Edgar F Rosas-Alquicira

Rafael Riosmena-Rodríguez

Julio Afonso-Carrillo

Ana I Neto

Ellis & Solander

Taxonomic biodiversity of geniculate coralline red algae (Corallinales, Rhodophyta) from the Macaronesian region: summary and analysis

Keywords: analysis, baseline, Corallinales, geniculate, Macaronesia, taxonomy uncertain

A catalogue and critical review of species and infraspecific taxa of non-fossil geniculate coralline red algae (Corallinales, Rhodophyta) previously reported from the Macaronesian region are presented along with an assessment of species diversity in the region. Published records of geniculate coralline algae are included along with comments relating to type material. Within the catalogue, taxa are organized alphabetically by genus and within this by final epithet. From the 31 taxa recorded, 4 are based on type collections from Macaronesian localities. The types of most species and infraspecific taxa reported from the region have yet to be re-examined in a modern context, and most Macaronesian records require verification. The biodiversity of Macaronesian geniculate coralline algae may be lower than current information indicates.

Introduction

The Macaronesian region sensu lacto includes the Azores, Madeira and Salvage Islands (Portugal), the Canaries (Spain) and Cape Verde Islands (Fig. 1). The first studies of (non-fossil) coralline geniculate red algae (Corallinales, Rhodophyta) in this region go back to the beginning of the XIX century with the paper of Lamarck (1815: 233, 237), who described Corallina millegrana and Corallina purpurata for the Canary Islands.

An important contribution to the knowledge of Macaronesian Corallinales, with an extensive collection for the region, was done by the Dutch oceanographic expeditions CANCAP, in the 1970s and 1980s, with material collected in the Azores, Madeira, Salvage, the Canaries and Cape Verde Islands [START_REF] Prud | Phytogeography of seaweeds of the Azores[END_REF].

Historical revisions of phycological studies including the coralline algae are those by [START_REF] Neto | Checklist of the benthic marine macroalgae of the Azores[END_REF] for the Azores, [START_REF] Levring | The marine algae of the archipelago of Madeira[END_REF] and [START_REF] Neto | Checklist of the benthic marine plants of the Madeiran Archipelago[END_REF] for Madeira, [START_REF] Afonso-Carrillo | Structure and reproduction of Spongites wildpretii sp. nov. (Corallinaceae, Rhodophyta) from the Canary Islands, with observations and comments on Spongites absimile comb[END_REF] and [START_REF] Haroun | Plantas marinas de las Islas Canarias. Canseco editores, Talavera de la Reina Haroun RJ, Gil-Rodríguez MC, Díaz de Castro J, Prud'homme van Reine WF[END_REF] for the Canary Islands and Prud'homme [START_REF] Prud | Phytogeography of seaweeds of the Azores[END_REF] for Cape Verde Islands. The accounts of the coralline algae published by [START_REF] Price | Seaweeds of the western coast of tropical Africa and adjacents islands: a critical assessment. IV Rhodophyta (Florideae) 1. Genera A-F[END_REF][START_REF] Price | Seaweeds of the western coast of tropical Africa and adjacent islands: a critical assessment. IV. Rhodophyta (Florideae) 3. Genera H-K[END_REF] include information on Macaronesian material but only for Cape Verde and the Canary Islands. The work of [START_REF] John | A taxonomic and geographical catalogue of the seaweeds of the western coast of Africa and adjacent islands[END_REF] also included data from Madeira but the Azores were not considered in any of these publications.

Currently there are 31 names of geniculate coralline seaweeds reported for the Macaronesian region but there is no published information compiling the data from the various archipelagos. Information is also lacking on basionym, type material locality, localization, and illustrations, current nomenclatural situation and taxonomic status.

The present study provides a baseline summary and analysis of existing taxonomic information on the geniculate Corallinales for the Macaronesian region sensu lacto, along with comments and/or nomenclatural notes as required.

Arrangement of the Catalogue

The species records were compiled from identification keys, floristic studies, checklists and published catalogues. Unpublished theses and reports were not considered because some involved names that are not effectively published in the context of the International Code of Botanical Nomenclature (ICBN, McNeill et al. 2006).

The type material of a number of taxa of geniculate Corallinales reported from the Macaronesian region has not been studied in the modern context of taxonomy, meaning that the descriptions are incomplete and factually inaccurate, include criteria that are unreliable and are not based on original research encompassing specific morphological, anatomical and ultrastructural investigations. The presence or absence of genicula in those taxa has been inferred from the genus in which the taxon was placed originally. Thus, taxa whose types have not been studied in a modern context but that originally were described as species or infraspecific taxa of Amphiroa J. V. Lamouroux, Cheilosporum (Decaisne) Zanardini, Corallina Linnaeus, Haliptilon (Decaisne) Lindley and Jania J. V. Lamouroux are presumed to possess genicula.

Taxa are listed in alphabetical order by the currently accepted name for the genera and constitutent species. For each taxon, the following information is provided: basionym, type material localization, type locality, published illustrations of type material, reference to its study in a modern context and current placement/name. Table 1 summarizes this information. Published records for the Macaronesian region are also provided, following a north-south latitudinal order: Azores, Madeira, Salvage Islands, Canary Islands and Cape Verde Islands. For each archipelago, homotypic synonyms are arranged in chronological order, with author citations and publications details provided for each.

In the case of taxa for which the type material is not known, or when known, was not revised, nor were the specimens studied in the modern context of taxonomy the status and/or disposition of the taxa is reported as

Amphiroa exilis Harvey

Basionym: Amphiroa exilis Harvey 1849: 95. Syntypes: TCD specimens Darwin 595 (with annotation Det. H.W. Johansen Sept 1967) and Darwin 629 (two specimens), BM Darwin 595 (one sheet with the stamp of Hookerianum Herbarium 1867 and the annotation A. exilis) and Darwin 629 (with the annotation A. exilis); illustrations: Porter (1987, BM Darwin 595, fig. 1, p. 188;BM Darwin 629, fig. 2, p. 189). Type locality: Botofogo Bay, Rio de Janeiro, Brazil (Porter 1987: 188-189); Algoa Bay, Cape Province, South Africa (Silva et al. 1996: 220).

Current placement/name: A. beauvoisii J. V. Lamouroux but status and disposition uncertain as the type was not studied in a modern context. Yendo (1905: 4) based on Madam Weber-van Bosse observations (1904: 100) of Harvey's plants (A. exilis presumed type material) proposed A. exilis as a heterotypic synonym of A. beauvoisii.

The synonym A. beauvoisii was accepted by Prud'Homme van Reine (1994: 70) based on the concept of [START_REF] Price | Seaweeds of the western coast of tropical Africa and adjacents islands: a critical assessment. IV Rhodophyta (Florideae) 1. Genera A-F[END_REF] for the Azorean material of A. exilis which had been collected and identified by [START_REF] Piccone | Alghe della Crociera del alle Azzorre[END_REF]. In contrast to [START_REF] Prud'homme Van Reine | A reinvestigation of Macaronesian seaweeds as studied by A. Piccone with remarks on those studied by A. Grunow[END_REF], we think the name A. exilis should be kept until more comparisons and study of type material have been conducted. gonimoblastic filaments arising from fusion cell margins; iii) male conceptacles chambers narrow with a short canal and iv) few tetrasporangia per conceptacle (Johansen and Silva 1978: 413;table 1, p. 414). According to these authors, Cheilosporum distinguishes from other Janieae genera by possessing a marginal rather than axial location of conceptacles and the presence of pronounced intergenicular lobes. A complete diagnosis of the genus was provided by Johansen (1981, appendix 1, p. 216). Womersley and Johansen (1996: 296) included a key for the Janieae genera in their book for Southern Australia where they mentioned as segregating generic characters, the branching pattern of the main axes, the intergenicular shape and the conceptacles position. [START_REF] Kim | Phylogenetic relationships within the tribe Janieae (Corallinales, Rhodophyta) based on molecular and morphological data: a reappraisal of Jania[END_REF], based on combined molecular (SSU rDNA) and anatomical data (table 1, p. 1313), determined that these characters were not useful to separate the three genera. They concluded that the Janieae should be merged only into the single genus Jania recognized by the generic characters previously listed by Johansen and Silva (1978: 413;table 1, p. 414). This conclusion was followed by [START_REF] Woelkerling | Recognition of Pachyarthron and Bossiella as distinct genera in the Corallinaceae, subfamily Corallinoideae (Coarllinales, Rhodophyta)[END_REF]. [START_REF] Walker | Biodiversity of coralline algae in the Northeastern Atlantic including Corallina caespitosa sp. nov. (Corallinoideae, Rhodophyta)[END_REF], based on cox1 and 18S rRNA analysis of Haliptilon squamatum and Jania rubens, also concluded they were not distinct but suggested that the clarification of the phylogenetic position of Haliptilon and Jania required more comparisons and study of original material of the genera involved. We share the opinion of [START_REF] Walker | Biodiversity of coralline algae in the Northeastern Atlantic including Corallina caespitosa sp. nov. (Corallinoideae, Rhodophyta)[END_REF], a reason why in the present catalogue, the genera and species of Cheilosporum, Haliptilon and Jania are treated separately.

Cheilosporum elegans J. E. Areschoug

Basionym: Amphiroa elegans J. D. Hooker & Harvey 1849: 101. Type: TCD Colenso specimen 630; illustrations: Harvey (1849, pl. 38 lower left, p. 101). Type locality: New Zealand (Woelkerling and Nelson 2004: 54).

Current placement/name: Cheilosporum elegans J. E. Areschoug but status and disposition of species uncertain as the type was not studied in a modern context (Woelkerling and Nelson 2004: 55). This conclusion was based on specimens originally described by Hooker and Harvey (in Harvey, 1849: 101) under the name Amphiroa elegans, an illegitimate name (ICBN Art. 53.1) since it is a later homonym of Amphiroa elegans Sonder (1845: 55), now considered a heterotypic synonym of Metagoniolithon stelliferum (Lamarck) Ducker (Silva et al. 1996: 260). Womersley and Johansen (1996: 315, 317) mentioned C. elegans J. E. Areschoug and also Amphiroa elegans J. D. Hooker & Harvey in Harvey, nom. illeg. as heterotypic synonyms of Cheilosporum sagittatum (Lamouroux) J. E. Areschoug. A similar suggestion was made by Moura and Guimarães (2002: 69) for C. elegans (J. D. Hooker & Harvey in Harvey) Areschoug. These suggestions, however, were made without reviewing type material. Later, [START_REF] Kim | Phylogenetic relationships within the tribe Janieae (Corallinales, Rhodophyta) based on molecular and morphological data: a reappraisal of Jania[END_REF] based on molecular and reproductive features proposed to merge material of Cheilosporum and Haliptilon within Jania genus and suggested the new combination Jania cultrata (Harvey) J. H. Kim, Guiry & H.-G. Choi comb. nov. This conclusion, however, was not based on type material observations.

