Mehdi Adjeroud
email: adjeroud@univ-perp.fr

Yannick Chancerelle

Muriel Schrimm

Thierry Perez

David Lecchini

René Galzin

Bernard Salvat

Murielschrimm

Detecting the effects of natural disturbances on coral assemblages in French Polynesia: a decade survey at multiple scales

Keywords: Coral reefs, Temporal variability, Bleaching events, Indicators, Pacific Ocean

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

Résumé -Evaluation des impacts des perturbations naturelles sur les assemblages de coraux en Polynésie française : résultats de 10 années de suivi à différentes échelles. Comme d'autres récifs à travers le monde, les écosystèmes coralliens de Polynésie française ont subi de nombreuses perturbations naturelles, et depuis les années 1980, 15 cyclones, sept phénomènes de blanchissement et plusieurs explosions démographiques d'Acanthaster planci.Afin d'examiner l'impact de ces perturbations sur les assemblages de coraux scléractiniaires, un programme de suivi à long terme a été mis en place, aux échelles locale et régionale. Le recouvrement corallien a été quantifié sur 20 stations localisées sur la pente externe de 13 îles. Nous analysons les résultats obtenus pour la décennie 1992-2002, et nous examinons la pertinence des indicateurs potentiels de l'état de santé des récifs. Sur les 13 îles, deux seulement n'ont subi aucune pertubation. Nos résultats montrent une forte variabilité de l'impact des phénomènes de blanchissement et des cyclones aussi bien à l'échelle locale que régionale. Trois tendances majeures sont observées : 1) diminution du recouvrement corallien pour 10 stations, suite au passage de perturbations successives ; 2) augmentation du recouvrement corallien pour neuf stations, malgré le passage de perturbations pour sept d'entre elles ; 3) stabilité du recouvrement corallien dans une station. Les réponses aux perturbations sont différentes selon les genres de coraux : Acropora est le plus sensible aux phénomènes de blanchissement, alors que les dommages physiques causés par les cyclones affectent les formes branchues des genres Acropora et Pocillopora. Les programmes de suivi pourraient être optimisés via la sélection d'indicateurs différents et complémentaires (l'un évaluant la variation de la diversité, l'autre l'évolution de l'abondance et/ou du recouvrement, ou encore le potentiel de recrutement), l'intégration de plusieurs échelles spatiales, et le choix d'espèces informatives. L'enregistrement de facteurs environnementaux (température de l'eau par exemple) se révèle également un outil complémentaire utile pour l'identification des causes des changements observés dans la structure des communautés.

Introduction

Community ecologists have long recognised the important contribution of disturbances to the structure and dynamic of marine communities [START_REF] Connell | Diversity in tropical rain forest and coral reefs[END_REF]1997;[START_REF] Sousa | The role of disturbance in natural communities[END_REF][START_REF] Hughes | Community structure and diversity of coral reefs: The role of history[END_REF]1994;Done 1992a;1992b;[START_REF] Van Woesik | Contemporary disturbances to coral communities of the Great Barrier Reef[END_REF][START_REF] Hughes | Multiple stressors on coral reefs: A long-term perspective[END_REF]. However, they have also pointed out the difficulty of discriminating the relative importance of natural and anthropogenic perturbations in causing the changes in community structure [START_REF] Brown | World wide death of corals -natural cyclical events or man-made pollution?[END_REF][START_REF] Grigg | Natural and anthropogenic disturbance on coral reef ecology[END_REF][START_REF] Karlson | Disturbances, coral reef communities, and changing ecological paradigms[END_REF]. In coral reef ecosystems, the major natural disturbances experienced by reef communities are cyclones [START_REF] Rogers | Cyclones and coral reefs: The intermediate disturbance hypothesis revisited[END_REF][START_REF] Harmelin-Vivien | The effects of storms and cyclones on coral reefs: A review[END_REF], coral-bleaching events [START_REF] Gleason | Effects of disturbance on coral communities: Bleaching in Moorea, French Polynesia[END_REF][START_REF] Hoegh-Guldberg | Climate change, coral bleaching and the future of the world's coral reefs[END_REF][START_REF] Wilkinson | Ecological and socio-economic impacts of 1998 coral mortality in the Indian Ocean: An ENSO impact and a warning of future change?[END_REF], long periods of low tides [START_REF] Eakin | Low tidal exposure and reef mortalities in the eastern Pacific[END_REF], dystrophic crisis linked with phytoplankton blooms and associated anoxic conditions [START_REF] Guzman | Coral mortality associated with dinoflagellate blooms in the eastern Pacific (Costa Rica and Panama)[END_REF][START_REF] Adjeroud | Mass mortality of macrobenthic communities in the lagoon of Hikueru atoll (French Polynesia)[END_REF]Salvat et al. 2002), outbreaks of predators, particularly the seastar Acanthaster planci in the tropical Pacific [START_REF] Moran | The Acanthaster phenomenon[END_REF][START_REF] Endean | Acanthaster planci populations outbreaks[END_REF], and mass mortalities of keystone species, such as the sea urchin Diadema antillarum in the tropical western Atlantic [START_REF] Lessios | Spread of Diadema mass mortality through the Caribbean?[END_REF][START_REF] Hughes | Catastrophes, phase shifts and large scale degradation of a Caribbean coral reef[END_REF]. The effects of these disturbances depend mainly on the temporal and spatial scales under consideration, the structure of the impacted communities, the life-history characteristics and growth forms of the dominant species, the geomorphology and depth of the reef zone, and on the chronology of the previous disturbances [START_REF] Witman | Physical disturbance and community structure of exposed and protected reefs: A case study from St. John, U.S. Virgin Islands[END_REF][START_REF] Connell | A 30-year study of coral abundance, recruitment, and disturbance at several scales in space and time[END_REF][START_REF] Hughes | Multiple stressors on coral reefs: A long-term perspective[END_REF]. These disturbances may have short-term or immediate direct effects, as well as long-term and indirect effects on population and community structures [START_REF] Karlson | Disturbances, coral reef communities, and changing ecological paradigms[END_REF][START_REF] Hughes | Multiple stressors on coral reefs: A long-term perspective[END_REF].

Over the last three decades, the frequency and severity of these natural perturbations, and particularly coral bleaching events, have greatly increased worldwide, and as a consequence, reef communities have suffered unprecedented levels of mortality [START_REF] Wilkinson | Ecological and socio-economic impacts of 1998 coral mortality in the Indian Ocean: An ENSO impact and a warning of future change?[END_REF][START_REF] Hughes | Climate change, human impacts, and the resilience of coral reefs[END_REF][START_REF] Pandolfi | Global trajectories of the long-term decline of coral reef ecosystems[END_REF]. In this context of increasing degradation of coral reefs, coral reef surveys have become commonplace as a means to document changes in reef communities (i.e. "monitoring") and the impacts of natural disturbances. Moreover, there has been also a major effort to develop methodologies for detecting changes in reef communities, and to determine reliable indicators of such changes [START_REF] Devantier | Ecological assessment of a complex natural system: A case study from the Great Barrier Reef[END_REF][START_REF] Hodgson | A global assessment of human effects on coral reefs[END_REF][START_REF] Dale | Challenges in the development and use of ecological indicators[END_REF][START_REF] Jameson | Charting a course toward diagnostic monitoring: A continuing review of coral reef attributes and a research strategy for creating coral reef indexes of biotic integrity[END_REF][START_REF] Diamant | MARS: Biological indicators of natural and man-made changes in marine and coastal waters: Scientific coordinators' introduction[END_REF][START_REF] Brown | Developement of benthic sampling methods for the Coral Reef Assessment and Monitoring Program (CRAMP) in Hawai'i[END_REF][START_REF] Hallock | Coral-reef risk assessment from satellites to molecules: A multi-scale approach to environmental monitoring and risk assessment of coral reefs[END_REF]. Two major types of coral reef monitoring surveys can be distinguished: 1) those that have focused on large scales (regional to global; [START_REF] Aronson | Large-scale, long-term monitoring of Caribbean coral reefs: Simple, quick, inexpensive techniques[END_REF][START_REF] Ninio | Temporal patterns in coral assemblages on the Great Barrier Reef from local to large spatial scales[END_REF][START_REF] Ninio | Spatial patterns in benthic communities and the dynamics of a mosaic ecosystem on the Great Barrier Reef, Australia[END_REF], including international monitoring networks such as the global coral reef monitoring network (GCRMN, in Wilkinson 1998), Reef Check [START_REF] Hodgson | A global assessment of human effects on coral reefs[END_REF]2000), coral reef assessment and monitoring program (CRAMP) in Hawaii [START_REF] Brown | Developement of benthic sampling methods for the Coral Reef Assessment and Monitoring Program (CRAMP) in Hawai'i[END_REF][START_REF] Jokiel | Hawai'i Coral Reef Assessment and Monitoring Program: Spatial patterns and temporal dynamics in reef coral communities[END_REF], or "Commission de l'Océan Indien" (COI; [START_REF] Conand | Guidelines: Coral reef monitoring in the South-West region of the Indian Ocean[END_REF]; and 2) those that have examined reef community changes at smaller scales (reef zone or island; [START_REF] Chou | Temporal variation in a coral reef community at Pattaya Bay, Gulf of Thailand[END_REF][START_REF] Witman | Physical disturbance and community structure of exposed and protected reefs: A case study from St. John, U.S. Virgin Islands[END_REF][START_REF] Bythell | Initial results of a long-term coral reef monitoring program: Impact of cyclone Hugo at Buck Island Reef National Monument, St. Croix, US Virgin Islands[END_REF][START_REF] Dollar | Recurrent storm disturbance and recovery: A long-term study of coral communities in Hawaii[END_REF][START_REF] Andres | Trends in community structure on a Jamaican reef[END_REF][START_REF] Shulman | Changes in the coral reefs of San Blas, Caribbean Panama: 1983-1990[END_REF][START_REF] Geister | Biotic changes in the reef complex of San Andres Island (southwestern Caribbean Sea, Colombia) occurring over nearly three decades[END_REF][START_REF] Ledesma | Coral reef monitoring in Tubbataha Reef National Marine Park, Sulu Sea, Philippines[END_REF][START_REF] Chabanet | Coral reef monitoring at Reunion island (Western Indian Ocean) using the GCRMN method[END_REF][START_REF] Edmunds | Long-term dynamics of coral reefs in St. John, US Virgin Islands[END_REF]. However, few surveys have documented the effects of natural disturbances on the dynamic of coral assemblages at multiple spatial scales (Done 1992b;[START_REF] Jokiel | Hawai'i Coral Reef Assessment and Monitoring Program: Spatial patterns and temporal dynamics in reef coral communities[END_REF]).

