Marc Verlaque

Habib Langar

A Ben Hmida

Christine Pergent

Gerard Pergent

Marcv Erlaque

Abib Langar

Ben Hmida

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

INTRODUCTION

With nearly 1000 marine introduced taxa identified, the Mediterranean Sea is one of the regions of the world most severely impacted by the introduction of species [START_REF] Zenetos | -Alien species in the Mediterranean Sea by 2010. Acontribution to the application of European Union'sM arine Strategy Framework Directive (MSFD). Part I. Spatial distribution[END_REF][START_REF] Zenetos | -Alien species in the Mediterranean Sea by 2012. Ac ontribution to the application of European Union's Marine Strategy Framework Directive (MSFD). Part 2. Patterns in introduction trends and pathways[END_REF][START_REF] Zenetos | Uncertainties in compiling alien species catalogues: Need for local and expert judgment in validating existing lists: the case of the Mediterranean Sea[END_REF]. In 2017, the number of marine macrophytes introduced into the Mediterranean Sea amounts to around 120-130 taxa (Verlaque et al.,2 015;M. Ve rlaque,unpub. data).

Within the framework of aP rogram of the RAC/SPA( Regional Activity Centre for Specially Protected Areas) and the University of Corsica, carried out on the coast of Tunisia, as pecies of Avrainvillea Decaisne [START_REF] Decaisne | Mémoire sur les corallines ou polypiers calcifères -Essai sur une classification des algues et des polypiers calcifères de Lamouroux[END_REF], at ropical genus hitherto unknown in the Mediterranean Sea, has been discovered in the region of Kerkennah Islands. The alga was identified as A. amadelpha (Montagne) A. Gepp &E .S. Gepp, at ropical species widely distributed in the Indo-PacificO cean. The aim of the present study is to report the species for the first time from the Mediterranean Sea and to describe the Mediterranean population and its ecology. The possible origins and pathways of introduction are considered. The risks of further spread of the species in the Mediterranean Sea are discussed.

MATERIAL AND METHODS

Avrainvilleaamadelpha was found and sampled during the field monitoring campaigns of the lower limits of Posidonia oceanica (L.) Delile beds of the Kerkennah Archipelago in Tunisia (MedPosidonia and CHANGEP rograms set up by the RAC/SPAand the FRES 3041 -University of Corsica) [START_REF] Pergent | Surveillance de l'herbier des îles Kerkennah (Tunisie) -Retour 2014[END_REF] (Fig. 1). The seawater temperature was recorded on acontinuous basis (24 measures. day -1 )atthe lower limit of a P. oceanica bed of the archipelago from 2008 to 2015.

Sampling and studies of the A. amadelpha population were carried out by SCUBA diving in July 2015. Specimens sampled by one of us (H.L.) were transferred to the laboratory in seawater,b efore being cleaned, pressed and dried. Anatomical studies were carried out under the binocular and light microscopes after re-hydration. Measurements and photomicrographs were made using aCoolpix 995 Nikon ® digital camera and an Optiphot-2 Nikon ® light microscope. Vo ucher dried specimens were deposited in the Ve rlaque Herbarium (HCOM), Marseille, France, with the following references: -H8307 to H8309, Avrainvillea amadelpha (Montagne) A. Gepp & E.S. Gepp, collection Habib Langar,T unisia, Kerkennah Archipelago, offG harbi Island (GPS location: 34°31' 2.20''Nand 11°07' 1.60''E), 26 July 2015, 22 md epth, at the lower limit of the Posidonia oceanica meadow,f ertile( Fig. 2).

The Tunisian material was compared with photographs of A. amadelpha specimens deposited in the Cryptogamic Herbarium of the Muséum National d'Histoire Naturelle, Paris (PC), especially those from Red Sea, with the following references: -PC0502136 -Avrainvillea amadelpha Gepp, collection Islam Elmanawy,S uez Canal, Egypt, July 1988; -PC0502137 -Avrainvilleaa madelpha (Mont.) A&E.S. Gepp, collection J.F.P apenfuss, Israel South Red Sea Expedition, determination J.F.P apenfuss and Y. M. Chiang, Romia Islet, Dhalak Archipelago, Eritrea, Red Sea, 29 March 1962; -PC0502138 -Avrainvillea amadelpha Gepp, collection Gruvel, Grand Lac Amer (Great Bitter Lake), Egypt, 1932. Herbarium abbreviations follow Thiers (2014). DNA extractionsf rom dry material and amplification of the TufA gene were performed as previously [START_REF] Vieira | -TufA gene as molecular marker for freshwater Chlorophyceae[END_REF].

RESULTS

Avrainvillea amadelpha (

Description of the Mediterranean material

Plant forming clusters; thallus non-calcified, 7-12 cm tall, differentiated into holdfast, stipes and blades; holdfast developed into mat from which numerous stipes arise; stipes once to twice-branched; each branch bearing as imple terminal blade; blades spongy,t hin, entire, sub-cuneate to flabellate, dark green to olive brown, zonate, 2.5-6.0 cm wide; growing margins smooth or slightly eroded (Figs 2-3); thallus composed of intertwined non-septate filaments (siphons); siphons cylindrical to torulose, tapering upwards, 25-18 µmto12.0-16.0 (-20) µmindiameter (measurements on segments between two consecutive dichotomies) (Fig. 4); siphons dichotomously branched with dichotomies deeply constricted (Fig. 5); distance between dichotomies decreasing upwards resulting in ah ighly ramified terminal region, referred to as apseudocortex, near the surface of the blade; apices of siphons rounded (Figs 6-8); presence of tiny sand grains trapped between the filaments of holdfasts, stipes and lower part of blades; gametangia subspherical to ovoid, 22-36 µml ong and 27-32 µmi nd iameter,s hortly pedicellate and laterally inserted on the filament, frequently below ad ichotomy (Figs 9-12); basal septum, division of gametangium contain and emission of gametes not observed. The amplification of the TufA gene failed (Line Le Gall, pers. com.).

