Claudio A González-Wevar

N I I Segovia

Sebastian Rosenfeld

Dominikus Noll

C S S Maturana

M Hüne

J Naretto

Karine Gérard

Angie Díaz

H G G Spencer

T Saucède

J-P Féral

S A Morley

P Brickle

N G Wilson

E Poulin

González-Wevar Ca

Segovia Ni

Maturana Cs

Spencer Hg

Morley Sa

Wilson Ng

Contrasting biogeographical patterns in Margarella (Gastropoda: Calliostomatidae: Margarellinae) across the Antarctic Polar Front

Keywords: Southern Ocean; Antarctic Polar Front, long-distance dispersal, benthic-protected development, rafting, Margarella

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

Introduction

The genus Margarella Thiele, 1893 includes Antarctic and sub-Antarctic small to medium-sized vetigastropods that are abundant on hard substrate inter-and shallow sub-tidal shores [START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF]. Near-shore species of the genus are frequently found in ecosystems dominated by macroalgae, on which they are commonly found grazing [START_REF] Adami | Structure and dynamics of the biota associated with Macrocystis pyrifera (Phaeophyta) from the Beagle Channel[END_REF][START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF][START_REF] Rosenfeld | Molluscan assemblages associated with Gigartina beds in the Strait of Magellan and the South Shetland Islands (Antarctica): a comparison of composition and abundance[END_REF][START_REF] Amsler | Abundance and diversity of gastropods accociated with dominant subtidal macroalgae from western Antarctic Peninsula[END_REF]. However, some species are restricted to deeper waters between 40 -1080 m [START_REF] Hain | Die beschalten benthischen Mollusken (Gastropoda und Bivalvia) des Weddellmeeres, Antarktis[END_REF].

The taxonomy of Margarella has had a confused history and even currently, specific identifications and relationships among Magellanic and Antarctic species are poorly understood [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF][START_REF] Forcelli | Moluscos Magallánicos: Guía de moluscos de Patagonia y Sur de Chile. Parte I Clase Gastropoda, Subclase Protobranchia[END_REF][START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF][START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF][START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF]. Several species were originally described in the genus Margarita Leach, 1819 (not Leach, 1814) (= Margarites Gray, 1847), a group restricted to the Northern Hemisphere that is now placed in a separate family, Margaritidae Thiele, 1924. [START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF], in a detailed morphological revision of the group, confirmed that Antarctic, South American and South Georgian species, previously identified as Margarites, should be placed in Margarella. More recently, [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF] used multilocus phylogenies to show that Margarella antarctica (Strebel, 1908) was a calliostomatid. Moreover, [START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF] confirmed this placement for four further species and, in recognition; [START_REF] Williams | Margarellinae: a new calliostomatid subfamily[END_REF] established the new subfamily Margarellinae. Conversely, several species from New Zealand, previously assigned to Margarella have proved to belong to the genus Cantharidus Montfort, 1810 (Trochidae: Cantharidinae) [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF]Willams, 2012;[START_REF] Donald | Phylogeographic patterns in New Zealand and temperate Australian catharidines (Mollusca: Gastropoda: Trochidae: Cantharidinae): Trans-Tasman divergences are ancient[END_REF], within a distinct clade, the subgenus Pseudomargarella [START_REF] Donald | Phylogeographic patterns in New Zealand and temperate Australian catharidines (Mollusca: Gastropoda: Trochidae: Cantharidinae): Trans-Tasman divergences are ancient[END_REF] The World Register of Marine Species database (http://www.marinespecies.org) records 18 Margarella species distributed in Antarctic and sub-Antarctic areas. Five -M. antarctica, M. refulgens (E.A. Smith, 1907) M. whiteana Linse, 2002, M. gunnerusensis Numanami, 1996 andM. crebrilirulata (E.A. Smith, 1907) -occur around the Antarctic Peninsula, the Ross Sea and East Antarctica. Three species are recognized along southern South America -M. expansa (Sowerby, 1838), M. violacea (King, 1832) and M. pruinosa (Rochebrune and Mabille, 1885) -and their shells differ primarily in external coloration and shape [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF][START_REF] Forcelli | Moluscos Magallánicos: Guía de moluscos de Patagonia y Sur de Chile. Parte I Clase Gastropoda, Subclase Protobranchia[END_REF].

The species M. pruinosa has a restricted distribution, from the Strait of Magellan to the Santa Cruz province in Argentina. Both, M. expansa and M. violacea are abundant in the Magellan province and are also found in the Falkland/Malvinas Islands where they overlap with the endemic M. wacei (Melvill and Standen, 1918).

Margarella expansa also occurs eastward to reach geographically distant sub-Antarctic oceanic areas including Crozet and Kerguelen Islands [START_REF] Cantera | Les Gastéropodes prosobranches des Iles Kerguelen et Crozet (de l'Ocean Indien) comparison écologique et particularities biologiques[END_REF][START_REF] Troncoso | Contribution to the marine molluscan fauna of Kerguelen Islands, South Indian Ocean[END_REF]), but M. violacea apparently does not, the record of [START_REF] Troncoso | Contribution to the marine molluscan fauna of Kerguelen Islands, South Indian Ocean[END_REF] from the Kerguelen Islands being erroneous (see [START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF]. Although there are reports of M. expansa from several locations south of the Antarctic Polar Front (namely, South Georgia, the Antarctic Peninsula and Cape Adare, West Antarctica), [START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF] reviewed these records (all of which are over 100 years old) and concluded that they were based on various misidentifications. [START_REF] Dell | Antarctic Mollusca: with special reference to the fauna of the Ross[END_REF] and [START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF] had reached the same conclusion about specific cases and, in further support, we note that there are no recent observations of M. expansa from any of these places nor did our sampling on the Antarctic Peninsula and South Georgia detect it either. The species M. porcellana [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF] has been recorded at Marion Island and the Kerguelen Islands [START_REF] Cantera | Les Gastéropodes prosobranches des Iles Kerguelen et Crozet (de l'Ocean Indien) comparison écologique et particularities biologiques[END_REF][START_REF] Troncoso | Contribution to the marine molluscan fauna of Kerguelen Islands, South Indian Ocean[END_REF]. South Georgia has at least six apparently endemic species -M. achilles (Strebel, 1908), M. steineni (Strebel, 1905), M. jason [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF], M. tropidophoroides (Strebel, 1908), M. obsoleta [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF]M. subantarctica (Strebel, 1908). Finally, M. bouvetia [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF]M. macquariensis Hedley, 1916 are narrow endemics from Bouvet and Macquarie Islands, respectively. Nevertheless, boundaries between these nominal species are still not clear. Moreover, the taxonomic separation of South American species is particularly difficult because, besides coloration, the shell-shape differences are subtle [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF][START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF]. Indeed, levels of intraspecific variation in some populations are sometimes greater than those reported among species [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF][START_REF] Forcelli | Moluscos Magallánicos: Guía de moluscos de Patagonia y Sur de Chile. Parte I Clase Gastropoda, Subclase Protobranchia[END_REF].

Like many Southern Ocean invertebrates, Margarella species lack a freeswimming dispersive stage and exhibits protected benthic development where free-crawling juveniles emerge from mature egg capsules [START_REF] Picken | Non-pelagic reproduction of some Antarctic prosobranch gastropods from Signy Island, South Orkney Islands[END_REF][START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF][START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF]. This key life-history trait seems to have played a significant role in the biogeography of several marine groups by enhancing their respective speciation potential (Poulin andFéral, 1996, Pearse et al., 2012;[START_REF] Thatje | Effects of capability for dispersal on the evolution of diversity in Antarctic benthos[END_REF]. At the same time, the ecological association of some species with buoyant macroalgae gives them a high potential for rafting, which may explain their wide distributions across different sub-Antarctic provinces, in spite of their low dispersive potential [START_REF] Helmuth | Long-distance dispersal of a subantarctic brooding bivalve (Gaimardia trapesina) by kelp-rafting[END_REF][START_REF] Nikula | Circumpolar dispersal by rafting in two subantarctic kelp-dwelling crustaceans[END_REF][START_REF] Cumming | Transoceanic genetic similarities of kelp-associated sea slug populations: long-distance dispersal via rafting?[END_REF][START_REF] Moon | Reconsidering connectivity in the sub-Antarctic[END_REF][START_REF] González-Wevar | Unexpected absence of island endemics: Long-distance dispersal in higher latitude sub-Antarctic Siphonaria (Gastropoda: Euthyneura) species[END_REF]. Other species, lacking such associations are more narrowly distributed and indeed, molecular comparisons might detect a series of unrecognized cryptic species across the Southern Ocean, as has been the case in other groups of marine invertebrates [START_REF] Hunter | Evaluating connectivity in the brooding brittle star Astrotoma agassizii across the Drake Passage in the Southern Ocean[END_REF][START_REF] Leese | Cryptic speciation in a benthic isopod from Patagonian and Falkland Island waters and the impact of glaciations on its population structure[END_REF][START_REF] Wilson | Ocean barriers and glaciation: evidence for explosive radiation of mitochondrial lineages in the Antarctic sea slug Doris kerguelenensis (Mollusca, Nudibranchia)[END_REF][START_REF] Janosik | Evolutionary history of Southern Ocean Odontaster sea star species (Odontasteridae; Asteroidea)[END_REF][START_REF] González-Wevar | Cryptic speciation in Southern Ocean Aequiyoldia eightsii (Jay, 1839): Mio-Pliocene trans-Drake Passage separation and diversification[END_REF].