To address this limitation of most coral reef monitoring projects, in 1992 we initiated a monitoring program that includes 13 islands (eight atolls and five high volcanic islands) in four of the five archipelagoes in French Polynesia, with the goal of documenting the effects of natural perturbations on coral assemblages at both local (between sites around an island separated from few meters to kilometers) and regional (between islands and archipelagoes, separated by up to 1880 km) scales. All surveys were conducted on the outer reef slope, since anthropogenic disturbances, such as dredging, construction activities, sewage discharges and runoffs, which may have important impacts on fringing reef communities, have a negligible one on the reef slope of high islands and atolls [START_REF] Salvat | Conséquences écologiques des activités d'une zone d'extraction de sable corallien dans le lagon de Moorea (île de la Société, Polynésie française)[END_REF][START_REF] Galzin | Variation interannuelle des peuplements récifaux du récif-barrière de Tiahura (île de Moorea, Polynésie française)[END_REF]. This multi-spatial scale survey complements our knowledge on the temporal variability and local-scale spatial patterns of benthic communities of Moorea [START_REF] Fagerstrom | Reef flat community dynamics, Tiahura, Moorea Island, French Polynesia: I. Degradation 1971-1987[END_REF][START_REF] Galzin | Long-term coral reef monitoring program: Heterogeneity of the Tiahura Barrier Reef (Moorea, French Polynesia)[END_REF]Adjeroud 1997a;[START_REF] Galzin | Variation interannuelle des peuplements récifaux du récif-barrière de Tiahura (île de Moorea, Polynésie française)[END_REF][START_REF] Adjeroud | Natural disturbances and interannual variability of coral reef communities on the outer slope of Tiahura (Moorea, French Polynesia): 1991 to 1997[END_REF].

In the present paper, we explore the results obtained during the first decade 1992-2002 (some preliminary results have been previously published in [START_REF] Salvat | Status of South East and Central Pacific Coral Reefs "Polynesia Mana Node": Cook Islands, French Polynesia, Kiribati, Niue, Tokelau, Tonga, Wallis and Futuna[END_REF][START_REF] Salvat | Status of Southeast and Central Coral Reefs "Polynesia Mana Node" 2002: Cook Islands, French Polynesia, Kiribati, Niue, Tokelau, Tonga, Wallis and Futuna[END_REF][START_REF] Salvat | French Polynesia Coral Reefs Status and Resources Report[END_REF], and discuss the adequacy of our approach in the context of recent initiatives to develop methodologies and indicators to assess coral reef health [START_REF] Jameson | Charting a course toward diagnostic monitoring: A continuing review of coral reef attributes and a research strategy for creating coral reef indexes of biotic integrity[END_REF][START_REF] Hallock | Coral-reef risk assessment from satellites to molecules: A multi-scale approach to environmental monitoring and risk assessment of coral reefs[END_REF][START_REF] Ben-Tzvi | Deterioration Index (DI): A suggested criterion for assessing the health of coral communities[END_REF]). The purpose of reviewing the recent strategies to detect the impacts of natural disturbances on coral reefs is to assist coral reef managers in their decision-making processes, notably in French Polynesia where enforcement of reef management is much needed [START_REF] Hutchings | The current status of coral reef management in French Polynesia[END_REF]Salvat and Aubanel 2002).

Materials and methods

Study sites

French Polynesia covers a vast region of the eastern Indo-Pacific province. It comprises five archipelagoes, including 34 high volcanic islands and 84 atolls, which represents a surface area of 4000 km 2 of land. The tides are semi-diurnal, with an amplitude rarely exceeding 40 cm. A total of 15 cyclones that have affected French Polynesia have been reported since the 1980s: in [START_REF] Pearson | Recovery and recolonization of coral reefs[END_REF][START_REF] Kaufman | Effects of Hurricane Allen on reef fish assemblages near Discovery Bay, Jamaica[END_REF][START_REF] Moran | The Acanthaster phenomenon[END_REF][START_REF] Brown | Assessing environmental impacts on coral reefs[END_REF], 1990[START_REF] Glynn | Coral reef bleaching in the 1980s and possible connections with global warming[END_REF], and 1997 (Météo France). During the same period, major bleaching events have occurred [START_REF] Kaufman | Effects of Hurricane Allen on reef fish assemblages near Discovery Bay, Jamaica[END_REF]: in , 1984[START_REF] Brown | World wide death of corals -natural cyclical events or man-made pollution?[END_REF][START_REF] Glynn | Coral reef bleaching in the 1980s and possible connections with global warming[END_REF]: in , 1994: in , 1998: in , and 2002[START_REF] Salvat | Blanchissement et mortalité des scléractiniaires sur les récifs de Moorea (archipel de la Société) en 1991[END_REF][START_REF] Gleason | Effects of disturbance on coral communities: Bleaching in Moorea, French Polynesia[END_REF][START_REF] Hoegh-Guldberg | Periodic mass-bleaching and elevated sea temperatures: Bleaching of outer reef slope communities in Moorea, French Polynesia[END_REF][START_REF] Galzin | Variation interannuelle des peuplements récifaux du récif-barrière de Tiahura (île de Moorea, Polynésie française)[END_REF]Mumby et al. 2001a,b; Penin and Adjeroud data not pub.). In Moorea, these bleaching events corresponded to periods when sea surface temperatures (SSTs) rose above 29.2 • C (i.e., the thermal threshold; Hoegh-Guldberg and [START_REF] Hoegh-Guldberg | Periodic mass-bleaching and elevated sea temperatures: Bleaching of outer reef slope communities in Moorea, French Polynesia[END_REF][START_REF] Adjeroud | Natural disturbances and interannual variability of coral reef communities on the outer slope of Tiahura (Moorea, French Polynesia): 1991 to 1997[END_REF]. Several Acanthaster planci outbreaks also occurred between 1978 and 1984 [START_REF] Bouchon | Quantitative study of scleractinian coral communities of Tiahura Reef (Moorea Island, French Polynesia)[END_REF][START_REF] Faure | Degradation of coral reefs at Moorea Island (French Polynesia) by Acanthaster planci[END_REF]), but have not occurred since, possibly because of the seastar-collecting campaigns organized by French Polynesian authorities. An inventory of major natural disturbances that have affected French Polynesian islands is presented (Table 1).

Sampling strategy and data analysis

Our monitoring survey focused on 13 islands, including five high volcanic islands (Bora Bora, Moorea, Raiatea, Tahiti, Tubuai) and eight atolls (Aratika, Marutea Sud, Mataiva, Nengo Nengo, Rangiroa, Takapoto, Tetiaroa, Tikehau), located on four archipelagoes (Fig. 1). A total of 20 sites were situated on these islands. On Moorea and Tahiti, six and three sites were established, respectively, whereas only one site was established on each of the other islands/atolls. On Tahiti, the three sites (Tahiti Wharf, Tahiti Pass, and Tahiti Airport) were separated by approximately 5 km (Fig. 1). In Moorea, four sites were located on the same area and separated by approximately 40 m (Moorea Tiahura 1-2, Moorea Tiahura 3-4, Moorea Tiahura 5-6, and Moorea Tiahura 7-8; [START_REF] Adjeroud | Natural disturbances and interannual variability of coral reef communities on the outer slope of Tiahura (Moorea, French Polynesia): 1991 to 1997[END_REF]. These four sites were separated from the two others sites of the island (Moorea Haapiti, and Moorea Vaipahu) by approximately 10 km) (Fig. 1). This sampling design allowed us to focus on the regional scale (between islands and archipelagoes, separated by 14 to 1880 km), but also to examine the local scale (between sites around an island separated from few meters to 10 km). The monitoring sites were located on the outer reef slope, around 10 m depth, since it is the place of highest diversity and abundance of coral assemblages (Adjeroud 1997a). Moreover, the reef slope has quite similar geomorphological features from one island to another, which allows better inter-island comparisons. The reef slope is also the place where anthropogenic perturbations are less intense, and are thus mainly under the influences of natural events.

Between 1992 and 1997, the sites were surveyed every one to four years, whereas from 1997 they were surveyed at least once every two years. Each study site consists of two permanent stainless stakes separated by 20 m. During the surveys, a stainless cable was stretched between the two stakes, and 20 metal markers were used to mark the position of 1 m 2 quadrat that was subdivided into 81 squares with string. A photograph of the quadrat was taken at each position with a Nikonos V Body camera equiped with a Nikkor 15 mm lens, a SB 104 flash and a Fuji Velvia film fine-grained low-sensibility photographic (ASA 50). On the films, dead and living coral colonies were distinguished at the generic level. Living coral cover values were obtained by the ratio of the number of points (rope cross) under which a living colony was identified to the total number of points (81) in the quadrat. Coral cover values between years were compared using a t test [START_REF] Scherrer | Small-scale distribution of great barrier reef bioeroding sponges in shallow water[END_REF]. Trends in temporal variability were analyzed using a Principal Component Analysis (PCA). The analysis was done with cover values (raw data were log (x + 1) transformed) of the six dominant coral genera obtained at the 20 sites during the study period (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002). In the biplot, successive surveys for each site were linked in order to visualize the extent and characteristics of the temporal variability. Trends in temporal variability of coral cover of the six major genera were then compared among the 20 sites.

Results

Table 2 presents coral cover values obtained between 1992 and 2002 at the 20 sites surveyed on the 13 islands. Coral cover ranged from 2.2% (Raiatea 2000) to 57.9% (Tahiti Wharf 2001), but there was high variation among sites on different islands, and significant but less pronounced variation among sites of the same island (Moorea and Tahiti).

For most of the sites, a significant temporal variability was found among successive surveys. Three major temporal trends were distinguished: 1) sites where coral cover decreased over the course of the study: Aratika, Mataiva, Moorea Vaipahu, Nengo Nengo, Raiatea, Tahiti Airport, Tahiti Pass, Takapoto, Tetiaroa, Tikehau; 2) sites where coral cover increased: Bora Bora, Marutea Sud, Moorea Tiahura 1-2, Moorea Tiahura 3-4, Moorea Tiahura 5-6, Moorea Tiahura 7-8, Moorea Haapiti, Tahiti Wharf, Tubuai; and 3) a site, Rangiroa, where no significant variation among successive surveys was observed.