Ecology

The alga was common and was growing gregariously in colonies, between 20-22 md epth, in sunny places (sub-horizontal substrates), in Cymodocea nodosa (Ucria) Ascherson meadows, Posidonia oceanica beds, on dead mattes of P. oceanica meadows and coarse sand bottoms, in association with Dictyotai mplexa (Desfontaines) J.V.L amouroux, Flabellia petiolata (Turra) Nizamuddin, Jania adhaerens J.V.L amouroux, Penicillus capitatus Lamarck, and the invasive exotic species Caulerpa cylindracea Sonder and Pinctada imbricata radiata (Leach, 1814). At the lower limit of the Posidonia oceanica beds, the seawater temperature varied between 12.9-14.8 °Ci nw inter and28.0-29.5 °Ci ns ummer (2008-2015 data).

DISCUSSION AND CONCLUSION

The Mediterraneans pecimens of Avrainvillea are in good agreement with descriptions and illustrations of A. amadelpha (Montagne) A. Gepp &E .S. Gepp [START_REF] &g | The Codiaceae of the Siboga Expedition including am onograph of Flabellarieae and Udoteae[END_REF][START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF]Coppejans &P rud'homme van Reine, 1989;[START_REF] De | Marine Algae of the Jubail Marine Wildlife Sancturary, Saudi Arabia[END_REF]Littler &L ittler,2 003;Abbott & Huisman, 2004;[START_REF] Huisman | Hawaiian reef plants[END_REF][START_REF] Coppejans E | -Sri Lankan seaweeds: Methodologies and field guide to the dominant species[END_REF], especially those from the Red Sea (Zanardini, 1858;Nasr,1 947;Aleem, 1978b[START_REF] Aleem | Contributions to the study of the marine algae of the Red Sea. IV -Algae and seagrasses inhabiting the Suez Canal[END_REF], and with the Red Sea specimens deposited in the PC herbarium.

On the basis of am orphologicala nalysis, Olsen-Stojkovich (1985) distributed the species of Avrainvillea in different groups. Avrainvilleaa madelpha belongs to the 'longicaulis group', along with A. asarifolia Børgesen, A. calathina Kraft &O lsen-Stojkovich, A. carteri Huisman, A. lacerata Harvey ex J.Agardh, A. levis M. Howe, A. longicaulis (Kützing) G. Murray &B oodle and A. pacifica A. Gepp &E .S. Gepp (Agardh, 1887;Murray &B oodle, 1889;[START_REF] Howe | -Phycological studies -II. New Chlorophyceae, new Rhodophyceae and miscellaneous notes[END_REF]Børgesen, 1909;[START_REF] &g | The Codiaceae of the Siboga Expedition including am onograph of Flabellarieae and Udoteae[END_REF]Kraft &O lsen-Stojkovich, 1985;[START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF][START_REF] Huisman | Algae of Australia: marine benthic algae of north-western Australia. 1. Green and brown algae[END_REF]. Characteristics of the 'longicaulis' group are (i) stipes simple to branched once to many times near base, each branch bearing a single terminal blade, (ii) siphons cylindrical moniliform, torulose to tortuous, and (iii) siphon dichotomies deeply constricted. Avrainvilleaamadelpha differs from the other members of the 'longicaulis' group by the following combination of diagnostic features: growth in cluster (gregarious carpet); holdfast mat-like; stipe mostly branched; blades spongy and thin; growing margins smooth; siphons 25 µmt o 12 µmi nd iameter; and pseudocortex present (Table I). The two closest species are A. carteri and A. lacerata,b ut the first has the stipes mostly unbranched, the blades spongy and firm and the siphons thinner,3 0µ mto 5 µm, and the second has the blades without zonation, the growing margins lacerate, the siphons thinner,2 8µ m to 6 µm, and does not possess pseudocortex (Table I). In another group, namely the 'nigricans' group sensu [START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF], A. mazei G. Murray &B oodle (Murray &B oodle, 1889) shares certain characters with A. amadelpha (thallus differentiated into holdfast, stipe and blade; thallus forming gregarious carpets; holdfast mat-like; stipes sometimesb ranched; blades spongy; growing margins smooth; and siphon dichotomies deeply constricted), but it differs by the greater size, up to 25 cm tall, including stipes up to 16 cm long, the blades never zonate, the siphons predominantly cylindrical and thicker (65 µmt o2 8µ m), and by the absence of pseudocortex [START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF].