Here, we present a molecular-genetic study of seven nominal species collected at high-latitude Margarella populations from the Antarctic Peninsula, southern South America, the Falkland/Malvinas Islands, South Georgia, Crozet and Kerguelen Islands. We carried out phylogenetic reconstructions based on mitochondrial and nuclear markers, species delimitation analyses, mitochondrial divergence-time estimations, as well as population-based analyses. Through the integration of these methodologies and the first molecular investigation of the type species (M. expansa), we aim to further understand evolutionary relationships within Margarella in the Southern Ocean. Moreover, we elucidate the distribution of lineages of this higher latitude calliostomatid genus, as well as the taxonomic status of the various populations. Understanding these specific issues in Margarella provides new insights about the biogeography and evolution of the near-shore marine benthic biota in this important area of the world.

Material and Methods

Sample collection, DNA preparation and sequence editing

Margarella individuals were collected from inter-and sub-tidal ecosystems at different localities in the Southern Ocean including the southern portion of the Magellan Province (MP) in South America, the Antarctic Peninsula (AP), South Georgia (SG), the Falkland/Malvinas Islands (FI) Crozet Island (CZ), and Kerguelen Islands (KI) (Fig. 1; Table S1). Specimens were identified following [START_REF] Powell | Antarctic and Subantarctic Mollusca: Pelecypoda and Gastropoda[END_REF], [START_REF] Troncoso | Contribution to the marine molluscan fauna of Kerguelen Islands, South Indian Ocean[END_REF], [START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF][START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF].

Whole specimens were fixed in 95% ethanol and DNA was extracted from the head and foot using standard salting-out methodology described by Aljanabi and Martínez (1997) and/or the QIAGEN DNEasy Blood & Tissue kit (QIAGEN Inc.).

Universal primers were used to amplify a partial fragment of the mitochondrial cytochrome-b gene (Cytb) [START_REF] Merrit | Universal cytochrome b primers facilitate intraspecific studies in molluscan taxa[END_REF] and the nuclear rRNA gene 28S [START_REF] Littlewood | The interrelationships of Proseriata (Platyhelminthes: Seriata) tested with molecules and morphology[END_REF]. The typically-used 'barcoding' gene of COI does not amplify in Margarella (see [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF]Williams, 2012, this study) and therefore could not be used. Forward and reverse sequences for each marker were assembled independently and edited using GENEIOUS R8 (http://www.geneious.com). Alignments and base composition of nucleotide sequences were analyzed for each marker independently in MEGA 7.0 [START_REF] Kumar | MEGA7: Molecular Evolutionary Genetics Analysis version 7.0 for bigger datasets[END_REF] using MUSCLE [START_REF] Edgar | MUSCLE: a multiple sequence alignment method with reduced time and space complexity[END_REF] with standard settings. Mitochondrial codon usage was determined using the Effective Number of Codons (ENC) in DnaSP v5 [START_REF] Librado | DnaSP v5: a software for comprehensive analysis of DNA polymorphism data[END_REF] following [START_REF] Wright | The effective number of codons' used in a gene[END_REF]. New Antarctic and sub-Antarctic Margarella sequences will be deposited at GenBank under the following Accession Numbers: Cytb (MT763288 -MT763345) and 28S rRNA (MT764782 -MT764786). Similarly, molecular information concerning museological material from the Western Australian Museum (WAM) will also be available in Table S2.

Phylogenetic reconstructions, species delimitation analyses and divergence time estimates

Mitochondrial (Cytb) phylogenetic reconstructions included between 3 and 15 sequences of each nominal Margarella species, together with new sequences of South American calliostomatid genera Calliostoma, Photinula, and Photinastoma, as well as sequences of the tegulid outgroups Tegula lividomaculata and T. brunnea. In the case of the broadly distributed species such as M. violacea and M. expansa, we included sequences from individuals collected from different sub-Antarctic provinces (i.e. MP, FI, CZ and KI).

Nuclear (28S rRNA) phylogenetic reconstructions used new and previously published [START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF] Margarella sequences, notably M. refulgens, M. biconica and M. crebrilirulata all from the Weddell Sea and M. sp. from Bouvet Island. For comparative purposes we included sequences of different vetigastropods groups and outgroups following [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF] and [START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF]. Our phylogenetic estimation used maximum parsimony (MP), maximum likelihood (ML) and Bayesian analyses (BA), performed in MEGA, PHYML [START_REF] Guindon | A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood[END_REF] and MrBayes v.3.1.2 [START_REF] Huelsenbeck | MRBAYES: Bayesian inference of phylogenetic trees[END_REF], respectively. The program JModelTest v.2.1.10 ( [START_REF] Darriba | jModelTest 2: more models, new heuristics and parallel computing[END_REF] was used to select the HKY + I + G (Cytb) and the TN93 (28S rRNA) as the optimal substitution models for the ML and BA analyses. Nodal support for MP and ML analyses was inferred using non-parametric bootstrap (BS) with 1,000 pseudoreplicates [START_REF] Felsenstein | Evolutionary trees from DNA sequences: A maximum likelihood approach[END_REF]. Bayesian-inference posterior probabilities (BPP) were estimated using the Metropolis coupled Markov-chain Monte-Carlo algorithm (MCMC) running four chains for 50 x 10 6 generations, with trees sampled every 1,000 generations. Stationarity of the analyses was inferred when the average standard deviation of split frequencies was less than 0.01 [START_REF] Huelsenbeck | MRBAYES: Bayesian inference of phylogenetic trees[END_REF]. The initial 10% of the parameter values were discarded (burn-in) and posterior probabilities were estimated as the fraction of trees showing a particular clade. Finally, posterior probability density was summarized as a maximum clade credibility tree using TreeAnnotator v.1.6.1 (http://beast.bio.ed.ac.uk/TreeAnnotator) and visualized using FigTree v.1.4.3 (http://tree.bio.ed.ac.uk/software/figtree).

Two different methods were used for the delimitation of species within Margarella: the Automatic Barcoding Gap Discovery (ABGD) [START_REF] Puillandre | ABGD, Automatic Barcode Gap Discovery for primary species delimitation[END_REF] and the Generalized Mixed Yule Coalescent (GMYC) [START_REF] Pons | Sequence-based species delimitation for the DNA taxonomy of undescribed insects[END_REF].

The ABGD method employs genetic distances to detect barcoding gaps between candidate species based on genetic distance values, which can be observed whenever the divergence among organisms belonging to the same species is smaller than divergence among organisms from different species [START_REF] Puillandre | ABGD, Automatic Barcode Gap Discovery for primary species delimitation[END_REF]. ABGD analysis was performed on the online web-server (http://www.abi.snv.jussieu.fr/public/abgd) and was run using the default settings (Pmin = 0.001, Pmax = 0.1, Steps = 10, X (relative gap width) = 1.5, Nb bins = 20).

The GMYC method was implemented in the R environment (R, version 2.4.1) [START_REF] Ihaka | R: A language for data analysis and graphics[END_REF] and attempts to detect the transition in the tree where the branching pattern switches from being attributed to speciation (one lineage per species) to when it can be attributed to the intra-species coalescent process [START_REF] Pons | Sequence-based species delimitation for the DNA taxonomy of undescribed insects[END_REF].

A relaxed molecular clock analysis was implemented for mtDNA sequences using an uncorrelated-lognormal (ucln) model of molecular evolutionary rate heterogeneity and the HKY + I + G substitution model implemented in BEAST v.1.7.5 [START_REF] Drummond | BEAST: Bayesian Evolutionary Analysis by Sampling Trees[END_REF][START_REF] Drummond | Bayesian phylogenetics with BEAUti and the BEAST 1.7[END_REF]. A birth-death speciation prior was used for branching rates in the phylogeny. Four chains were run twice for 50 x 10 6 generations, and trees were sampled every 1,000 generations. Given an absence of suitable Margarella fossils to calibrate our analysis, we used a conservative phylogenetic mtDNA mutation rate (1%), following previous studies in vetigastropods [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF][START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF].

Convergence of model parameters was estimated by plotting the marginal posterior probabilities versus the generations in Tracer v.1.5 (http://beast.bio.ed.ac.uk/Tracer). Effective sample-size values were estimated for each parameter to ensure adequate mixing of the MCMC (ESSs > 1,000).

Genetic diversity and structure, genealogical relationships and morphological comparisons.

We determined levels of mtDNA polymorphism in Margarella populations using standard diversity indices such as the number of haplotypes (k), haplotype diversity (H), number of segregating sites (S), average number of pairwise differences (∏) and nucleotide diversity (π) for each species and localities using DnaSP. We also estimated levels of mtDNA population differentiation following [START_REF] Pons | Measuring and testing genetic differentiation with ordered Versus unordered alleles[END_REF] through the haplotype frequencies (G ST ) and mean pairwise differences (N ST ) in Arlequin v. 3 [START_REF] Excoffier | Arlequin (version 3.0): An integrated software package for population genetics data analysis[END_REF]. The statistical significance of these analyses was determined using permutation tests (20,000 iterations).