Published records:

CAPE VERDE ISLANDS:

Cheilosporum elegans (J. D. Hooker & Harvey) J. E. Areschoug. Askenasy (1896: 26) and Price et al. (1986: 65). Harvey. Price et al. (1986: 65).

Cheilosporum elegans

Corallina

Currently the genus Corallina is recognized to belong to the Corallinaceae, subfamily Corallinoideae (Johansen 1981, table 9, p. 188;Harvey et al. 2003, table 4, p. 995). Its generic concept is consensual. The main characteristics are listed in Johansen (1981: 217), and a detailed diagnosis is provided by Womersley and Johansen (1996: 289-290). The relationship between Corallina and other Corallinoideae genera is provided by Woelkerling et al. (2008, table 4, p. 282;table 5, p. 287).

Corallina deshayesii Montagne

Basionym: Corallina deshayesii Montagne 1846: 130. Type: not found; illustrations: not found. Type locality: not found.

Current placement/name: C. deshayesii Montagne but status and disposition uncertain as the type was not studied in a modern context. Price et al. (1986: 73) mentioned that C. deshayesii may well be a synonym of Corallina mediterranea J. E. Areschoug. The designation/localization of the type material and its study in a modern context is required.

Published records:

SALVAGE ISLANDS: Price et al. (1986: 73).

Corallina elongata J. Ellis & Solander

Basionym: Corallina elongata J. Ellis & Solander 1786: 119. Lectotype: Ellis's illustrations designated by Irvine and Johansen (1994: 41); illustrations: Ellis (1755, pl. 24, fig. 3, p.49). Type locality: Cornwall, England (Irvine and Johansen 1994: 41).

Current placement/name: C. elongata J. Ellis & Solander according to Irvine and Johansen (1994: 41) based on the study of lectotype material. [START_REF] Walker | Biodiversity of coralline algae in the Northeastern Atlantic including Corallina caespitosa sp. nov. (Corallinoideae, Rhodophyta)[END_REF] Mediterranean. While the concept of the species is not disputed for those samples from Britain and Ireland, the samples from Greece are C. caespitosa, and those from elsewhere in the Atlantic are of an unknown species and should be re-evaluated. Higher divergences as observed in the sequences identified to the genus from Tenerife and Madeira in the cox1 gene can be interpreted as the result of geographical isolation and gene pool fragmentation [START_REF] Hebert | Biological identifications through DNA barcodes[END_REF]. These islands are geographically isolated in the Atlantic but it is not known if the populations interbreed with populations from elsewhere in the Atlantic and Mediterranean. For the relationship between C. elongata and C. mediterranea J. E. Areschoug see C. mediterranea entry.

Published records:

AZORES: Castro and Viegas (1983: 20), South and Tittley (1986: 42), Tittley and Neto (1994: 8), [START_REF] Toste | Life history of Colpomenia sinuosa (Scytosiphonaceae, Phaeophyceae) in the Azores[END_REF]Toste et al. ( : 1270) ) and Wallenstein and Neto (2006: 199).

Corallina elongata Johnst. Castro and Viegas (1987: 63).

Corallina elongata. [START_REF] Neto | Checklist of the benthic marine macroalgae of the Azores[END_REF]Neto ( : 26, 2000aNeto ( : 139, 2000b: 490) : 490) and Prud'homme van Reine et al. (1994: 81) and Tittley and Neto (2000: 20).

MADEIRA: Audiffred and Prud'homme van Reine (1985: 38) and John et al. (2004: 73).

Corallina elongata. Prud'homme van Reine et al. (1994: 81). SALVAGE ISLANDS: Price et al. (1986: 73), Prud'homme van Reine et al. (1994: 81) and John et al. (2004: 73).

CANARY ISLANDS: Price et al. (1986: 73), Viera-Rodríguez and Wildpret de la Torre (1986: 215), González et al. (1986: 316), Viera-Rodríguez (1987: 242), Viera-Rodríguez et al. (1987: 273), Reyes and Sansón (1991: 79), Ballesteros et al. (1992: 516), Pinedo et al. (1992: 36), Kristiansen et al. (1993: 95), Irvine and Johansen (1994: 42), Prud'homme van Reine et al. (1994: 81), Guadalupe et al. (1995: 37), Rojas- González and Afonso-Carrillo (2000: 129;2004: 138), Gil-Rodríguez et al. (2003: 25), Haroun et al. (2003: 108), Montañés et al. (2003: 124), Sangil et al. (2003aSangil et al. ( : 94 103 , 2003bSangil et al. ( : 311 , 2004Sangil et al. ( : 89, 2005: 326): 326), Afonso-Basionym: Corallina lobata J. V. Lamouroux 1816: 286. Holotype: CN; illustrations: not found. Type locality:

The Canaries (Lamouroux 1816: 286).

Current placement/name: C. lobata J. V. Lamouroux. Examination of a fragment of the type material revealed stable characters at the genus level (Garbary and Johansen 1982: 212), but the status as a distinct species within the genus remains uncertain until comparative studies of relevant types are undertaken. Afonso-Carrillo (unpublished information) verified that the type material of C. lobata was not different from the actual concept of Haliptilon virgatum (Zanardini) Garbary & H. W. Johansen (for further comments see Price et al. 1992: 125).

As C. lobata is an older name it would have priority over C. virgata Zanardini (1840) (Afonso-Carrillo and Sansón 1999: 151-152). For more information see Haliptilon virgatum entry.

Published records:

MADEIRA: Afonso-Carrillo and Sansón (1999: 151). SALVAGE ISLANDS: Afonso-Carrillo and Sansón (1999: 151).

CANARY ISLANDS: Lamouroux (1816: 286), [START_REF] Afonso-Carrillo | Adiciones y correcciones al catálogo de algas marinas bentónicas para el Archipiélago Canario[END_REF]: 46, 1984: 26, 30), Price et al. (1986: 75), Reyes and Afonso-Carrillo (1993: 127), Afonso-Carrillo and Sansón (1999: 151).

Corallina lobata. Delgado et al. (1984: 105). CAPE VERDE ISLANDS: Afonso-Carrillo and Sansón (1999: 151).

Corallina mediterranea J. E. Areschoug

Basionym: Corallina mediterranea J. E. Areschoug 1852: 568. Type: Herb. Reg. Acad. Scientiarum Holm; illustrations: not found. Type locality: Mediterranean (Agardh 1852: 568).

Current placement/name: C. mediterranea J. E. Areschoug but status and disposition uncertain as the type was not studied in a modern context. Ardré (1970: 226) (1989) concept. This synonym was generalized by [START_REF] Price | Seaweeds of the western coast of tropical Africa and adjacents islands: a critical assessment. IV Rhodophyta (Florideae) 1. Genera A-F[END_REF]: 73, as C. elongata Johnst. Newton 1931: 313) and published as valid by Irvine and Johansen (1994: 41) but only based on the study of the lectotype of C.

elongata.

For details on the relationship between C. mediterranea, C. elongata and C. officinalis, see C. mediterranea and C. officinalis entries.

Published records:

AZORES: Lemoine (1924: 130), [START_REF] Schmidt | Die marine Vegetation der Azoren in ihren Grundzügen dargestellt[END_REF]: 65), Feldmann (1946: 419), Ardré et al. (1974: 178), Tittley et al. (1998: 468) and Neto (2000b: 485;2001: 104).

MADEIRA: Grunow (1868: 77), Lemoine (1924: 130), Schmidt (1931: 101) and John et al. (2004: 73). SALVAGE ISLANDS: Price et al. (1986 : 73).

CANARY ISLANDS: Lemoine (1924: 130), Børgesen (1929: 68), Schmidt (1931: 101), Feldmann (1946: 407), Seoane-Camba (1965: 110), Kohlmeyer (1967: 143), Santos Guerra et al. (1970: 24), Acuña González (1972: 5), Santos Guerra (1972: 95), Perez-Cirera (1975: 19), Afonso-Carrillo et al. (1978: 232) and Price et al. (1986 : 73).

Corallina mediterranea. Vickers (1896: 295), Sauvageau (1912: 210) and González (1977b: 100).

Corallina mediterranea L. Gil-Rodríguez (1980: 138).

Corallina microptera Montagne

Basionym: Corallina microptera Montagne 1846: 130. Type: M Bourgeau; PC (Afonso-Carrillo and Sansón 1999: 152); illustrations: not found. Type locality: Orotava, Tenerife, the Canaries (Montagne 1846: 130).

Current placement/name: C. microptera Montagne. Examination of a fragment of the type material revealed stable characters at the genus level (Garbary and Johansen 1982: 212), but the status as a distinct species within genus remains uncertain until comparative studies of relevant types are undertaken. According to [START_REF] Bornet | Les algues de P.-K.-A. Schousboe recoltées au Maroc et dans la Méditerranée de 1815 a 1829[END_REF] C. microptera from the Canary Islands is just a small form of C. elongata (as C. mediterranea J. E. Areschoug, Afonso-Carrillo and Sansón 1999: 152). Revision of the type material revealed stable characters at the genus level (Garbary and Johansen 1982: 212). The study of type specimens in a modern context is required for specific diagnosis.

Published records:

AZORES:

Corallina microptera. Afonso-Carrillo and Sansón (1999: 152).

MADEIRA: Afonso-Carrillo and Sansón (1999: 152).

CANARY ISLANDS: Montagne (1846: 130).

Corallina millegrana Lamarck

Basionym: Corallina millegrana Lamarck 1815: 233. Holotype: PC 0028655 General Herbarium; illustrations: not found. Type locality: Tenerife, the Canaries (Lamarck 1815: 233).

Current placement/name: C. millegrana Lamarck. Examination of a fragment of the type material revealed stable characters at the genus level (Garbary and Johansen 1982: 212), but the status as a distinct species within genus remains uncertain until comparative studies of relevant types are done.

Published records:

CANARY ISLANDS: Afonso-Carrillo and Sansón (1999: 152).

Corallina officinalis Linnaeus

Basionym: Corallina officinalis Linnaeus 1758: 805. Lectotype: LINN 1293. 9 (Irvine and Johansen 1994: 44); Current placement/name: C. officinalis Linnaeus according to Irvine and Johansen (1994: 44) and Walker et al. (2009: 295) based on the study of lectotype material. Afonso-Carrillo et al. (1983: 46) Afonso-Carrillo (pers. comm.). However no revision of the type material was made. Irvine and Johansen (1994: 44) provided a detailed account of C. officinalis in the British Isles whilst Womersley and Johansen (1996: 291) provided an account of the species in southern Australia.