For the first category, the sharp decrease in coral cover always was associated with the occurrence of major natural disturbances. The 1998 bleaching event was probably responsible of the decrease in coral cover observed in Aratika, Mataiva, Nengo Nengo, Tahiti Airport, Tahiti Pass, Takapoto and Tikehau. Cyclones caused by the 1997-1998 El Niño Southern Oscillation event could be also associated with the coral decline recorded at Mataiva, Raiatea and Tikehau. However, several sites that were impacted by one of these natural perturbations showed no signs of coral cover decrease, but instead, some sites showed a trend of increase during this period (Bora Bora, Moorea Tiahura 1-2, Moorea Tiahura 3-4, Moorea Tiahura 5-6, Moorea Tiahura 7-8, Moorea Haapiti, Tahiti Wharf). For sites where no major perturbations were reported (Tubuai, Marutea Sud), coral cover increased.

Since the responses to natural perturbations can be different among coral genera, we examined the variability of cover values for the six dominant coral genera. We focused on two sites that were subjected to different stresses: Aratika was affected by the 1998 bleaching event, whereas Raiatea was impacted by two successive cyclones in 1997 (Martin in October, and Osea in November). In Aratika, surveys made before (August 1997) and after (June 1999) the event showed that coral cover clearly decreased for Acropora (4.3% in 1997, 0.5% in 1999) and Pavona (0.6% in 1997, 0.1% in 1999), whereas the decrease was less pronounced for other genera (Fig. 2). In Raiatea, the highest decrease in coral cover was found for Acropora (3.5% in 1994, 0.4% in 1998) and Pocillopora (2.0% in 1994, 0.6% in 1998), and to a lesser degree for Montipora (0.6% in 1994, 0.2% in 1998; Fig. 2). In contrast, the two other genera observed at this site, Pavona and Porites (massive growth forms), showed a slight increase in cover between successive surveys.

Trends in temporal variability of coral cover of the six major genera among the 20 sites were analyzed using a PCA. The cumulative percentage of variance of the first two axes of the PCA was 59.32%. Axis 1 (38.43%) was positively correlated to all six coral genera, whereas axis 2 (20.89%) was positively correlated to Pocillopora and Porites, and negatively to Montastrea (Table 3). These correlations explained, for example, the position of Marutea (high coral cover, notably for Acropora and Montastrea), Bora Bora (high coverages of Pocillopora), or Tubuai (low coverage values, particularly for Pocillopora and Porites) sites on the biplot of the PCA (Fig. 3). The biplot also showed that the patterns in temporal variability of coral cover of the six major genera were clearly different among the 20 sites (Fig. 3). A relatively high variation was found at Aratika, Mataiva, Nengo Nengo and Raiatea, whereas this temporal variability was less pronounced in Bora Bora, Marutea Sud, Rangiroa, Takapoto, or Tubuai (Fig. 3a). In Moorea, the pattern of temporal variability was relatively similar among the four sites located at Tiahura (Moorea Tiahura 1-2, Moorea Tiahura 3-4, Moorea Tiahura 5-6, Moorea Tiahura 7-8), whereas Moorea Vaipahu and Moorea Haapiti showed distinct patterns (Fig. 3b). In Tahiti, patterns of temporal variability of the six major genera were different among the three sites (Tahiti Airport, Tahiti Pass, Tahiti Wharf; Fig. 3c).

Discussion

Impact of natural perturbations on French Polynesian coral reefs

During the 10 year period of this survey (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002), French Polynesian reefs were subjected to three major coral [1992][1993][1994][1995][1996][1997][1998][1999][2000][2001][2002]. The percentage of variance of the first two axes are given. Successive surveys for each site were linked in order to visualize the extent and characteristics of the temporal variability. The six sites around Moorea (b), and the three sites around Tahiti (c) were plotted on separate figures to ease legibility.

bleaching events (1994,1998,2002) and three cyclones (1997) that were generated by El Niño Southern Oscillation events. Among the 13 islands selected in our survey, only two, Marutea Sud and Tubuai, were not affected by one of these disturbances. If we add major disturbances recorded before the beginning of this survey, it is a total of seven bleaching events, 15 cyclones, and several Acanthaster planci outbreaks that have affected French Polynesian coral reefs since the 1980s.

As for many other coral reefs worldwide, this increasing frequency of disturbances is a major concern for coral reef health, and several models predict that this trend will continue in the coming decades, largely as a result of the effects of global warming [START_REF] Hoegh-Guldberg | Climate change, coral bleaching and the future of the world's coral reefs[END_REF]2002;[START_REF] Wilkinson | Ecological and socio-economic impacts of 1998 coral mortality in the Indian Ocean: An ENSO impact and a warning of future change?[END_REF][START_REF] Hughes | Climate change, human impacts, and the resilience of coral reefs[END_REF][START_REF] Pandolfi | Global trajectories of the long-term decline of coral reef ecosystems[END_REF]. Our results show that the impacts of a natural disturbance such as bleaching events or cyclones may be largely variable among different sites around an island, and among islands within a region. This local and regional variability of the impacts of disturbances complements the variability reported on other reefs around the world [START_REF] Edmunds | The importance of sampling scale in ecology: Kilometer-wide variation in coral reef communities[END_REF][START_REF] Hughes | Multiple stressors on coral reefs: A long-term perspective[END_REF][START_REF] Edmunds | Long-term dynamics of coral reefs in St. John, US Virgin Islands[END_REF][START_REF] Kramer | Transient and lethal effects of the 1998 coral bleaching event on the Mesoamerican reef system[END_REF][START_REF] Ninio | Spatial patterns in benthic communities and the dynamics of a mosaic ecosystem on the Great Barrier Reef, Australia[END_REF]. An interannual survey of reef communities at Tiahura, Moorea, showed that the mortality of coral colonies following a bleaching event was decreasing with successive events, even if the latter have the same intensity [START_REF] Adjeroud | Natural disturbances and interannual variability of coral reef communities on the outer slope of Tiahura (Moorea, French Polynesia): 1991 to 1997[END_REF]. This spatial and temporal variability of the impacts observed at several scales during the present and previous surveys may reflect an acclimation and/or adaptation of local populations. In fact, coral colonies and/or their endosymbiotic zooxanthellae may be phenotypically (acclimation) and possibly genotypically (adaptation) resistant to bleaching events [START_REF] Rowan | Landscape ecology of algal symbionts creates variation in episodes of coral bleaching[END_REF][START_REF] Hoegh-Guldberg | Climate change, coral bleaching and the future of the world's coral reefs[END_REF][START_REF] Kinzie | The adaptive bleaching hypothesis: Experimental tests of critical assumptions[END_REF][START_REF] Coles | Coral bleaching -Capacity for acclimatization and adaptation[END_REF].

The results of our long-term monitoring program also show that the impacts of bleaching events and cyclones differ between coral genera, perhaps in relation to their life-history traits. The decline in coral cover attributed to bleaching events was particularly evident for Acropora species, a genus that is particularly susceptible to increasing SSTs [START_REF] Salvat | Blanchissement et mortalité des scléractiniaires sur les récifs de Moorea (archipel de la Société) en 1991[END_REF][START_REF] Gleason | Effects of disturbance on coral communities: Bleaching in Moorea, French Polynesia[END_REF][START_REF] Hoegh-Guldberg | Periodic mass-bleaching and elevated sea temperatures: Bleaching of outer reef slope communities in Moorea, French Polynesia[END_REF][START_REF] Fujioka | Mass destruction of the hermatypic corals during a bleaching event in Ishigaki Islands, southwestern Japan[END_REF][START_REF] Sugihara | Coral bleaching, geological ranges, and adaptation to high sea surface temperatures[END_REF][START_REF] Obura | Can differential bleaching and mortality among coral species offer useful indicators for assessment and management of reefs under stress?[END_REF]. For cyclones, the physical damages concerned mainly branching species of Acropora and Pocillopora, has occurred on many other coral reefs [START_REF] Randall | Effects of typhoon Pamela on the coral reefs of Guam[END_REF][START_REF] Highsmith | Survival of hurricanegenerated coral fragments and a disturbance model of reef calcification/growth rates[END_REF][START_REF] Grigg | Coral reef in an urban embayment in Hawaii: A complex case history controlled by natural and anthropogenic stress[END_REF]. In contrast, massive species such as Porites apparently were not affected by either of these disturbances, at least in term of coral cover [START_REF] Salvat | Blanchissement et mortalité des scléractiniaires sur les récifs de Moorea (archipel de la Société) en 1991[END_REF][START_REF] Gleason | Effects of disturbance on coral communities: Bleaching in Moorea, French Polynesia[END_REF][START_REF] Hoegh-Guldberg | Periodic mass-bleaching and elevated sea temperatures: Bleaching of outer reef slope communities in Moorea, French Polynesia[END_REF][START_REF] Fujioka | Mass destruction of the hermatypic corals during a bleaching event in Ishigaki Islands, southwestern Japan[END_REF]. Thus, the spatio-temporal variability of the impacts of a perturbation is also dependent, at least in part, on the species composition of coral assemblages.

Strategies for monitoring coral reef health and perturbation impacts

Our large-scale monitoring survey was initiated to detect the impacts of natural perturbations, particularly cyclones and bleaching events, on coral assemblages in French Polynesia. After a decade in which several major disturbances were recorded, it is timely to examine the adequacy and effectiveness of our approach in the context of the recent effort to define sampling strategies and indicators of reef degradation following disturbances [START_REF] Jameson | Charting a course toward diagnostic monitoring: A continuing review of coral reef attributes and a research strategy for creating coral reef indexes of biotic integrity[END_REF][START_REF] Diamant | MARS: Biological indicators of natural and man-made changes in marine and coastal waters: Scientific coordinators' introduction[END_REF][START_REF] Hallock | Coral-reef risk assessment from satellites to molecules: A multi-scale approach to environmental monitoring and risk assessment of coral reefs[END_REF]). Concerning the sampling strategy, our results clearly demonstrate the importance of integrating multiple scales in monitoring programs, as suggested by previous reports [START_REF] Edmunds | The importance of sampling scale in ecology: Kilometer-wide variation in coral reef communities[END_REF][START_REF] Edmunds | Long-term dynamics of coral reefs in St. John, US Virgin Islands[END_REF]Miller et al. 2002;[START_REF] Ninio | Spatial patterns in benthic communities and the dynamics of a mosaic ecosystem on the Great Barrier Reef, Australia[END_REF]. A possible way to take into account the local-scale variability is to select several sampling sites around each island, thus defining a hierarchical sampling design. High resolution images from satellite or airborne remote sensing could be also relevant for detecting this kilometer-wide variation, but these techniques generally are restricted to shallow and clear waters [START_REF] Ammenberg | Detection of coral bleaching using high spatial resolution satellite images[END_REF][START_REF] Andréfouët | Choosing the appropriate spatial resolution for monitoring coral bleaching events using remote sensing[END_REF]Yamano and Tamura 2002;Yamano et al. 2002;[START_REF] Mumby | The cover of living and dead corals from airborne remote sensing[END_REF]). An interesting perspective is also the recent method of the photo-tow developped by Chancerelle (unpublished data). This method allows the collection of coral cover data over large distances, thereby providing a quantitative analysis of the impact of disturbances at the island scale, as it was successfully done for the effects of bleaching on the reefs of Moorea (Chancerelle et al. unpublished data).