Genealogical relationships in Margarella populations were reconstructed using maximum parsimony networks in MEGA and visualized in Hapview [START_REF] Salzburger | The performance of phylogenetic algorithms in estimating haplotype genealogies with migration[END_REF]. For comparative purposes, we also constructed maximum parsimony networks based on 28S rRNA sequences including new and available Margarella sequences [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF][START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF]. Finally, in order to determine if shell coloration constitutes a suitable descriptor of specific status in Margarella we associated individuals' colors onto their respective mtDNA and nucDNA maximum parsimony networks.

Results

DNA polymorphism

The Cytochrome-b alignment of Antarctic and sub-Antarctic Margarella (n = 404) included a total of 396 nucleotide positions coding for 132 amino acids, with no indels or stop codons. Mitochondrial and nuclear sequences were not saturated at any position and no evidence for mtDNA codon bias was detected (ENC = 45.04).

A total of four fixed substitutions (positions 48, 71, 86, and 123) were recorded in the mtDNA data set and all of them differed between Antarctic and sub-Antarctic lineages. A total of 69 variable positions (17.42%) were recorded of which 54 (78.26%) were parsimoniously informative. Mitochondrial sequences were A-T rich (65.6%). Nuclear 28S rRNA (n = 84) sequences included a total of 740 nucleotide positions and were highly conserved. Only 8 positions (1.08%) were variable of which only 5 (62.5%) were parsimoniously informative. Nuclear sequences were G-C rich (58.7%).

Phylogeny and species delimitation analyses

The phylogenetic reconstructions clearly discriminated major taxonomic groupings of trochoideans with high bootstrap and posterior probabilities (Figs. 2 and3). Similarly, the monophyly of the clades within Margarella was strongly supported by the different markers/methods and all the analyses resolved the relationships within the genus with minor topological inconsistencies (Figs. 2 and3). Out of the seven nominal Margarella species we sequenced, however, phylogenetic reconstructions discriminated the presence of only four species-level clades. The first mtDNA clade (C1) comprised individuals of M. antarctica collected across the Antarctic Peninsula (Fig. 2). A second clade (C2) included individuals of M. steineni collected at Cumberland Bay, South Georgia and a single individual from Crozet Islands (Fig. 2). The third clade (C3) consisted of individuals identified as M. achilles collected at Cumberland and Grytviken bays, South Georgia (Fig. 2).

Finally, the fourth clade (C4) comprised sub-Antarctic Margarella individuals collected from different provinces and identified as the nominal species M. expansa (SA, FI and KI), M. violacea (SA, FI CZ and KI), M. pruinosa (SA), and M. porcellana (KI) (Fig. 2).

The nucDNA phylogenetic reconstructions recognized the presence of the same four different species-level clades within Margarella (Fig. 3), with the single sample of M. refulgens from Williams (2012) as a sister species to all our clades. Nevertheless, nucDNA relationships among them differed from the ones recorded through mtDNA reconstructions. For instance, mtDNA placed M. antarctica as sister to the remaining three clades (albeit with limited statistical significance), whereas nucDNA reconstructions recovered it as sister to M. steineni (Fig. 3).

Both ABGD and GMYC species-delimitation methods corroborated the mtDNA and nucDNA reconstructions within Margarella, recovering the same four groups.

Consequently, the specimens of Margarella that we sampled across the sub-Antarctic, including populations from South America, Falkland/Malvinas, Crozet and Kerguelen Islands were treated as a single evolutionary unit under the senior name, Margarella violacea, with which we synonymize M. expansa syn. nov, M. pruinosa syn. nov and M. porcellana syn. nov.

Divergence-time estimates and diversification-rate variation analyses

Levels of mtDNA genetic divergence between the four Margarella species (uncorrected p-distances) varied between 9.8% (M. antarctica vs M. achilles) and 2.8% (M. violacea vs M. achilles) (Table 1). Divergence-time estimations within Margarella based on mtDNA sequences suggest that the origin of the analyzed species occurred at the end of the Miocene around 7 Ma (8 -5 Ma) with the separation of M. antarctica from the clade of analyzed sub-Antarctic species (Fig. 4). Subsequently, the separation between M. steineni and the rest of the analyzed sub-Antarctic species (L3 and L4) may have occurred around 5 Ma (6.5 -4 Ma).

Finally, the separation between M. achilles from M. violacea was dated ~ 2 Ma (3 -1.5 Ma) (Fig. 4). Low levels of genetic diversity (mtDNA and nucDNA) and a complete absence of population structure characterized M. antarctica across its Antarctic Peninsula distribution (Table 2). For instance, levels of mtDNA polymorphism (H and ∏) varied between 0.065/0.065 (Doumer Island) and 0.259/0.271 (Fildes Bay) (Table 2). The more widespread sub-Antarctic species M. violacea showed higher levels of genetic diversity (Table 3) and a more complex pattern of genetic structure, with Puerto Williams (Beagle Channel), Possession Bay (eastern mouth of the Strait of Magellan), Hookers Point (FI) and Port (KI) the most differentiated populations. By contrast, the rest of the South American populations showed no evidence of significant genetic structure (Table S3). Standard diversity indices (H/∏) in sub-Antarctic populations of M. violacea varied between 0.069/0.069 (Puerto Williams) and 0.868/3.696 (Possession Bay) (Table 3).

Population-based analyses and genealogical relationships in

The maximum parsimony haplotype network for M. antarctica showed a star-like topology with a very short genealogy including six different haplotypes (Fig. 5a).

The central dominant haplotype (H1) in M. antarctica was broadly distributed across the Antarctic Peninsula and present in 88.4% of the analyzed individuals (Fig. 5a). By contrast, the network for M. violacea included 45 haplotypes and a more expansive genealogy (Fig. 5a). The network for M. violacea showed a dominant haplotype (H2), four medium-frequency ones (H3 -H6), several at lowfrequency (n = 8) and many unique (n = 33) haploypes (Figure 5a). The dominant (H2) haplotype in M. violacea was broadly distributed across southern South America, whereas two of the medium-frequency haplotypes (H3 and H4) were spread across the sub-Antarctic, from South America to Kerguelen Islands. The third medium-frequency haplotype (H5) was only recorded on Falkland/Malvinas Island and at Possession Bay, at the eastern mouth of the Strait of Magellan (Fig. 5a). Finally, a fourth medium-frequency haplotype (H6) was found in Crozet and Kerguelen Islands (Fig. 5a). Haplotype mtDNA networks for Margarella species at South Georgia exhibited two common haplotypes in M. steineni and several lowfrequency ones in M. achilles (Fig. 5). A single individual collected at Possession Island (Crozet Islands) showed two substitutional steps from the dominant haplotype recorded from South Georgian M. steineni.

The 28S rRNA network included a single allele (HI) shared by all the analyzed individuals of M. antarctica (n = 16) (Fig. 5b). Similarly, M. achilles individuals from South Georgia shared a single allele (HII), while M. steineni populations from South Georgia and Crozet Islands also shared a single allele (HIII) (Fig 5b). The species M. steineni and M. achilles were separated from M. antarctica by two and three substitutional steps, respectively (Fig. 5b). Finally, a single allele (HIV) was recorded in all but one M. violacea individual. This singleton allele was separated by one substitutional step from the dominant sequence recorded in the species.

Available 28S rRNA sequences of the species M. refulgens and Margarella sp. [START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF] were separated by two and three substitutional steps, respectively, from the dominant haplotype recorded in M. achilles. Accordingly, and considering the levels of nuclear divergence between species of Margarella that were clearly discriminated through mtDNA (M. antarctica, M. achilles and M. steineni), both M. refulgens and Margarella sp. could be valid species. In contrast, nucDNA sequences of the nominal species M. crebrilirulata and M. biconica [START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF] were identical to those recorded in this study for M. steineni.

Accordingly, the relationship among these three nominal taxa requires further studies; examining mtDNA sequences would make a good start.

Comparative morphological and genetic data within sub-Antarctic populations of Margarella showed a complete disassociation between shell coloration and mtDNA/nucDNA sequences (Fig. S1). Sub-Antarctic individuals identified as the nominal sub-Antarctic species M. expansa, M. pruinosa, M. porcellana and M. violacea were in most cases identical of their respective mtDNA and nucDNA sequences across their distributions in the different sub-Antarctic areas here analyzed (Fig. S1).

