Eric Pante

Les Watling
email: watling@hawaii.edu

Running head: Chrysogorgia from the NW Atlantic Chrysogorgia from the New England and Corner Seamounts: Atlantic -Pacific connections

Keywords: Chrysogorgia, morphometrics, allometric growth, msh1, connectivity, sclerite, growth, barcode, benthic survey, ROV

Recent exploration of the New England and Corner Seamounts revealed four new species of Chrysogorgia, described here using a combination of molecular and morphological data. These four species are characterized by a sinistral spiral, a character that, with one known exception, has only been reported for Pacific species. In addition, two species have a sclerite composition typical of the Pacific ("squamosae typicae"). This faunal connection between the Atlantic and the Pacific is confirmed by analysis of the mitochondrial msh1 gene. The exceptional preservation of specimens collected with remotely operated vehicles allows us to discuss the effect of growth on some morphological characters.

INTRODUCTION

Chrysogorgia is a relatively speciose genus, with 62 currently recognized species [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF][START_REF] Cairns | A new species of Chrysogorgia (Anthozoa : Octocorallia) from the Antarctic[END_REF][START_REF] Cairns | Calcaxonian octocorals (Cnidaria; Anthozoa) from Eastern Pacific Seamounts[END_REF]. Presently, only nine species are known from the northwestern Atlantic, all of which were described from environments associated with the continental slope and the lee of Caribbean islands, and from relatively shallow waters (over 40% of the observations reported in [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF] have an average depth < 500 m). Recently, a series of cruises on the New England and Corner Seamounts (northwestern Atlantic) revealed a wealth of octocorals [START_REF] Thoma | Deep-sea octocorals and antipatharians show no evidence of seamount-scale endemism in the NW Atlantic[END_REF][START_REF] Shank | Spotlight 4: New England and Corner Rise Seamounts[END_REF], including chrysogorgiids [START_REF] Watling | A review of the genus Iridogorgia (Octocorallia : Chrysogorgiidae) and its relatives, chiefly from the North Atlantic Ocean[END_REF][START_REF] Mosher | Partners for life: a brittle star and its octocoral host[END_REF][START_REF] Thoma | Deep-sea octocorals and antipatharians show no evidence of seamount-scale endemism in the NW Atlantic[END_REF], from much greater depths (for Chrysogorgia: 1533-3860 m). Among the specimens collected during these cruises, colonies of Chrysogorgia are of particular interest as they are large and are characterized by a sinistral spiral, a feature that until now was almost exclusively observed from Pacific specimens. In this contribution we describe the material collected on the New England and Corner Seamounts based on genetic and morphological data, and discuss their affinities with previously described species from the Atlantic and Pacific oceans.

Octocorals are relatively simple animals, with, in some groups, few characters available to taxonomists (e.g. [START_REF] Mcfadden | Molecular phylogenetic insights into the evolution of Octocorallia: A review[END_REF]. Unfortunately, recent comparative analyses revealed incongruence between several morphological traits (such as colony branching, polyp and sclerite morphology) and molecular phylogenetic information at multiple taxonomic levels [START_REF] France | Genetic analysis of bamboo corals (Cnidaria: Octocorallia: Isididae): does lack of colony branching distinguish Lepidisis from Keratoisis ?[END_REF][START_REF] Dueñas | Character lability in deep-sea bamboo corals (Octocorallia, Isididae, Keratoisidinae)[END_REF][START_REF] Pante | Pseudochrysogorgia bellona n. gen., n. sp.: a new genus and species of chrysogorgiid octocoral (Coelenterata: Anthozoa) from the Coral Sea[END_REF]. These results imply that morphological variation does not necessarily reflect evolutionary history, and it is therefore prudent to combine morphological information with other lines of evidence when describing new octocoral taxa. In Chrysogorgia, as in many other octocoral groups, attention is focused on branching patterns as well as sclerite morphology and arrangement (e.g. [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF]. No statistical analysis has been conducted in this group to estimate the amount of intra-specific variability, or validate the phylogenetic usefulness of these characters by comparing them with genetic data. Here, we present a multivariate analysis of the morphological variation among 23 Chrysogorgia colonies, and investigate the correlation between morphology and genetic variation at the mitochondrial locus msh1. We chose this marker because it may be the most variable mitochondrial gene in octocorals [START_REF] France | Analysis of variation in mitochondrial DNA sequences (ND3, ND4L, MSH) among Octocorallia (=Alcyonaria)(Cnidaria: Anthozoa)[END_REF]Wirshing et al., 2005;[START_REF] Mcfadden | Limitations of mitochondrial gene barcoding in Octocorallia[END_REF][START_REF] Van Der | Exploring the utility of an indel-rich, mitochondrial intergenic region as a molecular barcode for bamboo corals (Octocorallia: Isididae)[END_REF][START_REF] Herrera | Molecular systematics of the bubblegum coral genera (Paragorgiidae, Octocorallia) and description of a new deep-sea species[END_REF] and was useful in genetically distinguishing morphotypes of some deep-sea octocorals (e.g. [START_REF] France | Genetic analysis of bamboo corals (Cnidaria: Octocorallia: Isididae): does lack of colony branching distinguish Lepidisis from Keratoisis ?[END_REF].

Technological advances and the relative availability of remotely-operated vehicles (ROVs) catalyzed studies on the community ecology of deep, benthic ecosystems (e.g. [START_REF] Lundsten | Benthic invertebrate communities on three seamounts off southern and central California, USA[END_REF][START_REF] Mcclain | Endemicity, biogeography, composition, and community structure on a northeast Pacific seamount[END_REF], and many research groups now use in situ video footage and photographs to make faunal inventories. In fact, the resolution of the video equipment on ROVs allows researchers to observe individual coral polyps on live colonies, and even see minute details such as pinnules on tentacles. Such capabilities have led researchers to try to identify octocorals colonies to the species level. In this paper we will discuss the limits of using these technologies to identify Chrysogorgia colonies.

MATERIAL AND METHODS

Collection and preservation

Most of the material described here was collected during three expeditions to the New England (NES) and Corner Seamounts (CS). The first two expeditions, conducted in 2003 and 2004, were named Mountains-in-the-Sea I and II, respectively, and the 2005 expedition was named Deep Atlantic Stepping Stones. L. Watling was Chief Scientist on all three expeditions and can be contacted for details. Summaries of all expeditions can be found on the web site of NOAA"s Ocean Exploration Program (currently www.oceanexplorer.noaa.gov), and a map of the area with sampling locations can be found in [START_REF] Thoma | Deep-sea octocorals and antipatharians show no evidence of seamount-scale endemism in the NW Atlantic[END_REF]. Specimens were obtained by use of the deep submergence vehicle (DSV) "Alvin", in 2003 and the remotely operated vehicle (ROV) " Hercules", in 2004 and2005. In all cases, specimens were collected by use of a manipulator equipped with a claw that could break (in the case of "Alvin") or cut off (in the case of "Hercules") pieces of large colonies, or remove entire small colonies from the substrate. All collected colonies or pieces of colonies were put in an insulated collection box on the vehicle for return to the research vessel. On board, the specimens were kept in cold seawater until they could be fixed and preserved.

After removal of colony pieces for genetic and reproductive studies (herein referred as "isolates"), all specimens were fixed in a dilute formalin solution (4%) for 12 hours and then rinsed and stored in 70% ethanol. Specimens for molecular genetic analysis were preserved in 90-100% ethanol or frozen at -80°C. All specimens used for morphological analysis were deposited in the Yale Peabody Museum (YPM).

Microscopy

Polyps from preserved colonies were individually photographed using light microscopy, and one or more polyps per colony were examined for sclerite composition and morphology. Sclerites were dissolved from the surrounding polyp and branch tissue using household bleach. Following several washings in deionized water, individual sclerites from select specimens were mounted on standard scanning electron microscope (SEM) stubs with blackened doublesided tape. Individual polyps to be examined with SEM were removed from a branch, dehydrated to 100% ethanol, and dried using a Samdri Critical Point Dryer (except for the partially digested polyp of NAS201-2, Figure 7E, which was only air-dried). Digital images of sclerites and polyps were obtained using Hitachi S-800 SEM, S-3000N, and S-4800 SEMs. Sclerite and polyp images were isolated from the original image background, and their contrast and brightness were adjusted in Adobe Photoshop. Images were otherwise unaltered in accordance with current scientific image processing guidelines.

Branching sequence

Branching sequence was determined for all colonies based on the following parameters: the direction of the spiral, the number of branches that one needs to travel up the stem to recover the plane of a reference branch, and the number of revolutions necessary to do so [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF][START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF][START_REF] Cairns | A new species of Chrysogorgia (Anthozoa : Octocorallia) from the Antarctic[END_REF][START_REF] Cairns | Calcaxonian octocorals (Cnidaria; Anthozoa) from Eastern Pacific Seamounts[END_REF].

Traveling up the stem from the base to the tip of the colony (i.e., direction of colony growth), the spiral can be clockwise (dextral, abbreviated R) or counterclockwise (sinistral, abbreviated L). A three-dimensional model is presented in Figure 1 to explicitly show how to determine the branching sequence.

