D Aurelle
email: didier.aurelle@univmed.fr

J.-B Ledoux

C Rocher

P Borsa

A Chenuil

J.-P Fe

Á C Rocher

Á A Chenuil

Phylogeography of the red coral (Corallium rubrum): inferences on the evolutionary history of a temperate gorgonian

Keywords: Red coral, Phylogeography, Genetic structure, EPIC, Microsatellites

The red coral Corallium rubrum (Cnidaria, Octocorallia) is an exploited, long-lived sessile species from the Mediterranean Sea and the adjacent coastline in the Atlantic Ocean. Surveys of genetic variation using microsatellites have shown that populations of C. rubrum are characterized by strong differentiation at the local scale but a study of the phylogeography of this species was still lacking. Here, we used seven polymorphic microsatellite loci, together with sequence data from an intron of the elongation factor 1 (EF1) gene, to investigate the genetic structure of C. rubrum across its geographical range in the western Mediterranean Sea and in the Adriatic Sea. The EF1 sequences were also used to analyse the consequences of demographic fluctuations linked with past environmental change. Clustering analysis with microsatellite loci highlighted three to seven genetic groups with the distinction of North African and Adriatic populations; this distinction appeared significant with AMOVA and differentiation tests. Microsatellite and EF1 data extended the isolation by distance pattern previously observed for this species at the western Mediterranean scale. EF1 sequences confirmed the genetic differentiation observed between most samples with microsatellites. A statistical parsimony network of EF1 haplotypes provided no evidence of high sequence divergence among regions, suggesting no longterm isolation. Selective neutrality tests on microsatellites and EF1 were not significant but should be interpreted with caution in the case of EF1 because of the low sample sizes for this locus. Our results suggest that recent Quaternary environmental fluctuations had a limited impact on the genetic structure of C. rubrum.

Introduction

The phylogeographic approach yields insights into the evolutionary history of a species by revealing vicariance events, migration pathways and population expansion or bottleneck [START_REF] Avise | Phylogeography: the history and formation of species[END_REF]. Phylogeography also assists the management of threatened species by providing information on genetic subdivisions, gene flow and genetic diversity. This is crucial in the present context of global change (including climate change) where species dynamics is linked to dispersal and recolonisation abilities, and to the possibility of in situ adaptation. Despite the need of genetic data for adequate management strategies, such data are still scarce in most marine species [START_REF]How useful are the genetic markers in attempts to understand and manage biodiversity?[END_REF]. Until recently, this was also the case for the red coral, Corallium rubrum, in the Mediterranean Sea.

C. rubrum is a sessile cnidarian inhabiting caves, vertical cliffs and overhangs at depths ranging from 10 m to more than 800 m [START_REF] Garrabou | A 20-year study on life-history traits of a harvested long-lived temperate coral in the NW Mediterranean: insights into conservation and management needs[END_REF][START_REF] Costantini | Deep-water Corallium rubrum (L., 1758) from the Mediterranean Sea: preliminary genetic characterisation[END_REF]. It has a fragmented pattern of distribution and occurs in the western Mediterranean, in some parts of the eastern Mediterranean and on the neighbouring Atlantic coasts such as those of Morocco [START_REF] Zibrowius | La re ´partition du Corallium rubrum dans l'Atlantique (Cnidaria: Anthozoa: Gorgonaria)[END_REF]. C. rubrum has long been exploited for jewellery. C. rubrum has also been affected by mortality events linked with positive thermal anomalies in 1999 and 2003 [START_REF] Garrabou | Mass mortality in NW Mediterranean rocky benthic communities: effects of the 2003 heat wave[END_REF]) which may have impacted the population dynamics of this species [START_REF] Santangelo | Population dynamics and conservation biology of the over-exploited Mediterranean red coral[END_REF]. C. rubrum is a sessile species with relatively short larval phase (4-12 days in aquaria ;[START_REF] Vighi | Etude sur la reproduction du Corallium rubrum (L.)[END_REF][START_REF] Weinberg | The light-dependent behaviour of planula larvae of Eunicella singularis and Corallium rubrum and its implication for octocorallian ecology[END_REF]) and therefore, presumably low dispersal abilities. C. rubrum is an appropriate model to study the genetic consequences of past and current environmental fluctuations. Genetic consequences of Quaternary climatic fluctuations have been studied for terrestrial species [START_REF] Hewitt | The genetic legacy of the quaternary ice ages[END_REF][START_REF] Petit | Glacial refugia: hotspots but not melting pots of genetic diversity[END_REF] but less frequently in the marine realm. Concerning the Mediterranean Sea, at the last glacial maximum (LGM) 20,000 years ago, the sea level in the north western Mediterranean Sea was around 105-115 m below the present level [START_REF] Lambeck | Sea-level change along the French Mediterranean coast for the past 30 000 years[END_REF]. Few sessile species (necessarily more strongly affected by recent fluctuations than mobile ones) have been analysed from the point of view of the genetic consequences of sea-level variations in the Mediterranean Sea (but see [START_REF] Duran | Phylogeographical history of the sponge Crambe crambe (porifera, poecilosclerida): range expansion and recent invasion of the Macaronesian islands from the Mediterranean Sea[END_REF][START_REF] Serra | Genetic structure in the Mediterranean seagrass Posidonia oceanica: disentangling past vicariance events from contemporary patterns of gene flow[END_REF]. Two different scenarios can be proposed for the evolutionary history of red coral shallow-water populations in this context. The ''refugia'' scenario postulates that red coral populations would have established through long distance colonisation events from putative distant refugia within the last 20,000 years: the localization of these putative refugia and the possibility of long-distance migration events remain to be investigated. In the North Atlantic similar scenarios with different refugia (not only southern but also periglacial refugia) have been inferred from genetic data for benthic species [START_REF] Maggs | Evalutating signatures of glacial refugia for north atlantic benthic marine taxa[END_REF]). In the ''persistence'' scenario, the shallow-water populations would have originated from ancestral populations whose habitat gradually expanded upwards. A similar hypothesis has been proposed by [START_REF] Marko | The ''expansion-contraction'' model of pleistocene biogeography: rocky shores suffer a sea change?[END_REF] in the north eastern Pacific. These opposite scenarios are expected to leave different genetic signatures [START_REF] Hewitt | The genetic legacy of the quaternary ice ages[END_REF][START_REF] Marko | The ''expansion-contraction'' model of pleistocene biogeography: rocky shores suffer a sea change?[END_REF]) but intermediate hypotheses should be considered as well. Analysing past demographic changes and population connectivity may also provide valuable insights into the potential future evolution of populations in a context of global change [START_REF] Maggs | Evalutating signatures of glacial refugia for north atlantic benthic marine taxa[END_REF].

Previous genetic studies of C. rubrum have been performed with allozymes [START_REF] Abbiati | Genetic variation within and between two Tyrrhenian populations of the Mediterranean alcyonarian Corallium rubrum[END_REF], AFLP (del [START_REF] Gaudio | Genetic typing of Corallium rubrum[END_REF] and microsatellites [START_REF] Costantini | Development of microsatellite markers for the Mediterranean gorgonian coral Corallium rubrum[END_REF]Costantini et al. 2007aCostantini et al. , b, 2010;;Ledoux et al. 2010a, b). These studies indicated generalised genetic differentiation among populations, even at short distances (starting around 10 m) and therefore, low effective dispersal. No major genetic break was observed among the most distant populations and a regional pattern of isolation by distance was evidenced by Ledoux et al. (2010a) along with local spatial genetic structure between individuals (Ledoux et al. 2010b).

So far no study was specifically dedicated to the evolutionary history of red coral and nucleotide sequence data were still needed to evaluate divergence times and to analyse past demographic fluctuations. Mitochondrial DNA is not variable enough in this species [START_REF] Caldero ´n | Evaluation of the utility of COI and ITS markers as tools for population genetic studies of temperate gorgonians[END_REF]. Internal transcribed spacers (ITS) were used as nuclear sequence markers in red coral by Costantini et al. (2007b[START_REF] Costantini | Deep-water Corallium rubrum (L., 1758) from the Mediterranean Sea: preliminary genetic characterisation[END_REF], but they have shown high levels of intra-individual variability in another octocoral species, Eunicella cavolinii [START_REF] Caldero ´n | Evaluation of the utility of COI and ITS markers as tools for population genetic studies of temperate gorgonians[END_REF]). Here we present an evaluation of ITS intra-individual variability along with new data from an exon priming intron crossing (EPIC) marker from the elongation factor 1 (EF1) gene in C. rubrum. Nuclear sequence markers (including another part of EF1) have already shown much higher variability than mitochondrial DNA in cnidarians and have been used to reveal population isolation in Oculina sp. [START_REF] Eytan | Nuclear sequences reveal mid-range isolation of an imperilled deep-water coral population[END_REF]. We assess the variability of this new marker and use it for the study of the phylogeography of C. rubrum.

The present study includes samples of C. rubrum from the south western Mediterranean and the North Adriatic regions in addition to samples formerly studied with microsatellites by Ledoux et al. (2010a). Our objective is to investigate the phylogeography of the red coral across a larger part of its geographical range and to identify the main genetic subdivisions over this area. We extended the microsatellite data of Ledoux et al. (2010a) and analysed EF1 sequence data in order to assess the levels of divergence between populations and to look for potential signals of past demographic fluctuations.

Materials and methods

Samples

The samples and their geographical distribution are presented in Table 1 and Fig. 1. Sampling was hierarchical and included nine regions: the Adriatic Sea, North Africa, Corsica, South Italy (Ionian Sea), North Italy (Ligurian Sea), Balearic Islands, Marseilles, Monaco (Ligurian Sea) and Catalonia, with several localities in most cases, resulting in 39 samples. Regions were delineated according to microsatellite results (Ledoux et al. 2010a; our results) and to geographical breaks (e.g. island vs. mainland). The sampling protocol is described in Ledoux et al. (2010a).

For intron sequences we tried as far as possible to obtain samples scattered throughout the corresponding Ledoux et al. (2010a) were considered here along with six new samples: four from North Africa (TEN, TNS, FUE, DEL) and two from the Adriatic Sea (ALB, GHA; Table 1). Because the intra-regional genetic structure was not the aim of this paper, a maximum of six samples per region were analysed in order to avoid any over-representation of some regions (Marseilles for example) in the dataset.

Evaluation of intra-individual variability for internal transcribed spacers

We evaluated the intra-individual variability of ITS1. The corresponding methods and results are presented and discussed in supplementary material. We evidenced a high level of intra-individual variability for ITS1. Considering this variability we did not use this locus for further analyses and instead focused our sequencing effort on EF1.

Molecular analyses of EF1

Total DNA extraction Genomic DNA was extracted using the QIAmp DNA Mini Kit 50 (Qiagen Ò ), following manufacturer's instructions, or with phenol-chloroform protocol (Ledoux et al. 2010a).

In both cases extractions were performed from 5 to 15 polyps per colony or, when not possible, using coenenchyme scraped from the colony.