For details on the relationship between C. officinalis, C. elongata and C. mediterranea J. E. Areschoug see C. elongata and C. mediterranea entries.

Published records:

AZORES: Piccone (1889: 209), Gain (1914: 15, 22), [START_REF] Schmidt | Die marine Vegetation der Azoren in ihren Grundzügen dargestellt[END_REF]: 65), Feldmann (1946: 419), Levring (1974: 69), Audiffred (1985: 174), Weisscher (1983: 64), Audiffred and Prud'homme van Reine (1985: 38), South and Tittley (1986: 42), Neto (1994: 26), Tittley andNeto (1994: 8, 2000: 20) and Tittley et al. (1998: 468).

Corallina officinalis. Schmidt (1929a: 331).

MADEIRA: Piccone (1884: 42-43), Barton (1897: 374), Gain (1914: 7), Schmidt (1931: 101), Levring (1974: 69), Weisscher (1983: 64), Audiffred and Weischer (1984: 33), Audiffred (1985: 174) and Neto et al. (2001: 403).

Corallina mediterranea Aresch = Corallina officinalis L. Audiffred and Weisscher (1984 : 33).

Corallina officinalis. Augier (1985: 100). SALVAGE ISLANDS: Price et al. (1986: 75) and John et al. (2004:73).

CANARY ISLANDS: Price et al. (1986: 75), Viera-Rodríguez (1987: 242), Viera-Rodríguez et al. (1987: 273), Afonso-Carrillo and Sansón (1999: 195), Gil-Rodríguez et al. (2003: 25) and John et al. (2004: 73). CAPE VERDE ISLANDS: Price et al. (1986: 75).

Haliptilon

The generic concept of this genus is not consensual. For the relationship between Haliptilon and other Janieae genera see Cheilosporum entry. According to Womersley and Johansen (1996: 296) Haliptilon distinguishes from other Janieae genera by possessing a thallus pinnate with compressed axial intergenicula without lobes, usually bearing two or more subterete branchlets, sometimes adventitiously; conceptacles in terminal branchlets, usually single and with apical pores; spore producing conceptacles with 1-3 branchlets.

Haliptilon cubensis (Montagne ex Kützing) Garbary & H. W. Johansen

Basionym: Jania cubensis Montagne ex Kützing, 1849: 709-710. Type: Montagne Herbarium (Agardh 1852); illustrations: Garbary and Johansen (1982, fig. 10, p. 216) Canaries (1884) and Madeira (Grunow 1868) housed at PAD Herbarium considered it as H. virgatum (Zanardini) Garbary & H. W. Johansen, following the concept of Afonso-Carrillo and Sansón (1989: 25).

Nevertheless the type material was not observed. The presence of H. squamatum in the Archipelagos of Madeira and the Canaries is dubious and needs confirmation (Afonso-Carrillo et al. 1983: 46;Neto et al. 2001: 412). [START_REF] Kim | Phylogenetic relationships within the tribe Janieae (Corallinales, Rhodophyta) based on molecular and morphological data: a reappraisal of Jania[END_REF]Kim et al. ( : 1317) ) based on molecular and reproductive features proposed the new combination Jania squamata (Linnaeus) J. H. Kim, Guiry & H.-G. Choi.

Published records:

AZORES:

Corallina squamata J. Ellis & Solander. Schmidt (1929b: 171, 1931: 65) and Feldmann (1946: 419).

Haliptylon squamatum. Neto (1994: 26).

Haliptilon squamatum (Linnaeus) H.W. Johansen., L.M. Irvine & A.M. Webster. South and Tittley (1986: 42) and Tittley andNeto (1994: 9, 2005: 250).

MADEIRA:

Corallina squamata. Grunow (1868: 78).

Corallina squamata J. Ellis & Solander. Grunow (1868: 78) and Schmidt (1929bSchmidt ( : 171, 1931: 101): 101).

Haliptilon squamatum (Linnaeus) H. W. Johansen, L.M. Irvine & A.M. Webster. John et al. (2004: 86).

CANARY ISLANDS:1

Haliptilon squamatum (Linnaeus) H. W. Johansen, L. M. Irvine & A. M. Webster. Afonso-Carrillo et al. (1983: 46), Price et al. (1992: 125), Irvine and Johansen (1994: 49), Irvine and Johansen (1994: 49), Afonso-Carrillo andSansón (1999: 195), Gil-Rodríguez et al. (2003: 25) and John et al. (2004: 86).

Haliptilon virgatum (Zanardini) Garbary & H. W. Johansen

Basionym: Corallina virgata Zanardini 1844: 1025. Type: MCVE (Stafleu and Cowan 1988: 516); illustrations: not found. Type locality: Adriatic Sea (Zanardini 1844: 1025).

Current placement/name: H. virgatum (Zanardini) Garbary & H. W. Johansen. Examination of a fragment of the type material revealed stable characters at the genus level (Garbary and Johansen 1982: 212), but the status as a distinct species within genus remains uncertain until comparative studies of relevant types are done. [START_REF] Kim | Phylogenetic relationships within the tribe Janieae (Corallinales, Rhodophyta) based on molecular and morphological data: a reappraisal of Jania[END_REF] based on molecular and reproductive features proposed to merge Haliptilon within Jania genus (see Cheilosporum entry) but did not suggest a new combination for H. virgatum.

For the relationship between H. virgatum and Corallina lobata J. V. Lamouroux, see C. lobata entry.

Published records:

AZORES: Piccone (1889: 210) and Neto and Tittley (1995: 490).

Haliptylon virgatum (Zanardini) Garbary & H. W. Johansen. South and Tittley (1986: 42), Prud'homme van Reine et al. (1994: 81), Tittley and Neto (1994: 9), Tittley et al. (1998: 468) and Wallenstein and Neto (2006: 199).

MADEIRA:

Haliptilon virgatum (Zanardini) Garbary & H. W. Johansen. Audiffred and Prud'homme van Reine (1985: 41) and John et al. (2004: 87). SALVAGE ISLANDS: Price et al. (1992: 125).

CANARY ISLANDS: Piccone (1889: 210) and Price et al. (1992: 125).

Haliptilon virgata (Zanardini) Garbary & H. W. Johansen. Viera-Rodríguez and Wildpret de la Torre (1986: 217), Price et al. (1992: 125), Prud'homme van Reine et al. (1994: 94), Afonso-Carrillo and Sansón (1999: 195), Rojas-González andAfonso-Carrillo (2002b: 100), Gil-Rodríguez et al. (2003: 25) and Muñoz et al. (2007: 107).

Haliptilon virgatum. Gil-Rodríguez et al. (1992: 112) and Prud'homme van Reine et al. (1994: 81).

Haliptilon virgata. Afonso-Carrillo and Sansón (1989: 25).

Haliptilon virgatum (Zanardini) Garbary & H. W. Johansen. Elejabeitia et al. (1992: 8), Pinedo et al. (1992: 39), Guadalupe et al. (1995: 37), Haroun et al. (2003: 108), Montañés et al. (2003: 124), Sangil et al. (2003aSangil et al. ( : 103, 2003b[START_REF] Sangil | Zonación del fitobentos en el litoral Noroeste de La Palma (Islas Canarias)[END_REF]Sangil et al. ( : 89: 311, 2005: 326) : 326) and John et al. (2004: 87).

Jania

The generic concept of this genus is not consensual. For the relationship between Jania and other Janieae genera see Cheilosporum entry. According to Womersley and Johansen (1996: 296), Jania distinguishes from other Janieae genera by possessing a dichotomous thallus with terete or compressed intergenicula bearing axial conceptacles.

Jania adhaerens J. V. Lamouroux

Basionym: Jania adhaerens J. V. Lamouroux 1816: 270. Holotype: CN (Johansen 1971: 247;Cribb 1983); illustrations: not found. Type locality: Mediterranean (Lamouroux 1816: 270).

Current placement/name: J. adhaerens J. V. Lamouroux but status and disposition uncertain as the type was not studied in a modern context.

Published records:

Jania verrucosa J. V. Lamouroux

Basionym : Jania verrucosa J. V. Lamouroux 1816: 270. Holotype: CN Lamouroux Herbarium (Womersley and Johansen 1996: 305); illustrations: Lamouroux (1816, pl. 9, fig. 4 a.B, p. 270). Type locality: North America (Lamouroux 1816: 270).

Current placement/name: J. verrucosa J. V. Lamouroux but status and disposition uncertain as the type was not studied in a modern context. For the relationship between J. verrucosa, J. natalensis and J. cryptarthrodia see J. natalensis and J. cryptarthrodia entries.

Published records:

AZORES: Jania verrucosa. Neto (2000b: 491;2001:105). CAPE VERDE ISLANDS: Price et al. (1992: 136).

Discussion

From the thirty one names of species and infraspecific taxa of geniculate Corallinales recorded from the Macaronesian region, four are based on type material collected from localities within this region while the rest (87%) are based on types from localities elsewhere (Table 1). All species are validly published (ICBN,Art. 6.2,29.1,42.3 and 60). The correct application of these names to species and specific taxa, however, is linked to an understanding of the type material and to the provisions of the ICBN (McNeill et al. 2006).

For Haliptilon cubensis, H. virgatum and the four names based on Macaronesian collections (Corallina lobata, C. microptera, C. millegrana and Haliptilon purpurata), only a fragment of the holotype material was studied. The generic placement of the taxa was confirmed by ultrastructural investigations but the status of the species could not be determined [START_REF] Garbary | Scanning electron microscopy of Corallina and Haliptilon (Corallinaceae Rhodophyta): surfaces features and their taxonomic implications[END_REF]. As a result, published information does not include detailed specific morphological and anatomical accounts, and its nomenclature lacks the foundations essential for stability. Therefore, although those taxa are currently treated as distinct species by various authors, this treatment requires substantiation through morphological, anatomical and ultrastructural detailed studies of relevant type material.

From the list compiled in the present work, 15 taxa have not been studied in a modern context. Jania intermedia is a nomen nudum (ICBN, Art. 1) and therefore nomenclaturally illegitimate. The remaining 14 taxa, although listed as distinct species in various publications, require re-assessment through further studies of relevant type material. The same situation happens with the proposed heterotypic synonyms. An example is the synonymy of Corallina mediterranea with C. elongata published by Irvine and Johansen (1994: 41). The segregating characters defined by these authors for C. elongata, related to reproductive and vegetative morphology, cannot be contrasted with the available original description of C. mediterranea from Areschoug (1852: 568-569). Also, the presence in the main axes of intergenicula as long as wide, described by Walker et al. (2009: 295-296) as distinguishing feature for C. elongata, does not agree with the description of C. mediterranea. The occurrence of most of these taxa in Macaronesia has yet to be verified as most records represent occasional findings from one single location.