Discussion

Biogeography of Margarella

Our phylogenetic reconstructions and species-delimitation analyses in Margarella clearly support the critical role of the Antarctic Polar Front (APF) in the biogeography and evolution of this high-latitude trochoidean genus. Sub-Antarctic populations previously considered as four separate species from South America and Kerguelen Islands, both north of the APF [START_REF] Rintoul | The Southern Ocean in the Earth system[END_REF][START_REF] Park | Polar front around the Kerguelen Islands: An up-to-date determination and associated circulation of surface/subsurface waters[END_REF], formed a single clade with high levels of genetic homogeneity despite being separated by thousands of kilometers. We consider these populations to form just one biological species, M. violacea (= M. expansa, M. pruinosa and M. porcellana) exhibiting a wide range of colors that appear to be associated with different habitats. High levels of genetic homogeneity across thousands of kilometers have been reported in other sub-Antarctic shallow marine kelp-associated invertebrates including pulmonates of the genus Onchidella [START_REF] Cumming | Transoceanic genetic similarities of kelp-associated sea slug populations: long-distance dispersal via rafting?[END_REF] and Siphonaria [START_REF] González-Wevar | Unexpected absence of island endemics: Long-distance dispersal in higher latitude sub-Antarctic Siphonaria (Gastropoda: Euthyneura) species[END_REF], as well as in crustaceans [START_REF] Leese | Long-distance island hopping without dispersal stages: transportation across major zoogeographic barriers in a Southern Ocean isopod[END_REF][START_REF] Nikula | Circumpolar dispersal by rafting in two subantarctic kelp-dwelling crustaceans[END_REF]. Accordingl to molecular reconstructions, shell coloration and morphology does not represent effective descriptors of specific status in Margarella. In fact, field observations suggest that shell coloration in Margarella seems to be a better associated to habitat preferences considering that typical violet/purple individuals were largely associated with rocky ecosystems dominated by kelps and red macroalgae (i.e. Lessonia sp., Macrocystis pyrifera, Iridaea cordata, Gigartina skottsbergii) as recorded by [START_REF] Adami | Structure and dynamics of the biota associated with Macrocystis pyrifera (Phaeophyta) from the Beagle Channel[END_REF] and [START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF][START_REF] Rosenfeld | Richness, systematics, and distribution of molluscs associated with the macroalga Gigartina skottsbergii in the Strait of Magellan, Chile: A biogeographic affinity study[END_REF]. In contrast, olivaceous and green individuals were more abundant in areas dominated by soft sediments [START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF], while sub-Antarctic white individuals were frequently found in the lower intertidal closely associated with encrusting coralline algae (Rosenfeld pers. comm.).

Conversely, Margarella populations south of the APF showed high levels of genetic divergence and the presence of at least three species-level clades. One species was restricted to the Antarctic Peninsula (M. antarctica) while another clade was endemic to South Georgia (M. achilles). Finally, M. steineni was found in South Georgia but we also recorded a single individual at Crozet Islands. Such results contrast with previous phylogeographic studies in near-shore marine species showing that South Georgia represents the northern limit of several Antarctic species including the limpet Nacella concinna (Hoffmann et al., 2011;[START_REF] González-Wevar | Extinction and recolonization of maritime Antarctica in the limpet Nacella concinna (Strebel, 1908) during the last glacial cycle: toward a model of Quaternary biogeography in shallow Antarctic invertebrates[END_REF], the crinoid Promachocrinus kerguelensis [START_REF] Wilson | Multiple lineages and absence of panmixia in the "circumpolar" crinoid Promachocrinus kerguelensis from the Atlantic sector of Antarctica[END_REF][START_REF] Hemery | Comprehensive sampling reveals circumpolarity and sympatry in seven mitochondrial lineages of the Southern Ocean crionoid species Promachocrinus kerguelensis (Echinodermata)[END_REF], the sea star Odontaster validus [START_REF] Janosik | Evolutionary history of Southern Ocean Odontaster sea star species (Odontasteridae; Asteroidea)[END_REF], and fishes like Gobionotothen gibberifrons [START_REF] Matschiner | Gene flow by larval dispersal in the Antarctic notothenioid fish Gobionotothen gibberifrons[END_REF].

The contrasting biogeographical pattern in populations of Margarella north and south of the APF may be a consequence in part of the respective abundances of buoyant kelps, which are potential vectors for long-distance dispersal of these vetigastropods with low dispersal potential [START_REF] Picken | Non-pelagic reproduction of some Antarctic prosobranch gastropods from Signy Island, South Orkney Islands[END_REF][START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF][START_REF] Rosenfeld | Nuevos antecedentes sobre la biología y distribución del gasterópodo Margarella expansa (Sowerby, 1838)[END_REF][START_REF] Rosenfeld | Molluscan assemblages associated with Gigartina beds in the Strait of Magellan and the South Shetland Islands (Antarctica): a comparison of composition and abundance[END_REF]. According to this view, sub-Antarctic Margarella maintain connectivity through long-distance dispersal mediated by rafting. That these sub-Antarctic populations constitute a single species fits well with this hypothesis.

Contrarily, south of the APF, the absence of buoyant kelps in the Antarctic Peninsula seems to preclude the connectivity of Antarctic populations with those from South Georgia. The presence of the macroalgae Durvillaea antarctica and Macrocystis pyrifera on South Georgia might be held against our hypothesis, but we note that the prevailing winds and currents would likely keep algal wracks (and hence any rafting Margarella) south of the APF. The close relationship (and, indeed, possible synonymy) of M. biconica and M. crebrilirulata from the Weddell Sea and East Antarctica with M. steineni from South Georgia is congruent with our suggestions. The presence of buoyant kelps in South Georgia and the prevailing winds could also explain the close affinity recorded between the single individual from Crozet with the South Georgian species M. steineni.

The nuclear-gene based topology in Margarella was not consistent with the mitochondrial genetic splits (although the identity of the clades was). Similar patterns have been obtained in other groups of marine molluscs including Atrina [START_REF] Liu | Cryptic diversity in the pen shell Atrina pectinata (Bivalvia: Pinnidae): high divergence and hybridization revealed by molecular and morphological data[END_REF] and Monodonta [START_REF] Zhao | Cryptic diversity of marine gastropod Monodonta labio (Trochidae): did the early Pleistocene glacial isolation and sea surface temperature gradient jointly drive diversification of sister species and/or subspecies in the Northwestern Pacific?[END_REF]. Such conflict between mtDNA and nucDNA topologies may be the consequence of either incomplete lineage sorting or post-glacial introgression due to secondary contact [START_REF] Toews | The biogeography of mitochondrial and nuclear discordante in animals[END_REF], or a lack of discrimination power in the more conserved nuclear DNA.

Mitochondrial divergence-time estimates suggest that the most recent common ancestor (tmrca) of the analyzed Margarella lineages lived at about the Mio-Pliocene boundary, between 7 and 5.5 Ma, long after the isolation of the Antarctica and the formation of the APF. We suggest that three Margarella lineages (the ancestors of M. antarctica, M. steineni, and M. violacea) subsequently diversified almost simultaneously (based on uncorrected p-distances differences), following independent evolutionary pathways in the Antarctic Peninsula, South Georgia, and somewhere in the sub-Antarctic (probably southern South America), respectively.

We also recorded a recent cladogenetic process around 2 Ma, when M. violacea separated from the South Georgian species M. achilles, the result of a rare trans-APF dispersal event (although the nuclear tree suggests a different topology).

Finally, considering main oceanographic patterns in the Southern Ocean, we also found evidence of trans-APF long-distance dispersal event in which M. steineni from South Georgia colonized Crozet, > 5000 km north-eastward. Such recent long-distance dispersal events across the APF have been hypothesized in other Southern Ocean marine invertebrates including the limpets Nacella [START_REF] González-Wevar | Following the Antarctic Circumpolar Current: patterns and processes in the biogeography of the limpet Nacella (Mollusca: Patellogastropoda) across the Southern Ocean[END_REF] and the isopod Septemserolis [START_REF] Leese | Long-distance island hopping without dispersal stages: transportation across major zoogeographic barriers in a Southern Ocean isopod[END_REF], as well as in macroalgae [START_REF] Fraser | Kelp genes reveal effects of subantarctic sea during the Last Glacial Maximum[END_REF].