The results of our monitoring program provide clear evidence of selective mortality among coral species under natural disturbances. Species of Acropora and Pocillopora clearly are the most sensitive to bleaching events and cyclones. Morevover, other reports showed that these two genera are also particularly sensitive to Acanthaster planci predation [START_REF] Moran | The Acanthaster phenomenon[END_REF][START_REF] Faure | Degradation of coral reefs at Moorea Island (French Polynesia) by Acanthaster planci[END_REF]). Thus, it appears necessary to include and to focus on the dynamic of these two genera in monitoring programs on the impacts of natural disturbances.

Several descriptors recently have been proposed as indicators for the detection of the impacts of natural disturbances. Ideally, an effective indicator has to be relevant to the specified assessment objectives, easy to measure and interpret, and must also be sensitive to environmental effects. Additionally, it should have a high information content, and must be able to discriminate human-induced changes from natural variation [START_REF] Grigg | Natural and anthropogenic disturbance on coral reef ecology[END_REF][START_REF] Dale | Challenges in the development and use of ecological indicators[END_REF]. Clearly, the development of such standardized and reliably indicators is ad i fficult task, partly because the degradation of coral reef ecosystems and the subsequent mortality of reef organisms can be the consequence of one or several environmental factors, that can covary, and may act in synergy.

Most of the indicators currently available to detect the effects of natural disturbances on coral reefs concern scleractinian corals, which are particularly sensitive to environnemental disturbances [START_REF] Adjeroud | Natural disturbances and interannual variability of coral reef communities on the outer slope of Tiahura (Moorea, French Polynesia): 1991 to 1997[END_REF]. In the past, the most commonly used descriptors to detect coral reef degradation were species richness and diversity indexes, density/abundance of colonies, and living/dead coral coverages. In recent years, several coral descriptors were proposed to be used as indicators of reef health (Table 4). Other authors have also proposed multimetric indexes, such as the Molecular Biomarker System [START_REF] Downs | A molecular biomarker system for assessing the health of coral (Monstastraea faveolata) during heat stress[END_REF][START_REF] Woodley | A novel diagnostic system to assess the physiological status of corals[END_REF], the rarity and coral indexes [START_REF] Devantier | Ecological assessment of a complex natural system: A case study from the Great Barrier Reef[END_REF], the coral vitality indices [START_REF] Gomez | A review of the status of Phillipine reefs[END_REF][START_REF] Ginsburg | Rapid assessment of reef condition using coral vitality[END_REF], the [START_REF] Black | Heat shock Protein induction in Montastraea faveolata and Aiptasia pallida exposed to elevated temperatures[END_REF][START_REF] Fang | Methodology and measurement of ATP in coral[END_REF][START_REF] Sharp | Heat Shock Protein (HSP 70) expression in the tropical reef coral Goniopora djiboutiensis[END_REF][START_REF] Tom | Molecular characterization of the first Heat Shock Protein 70 from a reef coral[END_REF] biodiversity value [START_REF] Done | Ecological criteria for evaluating coral reefs and their implications for managers and researchers[END_REF], the coral reef health index [START_REF] Hodgson | A global assessment of human effects on coral reefs[END_REF], and the Deterioration Index [START_REF] Ben-Tzvi | Deterioration Index (DI): A suggested criterion for assessing the health of coral communities[END_REF]. These multimetric indicators are supposed to be more sensitive since they may respond to several stresses. However, the effectiveness and reliability of some of these potential indicators were severely critiqued [START_REF] Brown | Assessing environmental impacts on coral reefs[END_REF][START_REF] Brown | Evaluation of the environmental impact of dredging on intertidal coral reefs at Ko Phuket, Thailand, using ecological and physiological parameters[END_REF][START_REF] Edinger | Normal coral growth rates on dying reefs: Are coral growth rates good indicators of reef health?[END_REF]. Moreover, several of these indicators are difficult to incorporate into long-term monitoring programs, since they generally involve expensive equipements and laborious laboratory analyses, and need technical expertise to be interpreted.

Despite the fact that corals are the key component of the reef ecosystem, measuring the effects of disturbances on other target reef communities may offer complementary information to assess changes in coral reef community structure, especially of the cascading effects that follow a major disturbance. For example, surveys of temporal trends of the coral/macroalgae or coral/clionid cover (Schönberg 2001;[START_REF] Schönberg | Induced colonization of corals by a clionid bioeroding sponge[END_REF][START_REF] Bouchon | Critères d'évaluation de la dégradation des communautés coralliennes dans la région Caraïbe[END_REF]), bioeroder organisms [START_REF] Holmes | Eutrophication and its effect on bioeroding sponge communities[END_REF], or disease incidence and virulence of some marine invertebrates [START_REF] Harvell | Emerging marine diseases -Climate links and anthropogenic factors[END_REF], may provide complementary indication of reef health. Mortality rates and changes in benthic and fish assemblages following natural disturbances may also be indicative of the intensity of the impacts [START_REF] Kaufman | Effects of Hurricane Allen on reef fish assemblages near Discovery Bay, Jamaica[END_REF][START_REF] Williams | Temporal variation in the structure of reef slope fish communities (central Great Barrier Reef): Short-term effects of Acanthaster planci infestation[END_REF][START_REF] Chabanet | Disturbances impact on reef fish communities in Reunion Island (Indian Ocean)[END_REF][START_REF] Lewis | Effects of experimental coral disturbance on the population dynamics of fishes on large patch reefs[END_REF][START_REF] Lindahl | The 1997/1998 Mass Mortality of Corals: Effects on Fish Communities on a Tanzanian Coral Reef[END_REF].

The critical analysis of the available information and our results lead us to think that monitoring surveys could be improved by selecting different and complementary indicators, as suggested by several authors [START_REF] Dale | Challenges in the development and use of ecological indicators[END_REF][START_REF] Hallock | Coral-reef risk assessment from satellites to molecules: A multi-scale approach to environmental monitoring and risk assessment of coral reefs[END_REF][START_REF] Niemi | Application of ecological indicators[END_REF]. In order to detect the impacts of natural disturbances on coral assemblages, we propose to integrate three types of coral indicators: one that gives information of the variation in diversity (the generic richness, which avoid the identification difficulties, is sufficiently informative), one estimating changes in the abundance/coverage, and one estimating the potential for recovery following the disturbance (for example, by studying the density of recruits/juveniles; [START_REF] Pearson | Recovery and recolonization of coral reefs[END_REF][START_REF] Connell | A 30-year study of coral abundance, recruitment, and disturbance at several scales in space and time[END_REF][START_REF] Mcclanahan | Bleaching damage and recovery potential of Maldivian coral reefs[END_REF][START_REF] Ridgway | Reef recovery in disturbed coral reef ecosystems[END_REF][START_REF] Ben-Tzvi | Deterioration Index (DI): A suggested criterion for assessing the health of coral communities[END_REF].

Conclusion

Despite the recent efforts to identify and select indicators of reef health, it is clear that there is much to be done before standardized and reliably indicators of the impacts of natural disturbances on coral reef health are developed (see [START_REF] Dale | Challenges in the development and use of ecological indicators[END_REF][START_REF] Jameson | Charting a course toward diagnostic monitoring: A continuing review of coral reef attributes and a research strategy for creating coral reef indexes of biotic integrity[END_REF]. There is a critical need for additional physiological and observation studies to identify indicators species of certain type of perturbations [START_REF] Jameson | Charting a course toward diagnostic monitoring: A continuing review of coral reef attributes and a research strategy for creating coral reef indexes of biotic integrity[END_REF]. Measuring molecular parameters appears difficult within the framework of a monitoring program, and yet there is also an urgent need to develop reliable technologies to quickly determine the coral physiological status.

However, "classical" monitoring surveys may provide usefull information on the impacts of natural perturbations on reef communities. These surveys could be largely improved, by clearly integrating several spatial scales, by selecting at least the most informative species, and by focussing on three main types of indicators: diversity, abundance/coverage, and recruitment/recovery patterns. These monitoring programs should be also associated with high frequency recordings of environmental parameters (such as SSTs), as a complementary tools for identifying causal relationships. However, the type of monitoring programs that could be initiated is largely dependent of practical constraints such as the available expertise, logistic and fundings [START_REF] Brown | Developement of benthic sampling methods for the Coral Reef Assessment and Monitoring Program (CRAMP) in Hawai'i[END_REF][START_REF] Niemi | Application of ecological indicators[END_REF].

Fig. 1 .

 1 Fig. 1. Location of the 13 French Polynesian islands (eight atolls and five volcanic high islands) surveyed in the present monitoring program. On Moorea and Tahiti, respectively six and three sites were established, whereas only one site was disposed on the other islands/atolls. In Moorea, the four sites in Tiahura (Moorea Tiahura 1-2, Moorea Tiahura 3-4, Moorea Tiahura 5-6, and Moorea Tiahura 7-8) were separated by approximately 40 m.

Fig. 2 .

 2 Fig. 2. Variation of living coral cover of the six major coral genera in Aratika, which was affected by a bleaching event in 1998, and in Raiatea, which was affected by two successive cyclones in 1997 (Martin in October and Osea in November).

Fig. 3 .

 3 Fig. 3. Plots of the principal component analysis (PCA) performed on the cover values of the six major genera obtained at the 20 sites during the study period(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002). The percentage of variance of the first two axes are given. Successive surveys for each site were linked in order to visualize the extent and characteristics of the temporal variability. The six sites around Moorea (b), and the three sites around Tahiti (c) were plotted on separate figures to ease legibility.

Table 1 .

 1 Major natural disturbances that have affected French Polynesian islands since the 1980s.

Table 1 .

 1 Continued.

Table 2 .

 2 Mean coral cover values (%) obtained during the period 1992-2002 at the 20 sites disposed on the 13 islands of the monitoring survey. Standard errors are given in brackets.