Only ten types of Corallinales occurring in Macaronesia have been studied in a modern context. From these, two (Jania crassa and Amphiroa verruculosa) are considered heterotypic synonyms of other taxa. The heterotypic synonymy of Jania crassa with Jania verrucosa [START_REF] Johansen | Jania (Corallinales Rhodophyta) in southern Australia[END_REF], however, requires further studies comparing both types. The remaining 8 species are considered to be distinct taxa. Their diagnosing characters were emended based on, respectively, vegetative and reproductive anatomy in the case of Amphiroa (Norris and Johansen 1981: 5-6), vegetative and reproductive morphology in Corallina (Walker et al. 2009: 295;table 4, p. 296) and morphological and anatomical vegetative characters in Jania (Johansen and Womersley 1994: 606). The confirmation of these species in the Macaronesia requires the study of their voucher specimens in ligth of these new concepts.

To summarize, only 8 of the 31 species and infraspecific taxa of geniculate Corallinales listed for Macaronesia have been confirmed to represent distinct species. Three others have been found to be heterotypic synonyms of other taxa and one (Jania intermedia) is nomenclaturally illegitimate. There remains 19 taxa which have yet to be fully reassessed through detailed studies encompassing specific morphological, anatomical and ultrastructural investigations, preferably complemented with molecular studies. This task has many difficulties, starting with the fact that for three species (Corallina deshayesii, C. granifera and C. intermedia) the type collection whereabouts are uncertain. However, this kind of taxonomic work may confirm the molecular conclusions of [START_REF] Kim | Phylogenetic relationships within the tribe Janieae (Corallinales, Rhodophyta) based on molecular and morphological data: a reappraisal of Jania[END_REF] suggesting that the genera Cheilosporum, Haliptilon and Jania (tribe Janieae) should be merged into a single genus Jania recognized by the generic characters listed by Johansen and Silva (1978: 413, table 1, p. 414).

Conclusion

The present catalogue and its analysis represent initial steps in creating a reliable database on the species diversity of geniculate Corallinales in the Macaronesian region. Although 31 names of geniculate Corallinales have been recorded for this region, the actual number of species and genera present is uncertain and will continue to remain so until detailed monographic studies are undertaken. How many of the names previously used for the Macaronesian region taxa can correctly be applied to specimens for this region also remains uncertain as does the number of species present, but so far undetected. An accurate figure of the actual diversity for the Macaronesian geniculate corallines requires extensive work involving new collections, the detailed study of fresh material, historical collections and type material, complemented, if possible, with molecular evaluations.

  in their integrative taxonomic approach including phylogenetic reconstructions based on the cox1 and 18S rRNA genes in addition to a comparative morphological assessment study identified three clusters. C. officinalis sensu stricto and C. elongata from Britain corresponded to similar groups in the cox1 tree whereas the sequences of the unidentified Corallina specimens from Madeira and Tenerife clustered with sequences of C. caespitosa R. H. Walker, J. Brodie & L. M. Irvine and C. elongata from other locations. The results indicate that the name C. elongata has been misapplied in both the Atlantic and

  and Solms-Laubach (1881 inArdissone 1883: 464) mentioned that the criteria used to distinguish C. mediterranea and Corallina officinalis Linnaeus were unsatisfactory and that further research was needed before any decision to merge both species. The historical use of C. mediterranea or C. officinalis at Salvagens Islands (Madeira) and in the Canary Islands is discussed inPrice et al. (1986: 74).Prud'homme van Reine et al. (1994: 81) redefined the C. mediterranea material recorded by Grunow (1868: 77) for the Archipelago of Madeira as C. elongata J. Ellis & Solander in the Afonso-Carrillo and Sansón

  illustrations:Walker et al. (2009, C. officinalis, fig. 5a; Corallina compacta Crouan & Crouan (PC), fig. 5b; Corallina nana Zanardini (MCVE), fig. 5c; Corallina calvadosii J. V. Lamouroux (PC), figs 5 d-e, p. 296). Type locality: European Seas (Lamouroux 1816: 284).

  mentioned the presence of C. officinalis in the Canary Islands as doubtful. Prud'homme van Reine et al. (1994: 81) studying the material collected by Piccone and housed at PAD Herbarium redefined C. officinalis from Azores (Piccone 1889: 209), Canaries (Piccone 1884: 42) and Madeira (Piccone 1884: 42) as C. elongata J. Ellis & Solander in the concept of

  as Haliptilon cubensis (Montagne ex Kützing) Garbary & H. W. Johansen. Type locality: Cuba (Kützing 1849: 710). Current placement/name: H. cubensis (Montagne ex Kützing) Garbary & H. W. Johansen. Examination of a fragment of the type material revealed stable characters at the genus level (Garbary and Johansen 1982: 212), but the status as a distinct species within genus remains uncertain until comparative studies of relevant types are done. Following their suggestion to merge material of Cheilosporum and Haliptilon within the Jania genus (Kim et al. 2007, see Cheilosporum entry), these authors suggested the new combination J. cubensis (Montagne ex Kützing 1849, p. 709-10). According to Afonso-Carrillo (unpublished results) plants from the Canary Islands reported as Corallina cubensis (Montagne ex Kützing) Kützing or H. cubensis are not morphologically different from Haliptilon virgatum (Zanardini) Garbary & H. W. Johansen Published records: CANARY ISLANDS:

Zanardini G (1844) Corallinee. Encicl. Ital. (Venezia:Tasso) 6:1013-1036

Acknowledgements

We thank Drs. Willem F. Prud'homme van Reine (National Herbarium Nederland-L) and Bruno de Reviers (Muséum National d'Histoire Naturelle-PC) who provided specialized old literature and/or type material information, Ian Tittley (Natural History Museum), José M. N. Azevedo and Gustavo Martins for the English revision of the manuscript, Nuno Álvaro for the study area map, and to Dr. Inka Bartsch and an anonymous reviewer for their useful comments and suggestions. This work was partly supported by the Programme AlBan, the European Union Programme of High Level Scholarships for Latin America (through scholarship E05D060221MX) and "Consejo Nacional de Ciencia y Tecnología" doctoral scholarship 176162, the UNAMUNO Programme of PhD Scholarships for Europe, and "Centro de Investigação de Recursos Naturais", University of the Azores.

CAPE VERDE ISLANDS: Otero-Schmitt and Sanjuan (1992: 382), Price et al. (1992: 135) and Otero-Schmitt (1993: 51).

Jania crassa J. V. Lamouroux

Basionym: Jania crassa J. V. Lamouroux 1821: 23. Holotype: CN Lamouroux Herbarium under Jania in folder c8-f74 (Woelkerling and Nelson 2004: 53); illustrations: Lamouroux (1821, pl. 69, figs 9-10, p. 23) and Johansen (1971, fig. 10, p. 244) as J. crassa ; Johansen and Womersley (1994, fig. 37, p. 622) as Jania verrucosa J. V. Lamouroux; see comments. Type locality: Dusky Sound, South Island, New Zealand (Lamouroux 1821: 23).

Current placement/name: J. verrucosa J. V. Lamouroux but status and disposition uncertain as the type of J. verrucosa was not studied in a modern context. Johansen and Womersley (1994: 617) and Womersley and Johansen (1996: 305, 307) considered J. crassa as a heterotypic synonym of J. verrucosa stating that they are almost "certainly conspecific at least in southern Australia". This conclusion was only based on the study of the holotype of J. crassa. However, according to Woelkerling and Nelson (2004: 65) the proposed conspecifity needs to be confirmed through a comparative study of both types.

Published records:

AZORES: South and Tittley (1986: 43), Neto (1994: 26) and Tittley and Neto (1994: 9). Jania crassa. Prud'homme van Reine (1988: 179), Stengenga et al. (1997: 585) and Neto (2000aNeto ( : 140, 2000b: 490): 490). CAPE VERDE ISLANDS: Otero-Schmitt and Sanjuan (1992: 384) and Price et al. (1992: 136).

Jania intermedia (Kützing) P. C. Silva

Basionym: Corallina intermedia Kützing 1858: 37-38, 42. Type: not found; illustrations: Kützing (1858, pl. 79, fig. I, p. 36-38; pl. 86, fig. IV, p. 42). Type locality: Cape of Good Hope, South Africa (Silva et al. 1996: 242).

Current placement/name: J. intermedia (Kützing) P. C. Silva but status and disposition uncertain as the type was not studied in a modern context. Silva et al. (1996: 242) mentioned that the correct combination is J. intermedia and not Jania intermedia Kützing which was only a bibliographic reference and not the name of the basionym. Neto et al. (2001: 412.) studying Madeira specimens cited it as doubtful record mentioning that "it might be a variety of J. rubens (Linnaeus) J.V. Lamouroux". According to Woelkerling and Nelson (2004: 57), this name should be considered a nomen nudum as there are no valid diagnosis descriptions.

Published records:

21

MADEIRA:

Corallina intermedia Grunow. Neto et al. (2001: 412).

Jania longifurca Zanardini

Basionym: Jania longifurca Zanardini 1844: 1025. Type: probably in MCVE Zanardini's collections; illustrations: not found. Type locality: Dalmatia, Italy (Zanardini 1844: 1025).

Current placement/name: J. longifurca Zanardini but status and disposition uncertain as the type was not studied in a modern context. Sansón et al. (1991: 531) mentioned that this species is poorly known in the Canary Islands and needs further studies. The designation/localization of the type material and its study in a modern context is required.

Published records:

AZORES : Feldmann (1946: 421), South and Tittley (1986: 43), Neto (1994: 26), Tittley et al. (1998: 468) and Neto (2000aNeto ( : 140, 2000bNeto ( : 490, 2001:105):105).

MADEIRA: Levring (1974: 70), Sansón et al. (1991: 530) and Neto et al. (2001: 404).

CANARY ISLANDS: Sansón et al. (1991: 530), Afonso-Carrillo and Sansón (1999: 196), Haroun et al. (2002: 146) and Gil-Rodríguez et al. (2003: 25).

Jania micrarthrodia J. V. Lamouroux

Basionym: Jania micrarthrodia J. V. Lamouroux 1816: 271. Holotype: CN Lamouroux Herbarium; illustrations: Lamouroux (1816, pl. 9, fig. 5a; pl. 69, figs 7-8, p. 271); Johansen and Womersley (1994, figs 32-36, p. 622).

Type locality: Australasia (Lamouroux 1816: 271).