Mitochondrial divergence-time estimates in Margarella are in agreement with recent molecular studies in Southern Ocean marine invertebrates and fishes. For instance, the most diverse groups of nothothenioid fishes radiated between 11.6 and 5.3 Ma, more than 10 Ma after their origins [START_REF] Near | Ancient climate change, antifreeze, and the evolutionary diversification of Antarctic fishes[END_REF]. Similarly, levels of molecular divergence between Antarctic and sub-Antarctic populations of octocorals suggest a separation of lineages during the middle Miocene ~ 12-6 Ma [START_REF] Dueñas | The Antarctic Circumpolar Current as a diversification trigger for deep-sea octocorals[END_REF]. Moreover, the origin and diversification of Nacella around the Southern Ocean occurred approximately 12 Ma and 8 -5.5 Ma [START_REF] González-Wevar | Following the Antarctic Circumpolar Current: patterns and processes in the biogeography of the limpet Nacella (Mollusca: Patellogastropoda) across the Southern Ocean[END_REF]. Levels of mtDNA divergence between Antarctic and sub-Antarctic lineages of Margarella (~7.0%) are similar to those reported in bivalves [START_REF] Page | More evidence of speciation and dispersal across Antarctic Polar Front through molecular systematics of Southern Ocean Limatula (Bivalvia: Limidae)[END_REF][START_REF] González-Wevar | Cryptic speciation in Southern Ocean Aequiyoldia eightsii (Jay, 1839): Mio-Pliocene trans-Drake Passage separation and diversification[END_REF] and echinoderms [START_REF] Hunter | Evaluating connectivity in the brooding brittle star Astrotoma agassizii across the Drake Passage in the Southern Ocean[END_REF][START_REF] Janosik | Evolutionary history of Southern Ocean Odontaster sea star species (Odontasteridae; Asteroidea)[END_REF] suggesting that their respective radiations occurred at the end of Miocene, no more than 10 Ma. The middle Miocene is considered as an important time of oceanographic and climatic changes in the Southern Ocean associated with the intensification of the Antarctic Circumpolar Current (ACC) and to the re-establishment of Antarctic continental ice sheets [START_REF] Flower | The middle Miocene climatic transition: East Antarctic ice sheet development, deep ocean circulation and global carbon cycling[END_REF][START_REF] Zachos | Trends, rhythms, and aberrations in global climate 65 Ma to present[END_REF][START_REF] Lawver | Evolution of Cenozoic seaways in the circum-Antarctic region[END_REF]. Major oceanic circulation shifts during this period are probably associated with the complete development of a deep ACC [START_REF] Dalziel | A potential barrier to deep Antarctic circumpolar flow until the late Miocene?[END_REF]. As proposed for other Southern Ocean mollusks [START_REF] González-Wevar | Following the Antarctic Circumpolar Current: patterns and processes in the biogeography of the limpet Nacella (Mollusca: Patellogastropoda) across the Southern Ocean[END_REF][START_REF] González-Wevar | Cryptic speciation in Southern Ocean Aequiyoldia eightsii (Jay, 1839): Mio-Pliocene trans-Drake Passage separation and diversification[END_REF], fluctuations in latitudinal positioning and strengthening of the ACC after the MMCT may have favored the colonization of geographical distant provinces of the Southern Ocean.

Sub-Antarctic connectivity

Dispersal ability has been often assumed as good predictor of connectivity between local populations in aquatic ecosystems [START_REF] Jablonski | Larval ecology and macroevolution in marine invertebrates[END_REF][START_REF] Palumbi | Genetic divergence, reproductive isolation, and marine speciation[END_REF][START_REF] Hellberg | Genetic assessment of connectivity among marine populations[END_REF][START_REF] Shanks | Propagules dispersal distance and the size and spacing of marine reserves[END_REF][START_REF] Marko | What's larvae got to do with it?' Disparate patterns of post-glacial population structure in two benthic marine gastropods with identical dispersal potential[END_REF]Cowen and Sponaugle, 2007;[START_REF] Haye | Phylogeographic structure in benthic marine invertebrates of the Southeast Pacific coast of Chile with differing dispersal potential[END_REF]. Hence, species with broadcast spawning and pelagic larval development should exhibit higher levels of connectivity and less genetic structure across broad spatial scales than species with direct and/or benthic development [START_REF] Ronce | How does it feel to be like a rolling stone? Ten questions about dispersal evolution[END_REF][START_REF] Ayre | Does life history predict past and current connectivity for rocky intertidal invertebrates across a marine biogeographic barrier?[END_REF][START_REF] Gillespie | Long-distance dispersal: a framework for hypothesis testing[END_REF]. Nonetheless, many species display inconsistent patterns of genetic structure with those predicted solely from their developmental modes [START_REF] Weersing | Population genetics, larval dispersal, and connectivity in marine systems[END_REF][START_REF] Mercier | Pelagic propagule duration and developmental mode: reassessment of a fading link[END_REF][START_REF] Segovia | Lineage divergence, local adaptation across a biogeographic break, and artificial transport, shape the genetic structure in the ascidian Pyura chilensis[END_REF]. The high levels of genetic identity recorded in Margarella violacea, a species with protected benthic development, across thousands of kilometers in the sub-Antarctic is noteworthy considering that several comparable studies in the Southern Ocean have recovered the presence of locally endemic invertebrate lineages [START_REF] Leese | Cryptic speciation in a benthic isopod from Patagonian and Falkland Island waters and the impact of glaciations on its population structure[END_REF][START_REF] Strugnell | The thermohaline expressway: the Southern Ocean as a centre of origin for deepsea octopuses[END_REF][START_REF] Janosik | Evolutionary history of Southern Ocean Odontaster sea star species (Odontasteridae; Asteroidea)[END_REF][START_REF] González-Wevar | Following the Antarctic Circumpolar Current: patterns and processes in the biogeography of the limpet Nacella (Mollusca: Patellogastropoda) across the Southern Ocean[END_REF][START_REF] Moon | Reconsidering connectivity in the sub-Antarctic[END_REF]. (Nikula et al., 2010a;[START_REF] Cumming | Transoceanic genetic similarities of kelp-associated sea slug populations: long-distance dispersal via rafting?[END_REF][START_REF] González-Wevar | Unexpected absence of island endemics: Long-distance dispersal in higher latitude sub-Antarctic Siphonaria (Gastropoda: Euthyneura) species[END_REF], chitons (Nikula et al., 2011b) crustaceans [START_REF] Nikula | Circumpolar dispersal by rafting in two subantarctic kelp-dwelling crustaceans[END_REF], as well as non-buoyant kelps [START_REF] Fraser | Genetic affinities between trans-oceanic populations of nonbuoyant macroalgae in the high latitudes of the Southern Hemisphere[END_REF].

As we note above, the phylogeographical patterns recorded in Margarella across the sub-Antarctic closely resemble those found in the southern bull-kelp D. antarctica [START_REF] Fraser | Kelp genes reveal effects of subantarctic sea during the Last Glacial Maximum[END_REF], as well as in Southern Ocean kelp-associated invertebrates [START_REF] Leese | Cryptic speciation in a benthic isopod from Patagonian and Falkland Island waters and the impact of glaciations on its population structure[END_REF][START_REF] Nikula | Circumpolar dispersal by rafting in two subantarctic kelp-dwelling crustaceans[END_REF][START_REF] Cumming | Transoceanic genetic similarities of kelp-associated sea slug populations: long-distance dispersal via rafting?[END_REF][START_REF] González-Wevar | Unexpected absence of island endemics: Long-distance dispersal in higher latitude sub-Antarctic Siphonaria (Gastropoda: Euthyneura) species[END_REF]. Our findings are yet more evidence supporting that occurred several times during the Quaternary and generated a "demographic reset" during glacial maxima on the sub-Antarctic Islands followed by interglacial recolonization or "demographic reboots".

Conclusions

Molecular-based studies of shallow marine invertebrates are helping identify and define the distribution of evolutionary lineages in the Southern Ocean and aid our understanding of the underlying evolutionary processes [START_REF] Waters | Driven by the West Wind Drift? A synthesis of southern temperate marine biogeography, with new directions for dispersalism[END_REF][START_REF] Strugnell | The thermohaline expressway: the Southern Ocean as a centre of origin for deepsea octopuses[END_REF][START_REF] Fraser | Kelp genes reveal effects of subantarctic sea during the Last Glacial Maximum[END_REF][START_REF] Fraser | Poleward bound: biological impacts of Southern Hemisphere glaciation[END_REF][START_REF] Allcock | Southern Ocean diversity: new paradigms from molecular ecology[END_REF][START_REF] Near | Ancient climate change, antifreeze, and the evolutionary diversification of Antarctic fishes[END_REF][START_REF] Haye | Phylogeographic structure in benthic marine invertebrates of the Southeast Pacific coast of Chile with differing dispersal potential[END_REF][START_REF] González-Wevar | Following the Antarctic Circumpolar Current: patterns and processes in the biogeography of the limpet Nacella (Mollusca: Patellogastropoda) across the Southern Ocean[END_REF][START_REF] Crame | Key stages in the evolution of the Antarctic marine fauna[END_REF][START_REF] González-Wevar | Cryptic speciation in Southern Ocean Aequiyoldia eightsii (Jay, 1839): Mio-Pliocene trans-Drake Passage separation and diversification[END_REF][START_REF] Moon | Reconsidering connectivity in the sub-Antarctic[END_REF][START_REF] Crame | Key stages in the evolution of the Antarctic marine fauna[END_REF][START_REF] Halanych | Challenging dogma concerning biogeographic patterns of Antarctica and the Southern Ocean[END_REF]. As previously shown in Finally, we propose here that the geographic distribution of genetic lineages in Margarella across the Southern Ocean is closely related to the ecology of the species including their respective association with buoyant kelps, as well as its spawning behavior over macroalgae. [START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF][START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF]. A coloured circle represents each haplotype and indicate the main area where it was collected. The size of the circle is proportional to its frequency in the whole sampling effort.

  Margarella lineages Population-based analyses and genealogical reconstructions based on mtDNA sequences included a total of 305 individuals of M. violacea and 90 of M. antarctica. Because of the low number of individuals collected for M. pruinosa (n = 4), M. porcellana (n = 9), M. steineni (n = 11) and M. achilles (n = 10), these taxa were excluded from comparative population analyses.