EF1 sequencing

EF1 cDNA isolation and sequencing are described in supplementary material. The cDNA EF1 sequence was used to define primers with the online Primer 3 software [START_REF] Rozen | Primer3 on the WWW for general users and for biologist programmers[END_REF] in order to amplify overlapping fragments of 200-300 bp of the cDNA. These primers were applied to genomic DNA to identify introns. We considered that an intron was identified when the amplified fragment using the genomic DNA template was longer than the corresponding cDNA fragment. One primer pair (EF1 CR4 F: TAGA TAGCATTCTTCCTCCCAAAC and EF1 CR4 R: AACC AACATTATCTCCAGGAAGAG) gave regular amplification of an intron and its flanking regions. PCR conditions for this EF1 EPIC marker were: Promega Ò PCR buffer 1X, MgCl 2 2.5 mM, dNTPs 0.125 mM, 0.5 lM of each primer,

Microsatellites analysis and polymorphism

The samples analysed with microsatellites are described in Table 1. Seven loci (Mic13,20,24,26,27,COR9bis and COR46bis) were analysed following Ledoux et al. (2010a). The three other loci used by Ledoux et al. (2010a), Mic 22, 23 and 25, were not used here because they did not give any amplification in the Adriatic and North African samples. The parameters describing the levels of polymorphism (number of alleles by locus N a , unbiased expected heterozygosity H nb , and observed heterozygosity H obs ) have been computed with the Genetix 4.05.2 software (Belkhir et al. 1996). The departure from panmixia has been evaluated with the f estimator of F IS [START_REF] Weir | Estimating F-statistics for the analysis of population structure[END_REF]; we tested for its significance with 1,000 permutations with Genetix.

EF1 sequence data and polymorphism

Sequences were aligned with BioEdit 7.0.5.3 [START_REF] Hall | BioEdit: a user-friendly biological sequence alignment editor and analysis program for Windows 95/98/NT[END_REF]. For EF1 intron, individuals with ambiguous sites were considered as heterozygous. For individuals heterozygous at only one site, we directly inferred the two corresponding haplotypes. As some ambiguous/heterozygous positions were observed for various EF1 sequences, we tested whether this was due to heterozygous individuals by cloning the PCR product for twelve individuals: this confirmed that these individuals were indeed heterozygous and this allowed us to identify the corresponding haplotypes. Apart from the cloned PCR products, the haplotypes of the other heterozygous individuals were determined with the Phase 2.1 software [START_REF] Stephens | A new statistical method for haplotype reconstruction from population data[END_REF][START_REF] Stephens | Accounting for decay of linkage disequilibrium in haplotype inference and missing data imputation[END_REF]. The homozygous individuals and the heterozygous individuals for which the corresponding haplotypes had been identified were used as known phases resulting in 142 reference individuals. Five independent runs were performed with the multi-allelic option without stepwise mutation and other parameters set as defaults. Phase also allowed estimation of the recombination parameter q [START_REF] Li | Modelling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data[END_REF]. We did not get readable sequences for some individuals heterozygous for insertion-deletion (indels), and they were not used for further analyses (Table 1).

Observed heterozygosities for EF1 were calculated with the number of observed heterozygous individuals based on observed sequence ambiguities and cloning of PCR products. Nucleotide diversity (p) and gene diversity [START_REF] Nei | Molecular evolutionary genetics[END_REF] were calculated with DNAsp 5.0 [START_REF] Librado | DnaSP v5: a software for comprehensive analysis of DNA polymorphism data[END_REF] at the population and at the regional level according to the geographical groups indicated in Table 1.

Tests of mutation-drift equilibrium

We tested the null hypothesis of mutation-drift equilibrium for microsatellite loci with the Bottleneck 1.2 software [START_REF] Cornuet | Description and power analysis of two tests for detecting recent population bottlenecks from allele frequency data[END_REF]. We performed the one tail Wilcoxon's tests for heterozygosity excess or deficiency which could indicate a recent bottleneck or population expansion, respectively. The tests were based on 1,000 replications with a two-phase mutation model with 95% single-step mutations and 5% multiple-step mutations and a variance among multiple steps of 12, as recommended by [START_REF] Piry | BOTTLENECK: a computer program for detecting recent reductions in the effective population size using allele frequency data[END_REF].

DNAsp was used to test for mutation-drift equilibrium with EF1 sequence data with a comparison of three different tests. Fu's Fs test [START_REF] Fu | Statistical tests of neutrality of mutations against population growth, hitchhiking and background selection[END_REF] 2008) advise the use of R2 and Tajima's D [START_REF] Tajima | Statistical method for testing the neutral mutation hypothesis by DNA polymorphism[END_REF] test. Significance was assessed with coalescent simulations based on the observed theta per gene value with no recombination (according to Phase results) or intermediate levels of recombination (with R = 10 per gene and 494 sites). One thousand replicates were used for each analysis. As the power of neutrality tests may be greatly reduced for low sample sizes (Ramos-Onsins and Rozas 2002), they were also performed by grouping samples at the regional and global (all samples) levels. The interpretation of the results took into account the different properties of local, scattered and pooled samples in these tests [START_REF] Sta ¨dler | The impact of sampling schemes on the site frequency spectrum in nonequilibrium subdivided populations[END_REF].

Network reconstruction EF1 sequences were used for a network reconstruction with the statistical parsimony approach implemented in TCS 1.21 [START_REF] Clement | TCS: a computer program to estimate gene genealogies[END_REF] with a 95% limit to parsimony and indels considered as a fifth state.

Clustering analysis

Microsatellite loci were used for a Bayesian clustering analysis with the Structure 2.2 software [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF] from K = 1 to 25 groups with five replicates for each run. An admixture model with correlated allele frequencies was chosen [START_REF] Falush | Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies[END_REF] with the option of inferring alpha. Another analysis was also performed with independent allele frequencies and five replicates to check the stability of the results to the chosen model. Preliminary tests showed that a burnin of 50,000 iterations was enough to get a stationary evolution for the likelihood. For each run, this burn-in was followed by 200,000 iterations. The estimation of the number K of genetic groups was performed by considering the peaks in the second order rate of change of the likelihood function with respect to K (Delta(K); [START_REF] Evanno | Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study[END_REF] and by focusing on values of K that capture most of the structure in the data [START_REF] Pritchard | Documentation for structure software: version 2[END_REF].

Principal coordinate analysis

Genetic relationships among populations were studied with a Principal Coordinate Analyses (PCA) performed with the Genalex 6 software [START_REF] Peakall | GENALEX 6: genetic analysis in Excel. Population genetic software for teaching and research[END_REF]) on microsatellite data. The analysis used the algorithm of [START_REF] Orloci | Pillars of Hercules: is the Atlantic-Mediterranean transition a phylogeographical break?[END_REF] with the option of standardized distances and was based on F ST values.

Population differentiation and AMOVA

The analysis of population differentiation was performed with the Arlequin 3.0 software [START_REF] Excoffier | Arlequin (version 3.0): an integrated software package for population genetics data analysis[END_REF]). Pairwise comparisons with microsatellites were analysed with the h estimator of F ST [START_REF] Weir | Estimating F-statistics for the analysis of population structure[END_REF]. For EF1, pairwise comparisons were done using F ST and with U ST computed with proportion of differences between haplotypes [START_REF] Excoffier | Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data[END_REF]). Both F ST and U ST were tested with 1,000 permutations.

An analysis of molecular variance (AMOVA; [START_REF] Excoffier | Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data[END_REF]) was performed on EF1 and microsatellites with Arlequin 3.0 in order to evaluate genetic differentiation within groups and between groups of populations. Nine population groups were defined according to their geographical origin leading to the following groups: Adriatic Sea, North Italy (one population), South Italy (one population; not analysed with microsatellites), Monaco, Marseilles, Catalonia, Balearic Islands, Corsica and North Africa (Table 1). Grouping the two Italian populations did not change the general results, nor did the grouping of North Italy with Monaco (both in Ligurian Sea but quite different on the basis of clustering analysis). For microsatellites, the AMOVA was performed on the basis of allele frequencies (F ST like) and by taking into account the sum of squared differences of allele sizes (R ST like). For EF1, the AMOVA was performed without (F ST like) and with (U ST like) sequence information (proportion of differences). Results were tested with 1,000 permutations.

Isolation by distance

Isolation by distance was tested with microsatellite and EF1 data separately by comparing F ST /(1-F ST ) with geographical distance [START_REF] Rousset | Genetic differentiation and estimation of gene flow from F-statistics under isolation by distance[END_REF]. Geographical distances were measured on Google Earth as the shortest waterway between populations. IBD web service 3.16 [START_REF] Jensen | Isolation by distance, web service[END_REF] was used to compare non-transformed as well as logarithms of genetic and geographical distances and to test the correlation with a Mantel test applied with 1,000 permutations. A reduced major axis regression was performed.

For all analyses, when necessary, a correction for multiple tests was applied with a false discovery rate of 0.05 [START_REF] Benjamini | Controlling the false discovery rate-A practical and powerful approach to multiple testing[END_REF].

Results

Microsatellite polymorphism

Six hundred and ninety-nine individuals corresponding to 24 populations were genotyped with the seven microsatellite loci. The mean number of alleles per loci per population varied from 4.7 (FUE) to 18.7 (FOR) with a mean value of 10.2 (Table S2 supplementary material). The observed heterozygosity varied from 0.39 (TNS) to 0.70 (RIE) with a mean value of 0.56. Unbiased expected heterozygosity varied from 0.57 (ALB, GHA, TNS) to 0.84 (LPP) with a mean value of 0.71.The multilocus F IS varied from 0.07 (for RIE, Marseilles) to 0.36 (PZU, Corsica) with a mean value of 0.22. The permutation tests indicated a significant heterozygote deficiency for all populations except for the FUE sample (f = 0.09; P = 0.05) (Table S2).

EF1 sequence polymorphism

In all, 376 EF1 sequences corresponding to 188 individuals were analysed. The length of the sequence alignment was 494 bp, with 46 variables sites including four indels of one bp each. The alignment of genomic sequences with the EF1 cDNA sequences of red coral indicated that the length of the intron varied from 344 to 347 bp.

Observed heterozygosity varied from 0 (e.g. PZP, Corsica; n = 9 individuals) to 1 (RIE, Marseilles; n = 8). For the haplotype reconstruction, the five independent runs of the Phase software gave identical results. Most haplotypes were identified with high probability values for the considered sites (0.8-1). Only three different sites in three different individuals had lower probabilities: two at 0.50 and one at 0.56. The Phase analysis also indicated low recombination rate when considering all sequences with an estimated q value of 0.003, consistent over the five runs.

For the whole data set, 39 different haplotypes were observed with a nucleotide diversity of 0.006 (Table 2). The most frequent haplotype was found 105 times (frequency 0.28) and the second most frequent 49 times (frequency 0.13). Eleven haplotypes were observed at least ten times (minimum frequency in the total dataset 0.03); most other haplotypes corresponded to one to four occurrences. At the regional level the number of different haplotypes varied from two (North Italy) to 17 (for Marseilles, the region with the highest sample size; Table 2). Haplotype diversity varied from 0.36 (North Italy) to 0.83 (North Africa). Nucleotide diversity varied from 0.001 (North Italy) to 0.007 (Catalonia and Marseilles; Table 2). At the population level, when considering samples with at least ten sequences, the number of different haplotypes varied from 2 (PDA) to 11 (RIE). Haplotype diversity varied from 0.24 (LPP) to 0.95 (RIE). Nucleotide diversity varied from 0.001 (PDA and LPP) to 0.007 (POT; Table 2).

Tests of mutation-drift equilibrium

Bottleneck tests with microsatellites

The Wilcoxon's test did not allow detection of any significant heterozygosity excess or deficiency (Table 3). Six tests suggested a significant heterozygosity deficiency at The columns indicate the number of analysed sequences for each region or population (2n genes for n individuals; codes for samples as in Table 1), the number of observed haplotypes (h), the gene diversity (Hd), the nucleotide diversity (p), and the results of the analyses of the Fs, R2 and Tajima's D tests. For Fs and R2, the observed value is indicated followed by the mean value obtained over 1,000 coalescent simulations, and the probability that the observed value is higher than the simulated values (see text for details). The first part of the table (''region'') gives the results for pooled samples at the regional and global scale; the second part (''population'') gives the results at the population level for samples with at least 10 analysed sequences. Values in bold indicate significant tests after correction for multiple test with a false discovery rate of 0.05 the 0.05 level, but these tests were not significant after correction for multiple tests.