Observations on the reproduction of Avrainvillea spp. are very few. Ve getative propagation is more common and constant throughout the year (Olsen-Stojkovich, 1985; Guiry &G uiry,2 017). The life history of the genus has not been experimentally verified. Fragmentary observations strongly suggest holocarpy,w ith ar eproductive cycle similar to udoteacean genera, i.e. ad ioecious diploid erect thallus in which meiosis precedes gametogenesis [START_REF] Young | Ecological observations on the reproduction of the tropical marine alga Avrainvillea from Panama (Siphonales, Codiaceae)[END_REF][START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF]. Twotypes of gametangia, terminal or lateral, were described according to the species. The first and the most frequent type, the terminal type, was observed in A. nigricans Decaisne (type species of the genus), A. asarifolia Børgesen, A. asarifolia f. olivacea D.S. Littler &Littler, A. digitata D.S. Littler &Littler, A. erecta (Berkeley) A. Gepp &E.S. Gepp,A.fulva (M. Howe) D.S. Littler &Littler, A. mazei G. Murray &B oodle, A. obscura (C. Agardh) J. Agardh and A. rawsonii (Dickie) M. Howe [START_REF] Howe | -Phycological studies -III. Further notes on Halimeda and Avrainvillea[END_REF][START_REF] &g | The Codiaceae of the Siboga Expedition including am onograph of Flabellarieae and Udoteae[END_REF][START_REF] Kusel | Contribution to the knowledge of the seaweeds of Cuba[END_REF][START_REF] Young | Ecological observations on the reproduction of the tropical marine alga Avrainvillea from Panama (Siphonales, Codiaceae)[END_REF][START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF]Littler &L ittler,1 992;[START_REF] Cabrera | -2010 -Presencia de esporangióforos maduros en Avrainvillea asarifolia (Chlorophyta, Bryopsidales)[END_REF]-2010;[START_REF] Cabrera R | Estructuras reproductoras yepífitas del género Avrainvillea en aguas cubanas[END_REF]. In this group, terminal gametangia result from the transformation of one apical branch of ad ichotomy,t he other branch undergoing two or three more dichotomies. Gametangia are clavate, i.e. elongated, narrowing toward the base and gradually expanded toward the apex, and large (> 200-250 µmi nd iameter). The lateral type, which was hitherto only observed in two taxa, A. elliottii A. Gepp &E.S. Gepp and A. longicaulis f. laxa D.S. Littler &Littler [START_REF] Cabrera R | Estructuras reproductoras yepífitas del género Avrainvillea en aguas cubanas[END_REF], consists in smaller gametangia, usually <100 µmindiameter,subspherical to ovoid, shortly pedicellate and laterally inserted on the siphon. Gametangia of A. amadelpha,w hich are described here for the first time, belong to the lateral type.

The occurrence of populations of A. almadelpha in Tunisia is in good agreement with the hypothesis of ar ecent introduction because it is consistent with the criteriap roposed by [START_REF] Ribera | -Introduced marine plants, with special reference to macroalgae: mechanisms and impact[END_REF]: (i) the species had never been observed in the Mediterranean Sea; (ii) the first Mediterranean populations occupied as mall area; and (iii) they were discovered in ah ot-spot of species introductions (Southern Tunisia) where many exotic species native to the Red Sea and the Indo-PacificO cean have been reported [START_REF] Ben | Sur la présence de nouvelles espèces exotiques dans la Grande et la Petite Syrte[END_REF][START_REF] Zaouali | Contribution à l'étude des peuplements actuels des substrats solides de l'étage médiolittoral de la Méditerranéeméridionale[END_REF][START_REF] Ben | Les espèces non indigènes du macrobenthos des lagunes du sud-est tunisien: point sur la situation[END_REF]Oufini Ben Amor et al.,2015;Sghaier et al., 2016). Among the major pathways of introduction, the Suez Canal is ranked as the most important. Since its opening in 1869, the flow of Lessepsian species, i.e. Indo-Pacifics pecies introduced into the Mediterranean Sea via the Suez Canal, has never stopped (Nunes et al.,2 014). The introduction of A. amadelpha is an ew illustration of this phenomenon. In the absence of worldwide molecular data, the [START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF]. References: Agardh (1887), [START_REF] Howe | -Phycological studies -II. New Chlorophyceae, new Rhodophyceae and miscellaneous notes[END_REF], Børgesen (1909[START_REF] &g | The Codiaceae of the Siboga Expedition including am onograph of Flabellarieae and Udoteae[END_REF], Kraft &O lsen-Stojkovich (1985), [START_REF] Olsen-Stojkovich | -Asystematicstudy of the genus Avrainvillea Decaisne (Chlorophyta, Udoteaceae)[END_REF], Littler &L ittler (1992[START_REF] Littler | South Pacificr eef plants[END_REF], [START_REF] Abbott | Marine green and brown algae of the Hawaiian Islands[END_REF] identification of the donor region is not possible. New sequencing attempts will be considered with other genes (rbcL). However,t he Red Sea appears as ag ood candidate, A. amadelpha being native and common in this sea (Zanardini, 1858, as Chloroplegma sordidum;H arvey-Gibson, 1908;Harvey-Gibson &K night, 1913, as A. lacerata;N asr,1 947;Rayss, 1959;[START_REF] Papenfuss | -Ahistory,c atalogue, and bibliography of the Red Sea benthic algae[END_REF]Aleem, 1978a &b ;L ipkin &S ilva, 2002). Moreover,i th as been growing in the Suez Canal at least since the early 20 th century (Lami, 1932, confirmed by the herbarium specimen PC0502138; Lipkin, 1972;[START_REF] Aleem | Contributions to the study of the marine algae of the Red Sea. IV -Algae and seagrasses inhabiting the Suez Canal[END_REF]. Several potential vectors of species introduction have been considered in southern Tunisia: currents, shipping (via fouling and ballast water), pleasure boating and aquaculture (Oufini Ben Amor et al.,2015). In general, psammophytic macroalgae such as Avrainvillea spp. do not appear to have the mechanisms for long-distance dispersal such as those shown by hitch-hiking boat foulers, pelagic algae or species with long-lived resistant spores (Littler &L ittler, 1992). Only man-made structures that remain for along time in the same place, such as pontoons, pipelines, drilling and production platforms, seem to be suited to colonisation by Avrainvillea.I nt he case of A. amadelpha,t he first Mediterranean observation at the Kerkennah Islands, ac onsiderable distance from the Suez Canal, in spite of phycological field studies conducted along the Egyptian and Libyan coasts (Nizamuddin et al.,1 979;[START_REF] Shameel | -Notes on the seaweeds of Tripoli, Libya[END_REF][START_REF] Nizamuddin | The green marine algae of Libya[END_REF]Godeh et al., 1992;[START_REF] Aleem | Marine algae of Alexandria, Egypt[END_REF][START_REF] Bazairi | -Alien marine species of Libya: first inventory and new records in El-Kouf National Park (Cyrenaica) and the neighbouring areas[END_REF] suggests adirect introduction from the Red Sea to Tunisia through human activities. Southern Tunisia and western Libya constitute am ajor Mediterranean region of oil and gas production, with several petroleum terminals and offshore oil and gas exploitation facilities [START_REF] Zaouali | Contribution à l'étude des peuplements actuels des substrats solides de l'étage médiolittoral de la Méditerranéeméridionale[END_REF]Oufini Ben Amor et al.,2 015). Consequently,t he introduction of A. amadelpha and exotic invertebrates directly from oil and gas production sites in the Red Sea via drilling or production platforms, or recycled pipelines, would appear to be ap ossible scenario. Every time we are faced with anew introduction, we have to answer to the question: what are the risks of invasion?

