "2×√3" surface Brillouin zones is shown in Fig. 4(a). One notices that because of the expansion and compression mentioned above, the "2×√3" surface Brillouin zone is nearly a square, that is the Γ ̄ X ̄ Sn and Γ ̄ Y ̄ Sn distances are practically the same. The clean Au(111) surface exhibits the well-known Rashba spin splitting of the Shockley surface-state (S) around the Γ ̄ point, shown in Fig. 4 (b). With 0.6 Sn ML (S) has vanished, and a new parabolic surface electronic band is observed in Fig. 4 (c) and (d). We note that no signature of a Au-Sn alloy, i.e., typical Λ-shape bands around the Γ point, is present [START_REF] Sadhukhan | Electronic structure and morphology of thin surface alloy layers formed by deposition of Sn on Au(111)[END_REF]. The effective mass m* is calculated to be 0.41me, where me is the electron rest mass, which is significantly higher than for that of the bare Au(111) Shockley surface state (0.28me). The Fermi velocity is estimated to be 1.4 × 10 6 m/s. We have compared these experimental results to DFT calculations for the two commensurate (2×√3) approximant phases in Fig. 5. The surface band structure of the clean unreconstructed Au(111)1×1 surface is displayed in Fig. 5(a) in the range corresponding to X ̄ Sn-Γ ̄ -X ̄ Sn, revealing the (S) state, but significantly upward shifted. Fig. 5(b) and (c) show the calculated dispersions along X ̄ Sn-Γ ̄ -X ̄ Sn for the Sn related bands of the (2×√3) phases at 0.5 and 0.75 Sn ML, respectively. However, there is no clear correspondence with the experimental dis-persion in Fig. 4(c), except possibly for the calculation shown in Fig. 5(c) for the 0.75 ML coverage, i.e., for the honeycomb-like struc-ture, or, in other words, the stanene-like structure, if we consider a likely up-shift. Hence, the stanene-like structure is more favorable in our experimental conditions, although, indeed, the DFT calculations for the commensurate (2×√3) approximant phase are just indicative. Both experimental and theoretical parabolic dispersions clearly differ from the cone-like one expected for free-standing stanene, which is no surprise since, for one, the stanene-like Sn overlayer is not purely honeycomb, and, for two, is interacting with the Au(111) substrate.

However, we stress that the structural flatness of the stanene-like phase is likely to drive a large QSH effect, possibly even at RT [START_REF] Gou | Strain-induced band engineering in monolayer stanene on Sb(111)[END_REF].

Conclusion

In conclusion, the tin sheet forms a nearly planar structure on the Au(111) surface with a "2×√3" superstructure in large surface areas, identified by LEED patterns and STM images. In addition, based on experimental results, we proposed zigzag chain and honeycomb-like structures characterized by STM observations and DFT calculations. Meanwhile, the core-level spectra of Sn deposited onto the Au(111) surface reveal that a structurally flat stanene-like sheet lays almost di-rectly on Au(111) surface. Both experimental and theoretical band structures favor a stanene-like honeycomb structure with three Sn atoms per unit cell.

  (a) and (b) show the LEED pattern and STM images of the well characterized Au (111)22×√3 herringbone reconstruction [35]. Terraces are separated by atomic steps 0.23 nm in height, as shown by the AB profile in Fig. 1(b) and (f).

Fig. 1 .

 1 Fig. 1. (a) LEED pattern of the pristine Au(111) surface (55 eV). (b) large-scale STM image of the bare Au(111) surface showing the herringbone superstructure (Us = 1.0 V, I = 0.2 A). (c) and (d) LEED pattern (55 eV) and the large-scale STM image (Us = 1.0 V, I = 0.2nA) of 0.6 ML Sn deposited onto the Au(111) surface at RT. (e) Simulated LEED pattern of the "2×√3" superstructure. (f) and (g) Sectional profiles along the A-B and C-D lines in (b) and (d). (h) Growth model of tin on the Au(111) surface.

Fig. 2 .

 2 Fig. 2. (a) High-resolution STM image of the Sn covered Au(111) surface (0.6 ML; Us = 0.3 V, I = 0.2nA). (b) and (c) Top and side views of the zigzag chain-like (2×√3) approximant structure. (e) and (f) Top and side views of the honeycomb-like (2×√3) approximant structure. Yellow and gray balls denote Au and Sn atoms, respectively. Yellow and black squares indicate the (2×√3) unit cell. (d) and (g) are the simulated STM images for the zigzag chain-like and honeycomb-like structures, respectively.

Fig. 3 .

 3 Fig. 3. The core level spectra of Au 4f and Sn 4d measured at 10 K and taken at hν = 135 eV and 75 eV, respectively. (a) Au 4f7/2 for a clean bare Au(111) single crystal, (b) and (c) Au 4f7/2 and Sn 4d of stanene on Au(111) surface. The orange circle line is the fit line, and the black line is the experiment's data.

Fig. 4 .

 4 Fig. 4. ARPES dispersion at hν = 70 eV, measured at 10 K. (a) Scheme of the Au (111) surface Brillouin zone in black and of the "2×√3" Sn phase in red. (b) Shockley surface state of the clean Au(111) surface along the M ̄ Au-Γ ̄ -M ̄ Au di-rection. (c) and (d) electronic band structures of the "2×√3" stanene-like phase on the Au(111), measured along the M ̄ Au-X ̄ Sn-Γ ̄ -X ̄ Sn-M ̄ Au and K ̄ Au-Y ̄ Sn-Γ ̄ -Y ̄ Sn-K ̄ Au directions.

Fig. 5 .

 5 Fig. 5. (a) The calculated surface band structures along the X ̄ Sn-Γ ̄ -X ̄ Sn interval for bare Au(111)1×1 surface. (b) The Sn-related band structure for the chain-like phase at 0.5 ML Sn coverage. (c) The Sn-related band structure for the stanene-like phase at 0.75 ML Sn coverage.

Acknowledgments

The authors are grateful to Nagoya University Synchrotron Radiation Research Center for financial support for ARPES measure-ments, which were conducted at BL7U of Aichi Synchrotron Radiation Center, Aichi Science & Technology Foundation. JY acknowledges financial support from Murata Science Foundation in 2019. GLL ac-knowledges support from Nagoya University thanks to an "Eminent Foreign Scientist" Invitation Award in 2015-2016 and 2019-2020, as well as an Invitational Fellowship for Research in Japan by the Japan Society for the Promotion of Science (JSPS) in 2017. M.A. is partly supported by JSPS KAKENHI Grant Number 19H04541. The computa-tion in this work has been done in part using the facilities at the Information Technology Center, Nagoya University.