		2002			46.3 (2.0)*	19 Feb.													35.3 (2.0)	14 Sept.
		2001	24.1 (2.1)*	21 Sept.			54.0 (2.8)	27 Sept.	11.0 (1.5)*	4 May	45.4 (2.5)*	15 June	40.7 (2.5)	15 June	34.1 (2.9)*	15 June	48.2 (2.1)*	15 June
		2000			40.7 (19)*	4 March													42.8 (3.5)*	7 June
		1999	19.6 (1.7)*	22 June			54.1 (2.2)	14 Sept.	4.6 (0.6)*	12 Feb.	34.5 (2.8)	14 April	32.9 (1.5)	24 April	26.5 (2.6)	14 April	39.6 (2.7)	14 April
	0.05). Dates of surveys are indicated in italics.	1996 1997 1998	27.7 (2.5)	5 Aug.	32.6 (2.2)	1 Sept.	49.1 (1.9)*	21 May			33.0 (2.6)	7Nov .	31.8 (3.2) 34.0 (2.0)	6Nov . 12 Aug.	27.5 (2.8)	7Nov .	34.9 (2.6)	14 Nov.	29.3 (2.6) 33.2 (3.3)	5Nov . 10 Aug.
	*: values significantly different from previous survey at the same site (t test, p <	1992 1993 1994 1995	Aratika		Bora Bora		Marutea Sud 36.9 (1.5)	1 Aug.	Mataiva 24.8 (1.7) 24.6 (2.9)	1 Sept. 19 July	Moorea	Tiahura	Moorea	Tiahura 3-4	Moorea	Tiahura 5-6	Moorea	Tiahura 7-8	Moorea 16.1 (1.5) 24.9 (2.1)*	Va i p a h u 14 March 8 May	Moorea 12.7 (1.6)	Haapiti 15 Nov.

Table 3 .

 3 Correlations of variables (six dominant coral genera) with first two ordination axes of the PCA performed on the coral cover values obtained at the 20 sites during the study period(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002).

	Variables	Axis 1	Axis 2
	Acropora	0.67	-0.33
	Montastrea	0.49	-0.66
	Montipora	0.57	-0.21
	Pavona	0.52	0.02
	Pocillopora	0.50	0.59
	Porites	0.48	0.50

Table 4 .

 4 Major coral descriptors that have recently been proposed as indicators of coral reef health and perturbation impacts.

	Potential indicators	References
	Growth of adult colonies or transplants	Cortes and Risk 1985; Brown 1988; Guzman et al. 1994; Naim
		et al. 2001
	Skeletal density	Atkinson et al. 1995; Steven and Broadbent 1997
	Partial mortality	Ginsburg et al. 2001; Bouchon et al. 2004
	Tissu regeneration potential	Meesters and Bak 1993
	Depth of skeleton occupied by coral tissue	Barnes and Lough 1992
	Acid-insoluble, metals and phosphorus	Dodge et al. 1984; Hanna and Muir 1990; Edinger
	contents in skeleton	et al. 2000
	Stable isotopes of nitrogen	Mendes et al. 1997; Heikoop et al. 2000
	Size-frequency distribution	Bak and Meesters 1998; 1999; Meesters et al. 2001
	Fecundity of coral colonies	Ward and Harrison 2000
	Recruitment rates	Hunte and Wittenberg 1992; Miller and Barimo 2002
	Coprostanol concentrations	Risk et al. 1994
	RNA/DNA	Meesters et al. 2002
	Lipid content	Harriott 1993
	Stress protein expressions (heat shock proteins and
	ubiquitine)

Acknowledgements. We thank "la Fondation d'entreprise TOTAL" which has funded the coral monitoring network since 2000, the private companies Tahiti Perles (Robert Wan), and Pacific Perles (Dora Fourcade), which have offered field assistance and flight transportation to Marutea, Nengo Nengo and Aratika, "le Service de la Pêche" and "le Service de la Perliculture" for field assistance on Raiatea, Rangiroa and Takapoto. Special thanks to all the local dive buddies and boat pilots who offered assistance and knowledge of the sea. The authors wish to thank P. Edmunds, J. Ferraris, H. Lenihan and three anonymous reviewers for their critical comments and suggestions on the first draft. This work is a contribution to the Nouméa workshop on indicators, that was carried out within the frame of the "Programme National sur l'Environnement Côtier" (PNEC), and to the programme CoRéUs (IRD).


F Sinniger

Ae J I Montoya-Burgos

Ae J Pawlowski

P Chevaldonne´ae

J I Montoya-Burgos

P Chevaldonné

J Pawlowski

Phylogeny of the order Zoantharia (Anthozoa, Hexacorallia) based on the mitochondrial ribosomal genes

Zoantharia (or Zoanthidea) is the third largest order of Hexacorallia, characterised by two rows of tentacles, one siphonoglyph and a colonial way of life. Current systematics of Zoantharia is based exclusively on morphology and follows the traditional division of the group into the two suborders Brachycnemina and Macrocnemina, each comprising several poorly defined genera and species. To resolve the phylogenetic relationships among Zoantharia, we have analysed the sequences of mitochondrial 16S and 12S rRNA genes obtained from 24 specimens, representing two suborders and eight genera. In view of our data, Brachycnemina appears as a monophyletic group diverging within the paraphyletic Macrocnemina. The macrocnemic genus Epizoanthus branches as the sister group to all other Zoantharia that are sampled. All examined genera are monophyletic, except Parazoanthus, which comprises several independently branching clades and individual sequences. Among Parazoanthus, some groups of species can be defined by particular insertion/deletion patterns in the DNA sequences. All these clades show specificity to a particular type of substrate such as sponges or hydrozoans. Substrate specificity is also observed in zoantharians living on gorgonians or anthipatharians, as in the genus Savalia (Gerardia). If confirmed by further studies, the substrate specificity could be used as reliable character for taxonomic identification of some Macrocnemina.

Introduction

The order Zoantharia (= Zoanthidea, Zoanthiniaria) is characterised by colonies of clonal polyps possessing two rows of tentacles, a single ventral siphonoglyph linked together by a coenenchyme. The name Zoantharia is used here to give homogeneity to the order names in subclass Hexacorallia (Actiniaria, Antipatharia, Ceriantharia, etc.). Based on the organisation of septa, the Zoantharia are currently divided in two suborders, Macrocnemina and Brachycnemina (Haddon and Schackelton 1891). The suborders differ by the fifth pair of septa, which is complete in the suborder Macrocnemina (Fig. 1) and incomplete in the Brachycnemina. The separation between both suborders is also supported by the few data available on sexual reproduction. Brachycnemina produce planktonic larvae, called zoanthella or zoanthina depending on the family, whereas no planktonic larvae have been reported for Macrocnemina [START_REF] Ryland | Reproduction in Zoanthidea (Anthozoa: Hexacorallia)[END_REF].

While the separation between the two suborders of Zoantharia is well accepted, the interpretation of families and genera is not always very clear, especially within Macrocnemina. Identification at the species level is also difficult because most diagnoses are incomplete, and type specimens are often missing. The main characters used for species identification are (1) the number of tentacles or septa, (2) the colour, (3) the shape and position of the sphincter muscle and (4) the size and distribution of different types of nematocysts. The position of the sphincter is useful mainly at the generic level whereas the characters associated with nematocysts seem to be useful at the interspecific level but they necessitate a precise analysis of many samples of nematocysts within and between different polyps of a colony [START_REF] Ryland | Use of cnidae in taxonomy: implications from a study of Acrozoanthus australiae (Hexacorallia, Zoanthidea)[END_REF]). Both analyses of sphincter and nematocysts require high-quality histological preparations.

Because of identification problems, zoantharians are often overlooked in ecological surveys in spite of their abundance and cosmopolitan distribution. Some field guides propose the use of ecological factors, such as an association between Zoantharia and their substratum, as alternative criterion for taxonomic identification. However, their specificity to one or a few clearly defined substrate types has not been investigated for most species.

Current classification of Zoantharia (Table 1)i s based exclusively on morphological characters [START_REF] Ryland | Order Zoanthidea (Class Anthozoa, Zoantharia)[END_REF][START_REF] Ryland | Revision of methods for separating species of Protopalythoa (Hexacorallia: Zoanthidea) in the tropical West Pacific[END_REF]. It follows the taxonomic scheme presented by [START_REF] Haddon | Reports on the zoological collections made in Torres Straits by Professor A.C. Haddon, 1888-1889[END_REF], based mostly on septa characteristics (Fig. 2a). [START_REF] Schmidt | On the evolution in the Anthozoa[END_REF] challenged this classification proposing a phylogeny based on cnidome analysis and suggested a derived position of the special microbasic b-mastigophores nematocysts in Parazoanthus and Zoanthus (Fig. 2b). These results were supposed to be supported by sperm structure analyses [START_REF] Schmidt | Die Spermien der Anthozoen und ihre phylogenetische Bedeutung[END_REF], however, in this study, none of Zoanthus species was considered. More recently, Haddon and Shackleton's classification has been supported by a phylogenetic study of allozymes [START_REF] Burnett | Zoanthids (Anthozoa, Hexacorallia) from the Great Barrier Reef and Torres Straits, Australia: Systematics, evolution and a key to species[END_REF] which, however, only focussed on Australian brachycnemic species, using Parazoanthus as an outgroup (Fig. 2c).

In the present study, 24 sequences of mitochondrial 12S and 16S rRNA genes were obtained to infer the molecular phylogeny of the order Zoantharia. These two mitochondrial ribosomal genes were chosen following their successful use in inferring molecular phylogeny of octocorals [START_REF] Sanchez | Phylogenetic analyses among octocorals (Cnidaria): mitochondrial and nuclear DNA sequences (lsu-rRNA, 16S and ssu-rRNA, 18S) support two convergent clades of branching gorgonians[END_REF]scleractinians (Le Goff-Vitry et al. 2004). In the light of our molecular results, morphological characteristics classically used for the classification of Zoantharia are reassessed and their specificity to different types of substrata is discussed.

Material and methods

Sampling

The Zoantharia examined in this study (Table 2) were collected from Honduras and the Mediterranean Sea, by a Only one sample is known from that genus [START_REF] Gravier | Note sur une Actinie (* Thoracactis* n. g., * topsenti* n. sp.) et un Anne´lide Polyche`te (* Hermadion Fauveli* n. sp.), commensaux d'une E ´ponge siliceuse (* Sarostegia oculata* Topsent)[END_REF]) and it was not conserved well enough for genus identification, it could then be any zoantharian but more likely Epizoanthus b Despite the frequent use of the name Gerardia (Lacaze-Duthiers 1864), considering the anteriority rule and the use of this name in recent publications [START_REF] Ha¨ussermann | Zoanthidea. In: Das Mittelmeer, besti-mmungsfu¨hrer Band II/1[END_REF], the name Savalia Nardo, 1844 is used in this publication DNA extraction, PCR amplification and sequencing DNA was extracted using the DNeasy Plant Minikit (QIAGEN) from previously dried ethanol-preserved samples. The following PCR primers were designed: 16Sant1a: 5¢-GCCATGAGTATAGACGCACA-3¢, 16S bmoH: 5¢-CGAACAGCCAACCCTTGG-3¢, 12S1a: 5¢-TAAGTGCCAGCMGACGCGGT-3¢, 12S3r: 5¢-ACGGGCNATTTGTRCTAACA-3¢. PCR amplifications were performed as follows: 2¢ at 94°C, then 40 cycles: 30¢¢ at 94°C, 1¢ at 52°C, 2¢ at 72°C, followed by 5¢ final elongation at 72°C. Direct sequencing was carried out using a BigDye Terminator Cycle Sequencing Ready Reaction Kit (Applied Biosystems). Sequences were runned on an ABI-3100 Avant automatic sequencer. GenBank accession numbers of the obtained sequences are shown in Table 2.