In the global distribution of marine species, there are two different types of temperature boundaries, namely the lethalb oundaries and the growth and/or reproduction boundaries [START_REF] Hutchins | The bases for temperature zonation in geographical distribution[END_REF][START_REF] Hoek | Seaweed Biogeography of the North Atlantic: where are we now?[END_REF]. Lethal boundaries are set by the species' capacity to survive during the adverse season (i.e. the cold season for aw arm-water species). Macroalgal species with tropical to warm temperate distribution patterns have al ower temperature tolerance limit of 10°Ct o 15°C [START_REF] Cambridge | Temperature responses of tropicalt ow arm temperate Cladophora species in relation to their distribution in the North Atlantic Ocean[END_REF](Cambridge et al., , 1990a, b;, b;[START_REF] Breeman | Relative importance of temperature and other factors in determining geographic boundaries of seaweeds: experimental and phenological evidence[END_REF][START_REF] Pakker | -Ac omparative study of temperature responses of Caribbean seaweeds from different biogeographic groups[END_REF]. In the case of A. amadelpha,t he 15°Cw inter isotherm corresponding to the mean seasurface temperature of the coldest month does correlate well with the limits of its global distribution (Fig. 13). So if we consider the coldest sea-surface temperatures (data from February), al arge part of the Mediterranean Sea that never drops below 15°C, is compatible with the temperature requirements of A. amadelpha (Fig. 14).

In tropical seas, A. amadelpha grows on aw ide range of substrates (rocks, reef crests, dead corals, rock crevices, coral rubble, mangroves, sandy reef flats, sand plains, sandy muds and seagrass beds), from the intertidalz one down to 50 m (-90 m) depth [START_REF] &g | The Codiaceae of the Siboga Expedition including am onograph of Flabellarieae and Udoteae[END_REF]Smith et al.,2 002;Littler &L ittler,2 003;[START_REF] Abbott | Marine green and brown algae of the Hawaiian Islands[END_REF]Coppejans et al.,2 004, 2009;Godwin et al.,2 006;Huisman et al.,2 007;Menza et al.,2 010;[START_REF] Spalding | Ecology of mesophotic macroalgae and Halimeda kanaloana meadows in the main Hawaiian Islands[END_REF]. The species has been observed all year round [START_REF] Abbott | Marine green and brown algae of the Hawaiian Islands[END_REF][START_REF] Peyton | Aquatic invasive species impacts in Hawaiian soft sediment habitats[END_REF]. Except for A. calathina,w hich can be heavily grazed, most species of Avrainvillea produce toxic secondary metabolites and appear to be grazer-resistant [START_REF] Sun | Avrainvilleol, abrominated diphenylmethane derivative with feeding deterrent properties from the tropical green alga Avrainvillea longicaulis[END_REF][START_REF] Kraft | -Avrainvillea calithina (Udoteaceae, Bryopsidales), an ew green alga from Lord Howe Island, NSW,Australia[END_REF]Littler &Littler,1992). Only highly specialised herbivores Stars: locations of introduced populations. Broken lines: 15°Cw inter isotherm corresponding to the mean sea-surface temperature of the coldest month according to Gorshkov (1976Gorshkov ( , 1978Gorshkov ( , 1980)). belonging to Sacoglossan gastropods and decapods are capable of ingesting them (Hay et al.,1 990).