Measurements

Polyp height was measured from the base (on branch) to the mouth. Polyp width was measured at the neck (sensu [START_REF] Bayer | Illustrated trilingual glossary of morphological and anatomical terms applied to Octocorallia[END_REF]plate 2, p 39).

Measurements (e.g. colony height) were taken directly on the preserved colony when possible, or from photographs using the program ImageJ [START_REF] Abramoff | Image processing with ImageJ[END_REF]Rasband, 1997Rasband, -2008) ) when measuring directly was not practical (e.g. measurement of angles). The orthostiche distance, defined by [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF] as the distance separating aligned branches along the axial skeleton (and see [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF], was determined using standard calipers. The angle between the stem and the branch was measured so that it is obtuse if the branches are oriented upwards. All measurements of sclerites were done from light microscope imagery using ImageJ. Measurements are reported as mean ± one standard deviation, range, and sample size.

Genetic analysis

DNA was extracted from frozen (-80°C) or ethanol-preserved (95%) tissue using a modified CTAB protocol [START_REF] France | DNA sequence variation of mitochondrial large-subunit rRNA provides support for a two-subclass organization of the Anthozoa (Cnidaria)[END_REF] or using the MasterPure DNA purification kit (Epicenter). The first 697 bp of the protein-coding, mitochondrial msh1 gene were amplified and sequenced as described in [START_REF] Thoma | Deep-sea octocorals and antipatharians show no evidence of seamount-scale endemism in the NW Atlantic[END_REF].

DNA sequences of specimens representing each haplotype, for each seamount peak, were submitted to GenBank. The phylogenetic relationship between the species presented here and other Chrysogorgia species will be presented in a forthcoming publication.

Statistical analysis

Variation in sclerite length across haplotypes and polyp body compartments was characterized using frequency histograms. The effect of growth on continuous variables related to colony morphology was assessed by plotting ordered measures (taken from the base to the tip of the colony) for the two specimens that were sampled with their holdfast (KEL407-2 and NAS201-2) and a third, tall colony (KEL619-1) that was sampled very close to its base. The interbranch distance is used as an example. Eight continuous and two discrete (presence / absence, coded as 0 and 1) variables were used in a Principal Components Analysis (PCA; characters listed in Table 1). Measures from individual specimens were used, and continuous variables were summarized as means. Specimen LYM201-2 (YPM 38593, Haplotype A) from Yakutat Seamount was removed from the analysis as the colony was highly damaged and all characters could not be scored with confidence. All statistical analyses and plotting were done in R (R Development Core Team, 2010).

RESULTS

Correspondence between msh1 haplotypes and morphotypes

Four msh1 haplotypes (A, B, C, E) were found among the 23 colonies sampled on the NES and CS. Haplotypes A and B differ by one base pair only. The mutation is unique to A among our samples, and appears to be the derived state, when compared to haplotypes B, C and E, the chrysogorgiid Radicipes gracilis (Verrill, 1884) (Genbank ID DQ297424) and the primnoid Narella dichotoma Versluys, 1906 (Genbank ID EF060048). Haplotypes C and E differ from A by 3 and 7 bp, respectively.

Groupings based on msh1 haplotypes were congruent with the morphological characters measured (Figures 2 and3). The first two axes of the PCA explained 59% of the overall variance (component loadings: Table 1). Based on the ten characters used in the PCA, Haplotypes A and B were most distinguishable from each other based on the presence / absence of polyps on the main stem, the presence / absence of sclerites in the branch coenenchyme, and distances between (1) branches on the stem and (2) stem and first branch internode.

Haplotype E fell intermediate between these two groups. Haplotype C, represented by a single specimen, was most distinguishable by its tall polyps, its large orthostiche distance (driven by its unusual 3/8L branching sequence), and the angle between bifurcating branches. This last character was greatly influenced by the arched morphology of branchlets (see description). Each species described below is characterized by a discrete msh1 DNA sequence (haplotype). A list of diagnostic characters for each group is provided in Table 2.

Effect of growth on continuous morphological characters

There is a clear increase in measures pertaining to branching morphology along the stem. Moving distally, branches are more widely spaced (Figure 4). The same observation was made for the orthostiche interval and the distance from the stem to the first internode on a branch. This pattern was more or less important, depending on the colony. For KEL407-2, the interbranch distance is about 2 mm toward the base, and between 5 and 6 mm toward the tip. These allometric differences also appeared between the different colonies of haplotype E (Figure 3). Only a juvenile (VER202-1) and an adult (NAS204-1) were successfully sampled for this haplotype (Figure 12, and comments in the Systematics section). All morphological measures (except the angle between branches) were larger for the adult, even the height and width of polyps (Figure 3).

Sclerite size distribution

A total of 11,385 sclerites from polyps of all available colonies were measured.

The range of sclerite lengths did not vary significantly among the four haplotypes, and among the three polyp body compartments considered (branch coenenchyme, body wall and tentacles). There were some more substantial differences among haplotypes in the mean and skew of the sclerite lengths distributions (Figure 5). Not all haplotypes possessed sclerites in the branch coenenchyme (see taxonomic description). The distributions were highly rightskewed for sclerites from the polyp body wall in haplotypes C and E. These two haplotypes are characterized by a mix of sclerite types in different proportions: scales are small but abundant, and rods are much larger but more scarce. Despite these differences, there is no indication that sclerite length per se can be used as a diagnostic character.

There were significant differences between the sclerite length distributions from different individuals of haplotype A. Some polyps, for example, had smaller sclerites, regardless of the polyp body compartment. Examples are GOO110-2 and MIL101-5. Differences are particularly strong in the coenenchyme. BAL211- Wright & Studer, 1889: xli, 23;Versluys, 1902: 17-33;Nutting, 1908: 588;Kükenthal, 1919Kükenthal, : 505-511, 1924: 388-390;: 388-390;Deichmann, 1936: 227-228;Hickson, 1940: 307;Madsen, 1944: 49;Bayer, 1956: F216;Bayer & Stefani, 1988: 259;Williams, 1992: 252;[START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF]: 754, 2007: 512. Dasygorgia Verrill, 1883: 21;Studer, 1887: 41;Wright & Studer, 1889: xli, 6-9, 278.

Type species

Chrysogorgia desbonni Duchassaing & Michelotti, 1864, by monotypy.

Diagnosis

Colony branching is sympodial, in the form of an ascending spiral (clockwise or counterclockwise), a fan (planar colony), or two fans emerging from a short main stem (biflabellate colony). Axis with a metallic shine, dark to golden in color.

Branches divide dichotomously or pinnately. Most polyps large relative to the size of the branches they sit on. Sclerites in the form of spindles, rods and scales with little ornamentation. Discussion [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF] proposed to place Chrysogorgia species into two categories based on the zonation of sclerite types (scales and rods / spindles) in the polyp. The "Spiculosae" (also called Group A) consists of species that have rods and or spindles in the polyp body wall and tentacles. The "Squamosae typicae" (Group C) consists of species with scales in the polyp body wall and tentacles. [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF] defined the "Squamosae aberrantes," a group intermediate between groups A and C. This Group B is defined by species with scales in the polyp body wall and rods / spindles in the tentacles. Groups were further divided based on branching sequence. Remarks [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF] provided a detailed diagnosis of the genus, and listed the 59 valid species of Chrysogorgia and reviewed the North Atlantic species. He later described one additional species from Antarctica [START_REF] Cairns | A new species of Chrysogorgia (Anthozoa : Octocorallia) from the Antarctic[END_REF] and two new species from northeastern Pacific seamounts [START_REF] Cairns | Calcaxonian octocorals (Cnidaria; Anthozoa) from Eastern Pacific Seamounts[END_REF]

DESCRIPTION

The holotype is 42 cm tall and 19 cm wide. It was collected from a hard substrate, and cut by the ROV manipulator arm very close from its base. In situ photographs show a white / yellow discoidal holdfast for this specimen. Some colonies (NAS201-2, GOO108-1) were collected with their discoidal holdfast.

The colony consists of a wide 1/3L spiral, and when viewed from below shows three large passageways produced by the regularity of the branching. The stem has a deep golden color and a metallic luster. It is stiff and significantly thicker than the base of branches along most of the colony (proximal area: stem at least twice as thick as branches; distal area: stem and branches almost equally thick).

Every time it gives off a branch, the stem deviates from the main axis, producing a zigzag pattern typical of Chrysogorgia. On the holotype, the interbranch distance varies between 6 and 15 mm (average 11 mm ± 2; all specimens: 10 ± 3 mm, 4-30 mm, n=219), and the orthostiche interval is about three times as much (holotype: 30.7 ± 5.6 mm, 16.7-38.9 mm, n=23; all specimens: 27 ± 7 mm, 14-42 mm, n=124). Branches are as stiff as the stem at their base (diameter, holotype: 1.1 ± 0.2 mm, 0.8-1.4 mm, n=12; all specimens: 0.7 ± 0.3 mm, 0.1-1.6 mm, n=148), and thinner and more flexible toward their tip. They emerge from the main stem at an obtuse angle (holotype: 121.8 ± 11.6°, 106.3-135.9°, n=12; all specimens: 114 ± 11°, 93-144°, n=95) at regular intervals. Branches are straight, some (the most distal) having a slight curvature. Branching occurs in multiple planes, and branching order varies along the colony, the middle being the bushier part of the colony (10 th order of branching). Among the rest of the specimens, branching order varies between 3 (small colony KEL601-4) and 19 (NAS201-2). Anastomosing of branches was never observed. The angle between subdividing branches is regularly acute (holotype: 76.2 ± 10.2°, 59.3-95.5°, n=15; all specimens: 77 ± 14°, 47-121°, n=250). The distance between the stem and first branch node (holotype: 12.1 ± 2.9 mm, 8.6-18.3 mm, n=11; all specimens: 13 ± 3 mm, 5-21 mm, n=117) is similar to the interbranch and the internode distances, although the internode distance may slightly decrease toward the tip of the branch. The size of the terminal branchlet directly correlates with the number of polyps that sit on it.