Selective neutrality tests on EF1

The results of selective neutrality tests without recombination are presented in Table 2 for samples with at least ten sequences (five individuals) and at global and regional scales (grouped samples). After corrections for multiple tests, only the Fu's Fs test indicated a significant deviation from mutation-drift equilibrium when considering the whole data set, with a highly negative Fs value indicating an excess of rare alleles/rare mutations. The low R2 value (P = 0.04) was concordant with this observation. At the regional scale, the signal varied from one region to another and did not evidence any significant or generalised pattern. The analyses of Fu's Fs and R2 with intermediate levels of recombination gave similar results (data not shown). At the population level, only RIE (Marseilles) showed significant

Fs and R2 values (P = 0.01 and 0.05, respectively) but these values were not significant after correction for multiple tests.

EF1 network reconstruction

The EF1 TCS network is presented in Fig. 2. Most links between haplotypes corresponded to one or two mutations. The highest divergence was observed for four sequences (haplotype XXXVII) from two individuals from RII (Marseilles) which differed by nine mutations from the nearest haplotype (XI). Several loops were present in the network, indicating possible alternative relationships among haplotypes. Several haplotypes (e.g. haplotypes I, III, X, XI) were shared among distant locations, such as the most frequent one (X) which was observed in Marseilles, Monaco, North Italy, Corsica, Catalonia and North Africa.

Nevertheless the network showed heterogeneous distribution of the haplotypes.

Clustering analysis

The application of the Structure software to microsatellite data revealed a first peak in the evolution of Delta(K) at K = 3 followed by four smaller peaks at K = 7, 13, 21 and 23 (Fig. S2). The model with independent allele frequencies indicated a first peak at K = 3 with a second minor peak at K = 5; but for identical K values the clustering schemes were similar with the two models (data not shown). The solutions with K [ 7 did not provide much more information than with K = 7 and the individual assignment profiles were usually much more complex, therefore, we focused on K = 3 and 7 (Fig. 3). For K = 3, an African-Adriatic group appeared as separated from a second group with North Italy, Monaco and Marseilles, and a third group with the remaining populations. Apart from the North Italy (PDA) and Balearic samples (FOR, LPP) most samples presented high and homogeneous membership coefficients for their corresponding groups. For K = 7, clustering globally followed geographical distribution with more heterogeneous membership coefficients than for K = 3. However, Adriatic and African individuals appeared well differentiated from other samples with high membership coefficients. One out of five runs grouped GHA (Adriatic) and CAR (Marseilles).

In the four other runs GHA was grouped with the other Adriatic sample (ALB). Corsican and Catalonian samples were also well characterized, apart for SRE (Catalonian) which appeared highly admixed. Samples from Marseilles, Monaco, North Italy and Balearic Islands appeared admixed. Despite this admixture the distribution of the yellow cluster suggested a proximity between samples from Marseilles (except CAR) and those from Monaco. The PDA sample (north Italy) appeared admixed but with a predominance of the Corsican cluster.

Principal coordinate analysis

The Principal Coordinate Analyses (PCA) of genetic relationships between populations based on microsatellites F ST is presented in Fig. 4. Axis 1 indicated a gradient between North Africa and Adriatic Sea and axis 2 separated these samples from the other ones which are grouped, except for CAR (Marseilles). The analysis of axis 3 only separated a few populations from this last grouping (MON, Monaco on one side and PZU, Corsica on the other side for example; data not shown).

Population differentiation and AMOVA

Genetic differentiation between populations

For microsatellites, tests of differentiation at the population level indicated significant differentiation for all pairwise comparisons except for the comparisons: RIE-RII, PON-CRO, CDR-POT (Table S3). Highest F ST values reached 0.41 and 0.44 for comparisons of GHA (Adriatic) with TEN and TNS (North Africa), respectively. Differentiation tests between regions (as defined in Table 1) were all significant. For EF1, the estimates (U ST and F ST ) of pairwise population differentiation and results of permutation tests are presented in Tables S4 andS5. The U ST values varied between -0.75 and 1, whereas F ST varied between -0.3 and 1. Permutation tests indicated significant differentiation for the comparisons involving the most distant populations such as populations from North Africa or the Balearic Islands compared to those from other regions. When considering all populations, 41% of the pairwise comparisons were significant with F ST and 38% with U ST . The lowest geographical distance for which significant differentiation was observed with EF1 corresponded to the comparison between RII and RIE: two samples from the same site, but in different environments (inside and outside cave) and about 15 m apart. For the differentiation test between regions, when using U ST , five tests over 36 comparisons were not significant after correction for multiple tests: Adriatic-South Italy, Marseilles-Catalonia, Marseilles-Monaco, Marseilles-Corsica and Monaco-Corsica. For F ST comparisons, seven tests were not significant: Adriatic-South Italy, Monaco-North Italy, Marseilles-Monaco, Marseilles-North Italy, Marseilles-Corsica, North Italy-Corsica and Monaco-Corsica.

AMOVA

For microsatellites, the AMOVA based on R ST indicated that around 3% of the variation corresponded to differences between regions and 18% to differences between populations within regions (Table 4). With F ST like analysis, these percentages were 5 and 8%, respectively. Apart from the comparison between regions with R ST , permutation tests Populations were subdivided into nine groups: Adriatic Sea, South Italy, North Italy, Monaco, Marseilles, Catalonia, Corsica, Balearic Islands and North Africa (see Table 1 and text for details). The first part of the table (U ST or R ST like) corresponds to the computation of AMOVA using the sum of squared differences (microsatellites) or the pairwise differences between sequences (EF1); the second part of the table (F ST like) only takes into account allele frequencies and is equivalent to conventional F ST . The P values for fixation indices have been obtained with 1,000 permutations indicated significant differentiation at all levels of analysis. The AMOVA on EF1 sequences performed by taking into account sequence differences (U ST -like) indicated that around 13% of genetic variance was due to differences between regions and 16% to differences between populations within regions (Table 4). When AMOVA was performed based on haplotype frequencies (F ST -like) these percentages were 15 and 13%, respectively.

Isolation by distance

The Mantel test applied to microsatellites was significant for all comparisons of genetic and geographical distances either with logarithm or non transformed distances (P \ 0.001 in all cases). For the comparison of F ST /(1-F ST ) with logarithm of geographical distance the reduced major axis regression indicated a positive correlation with r = 0.577 (estimated slope: 0.127; intercept: -0.173). For EF1 data, the Mantel test was significant only when comparing the logarithm of both distances (P = 0.014). The reduced major axis regression indicated a positive correlation with r = 0.133 (estimated slope: 1.953; intercept: -5.208).

Discussion

The analysis of genetic differentiation with microsatellite and EF1 suggests a low level of gene flow between red coral shallow-water populations, even at short distance.

The genetic structuring of red coral in the north western Mediterranean Sea is congruent with the geographical locations of the populations and led to the identification of three to seven geographical groups. These groups were indeed genetically differentiated which may correspond to barriers to gene flow. Nevertheless the isolation by distance pattern could also explain this geographical structuring. This structuring in geographical groups does not correspond to long-term divergence as suggested by the sharing of EF1 haplotypes between distant locations and by the low level of differences between most haplotypes. The null hypothesis of mutation-drift equilibrium was not rejected.

Along with low sequence divergence, this suggests that past environmental fluctuations did not strongly impact the genetic structure and diversity of this species.

Patterns of genetic differentiation

Significant genetic differentiation was evidenced with microsatellites for almost all comparisons between populations and between regions. This agrees with previous studies on red coral using microsatellites (Costantini et al. 2007a, b;Ledoux et al. 2010a). At the population level EF1 data evidenced genetic differentiation at various geographic distances but with a reduced number of significant comparisons when compared with microsatellites. This discrepancy between markers could be linked with differences in sample sizes (lower for EF1). The observation of genetic differentiation starting from short distances is in agreement with the low dispersal abilities of red coral (Costantini et al. 2007a;Ledoux et al. 2010a, b). Nevertheless, the occurrence of individuals with incorrect cluster assignment when considering their geographical origin (Ledoux et al. 2010a; our results) could indicate migration events. Sporadic long distance migration (compared to the mean dispersal distance) might be compatible with genetic differentiation if the level of genetic drift is high enough to overcome gene flow [START_REF] Tatarenkov | Microgeographic population structure of green swordail fish: genetic differentiation despite abundant migration[END_REF]. High genetic drift may come from low effective size as is assumed for C. rubrum populations (Costantini et al. 2007a;Ledoux et al. 2010b). Sporadic migration may also explain the sharing of EF1 haplotypes among distant locations. A more precise study of migration events should involve individual assignment tests and should be based on a more extensive sampling at regional or local scale.

The spatial pattern of genetic structuring evidenced here extended at higher distances the isolation by distance (IBD) pattern observed by Ledoux et al. (2010a). The Structure and PCA analyses indicated that this genetic structuring agreed well with the geographical location of the populations. Nevertheless, except for North Africa and the Adriatic Sea, individual assignment values obtained with Structure were often low at K = 7. This could be linked to reduced discriminating power when compared to the results obtained with 10 loci (Ledoux et al. 2010a) or to the effect of unsampled populations, including deep ones. Under isolation by distance (IBD) (as identified in red coral; Ledoux et al. 2010b), the number of clusters inferred by Bayesian structuring can also be overestimated [START_REF] Frantz | Using spatial bayesian methods to determine the genetic structure of a continuously distributed population: clusters or isolation by distance?[END_REF], potentially leading to low assignment values [START_REF] Pritchard | Documentation for structure software: version 2[END_REF]. Other factors can potentially bias the clustering approach such as homoplasy with microsatellites at high divergence levels [START_REF] Viard | Variation of microsatellite size homoplasy across electromorphs, loci, and populations in three invertebrate species[END_REF] or an evolutionary history not compatible with this clustering model [START_REF] Kalinowski | The computer program STRUCTURE does not reliably identify the main genetic clusters within species: simulations and implications for human population structure[END_REF]); this could for example explain the grouping of Adriatic and North Africa samples at K = 3. The high assignment values observed for North Africa and Adriatic Sea at K = 7 seems to correspond to a real distinction of these populations but the analysis of geographically intermediate samples would be necessary to precise this point.

In any case, the differentiation between the geographical groups was significant and the percentage of genetic variation between groups was higher than previously reported (Costantini et al. 2007b;Ledoux et al. 2010a) possibly because of more restricted geographical sampling for these previous studies. Higher variation was observed between groups with EF1 than with microsatellites. This may be another consequence of microsatellite allele size homoplasy [START_REF] Viard | Variation of microsatellite size homoplasy across electromorphs, loci, and populations in three invertebrate species[END_REF] or a consequence of the upper limit of F ST estimates inherent to their statistical properties when applied to highly variable markers [START_REF] Jost | G ST and its relatives do not measure differentiation[END_REF]. Including EF1 sequence differences in the AMOVA slightly lowered the percentage of variation between groups indicating that this differentiation was not associated with high sequence divergence (see below).