Avrainvillea amadelpha is considered as introduced and invasive in the Hawaiian Archipelago [START_REF] Brostoff | Avrainvillea amadelpha (Codiales, Chlorophyta) from Oahu, Hawaii[END_REF]Huisman et al.,2 007). The species spread rapidly along the southern shore of the island of its first record (O'ahu Island), and it extended its range to the neighbouring Kaua'i Island (Smith et al.,2 002;Godwin et al.,2 006). Avrainvillea amadelpha traps large quantities of sediment between its holdfast and significantly increases the sedimentation rate [START_REF] Martinez | The effects of an alien invasive alga on sediment retention and resuspension in coastal Hawaiian waters and the influence of community based restoration[END_REF]. In some Hawaiian areas, A. amadelpha accounted for up to 100% cover,f orming extensive mounds with soft sediment more than 30 mi nd iameter at the margin of Halophila hawaiiana Doty &B .C. meadows, stone beds and on coral patches [START_REF] Peyton | Aquatic invasive species impacts in Hawaiian soft sediment habitats[END_REF][START_REF] Spalding | Ecology of mesophotic macroalgae and Halimeda kanaloana meadows in the main Hawaiian Islands[END_REF]. In invaded areas, changes in the community composition and overgrowths of H. hawaiiana meadows, Halimeda spp. beds and coral patches have been reported [START_REF] Rodgers | Reducing potential impact of invasive marine species in the North-western Hawaiian Islands marine national monument[END_REF]Longenecker et al.,2 011;[START_REF] Spalding | Ecology of mesophotic macroalgae and Halimeda kanaloana meadows in the main Hawaiian Islands[END_REF].

CONCLUSION

Avrainvillea amadelpha is as pecies possessing av ery high development potential: (i) wide ecological niche; (ii) gregarious perennial thallus; (iii) high competition capability; (iv) high resistance to grazing; (v) capability to change the composition of communities and to alter habitats through sedimentation increase; (vi) it reproduces in Tunisia; and (vii) it is invasive in the Hawaiian Archipelago. In the Mediterranean Sea, it seems to be capable of colonizing the southern and the eastern basins, except for the coldest waters of the north-western Aegean Sea. In conclusion A. amadelpha must be regarded as an ew potential invader in the Mediterranean Sea and therefore calls for special attention.

Fig. 1 .

 1 Fig. 1. Study area in Tunisia with detail of the Kerkennah Islands region. Star: location of the first population of Avrainvillea amadelpha (Montagne) A. Gepp &E.S. Gepp discovered in the Mediterranean Sea.

Fig. 2 .

 2 Fig. 2. Avrainvillea amadelpha (Montagne) A. Gepp &E.S. Gepp growing on a dead matte of Posidonia oceanica (L.) Delile off Gharbi Island (Kerkennah Islands), July 2015, 22 m depth. Figure 3. Pressed habit of fertile Tunisian specimens of Avrainvillea amadelpha (specimens H8307 to H8309, Herbarium HCOM, Aix-Marseille University). Bar = 5c m.

Figs 4

 4 Figs 4-8. Anatomy of Tunisian specimens of Avrainvillea amadelpha (Montagne) A. Gepp &E.S. Gepp. 4. Intertwined non-septate filaments (siphons) of the blade. Bar =1 00 µm. 5.T orulose filament with a deeply constricted dichotomy.Bar =50µm. 6. Detail of the upper part of filaments showing the upward decreasing distances between dichotomies. Bar =1 00 µm. 7-8. Detail of the growing margin with filaments organized in pseudocortex. Bars =1 00 µm.

  Figs 9-12. Reproductive structures of Tunisian specimens of Avrainvillea amadelpha (Montagne) A. Gepp &E.S. Gepp. 9-10. Shortly pedicellate gametangia inserted laterally at the base of a dichotomy.B ars =3 0µ m. 11-12. Shortly pedicellate gametangia inserted laterally on a filament. Bars = 30 µm.

Fig. 13 .

 13 Fig. 13. World distribution of Avrainvillea amadelpha (Montagne) A. Gepp &E .S. Gepp according to Aleem (1978a &b ,1 980), Coppejans &P rud'homme van Reine (1989), Ve rheij &E rftemeijer (1993), De Clerck &C oppejans (1996), N'Yeurt (1996), Saifullah (1996), Coppejans et al. (2000), Hodgson & McDermid (2000), Aungtonya &L iao (2002), Tsuda (2002), Tsuda et al. (2008), Lee et al. (2009), Kaladharan et al. (2011), Xia et al. (2013), Aziz et al. (2015), and references in Guiry &G uiry (2017).Stars: locations of introduced populations. Broken lines: 15°Cw inter isotherm corresponding to the mean sea-surface temperature of the coldest month according toGorshkov (1976Gorshkov ( , 1978Gorshkov ( , 1980)).

Fig. 14 .

 14 Fig. 14. Mean sea-surface temperature isotherms of the coldest month in the Mediterranean Sea (data from February 2008). Measurements obtained by available satellite infrared sensors developed and distributed by the Gruppo di Oceanografiad aS atellite (GOS)(Alhammoud et al.,2 012). Shaded area: region with sea-surface temperatures higher than 15°C.

Montagne) A. Gepp &E .S. Gepp Reference:G epp

	&G epp (1911), pp. 42-44, figs 112-115.
	Basionym: Udotea amadelpha Montagne (1857), p. 136. Type locality: Agalega
	Islands, NE of Madagascar,I ndian Ocean.
	Heterotypic synonyms: Chloroplegma sordidum Zanardini (1858), p. 83, figs 1,
	1a-c. Type locality: Suez, Tor, Red Sea.
	Avrainvillea lacerata Harvey ex J. Agardh f. robustior A. Gepp &E.S. Gepp (1911),
	pp. 38-39, figs 108-109. Type locality: Singapore, Indian Ocean.

Table I .