Histology and thin sections

Samples fixed and preserved in 4% seawater formalin were decalcified by chelation and then put into fluorhydric acid to dissolve siliceous sponge spicules and sand grains. Samples were then embedded in paraffin and cut into 8 lmslices. For microscopic observation, the slices were then stained with Masson's trichrome. To assess the presence or absence of a zoantharian secreted layer on the substrate, the antipatharian on which the Cape Verde species was found was cut into thin crosssections. The samples were put into Araldite, and then cut at low speed with a circular saw into slices of 0.5 mm. The sections were polished to a thickness of ca. 0.2 mm. In some cases, sections were then stained with toluidine blue to increase contrast, and obtain information on the tissues around the axis. The same protocol was used to cut several polyps of Parazoanthus axinellae (Fig. 1).

Phylogenetic analysis

Sequences were manually aligned using BioEdit 5.0.9 [START_REF] Hall | BioEdit: a user-friendly biological sequence alignement editor and analysis program for Windows 95/98/NT[END_REF]) and uncertain alignment positions were removed. The methods of maximum likelihood (ML) and Bayesian inference (BI) were used for phylogenetic reconstructions. For ML method, the best evolutionary model was defined using Modeltest [START_REF] Posada | MODELTEST: testing the model of DNA substitution[END_REF]. Robustness of the ML trees was tested by bootstrapping (1,000 replicates). The Kishino-Hasegawa (KH) test [START_REF] Kishino | Evaluation of the maximum likelihood estimate of the evolutionary tree topologies from DNA sequence data, and the branching order in Hominoidea[END_REF] was used to determine if Bayesian topology was significantly different from ML topology. ML method and KH tests were performed using Paup*4.0 beta 10 (Swofford 2002). Bayesian analyses were made using Mr. Bayes 3.0 [START_REF] Huelsenbeck | MrBayes: a program for the Bayesian inference of phylogeny[END_REF].

Results

Species identification

Mediterranean species were identified by using the morphology of the polyps and of the colonies. The specimens of Parazoanthus from Honduras were initially identified based on their presumed substrate specificity [START_REF] Crocker | Host specificity in spongeencrusting Zoanthidea (Anthozoa: Zoantharia) of Barbados, West Indies[END_REF] and confirmed later by the morphology of the polyp and the number of septa. Substrate type (anthipatharian) was also used for preliminary identification of Cape Verde and Principe specimens as belonging to Savalia macaronesica (Ocan˜a and Brito 2003). However, since the main feature distinguishing Savalia from Parazoanthus is the secretion of a scleroprotein layer, this character was examined by thin cross-section analyses. No Zoantharia-secreted axis was observed in specimens from Cape Verde and Principe, their identification as Savalia was not confirmed.

Parazoanthus gracilis was tentatively identified to the species level by histological interpretation and its specificity to the colonised hydrozoan (Plumularia habereri), while Epizoanthus illoricatus was provisionally identified based on the general morphology of the colony and its attachment to a eunicid worm tube. As available literature on Zoantharia contains only few precise descriptions for some of our collection localities, some specimens were not identifiable to the species level.

Phylogenetic analysis

Partial sequences of 12S and 16S mt rDNA were obtained. The sequences of 12S varied in length between 676 bp (Acrozoanthus sp.) and 709 bp (''Yellow polyps''), whereas the sequences of 16S varied between 663 bp (Savalia spp.) and 768 bp (E. paxi, E. vagus). The analyses were performed on both genes separately and then their sequences were concatenated. The concatenated alignment contained 1,210 characters of which 962 were constant and 117 were parsimony informative. The mean base frequencies were A: 0.3076 C: 0.1887 G: 0.2683 T: 0.2454, the homogeneity test of base frequencies showed no significant divergences across taxa (v 2 =37.6941; df=72; P=0.9997).

Since the trees obtained by separate analyses of both genes do not show enough resolution, only the analysis of concatenated sequences is presented here. The phylogeny of Zoantharia inferred using the Bayesian method is shown in Fig. 3. The trees obtained by using Bayesian and ML methods are very similar. They differ only by the relationships between P. puertoricense and Parazoanthus. sp5, which are monophyletic in the Bayesian tree and paraphyletic in the ML tree. The comparison of Bayesian and ML trees using the KH test revealed no significant differences between their topologies (Dln L=0.57557, P= 0.391).

The general structure of Zoantharia tree shows paraphyletic Macrocnemina, within which the Brachycnemina form a monophyletic lineage (Fig. 3). Within the Brachycnemina, two relatively well-supported monophyletic groups can be distinguished. The first group comprises Palythoa and Protopalythoa, and the second group includes Isaurus, Zoanthus and Acrozoanthus. Within Macrocnemina, the genus Epizoanthus branches as a sister group to the rest of Zoantharia analysed. The sequences of the genus Parazoanthus form several independent clades or individual branches. The position of some representatives (P. axinellae, P. sp3 from Sulawesi and P. swiftii) are not resolved. The position of P. parasiticus, branching as a sister group of the Cape Verde/Principe species, is also weakly supported. The white form of P. tunicans (P. tunicans W) appears closer to P. gracilis than to the black form of the same species (P. tunicans B). The specimens of S. savaglia from Mediterranean Sea and S. macaronesica from Canaries have identical sequences. The Cape Verde and Principe specimens initially identified as belonging to S. macaronesica branch independently within the Parazoanthus group of sequences.

Indels as phylogenetic markers

To obtain complementary information on phylogenetic relations among Zoantharia, we identified and analysed several insertion/deletions (indels) that were not included in our phylogenetic analyses (Fig. 4). In the 12S alignment, two indels (V1, V2) are variable in length and sequence whereas a third (V3) consists of a 28 bp insertion in the ''Yellow polyps'' sequence. The 16S fragment contains five variable regions (V4-V8). V4 is an insertion shared only by P. gracilis and P. tunicans that live on hydrozoans. The second variable region V5 is informative at an intergeneric level (Fig. 4). This indel is located within a region corresponding to the domain V of E. coli 23S [START_REF] Beagley | The Mitochondrial genome of the sea anemone Metridium senile (Cnidaria): introns, a paucity of tRNA genes, and a nearstandard genetic code[END_REF]) and supports the monophyly of the following groups: Epizoanthus (V5a), Savalia (V5b), the two specimens from Cape Verde and Principe (V5c), Parazoanthus sp5 from Sulawesi and P. puertoricense (V5d), Parazoanthus sp3 from Sulawesi, P. axinellae, P. swiftii and P. parasiticus (V5e), the ''Yellow polyps'', P. tunicans and P. gracilis (V5f) and the Brachycnemina (V5g). Despite the identical length of the indel, the two brachycnemic families (Sphenopidae and Zoanthidae) can be distinguished by the sequence variations within the V5g indel. The third variable region V6 is a 51-53 bp insertion in Epizoanthus, which corresponds to a polyC (6-8 bp) in the rest of the Zoantharia (only in the two Acrozoanthus does this polyC start with a single T). The fourth variable region V7 consists of a polyC followed by a polyG and the last variable region V8 is an indel variable in size and sequence within the order. In all these regions (V1-V8), the Brachycnemina have almost identical sequences.

Discussion

Molecular phylogeny versus morphological classification of Zoantharia

Traditional morphology-based classification is only partially confirmed by our molecular data. Although the suborder Brachycnemina was found to be monophyletic, the suborder Macrocnemina appears as a paraphyletic group within which Brachycnemina diverged. Our trees confirm the imperfect status of the fifth septum as a synapomorphic trait of Brachycnemina, but the perfect fifth septum in Macrocnemina appears to be a symplesiomorphic trait. In view of our data, Schmidt's ''later'' and ''earlier'' Zoanthidea are not valid groupings, especially concerning the position of the genus Zoanthus, (Fig. 2b). Unfortunately, [START_REF] Schmidt | Die Spermien der Anthozoen und ihre phylogenetische Bedeutung[END_REF] did not examine the sperm structure of the genus Zoanthus and establish its position exclusively on nematocysts study. However, Schmidt's aim was to resolve the relationships within the class Anthozoa rather than to establish the phylogeny of Zoantharia.

At a lower taxonomic level, our study confirms the monophyly of the two families of Brachycnemina: the family Zoanthidae characterised by loss of the ability to incorporate sand grains, spicules and other particles in the column wall and the family Sphenopidae as recently characterised by its ability to incorporate sand in the column wall, a zoanthella larva and the absence of bmastigophore nematocysts in the cnidome [START_REF] Ryland | Semper's (zoanthid) larvae: pelagic life, parentage and other problems[END_REF][START_REF] Ryland | Use of cnidae in taxonomy: implications from a study of Acrozoanthus australiae (Hexacorallia, Zoanthidea)[END_REF]. Within Sphenopidae, the low genetic divergence observed between Palythoa and Protopalythoa confirms the suggestion of [START_REF] Burnett | Zoanthids (Anthozoa, Hexacorallia) from the Great Barrier Reef and Torres Straits, Australia: Systematics, evolution and a key to species[END_REF] that these two genera could be grouped in a single one.

Within Macrocnemina, two of the three examined genera (Savalia, Epizoanthus) are shown to be monophyletic. Only two species collected from the Mediterranean and Canary Islands are considered as belonging to the genus Savalia. These two species have identical sequences, however, they are characterised by different morphology and ecology [START_REF] Ocan˜a | A review of Gerardiidae (Anthozoa: Zoantharia) from the Macaronesian islands and the Mediterranean sea with the description of a new species[END_REF] and therefore, we suspect that the genes examined here are Fig. 3 Bayesian tree of the concatenated mitochondrial 12S and 16S rRNA genes. The Actiniaria used as outgroup is Metridium senile. Posterior probabilities are given as the first number; the second number represents bootstrap values, the nodes supported by the variable regions (not included in the analyses) are marked with a black circle. Although not represented as a monophyletic clade on the tree, the species followed by a white square are supported as monophyletic by insertions too conserved to resolve their interspecific relationships. As shown by our data, the specimens described as S. macaronesica from Cape Verde and Principe form a separate clade and may represent a new genus.