Current placement/name: J. micrarthrodia J. V. Lamouroux according to Johansen and Womersley (1994: 611-613) based on the study of type material. Gil-Rodríguez et al. (2003: 212) mentioned that the material of J. micrarthrodia for the Canaries could not be located.

Published records:

CANARY ISLANDS: Price et al. (1992: 136) and Afonso-Carrillo and Sansón (1999: 196).

Jania natalensis Harvey

Basionym: Jania natalensis Harvey 1849: 107. Type: TCD (Johansen 1971: 247); illustrations: not found. Type locality: Port Natal, South Africa (Johansen 1971: 247).

Current placement/name: Jania verrucosa J. V. Lamouroux but status and disposition uncertain as the type was not studied in a modern context. Johansen and Womersley (1994: 616) merged J. natalensis in synonymy with J. verrucosa but no revision of the type material was made. Agardh (1870: 363) cited J. natalensis as doubtful to the Azores (Santa Maria).

Published records:

AZORES: Schmidt (1929b:172; 1931: 66). Kützing. Neto (2000b: 485).

Corallina natalensis

Jania natalensis?. Agardh (1870: 363) and Piccone (1889: 214).

Jania? Natalensis Harvey. Gain (1914: 22).

Jania pumila J. V. Lamouroux

Basionym : Jania pumila J. V. Lamouroux 1816: 269. Holotype: CN Lamouroux Herbarium; illustrations: Lamouroux (1816, pl. 9, fig. 2, p. 269). Type locality: Red Sea and Western Indies (Lamouroux 1816 : 269).

Current placement/name: J. pumila J. V. Lamouroux but status and disposition uncertain as the type was not studied in a modern context. The holotype specimen of J. pumila housed in Lamouroux's Herbarium in Caen is in depauperate and/or sterile conditions being difficult to interpret (Johansen and Womersley 1994: 610; Abbott 1999: 189). Villena-Balsa et al. (1987: 20) revising material from the Canary Islands identified it provisionally as J. pumila. They mentioned that the material could belong to other species also characterized by reduced-size plants and not correctly described e.g. Jania gibbosa J. V. Lamouroux, J. pygmea J. V. Lamouroux, J. compressa J. V. Lamouroux and J. capillacea Harvey.

Published records:

MADEIRA: Levring (1974: 70), González (1978: 48) and Neto et al. (2001: 404). SALVAGE ISLANDS: Price et al. (1992: 136) and John et al. (2004: 93).

CANARY ISLANDS: Price et al. (1992: 136), Afonso-Carrillo et al. (1978: 232, 1983: 30, 1984: 30), González (1978: 48), Gil-Rodríguez and Afonso-Carrillo (1980: 36), Pinedo et al. (1992: 40), Afonso-Carrillo and Sansón (1999: 196), Haroun et al. (2003: 112), Gil-Rodríguez et al. (2003: 25), Sangil et al. (2003aSangil et al. ( : 103 , 2005: 326) : 326) and John et al. (2004 :93).

Jania pumila. Afonso-Carrillo and Sansón (1989: 25) and Price et al. (1992: 136).

Jania rubens (Linnaeus) J. V. Lamoroux var. corniculata (Linnaeus) Yendo

Basionym: Corallina corniculata Linnaeus 1758: 806. Lectotype: LINN 1293.19 (Irvine and Johansen 1994: 56); illustrations: not found. Type locality: European Ocean (Irvine and Johansen 1994:56).

23

Current placement/name: Jania rubens (Linnaeus) J. V. Lamoroux var. corniculata (Linnaeus) Yendo, but status and disposition uncertain as the type was not studied in a modern context. Irvine and Johansen (1994: 56) in their revision of the British Isles material considered the name J. rubens var. corniculata (Linnaeus) Yendo as valid but without checking the type material. Recently John et al. (2004: 93) considered J. corniculata (Linnaeus) J. V.

Lamouroux as a synonym of Jania rubens (Linnaeus) J. V. Lamouroux but did not provide any taxonomic comments. In their integrative taxonomic approach including phylogeny reconstructions based on the cox1 and 18S rRNA genes in addition to a comparative morphological assessment study Walker et al. (2009) observed that J. rubens var. rubens and J. rubens var. corniculata clustered together in both phylogenies suggesting that for those genes there was no genetic basis for the morphological variation. These conclusions however were not based on type material observations.

Published records:

AZORES: Gain (1914: 22), Tittley et al. (1998: 468) and Neto (2000bNeto ( : 485, 2001: 105): 105). Jania corniculata J. V. Lamouroux. Piccone (1889: 213).

Jania corniculata (Linnaeus) J. V. Lamouroux. South and Tittley (1986: 42). Jania cf. corniculata (Linnaeus) J.V. Lamouroux. Neto (1994: 26) and Tittley and Neto (1994: 9). Jania rubens J. V. Lamouroux var. corniculata (Linnaeus) Yendo. Schmidt (1931: 66).

MADEIRA:

Jania cf. corniculata. Neto et al. (2001: 404).

Jania corniculata (Linnaeus) J. V. Lamouroux. Audiffred and Prud'homme van Reine (1985: 43).

SALVAGE ISLANDS :

Jania cf. corniculata. John et al. (2004: 93).

CANARY ISLANDS:

Jania corniculata (Linnaeus) J. V. Lamouroux. Gil-Rodríguez and Afonso-Carrillo (1980: 36), Afonso-Carrillo et al. (1983: 30, 1984: 30) and Price et al. (1992: 135).

Jania corniculata. Afonso-Carrillo and Sansón (1989: 26).

Jania rubens (Linnaeus) J. V. Lamouroux var. corniculata (Linnaeus) Yendo. Price et al. (1992: 135) and Irvine and Johansen (1994: 57).

Jania rubens (Linnaeus) J. V. Lamoroux var. rubens 24 Basionym: Corallina rubens Linnaeus 1758: 806. Lectotype: UPS Herb. Burser vol. XX, 72; designated by Irvine and Johansen (1994: 56); illustrations: Lamoroux (1816, pl. 9, figs 6-7, p. 272) as Jania rubens (Linnaeus) J. V.

Lamouroux. Type locality: European Ocean (Linnaeus 1758: 806).

Current placement/name: J. rubens (Linnaeus) J. V. Lamoroux var. rubens, a conclusion of Irvine and Johansen (1994: 56) after studying the lectotype in a modern context. Price et al. (1992: 136) suggested that J. rubens and Corallina rubens J. Ellis & Solander in González (1977a: 26) are synonyms. Prud'homme van Reine et al. (1994: 94) confirmed the diagnosis of the J. rubens material from Cape Verde Islands collected by Piccone ( 1886) and housed at PAD and W Herbarium but recognized that material was from Tenerife (the Canaries) and not from Cape Verde Islands. They followed Taylor's (1960) concept and did not review the type material.

Published records:

AZORES: Gain (1914: 15, 22) and Prud'homme van Reine et al. (1994: 94).

Jania rubens. Schmidt (1929a: 331).

Jania rubens (Linnaeus) J. V. Lamouroux. Feldmann (1946: 417), Castro and Viegas (1983: 20, 1987: 63), Weisscher (1983: 70), South and Tittley (1986: 43), Tittley and Neto (1994: 9), Neto (2000aNeto ( : 140, 2000b: 490-491): 490-491), Toste et al. (2003Toste et al. ( : 1270) ) and Wallenstein and Neto (2006: 199). Jania rubens J. V. Lamouroux. Schmidt (1931: 66).

Jania rubens. Agardh (1870: 363), Palminha (1957: 66), Neto (1994Neto ( : 26, 2000b: 490) : 490) and Neto and Tittley (1995: 489).

Jania rubens (Linnaeus) Areschoug. Lemoine (1924: 130).

Jania rubens (Linnaeus) J. V. Lamouroux var. rubens. Audiffred and Prud'homme van Reine (1985: 43) and Irvine and Johansen (1994: 55).

MADEIRA:

Corallina rubens J. V. Lamouroux. Gain (1914: 10) and John et al. (2004: 93). Jania rubens J. V. Lamouroux. Piccone (1884: 10), Gain (1914: 9) and Schmidt (1931: 101).

Jania rubens (Linnaeus) J. V. Lamouroux. Grunow (1868: 78) and Levring (1974: 70). Jania rubens. Johnston (1969: 215), Augier (1985: 100) and Afonso-Carrillo and Sansón (1989: 26).

Jania rubens (Linnaeus) J. E. Areschoug. Lemoine (1924: 130). SALVAGE ISLANDS: Price et al. (1992 : 136) and John et al. (2004: 93).

CANARY ISLANDS:

Corallina (Jania) rubens Linnaeus. Askenasy (1896: 26) and Prud'homme van Reine et al. (1994: 94).

25

Jania rubens. Johnston (1969: 215), González (1977b: 100), Delgado et al. (1984: 106), Gil-Rodríguez et al. (1992: 109) and Price et al. (1992: 136).

Jania rubens (Linnaeus) J. V. Lamouroux. Ardré (1970: 229), Santos Guerra et al. (1970: 24), Cordeiro-Marino (1978: 50), González (1978: 48), Afonso-Carrillo et al. (1978: 232, 1984: 30), Afonso-Carrillo and Gil-Rodríguez (1980: 165), Gil-Rodríguez and Afonso-Carrillo (1980: 36), López Hernández and Gil-Rodríguez (1981: 156), Weisscher (1983: 70), González et al. (1986: 319), Viera-Rodríguez and Wildpret de la Torre (1986: 216), Reyes and Sansón (1991: 79), Pinedo et al. (1992: 40), Medina and Haroun (1993: 110), Kristiansen et al. (1993: 95), Guadalupe et al. (1995: 37), Afonso-Carrillo and Sansón (1999: 196), Gil-Rodríguez et al. (2003: 25), Rojas-González and Afonso-Carrillo (2002a: 33), Haroun et al. (2003: 112), Montañés et al. (2003: 124), Sangil et al. (2003a: 103), John et al. (2004: 93), Rojas-González and Afonso-Carrillo (2004: 138) and Muñoz et al. (2007: 107). Jania rubens J. V. Lamouroux. Vickers (1896: 306), Schmidt (1931: 101 and Price et al. (1992: 136).

Jania rubens (Linnaeus). Piccone (1884: 42, 56) and Acuña González (1972: 5).

Jania rubens. Price et al. (1992: 136).

Jania rubens (Linnaeus) J. V. Lamouroux var. rubens. Irvine and Johansen (1994: 55).

CAPE VERDE ISLANDS:

Corallina (Jania) rubens Linneaus. Price et al. (1992: 136).

Jania rubens (Linnaeus) J. V. Lamouroux. Piccone (1886: 66), Price et al. (1992: 136) and Prud'homme van Reine et al. (1994: 94). Jania rubens J. V. Lamouroux. Schmidt (1931: 101). Jania cf. rubens (Linnaeus) J. V. Lamouroux. Otero-Schmitt and Sanjuan (1992: 382).