 I Comparison of diagnostic characters of representative Avrainvillea species of the longicaulis group sensu

Acknowledgements. This work was funded through the MedPosidonia and CHANGE Programs set up by the RAC/SPAa nd the FRES -University of Corsica. The authors wish to thank Michèle Perret-Boudouresque for documentation assistance, Prof. Bruno de Reviers and Dr B. Dennetière of the Museum National d'Histoire Naturelle (Paris) for permission to consult the collections of A. amadelpha through the Sonnerat database (https://science.mnhn.fr/all/search), and Michael Paul for revising the English. Many thanks go to the anonymous reviewers for their comments and constructive criticism of the manuscript.


Ali Mokh

Maryline Hélard

Matthieu Crussière

Extended Space Shift Keying Modulation With Different Receiver Strategies

Keywords: MIMO, Spatial Modulation, Space Shift Keying, Zero Forcing, Equalization

Space Shift Keying is a MIMO transmission schemes that has been recently studied as promising solution for low computational complexity devices. Such scheme is based on the concept of spatial modulations (SM) where the information is mapped to the index of the transmit (resp. the receive) antenna. When only one antenna is used per symbol duration, an SSK symbol is able to transmit base 2 log of the number of transmit antenna (Nt). In this paper, we introduce an extended version of the conventional SSK scheme, refereed to as Extended SSK (ESSK). The proposed technique allows the overall spectral efficiency to be increased such that the total amount of bits reaches Nt instead of log 2 (Nt) in conventional approaches. In ESSK, one so-called spatial symbol corresponds to a set of bits that are mapped to a set of transmit antennas of variable size that are activated at each time symbol. The performance of ESSK is analyzed in this paper and validated through simulations.

I. INTRODUCTION

Spatial modulation (SM) schemes based on Multiple-input and multiple-output (MIMO) wireless systems, appeared in the early 2000s, consisting in exploiting the index of the transmit or receive antennas to transmit additional information bits. First proposed SM schemes concerned open loop systems because requiring no channel state information (CSI) at the transmitter side. They can be called TSM for transmit SM schemes; the spatial information is carried out by the index of the transmit antennas. One popular of these TSM schemes is Space Shift Keying (SSK) scheme [START_REF] Chau | Space modulation on wireless fading channels[END_REF] whose main principle is to take advantage of the various propagation characteristics associated to the different antennas of the system [START_REF] Jeganathan | Space shift keying modulation for mimo channels[END_REF]. The signal processing at the receiver can also be simplified as data are transmitted through a single spatial stream in SM-MIMO systems [START_REF] Di Renzo | Spatial modulation for generalized mimo: Challenges, opportunities, and implementation[END_REF]. A generalized technique for SSK, further referred to as Generalized Space Shift Keying (GSSK), was proposed in [START_REF] Chang | New space shift keying modulation with hamming code-aided constellation design[END_REF]. Such a scheme overcomes the constraint in SM that the number of transmit antennas N t has to be a power of two, by activating during each symbol duration a subset of N a TAs out of the N t available at the transmit antenna array, to increase the overall SE.

The same concept of SM-MIMO has been applied to the receiver, called Receive-Spatial Modulation (RSM) [START_REF] Yang | Transmitter preprocessing aided spatial modulation for multiple-input multiple-output systems[END_REF] [6], or Receive Antenna Shift Keying (RASK) [START_REF] Phan-Huy | Receive antenna shift keying for time reversal wireless communications[END_REF] [START_REF] Mokh | Time reversal receive antenna shift keying on mimo los channel[END_REF], where the index of the targeted receive antenna (RA) carries the additional spatial information, using a pre-processing technique to target the RAs. A generalization of the RSM principle, further referred to as GPSM (Generalised Pre-coding aided Spatial Modulation), is proposed in [START_REF] Zhang | Generalised precoding aided spatial modulation[END_REF] where the transmit antennas concentrate the signal energy towards a fixed and constant number of RAs to increase the SE. Opposed to conventional SM where a subset of RF chains is deployed, here all TAs and RAs are active. Finally, an extended model of RASK is introduced in [START_REF] Mokh | Extended receive antenna shift keying[END_REF], referred to as ERASK, where all possible combinations of targeted RAs are used, even that one where zero RA is targeted, i.e. no signal is emitted. Among other candidates, this last scheme offers the highest spectral efficiency at the level of the spatial bits, i.e. equal to the number of receive antennas [START_REF] Mokh | Performance analysis of the maximum ratio transmission preprocessing for extended receive antenna shift keying[END_REF] [START_REF]Performance analysis of extended rask under imperfect channel estimation and antenna correlation[END_REF]. With same analogy at the transmitter, Extended SSK (ESSK) has been proposed in [START_REF] Mokh | Space shift keying modulations for low complexity internet-ofthings devices[END_REF] for transmit SM concept where the number of active antenna is variable, giving a SE equal to N t . In this paper, we evaluated the performance of ESSK scheme using different detection strategies. The Maximum Likelihood detector that can be carried out at the receiver side is first proposed and studied as well as the expected theoretical performance. Also, we compare its performance to the performance of the system when Zero-Forcing equalization is performed at the receiver before the detection. At the end of this paper, we demonstrate the duality of ESSK with the ERASK scheme.

II. SYSTEM MODEL AND BLOCK DIAGRAM

In this part, we first set up the model for a communication system making use of the ESSK scheme. Then, we describe the block diagram of ESSK transmission.