Polyps are orange while alive and turn white in ethanol. All colonies are characterized by axial polyps placed on the interbranch. In most cases, one polyp is placed on branch nodes, and one is placed on branch internodes. The number of polyps per internode most commonly is one, but two or three polyps can be observed, in which case they are equally spaced. Branch tips carry one to four polyps, but most have one or two. On average, polyps are oriented upwards.

Most are in the shape of pitchers, and are almost as wide (holotype: 0.8 ± 0.2 mm, 0.5-1.2 mm, n=15; all specimens: 1 ± 0.3 mm, 0.4-2.4 mm, n=309) as they are tall (holotype: 1.2 ± 0.2 mm, 1-1.6 mm, n=17; all specimens: 1.1 ± 0.3 mm, 0.5-2.3 mm, n=320). Cnidal papillae are present on the polyp body. On some polyps, the back of tentacles is almost entirely covered by sclerite-free tissue resembling a gland (Figures 7D,7E,7F). To date, these features are of unknown origin and function, although they do not appear to be larvae or parasites (Watling and Simpson, unpublished histological examination).

Sclerites of the polyp body are in the form of smooth scales. In the coenenchyme, they are elongated, with a slight constriction in the middle, and run parallel to the branch (all specimens: 126 ± 57 µm, 17-334 µm, n=2686). Sclerites In the polyp body wall can be rounded on their distal ends with a strong constriction in the middle (e.g. Figure 7, 3rd sclerite of the polyp body wall; all specimens: 154 ± 56 µm, 26-441 µm, n=3082). They are densely packed and arranged parallel to the branch (as in Madsen"s 1944 description of C. campanula). The sclerites are found stacked horizontally in the back of the tentacle (perpendicular to the axis of the tentacle), and tend to be smaller and more longitudinally arranged toward the tip of the tentacle (all specimens: 143 ± 60 µm, 19-352 µm, n=3489). Sclerites rarely extend into the pinnules, which are otherwise sclerite-free. Tentacle sclerites are smooth, flat scales or idiosyncratic shapes. ETYMOLOGY Species epithet is Latin for "three passages" ("tri" and "caulus" in combination) in reference to the large passageways visible when the colony is viewed from below.

DISTRIBUTION

This species was found throughout the NES and CS chains, from Bear Seamount (NW) to Yakutat Seamount (SE), from 1533 m to 3860 m depth. With fifteen colonies, this is the most abundant species collected on the NES and CS.

REMARKS

Paratypes were chosen to cover the range of variation revealed by the PCA.

Colony silhouette varies across specimens. While most are tall bottlebrushes, much taller than they are wide, some are as wide as they are tall. For example, NAS201-2 is 27 cm tall and 30 cm wide, while KEL613-1 (holotype) is 42 cm tall and 19 cm wide. Ten of the 14 colonies examined have a very regular 1/3L branching pattern. However, variation was observed in four specimens (GOO108-1, LYM201-2, KEL202-2, NAS103-2). One of them is particularly noteworthy: ten centimeters from the holdfast, the axis of the GOO108-1 shifts by 43°, perhaps indicative of a response to the overall position of the colony relative to environmental conditions such as current flow. Also, most of the branches of LYM201-2 fell off shortly after fixation. The size frequency of sclerites was variable between polyps from different colonies (see results section). Multiple colonies were found with egg cases of an unknown "dumbo" octopus (KEL613-1, GOO110-2, BAL211-1, LYM310-1) and the shrimp Bathypalaemonella serratipalma Pequegnat, 1970 (KEL613-1, BAL211-1). While fourteen colonies were examined, we obtained a few branch fragments from a fifteenth one (RET101-1), which corresponds to the deepest occurrence of msh1 haplotype A, and is the deepest recorded occurrence of any species in the genus.

COMPARISONS

There are eight species of Squamosae typicae (Group C) with a 1/3L branching sequence, none of which fit the description of Chrysogorgia tricaulis sp. nov. C. axillaris [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF] and C. geniculata [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF]) are short, flexible colonies with interbranch and orthostiche distances that are significantly shorter than documented here. According to [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF], C. rigida [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF] is almost identical to C. geniculata, and these could belong to the same species. C. cavea [START_REF] Kinoshita | Studien uber einige Chrysogorgiiden Japans[END_REF] is a very robust, short bush. Its mode of colony growth is strikingly different from that of Chrysogorgia tricaulis sp. nov. (photo in [START_REF] Kinoshita | Studien uber einige Chrysogorgiiden Japans[END_REF]. C. sibogae [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF] (described from one specimen) is a short colony with very tightly-spaced branches (1-3 mm), few branch internodes and a significant disparity between the lengths of the proximal and distal branch internodes. C. excavata Kükenthal, 1908 has very particular tentacular sclerites, in the form of elongated, curved needles with a serrated edge (Kükenthal, 1908, Figures 45 and 47). The branches of that species are not fully bifurcating, producing a lyrate appearance in places (Figure 44). The

DESCRIPTION

The holotype is a narrow bottlebrush colony, 25 cm tall and 11 cm wide. It was collected with its discoidal holdfast. The colony consists of a narrow 2/5L spiral.

The stem has a brown-golden color and the metallic luster typical of Chrysogorgia. Every time it gives off a branch, the stem deviates from the main axis, producing a zigzag pattern. The stems of older colonies have a darker color. About 4 cm from the holdfast, a side branch forms a secondary stem, itself characterized by a regular, narrow 2/5L spiral. It is stiff and significantly thicker than the basal branches along most of the colony (proximal area: stem over twice as thick as branches; distal area: stem and branches almost equally thick). The interbranch distance is short (holotype: 3.3 ± 1.3 mm, 1.8-6.2 mm, n=27; all specimens: 4 ± 1 mm, 2-10 mm, n=122). Moving distad along the stem, the interbranch distance progressively increases from about 2 mm to almost 6 mm (Figure 5). The orthostiche distance is about five times the interbranch distance (holotype: 18.8 ± 2.4 mm, 15-21 mm, n=8, all specimens: 20 ± 4 mm, 11-30 mm, n=74). Branches are as stiff as the stem at their base (diameter, holotype: 0.7 ± 0.2 mm, 0.4-1.2 mm, n=24; all specimens: 0.7 ± 0.3 mm, 0-1.3 mm, n=55), and thinner and more flexible toward their tip. They emerge from the main stem at an obtuse angle (holotype: 121 ± 10.8°, 102.7-134.8°, n=10; all specimens: 121 ± 9°, 97-138°, n=45) at regular intervals. On average, the internodes are as short as the interbranch distance (distance between the stem and the first internode, holotype: 4.7 ± 1.6 mm, 2.4-6.5 mm, n=10; all specimens: 6 ± 1 mm, 2-9 mm, n=56). Branching occurs in multiple planes, and branching order is stable along the colony, varying between the 6 th and the 8 th order. There is no evidence of anastomosing between the branches of the holotype, but two of the four colonies examined exhibited fused branches (KUK205-1 and MIL102-3). The angle between subdividing branches is regularly acute (holotype: 76.3 ± 10.5°, 60.3-89.4°, n=7; all specimens: 87 ± 12°, 60-117°, n=59), and the internode length tends to decrease from the first node on.

Polyps are orange while alive and turn white in ethanol. Axial polyps were observed on none of the colonies examined. There is one polyp per branch node (or just next to the node) on the holotype, and other examined colonies can carry between zero to two polyps on the internode in addition to the polyp situated directly on or next to the node. Branch tips carry one or two polyps. This is the general case, but up to five polyps can be observed on the terminal branchlet.

Polyps overall are oriented upward, with many exceptions. They are on average as wide (holotype: 1.1 ± 0.3 mm, 0.6-1.4 mm, n=20; all specimens: 0.9 ± 0.3 mm, 0.6-1.7 mm, n=76) as they are tall (holotype: 1.3 ± 0.3 mm, 0.8-1.9 mm, n=40; all specimens: 1.1 ± 0.3 mm, 0.4-1.9 mm, n=100), and can be slightly constricted at the neck. No cnidal papillae were observed on the polyp or the branch coenenchyme.