Putative barriers to gene flow

The genetic structure of red coral agrees well with the gaps in suitable habitats (such as between Marseilles and Catalonia or for insular populations) or with the boundaries between different hydrographic regions as for example between Adriatic and Mediterranean populations. The differentiation of Adriatic populations had been observed for C. rubrum (Costantini et al. 2007b; a single sample) and for other marine organisms (e.g. Ruggiero et al. 2002, for Posidonia oceanica). For C. rubrum, further analyses are required to test whether this differentiation is due to IBD or is reinforced by a barrier to gene flow. Moreover EF1 allele frequencies did not demonstrate significant genetic differentiation between samples from South Italy (APU) and Adriatic Sea; this may be linked to small sample sizes or indicate that the putative barrier between the Adriatic Sea and the rest of the Mediterranean Sea is not located between these locations. In any case the lack of high divergence with EF1 sequences and the geographical distribution of haplotypes did not support the hypothesis of long-term barriers to gene flow [START_REF] Avise | Phylogeography: the history and formation of species[END_REF]. This is also in agreement with a recent recolonisation of the northern part of the Adriatic Sea following its emersion during glacial events [START_REF] Ruggiero | Genetic identity and homozygosity in north-adriatic populations of Posidonia oceanica: an ancient, post-glacial clone?[END_REF][START_REF] Thiede | A glacial Mediterranean[END_REF]. The presence of a Siculo-Tunisian genetic break [START_REF] Borsa | Intraspecific zoogeography of the Mediterranean: population genetic analysis on sixteen atlanto-mediterranean species (fish and invertebrates)[END_REF]) also remains to be tested.

Genetic differences were also evidenced between red coral populations from the northern and the southern parts of the western Mediterranean. Nevertheless, as in the case of the Adriatic Sea, there was no deep genetic divergence and the IBD pattern may explain the higher differentiation of the southern samples. South western Mediterranean has been poorly sampled in most phylogeography studies. In the rare cases where the sampling design was suitable, the studied species possessed high dispersal ability and no genetic differentiation was observed [START_REF] Bahri-Sfar | Fragmentation of sea bass populations in the western and eastern mediterranean as revealed by microsatellite polymorphism[END_REF]. This north-south differentiation was suspected in Sparus aurata [START_REF] Chaoui | Forte diffe ´renciation ge ´ne ´tique de la daurade Sparus aurata (L., 1758) entre les deux rives de la Me ´diterrane ´e occidentale[END_REF]), but the sampling scheme did not allow to precise the origin of this differentiation.

Although the Atlantic-Mediterranean differentiation remains to be investigated more thouroughly in C. rubrum, our data provide preliminary information on this point. For various marine organisms the Atlantic-Mediterranean break, when present, is located at the Almeria-Oran front [START_REF] Borsa | Intraspecific zoogeography of the Mediterranean: population genetic analysis on sixteen atlanto-mediterranean species (fish and invertebrates)[END_REF]Patarnello et al. 2007 and references therein). The comparison of C. rubrum samples from Ceuta (FUE and DEL) and Algeria (TEN and TNS) located on either side of this front, did not show any particular genetic break with EF1 and these samples were grouped by the clustering analysis (but quite heterogeneous on PCA). This suggests either a more extended influence of Atlantic populations in the Mediterranean, or a lack of such a phylogeographic break for this species. The analysis of Atlantic samples would be necessary to test these hypotheses.

The low divergence among EF1 haplotypes and the sharing of these haplotypes suggest that all the previously discussed barriers did not imply long-term isolation which should have been visible considering the total number of EF1 sequences considered here. This lack of deep divergence may result from a low evolutionary rate for EF1. Though we have no way to estimate the mutation rate for this intron, the observed levels of nucleotide diversity at this locus for C. rubrum (0.006) were within the range of values observed in other marine organisms: the deep-water coral Oculina sp. [START_REF] Eytan | Nuclear sequences reveal mid-range isolation of an imperilled deep-water coral population[END_REF]) and the deep-sea mussels Bathymodiolus thermophilus and B. azoricus [START_REF] Faure | Evidence for a slightly deleterious effect of intron polymorphisms at the EF1a gene in the deep-sea hydrothermal vent bivalve bathymodiolus[END_REF] for example. This observation does not suggest a particularly low rate of evolution of this marker in red coral. Therefore, a scenario of long-term divergence between regions does not seem probable for red coral. This low divergence also implies that the main genetic groups evidenced here should be considered as management units as suggested in Ledoux et al. (2010a), but not as different evolutionary significant units (sensu [START_REF] Moritz | Strategies to protect biological diversity and the evolutionary processes that sustain it[END_REF].

Mutation-drift equilibrium

For EF1, selective neutrality tests (Fs and R2) were significant and suggested a population expansion only when grouping all sequences. These tests were not significant at regional or population scales which may be a consequence of reduced power for these tests with the sample sizes used here (Ramos-Onsins and Rozas 2002). Conversely, the significant signal for the whole dataset could be a false positive signal of expansion induced by grouping genetically differentiated samples [START_REF] Sta ¨dler | The impact of sampling schemes on the site frequency spectrum in nonequilibrium subdivided populations[END_REF], even if it is not clear whether our sampling scheme and the observed level of differentiation for EF1 could generate this effect. Selection may also produce an apparent expansion signal. This selective hypothesis would require a hitch-hiking effect on a selected locus linked to this intron and a similar scenario has been proposed for EF1 in Mytilus spp. [START_REF] Faure | Genetic hitchhiking in a subdivided population of Mytilus edulis[END_REF]. The demographic hypothesis agrees well with the data of Ledoux et al. (2010a) which evidenced a putative signal of population expansion with microsatellites, but only for 16 out of 40 C. rubrum samples. In our case, the tests applied on microsatellite data were not significant after correction for multiple tests. The analysis of additional nuclear sequence markers and the use of higher sample sizes at population level will be necessary in order to study more precisely the potential departures from mutation-drift equilibrium and to potentially discriminate between the demographic and the selective hypotheses.

Evolutionary history of C. rubrum

The above results on genetic differentiation and selective neutrality tests shed light on the evolutionary history of C. rubrum. Two distinct scenarios can be discussed in the context of Quaternary sea-level fluctuations. In the ''refugium'' scenario, climatic fluctuations would have induced important changes in the distribution area of C. rubrum which could have persisted in geographically distant refugia at the LGM. This should have led to high divergence between source populations and various impacts on genetic diversity including bottlenecks [START_REF] Hewitt | The genetic legacy of the quaternary ice ages[END_REF][START_REF] Petit | Glacial refugia: hotspots but not melting pots of genetic diversity[END_REF], but secondary contacts can modify this pattern [START_REF] Petit | Glacial refugia: hotspots but not melting pots of genetic diversity[END_REF]. During the last glacial events, the connections between the different basins of the Mediterranean were also potentially more restricted than at present due to sea level variations [START_REF] Thiede | A glacial Mediterranean[END_REF]. This could have induced a longterm divergence pattern at least between basins. Alternatively, in the ''persistence'' scenario, C. rubrum would have persisted in most non-emerged areas with a gradual displacement of populations matching sea level variations. This scenario would have had less marked consequences for genetic structure. The low divergence between populations evidenced in red coral with EF1 sequences and microsatellites offers little support to the refugium scenario but tends to support that of persistence with gradual population displacement. Other observations support the persistence scenario such as the IBD pattern, which could have been broken in case of long distance recolonization (see [START_REF] Castric | The rise and fall of isolation by distance in the anadromous brook charr (Salvelinus fontinalis Mitchill)[END_REF]. More precise data on selective neutrality tests should help identify potential demographic fluctuations linked with recolonisation.

Therefore, C. rubrum populations may have persisted on the studied geographical area through the last Quaternary fluctuations, potentially with a demographic expansion during the last sea level rise. In a comparative study of 14 rocky-shore species from the northeastern Pacific, [START_REF] Marko | The ''expansion-contraction'' model of pleistocene biogeography: rocky shores suffer a sea change?[END_REF] suggested a regional persistence during the LGM: half of these species had histories consistent with long-term stability in population size. A persistence scenario is also coherent with the ecological characteristics of C. rubrum. In the north western Mediterranean, sea-surface temperatures were lower at the LGM than at present, with estimates of around 7°C in winter and 9-13°C in summer [START_REF] Thiede | A glacial Mediterranean[END_REF][START_REF] Hayes | Glacial mediterranean sea surface temperatures based on planktonic foraminiferal assemblages[END_REF]. This temperature may have been compatible with the presence of C. rubrum in most parts of western Mediterranean Sea as suggested by our results. Few fossil data have been published concerning the genus Corallium, but they suggest that populations of C. rubrum have been present without interruption in the Mediterranean basin since the early Pleistocene more than 2,000,000 years ago [START_REF] Vertino | Fossil ancestors of family Coralliidae in the Mediterranean Sea[END_REF]). The study of ''deep'' samples (i.e. under the depth corresponding to sea level during the LGM) would also be useful to elucidate the evolutionary history of this species, in particular for the identification of putative refugia, either deeper in the same geographical area or in remote areas. Moreover the comparison of the genetic diversity and structure of deep and shallow populations would shed some light on the genetic impact or recolonization processes. Genetic data have been published on deep samples (600-800 m) revealing differences with shallow populations [START_REF] Costantini | Deep-water Corallium rubrum (L., 1758) from the Mediterranean Sea: preliminary genetic characterisation[END_REF], but the analysis of more individuals, difficult though it be, is required for further interpretation.

Additional nuclear markers will help testing the hypothesis of persistence. Multimarker analyses are required to take into account the inherent variance in genetic and demographic processes. The advances in sequencing technology now allow an easier access to multi-locus data. These data would be useful for a comparative analysis of various evolutionary scenarios. The extension of such studies to other Mediterranean species should help understand the evolutionary history of marine organisms during past environmental fluctuations and to analyse the potential evolution of these organisms in a context of global change.

Fig. 1

 1 Fig. 1 Map of sampling localities of Corallium rubrum.Population codes are presented in Table 1. FUE and DEL samples are about 2 km apart; TEN and TNS correspond to two samples from the same site but at different depths (Table 1). Asterisks indicate regions covering several sampling sites, detailed in Table1; the precise locations of populations inside these regions are described inLedoux et al. (2010a)

  and the R2 test (Ramos-Onsins and Rozas 2002) are among the most powerful selective neutrality tests when there is no recombination (Ramı ´rez-Soriano et al. 2008; Ramos-Onsins and Rozas 2002). When recombination is suspected, Ramı ´rez-Soriano et al. (

Fig. 2 Fig. 3

 23 Fig. 2 Statistical parsimony network (TCS) of C. rubrum EF1 haplotypes. Blue Roman numbers correspond to haplotype identifiers. The colors correspond to the regions of origin of the sequences. Pie size indicates the frequency of each haplotype in the total dataset

Fig. 4

 4 Fig. 4 Principal Coordinates Analysis of the genetic relationships between regions for microsatellite data in C. rubrum. F ST values were used for population comparison. Percentages of variation explained by the axis: axis 1: 46.6%; axis 2: 18.4%; axis 3 (not shown): 15.4%

Table 1

 1 Corallium rubrum samples: location, hydrographic region, identification code, depth, sample size for microsatellites, sample size for EF1, and observed heterozygosity (Hobs) for EF1