Concerning the genus Epizoanthus, its extremely divergent position is quite unexpected. Indeed, we do not observe striking morphological differences between Epizoanthus and other zoanthids. Our results confirm the validity of the families Epizoanthidae and Parazoanthidae created by [START_REF] Delage | Traite´de Zoologie concre`te Volume 2 les Coelente´re´s[END_REF] essentially based on the position of the sphincter, and the presence/absence of a lacuna in the mesoglea of the column. Within the genus Epizoanthus, E. illoricatus branches separately from the three others confirming the doubts concerning the assignment of this species to this genus, expressed already in its original description (Tischbierek 1930).

The phylogeny of species growing on sponges belonging to the genus Parazoanthus is unresolved. This lack of resolution can be explained by the low divergence between analysed sequences of this genus. Interestingly, significant differences observed in Parazoanthus indels indicate close relationships between species according to their substrate. In view of our data, the diagnostic morphological characters of this genus (endodermic sphincter, well-developed canal system in the mesoglea) should be reconsidered. In the future, new genera could be defined based on molecular groupings, substrate specificity in certain cases and, maybe, a detailed revision of their morphology; although no reliable morphological characters resolving relationships within Parazoanthus have been found until now.

Substrate specificity

Epizoism is a well-known trait of the ecology of Zoantharia, but the causes and the range of this association is not well understood. Macrocnemina live generally attached to different animal substrates. Most of the species of the genus Epizoanthus live at great depths (down to 5,000 m) where hard substrates are seldom found and are usually associated with molluscs, pagurids or stems of hyalonematid glass sponges [START_REF] Ryland | Semper's (zoanthid) larvae: pelagic life, parentage and other problems[END_REF]. Colonies associated with pagurids create a carcinoecium around the shell inhabited by the crustacean. E. illoricatus grows on the tube secreted by a sedentary polychaete belonging to the Eunicidae. This trait of colonisation of eunicid tubes is shared with the brachycnemic genus Acrozoanthus. In this case, the substrate character can be considered homoplasic. The other brachycnemic species live on rocks or are buried in the sand as the genus Sphenopus. In the genera Parazoanthus and Savalia, some species are currently identified according to their substratum, but their morphological identification is not sufficient to confirm the specificity of such relationships.

By resolving the phylogenetic relations among Zoantharia, our study allows us to test substrate specificity in this group. In the genus Parazoanthus, all monophyletic lineages are associated with well-defined substrates. For example, P. tunicans and P. gracilis, which form a relatively well-supported clade, live specifically on hydrozoans. Substrate specificity is also observed in the clade of Parazoanthus sp5 and P. puertoricense found on the sponge Agelas. The monophyly of this group, characterised by very small polyps, is not well supported by posterior probabilities or bootstrap values but both species share the same V5 and V8 indels (Fig. 4), suggesting a close relationship. Indels also indicate close relationships between the other four Parazoanthus living on sponges and characterised by bigger polyps, despite their unclear position in our tree. The situation is similar in the case of genus Savalia, growing on gorgonians or antipatharians, and the species from Cape Verde and Principe growing exclusively on the antipatharian Tanacetipathes cavernicola. If these data are confirmed by further studies, substrate specificity could be used as a reliable indicator for taxonomic identification of some Macrocnemina.

Fig. 1

 1 Fig. 1 Thin cross-section of Parazoanthus axinellae. The lower part of the pharynx is visible on the bottom right, whereas the rest of the picture is in the upper part of the gastric cavity. The numbers indicate the five first pairs of septa (1,3=incomplete; 2,4,5=complete). Sand grains and sponge spicules are incorporated in the ectoderm. S indicates the siphonoglyph

Fig. 2

 2 Fig. 2 Classical phylogenies of Zoantharia, (adapted from Burnett et al. 1997), based on a morphological characters, particularly the septa (Haddon and Schackelton 1891), b nematocysts[START_REF] Schmidt | On the evolution in the Anthozoa[END_REF], and c allozymes[START_REF] Burnett | Zoanthids (Anthozoa, Hexacorallia) from the Great Barrier Reef and Torres Straits, Australia: Systematics, evolution and a key to species[END_REF]

Fig. 4

 4 Fig. 4 Alignment of the second INDEL sequence. The different letters represent different variations in the V5 region

Table 1

 1 Classical organisation of the order Zoantharia

	Class	Subclass	Order	Sub-order	Family	Genus
	Anthozoa	Hexacorallia	Zoantharia	Brachycnemina	Neozoanthidae	Neozoanthus
					Sphenopidae	Palythoa
						Protopalythoa
						Sphenopus
					Zoanthidae	Acrozoanthus
						Isaurus
						Zoanthus
				Macrocnemina	Epizoanthidae	Epizoanthus
						Paleozoanthus (Thoracactis) a
					Parazoanthidae	Isozoanthus
						Parazoanthus Savalia (Gerardia) b

Acknowledgments We are grateful to L. Zaninetti for her enthusiasm and constant support for this study and to H. Zibrowius for his precious naturalist advices and ideas. We thank the divers who collected the samples: M. Boyer and P. Wirtz; J. Wuest and M. Crevecoeur's group (Geneva), C. Bezac and C. Marschal (Marseille) for their help with the histology, J.D. Reimer for his advice on the manuscript, as well as to P. Schuchert and J. Vacelet for help in identification of hydrozoans and sponges. All the experiments comply with the current laws of the country in which they were conducted.


Franck Pierre Palud

Franck Le Petit

Pierre Chainais

Emeric Bron

Pierre-Antoine Thouvenin

Mixture of noises and sampling non log-concave distributions

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

Mixture of noises and sampling non log-concave distributions

Pierre Palud 1,2 , F. Le Petit 1 , P. Chainais 2 , E. Bron 1 , P.-A. Thouvenin 2 , ORIONB consortium 1 LERMA, Obs. de Paris, PSL Research Univ., CNRS, Meudon 2 Univ. Lille, CNRS, Centrale Lille, UMR 9189 -CRIStAL, France

1/ Aims and contributions

Real life inverse problems: multiple noises, non-linear models, need for uncertainty quantification.

Bayesian inference with ¥ Mixture of noises ¥ Non-log-concave posterior (multimodal) ¥ Non-gradient-Lipschitz log-posterior # Likelihood approximation for a mixture of noises, # New kernel to efficiently sample from posterior, # Application to astrophysical data.

2/ Observation model

Forward model f : Θ ∈ R N D → Y ∈ R N L ,
strictly positive, twice differentiable, covers multiple decades.

Observation model:

y n, = max ω, (m) n, f (θ n ) + (a) n, with      ω > 0 (a) n, ∼ N 0, σ 2 a i.i.d. (m) n, ∼ log N 0, σ 2 m i.i.d. =⇒ untractable likelihood π (Y | Θ).
Literature often neglects one noise [START_REF] Nicholson | An additive Approximation to Multiplicative Noise[END_REF]. But when f covers many decades: dominant noise depends on θ n . =⇒ need to address full mixture model. Gaussian approx

1-λ a (θ n ) π (m) (y n, |θ n ) lognormal approx λ a (θ n )
with λ a ∈ [0, 1], twice differentiable, parametrized with a ∈ R 2 =⇒ negative log of this approx: easy to work with.

1 . 2 .

 12 How to approximate the likelihood with controlled error? → See 4/ 4/ Mixture of noises: Likelihood approximation Build 2 likelihood approximations with moment matching: Gaussian approx π (a) lognormal approx π (m) y n, f (θ n ) + e n, ∼ N (m a,n, , s 2 a,n, ) e (m) n, ∼ log N (m m,n, , s 2 m,n, ) Combine approximations with weight function λ a : πa (y n, |θ n ) ∝ π (a) (y n, |θ n )

3 /

 3 Tuning a : Approx error = Kolmogorov-Smirnov-based metric ϕ(a ). ϕ minimized with Bayesian Optimization (BO). From approx error: πa better than π (a) or π (m) alone. grid eval oflog 10 ϕ BO, 25 points f (θ n ) hist. and λ a Bayesian approach & sampling Combine likelihood with informative prior π(Θ): yields Posterior distribution: π(Θ | Y ) ∝ π(Y | Θ) π(Θ) Sampling: MCMC =⇒ uncertainty quantification Model: Non-linear =⇒ multimodal distribution Preconditioned-MALA [2]: local exploration MTM [3]: jumps between minima. 5/ Astrophysics synthetic dataset Θ ∈ R 900×4 : high dimensional π(Θ): spatial (Laplacian L 2 -norm) Forward model: Meudon PDR code [4] non-linear non-gradient-Lipschitz Synthetic observations Y ∈ R 900×10 : integrated intensities of excited lines of CO Θ •1 : Scaling Θ •2 : Pressure Θ •3 : Radiative Θ •4 : Depth Mixture of noises =⇒ likelihood approx. Non-log-concave posterior =⇒ MTM kernel. Non-gradient-Lipschitz log-posterior =⇒ P-MALA kernel. Application on astrophysical inverse problem. ¥ Application to Orion-B data, James Webb Spatial Telescope, etc.


François Lemaire

Louis Roussel

Integral equation modelling and deep learning

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

Integral Equation Modelling and Deep Learning

François Lemaire, Louis Roussel CFHP team, Laboratoire CRIStAL, Université de Lille

Integral equation modelling

Dynamical system ẋ1 (t) = x 2 (t) ẋ2 (t) = θx 1 (t) y(t) = x 2 (t) (known) y(t) -y 0 = θ t 0 τ 2 0 y(τ 1 )dτ 1 dτ 2 + θx 1 (0)t ÿ(t) = θy(t) Integral Elimination Differential Elimination [START_REF] Boulier | The blad libraries[END_REF] [2, Integrate] Algorithm Many models (such as the SIR epidemiology model) consist of non-linear differential equations, involving unknown numerical parameters. Recent work investigates the treatment of integro-differential equations i.e. equations involving both derivatives and integration operators. The introduction of integral equations helps to increase the expressiveness of the models, improve the estimation of parameters and reduce the size of the intermediate equations.

Integration of equations with deep learning [3]

Through learning techniques used for the translation of texts, Lample and Charton [START_REF] Lample | Deep learning for symbolic mathematics[END_REF] succeed in calculating primitives of mathematical expressions, and solutions of differential equations.

The model used is called

Transformer and is widely used in natural language processing [START_REF] Vaswani | Attention is all you need[END_REF]:

• It takes a list of words as input and returns the list of translated words as output,

Adaptation of [3] to integro-differential equations

In order to integrate integro-differential equations, we modified the implementation of [START_REF] Lample | Deep learning for symbolic mathematics[END_REF] (based on PyTorch) to fit our needs.