Throughout the polyp body, sclerites are in the form of smooth scales (all specimens: 174 ± 48 µm, 62-338 µm, n=458). They are absent from the branch coenenchyme. In the polyp body wall, sclerites are densely packed and arranged parallel to the branch in a way that is very similar to what is observed in Chrysogorgia tricaulis sp. nov. They are rounded on their distal ends with a constriction in the middle. Some short rods (some curved) can occasionally be observed (seen in KEL407-2 and KUK205-1). Sclerites are found stacked laterally in the back of the tentacle (perpendicular to the axis of the tentacle; all specimens: 161 ± 42 µm, 40-309 µm, n=514). These are smooth, flat scales or idiosyncratic shapes. Some rare sclerites partially extend into the pinnules, which are otherwise sclerite-free. These sclerites do not appear any different from the other sclerites found in the tentacles. ETYMOLOGY Species epithet is Latin for "tight spiral" ("arto" and "spira" combined)

REMARKS

This species was found in association with egg cases of an unknown "dumbo" octopus (KEL619-1 and MIL102-3), fish eggs (MIL102-3), a comatulid crinoid (MIL102-3), scale worms (KEL407-2, KEL619-1), and a cladorhizid carnivorous sponge (KEL619-1).

COMPARISONS

Based on the list of valid species compiled by [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF], only three species of the Squamosae typicae are characterized by a 2/5L spiral: C. acanthella [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF], C. pendula [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF]C. campanula Madsen, 1944. While the first two were described from the southwestern Pacific (Kermadec, 1097 m and Banda Sea, 1595 m, respectively), C. campanula was described from Icelandic waters (2448 m), and might therefore be closely related to Chrysogorgia artospira sp. nov. [START_REF] Madsen | Octocorallia[END_REF] noted that this species seems "more closely related to C. acanthella (Wright & Studer), from which it may, however, be distinguished by its larger zooids, the absence of cnidal papillae, and its much closer layer of scales in the coenenchyma." The polyps of C. campanula are indeed stout and densely packed with sclerites. They have a "trumpet" shape (the width of the polyp increases from its base upwards) that Chrysogorgia artospira sp. nov. clearly lacks. The tentacles of C. campanula are thicker than those of Chrysogorgia artospira sp. nov. Although the interbranch distances (3-3.5 mm) and internodal distances (2.5-9 mm) reported in [START_REF] Madsen | Octocorallia[END_REF] are similar to ours, the colony examined by Madsen was 8.5 tall, while the specimens we examined were no smaller than 23 cm in height (this height difference may simply reflect an age difference). Both C. campanula and C. acanthella differ from Chrysogorgia artospira sp. nov. by the presence of polyps on the stem and sclerites in the branch coenenchyme. C. acanthella has abundant verrucae in the coenenchyme (giving it a rugged appearance) and an interbranch distance of 1.5 mm. C. pendula was described from part of a highly damaged colony characterized by unusual descending size branches. This species has an abundance of sclerites in the branch coenenchyme.

DESCRIPTION

This species is described from a single specimen. The holotype is 42 cm tall and 25 cm wide. It was collected from a tall colony, the main stem having been cut by the ROV manipulator claw near the base of the colony. Based on extrapolation from lab and in-situ photographs, the colony was about 45 cm tall. The holdfast is a very small disk, about 1-2 cm diameter. The colony consists of a wide 3/8L spiral. The stem has a golden color with a faint green tinge and a metallic luster.

Every time it gives off a branch, the stem deviates from the main axis, producing a zigzag pattern. The stem is stiff and significantly thicker than the base of branches along most of the colony (proximal area: stem twice as thick as branches; distal area: stem and branches almost equally thick). The interbranch distance varies between 9 and 13 mm (average 11 ± 1 mm), and the orthostiche interval is particularly long (76 ± 1 mm, 75-78 mm, n=4). Branches are as stiff as the stem at their base (diameter: 1.1 ± 0.2 mm, 0.8-1.6 mm, n=14), and thinner and more flexible toward their tip. They emerge from the main stem at an obtuse angle (104 ± 10°, 97-122°, n=10) at regular intervals. Internodes are characterized by a slight curvature; bifurcations are "U"-shaped as a result (this curvature makes the angle between bifurcating branches particularly obtuse: 108 ± 10°, 91-124°, n=15). Branching occurs in multiple planes, and branching order varies along the colony (base: 6th -8th order, middle: 9th -12th order, top: 10th order). There is no evidence of anastomoses between branches. The distance between the stem and the first branch node is 17 ± 2 mm (13-19 mm, n=6), and the internodal distance progressively decreases moving distad (size of branchlet: 8 ± 4 mm).

Polyps are yellow / orange while alive and turn white in ethanol. Axial polyps were not observed, and polyp occurrence most often starts on the first branch internode. Most internodes carry zero to two polyps, most commonly one to two. Polyps are equally spaced on the internodes, and are not found on the nodes. Terminal branchlets carry one to three polyps, but most have one. Most polyps are oriented up and outwards. They are on average longer (1.5 ± 0.3 mm, 1.1-1.9 mm, n=13) than they are wide (0.7 ± 0.1 mm, 0.5-1 mm, n=20), and are slightly constricted at the neck. Cnidal papillae are present on the polyp body wall and the branch coenenchyme (Figure 11E). Egg-bearing polyps are characterized by two pouches that sit on each side of the branch, as if they were saddle bags (Figure 11D; arrow pointing to an egg: Figure 11 F).

The branch coenenchyme contains few, small sclerites in the form of rods

DIAGNOSIS

Wide bottlebrush colony with a 1/3L, 1/4L or irregular (counterclockwise) spiral.

Polyps with a strong constriction at the neck, placed on internodes and nodes.

Polyps absent from the main stem. Sclerites in the form of scales in the coenenchyme, scales and rods in the polyp body wall, and rods in the tentacles (diagnostic of the Spiculosae). msh1 haplotype E.

DESCRIPTION

The holotype is a small, narrow, sparsely branched colony with a bottlebrush shape. It is 16 cm tall and 7 cm wide. The paratype NAS204-1 is much taller (29 cm) and wider ( 24), but in very poor condition, most branches having fallen off the stem after fixation of the specimen. It is not bottlebrush-shaped, but rather a bush of branches perched on top of a long stem. From in situ photos, it can be estimated that the colony was about 50 cm tall, 20 cm wide, and started branching about 20 cm from its base. The holdfast of the holotype is only slightly visible in the in situ photos, and appears to be a small disk attached to some exposed basalt with a veneer of biogenic sand. In the paratype the holdfast is a small disk about 1 cm diameter. Colonies are golden with a metallic luster and have a counter-clockwise (L) spiral. The branching sequence is irregular, 1/3 or 1/4 in places. The holotype is slender, but the paratype is stiff, with thick axis (diameter 2.2 mm at the base) and branches (diameter at the base: 0.9-1 mm, n=2). In both specimens, the axis is thicker than the branches near the base, but gets thinner when moving distad. Towards the tip of the colonies, the stem is as thick as the side branches. Every time it gives off a branch, the stem deviates from the main axis, producing a zigzag pattern typical of Chrysogorgia. The interbranch distance is short on the holotype (5. 1 ± 0.6 mm, 4.3-6.8, n=20) and twice as long on the paratype (10.7 ± 3 mm, 7.5-15, n=9). Branches emerge from the main stem at an obtuse angle (holotype: 98.4 ± 5.9°, 92.3-109.3°, n=9; paratype: 112.4 ± 2.7°, 110.5-114.3°, n=2) at regular intervals. The distance from the stem to the first interbranch is 8.5 ± 2.1 mm (6.1-11 mm, n=6) on the holotype. This parameter could only be measured on two instances on the paratype, and is about 16 mm in both cases. The angle between subdividing branches is acute (holotype: 92.2 ± 8. 5°, 83.3-102.2°, n=4, n=15; paratype: 72.3 ± 11.6°, 54.7-86.3°, n=10). They bifurcate only once or twice on the holotype.

Branching order is much higher in the paratype, although this parameter is hard to assess due to the poor preservation of the specimen. While anastomoses were not observed on the holotype, fused polyps (different polyps attached at their base) were observed on the paratype. On the holotype, internodes bear one or two polyps, one being close to the node. This character cannot be assessed from the paratype. Terminal branchlets bear one to three polyps on the holotype, and one to six polyps on the paratype.

Polyps are orange while alive and turn white in ethanol. Axial polyps were not observed. Polyps are mostly oriented upward. They are on average longer (both specimens: 1.5 ± 0.4 mm, 0.8-2.2 mm, n=27) than they are wide (both specimens: 0.9 ± 0.2 mm, 0.6-1.4 mm, n=27), and are strongly constricted at the neck. No cnidal papillae were observed on the polyp or the branch coenenchyme.

The branch coenenchyme bears small, rugged scales (both specimens: 135 ± 40 µm, 19-238 µm, n=80). In the polyp body wall, sclerites are in the form of rods (both specimens: 227 ± 78 µm, 60-399 µm, n=160) and smooth, elongated scales of idiosyncratic shapes (both specimens: 120 ± 43 µm, 38-251 µm, n=250). They are mostly found transversally and longitudinally arranged (i.e. parallel to the polyp axis). The tentacles contain rods exclusively (both specimens: 154 ± 67 µm, 42-356 µm, n=231), and pinnules are free of sclerites.

Rods form longitudinal rows, four to five sclerites wide along the back of the tentacle. ETYMOLOGY Species epithet is Latin for "dissimilar," in reference to the different overall morphologies of the colonies examined, including the branching sequence.

DISTRIBUTION

Known from the CS (Caloosahatchee Seamount) and the Southern tip of the NES (Nashville Seamount), between 2110 and 2246 m depth.