	Regions, Sampling site	Hydrographic	Code	Depth (m)	Sample size	Sample size EF1	Hobs EF1
		region			microsatellites	(individuals)
					(individuals)
	Adriatic Sea
	Sazan, Albania	Adriatic Sea	ALB	58	20		0.50
	Garmenjak Veli Islet, Croatia	Adriatic Sea	GHA	57	30		0.29
	Total Adriatic Sea				50
	North Africa
	Tenes	SW Mediterranean	TEN	47	15		0.80
	Tenes	SW Mediterranean	TNS	33-36	15
	Ciclon de Fuera	Alboran Sea	FUE	25-30	22		0.72
	Cueva del Coral	Alboran Sea	DEL	42	15		0.44
	Total North Africa				67
	Corsica
	Baja Casju	NW Mediterranean	BCA	30	28		0
	Cala di Ponte	NW Mediterranean	CDP	26-27			0
	Palazzinu (cave)	NW Mediterranean	PUA	40			0
	Palazzu	NW Mediterranean	PZU	22	34		0.29
	Palazzu deep	NW Mediterranean	PZP	40			0
	Porto	NW Mediterranean	POR	24	30		0
	Total Corsica				92
	South Italy
	Apulia	Ionian Sea	APU	45			0.57
	Total South Italy
	North Italy
	Portofino	Ligurian Sea	PDA	35	30		0.43
	Total North Italy
	Balearic Islands
	Cap Formentor	Balearic Sea	FOR	36-38	32		0.25
	Llosa des Patro Pere	Balearic Sea	LPP	34-36	30		0.25
	Total Balearic Islands				62
	Marseilles
	Carro	Gulf of Lion	CRO	21	35		0.33
	Carry le Rouet	Gulf of Lion	CAR	20	37		0
	Figuier (cave)	Gulf of Lion	FII	20			0
	Grand Congloue ´Gulf of Lion	GC	40			1
	Grotte a `Peres (inside cave)	Gulf of Lion	GPI	20			1
	Grotte a `Peres (outside cave)	Gulf of Lion	GPE	20			0
	Impe ´riales du Large	Gulf of Lion	IML	60			0.40
	Plane	Gulf of Lion	PLA	38-41			0
	Ponteau	Gulf of Lion	PON	21	28		0
	Riou (inside cave)	Gulf of Lion	RII	20	36		0.14
	Riou (outside cave)	Gulf of Lion	RIE	20	30		1
	Riou deep (outside cave)	Gulf of Lion	RIO	40			1
	Tiboulen du Frioul	Gulf of Lion	TFR	38-40	42		0
	Tremies (cave)	Gulf of Lion	TRM	14-15			0
	Total Marseilles

Table 1 .

 1 FUE and DEL samples are about 2 km apart; TEN and TNS correspond to two samples from the same site but at different depths (Table1). Asterisks indicate regions covering several sampling sites, detailed in Table1; the precise locations of populations inside these regions are described inLedoux et al. (2010a)

	Table 1 continued
	Regions, Sampling site	Hydrographic	Code	Depth (m)	Sample size	Sample size EF1	Hobs EF1
		region			microsatellites	(individuals)
					(individuals)
	Co ˆte d'Azur
	Monaco	Ligurian Sea	MON	35-38	23	7	0.43
	Villefranche sur Mer	Ligurian Sea	VIL	22-24	36	2	0
	Total Villefranche-Monaco				59	9
	Catalonia
	Cap de Norfeu	NW Mediterranean	NOR	24	31	8	0
	Cova de la Reina	NW Mediterranean	CDR	14-17	38	3	0.33
	Cova de la Vaca	NW Mediterranean	COV	18		1	0
	Meda Xica	NW Mediterranean	XIC	35		2	0.50
	Pota del Lop	NW Mediterranean	POT	35	35	8	0.63
	Cap de l'Abeille	NW Mediterranean	BAN	25		1	1
	Sec Rederis	NW Mediterranean	SRE	23-24	27	5	0.60
	Total Catalonia				131	28
	For microsatellites, sample sizes in bold correspond to samples analysed for this paper; other sample sizes correspond to data from Ledoux et al.
	(2010a). EF1 data have all been obtained for the current article

Table 2

 2 Sequence polymorphism for the locus EF1 in C. rubrum

	Region/population Sample	h	Hd	p	Observed	Mean	P (Fs	Observed	Mean	P (R2	Tajima's
		size				Fs value	simulated	sim B obs)	R2	simulated	sim B obs)	D
		(2n genes)					Fs		statistics	R2
	All	376	39 0.88 0.006 -20.95	-0.55	0.00	0.03	0.07	0.04	-1.73
	Adriatic Sea	42		7 0.64 0.003	-1.43	-0.03	0.22	0.11	0.12	0.47	-0.26
	North Africa	64	11 0.83 0.005	-1.29	-0.22	0.31	0.14	0.10	0.86	0.81
	Corsica	48		9 0.79 0.004	-1.09	-0.05	0.33	0.11	0.11	0.58	0.07
	South Italy	14		5 0.77 0.003	-0.67	0.11	0.30	0.18	0.17	0.64	0.56
	North Italy	14		2 0.36 0.001	0.64	0.31	0.69	0.18	0.20	0.45	0.32
	Balearic Islands	24		5 0.38 0.001	-2.08	0.18	0.05	0.10	0.15	0.10	-1.52
	Marseilles	96	17 0.77 0.006	-2.69	-0.29	0.19	0.05	0.09	0.08	-1.39
	Villefranche-	18		4 0.66 0.002	0.18	0.08	0.57	0.14	0.16	0.35	-0.05
	Monaco
	Catalonia	56		6 0.81 0.006	3.28	-0.17	0.91	0.16	0.10	0.94	1.24
	Population
	ALB	28		6 0.66 0.003	-0.71	0.06	0.34	0.12	0.13	0.48	-0.23
	GHA	14		3 0.62 0.002	0.78	0.23	0.69	0.24	0.18	0.81	1.46
	TEN	10		7 0.93 0.005	-2.36	0.16	0.05	0.27	0.18	0.97	2.09
	FUE	36		6 0.75 0.004	0.64	-0.03	0.66	0.16	0.12	0.87	1.01
	DEL	18		4 0.73 0.006	2.78	0.05	0.91	0.21	0.14	0.96	1.40
	PZU	14		4 0.50 0.004	1.22	0.22	0.77	0.14	0.16	0.35	-0.30
	PZP	18		4 0.55 0.002	0.09	0.14	0.55	0.14	0.16	0.33	-0.17
	APU	14		5 0.77 0.003	-0.68	0.24	0.28	0.18	0.17	0.62	0.59
	PDA	14		2 0.36 0.001	0.64	0.30	0.70	0.18	0.20	0.44	0.32
	LPP	16		3 0.24 0.001	-0.98	0.25	0.10	0.13	0.19	0.21	-1.04
	IML	10		4 0.80 0.005	1.26	0.28	0.77	0.21	0.18	0.78	1.06
	RII	28		6 0.79 0.008	2.65	0.01	0.88	0.15	0.12	0.79	0.56
	RIE	16	11 0.95 0.008	-3.82	0.17	0.01	0.09	0.14	0.05	-1.03
	MON	14		3 0.60 0.002	0.46	0.25	0.64	0.19	0.19	0.65	-0.39
	NOR	16		4 0.77 0.006	2.85	0.11	0.91	0.20	0.15	0.91	1.13
	POT	16		5 0.83 0.007	1.80	0.07	0.82	0.18	0.15	0.83	0.91
	SRE	10		5 0.82 0.005	-0.05	0.19	0.48	0.15	0.18	0.17	-0.42

Table 3

 3 Tests of mutation-drift equilibrium with microsatellites in C. rubrum: P values for the one-tail Wilcoxon test for heterozygosity excess and deficiency, respectively

	Population	Heterozygosity	Heterozygosity
		excess	deficiency
	ALB	0.42	0.66
	GHA	0.96	0.05
	TEN	0.98	0.04
	TNS	0.96	0.05
	FUE	0.19	0.85
	DEL	0.47	0.59
	BCA	0.81	0.23
	PZU	0.85	0.19
	POR	0.96	0.05
	PDA	0.85	0.19
	FOR	0.85	0.19
	LPP	0.96	0.05
	CRO	0.97	0.04
	CAR	0.96	0.05
	PON	0.81	0.23
	RII	0.77	0.29
	RIE	0.95	0.15
	TFR	0.53	0.53
	MON	0.85	0.19
	VIL	1	0.00
	NOR	0.85	0.19
	CDR	1	0.01
	POT	0.99	0.01
	SRE	0.98	0.02
	No value was significant after correction for multiple tests with a false
	discovery rate of 0.05

Acknowledgments We thank Joaquim Garrabou, Olivier Bianchimani, Christian Marschal, Pierre Chevaldonne ´, Fre ´de ´ric Zuberer, Roland Graille and Thierry Pe ´rez for providing samples and Didier Forcioli and Helmut Zibrowius for useful comments. We thank Charlotte Roby, Kenza Mokhtar-Jamaı ¨, Emmanuelle Renard, Carole Borchiellini, Emilie Egea, Gwilherm Penant, Eve Gazave and Pascal Lape ´bie for their help in the laboratory. This work was funded by the French ANR (National Research Agency) in the Medchange program (www.medchange.org). This was also part of the EPIC project in the European Union Network of Excellence Marine Genomics. Some samples were obtained through the GBIRM project in the European Union Network of Excellence MARBEF. J.-B.L's PhD was funded by the Re ´gion Provence Alpes Co ˆte d'Azur. Two anonymous reviewers helped us to improve previous versions of this article.


Morgan Almanza
email: morgan.almanza@ens-cachan.fr

Alexandre Pasko

Frédéric Mazaleyrat

Martino Lobue

Numerical study of thermomagnetic cycle

Keywords: magnetocaloric materials, thermal energy harvesting, thermomagnetic cycle, simulation

We estimate the efficiency and power of a thermal energy harvesting thermodynamic cycle using magnetocaloric material as active substance. An accurate model of material, based on measurement, or theoretical are used to simulate a thermodynamic cycle and foresee magnetic work and then compare it to the maximum work. Afterwards power is estimated using a simple thermal exchange model. Simulations of different cycles for different working points illustrate the tradeoff between power and efficiency.

I. INTRODUCTION

Nowadays much of the industrial energy consumption consists in thermal processes such as cement and steel production, where about one third of the used energy is discarded as low grade heat. Therefore the supply of waste heat is sufficiently abundant as to make it a key target for technology development. A thermal energy harvesting system with high power density and/or efficiency does not currently exist. Many efforts have been done on thermoelectric systems (TE). However TE efficiency and power density are still too low for application purposes. Energy harvesting systems from waste heat based on thermo magnetic generation (TMG) have been studied since the 1948 paper by Brillouin and Iskenderian [START_REF] Brillouin | Thermomagnetic generator[END_REF] and the Patents by Edison and Tesla in 1890. The advent of giant magnetocaloric material (MCM) imposes a fresh assessment of the potential of TMG in term of efficiency and power and an increasing interest towards this opportunity is apparent from recent publications [START_REF] Vuarnoz | Quantitative feasibility study of magnetocaloric energy conversion utilizing industrial waste heat[END_REF][START_REF] Christiaanse | Proof-of-Concept Static Thermomagnetic Generator Experimental Device[END_REF]. As in the case of TE an issue too often neglected is that a tradeoff exists between efficiency and power density [START_REF] Hsu | Thermomagnetic conversion efficiencies for ferromagnetic materials[END_REF]. In this paper we focus on this aspect presenting numerical simulations, based on a simple thermal exchange model, to estimate efficiency and power density. TMG from waste heat involve harnessing the pyromagnetic effect (PE), namely the induction of a magnetization by the action of a temperature change. Two approaches are commonly envisaged: the first consists in cycling the active material around the maximum temperature-field coupling point while temperature change between the hot and the cold reservoir produce a magnetization change in time, which drives an electric current [START_REF] Vuarnoz | Quantitative feasibility study of magnetocaloric energy conversion utilizing industrial waste heat[END_REF]; the second uses the magnetization change in the active substance and the related force/couple exerted on a secondary material to directly produce mechanical work [START_REF] Christiaanse | Proof-of-Concept Static Thermomagnetic Generator Experimental Device[END_REF]. Efficiency and power density depend on many parameters: the heat exchanger, the material, the magnetic field available, the thermodynamic cycle used and the way we convert the magnetization change to electrical energy. Here we propose to examine in detail the tradeoff between efficiency and power on a single Ericsson cycle working between two heat sources, namely a hot one and a heat sink. Eventually the possibility to use the same approach to regenerative multiple heat sources cycle will be discussed.