  For instance, comparative genetic analyses of sub-Antarctic broadcast-spawners like Aequiyoldia (González-Wevar et al. 2019) and Nacella (González-Wevar et al. 2017) identified different evolutionary units in South America, the Falkland/Malvinas and Kerguelen Islands that have been separated for several millions of years. In contrast, phylogeographic and populations-based studies in other Southern Ocean species with benthic-protected development have demonstrated the major role of long-distance dispersal. Examples include gastropods

  several sub-Antarctic invertebrates with protected benthic development, Margarella populations form a single broadly distributed evolutionary unit over large geographic distance, suggesting the existence of long-distance dispersal, at least between South America and the Kerguelen Islands. This pattern is in contrast to broadcast-spawning molluscs like Nacella (González-Wevar et al. 2017) and Aequiyoldia (González-Wevar et al. 2019), which are characterized by the presence of different lineages in these provinces, showing limited larval dispersal at such geographic scale. In the sub-Antarctic, the combination of protected benthic development with rafting is more effective at long-distance dispersal than free-living larval stages. However, in contrast to the sub-Antarctic populations, Margarella south of the APF constitutes several species-level genetic lineages endemic to South Georgia (with the exception of a single M. steineni specimen found in Crozet Islands) and the Antarctic Peninsula. South of the APF, Margarella species showed low levels of genetic diversity reflecting the impact of Quaternary glacial cycles that we suggest exterminated local populations during their maxima.

Fig. 1 .

 1 Fig. 1. Nominal species of Margarella analyzed and their respective distributions in the Southern Ocean including South America, the Antarctic Peninsula and sub-Antarctic Islands (Falkland/Malvinas, South Georgia, Crozet and Kerguelen).

Fig. 2 .

 2 Fig. 2. Bayesian maximum clade credibility tree of Margarella relationships based on mtDNA (Cytb) sequences. Bootstrap support values (MP and ML) and BPP are shown above the nodes (in that order). Species delimitation analyses based on the Automatic Barcoding Gap Discovery (ABGD) and Generalized Mixed Yule Coalescence (GMYC) methods are also shown. The colour of the nodes indicate the association of individuals to the recorded clades where red includes sub-Antarctic specimens belonging to the nominal species M. violacea, M. pruinosa, M. expansa and M. porcellana; dark blue = Margarella antarctica; blue = Margarella light blue = Margarella steineni.

Fig. 3 .

 3 Fig. 3. Bayesian maximum clade credibility tree of Margarella relationships based on nucDNA (28S rRNA) sequences. Bayesian posterior probability support values are shown above the nodes. Species delimitation analyses in Margarella based on the Automatic Barcoding Gap Discovery (ABGD) and Generalized Mixed Yule Coalescence (GMYC) methods are also shown. The colour of the nodes indicate the association of individuals to the recorded lineages where red includes sub-Antarctic specimens belonging to the nominal species M. violacea, M. pruinosa, M. expansa and M. porcellana; dark blue = Margarella antarctica; blue = Margarella achilles; light blue = Margarella steineni.

Fig. 4 .

 4 Fig. 4. Bayesian maximum clade credibility tree based on mtDNA (Cytb), showing divergence time estimates within trochoidean gastropods. Posterior probabilities are shown above the clades. Grey shaded regions depict 95% bayesian credible intervals (BCIs) for relative divergence times.Fig.5. A) mtDNA (Cytb) maximum parsimony networks including Margarella species collected at different localities in the Southern Ocean. B) nucDNA (28S rRNA) maximum parsimony network including new Margarella sequences from different localities in the Southern Ocean, as well as available ones from previous studies[START_REF] Williams | Molecular systematics of the marine gastropod families Trochidae and Calliostomatidae (Mollusca: Superfamily Trochoidea)[END_REF][START_REF] Williams | Advances in molecular systematics of the vetigastropod superfamily Trochoidea[END_REF]. A coloured circle represents each haplotype and indicate the main area where it was collected. The size of the circle is proportional to its frequency in the whole sampling effort.

Fig. S1 .

 S1 Fig. S1. Compared morphologies/shell coloration and haplotypes of individuals of the sub-Antarctic, nominal species Margarella expansa, Margarella violacea, Margarella porcellana, and Margarella pruinosa collected from South America (SA), the Falkland/Malvinas Islands (FI), Crozet (CZ), and Kerguelen Islands (KI). A) maximum parsimony networks constructed based on mtDNA (Cytb) data. B) maximum parsimony network constructed based on nucDNA (28S rRNA) sequences.



  Where: n = number of analyzed individuals; k = number of haplotypes; S = polymorphic sites; H = haplotype diversity;  = average number of pairwise differences;  = nucleotide diversity. *p<0.05, **p<0.01, *** p<0.001. Higlights Molecular analyses in Margarella contradict the current taxonomic knowledge in the group  The Antarctic Polar Front (APF) represents an effective biogeographic barrier  North of the APF Margarella includes a single and broadly distributed species  South of the APF Margarella includes at least three different lineages  The presence/absence of buoyant kelps plays a key role in Margarella's biogeography

Table 1 .

 1 Pairwise levels (%) of genetic mtDNA (Cytb) divergence (uncorrected pdistances) between the recorded species of Margarella.

		M. antarctica M. steineni M. achilles M. violacea
	M. antarctica	****
	M. steineni	9.2	****
	M. achilles	9.8	7.4	****
	M. violacea	7.3	6.4	2.8	****

Table 2 .

 2 Mitochondrial (Cytb) diversity indices and neutrality tests in Margarella antarctica across its distribution in the Antarctic Peninsula.

	Locality	n	k	H	S			Tajima´s D Fu´s FS
	Fildes Bay	29 4 0.259 3 0.271 0.0006
	Doumer Island	30 2 0.065 1 0.065 0.0001
	Ryder Bay	31 4 0.251 3 0.262 0.0006
	Total	90 6 0.190 5 0.198 0.0005	-1.73	-6.203**

Where: n = number of analyzed individuals; k = number of haplotypes; S = polymorphic sites; H = haplotype diversity;  = average number of pairwise differences;  = nucleotide diversity. *p<0.05, **p<0.01, *** p<0.001.

Table 3 .

 3 Mitochondrial (Cytb) diversity indices and neutrality tests in Margarella violacea across its distribution in the sub-Antarctic where SA = South America, FI = Falkland/Malvinas Islands, CZ = Possession Island, Crozet and KI = Kerguelen Islands.

	Locality		n	k	H	S			Tajima´s D	Fu´s FS
	Carlos III Island (SA)	16	4	0.575	3	0.708 0.0017
	San Isidro (SA)		26	7	0.415	7	0.674 0.0016
	Port Famine (SA)	33	4	0.229	3	0.239 0.0005
	Tierra del Fuego (SA)	44	8	0.434	8	0.635 0.0015
	Possession Bay (SA)	42	14	0.868	14	3.696 0.0091
	Yendegaia Bay (SA)	34	7	0.704	6	1.050 0.0025
	Puerto Williams (SA)	29	2	0.069	1	0.069 0.0001
	Hookers Point (FI)	39	10	0.487	10	0.659 0.0016
	Possession	Island	14	4	0.396	3	0.429 0.0010
	(CZ)
	Port-Aux Francais (KI)	41	6	0.490	5	0.556 0.0013
	Total		319	48	0.762	35	2.613 0.0066	-1.60	-39.65***

Acknowledgements.

This study was supported by Fondecyt Initiation Project 11140087, Program FONDAP, Project Nº 15150003 and INACH Office Project RG_18-17 to C.A.G-W; Projects P05-002 ICM, PFB 023 (Instituto de Ecología y Biodiversidad IEB, Universidad de Chile), and project GAB (ACT172065) to C.A.G-W, N.I.S., S.R, C.S.M., K.G., A.D and E.P. Fondecyt Regular Project 1151336 to E.P and C.A.G-W. Part of the field work was carried out during the Antarctic Circumnavigation Expedition (carried out by the Swiss Polar Institute, supported by the ACE Foundation and Ferring Pharmaceuticals) to N.G.W. and J.N. Field access facilities to Crozet and Kerguelen Islands were supported by the French Polar Institute-IPEV (program n°1044-Proteker) and the LTSER Zone Atelier Antarctique et Subantarctique (ZATA), France to T.S., J-P. F., E.P, and C.A.G-W. British Antarctic Survey were supported by core funds from UKRI-NERC to the BEA Team.

long-distance dispersal mediated by bull-kelp rafting is key to understanding much Southern Ocean biogeography, especially for species like M. violacea that use macroalgae as a spawning substrate [START_REF] Zelaya | The genus Margarella Thiele, 1893 (Gastropoda: Trochidae) in the southwestern Atlantic Ocean[END_REF].