REMARKS

While VER202-1 is the smallest colony of this species (and the smallest Chrysogorgia collected on the NES and CS), and therefore probably a juvenile colony, it was chosen over NAS204-1 as the holotype for its better preservation.

A third colony (NAS102-3) corresponding to haplotype E was collected. However, everything but a few branches was lost during ROV maneuver. Based on in situ photographs, this colony was bottlebrush-shaped, and much taller (about 60 cm) than it is wide (about 13 cm). It had a discoidal holdfast, and was bifurcating about 21 cm from its holdfast, in a manner very similar to what as described for KEL407-2. This colony started branching 15 cm from the holdfast. Both specimens collected were host to the shrimp Bathypalaemonella serratipalma Pequegnat, 1970.

COMPARISONS

Only one species of Spiculosae (group A) was described with an irregular counter-clockwise spiral [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF]: C. dichotoma [START_REF] Thomson | An account of the alcyonarians collected by the Royal Indian Marine Survey Ship Investigator in the Indian Ocean. Part 1. The Alcyonarians of the deep sea[END_REF]. This specimen, described from the Bay of Bengal at 165 m depth, is among the shallowest Chrysogorgia reported to date. Chrysogorgia abludo sp. nov. differs from this species in its mode of branching (internode distance 10+ mm, and see Plate 6, Figure 3 of [START_REF] Thomson | An account of the alcyonarians collected by the Royal Indian Marine Survey Ship Investigator in the Indian Ocean. Part 1. The Alcyonarians of the deep sea[END_REF], polyp arrangement (polyps are aligned, and do not form a spiral) and morphology of polyps (long, narrow with strong constriction; not short and conical). The Spiculosae group does not contain species with a 1/3L spiral. However, it contains 12 1/4L turners (some parts of VER202-1 conform to a 1/4L sequence), all from the Indo-Pacific, mostly from depths much shallower than what was observed for C. abludo. (146 -1901 m). None of those species conform to the morphology of C. abludo sp. nov.; most are small bushes with a very short interbranch distance (C. cupressa [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF], C. lata [START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF], C. tetrasticha Versluys, 1902, C. pusilla Versluys, 1902, C. dispersa Kükenthal, 1908, C. minuta Kinoshita, 1913and C. sphaerica Aurivillius, 1931).

Others are small bushes with a larger interbranch distance (C. rotunda Kükenthal, 1908, C. okinensis Kinoshita, 1913), or have other inconsistent characters (C. pyramidalis Kükenthal, 1908, C. comans Kinoshita, 1913: bottlebrush, short interbranch, very long, whip-like branches; C. papillosa Kükenthal, 1908: profusion of papillae).

DISCUSSION

Species delimitation and identification

The four msh1 haplotypes were matched to four, non-overlapping morphotypes (PCA, Figure 2), suggesting that the species described here are true evolutionary units rather than artificial groupings. These results underline the usefulness of msh1 as a barcode for Chrysogorgia on the NES and CS chains. As well, the use of PCA was shown to be particularly useful to assign Chrysogorgia specimens to a particular species. Many of the characters used to separate Chrysogorgia species are continuous, and in many cases, there can be significant overlap between character ranges for different species. For example, interbranch distance was shown to be a useful character to separate haplotypes A and B, as the interbranch distance of A was significantly larger than that of B (Kruskal-Wallis rank sum test: X 2 = 204, df = 1, p-value < 0.001). However, the two distributions still overlap, as the minimum interbranch distance is 4 mm for Chrysogorgia tricaulis sp. nov., while the maximum distance is 10 mm for Chrysogorgia artospira sp. nov. The PCA might prove particularly valuable to examine such overlap between groups of individuals from different species (i.e., overlap between clouds of points from different species on Figure 3), should intermediate morphotypes or haplotypes be collected.

There was a clear trend towards increasing spacing between branches along the stem in the direction of growth (Figure 5). In the case of KEL407-2, the interbranch distance almost triples from its base to its tip. The effect of growth on colony morphometrics has previously been reported [START_REF] Kinoshita | Studien uber einige Chrysogorgiiden Japans[END_REF]description of C. aurea), and has strong implications for species identification. It should be taken into account when diagnosing juvenile or older but fragmentary colonies. This set of specimens exemplifies the difficulty of identifying colonies to the species-level based on in situ images and videos. There is a rapid increase in the number of studies using remotely-operated vehicles to survey deep benthic communities and make faunal inventories (e.g. [START_REF] Mortensen | Occurrence of deep-water corals on the Mid-Atlantic Ridge based on MAR-ECO data[END_REF][START_REF] Lundsten | The biogeography and distribution of megafauna at three California seamounts[END_REF], Lundsten et al., 2009[START_REF] Mcclain | Endemicity, biogeography, composition, and community structure on a northeast Pacific seamount[END_REF] 13 abstracts presented at the 12 th Deep-sea Biology Symposium in Reykjavík, Iceland, 2010). While this might be an achievable goal at the genus level (in select biogeographic regions), is it impracticable at the species level within the Chrysogorgiidae. Chrysogorgia is one of the most speciose of the alcyonacean genera [START_REF] Cairns | A new species of Chrysogorgia (Anthozoa : Octocorallia) from the Antarctic[END_REF]. Groups of species can be distinguished using the zonation of sclerite types within the polyp (groups A, B, C - [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF][START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF][START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF] and branching sequence. While sclerite zonation is impossible to assess from videos, branching sequence is impracticable to assess, because of lack of perspective from videos and the profusion of branches in some species (masking the stem and its branching pattern). Differences between species within a set defined by sclerite zonation and branching sequence are subtle, and include characters such as the number of internodes and placement of polyps on branches, orientation of sclerites on the polyp, presence / absence of specialized sclerites, all of which are impracticable or impossible to get from photographs or videos.

One tempting solution is to identify specimens based on the known distributional range of a particular species. However, most deep-sea octocorals have very poorly known distributional ranges (except for many pennatulaceans, which have relatively well-established bathymetric ranges -G.C. Williams, pers. comm.), and our genetics-based studies are suggest that many taxa have distributions far wider than previously known. Finally using video for faunal inventories is likely to [START_REF]YPM 38608, Isolate BEA[END_REF] severely reduce estimates of diversity, as the rate of species discovery is still very high for this group of organisms and (2) bias estimates of distributional ranges, as the rate of species misidentification could be high.

The limits of barcoding with msh1

All four msh1 haplotypes were recently found on the Bahama Escarpment during the 2009 Bahamas Deep Coral cruise. While the morphology of specimens (branching sequence and sclerites) from two haplotypes (A and E) conforms well to the morphological profile based on the NES and CS samples, morphology of two other haplotypes (B and C) could not be easily predicted based on msh1.

Haplotype B, consistently characterized by a 2/5L and a short interbranch distance on the NES and CS, was represented in the Bahamas by 1/3L-1/4L colonies with a long interbranch interval. These colonies, however, belong the Squamosae typicae (group C; rods in the polyp body wall and tentacles), as would be expected for haplotype B. Because more extensive genetic sampling suggests that haplotype A is derived from haplotype B, we can hypothesize that morphological characters such as branching sequence can evolve faster than msh1. As a result, Chrysogorgia specimens with identical msh1 sequences may not necessarily belong to the same species, but rather belong to different, recently-diverged sister species. Indeed, this pattern is not uncommon among octocorals (e.g. [START_REF] Mcfadden | Limitations of mitochondrial gene barcoding in Octocorallia[END_REF]. We must caution that only about 700 bp of msh1 were used in this study, and additional sequencing will be required to reliably separate specimens from closely-related species. In addition, morphological analysis of the Bahamas material is preliminary, and a more thorough analysis will be required.

Comparisons with NW Atlantic Chrysogorgia

There is a sharp contrast between the previously-described NW Atlantic fauna (reviewed in [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF] and the specimens collected on the NES and CS.

Most species reported by [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF] are small (less than 25 cm tall), slender colonies, with closely-spaced branches (interbranch 0.5 -6 mm). Three of the nine described species have a rhizoidal holdfast, adapted to soft sediments.

Overall, these specimens were sampled from significantly shallower depths, on slope environments (Figure 14). Only 10% of the specimens reported in Cairns In contrast, the specimens presented in this paper were sampled from the summit and flanks of old seamounts of volcanic origin [START_REF] Sleep | Monteregian hotspot track: a long-lived mantle plume[END_REF]. While the species reported in [START_REF] Cairns | Studies on western Atlantic Octocorallia (Coelenterata : Anthozoa). Part 1: The genus Chrysogorgia Duchassaing & Michelotti[END_REF] and the ones described here seem to be sympatrically distributed (Figure 14), they are in fact found in disjunct habitats, as our NW-most samples were collected on seamounts impinging on the continental margin (e.g. Bear Seamount), and not on the slope itself. In situ photographs confirm that all colonies reported here were sampled directly on hard substrates or lightly sedimented areas, and all four species have encrusting, discoidal holdfasts adapted to attachment to hard surfaces. Previously described NW Atlantic species may therefore be adapted to different environments, characterized by more sedimented substrates, higher primary productivity and different hydrological regimes. This hypothesis is supported by our recent observations from the Bahamas Escarpment: all four msh1 haplotypes from the NES and CS were sampled in the Bahamas from deep waters (between 1073 and 2258 m depth) and from hard substrates. The distribution of NW Atlantic species might, therefore, not be directly affected by the geological origin of the substrate (i.e. continental vs. oceanic), but rather its nature (i.e. hard vs. soft). Indeed, Metallogorgia melanotrichos [START_REF] Wright | Report on the Alcyonaria collected by the H.M.S. Challenger during the years 1873-76 -Report on the scientific results of the voyage of H.M.S[END_REF], previously thought to be a seamount specialist, was also recently collected from the Bahamas Escarpment.