Jania tenella (Kützing) Grunow

Basionym: Corallina tenella Kützing 1858: 41. Holotype: L (Dawson 1953: 121); illustrations: Kützing (1858, pl. 85, fig. II, p. 41). Type locality: Naples, Italy (Silva et al. 1996: 244).

Current placement/name: J. tenella (Kützing) Grunow but status and disposition uncertain as the type was not studied in a modern context.

Published records:

CAPE VERDE ISLANDS:

Corallina (Jania) tenella Kützing. Price et al. (1992: 136).

Figure Captions

Fig. 1 The Macaronesian region.


Axel C Carlsson

• Holger

Theobald • Per

E Wändell

Health factors and longevity in men and women: a 26-year follow-up study

Keywords: Body mass index, alcohol consumption, tobacco smoking, physical fitness, health factors, mortality

Health factors have the power to prevent and postpone diseases and death; however, studies using the same methodology in both men and women are sparse. We aimed to study the ability of health factors to prevent mortality in a population-based, 26-year follow-up of Swedish men and women.During 1969-70, a health-screening programme was offered to a stratified sample of 3064 individuals aged 18-64 years to estimate health-care needs. Missing data (largely according to protocol) for physical fitness, BMI, and smoking habits left 935 subjects, 463 men and 472 women. Alcohol consumption in grams per week and BMI was calculated. Tobacco smoking was recorded as yes/no. Multivariate analysis was performed by Cox regression with age adjusted hazard ratios (HR) and 95% confidence interval (CI).

Moderate alcohol consumption did not lead to any decrease in mortality. Having two health factors halved the mortality risk in men and women (hazard ratio (HR) 0.52, confidence interval (CI) 0.39-0.70). A further risk reduction was seen in men with three health factors (HR 0.17, CI 0.074-0.41). Men had about 70 per cent higher risk of mortality compared with women after adjustments for all health factors (HR 1.67,. Men compared to women had greater benefit of all three health factors. This in combination with the overall higher mortality risk in men makes a healthy lifestyle more important for them. The benefit of moderate alcohol consumption could not be detected in this study, and may be explained by an unhealthy drinking pattern in Sweden.

Introduction

Health factors have the power to prevent and postpone the development of cardiovascular diseases, cancer and type II diabetes [START_REF] Jiao | A combined healthy lifestyle score and risk of pancreatic cancer in a large cohort study[END_REF][START_REF] Perry | Healthy diet and lifestyle clustering and glucose intolerance[END_REF][START_REF] Yusuf | Effect of potentially modifiable risk factors associated with myocardial infarction in 52 countries (the INTERHEART study): case-control study[END_REF]. Several factors have been studied, usually: being physically active or being physically fit, having a healthy dietary pattern, non-smoking, low waist/hip ratio or normal BMI, and moderate alcohol consumption. As an example, in a study of over 24,000 postmenopausal women, a healthy lifestyle was shown to have the potential to prevent 77% of all myocardial infarctions [START_REF] Akesson | Combined effect of low-risk dietary and lifestyle behaviors in primary prevention of myocardial infarction in women[END_REF]. Studies of healthcare workers in the US have shown impressive preventive results regarding hypertension prevention in women and heart failure prevention in men [START_REF] Djousse | Relation between modifiable lifestyle factors and lifetime risk of heart failure[END_REF][START_REF] Forman | Diet and lifestyle risk factors associated with incident hypertension in women[END_REF]. In a study of a British civil service based cohort, cardioprotective effects were seen with a health score comprising of similar factors, but moderate alcohol consumption was only shown to be beneficial in individuals with an otherwise unhealthy lifestyle [START_REF] Britton | Who benefits most from the cardioprotective properties of alcohol consumption--health freaks or couch potatoes?[END_REF]. In contrast, a study of health factors in men and the risk of myocardial infarction showed benefits of moderate alcohol intake among individuals with many health factors as well as in those with many unhealthy factors [START_REF] Mukamal | Alcohol consumption and risk for coronary heart disease in men with healthy lifestyles[END_REF]. These conflicting results regarding the potential benefits of moderate alcohol consumption in individuals with a healthy lifestyle call for additional studies in other cohorts. In addition, none of these previous studies have data on both men and women. Possible interactions with gender have therefore not been analysed.

In the early 1970s, a cohort was initiated to estimate the healthcare need in the population of Stockholm, Sweden. Both men and women were included. The cohort has been linked to the National Cause of Death Register in Sweden, and several long-term follow-up studies have been published recently [START_REF] Carlsson | Cardiovascular and total mortality in men and women with different blood pressure levels -A 26-year followup[END_REF][START_REF] Wandell | The association between BMI value and longterm mortality[END_REF][START_REF] Wandell | Effect of heart-rate recovery on long-term mortality among men and women[END_REF]. We identified four health factors in the baseline investigation: moderate alcohol consumption, non-smoking, body mass index (BMI) and physical fitness based on an exercise test.

The aim of this study was to calculate the beneficial effects of health factors and to calculate their combined effects in a 26-year follow-up of total mortality. A secondary aim was to study the health effect of moderate alcohol consumption additional to the other three health factors and to study interactions between the various health factors. All variables will be analysed in men and women separately.

Methods

Study population

The baseline examination was performed during the period 1969-70. From the total population aged 18-64 years in Stockholm County (a total of 445,000 inhabitants), a sample of 32,185 individuals was drawn. The individuals in the sample received a postal questionnaire including 30 questions concerning physical and social difficulties in daily life and healthcare needs. The total response rate was 87%. The sample was stratified into three age groups, 18-24 years, 25-44 years and 45-64 years. A random sample was drawn from each of the age strata, in a ratio of 3 to 2 to 1, resulting in more individuals in the younger age groups. The subjects were classified into four different groups according to their estimated healthcare needs. This estimation was made based on the postal questionnaire answers and on data obtained from registers containing information regarding hospitalisation and sick leave.

Thereafter, a further randomisation procedure was performed in which a higher proportion of individuals with high needs were selected, as they were expected to be rather few, especially in the younger age groups. In this way, a group of 3064 individuals was obtained. These subjects were invited to the health-screening programme, on average one year after the questionnaire survey, with an attendance rate of 84% (n=2578). According to the original protocol of the healthcare need investigation, an exercise test was performed in 1066 individuals. Missing data for physical fitness, BMI, and smoking habits left 935 subjects that could be included in this sub-study, 463 men and 472 women.

The study was approved by the ethics committee at the Karolinska Institutet and all participants gave their consent.

Health factors

Alcohol habits were self-reported in the questionnaire, and these questions have been validated [START_REF] Theobald | Validity of two questions on alcohol use in a health survey questionnaire[END_REF]. Healthy moderate alcohol consumption was defined as a weekly consumption of 70-210g for men and 70-140g for women, which corresponds to an average daily consumption of 1-3 drinks/day for men and 1-2 drinks/day for women [START_REF] Mukamal | Alcohol consumption and risk for coronary heart disease in men with healthy lifestyles[END_REF][START_REF] Greenfield | Moderate alcohol consumption, estrogen replacement therapy, and physical activity are associated with increased insulin sensitivity: is abdominal adiposity the mediator?[END_REF][START_REF] Wandell | High intake of alcohol is associated with newly diagnosed diabetes in 60 years old men and women[END_REF]. This was compared with abstinence, low alcohol consumption and heavy drinking. Smoking habits were classified as non-smokers and smokers. Non-smoking was classified as healthy. BMI was calculated from weight and height measurements and expressed in kg/m 2 . Based on a mortality follow-up in this cohort, a BMI of 20-29.9 was associated with lower mortality [START_REF] Wandell | The association between BMI value and longterm mortality[END_REF], and in this study we defined individuals with a BMI lower than 30 as having a healthy BMI. Physical fitness was defined as above median VO2 max, i.e. above 30mL/kg/min in both men and women [START_REF] Theobald | Effect of heart rate on long-term mortality among men and women[END_REF]. Age was adjusted for in 5-year intervals. This adjustment also compensates for the age-stratification in the baseline investigation.

Health score

The health factors above were combined into a score to predict the associated risk of mortality with in individuals with different levels of health. Only factors that were significant in the final sex-adjusted model containing all individuals were included.

Follow-up

All participants were followed up in the National Cause of Death Register for 26 years. This register contains records of all deaths among the people of Sweden and is more than 99% complete, with the exception of certain emigrants.

Statistical analysis

Hazard ratios for total mortality were calculated using Cox regression with the PHREG procedure in the SAS data package. 95% confidence intervals were used and considered significant in the adjusted full models. Interactions were studied between the health factors and sex. Adjustments for healthcare need could not be made as this variable is largely based on the health variables studied. The 1% that was lost to follow-up was censored in the Cox regression models. All calculations were performed during 2009.

Results

In total, 80 out of the 472 women and 121 out of the 463 men died during the 26-year followup. The study participants' health factors and the health score are presented in relation to mortality in table 1. Few individuals had no health factors, and to get an "unhealthy" reference group we decided to define "unhealthy" as a health score of 0-1.

Table 2 shows the health factors and their relation to total mortality as hazard ratios. Moderate alcohol consumption was not associated with mortality and could not be included in the full models. The other health factors were significant in the crude models among men. Nonsmoking was significant in all models in men and women. The full model with both men and women showed significant hazard ratios for all included health factors. Sex adjustments revealed an approximately 70% higher mortality risk in men.

Hazard ratios for mortality of the combined health score variable are shown in table 3. Having no or one factor was used as reference. Having two out of three health factors halved the mortality risk. The men with all three health factors decreased their hazard ratio to 0.17, whereas women with three factors did not seem to decrease their risk dramatically more than women with two factors.

No significant interaction between either sex or any of the health factors or the combined health score variable was found (data not shown). Adjustments for healthcare need could not be done due to co-linearity with the health factors (data not shown).

Discussion

Non-smoking, being physically fit and having a healthy BMI were mortality risk reducers and worked well as a composite health score in this long-term follow-up of Swedish men and women. In contrast to some previous studies, moderate alcohol consumption did not lead to any decrease in mortality and was not included in the health score. Having two health factors halved the mortality risk in men and women. A further dramatic risk reduction was seen in men with all three health factors. Men had about 70 per cent higher risk of age-adjusted mortality compared with women after adjustments for the health scores. These findings expand the knowledge on gender aspects of health factors, as we used the same methodology in both men and women.