Quaternary genetics

Earth's climate has undergone recurring fluctuations during the Quaternary Ice Ages of the last 2.5 million years. Many studies have demonstrated the severe impact of Quaternary glacial cycles on population dynamics at higher latitudes of the Southern Ocean including Antarctica [START_REF] Convey | Exploring biological constraints on the glacial history of Antarctica[END_REF][START_REF] Allcock | Southern Ocean diversity: new paradigms from molecular ecology[END_REF][START_REF] Fraser | Poleward bound: biological impacts of Southern Hemisphere glaciation[END_REF][START_REF] González-Wevar | Extinction and recolonization of maritime Antarctica in the limpet Nacella concinna (Strebel, 1908) during the last glacial cycle: toward a model of Quaternary biogeography in shallow Antarctic invertebrates[END_REF][START_REF] Crame | Key stages in the evolution of the Antarctic marine fauna[END_REF][START_REF] Halanych | Challenging dogma concerning biogeographic patterns of Antarctica and the Southern Ocean[END_REF] and the sub-Antarctic (for a review see [START_REF] Moon | Reconsidering connectivity in the sub-Antarctic[END_REF][START_REF] Waters | Driven by the West Wind Drift? A synthesis of southern temperate marine biogeography, with new directions for dispersalism[END_REF][START_REF] Cumming | Transoceanic genetic similarities of kelp-associated sea slug populations: long-distance dispersal via rafting?[END_REF][START_REF] González-Wevar | Unexpected absence of island endemics: Long-distance dispersal in higher latitude sub-Antarctic Siphonaria (Gastropoda: Euthyneura) species[END_REF].

As general pattern, Margarella antarctica showed strong signals of postglacial population expansion with the presence of: a) low levels of genetic diversity, b) the presence of a broadly distributed dominant haplotype, c) a star-like and very short genealogies (Fig. 5; Table 2). Conversely, sub-Antarctic M. violacea showed higher levels of genetic diversity, evidence of spatial structure and a more expanded and complex genealogy (Fig. 5; Table 3). Genetic comparisons in higher latitude Margarella populations identified an inverse correlation between genetic diversity and latitude, as reported in other marine near-shore invertebrates [START_REF] González-Wevar | Patterns of genetic diversity and structure in Antarctic and sub-Antarctic Nacella (Patellogastropoda: Nacellidae) species[END_REF]. [START_REF] Fraser | Kelp genes reveal effects of subantarctic sea during the Last Glacial Maximum[END_REF] showed that the southern bull-kelp Durvillaea antarctica recently recolonized the sub-Antarctic, evidenced by the striking genetic homogeneity at scales of thousands of kilometers from South America to Macquarie Island. Following these arguments, and as recently suggested for two sub-Antarctic Siphonaria species [START_REF] González-Wevar | Unexpected absence of island endemics: Long-distance dispersal in higher latitude sub-Antarctic Siphonaria (Gastropoda: Euthyneura) species[END_REF], we hypothesize that any Margarella species became extinct in the Kerguelen Islands during the LGM, before the islands were colonized during the glacial-interglacial transition by rafting M. violacea from geographically distant refugia, such as southern South America, where glacial impact is known to have been lower, particularly on the southwestern Atlantic coast [START_REF] Rabassa | Chronology of the Late Cenozoic Patagonian glaciations and their correlation with biostratigraphic units of the Pampean region (Argentina)[END_REF]. Such a process could have


Julie Séguéla
email: jseguela@multiposting.fr

Gilbert Saporta
email: gilbert.saporta@cnam.fr

A hybrid recommender system to predict online job offer performance

With the expansion of internet to advertise, the number of potential channels is increasing every day. In the Human Resource domain, recruiters have to choose between hundreds of job search web sites when they post a job offer on the internet. In order to save costs, assessing job board expected performance has become necessary. In this paper, three recommender systems providing job board performance estimation for a given job posting are introduced. This work refers principally to the new item problem, which is still a challenging topic in the literature. The first system (PLS-R) is a content-based approach, while others are hybrid recommendation approaches. Estimation is made on item neighborhood according to a "naive" similarity or a supervised similarity measure. These predictive algorithms are compared through experiments on a real dataset. In this application, supervised similarity-based system overcomes the lacks of other approaches and outperforms them.

Introduction

Context and objectives. In domains such as Marketing, Advertising or even Human Resources (sourcing), decisionmakers have to choose the most suitable channels according to their objectives when starting a campaign. With the expansion of internet to advertise, the number of potential channels (and targets) is exponentially growing. Today, a great challenge common to several research domains is the development of intelligent tools to support users in their choices. In this work, we focus on an issue encountered in the Human resource area. The rapid increase in the number of job search web sites (job boards) has made crucial the assessing of job posting performance. A job posting is a job offer published on the web, possibly on several job boards simultaneously. Performance is assumed to be the number of applications received on a job board. Posting a job offer on a job board is very expensive, so choosing wisely the channels to use is a very relevant task.

In this context, we are introducing a predictive algorithm of job posting performance (or return) on job boards. We resort to an innovative application of recommender systems: the goal of such systems is to help users to find items that they should appreciate from huge catalogues on the basis of previously attributed ratings. In our application:

items are assumed to be job postings, -users are assumed to be job boards, -ratings are assumed to be observed returns of job postings on job boards. Given the context, our system can be considered as a particular case of recommender systems commonly encountered in the literature [START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF].

Data complexity and issues. Dataset is provided by Multiposting.fr, an online job posting solution which distributes jobs simultaneously on several dozens of job boards. We want to predict the number of applications received on the job board studied for a new job posting. Job postings are characterized by textual data (job description) and some structured data. These structured and unstructured data have to be handled simultaneously. Structured data are job characteristics (contract type, industry, education level required, etc.) represented by categorical variables and location characteristics represented by quantitative variables (population, unemployed people, etc.).

Thousands of features are extracted from job description texts thanks to information retrieval techniques. Since we have to deal with high dimensional data, job features have to be weighted in the predictive algorithm according to their power of explanation.

Section 2 is dedicated to a brief overview of recommender system literature and to the introduction of our system as a particular case (conditioned by the context and the type of our data). Then, approach is presented in section 3: handling of data is explained, and predictive algorithms are introduced (PLS regression and two versions of a hybrid recommender with a collaborative estimation). Experiments on our dataset and results are presented in section 4: different text representation techniques and three predictive algorithms are compared.

Recommender systems

Context

Today, companies are registering purchases, preferences and ratings of their customers or users. They want to make the most of those informations in order to provide personalized recommendations for the next purchases of their customers.

Recommender systems are involving three elements: items, which are exposed to users, who give them ratings. Data are represented in a matrix which rows and columns are users and items, and which elements are ratings. For example, users can be the customers of an ondemand film provider, items are movies, and ratings are integer values between 0 and 5 given by users for the movies they have seen. Purpose of the recommender system is to suggest to the user movies he has not seen yet and to which he is likely to give a high rating. In general, a ranking of items is provided by the system for a given user.

General issues are occuring in the literature. Most of the time, the total number of items is very high and each user has rated a small proportion of items, so the datatable is very sparse. Moreover, some items have very few or no ratings, and symmetrically, a new user has not given a rating yet. This issue is known as "cold-start" problem (related to new items or new users).

Brief overview of recommender systems

Recommender systems are usually classified into three main categories: content-based recommendations, collaborative recommendations, and hybrid approaches. In a content-based system, recommendations are generated from the features associated with items and the ratings that a user has given them, and the system recommends items similar to the ones the user liked in the past (e.g. [START_REF] Pazzani | Learning and revising user profiles: The identification of interesting web sites[END_REF][START_REF] Mooney | Content-based book recommending using learning for text categorization[END_REF]. Collaborative systems recommend to a given user items that people with similar preferences liked in the past (e.g. [START_REF] Shardanand | Social information filtering: Algorithms for automating "word of mouth[END_REF][START_REF] Konstan | Grouplens: Applying collaborative filtering to usenet news[END_REF]. Collaborative systems are based on user/item similarities (regarding to ratings) and expected ratings are computed as an aggregate of the ratings of most similar users/items. Hybrid approaches are combinations of collaborative and content-based methods, which helps to avoid limitations of each system (e.g. [START_REF] Balabanovic | Fab: Content-based, collaborative recommendation[END_REF][START_REF] Schein | Methods and metrics for cold-start recommendations[END_REF].

To assess the capability of a system to provide good rating estimations, predicted ratings are usually compared to actual ratings thanks to the mean absolute error (MAE) or the root mean squared error (RMSE).

A particular case of recommender system

Our objective is to recommend job postings (items) to job boards (users) according to the expected return. In our case study, a new item is introduced and we want to suggest it to the users the most likely to appreciate it. The set of job boards is given but the perimeter of job postings is not limited. Indeed, each new recruiting campaign can be different of the previous ones. However, if a new job posting is identified as being the same as a previous posting, prior returns are used to improve the prediction. The dataset is made up of jobs posted on one or several job boards and which returns have been observed on each used channel. For each job posting, few channels are used, so few ratings are known. Consequently, the resulting matrix is very sparse. Some of our issues are not usual in recommender system literature. Most of applications concerns very large datasets (thousands of users and items) where users have already rated several items according to their preferences. Our application concerns only about thirty users and our main case is the new item problem: ratings are estimated for items which have never been rated by users yet. In that case, only descriptive variables are used. It is not possible to obtain ratings for new items because each item is only recommended once to one or several users at the same time. Moreover, rating variability within and between users is high (see figure 1), instead of being limited to integer values between 0 and 5 (or 0 and 10) as usually.