A. System Model

MIMO system with N t transmit antennas and N r receive antennas is considered. Assuming a flat fading channel between the transmitter and the receiver, the receive signal vector can be written as:

y = 2 N t H.x + n (1)
where H ∈ C Nr×Nt is the MIMO channel matrix with element h j,i representing the complex channel coefficient between the i-th transmission antenna, denoted by T i , and the j-th receiving antenna, denoted by R j . y ∈ C Nr×1 is the vector of the received signals at all the receive antennas, x ∈ N Nt×1 is the vector of the spatial symbol that will be transmitted by all the transmit antennas, and n ∈ C Nr×1 is the vector of additive white Gaussian noise (AWGN) samples η j such that η j ∼ CN (0, σ 2 n ).

B. Principle Block Diagram

The ESSK scheme is built on the SSK concept at the transmitter where the number of active antennas N a is variable during each time symbol T s (0 ≤ N a ≤ N t ). As for ERASK [START_REF] Mokh | Extended receive antenna shift keying[END_REF], N a can take all possible values between 0 and N r depending on the useful information to transmit so that the number of possible spatial symbols is M = 2 Nt providing the transmission of N t bits per spatial symbol.

Symbol 00 01 10 11

Active Antennas x

T 2 T 1 T 1 ,T 2 Table I ESSK SPATIAL MAPPING FOR Nt=2
Table I provides an illustration of the ESSK symbol mapping with 2 transmit antennas, and is able to transmit 2 bits/symbol. The block diagram of the ESSK system is depicted in Figure 1. A group of m = N t bits is mapped to a spatial symbol x ∈ C Nt×1 which is written as:

x = x 1 x 2 ... x Nt T where x i ∈ {0, 1}.
The value taken by each x i entry determines the set of active transmit antennas such that:

x i = 0, if T i is not active, 1, if T i is active. (2)
The spatial symbol vector is normalized by a factor f = 2 Nt before being emitted, used to guarantee that the average total transmit power Pt is equal to 1.

III. DETECTION STRATEGIES

A. Maximum Likelihood (ML) 1) ML detection equation: At the receiver, a number N r of receive antennas detect the signal. From equation ( 1), if we are sending the spatial symbol k, the received signal vector writes:

y k = f Nt i=1 h i x i (k) + n = f h eq k + n (3)
where h eq k is the equivalent channel vector received when sending the spatial symbol k. The detector has to estimate the index of antenna(s) that have been activated. The equation of the ML is:

k = argmin j y -f h eq j 2 (4)
2) Performance analysis: The Bit Error Probability (BEP) performance of the ESSK is given by the union bound equation:

P e = j k d(x j , x k ) M P(x j → x k ) (5)
where P(x k → x j ) is the Pairwise Error Probability (PEP) and d(x k , x j ) is the hamming distance between two spatial symbols x k and x j . Using Equation ( 4), the PEP conditioned on H is given as:

P(x k → x j |H) = P(d k > d j |H) = P {n H (h eq j -h eq k )} > 1 2 h eq j -h eq k 2 |H = Q( √ κ) (6)
where 2 dt. We have also:

d j = y -f h eq j 2 and Q(x) is the Gaussian distribu- tion function: Q(x) = ∞ x 1 2π e -t 2
κ = h eq j -h eq k 2 2σ 2 n = 2Nr i=1 α 2 i 2σ 2 n ( 7
)
where

α i ∼ N (0, σ 2 α ) with σ 2 α = f 2 d(xj ,x k ) 4
. The Average PEP for different channel realization is given by:

P(x k → x j ) = E H [P(x k → x j )] = ∞ 0 Q( √ u)p κ (u)du, (8)
where p κ is the PDF of κ. The random variable κ is chisquared distributed with c=2N r degrees of freedom, so we have:

p κ (u) = u c 2 -1 exp -u 2σ 2 α (2σ 2 α ) c 2 Γ( c 2 ) , (9)
which has a closed form expression given in [START_REF] Alouini | A unified approach for calculating error rates of linearly modulated signals over generalized fading channels[END_REF]:

P(x k → x j ) = γ Nr α Nr-1 k=1 C Nr-1+k k (1 -γ α ) k (10)
where

γ α = 1 2 1 - σ 2 α 1+σ 2 α .

B. Equalization

In the ERASK scheme, the channel estimation is used to create the precoding matrix used to transmit the spatial symbol. The same matrix can be used in uplink for the equalization, which is why it is interesting to evaluate the performance of the ESSK when using equalization.

1) Equalized Signal: The received signal y given in equation (1) is further equalized. Assuming perfect channel estimation at the receiver side, the equation of spatially equalized signals is:

z = f WHx + Wn (11)
where W ∈ C Nt×Nr is the equalization matrix. As a final step, a detector is used to estimate the spatial symbols from the equalized signal and demappes it to deliver the bit sequence corresponding to the mapping rule described above.

The receiver uses the spatial equalization step to reconstruct the spatial symbol vector. The ZF equalization is employed, so:

W = (H H H) -1 H H . ( 12
)
Since the channel matrix is expected to be converted into an identity matrix after ZF equalization, any inter-antenna interference is removed at this step. To make it possible, the required number of antennas should however satisfy the constraint N t ≤ N r so that the matrix inversion remains possible. Assuming such a constraint is fulfilled, it is then straightforward to obtain the expression of the equalized signals:

z = f x + µ (13)
where µ = Wn. Let µ i be the i-th component of the vector µ ∈ C Nt×1 , and w i,j be the complex coefficient of matrix W in the i-th row and j-th column:

µ i = Nr j=1 w i,j η j . (14)
To estimate the spatial symbols, the receiver should detect whether each transmit antenna is activated or not. From equation [START_REF] Mokh | Space shift keying modulations for low complexity internet-ofthings devices[END_REF], the detector has to analyze the following set of signals:

∀i, z i = f + µ i if T i is activated µ i otherwise. ( 15
)
Since the ZF spatial equalization scheme is used, no interference appears between signal samples impinging at each receive antenna. In addition, since all activated antenna combinations are possible with the ESSK scheme, no correlation exists between the receive equalized signals. Consequently, the demodulation process can be led through an independent and parallel signal analysis per symbol, thereby simplifying the application of the maximum likelihood decision criterion. This is a strong asset of ESSK compared to conventional SM or GSM.