II. MATERIALS MODELING

MCM are classified following the order of the phase transition driving the effect. Second order materials present a continuous ferromagnetic to paramagnetic transition at the Curie temperature (𝑇𝑇 𝐶𝐶 ) while the first order ones have an abrupt transition with a discontinuity in the magnetization versus temperature curve. Besides a strong magneto-elastic coupling and sometimes a structural transition are often associated with the first order magnetic phase change. As in most of first order phase transitions, hysteresis and metastability can be present. The most promising MCMs are the LaFeSi or the MnFePSi based compounds [START_REF] Sandeman | Magnetocaloric materials: The search for new systems[END_REF]. These materials have a very sharp transition with critical temperature adjustable with compositions. Some of these compounds are available at industrial scale. The estimation of TMG performance is based on the reliably of the material modeling. Historically, Brillouin have used Curie-Weiss law. Here, for second order materials, we shall use Weiss-Debye-Sommerfield [START_REF] Vuarnoz | Quantitative feasibility study of magnetocaloric energy conversion utilizing industrial waste heat[END_REF], to take into account the effect of field and temperature on thermal capacity, and data from real materials as Pr0.65Sr0.35MnO3 [START_REF] Almanza | Magnetic refrigeration: recent developments and alternative configurations[END_REF]. For first order materials we shall use a Bean and Rodbell like approach [START_REF] Bean | Magnetic Disorder as a First-Order Phase Transformation[END_REF].

III. THERMODYNAMIC CYCLE AND SIMULATIONS

Some ideal thermomagnetic cycles are shown in Fig. 1. The material is assumed to be always at thermodynamic equilibrium (i.e. the phase transition, whatever its order, is assumed to take place at equilibrium). Therefore, assuming the usual entropy balance expression, ds = dse + dsi, dse = 𝛿𝛿Q/T represents the reversibly exchanged specific entropy, and dsi ≥ 0 is the entropy production associated with irreversible heat exchange. From standard thermodynamic relations applied on an elementary volume (i.e. volume specific quantities), we can write,

𝑑𝑑𝑑𝑑 = 𝛿𝛿𝛿𝛿 -𝑀𝑀 ��⃗ 𝑑𝑑𝐵𝐵 �⃗

(1)

𝑇𝑇𝑑𝑑𝑇𝑇 = 𝑐𝑐 𝐻𝐻 𝑑𝑑𝑇𝑇 + 𝑇𝑇 𝜕𝜕𝑇𝑇 𝜕𝜕𝜕𝜕 𝑑𝑑𝜕𝜕 = 𝛿𝛿𝛿𝛿 (2)
In (1) 𝑑𝑑 is the internal energy, -𝑀𝑀𝑑𝑑𝐵𝐵 the magnetic work, 𝛿𝛿 the heat exchange, 𝑇𝑇 the entropy and 𝑐𝑐 𝐻𝐻 the heat capacity at constant field, all these quantities being defined per unit of volume. The efficiency of the cycles, defined by how much work is produced compared to the heat absorbed, only depends of 𝜕𝜕, 𝑇𝑇 path.

𝜂𝜂 = - 𝑊𝑊 𝑚𝑚𝑚𝑚𝑚𝑚 𝛿𝛿 ℎ𝑜𝑜𝑜𝑜 = 1 + 𝛿𝛿 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 𝛿𝛿 ℎ𝑜𝑜𝑜𝑜 (3)
When the MCM is said to be in thermal contact with the hot reservoir then 𝑘𝑘 ℎ𝑜𝑜𝑜𝑜 is more or less a big number depending on the exchange efficiency and 𝑘𝑘 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 is null and vice versa. Using the material model and ( 2) in (4) integrated, the period of the cycle is computed as represented in the Fig. 3. To evaluate how far the cycle is from the maximum work cycle for given reservoirs, the entropy production dues to heat exchange has to be considered,

𝛿𝛿𝑇𝑇 𝑝𝑝 (𝑇𝑇, 𝜕𝜕) = � 1 T - 1 T s (T, H) � δQ(T, H) (5)
The system studied is now the MCM and the sources. The temperature of the source 𝑇𝑇 𝑠𝑠 which the MCM exchanges, is alternatively 𝑇𝑇 ℎ𝑜𝑜𝑜𝑜 and 𝑇𝑇 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 . For example, in Ⓐ cycle entropy production is due to irreversible heat exchange along the transformation at constant temperature. If, and only if, there is only two reservoirs, the cold and the hot, entropy production is linked to the efficiency of the Carnot cycle, the cycle which in this case extracts the maximum work or which doesn't produce entropy due to the heat exchange:

𝜂𝜂 = 1 - 𝑇𝑇 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 𝑇𝑇 ℎ𝑜𝑜𝑜𝑜 - 𝑇𝑇 𝑝𝑝 𝑇𝑇 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 𝛿𝛿 ℎ𝑜𝑜𝑜𝑜 = 𝜂𝜂 𝐶𝐶𝑚𝑚𝑝𝑝𝐶𝐶𝑜𝑜𝑜𝑜 - 𝑇𝑇 𝑝𝑝 𝑇𝑇 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 𝛿𝛿 ℎ𝑜𝑜𝑜𝑜 (6)
Relative efficiency 𝜂𝜂 𝑝𝑝𝑝𝑝𝑐𝑐 is the ratio of the cycle efficiency to the efficiency of the Carnot cycle:

𝜂𝜂 𝑝𝑝𝑝𝑝𝑐𝑐 = 𝜂𝜂 𝜂𝜂 𝐶𝐶𝑚𝑚𝑝𝑝𝐶𝐶𝑜𝑜𝑜𝑜 = 1 - 𝑇𝑇 𝑝𝑝 𝑇𝑇 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 𝜂𝜂 𝐶𝐶𝑚𝑚𝑝𝑝𝐶𝐶𝑜𝑜𝑜𝑜 𝛿𝛿 ℎ𝑜𝑜𝑜𝑜 (7)
Faster is the cycle, with 𝑇𝑇 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑜𝑜𝑐𝑐 = ∞, 30, 10 𝑚𝑚𝑇𝑇 i.e exchange heat, faster the relative efficiency decreases with respectively 𝜂𝜂 𝑝𝑝𝑝𝑝𝑐𝑐 = 1, 0.5, 0. In the final paper, comparison between cycles with estimation of power and efficiency based on simple heat exchange model, will be done for the experimental and the theoretical material model for second order material and with theoretical material model only for the first order. And different optimum working point for magnetic power production and tradeoff will be proposed.

Fig. 1 .

 1 Fig. 1.Examples of two ideal cycles: Ⓐ Carnot, Ⓑ isofield-isothermal Ericson cycle, and of a generic cycle Ⓒ.

Fig. 2

 2 Fig. 2 Magnetic work for the cycle Ⓐ for different 𝑇𝑇 1 temperature with an applied field of 1T with Pr0.65Sr0.35MnO3 To estimate power of a cycle, the following simple heat exchange model describes the thermal exchange with the two reservoir where are 𝑘𝑘 ℎ𝑜𝑜𝑜𝑜 (𝑇𝑇, 𝜕𝜕) and 𝑘𝑘 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 (𝑇𝑇, 𝜕𝜕) in [𝑊𝑊. 𝐾𝐾 -1 . 𝑚𝑚 -3 ]. 𝛿𝛿𝛿𝛿 = [-𝑘𝑘 ℎ𝑜𝑜𝑜𝑜 (𝑇𝑇 -𝑇𝑇 ℎ𝑜𝑜𝑜𝑜 ) -𝑘𝑘 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 (𝑇𝑇 -𝑇𝑇 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐 )]dt,(4)

Fig. 3 .

 3 Fig. 3. Example of Ⓐ cycle with its period 𝑇𝑇 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑜𝑜𝑐𝑐 where different temperature difference is used for the heat exchange

3 ,

 3 from the red to the black cycle in the Fig.3. This glance reveals the trade-off between power and efficiency, with some assumptions and with cycle Ⓐ the following expression exhibits this trade-off:


First vs second order magnetocaloric material for thermomagnetic energy conversion

Morgan Almanza 1 , Alexandre Pasko 1 , Frédéric Mazaleyrat 1 , Martino LoBue 1 1 SATIE, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France morgan.almanza@ens-cachan.fr

The supply of waste heat represents a huge and freely available amount of energy that make it a key target for energy conversion technologies, notwithstanding the small thermodynamic efficiency to be expected because of the limited working temperature difference. Energy harvesting systems from waste heat based on thermomagnetic generation (TMG) have been studied since the 1948 paper by Brillouin and Iskenderian [START_REF] Brillouin | Thermomagnetic generator[END_REF]. The new generation of magnetocaloric materials (MCM) raised a renewed interest towards this technology [START_REF] Vuarnoz | Quantitative feasibility study of magnetocaloric energy conversion utilizing industrial waste heat[END_REF]. Recently we published numerical simulations of isofield-isotemperature and adiabatic-isotemperature cycles in finite time thermodynamics [START_REF] Almanza | Numerical study of thermomagnetic cycle[END_REF] (i.e. where thermal exchange is taken into account in a non-quasistatic regime), allowing to estimate the efficiency at maximum power (EMP) using first and second order phase transition magnetocaloric materials as active substance. Our preliminary results made possible the comparison with thermoelectric generators [START_REF] Almanza | Thermal energy harvesting: thermomagnetic versus thermoelectric generator[END_REF], showing a similar power density for temperature span lower than 10°C, but a much higher relative efficiency from 0.05 to 0.2 in the case of thermomagnetic cycles. However, these cycles are still highly idealized ones as they assume a perfect control of their shape based on field feedback. Indeed, iso-temperature transformations used in [START_REF] Almanza | Numerical study of thermomagnetic cycle[END_REF] to work out best efficiencies can be hardly achieved in an actual device that would more easily work on a iso-field-adiabatic cycle (i.e. a Brayton cycle).

Here we shall show how the constitutive relation (i.e. the equation of state) of the material leads the actual shape of a finite time thermodynamic cycle. Our main result is to show that for first-order MCM the iso-field transformation stays closer to an iso-temperature one allowing a significant efficiency improvement with respect to second order MCM.

Using the method presented in [START_REF] Almanza | Numerical study of thermomagnetic cycle[END_REF], we study the potential benefit of first order MCM in terms of power density and efficiency compared to the second order MCM for cycle with adiabatic and iso-field process. Results will also be compared with thermoelectric generator at maximum power [START_REF] Almanza | Thermal energy harvesting: thermomagnetic versus thermoelectric generator[END_REF].

I. SYSTEM AND MATERIAL MODELING

Two approaches are commonly envisaged to harvest the magnetic energy produced by the cycling of the active material around a temperature induced ferromagnetic-paramagnetic transition. The first uses the magnetization change in time to drive an electric current [START_REF] Christiaanse | Proof-of-Concept Static Thermomagnetic Generator Experimental Device[END_REF] whereas the second uses the mechanical work associated with the difference of magnetic force due to a magnetization change [START_REF] Hsu | Thermomagnetic conversion efficiencies for ferromagnetic materials[END_REF]. Due design constraints, a thermodynamic cycle composed by two iso-field and two adiabatic processes (i.e. Brayton cycle), is the commonest choice for systems of the latter class. Here we compute the thermodynamic cycle following [START_REF] Almanza | Numerical study of thermomagnetic cycle[END_REF], namely using an equation of state, deduced from a phenomenological Landau model and describing the heat exchange using a coefficient 𝑘𝑘 ℎ𝑖𝑖𝑖𝑖ℎ of 1 𝑊𝑊 • 𝑐𝑐𝑚𝑚 -3 • 𝐾𝐾 -1 .