Previous studies have shown beneficial effects of health factors in either men or women [START_REF] Akesson | Combined effect of low-risk dietary and lifestyle behaviors in primary prevention of myocardial infarction in women[END_REF][START_REF] Djousse | Relation between modifiable lifestyle factors and lifetime risk of heart failure[END_REF][START_REF] Forman | Diet and lifestyle risk factors associated with incident hypertension in women[END_REF].

The findings in our study revealed that although beneficial effects were present with more health factors in both men and women, men had more additional benefit of having all three studied health factors. This is an important finding considering the overall higher age-adjusted morbidity and mortality seen in men seen in this and other studies [START_REF] Carlsson | Cardiovascular and total mortality in men and women with different blood pressure levels -A 26-year followup[END_REF][START_REF] Li | Sex-specific cardiovascular morbidity and mortality in a cohort treated for hypertension[END_REF], indicating that this excess mortality risk may partly be possible to battle with lifestyle interventions.

The finding that moderate alcohol consumption did not decrease mortality is interesting considering the body of evidence supporting the health benefits of such consumption [START_REF] Yusuf | Effect of potentially modifiable risk factors associated with myocardial infarction in 52 countries (the INTERHEART study): case-control study[END_REF][START_REF] Akesson | Combined effect of low-risk dietary and lifestyle behaviors in primary prevention of myocardial infarction in women[END_REF][START_REF] Mukamal | Alcohol consumption and risk for coronary heart disease in men with healthy lifestyles[END_REF][START_REF] Burger | Alcohol consumption and its relation to cardiovascular risk factors in Germany[END_REF][START_REF] Caimi | Wine and endothelial function[END_REF][START_REF] De Lange | Drink to prevent: review on the cardioprotective mechanisms of alcohol and red wine polyphenols[END_REF]. This may be explained by the drinking pattern in Sweden in the 1960s and 1970s, with most of the alcohol consumed during the weekends as seen in "vodka belt" countries [START_REF] Messner | Alcohol consumption and ischemic heart disease mortality in Sweden[END_REF], a pattern known as binge drinking. Thus, while drinking moderately daily prevents cardiovascular disease, drinking the whole week's consumption on one or two occasions does not seem to reduce the mortality risk. As mentioned in the introduction, the health benefits of moderate alcohol consumption have shown conflicting results in individuals with an otherwise healthy lifestyle [START_REF] Britton | Who benefits most from the cardioprotective properties of alcohol consumption--health freaks or couch potatoes?[END_REF][START_REF] Mukamal | Alcohol consumption and risk for coronary heart disease in men with healthy lifestyles[END_REF]. These conflicting results can perhaps be explained by drinking pattern. For example, high blood pressure is a prevalent cardiovascular risk factor [START_REF] Carlsson | Cardiovascular and total mortality in men and women with different blood pressure levels -A 26-year followup[END_REF][START_REF] Carlsson | Prevalence of hypertension in immigrants and Swedish-born individuals, a cross-sectional study of 60-year-old men and women in Sweden[END_REF], and alcohol in general and especially high consumption has been associated with increases in blood pressure [START_REF] Carlsson | Risk factors associated with newly diagnosed high blood pressure in men and women[END_REF][START_REF] Parekh | Alcohol: role in the development of hypertension and end-stage renal disease[END_REF], In contrast, drinking alcohol with meals was not associated with increased blood pressure in a study of New Yorkers free from cardiovascular disease [START_REF] Stranges | Relationship of alcohol drinking pattern to risk of hypertension: a population-based study[END_REF]. This is in agreement with a meta-analysis showing slightly increased risk of coronary heart disease in occasional heavy drinkers or binge drinkers, whereas regular heavy drinkers had a risk reduction [START_REF] Bagnardi | Does drinking pattern modify the effect of alcohol on the risk of coronary heart disease? Evidence from a meta-analysis[END_REF].

Interactions between the health factors and between men and women could possibly reveal that certain combinations are extra beneficial. Despite thorough analysis, we were not able to detect any statistically significant interactions. Considering this, there is a need to explore interactions between gender and health factors in larger populations. Furthermore, the important risk factors for cardiovascular diseases may be influenced by health factors to different degrees, and this interplay needs to be explored in order to identify the patients that have the greatest health gain from lifestyle interventions.

There are some limitations in this study. The physical examination was performed on only one occasion, which could weaken the associations, as changes in the different factors were not registered. Despite this, the healthy lifestyle factors were found to be predictive for longevity. Besides, a recent paper from the Whitehall study showed that although many variables changed over time, the baseline data were predictive for mortality [START_REF] Clarke | Life expectancy in relation to cardiovascular risk factors: 38 year follow-up of 19,000 men in the Whitehall study[END_REF]. We have no data on dietary factors or physical activity. However, the baseline investigation included an exercise test. The sample was drawn with larger proportions of individuals with healthcare needs so the results are valid for a population of patients rather than the general population [START_REF] Theobald | Effects of an assessment of needs for medical and social services on long-term mortality: a randomized controlled study[END_REF].

The strengths of the study include the high quality of population registers in Sweden, allowing us to reach the whole population and link each individual to The National Cause of Death

Register. We had data on men and women which allowed a unique comparison of the healthy lifestyle factors. The baseline investigation had a high attendance rate and a long follow-up time, 26 years. The follow-up was almost complete (99%) except for some emigrants. Finally, most of the participants of this study were young, whereas many other studies have analysed lifestyle factors in older individuals. We analysed men and women in the same study and also possible interactions between health factors and gender.

Conclusion

A high health score is associated with longevity in both men and women. Men compared to women had greater benefit of all three health factors. This in combination with the overall higher mortality risk in men makes a healthy lifestyle more important for them. The benefit of moderate alcohol consumption could not be detected in this study, and may be explained by an unhealthy drinking pattern.

Funding

The study was supported by the Stockholm County Council. Moderate alcohol consumption defined as a weekly consumption of 70-210g for men and 70-140g for women and non-moderate alcohol consumption below or above these values, being physically fit was defined as having above median VO2 max, i.e. above 30mL/kg/min and a healthy BMI was defined as having a BMI below 30. The score of healthy lifestyle factors included: being a non-smoker, being physically fit and having a healthy BMI.

Table 1

 1 Basic characteristics are shown in men and women in relation to all-cause mortality

	Variable	Alive	Dead	Alive	Dead
		men	men (%)	Women	women (%)
	Moderate alcohol consumption	286	76 (21%) 432	72 (16%)
	Non-moderate alcohol consumption 190	45 (19%) 65	8 (11%)
	Being a non-smoker	197	41 (17%) 264	47 (15%)
	Smoker	279	80 (22%) 233	33 (12%)
	Being physically fit	252	34 (12%) 210	16 (7%)
	Being unfit	224	87 (28%) 287	64 (18%)
	Having a healthy BMI	441	102 (19%) 473	70 (13%)
	BMI ≥30	35	19 (35%) 24	10 (29%)
	0 Healthy lifestyle factors	10	7 (41%)	5	1 (17%)
	1 Healthy lifestyle factors	136	57 (30%) 128	32 (20%)
	2 Healthy lifestyle factors	236	51 (18%) 273	40 (13%)
	3 Healthy lifestyle factors	94	6 (6%)	91	7 (7%)

Moderate alcohol consumption defined as a weekly consumption of 70-210g for men and 70-140g for women and non-moderate alcohol consumption below or above these values was used as reference, being physically fit was defined as having above median VO2 max, i.e. above 30mL/kg/min and a healthy BMI was defined as having a BMI below 30 and BMI≥30 was used as reference.

Alcohol consumption was excluded from the full models as it was non significant and did not change results. The score of health factors included: being a non-smoker, being physically fit and having a healthy BMI.


Adrien Dubouloz
email: adrien.dubouloz@u-bourgogne.fr

AFFINE OPEN SUBSETS IN A 3 WITHOUT THE CANCELLATION PROPERTY

Keywords:

We give families of examples of principal open subsets of the affine space A 3 which do not have the cancellation property. We show as a by-product that the cylinders over Koras-Russell threefolds of the first kind have a trivial Makar-Limanov invariant.

Introduction

The generalized Cancellation Problem asks if two algebraic varieties X and Y with isomorphic cylinders X × A 1 and Y × A 1 are isomorphic themselves. Although the answer turns out to be affirmative for a large class of varieties including the case when one of the varieties is the affine plane A 2 [START_REF] Iitaka | Cancellation theorem for algebraic varieties[END_REF][START_REF] Miyanishi | Affine surfaces containing cylinderlike open sets[END_REF], counter-examples exists for affine varieties in any dimension≥ 2, and the particular case when one of the two varieties is an affine space A n , n ≥ 3, still remains a widely open problem. The first counter-example for complex affine varieties has been constructed by Danielewski [START_REF] Danielewski | On a cancellation problem and automorphism groups of affine algebraic varieties[END_REF] in 1989: he exploited the fact that the non isomorphic affine surfaces S 1 = xz = y 2 -1 and S 2 = x 2 z = y 2 -1 in A 3 C can be equipped with free actions of the additive group G a admitting geometric quotients in the form of non trivial G a -bundles ρ i : S i → Ã1 , i = 1, 2 over the affine line with a double origin. It then follows that the fiber product S 1 × Ã1 S 2 inherits simultaneously the structure of a G a -bundle over S 1 and S 2 via the first and the second projection respectively, but since S 1 and S 2 are both affine, the latter are both trivial, providing isomorphisms

S 1 × A 1 ≃ S 1 × Ã1 S 2 ≃ S 2 × A 1 .
Since then, Danielewski's fiber product trick has been the source of many new counter-examples in any dimension [START_REF] Fieseler | On complex affine surfaces with C + -action[END_REF][START_REF] Dubouloz | Additive group actions on Danielewski varieties and the Cancellation Problem[END_REF][START_REF] Finston | The automorphism group of certain factorial threefolds and a cancellation problem[END_REF][START_REF] Dubouloz | Non cancellation for smooth contractible affine threefolds[END_REF], some of these being very close to affine spaces either from an algebraic or a topological point of view.

However, a counter-example over the field of real numbers was constructed earlier by Hochster [START_REF] Hochster | Nonuniqueness of coefficient rings in a polynomial ring[END_REF] using the algebraic counterpart of the classical fact from differential geometry that the tangent bundle of the real sphere S 2 is non trivial but 1-stably trivial. His argument actually applies more generally to the situation when a finitely generated domain R over a field k admits a non trivial projective module M of rank n -1 ≥ 1 such that M ⊕ R ≃ R ⊕n = R ⊕n-1 ⊕ R. Indeed, these hypotheses immediately imply that the varieties X = Spec R (Sym (M )) and Y = Spec(R[x 1 , . . . , x n ]) are not isomorphic as schemes over Z = Spec(R) while their cylinders are. Of course, there is no reason in general that X and Y are not isomorphic as k-varieties, but this holds for instance when Z does not admit any dominant morphism from an affine space A n k since then any isomorphism between X and Y necessarily descends to an automorphism of Z ( [START_REF] Iitaka | Cancellation theorem for algebraic varieties[END_REF][START_REF] Drylo | Non uniruledness and the cancellation problem II[END_REF]). Recently, Jelonek [START_REF] Jelonek | On the cancellation problem[END_REF] gave revival to Hochster idea by constructing families of examples of non uniruled affine open subsets of affine spaces of any dimension ≥ 8 with 1-stably trivial but non trivial vector bundles, which fail the cancellation property.