2) Equalized ML detection : The ML detection for the equalized signal can be reduced to a simple real part threshold as proofed in [START_REF] Mokh | Space shift keying modulations for low complexity internet-ofthings devices[END_REF]:

x i = 0, if {z i } ≤ ν, 1, if {z i } ≥ ν, (16)
where the optimal threshold is easily deduced from:

ν = E {z i0 } + {z i1 } 2 = f 2 (17)
with z i0 (resp. z i1 ) the i-th element of equalized receive signal vector if the antenna T i wasn't active (resp. active). Note that such a threshold can in practice be estimated during a calibration phase using dedicated pilot symbols. As proofed in [START_REF] Mokh | Space shift keying modulations for low complexity internet-ofthings devices[END_REF], using such a threshold detector, the theoretical BEP can be expressed as follows:

P e = 1 N t Nt i=1 Q 1 N t w i 2 σ 2 n . (18)

IV. SIMULATION RESULTS

A. Simulation descriptions

The performance of the proposed system is evaluated through the measurement of the BER versus the Signal to Noise Ratio (SNR) that is equal to the ratio between the average transmit power level and noise level, i.e. SNR= Pt σ 2 n . It is assumed that H is a MIMO flat fading channel matrix where h j,i are complex coefficients following an i.i.d. Rayleigh distribution. The power for each sub-channel is normalized:

E h j,i 2 = 1
Finally, we consider that the channel response is perfectly known at the receiver, so that perfect ZF equalization is performed. Simulations are run by implementing a sufficient number of iterations for different channel realizations, and taking the mean value of the BER for each value of SNR.

B. Theoretical Result Validation

Analytical derivations of the BER are compared to the simulation results in Figure 2. An ESSK system with N r = 8 receive antennas and N t = 4 transmit antennas is considered. The performance is evaluated using the ML and EQ-ML detection. As evident from the obtained curves, theoretical results perfectly match simulation results. Also, it is seen that the ML without equalization outperforms the ML after equalization (EQ-ML).

C. ML vs EQ-ML performance

In Figure 3, we compare the performance of ML and EQ-ML detection considering different configurations for N r , and for the same N t =4. ESSK systems with N r = 4, 8, 16 and 32 are simulated using the two detection methods. It is shown that ML detection outperforms the EQ-ML detection, but the

BER

Nr=4, ML Nr=4, EQ-ML Nr=8, ML Nr=8, EQ-ML Nr=16, ML Nr=16, EQ-ML Nr=32, ML Nr=32, EQ-ML Nr=64, ML Nr=64, EQ-ML Figure 3. BER performance of 2x8 ESSK system, using ML and EQ-ML detection, theoretical and simulation comparison more N r increases, the more the difference in performance decreases, and they become approximately the same for N r = 32.

D. Duality ESSK ERASK

The uplink/ downlink duality in the MIMO wireless systems has been studied for different precoding-postcoding strategies [START_REF] Endeshaw | Mse uplink-downlink duality of mimo systems under imperfect csi[END_REF]- [START_REF] Ding | Uplink-downlink duality in normalized mse or sinr under imperfect channel knowledge[END_REF]. Since the SM is a special kind of MIMO system, then a duality can be deduced between the transmit and receive SM.

In Figure ??, we provide the simulation results considering an ESSK system with N r = 8 receive antennas at the base station and 4 different transmit antenna array dimensions, namely N t = 2, 3 and 4 at the device. On the other hand, in Figure 4, the simulation results considering an ERASK system with N t = 8 transmit antennas at the base station and 4 different receive antenna array dimensions, namely N r = 2, 3, 4 and 5 at the device. The two configurations seem to be the uplink and downlink transmission between the base station and a connected device. Note that for both scenarios, we are measuring the BER versus the SNR at the connected device. The performance is evaluated using the EQ-ML detection for ESSK and ML for ERASK. For both configurations, increasing the order of modulation, i.e. N t for ESSK or N r for ERASK, leads to a degradation in performance. Also, for the same order of modulation, we have approximately the same performance in the two transmissions, which proves the duality of transmission between ERASK and ESSK.

V. SUMMARY

In this paper, the concept of ESSK was presented, and we demonstrated how ESSK provides transmission of m = N t bits per spatial symbol duration. We also studied the ML detector, as well as the expected theoretical performance, and then the performance of the system when ZF equalization is performed. The ML detector outperforms the based equalizer detector, but results showed that the more the number of transmit antennas increases, the smaller the difference in performance is. Finally, we demonstrated the duality in performance between ERASK, and ESSK such that the based equalizer detector is implemented.

Figure 1 .

 1 Figure 1. Block Diagram for Extended-SSK

Figure 2 .

 2 Figure 2. BER performance of 4x8 ESSK system, using ML and EQ-ML detection, theoretical and simulation comparison

Figure 4 .

 4 Figure 4. ERASK performance using ML detection with Nt = 8 -Theoretical and simulation comparison

ACKNOWLEDGMENT

The authors would like to thank the SPATIAL MODU-LATION project funded by the French National Research Agency (ANR)