II. THERMODYNAMIC SIMULATION

Given the power density, the maximum relative efficiency 𝜂𝜂 𝑟𝑟𝑟𝑟𝑟𝑟 , with respect to the Carnot efficient 𝜂𝜂 𝐶𝐶𝐶𝐶𝑟𝑟𝐶𝐶𝐶𝐶𝐶𝐶 , is achieved by minimizing the entropy production 𝑠𝑠 𝑖𝑖 . Here we take into account only 𝑠𝑠 𝑖𝑖 associated with the finite-time heat exchange (i.e. hysteresis and kinetics associated with the magnetic transition are neglected). To do that we use a linear model of heat exchange where, as shown in [START_REF] Almanza | Numerical study of thermomagnetic cycle[END_REF], entropy production is minimum when heat exchange takes place at constant temperature difference (HECTD). This means that efficiency is maximum when the difference between the temperature 𝑇𝑇(𝑡𝑡) of the MCM as a function of time t and the temperature of the reservoirs, 𝑇𝑇 ℎ𝐶𝐶𝐶𝐶 or 𝑇𝑇 𝑐𝑐𝐶𝐶𝑟𝑟𝑐𝑐 , respectively for the hot reservoir and the heat sink, are constant during the heat exchange process (that is why we use the term iso-temperature rather than isotherm to name this transformation). Calculations of cycles, as shown in the Figure 1, with 𝑇𝑇 ℎ𝐶𝐶𝐶𝐶 = 298 𝐾𝐾, 𝑇𝑇 𝑐𝑐𝐶𝐶𝑟𝑟𝑐𝑐 = 291 𝐾𝐾 for first and second order MCM give for the small cycles,𝑃𝑃 𝑚𝑚𝐶𝐶𝑖𝑖 = 10 𝑚𝑚𝑊𝑊. 𝑐𝑐𝑚𝑚 -3 , 𝜂𝜂 𝑟𝑟𝑟𝑟𝑟𝑟 = 0.45, 𝑡𝑡 𝑝𝑝𝑟𝑟𝑟𝑟𝑖𝑖𝐶𝐶𝑐𝑐 = 0.1 𝑠𝑠 while for large cycle we have for first order 𝑃𝑃 𝑚𝑚𝐶𝐶𝑖𝑖 = 9.2 𝑚𝑚𝑊𝑊. 𝑐𝑐𝑚𝑚 -3 , 𝜂𝜂 𝑟𝑟𝑟𝑟𝑟𝑟 = 0.41, 𝑡𝑡 𝑝𝑝𝑟𝑟𝑟𝑟𝑖𝑖𝐶𝐶𝑐𝑐 = 10 𝑠𝑠 and for second order 𝑃𝑃 𝑚𝑚𝐶𝐶𝑖𝑖 = 8.2 𝑚𝑚𝑊𝑊. 𝑐𝑐𝑚𝑚 -3 , 𝜂𝜂 𝑟𝑟𝑟𝑟𝑟𝑟 = 0.41, 𝑡𝑡 𝑝𝑝𝑟𝑟𝑟𝑟𝑖𝑖𝐶𝐶𝑐𝑐 = 10 𝑠𝑠. In the Figure 1 we show that first order MCMs in iso-field processes keep closer to a HECTD, during the transition, than second order MCM allowing to get closer to the optimum cycle. The difference is apparent comparing the low temperature isofield line, in Figure 1, the first order material (red line) shows a horizontal line (a perfect iso-temperature transformation) whereas the second order one (black line) shows finite slope. Nevertheless, it is worth noting that both second and first order MCM can approach HECTD by drastically reducing the span of the iso-field process, as in the dashed line cycles in Figure 1. This means EPM for first and second order materials will be very similar when working on tiny cycles at a rather high frequency. In the Figure 2, we show the maximum power for different 𝑡𝑡 𝑝𝑝𝑟𝑟𝑟𝑟𝑖𝑖𝐶𝐶𝑐𝑐 , a slight increase of the power density for the first order MCM for longer periods is apparent. Small period cycles are expected to be achievable only in the case of micro-systems where fast switching can be achieved. However, high frequency excitation will very possibly increase the role of transition kinetics (neglected in our approach) in the case of first-order MCM. Thus we can conclude that, while first order materials are better suited for bulk applications, highfrequency micro-systems will be more efficiently designed using second order materials.

Figure 1

 1 Figure 1 Brayton cycles on T-S diagram for the second order MCM (black) on the left and the first order MCM (red) on the right for large (full line) and small cycles (dotted line). Thin lines represent three isofields in black for second order and in blue for first order MCM.

Figure 2

 2 Figure 2 Maximum magnetic power and its relative efficiency for different time periods for first order in full line (𝐻𝐻 𝐶𝐶𝑝𝑝𝑝𝑝𝑟𝑟𝑖𝑖𝑟𝑟𝑐𝑐 = 0.67 𝑇𝑇, max (∆𝑇𝑇 𝐶𝐶𝑐𝑐𝑖𝑖𝐶𝐶 ) = 3.4 𝐾𝐾)and for second order in dashed line (𝐻𝐻 𝐶𝐶𝑝𝑝𝑝𝑝𝑟𝑟𝑖𝑖𝑟𝑟𝑐𝑐 = 1 𝑇𝑇, max (∆𝑇𝑇 𝐶𝐶𝑐𝑐𝑖𝑖𝐶𝐶 ) = 3.4 𝐾𝐾).


Jean-Pierre Feral
email: jean-pierre.feral@univmed.fr

Élie Poulin
email: epoulin@uchile.cl]

Kerguelen Islands: a living laboratory to understand the benthic biodiversity of the Antarctic by

Keywords: Brooding invertebrates -Coastal communities -Southern ocean -Biodiversity. (1) uMr 6540 Diversité, évolution et écologie fonctionnelle marine, Station marine

The high proportion of brooding (50 to 70% depending on phyla) compared with broadcaster species among invertebrates living along the coast of the Southern ocean has been traditionally interpreted as an adaptation to local environmental conditions. Currently, however, species with a planktotrophic developmental mode are ecologically dominant along coastal areas, in terms of abundance of individuals. The fact that Kerguelen island is inhabited by such species and that the French base Port-aux-Français, with its equipped marine laboratory, made it possible to address questions as to why are there so many brooders in the coastal waters of the Southern ocean and if the apparent ecological success of broadcasters related to their developmental mode. We argue that the present shallow antarctic benthic invertebrate fauna is the result of two processes acting at different temporal scales. First, the high proportion of brooding species compared with coastal communities elsewhere corresponds to species-level selection occurring over geological and evolutionary times which explains the very high biodiversity observed in coastal waters. Second, the ecological dominance of broadcasters is the result of processes operating at ecological timescales that are associated with the advantage of having pelagic larvae under highly disturbed conditions (e.g., ice scouring).

rÉsUMÉ. -les îles Kerguelen : un laboratoire vivant pour la compréhension de la biodiversité benthique en antarctique. la proportion élevée (50 à 70% selon les phylums) d'espèces incubantes comparée à celle des espèces dispersantes d'invertébrés vivant dans les eaux côtières de l'océan austral a été traditionnellement interprétée comme une adaptation aux conditions environnementales locales. Cependant, de nos jours, les espèces à développement planctotrophique y sont écologiquement dominantes, en termes d'abondance. le fait que les îles Kerguelen abritent de telles espèces et que la base de Port-aux-Français possède un véritable laboratoire marin a permis de développer des programmes pour répondre à des questions comme : pourquoi y-a-t-il tant d'espèces incubantes dans les eaux côtières de l'océan austral ? ou bien, le succès écologique apparent des espèces dispersantes est-il lié à leur mode de développement ? nous soutenons que la faune actuelle d'invertébrés benthiques côtiers antarctiques est le résultat de deux processus agissant à des échelles temporelles différentes : (1) la proportion élevée d'espèces incubantes, comparée aux communautés côtières partout ailleurs, correspond à une sélection au niveau de l'espèce se produisant à des échelles de temps géologiques qui explique la biodiversité très élevée observée dans les eaux côtières, (2) la dominance écologique actuelle des espèces dispersantes est le résultat de processus fonctionnant à des échelles de temps écologiques qui sont associés à l'avantage de posséder des larves pélagiques dans des conditions fortement perturbées (p. ex., rabotage des fonds par les icebergs).

Since the seventies, benthic biodiversity was assessed in Kerguelen during the cruises of the Marion Dufresne and thanks to programs by r. Delépine and others focused on algae, P. arnaud, a. Guille, J.-P. Féral on macrobenthos and by J.-C. Hureau and G. Duhamel on fishes. Pioneering efforts to study the antarctic biodiversity in Terre adélie were conducted by P. arnaud and J.-C. Hureau in the early sixties and in 1987 by the first diving expedition by J.-P. Féral. Initial investigations of antarctic marine biology started with macrobenthos and fishes. The use of scuba diving, limited exploration only until 30 m depth; the use of a remote operated vehicle (roV) in 2000 permitted the study of biodiversity at 150 m depth. The Astrolabe, equipped with a ROV, verified previous observations.

Contrary to an accepted (continental-based) paradigm that biodiversity declines from the equator to the poles, marine biodiversity, at least coastally, is very high along the antarctic continent and the sub-antarctic islands. as the observed biodiversity at a time is the result of the histories of the species, of the climate and of the ocean basins, it is necessary to consider different time scales to understand the present biodiversity. To only compare contemporary conditions with the characteristics of the fauna and flora is quite risky. Hence, we propose to first consider exceptional biological properties of the antarctic fauna, using model species.

the southern Ocean's coastal waters are remarkable because they are inhabited by a great majority of brooding invertebrate species

Marine invertebrates display a great variety of life-history traits and reproductive strategies. each broad type of free and protected development is found in all the oceans, but comparisons of the principal reproductive modes between different geographic regions have shown that they are not equally distributed. Frequency of pelagic development (planktotrophic and lecithotrophic) decreases from the equator to the antarctic, where brood-protecting becomes dominant. The high proportion of brooding (50-70% depending on phyla) compared with broadcasting species among invertebrates living along the coast of the Southern ocean has been traditionally interpreted as an adaptation to local environmental conditions. on the other hand, in the present days, species with a planktotrophic developmental mode are ecologically dominant along coastal areas of the Southern ocean, in terms of abundance of individuals.

Developing explanatory hypotheses

numerous theories have been proposed to explain the richness of non-pelagic development in most marine invertebrates within the Southern ocean. These theories can be grouped into three categories: larval survival (where selection acts on larvae), energy allocation, and dispersal. all of them consider the adaptive significance of brood-protecting as the key to the success of this strategy in the antarctic. However, the adaptive significance of brooding and the evolutionary success of this strategy in the antarctic must be considered as two separate issues.