While affine affine open subsets of affine spaces of dimension ≤ 2 always have the cancellation property (see e.g. loc.cit ), we derive in this note from a variant of Danielewski's fiber product trick that cancellation already fails for suitably chosen principal open subsets of A 3 .

As an application of our construction we also obtain that all cylinders over Koras-Russell threefolds [START_REF] Kaliman | On the Russell-Koras contractible threefolds[END_REF], have a trivial Makar-Limanov invariant [START_REF] Makar-Limanov | On the hypersurface x + x 2 y + z 2 + t 3 = 0 in C 4 or a C 3 -like threefold which is not C 3[END_REF].

X d,k,l = x d z = y l + x -t k = 0 ⊂ A 4 , d ≥ 2 and 2 ≤ l < k relatively prime

Principal open subsets in A 3 without the cancellation property

For every d ≥ 1 and l ≥ 2, we denote by B d,l the surface in Proof. We exploit the fact that every U d,l admits a free G a -action defined by the locally nilpotent derivation

A 3 = Spec (C [x, y, z]) defined by the equation f d,l = y l + x -x d z = 0 and by U d,l = A 3 \ B d,l ≃ Spec(C [x, y, z] f d,l ) its open complement. By construction, U d,l comes equipped with a flat isotrivial fibration f d,l | U d,l : U d,l → A 1 * = Spec(C t ±1 ) with closed fibers isomorphic to the surface S d,l ⊂ A 3 = Spec (C [X, Y, Z]) defined by the equation X d Z = Y l + X -1. A surface S d,l having no non constant invertible function, an isomorphism ϕ : U d,l ∼ → U d ′ ,l ′ necessarily maps closed fibers of f d,l isomorphically onto that of f d ′ ,l ′ . But since S d,l is isomorphic to S d ′ ,l ′ if and only if (d ′ , l ′ ) = (d, l) (see e.
x d ∂ y + ly l-1 ∂ z of its coordinate ring C [x, y, z] f d,l .
A free G a -action being locally trivial in the étale topology, it follows that a geometric quotient ν d,l : U d,l → S d,l = U d,l /G a exists in the form of an étale locally trivial G a -bundle over a certain algebraic space S d,l . Then it is enough to show that for every fixed l ≥ 2, the algebraic spaces S d,l are all isomorphic, say to a fixed algebraic space S l . Indeed, if so, then for every d, d ′ ≥ 1, the fiber product U d,l × S l U d ′ ,l will be simultaneously a G a -bundle over U d,l and U d ′ ,l via the first and second projection respectively whence will be simultaneously isomorphic to the trivial G a -bundles U d,l × A 1 and U d ′ ,l × A 1 as U d,l and U d ′ ,l are both affine.

The algebraic spaces S d,l can be described explicitly as follows: one checks that the isotrivial fibration f d,l : U d,l → A 1 * becomes trivial on the Galois étale cover ξ l :

A 1 * = Spec(C u ±1 ) → A 1 * , u → t = u l , with isomorphism Φ d,l : S d,l × A 1
is absurd since (0, 1) does not even have a separated µ l -invariant open neighborhood in C (l) × A1 * . This implies in turn that the free G a -action on U d,l defined by the locally nilpotent derivation x d ∂ y + ly l-1 ∂ z is not locally trivial in the Zariski topology. In contrast, the latter property holds for its lift to S d,l × A 1 * via the étale Galois cover π d,l : S d,l × A 1 * → U d,l .

Remark 3. In Danielewski's construction for the surfaces S i = {x i z = y 2 -1} ⊂ A 3 , i = 1, 2, the geometric quotients S i /G a ≃ Ã1 , i = 1, 2, were obtained from the categorical quotients S i //G a = Spec(C [x]) taken in the category of affine schemes by replacing the origin by two copies of itself, one for each orbit in the zero fiber of the quotient morphism q = pr x : S i → A 1 . For the threefolds U d,l , the difference between the quotients U d,l //G a = Spec(C [x, y, z] Ga f d,l ) taken in the category of (affine) schemes and the geometric quotients S l = U d,l /G a is very similar : indeed, we may identify U d,l with the closed subvariety of

A 3 ×A 1 * = Spec(C[x, y, z][t ±1 ]) defined by the equation x d z = y l +x-t in such a way that f d,l : U d,l → A 1
* coincides with the projection pr t | U d,l . Then, the kernel of the locally nilpotent derivation x d ∂ y + ly l-1 ∂ z of the coordinate ring of U d,l coincides with the subalgebra C[x, t ±1 ] and so, the G a -invariant morphism q = pr x,t :

U d,l → A 1 ×L = Spec(C[x][t ±1 ])
is a categorical quotient in the category of affine schemes. One checks easily that q restricts to a trivial G a -bundle over the principal open subset {x = 0} of

A 1 × A 1 * whereas the inverse image of the punctured line {x = 0} ≃ L is isomorphic to L × A 1 = Spec(C[y, t ±1 ]/(y l -t)[z]
) where G a acts by translations on the second factor. So we may interpret the geometric quotient S l = U d,l /G a as being obtained from U d,l //G a = A 1 × L by replacing the punctured line {x = 0} ≃ L not by l disjoint copies of itself but, instead, by the total space L of the nontrivial étale Galois cover pr t : L → L.

The Koras-Russell threefolds X d,k,l are smooth complex affine varieties defined by equations of the form x d z = y l + x -t k , where d ≥ 2 and 2 ≤ l < k are relatively prime. 1 While all diffeomorphic to the euclidean space R 6 , none of these threefold is algebraically isomorphic to the affine A 3 . Indeed, it was established by Kaliman and Makar-Limanov [START_REF] Makar-Limanov | On the hypersurface x + x 2 y + z 2 + t 3 = 0 in C 4 or a C 3 -like threefold which is not C 3[END_REF][START_REF] Kaliman | On the Russell-Koras contractible threefolds[END_REF] that they have fewer algebraic G a -actions than the affine space A 3 : the subring ML(X d,k,l ) of their coordinate ring consisting of regular functions invariant under all algebraic G a -actions on X d,k,l is equal to the polynomial ring C [x], while ML A 3 is trivial, consisting of constants only. However, it was observed by the author in [START_REF]The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant[END_REF] that the Makar-Limanov invariant ML fails to distinguish the cylinder over the so-called Russell cubic X 2,2,3 from the affine space A 4 . This phenomenon holds more generally for cylinders over all Koras-Russell threefolds X d,k,l : Corollary 4. All the cylinders X d,k,l × A 1 have a trivial Makar-Limanov invariant.

Proof. We consider X d,k,l × A 1 as the subvariety of Spec (C [x, y, z, t] [v]) defined by the equation

f d,l -t k = 0. Since ML(X d,k,l × A 1 ) ⊂ ML(X d,k,l ) = C [x], it is enough to construct a locally nilpotent derivation of C [x, y, z] [v] /(f d,l -t k ) which does not have x in its kernel. One checks easily that ML(U 1,l ) = C[f ±1
1,l ] is the intersection of the kernels of the locally nilpotent derivations x∂ y + ly l-1 ∂ z and ly l

-1 ∂ x + (z -1) ∂ y of C [x, y, z] f 1,l . Theorem 1 above implies in particular that ML(U d,l × A 1 ) ≃ ML(U 1,l × A 1 ) = C[f ±1
1,l ] and so, there exists a locally nilpotent derivation

δ d,l of Γ(U d,l × A 1 , O U d,l ×A 1 ) = C [x, y, z] f d,l [v]
which does not have x in its kernel. Up to multiplying it by a suitable power of f d,l ∈ Ker(δ d,l ), we may further assume that δ d,l is the extension to

C [x, y, z] f d,l [v] of a locally nilpotent derivation of C [x, y, z] [v] which has f d,l but not x in its kernel. This implies in particular that B d,l × A 1 = Spec (C [x, y, z] /(f d,l ) [v]) is invariant under the corresponding G a -action on A 4 = Spec(C [x, y, z] [v]
). The projection p = pr x,y,z,v : X d,k,l × A 1 → A 4 being a finite Galois cover with branch locus B d,l × A 1 , it follows that the G a -action on A 4 lifts to a one on X d,k,l × A 1 for which p : X d,k,l × A 1 → A 4 is G a -equivariant. By construction, the corresponding locally nilpotent derivation of C [x, y, z] [v] /(f d,l -t k ) does not have x in its kernel.

In the proof above, we used the following classical fact that we include here because of a lack of an appropriate reference. Lemma 5. Let X be a variety defined over a field of characteristic zero and equipped with a non trivial G a -action, let Z be a normal variety and let p : Z → X be a finite surjective morphism. Suppose that there exists a G a -invariant affine open subvariety U of X over which p restricts to an étale morphism. Then there exists a unique G a -action on Z for which p : Z → X is a G a -equivariant morphism.

Proof. The induced G a -action on the invariant affine open subvariety U of X is determined by a locally nilpotent derivation ∂ of Γ(U, O U ). Since p : p -1 (U ) → U is étale and proper, p -1 (U ) is an affine open subvariety of Z and ∂ lifts in a unique way to a derivation of Γ(p -1 (U ), O p -1 (U) ) which is again locally nilpotent by virtue of [START_REF] Vasconcelos | Derivations of commutative noetherian rings[END_REF]. By construction, the latter defines a G a -action on p -1 (U ) for which the restriction of p to p -1 (U ) is equivariant. Now the assertion follows from [START_REF] Seshadri | Quotient spaces modulo reductive algebraic groups[END_REF]Lemma 6.1] which guarantees that the G a -action on p -1 (U ) can be uniquely extended to a one on Z with the desired property.

  g. [6, Theorem 3.2 and Proposition 3.6]), it follows that the threefolds U d,l , d ≥ 1, l ≥ 2, are pairwise non isomorphic. In contrast, we have the following result: Theorem 1. For every fixed l ≥ 2, the fourfolds U d,l × A 1 , d ≥ 1, are all isomorphic.

These are called Koras-Russell threefolds of the first kind in[START_REF] Moser-Jauslin | Automorphism group of Koras-Russell threefolds of the first kind[END_REF].