Finally, sampling strategy might explain why the species described herein were apparently never sampled before. Hard substrates from escarpments and walls were targeted during the NES, CS and Bahamas cruises. These areas, chosen because they are most often associated with accelerated currents preferred by filter-feeding invertebrates such as corals, are difficult or impossible to sample using dredges or trawls.

Atlantic-Pacific connections

All Chrysogorgia colonies collected on the NES and CS have a sinistral (L) spiral.

With the exception of C. campanula from the Denmark Strait, off Iceland, all other species from the Atlantic were described with a dextral (R) spiral. Species characterized by a sinistral spiral have been described from the Coral Triangle, Japan, Hawaii and the Gulf of Panama. Two of the four species found on the NES and CS have smooth scales in their polyp body wall and tentacles (Squamosae typicae, group C). Again, with the exception of C. campanula, this group has previously been described exclusively from Pacific locations. Finally, one species (Chrysogorgia artospira sp. nov.) is represented on the NES and CS by the msh1 haplotype B, which has been sampled twice from Hawaii (e.g. specimen LAD23; [START_REF] Thoma | Deep-sea octocorals and antipatharians show no evidence of seamount-scale endemism in the NW Atlantic[END_REF]. There is no evidence at present that all specimens characterized by haplotype B belong to the same species (see discussion of material from the Bahama Escarpment above). However, these specimens are likely very closely related. These three lines of evidence (direction of the spiral, zonation of sclerite types and msh1 haplotyping) all suggest a faunal connection between the Atlantic and Pacific. This is further supported by the fact that Iridogorgia, Radicipes and Metallogorgia (Chrysogorgiidae) all possess msh1 haplotypes that are shared between Atlantic and Pacific locations [START_REF] Thoma | Deep-sea octocorals and antipatharians show no evidence of seamount-scale endemism in the NW Atlantic[END_REF]. While the phylogenetic extent and the age of the connection between Atlantic and Pacific will need further investigation, we can hypothesize that this connection was sustained for the major part of the morphological diversification of Chrysogorgia, as all major morphological characters (spiral direction, major branching groups such as 1/3, 1/4 and 2/5, and sclerite groups A, B and C) are present in both ocean basins. one counts the number of branches required to be in the same plane as a reference branch (white). In this example, the 6 th branch (black) is in the same plane as the reference branch, and only one revolution is necessary to spiral back to the reference plane. Also, in this case the spiral is clockwise when looking upward (in the direction of colony growth). This hypothetical colony therefore has a 1/6R sequence. On Seamounts are made apparent using contour lines between 1500 and 4000 m depth (1000 m intervals). The depth distribution of both groups of specimens is presented as an insert (sample size under each boxplot).

  , with Chrysogorgia pinnata being the first described pinnately-branching species. Pante & France (2010) recently described Pseudochrysogorgia, a new chrysogorgiid genus that closely resembles Chrysogorgia morphologically, but is most closely related to Metallogorgia based on a multi-gene phylogeny. Distribution Known from all ocean basins between 100 and 3375 m depth (Cairns, 2001); the depth limit of Chrysogorgia colonies from this study is 3860 m and extends Cairns" range by almost 500 m. Recently, ROV-based exploration revealed to presence of Chrysogorgia between 4163 and 4492 m depth on Derickson Seamount in the Gulf of Alaska (specimen deposited at the Smithsonian Institution, catalogue number USNM 1081181). Chrysogorgia tricaulis sp. nov. with a 1/3L (counterclockwise) spiral and a large orthostiche interval. Branches stiff and straight. Pitcher-shaped polyps on the main stem and branches, placed on internodes and nodes. Sclerites in the form of scales in the branch coenenchyme (abundant), polyp body wall and tentacles, diagnostic of the Squamosae typicae. msh1 haplotype A.

  description of C. delicata Nutting, 1908 is very succinct, and based on 5 cm of a single, damaged colony. It differs from Chrysogorgia tricaulis sp. nov. by a short interbranch distance (4 mm), longitudinally arranged sclerites in the polyp body wall, and curved, transversally-arranged tentacular sclerites. C. fruticosa (Studer, 1894) is a short colony with a short interbranch distance, and the mode of branch ramification ("Cyma helicoidea unipara") is different from that observed in Chrysogorgia tricaulis sp. nov. Chrysogorgia artospira sp. nov. (Figures 8-9) TYPE MATERIAL Holotype: Kelvin Seamount, NES, Station 407, 38°46.98'N 63°57.77'W, 2253 m depth, 19-May-2004, YPM 38596, Isolate KEL407-2, Genbank ID GQ180132. Paratypes: Kelvin Seamount, NES, Station 619, 38°46.23"N 64°05.56"W, 1965 m depth, 31-Aug-2005, YPM 38605, Isolate KEL619-1, Genbank ID GQ868346; Kükenthal Peak, Corner Seamount, CS, Station 205, 35°33.41"N 51°48.89"W, 1846 m depth, 22-Aug-2005, YPM 38604, Isolate KUK205-1, Genbank ID GQ180133; Milne Edwards Peak, Caloosahatchee Seamount, NES, Station 102, 34°48.99'N 50°30.36'W, 1650 m depth, 17-Aug-2005, YPM 38599, Isolate MIL102-3, Genbank ID GQ180134. DIAGNOSIS Elongated bottlebrush colony with a 2/5L (counterclockwise) spiral and a short orthostiche interval. Branches straight and stiff. Pitcher-shaped polyps on the main stem and branches, placed on internodes and nodes. Sclerites in the form of scales in the polyp body wall and tentacles, diagnostic of the Squamosae typicae. Sclerites rare or absent from the branch coenenchyme. msh1 haplotype B.

  in reference to the 2/5 branching sequence, the tightest spiral for any colony of Chrysogorgia observed on the New England and Corner seamounts. DISTRIBUTION Species known from Kelvin Seamount, located approximately in the middle of the NES, as well as Corner and Caloosahatchee Seamounts on the CS. Depth distribution extends from 1650 to 2253 m.

  with a 3/8L (counterclockwise) spiral and a very wide orthostiche interval. Branches slightly curved, forming "U"-shaped bifurcations.Polyps long and narrow, placed on the internodes, not on the nodes. Sclerites in the form of flat rods and scales in the branch coenenchyme, rods and scales in polyp body wall, and rods in tentacles (diagnostic of the Spiculosae). msh1 haplotype C.

(

  122 ± 30 µm, 43-182 µm, n=100). The polyp body wall contains scales(most abundant; 96 ± 23 µm, 41-196 µm, n=150) and rods (more or less blunt-ended; 181 ± 60 µm, 79-334 µm, n=35). Sclerites are longitudinally arranged in the polyp body. Scales and rods are particularly abundant at the base. Moving distad along the polyp body wall, rods become larger and more aggregated in the grooves between the tentacles. At the oral disc, rows of sclerites from adjacent grooves meet at the tentacle base and form longitudinal rows, four to five sclerites wide, along the back of the tentacle (186 ± 53 µm, 62-301 µm, n=150). Tentacles contain rods only, and pinnules are free of sclerites. ETYMOLOGY Species epithet is Latin for "saddle bag," in reference to the morphology of mature polyps, with their two "pockets," containing eggs and extending below each side of the branch.DISTRIBUTIONOnly known from the northwestern Atlantic at the type location, namely Lyman Peak, Yakutat Seamount in the Corner seamount chain, 2379 m depth.REMARKSThe zonation of sclerite types (rods present in the tentacles and polyp body wall) places this species in the "Spiculosae" (Group A). The holotype was collected with the shrimp Bathypalaemonella serratipalma Pequegnat, 1970.COMPARISONSThis species represents the first recorded occurrence of the 3/8L branching sequence. C. herdendorfi Cairns, 2001, described from deep waters off the coast of South Carolina, is characterized by a 2-5R-3/8R spiral. This later is characterized by significantly shorter interbranch (2.5-3 mm), orthostiche (14-17 mm) and stem-to-first branch node (4-7 mm) distances. Also, the branches of C. herdendorfi emerge from the main stem with a more obtuse angle (i.e. they are more pointed toward the top of the colony), and the colony is significantly more slender than Chrysogorgia averta. Finally, branches are not nearly as stout, and do not arc as the branches of C. averta. These differences, however, could be attributed to growth, as the maximum height for C. herdendorfi is 22 cm, half the size of C. averta. Other parameters (sclerite composition, number of polyps on first internode) are congruent, and these species may be closely related. Both species were collected from the northwestern Atlantic from similar depths, and while C. averta was collected on a seamount (on the upper edge of a wall), C. herdendorfi was collected from a wreck. Chrysogorgia abludo sp. nov. (Figures 12-13) TYPE MATERIAL Holotype: Verrill Peak, Caloosahatchee Seamount, CS, Station 202, 34°31.84'N 49°47.39'W, 2110 m depth, 19-Aug-2005, YPM 38606, Isolate VER202-1, Genbank ID GQ180139. Paratype: Nashville Seamount, NES, Station 204, 34°28.73"N 56°44.04"W, 2121 m depth, 25-Aug-2005, YPM 38600, Isolate NAS204-1. COMPARATIVE MATERIAL EXAMINED Nashville Seamount, NES, Station 102, fragments only; 34°34.97"N 56°50.60"W, 2246 m depth, 24-Aug-2005, Isolate NAS102-3, Genbank ID GQ180138.