Considering the problem from an evolutionary level, the consequences of different reproductive strategies on the genetic structure of species and on the long-term evolution of the clade were examined.

sea urchins as a model class in echinoids, the reduction of larval stage duration is associated with a decrease in gene flow and consequently of the geographical scale of genetic differentiation. Four patterns of larval development are generally recognized: planktotrophy, pelagic lecithotrophy, bottom dwelling and brood-protecting. non-pelagic development is clearly the rule for antarctic echinoids. The 79 nominal echinoid species known from antarctic and Subantarctic areas belong to nine families (four being exclusively abyssal). around 65% have non-pelagic development (all brooding) and 35% with pelagic development. Two families, the Schizasteridae (Spatangoida) and the Cidaridae (Cidaroida), consist almost entirely of brooding species. The developmental type of a few cidaroid species is still unknown. a third family, the echinidae (echinoida), consists of six species that have a planktotrophic larva. These three families are the typical echinoids in the antarctic coastal and shallow waters. The echinothuriidae and the three families of Holasteroida known from antarctic waters, the urechinidae, the Plexechinidae and the Pourtalesiidae are essentially deep-sea forms with a wide distribution in the ocean basins.

Where and how to study the diversification of echinoids?

To understand the impacts and the interest in brood protection, it was necessary to study the echinoids' life cycle and ecology. Because most life cycles are annual, and given the constraints of scuba diving in Terre adélie during winters, we took advantage of the fact that Kerguelen island is inhabited by these species. The French base Portaux-Français has a marine laboratory which made it possible to investigate the population of brooders in the coastal waters of the Southern ocean and their apparent ecological success relative to their developmental pattern.

results summarized here are mostly taken from the PhD thesis and major articles of the program "Benthos-mac" [START_REF] Poulin | la recherche et la Technologie Polaires/ institut Paul emile Victor (iFrTP/iPeV) programs 195 (Benthos-mac) and 345 (Benthadel). We thank the numerous people who helped us, particularly the Volontaires de l'aide Technique (VaTs) who made it possible on the field and in the laboratory and also to colleagues who participated in a way or another[END_REF][START_REF] Magniez | -reproductive cycle of the brooding echinoid Abatus cordatus (echinodermata) in Kerguelen (antarctic ocean): changes in the organ indices, biochemical composition and caloric content of the gonads[END_REF]Schatt andFéral, 1991, 1996;[START_REF] Poulin | The fiction and the facts of Antarctic incubation -population genetics and phylogeny of schizasterid echinoids[END_REF][START_REF] Poulin | Pattern of spatial distribution of a brood-protecting schizasterid echinoid, Abatus cordatus, endemic to the Kerguelen islands[END_REF], 1996[START_REF] Poulin | Why the difference in species numbers of coastal echinoids in two trophic groups at Terre adélie (antarctica): functional or historical diversity?[END_REF][START_REF] Poulin | Genetic structure of the brooding sea urchin Abatus cordatus, an endemic of the Subantarctic Kerguelen island, and the origin of the diversity of antarctic echinoids[END_REF][START_REF] Poulin | Combined ecological factors permit classification of developmental patterns in benthic marine invertebrates: a discussion note[END_REF][START_REF] Poulin | evolutionary versus ecological success of developmental modes in coastal antarctic benthic invertebrates[END_REF] who studied the ecology, life cycle, development and the genetic structuring of the spatangoid sea urchin Abatus cordatus (Verrill, 1876) in Kerguelen. other results were taken from a collaborative project between France and Chile.

Main features of Abatus cordatus

The species A. cordatus (Fig. 1) lives in the sediment. Females brood eggs and juveniles in four dorsal pouches. The dispersal of this species is therefore characterized by limited mobility among adults and the lack of a free-swim-ming larval phase. using scuba and dredging, A. cordatus was sampled all around Kerguelen (Fig. 2). The spatial distribution from the island scale to the bay scale shows discontinuities on two levels. First, at the island scale, favorable sectors (principally characterized by jagged coastline with numerous sheltered bays) are separated by linear coastline or swell exposed sectors; secondly, at the bay scale, A. cordatus lives in high density, isolated demes in the shallow waters of sheltered bays (inset Fig. 2). Sediment preference ranged from medium to fine sand. The granulometry of the sediment and the lack of predation determine the aggregated spatial distribution pattern. Beside these high density local populations, isolated individuals are found from 1 m to more than 500 m depth.

isoenzymes analyses (Fig. 3) demonstrated that the geographical distance of differentiation is of the order of 10 km, that the demes are genetically differentiated populations, and that genetic differentiation follows a stepping stone model.

consequences on the long term evolution of the clade

if the likelihood of genetic exchange between populations of species with planktotrophic larvae is high, the reduced gene flow associated with non-dispersive larvae can induce high speciation rates (Fig. 4a). This differential speciation rate model theoretically leads to a progressive increase with time in the proportion of species with nonplanktotrophic and non-pelagic development. However, this model alone cannot explain the high diversity of brood protecting echinoids in the Southern ocean, because it predicts a continuous increase with time in the proportion of such species not only around antarctica but anywhere else. indeed, this model does not explain the differences in developmental strategy observed between low and high latitudes.

The climatic evolution of the antarctic and the Southern ocean is characterized by a long-term cooling, which started at about 52 Ma, close to the early/Middle eocene boundary. This allows the reconsideration of the high speciation rate model (based on isolation by distance) and to reconstruct it with the addition of differential extinction rates between planktotrophic and brooding species in relation to the climatic history of the antarctic. This differential extinction-rate model between pelagic developing species and brooders could explain the present predominance of brooding echinoids in this area (Fig. 4b). During the coldest phases, the ice sheet blankets the continental shelf, and the surrounding ocean is covered by a thick layer of permanent sea-ice. The direct consequence was a significant reduction in the amount of light, which led to a decrease in primary productivity around antarctica. The duration of these episodes was typically much larger than the life span of organisms and could have caused the local extinction of many species or even entire clades with planktotrophic development. This model, based on negative selection at the species level, is well supported by antarctic echinoids. The low number of echinoid families present in antarctic and Subantarctic areas (6 of 50 known), indicates the extinction of entire planktotrophic taxa and the difficulty for such species to colonize and/or recolonize these areas due to the geographical, bathymetric and hydrological isolation of antarctica and the barrier posed by the antarctic circumpolar current.

an increase in the number of brooding species could have also been enhanced through vicariant speciation, particularly during episodes of partial deglaciation. Therefore, the high proportion of brooding species among antarctic benthic invertebrates could correspond to a macroevolutionary trend resulting from sorting at the species level because of contrasting developmental modes experiencing differential extinction rates during adverse environmental conditions.

A paradoxical observation

in spite of the high number of brooding species, the antarctic shallow subtidal zone is dominated by numerous individuals of just a few species with a planktotrophic developmental mode, particularly echinoderms. a quick glance into the shallow subtidal zone shows the conspicuousness of planktotrophic species, such as the sea urchin Sterechinus neumayeri (Meissner, 1900), described as one of the most abundant macrobenthic organisms in shallow antarctic waters; the asteroids Odontaster validus Koehler, 1906, O. meridionalis (e.a. Smith, 1876) and Porania antarctica e.a. Smith, 1876; the ophiuroid Ophionotus victoriae Bell, 1902; the antarctic scallop Adamussium colbecki (Smith, 1902), and the clam Laternula elliptica (King and Broderip. 1831). in view of this pattern, and that antarctica currently experiences interglacial conditions, one might ask if the apparent ecological success of these species is related to the possession of a dispersive larval phase.

Effects of ice disturbances on Antarctic shallow macrobenthos

in shallow antarctic environments, ice is the most common physical disturbance. There are diverse types of icerelated disturbance such as the formation of icefoot along the coast down to a depth of 10 m, which significantly impacts intertidal and shallow subtidal habitats during most of the year; the formation of anchor ice during winter (down to a depth of 30 m); and the destructive effect of icebergs ploughing down to depths of 500 m. These disturbances favor mobile species and those with pelagic larval development.

The occurrence of such disturbances has been recognized as an important factor determining the success of different dispersal strategies. Models have also shown that habitat instability favors species with high dispersal capabilities (such as those with planktotrophic larvae), mainly through recolonization. For marine invertebrates with reduced mobility, larvae are the main vehicles for recolonizing recently disturbed habitats, which typically exist after iceberg scouring events. The antarctic interglacial environmental condition is characterized by the common occurrence of disturbances and is unlikely to be favorable for brooding species in the shallow subtidal zone. in Subantarctic latitudes, however, where ice impact is less common or nonexistent, ecological dominance of planktotrophic species in shallow habitats is not as evident.

Evolutionary success of brooding versus ecological success of planktotrophy

The arguments presented here suggest that both macroand microevolutionary processes are responsible for the biodiversity patterns of marine invertebrates currently observed in antarctica. on the one hand, the high number of brooding invertebrate species (evolutionary success) could be interpreted as the result of a species-sorting process operating during the coolest periods of the late Cenozoic. on the other hand, the current ecological dominance of only a few species with planktotrophic development (ecological success) could be related to the capacity of their larvae to recolonize highly disturbed shallow habitats.

The hypothesis of two processes acting at different timescales, as exemplified here with echinoderms, needs to be broadened to include other taxa. More detailed investigation of the developmental modes of shallow benthic invertebrates and their spatial distribution will enhance our understanding of the evolutionary and ecological processes affecting antarctic fauna.

Origin and evolution of marine invertebrates in the southern Ocean

recent and ongoing studies are using molecular markers to reconstruct the evolutionary history of marine benthos in the Southern ocean and establish the relationship between antarctic and Subantarctic areas, as well as shallow and deep-sea water. as shown in our most recent publications on echinoids and limpets, Kerguelen Plateau appears as an indispensable place for such studies, because of its geographic location and the extent of shallow water habitats.

Figure 1 .

 1 Figure 1. -Abatus cordatus. (a) natural aspect (b) female individual with removed spines over the brooding pouches (white star) showing the offspring (white arrow), (c) female test showing the four aboral brooding pouches (black star) and the three gonopores (black arrow). © photos by J.C. Duchêne (a), J.P. Féral (b) and P. Magniez (c).

Figure 2 .

 2 Figure 2. -Sampled sites around Kerguelen (red dots). inset: details of the distribution pattern of adult Abatus cordatus in three very sheltered bays in Bras de la Fonderie [ high density, medium density, low density] showing that A. cordatus is characterized by numerous dense isolated demes in shallow waters. The observed densities are decreasing with the depth.

Figure 3 .

 3 Figure 3. -edwards's genetic distance among populations of abatus cordatus sampled along the north (yellow) and the south (green) coasts of Kerguelen and in the Golfe du Morbihan. There is a link between the geographic distance and the importance of the genetic differentiation. north. PC: Port Couvreux, aT: anse Thomas, PMa: Port Matha, aJ: anse du Jardin, Bl: Baie du Brise lame; G. Morbihan. Pr: Port raymond, iH: ile Haute, Gl: Îlots Glénan, SuM: ile Suhm, aH: anse du Halage; South. SWa: Baie des Swains, Mou: Baie de la Mouche.

Figure 4 .

 4 Figure 4. -Hypotheses based on dispersal abilities of species and on their consequences on the long-term evolution of the clade. (a) The high-rate-speciation model: lineage pattern of two clades with different dispersal strategies -differential speciation. (b) The differential extinction-rate model: lineage pattern of clades with different dispersal strategies through a climatic crisis -differential mortalities. Green: low/non dispersal species. red: high dispersal species. Gray zone symbolizes a climatic crisis.

Figure 5 .

 5 Figure 5. -examples of antarctic species with larval phase development (a) Odontaster validus (Terre adélie, Chenal du lion, 20 m, scuba); (b) Sterechinus neumayeri (King George island, 5 m, scuba); (c) Adamussium colbecki (Terre adélie, Baie de l'empereur, 58 m, roV); (d) Ophionotus victoria (Terre adélie, nunatak du Bon Docteur, 110 m, roV). © photos by P. laboute (a) and J.-P. Féral (b to d).

Acknowledgements. -These works were supported by the institut