Generation

The generation process has been modified to handle the ∂ and operators. Time dependent functions have also been added. Thus, the main changes concern the unary-binary tree generator and the use of SymPy to handle these additions.

+ * a 0 ∂ x(t) y(t) f : [+, * , a 0 , ∂, x, , y] f : a 0 ẋ(t) + y(t) f ′ : a 0 ẍ(t) + y(t)

Experiment

For our experiment, we generated functions that include the following operations/operators: +, -, * , ÷, ∂, . We used two functions: x(t), y(t) and a parameter, a 0 . The generated functions are then differentiated in order to obtain pairs (f ′ , f ).

Function f

′ Solution f 1 x -tx ( x) 2 t x (-a 0 x-1) xy+ÿ(t+a 0 x)+a 0 xy x+xyt-a 0 ẏx- ẏ (t+a 0 x) 2 ẏ+ xy t+a 0 x

Conclusion

We achieve a quite good accuracy on the integration of a specific set of integrodifferential equations. Different data generation methods could be investigated (such as [START_REF] Lample | Deep learning for symbolic mathematics[END_REF]IBP and FWD methods]). Our next goal will be focused on the integral elimination of differential systems with deep learning.

Figure 1 :

 1 Figure 1: Modelling, elimination and [2, Integrate] algorithm.

Figure 2 :

 2 Figure 2: A signal, its derivative and its integral (with noise in red).

fFigure 4 :Figure 5 :

 45 Figure 4: Generation process

Table 1 : Accuracy of the model versus the accuracy of Maple.

 1

	Generation 601 000 pairs		Training 600 000 pairs	Evaluation of the accuracy 1 000 pairs
	Accuracy =	number of correct integrals (Figure 5) number of equations of the test dataset
	Figure 6: Learning process and accuracy measurement
				Results
		Accuracy	Comments
	Maple	75.8%	We use int(f, t). Could be enhanced with
				integration by parts, but it is difficult to automate.
	Transformer	96%		Our adapted version of [3].

Table 2 : Functions that the model can integrate, but not Maple.

 2


Caroline Lecroisey

Pierre Chevaldonné

Christophe Lejeusne

Yohan Pillon

Charlotte Dehollain

Claire Lecroisey

Caroline Rocher

Didier Aurelle

Anne Chenuil

Thierry Pérez

Nicole Boury-Esnault

Jean Vacelet

Molecular phylogeography of Mediterranean and Eastern Atlantic sponges of the genus Aplysina

come

Aplysina spp. (Verongida: Aplysinidae) are common Demospongiae represented by 2 described species in the Mediterranean and nearby Atlantic. A. aerophoba, shallow and photophilic, is known from the entire Mediterranean and in the Macaronesian archipelagos, down to Senegal on the West African coast. A. cavernicola, almost identical except for a slightly different color and shape, usually lacks symbiotic Cyanobacteria, and has a very different ecology. A. cavernicola is sciaphilic, being often found at cave entrance or under shaded overhangs. It has been reported from the Mediterranean in the western basin to the Gibraltar Straits, in the Adriatic and the Aegean Seas. In some areas such as the NW basin, the two species have very contrasting ecologies which makes them easy to identify. However in areas such as the eastern basin or the Adriatic, the ecological transition is not so sharp and identification is sometimes difficult. Because the main difference lies in their ecology, it has been proposed by some authors to synonimize the 2 species, but the matter has remained unsettled. A third form of Aplysina (here mentioned as "n. sp.") has been found in the Atlantic from the Basque Country to the Algarve coast of Portugal and Madeira. It has the ecology of A. cavernicola but it is much smaller, encrusting, with long budding filaments. Very similar species of Aplysina occur in the Carribean, across the Atlantic, where the diversity of Verongida is high. For comparative purposes, we could study Verongida from the Carribean, Western Australia, and a putative Aplysina aerophoba from Senegal.

Allele frequencies of minisatellite Miac 1

The success of each marker was highly irregular. Some samples worked well for one and not for another. Cloning PCR products was necessary for COI, ITS2 and 18S. Several other samples (not listed here) did not amplify. Phylogenetic trees were constructed using different methods (only Neighbour Joining shown here) all producing congruent results.

The Miac 1 minisatellite finally allowed us to get an answer concerning the three taxa of Aplysina present in the Mediterranean and nearby Atlantic: the three taxa must be 3 different valid species of Aplysina. Allele frequencies are indeed very different even when the sponges are found in sympatry. Although such results are preliminary (more is to be learned from microsatellites currently being obtained), the value of I calculated between A. aerophoba and A. cavernicola is more in the range known for interspecific indentities rather than for intraspecific ones. Also, COI was interesting in providing a possible case of hybrids between the 2 species in the Adriatic, although this remains to be further confirmed. COI and ITS2 seem to be useful markers at the inter-specific or sometimes intra-specific levels for some groups of sponges. They are however not variable enough for some species groups of Aplysina spp.

Mitochondrial COI proved to be rather poorly informative at the peri-specific level: it failed to discriminate the small Aplysina n. sp. from A. aerophoba, and the differentiation between A. aerophoba and A. cavernicola is very weak. The sample from Senegal appears not to be A. aerophoba, according to COI. It is placed close to the A. fistularis from the Carribean. This will require further studies. COI consistently discriminates A. cavernicola from the group A. aerophoba / Aplysina n.sp. even when samples came from the same location.

There are however two exceptions (black arrows) where Croatian, positively identified, A. aerophoba grouped with the A. cavernicola sequences.

ITS-2 results were difficult to analyse due to the presence of multiple copies in the genome. It also failed to adequately resolve the relationships between our 3 target taxa. However, our 3 taxa are well separated from the series of Aplysina species found in the Carribean and California. Also, ITS2 brings Suberea (family Aplysinellidae) closer to Aplysina than to Verongula (both in Aplysinidae). Finally the GenBank A. lacunosa "soft" appears to be a Verongula.

18S results (not shown) were not clear cut and require further work. They suggest Aplysina n. sp. is indeed well separated from A. aerophoba and A. cavernicola but they failed to unambiguously discriminate between the latter two species.

Aplysina aerophoba Aplysina cavernicola Aplysina n. sp. Aplysina n. sp.

				NJ -COI		Aplysina n. sp. Basque Country	Aplysina aerophoba Medes Aplysina aerophoba GenBank	NJ -ITS2
				656 bp		ca. 363 bp
				1000 bootstrap		1000 bootstrap
				replicates		replicates
					621
						Aplysina cavernicola GenBank
					642	Aplysina cavernicola Port-Cros
						Aplysina aerophoba Pula	782
						Aplysina aerophoba Pula	0.02
						Aplysina aerophoba Pula
						Aplysina cavernicola Dugi Otok
						Aplysina cavernicola Dugi Otok	Aplysina fistularis Caribbean GenBank
				0.01	563	Aplysina cavernicola Vis Aplysina cavernicola Marseille Aplysina cavernicola Marseille	Aplysina fistularis Martinique Aplysina fistularis Martinique Aplysina fistularis Martinique Aplysina fistularis Martinique	981
						Aplysina cavernicola Marseille	Aplysina fistularis California GenBank
					689	Aplysina cavernicola Marseille	Aplysina insularis GenBank
						Aplysina cavernicola Marseille	Aplysina cauliformis "thick" GenBank
				825	Aplysina cavernicola Medes	Aplysina fulva GenBank	757	1000
					"Aplysina aerophoba" Senegal	Aplysina lacunosa "hard" GenBank Aplysina sp. CAR Martinique
					Aplysina fistularis Martinique	Aplysina sp. CAR Martinique
				1000	Aplysina fistularis Martinique Aplysina fistularis Martinique	Aplysina cauliformis "thin" GenBank Aplysina archeri GenBank
					Aplysina fistularis Martinique	Aplysina fistularis Bermuda GenBank
						Aplysina fistularis Bermuda GenBank	Suberea laboutei Australia
					996	Aplysina sp. WAM2 Australia Aplysina sp. WAM1 Australia	Verongula rigida Martinique Aplysina lacunosa "soft" GenBank Verongula rigida Martinique	1000
					Verongula rigida Martinique	Ailochroia crassa GenBank
					Hexadella racovitzai Marseille	Verongula gigantea GenBank	1000
	A. aerophoba	A. cavernicola	Aplysina n. sp.
			Allele numbers
			120	218
			230 270	250 300
			330	360
			400
	Index of gene identity I (Nei, 1972)
	I = 0.49

632 Aplysina aerophoba Pula Aplysina aerophoba Madeira Aplysina aerophoba Madeira Aplysina aerophoba Port-Cros Aplysina aerophoba Banyuls Aplysina aerophoba Medes Aplysina aerophoba Medes Aplysina aerophoba Madeira Aplysina n. sp. Algarve Aplysina n. sp. Berlenga Aplysina n. sp. Berlenga Aplysina n. sp. Basque Country Aplysina n. sp. Basque Country Aplysina n. sp. Basque Country Aplysina n. sp. Berlenga Aplysina n. sp. Berlenga Aplysina n. sp. Algarve Aplysina n. sp. Algarve Aplysina n. sp. Algarve Aplysina cavernicola Port-Cros Aplysina cavernicola Port-Cros Aplysina aerophoba Corsica Aplysina aerophoba Corsica Aplysina cavernicola Vis Aplysina cavernicola Vis Aplysina cavernicola Vis Aplysina cavernicola Villefranche Aplysina cavernicola Medes

Acknowledgements are due to the many people who assisted us diving or provided sponge samples: R. Graille, F. Zuberer, B. De Ligondes, J. Garrabou, T. Bakran-Petricioli, P. Louisy, A.V. Ereskovsky, M.N. de Casamajor, R. Calado, A.J. Almeida, M.J. Biscoito, R. Araujo, J.G. Harmelin, H. Zibrowius, C.N. Bianchi, G. Bitar, P. Petit de Voize, R. Lion, J. Fromont, the guards at Berlenga Natural Reserve, and the City Museum of Funchal. Financial support was provided by the French Institute for Biodiversity, Total, and the French-Portuguese Program "Study of shallow-water cave communities of Madeira".

Sampling area

Taxon COI ITS2 18S Miac1 Lebanon (Batroun)

A. aerophoba X Adriatic (Pula)

A. aerophoba XX Adriatic (Dugi Otok) The relationships between these taxa were sorted out with the help of several molecular markers. No single marker proved to be efficient and informative enough, but the combination of information obtained from the mitochondrial gene of the Cytochrome Oxydase I (COI), the Internal Transcribed Spacer 2 (ITS2) of ribosomal DNA, 18S rRNA gene (18S), and a minisatellite (Miac1), could provide significant insights on these relationships.