(

  2001) were collected within the depth range reported in this study. Those specimens (belonging to C. agassizii, C. elegans, C. fewkesii, C. herdendorfi and C. spiculosa) are all directly associated with the continental slope (from New England to northern Mexico, Columbia and Guyana), and three of the five species represented have a rhizoidal holdfast.

Figure 1 .

 1 Figure 1. On the left: model representing the main stem and some branches of a hypothetical Chrysogorgia colony. To determine branching sequence,

  the right: original (Figure21page 21) from[START_REF] Versluys | Die Gorgoniden der Siboga-Expedition. I. Die Chrysogorgiiden[END_REF], representing the branching sequence of a 1/3L spiral.

Figure 2 .

 2 Figure 2. Principal Component Analysis (PCA) based on eight continuous and two discrete morphological characters coded as 0/1. The proportion of variance explained by each axis is given in parentheses (cumulative variance: 59%). Specimen identifiers are the genetic isolate names.

Figure 3 .

 3 Figure 3. Box-and-whisker plots of the eight continuous variables used in the PCA, for each msh1 haplotype. The number of measurements is given above each plot. Black triangles represent mean values for each individual specimen.

Figure 4 .

 4 Figure 4. Plot of the distance between branches along the stem, ordered from near the base to near the tip of the colony. NAS201-2 belongs to Chrysogorgia tricaulis sp. nov. (haplotype A). KEL619-1 and KEL407-2 belong to Chrysogorgia artospira sp. nov. (haplotype B).

Figure 5 .

 5 Figure 5. Distribution of sclerite length (µm) from the coenenchyme, polyp body wall and tentacles of the four msh1 haplotypes (Hap). Sample size is given in parentheses for each group.

Figure 6 .

 6 Figure 6. Chrysogorgia tricaulis sp. nov (haplotype A). In situ photographs of holotype KEL613-1 (A) and paratype GOO108-1 (B) before and during collection, respectively.

Figure 7 .

 7 Figure 7. Chrysogorgia tricaulis sp. nov (haplotype A; A-D: KEL613-1, holotype; E: NAS201-2, paratype; F: GOO108-1, paratype). (A) Sclerites from the polyp body wall; (B) sclerites from the branch coenenchyme; (C) sclerites from tentacles; (D) light microscopy of an entire polyp; (E) SEM of a partially digested polyp; (F) SEM of the tentacles and their uncharacterized features (arrows).

Figure 8 .

 8 Figure 8. Chrysogorgia artospira sp. nov (haplotype B). In situ photographs of (A) holotype KEL407-2 and (B) paratype MIL102-3 during collection. (C) Paratype KEL619-1 photographed in the laboratory aboard ship.

Figure 9 .

 9 Figure 9. Chrysogorgia artospira sp. nov (haplotype B; KEL407-2, holotype). (A) Sclerites from the polyp body wall; (B) sclerites from tentacles; (C) LM of a polyp; (D) SEM of a polyp; (E) ) LM of a polyp cleared with clove oil to reveal the arrangement of sclerites (photograph inverted).

Figure 10 .

 10 Figure 10. Chrysogorgia averta sp. nov. (haplotype C; LYM201-1, holotype). (A)In situ and laboratory photographs.

Figure 11 .

 11 Figure 11. Chrysogorgia averta sp. nov. (haplotype C; LYM201-1, holotype). (A) Sclerites from the polyp body wall; (B) sclerites from the branch coenenchyme; (C) sclerites from tentacles; (D) SEM of an mature polyp; (E) LM of a mature polyp, arrow points to cnidal papillae; (F) LM of a mature polyp treated with clove oil to reveal position of sclerites, arrow points to an egg; (F) LM of an immature polyp treated with clove oil.

Figure 12 .

 12 Figure 12. Chrysogorgia abludo sp. nov. (haplotype E). Photographs of (A) holotype VER202-1 (laboratory) and (B) paratype NAS204-1 (in situ).(C) Close-up of the polyps and associate of NAS204-1.

Figure 13 .

 13 Figure 13. Chrysogorgia abludo sp. nov. (haplotype E; VER202-1, holotype). (A) Sclerites from the polyp body wall; (B) sclerites from the branch coenenchyme; (C) sclerites from tentacles; (D) LM of polyp; (E) LM of polyp treated with clove oil to reveal position of sclerites.

Figure 14 .

 14 Figure 14. Map of the northwestern Atlantic, with the specimens described in Cairns (2001) and in this study represented by filled circles and open triangles, respectively. The continental slope is made evident by plotting contour lines between 0 and 1000 m depth (200 m intervals).

Table 1 .

 1 Proportion of variance and loadings for the first four components of the PCA.

	Comp.	Comp.	Comp.	Comp.
	1	2	3	4

Table 2 .

 2 Diagnostic morphological and molecular characters for each species.Continuous measures are means ± standard deviation and range, in mm.

		C. tricaulis	C. artospira	C. averta	C. abludo
	msh1 haplotype	A	B	C	E
	Branching sequence	1/3L	2/5L	3/8L	1/3-1/4-irreg L
	Sclerite arrangement	group C	group C	group A	group A
	Polyps on the stem?	yes	no	no	no
	Interbranch distance	9.8 ± 3.1	4.2 ± 1.3	10.7 ± 1	6.9 ± 3.1
		4.1-30	1.8-10.1	9.1-12.8	4.3-15
	Orthostiche interval	26.7 ± 6.7	20.5 ± 3.9	76.2 ± 1.3	NA
		13.8-42	11.2-29.6	75-78	NA
	Shape of polyps	pitcher	pitcher	long, narrow	long, narrow,
					constriction at
					neck
	Shape of branches	straight	straight	arched	straight
	Position of polyps	on nodes	on nodes	on internodes	on nodes
	Sclerites in branch	yes	no	yes	yes
	coenenchyme?

ACKNOWLEDGMENTS

This work was made possible by generous funding provided by the NOAA Ocean Exploration program (NA66RU0186, NA03OAR4600116, NA05OAR4301001, NA05OAR4601061, NA08OAR4600756). We would like to thank LW"s coprincipal investigators, P. Auster, S. France, I. Babb, L. Mullineaux, J. Moore and K. Scanlon for their help in securing the necessary funding to allow us to explore NW Atlantic seamount communities. The comparative Chrysogorgia material from the Bahamas was recently collected during the NOAA-funded Bahamas Deep Coral cruise (PI S. France). Our sincere thanks to the captains and crew of the RV Atlantis, the RV Ronald H. Brown, and the RV F.G. Walton Smith, who together with the skillful pilots of the DSV Alvin and ROVs Hercules (NW Atlantic) and Global Explorer (Bahamas) made it possible to collect high quality imagery and specimens from great depths. We are very grateful to S. D. Cairns (Smithsonian Natural History Museum) for sharing his expertise on the taxonomy of Chrysogorgia. O. S. Tendal (Natural History Museum of Denmark) provided comparative material and photographs of Chrysogorgia campanula Madsen 1944. We are also indebted to T. Carvalho (University of Hawaii PBRC Electron Microscope Facility), H. Ylitalo-Ward (University of Hawaii), M. Purpera and T. Pesacreta (Microscopy Center, UL Lafayette) for their assistance with scanning electron microscopy. Members of the France Lab at UL Lafayette (M. R. Brugler, J. N. Thoma, E. N. Heestand, J. van der Ham) provided support and help throughout the study. We warmly thank S. France, who provided assistance and advice in all stages of the study, from material collection to manuscript preparation. Funding for genetic analyses was provided by NSF (OCE-0624601; Cnidarian Tree of Life EF-0531570, EF-0531779).


Yanwen Chen

Yixiang Chen

Eric Madelaine

Investigation on Time Properties of Timed-pNets

Timed-pNets is a semantic model to specify the communication behaviours of distributed systems. It has a tree style hierarchical structure. The leaves are timed specifications which consist of a set of logical clocks and clock relations. These logical clocks are encoded with delay variables and delay bound. In this paper we discuss how to detect time constraint conflicts and how to compute delay variables of clocks in the non-leaf nodes. Then we can check system's time properties like deadline. From our formalization of timed-pNets, we generate a system of logical clocks that can be simulated in the TimeSquare tool. We take a simple use case from ITS to simulate and check some time properties.

Introduction

Timed-pNets [START_REF] Chen | Timed-pNets: A formal communication behavior model for distributed systems[END_REF] has been proposed to specify communication behaviours of heterogeneous distributed systems. This timed model is able to specify time constrains based on logical time. Logical time has proved its benefits in several domains. It was first introduced by Lamport to represent the execution of distributed systems [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF]. Logical time can be multiform, a global partial order built from local total orders of clocks. The multiform nature of logical time consists in the ability to use any repetitive event as a reference for the other ones [START_REF] Boussinot | The esterel language[END_REF]. Inspired by the CCSL [START_REF] André | Syntax and Semantics of the Clock Constraint Specification Language (CCSL)[END_REF], we design clock relations to express the systems logical time constraints. So our model is a logical constraint model that is expressed by a set of logical clocks and clock constraints.

However, the logical constraint model cannot be directly used to check some time properties like deadline property since the distance of two clocks cannot be measured. In this paper, we focus on address the issue of transferring our logical constraints model to schedulable model in which the time properties like deadline can be checked. We propose a virtual timestamp to link those logical clocks. In Lamport, virtual time is identifiable by the succession of events (and therefore is discrete). It does not flow by its own means like real time whose passage we can not escape or influence. Based on his work, we define our virtual timestamp as two dimension values, and the number we assign to clocks as virtual timestamp is based on a reference clock. By this way, we can compare the delay variables from different logical clocks. Furthermore, we propose a theorems about computing delay variable of global clocks in timed-pNets. In the end, we take a use case from ITS (Intelligent Transportation Systems) for simulation. We define a virtual timestamp as a pair of natural numbers: one represents when a timed-action occurs in terms of a reference clock (X-axis), another represents the order of the occurrences of a timed-action (Y-axis). Fig. 1 shows us an example in which the timed-actions are assigned with virtual timestamps. In the figure, the processes are presented as solid black lines. The sequence of timedactions executed in these processes are presented as solid black points on these black lines. The actions in each process are totally ordered. The communications between processes are represented by clock relations. For example, in the Fig. 1, the clock C a and clock C d are coincident. We use a sequence of red lines to represent the coincidence relation of two clocks. Similarly, we use a sequence of red arrows to represent the precedence relations (e.g. C a ≺ C b ). We define the virtual timestamps and their assignment rules as follows.

Virtual Timestamps and Delay Bounds

Definition 1 (Virtual Timestamps). A virtual timestamp (denoted as

T (α i)) of a timed-action occurrence α i is a pair of natural numbers (x α i , i) (x α i ∈ N, i ∈ N). Definition 2 (Virtual Timestamp Assignment Rules). Let T (α i) (x α i , i)
be the virtual timestamp of the occurrence α i of the clock C α (α ∈ L A,T ,P ), and T (β i) (x β i , i) be the virtual timestamp of the occurrence β i of the clock C β (β ∈ L A,T ,P ). Then we have:

-C α = C β ⇒ ∀i, x α i = x β i := max(x β i , x α i ) -C α ≺ C β ⇒ ∀i, x α i < x β i and x β i := max(x α i , x β i ) + t βi (the variable
t βi presents the delay time from the occurrence α i to β i in terms of the reference clock that a user chose.

t βi ≥ 1, t βi ∈ N)
Initially, for an independent clock (without any relation with other clocks), the X-axis value of the timestamps of the clock can be set with any natural number. The values will be updated according to the clock relations applied on this clock. Take the clock C b in the Fig. 1(a) as an example, we know the relation C a ≺ C b ≺ C c . According to the assignment rules, we must have x a 1 < x b 1 < x c 1 . In this figure, the timestampe of the first occurrence of clock C b is initially set as [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF][START_REF] André | Syntax and Semantics of the Clock Constraint Specification Language (CCSL)[END_REF]. It can also be initially set as (7, 1) only if it satisfied the condition x a 1 < x b 1 < x c 1 . When adding new clock constraints, these timestamps in the Fig. 1 may also be updated according to the assignment rules. For example, assume that we add other four clock relations

(C a ≺ C g , C g ≺ C e , C f ≺ C c , C e = C p ). If the delay from C f to C c is 2,
then the virtual timestamps may be updated by following the rules (as shown in the Fig. 1(b)).

Time Constraint Conflicts

Since the timestamps may be updated, the clock delays may also be updated, which may cause time constraint conflicts. For example, in the Fig. 1

Compute Delay and Delay Bounds

In timed-pNets, non-leaf nodes are the synchronization devices of their subsystems. The delays and delay bounds of the global logical clocks in these non-leaf nodes are computed in terms of the local logical clocks of the subsystems. When building these non-leaf nodes, time constraint conflicts may happen. Here, we propose a theorem to compute the delays and delay bounds of these global clocks so that we can check if time constraint conflicts exist.

Theorem 1 (The Delay Bounds of Global Clocks). Given a timed-pNet

< P, A G , C G , J, A J , C J , R J , - → V >.
= {C g k }(k ∈ N) be the set of causal clocks of C γ (C g ⊆ C G , C γ ∈ C G , γ γ(p γ ) tγ |bt γ ).
( 1 We simulate the system of the Fig. 3 by means of the TimeSquare tool [START_REF] Deantoni | TimeSquare: Treat your Models with Logical Time[END_REF] to check system time constraint conflicts. For simplification, we choose a reference clock that ticks periodically. All delays and delay bounds of other logical clocks are specified in terms of this reference clock. In our simulation, we assume that the delay bounds of all action occurrences are between [START_REF] André | Syntax and Semantics of the Clock Constraint Specification Language (CCSL)[END_REF][START_REF] Chen | Timed-pNets: A formal communication behavior model for distributed systems[END_REF] in the sense that the delays of those actions should stay between the first and the third occurrences of the reference clock. The simulation result tells us if conflicts exist in the system.

P Cm k ′ →Cα )|k ′ ∈ N}, min{l(b P Cn k ′′ →C β )|k ′′ ∈ N}}, max{max{u(b P Cm k ′ →Cα )|k ′ ∈ N}, max{u(b P Cn k ′′ →C β )|k ′′ ∈ N}}] (C m k ′ ∈ C m , C n k ′′ ∈ C n , k ′ , k ′′ ∈ N); (1.2) If < . . . , C m k ′ , . . . , . . . , . . . >→ C g k as shown the case (1.2) in Fig. 2, then b Cγ = [min{l(b P Cm k ′ →Cα )|k ′ ∈ N}, max{u(b P Cm k ′ →Cα )|k ′ ∈ N}] (C m k ′ ∈ C m , k ′ ∈ N), (1.3) If < . . . , . . . , . . . , C n k ′′ , . . . >→ C g k as shown the case (1.3) in Fig. 2, then b Cγ = [min{l(b P Cn k ′′ →C β )|k ′′ ∈ N}, max{u(b P Cn k ′′ →C β )|k ′′ ∈ N}] (C n k ′′ ∈ C n , k ′′ ∈ N), (2)
Result: TimeSquare reports us an error. The main reason is that the communications between those component create conflicts. By analyzing those updated virtual timestamps in the Fig. 4

Conclusion

In this paper, we investigated the time constraints and properties of timed-pNets model. We took a use case from ITS to build a timed-pNets communication model. From our formalization of timed-pNets, we generated a system of logical clocks and solved the issue of detecting time constraint conflicts.

Fig. 1 :

 1 Fig. 1: Time Diagram and Updated One

  , assume the delay bound of C c is [2, 5]. Before we add the relation C f ≺ C c , there is no time constraint conflict since t Cc[1] = 8 -5 = 3 ∈ [2, 5]. However, after adding this relation, we found out that t Cc[1] = 12 -5 = 7 ∈ [2, 5]. Here we give a formal definition of time constraint conflicts. Definition 3 (Time Constraints conflicts). Let C α be a clock built on timedaction α(p) tα|bt α . A time constraint conflict of clock C α exists if ∃i ∈ N, t αi ∈ b tα i .

Fig. 2 :

 2 Fig. 2: Three cases in Theorem 1

  ) When -→ v =< ..., C α , ..., C β , ... >→ C γ . As shown in Fig. 2, let C m = {C m k ′ }(k ′ ∈ N) be a set of local clocks that are in the same hole as C α , and that contribute to generate the global clocks in C g . Let C n = {C n k ′′ } be a set of local clocks that are in the same hole as C β , and that contribute to generate the global clocks also in C g . (1.1) If < . . . , C m k ′ , . . . , C n k ′′ , . . . >→ C g k as shown the case (1.1) in Fig. 2, then b Cγ = [min{min{l(b

Fig. 3 :

 3 Fig. 3: Example of a Timed-pNets subsystem

  (a), we can see that a time constraint conflict happens on the clock C {2s-1} ?Ack(x C {2s-1} ?ack [1]x C {2s} !notif y [1] = 9 -5 = 4 ∈ [1, 3]). Solution: To fix the issue, we set the delay of ?N otif y i in component "CommRes" to 1 and limit the delays of all clocks less than 2 except the clock C {2s-1} ?Ack . After redoing the simulation, we found out that no conflict exists. TimeSquare outputs VCD view as shown in Fig.4(b).

Fig. 4 :

 4 Fig. 4: Conflict Analysis and Results

  Assume that all local clocks (in the set C J ) have no time constraint conflict. Consider a global clock C γ and let C g

⋆ This work was funded by DAESD of INRIA and ECNU; by NSFC (No. 61321064 and No. 61370100); by Shanghai Knowledge Service Platform Project (No. ZF1213).