Approach

An overview of our approach is presented in figure 2.

Data handling

As said previously, we have to handle simultaneously structured and unstructured data (textual data). Unstructured data are job description texts from which features are extracted thanks to an information retrieval technique, after a preprocessing of texts. These features will be used as input in learning approaches.

Preprocessing of texts

First, text preprocessing is made as following :

-Lemmatization and tagging, with algorithm proposed by [START_REF] Schmid | Probabilistic part-of-speech tagging using decision trees[END_REF].

-Filtering according to grammatical category. Job offers are short texts (between 1000 and 3000 characters), compouned with short sentences and task listings, so we decide to keep only nouns, verbs and adjectives (as in [START_REF] Kessler | Traitement automatique d'informations appliqué aux ressources humaines[END_REF]. -Filtering words occuring in less than five postings (a minimum number of occurrences is necessary to use terms in learning based methods). The well-known Vector Space Model (also called "bag-of-word" representation; [START_REF] Salton | A vector space model for automatic indexing[END_REF] is used to obtain a vector of term frequencies for each job posting.

Feature extraction

To improve text representation we will use the TF-IDF (term frequency-inverse document frequency) measure [START_REF] Salton | Automatic Text Processing[END_REF]. This common weighting technique decreases weights of keywords which appear in many documents and are not useful to discriminate documents. After weighting, documents will be indexed by Latent Semantic Analysis (LSA), a dimensionality reduction technique through a singular value decomposition of term-document matrices [START_REF] Deerwester | Indexing by latent semantic analysis[END_REF][START_REF] Martin | Mathematical foundations behind latent semantic analysis[END_REF]. The basic postulate is that there is an underlying latent semantic structure in word usage data that is partially hidden or obscured by the variability of word choice (synonymy problem). Correspondence Analysis (CA), widely used in statistical data analysis, strongly resembles to LSA when used in the context of textual data [START_REF] Lebart | Exploring Textual Data[END_REF]. In a previous work [START_REF] Séguéla | A comparison between latent semantic analysis and correspondence analysis[END_REF], we noticed the good performance of Correspondence Analysis in document representation task, so we will add this indexing technique to the list of experiments.

Other unsupervised methods, such as pLSA [START_REF] Hofmann | Probabilistic latent semantic indexing[END_REF] and LDA [START_REF] Blei | Latent dirichlet allocation[END_REF], can be used to model semantics. However, these methods are not reported to generally outperform LSA [START_REF] Gehler | The rate adapting poisson model for information retrieval and object recognition[END_REF], so we will not try these techniques to avoid unnecessarily experiments. In section 4, feature indexing methods will be compared to underline their impact or absence of impact on recommender system performance.

PLS regression (PLS-R)

Introduced by Wold et al. (1983a,b) and first presented as an algorithm used for computing eigenvectors, Partial Least Squares regression (PLS-R) was rapidly interpreted in a statistical framework (e.g. [START_REF] Helland | PLS regression and statistical models[END_REF]. PLS-R is a technique that generalizes and combines features from principal component analysis and multiple regression (for further details, see [START_REF] Abdi | Partial least square regression, projection on latent structure regression, PLSregression[END_REF]. This method is used when the number of predictors is large, and even large compared to the number of observations. The higher the number of predictors is, the higher the risk of important correlations between variables is. In case of high correlations between predictors, standard regression methods fail in estimating coefficients. As an alternative, PLS-R provides robust components (linear combination of predictors), independant and highly correlated with the dependent variable. In this work, we have to face to a large number of predictors (number of features extracted from job descriptions and structured variables) and high correlations, so PLS-R seems to be a very suitable technique.

Computing of PLS components

One part of PLS-R algorithm consists in computing non-correlated components, highly correlated with the dependent variable. The computing of components is based on NIPALS algorithm, first introduced by [START_REF] Wold | Estimation of principal components and related models by iterative least squares[END_REF] for principal component analysis. Considering (x 1 , ..., x p ) a set of features, potentially highly correlated, and a dependent variable r, the first component is:

t 1 = w 11 x 1 + . . . + w 1p x p , where w 1j = cov(xj ,r) p j=1 cov 2 (xj ,r)
. Residual r 1 is obtained by regressing r on t 1 . The second component t 2 is a linear combination of x 1j , residuals coming from the regressions of x j on t 1 : t 2 = w 21 x 11 + . . . + w 2p x 1p , where

w 2j = cov(x1j ,r1) p j=1 cov 2 (x1j ,r1)
. The regression of r on t 1 and t 2 gives the residual r 2 . This iterative process continues until reaching H components, where H is determined by cross validation [START_REF] Hoskuldsson | PLS regression methods[END_REF]. In PLS regression, r is then regressed on components:

r = c 1 t 1 + c 2 t 2 + . . . + c H t H + r H .

VIP indicator

To measure the importance of x j variable to explain r through t h components, we use VIP criterion (Variable Importance in the Projection):

V IP hj = p h l=1 cor 2 (y, t l ) h l=1 cor 2 (y, t l )w 2 lj Since p j=1 V IP 2
hj = p, the minimum threshold to keep a variable is often fixed to 1. We will use this rule to select variables used in the computing of PLS components.

A hybrid recommender system

In our context, items (job postings) are described by a set of features, extracted from their textual description and from structured variables (contract type, location, education level required, etc.). The description is a text on which we have applied information retrieval techniques mentioned in section 3.1.2. The following notations will be used in this section:

-X = (x 1 , . . . , x p ) is the set of features describing items, -X i = (x 1i , . . . , x pi ) is the vector of features describing item i, -r u,i is the actual rating of item i for user u, -p u,i is the predicted rating of item i for user u.

Computing of similarity between two job postings

Hybrid systems introduced in this paper are based on the computing of similarities between items, supposing that similar items have similar ratings for a given user. We propose to compute similarities in two different ways: a naive similarity between two sets of features, and a supervised similarity in order to identify nearest neighbors with respect to relevant features. Relevant features are those which are contributing in explaining job board returns. When a new item has to be rated for all users, his similarity with respect to all past items is computed.

Similarity functions. To compare two vectors of features extracted from texts, we first use cosine similarity measure (Baeza-Yates and Riberto-Neto, 1999) between items i 1 and i 2 :

sim(i 1 , i 2 ) = cos(X i1 , X i2 ) = p j=1 x ji1 x ji2 p j=1 x 2 ji1 p j=1 x 2 ji2
Other similarity functions based on Euclidean distance d i1,i2 are used (the lower the Euclidean distance, the greater the similarity). As a particular case, we will test constant similarity measure. We use the same method as [START_REF] Shardanand | Social information filtering for music recommendation[END_REF] to generate a third similarity measure:

sim(i 1 , i 2 ) = max i k ∈K (d i1,i k ) -d i1,i2
where K is the set of |K| nearest neighbors of i 1 according to Euclidean distance.

Finally, we will test two additional similarity functions: gaussian and exponential functions decreasing with Euclidean distance. These functions are depending on a standard deviation parameter, for which we will try different values. Let σ d be the standard deviation of distance between two items, gaussian and exponential similarity functions are respectively defined by:

sim(i 1 , i 2 ) = exp - 1 2 d i1,i2 σ d 2 and sim(i 1 , i 2 ) = exp - d i1,i2 σ d
"Naive" vs supervised similarity measure. Two different approaches are proposed. In the first approach, ratings are predicted with an heuristic technique. This approach assumes that similar items regarding to their features should have similar ratings for a given user. It is based on a "naive" similarity since it assumes that all item features have the same importance in the explaining of ratings. In order to not take into account non relevant features while searching item neighborhood, we propose a supervised similarity measure "rating-oriented" in a second approach. Instead of computing Euclidean distance on item features, it is computed on PLS components (see section 3.2.1), linear combinations of initial features extracted so as to explain as much as possible actual ratings.

Performance estimation

Ratings are estimated thanks to an aggregating function computed on item neighborhood (e.g. [START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF]. Expected rating of user u for item i 1 is given by:

p u,i1 = i k ∈K sim(i 1 , i k ) × r u,i k i k ∈K sim(i 1 , i k )
where K is the set of |K| nearest neighbors of i 1 with respect to the correspondent similarity measure. For constant similarity, which means computing average rating on i 1 neighborhood, nearest neighbors are determined by Euclidean distance.

Prediction improvement by relevance feedback

Sometimes, a new offer is in fact exactly the same as a previously posted one. An offer which has already been posted is called a repost. Indeed, some vacations are recurrent jobs and recruiters may need to post again an old job offer. When a repost is identified, we have an additional information: returns on job boards which have been chosen by the recruiter previous time (eventually several times).

We remind that X i = (x 1i , . . . , x pi ) is the vector of features describing job posting i. We discretize job board return into l classes and code them through dummy variables. We create an enriched vector Xi = (x 1i , . . . , x pi , r 1 u1i , . . . , r l u1i , . . . , r 1 u N i , . . . , r l u N i ) which will be used to modelize and estimate job board returns in case of repost. In Xi vector, r l ui is equal to 1 if the observed return of posting i on job board u belongs to class l.

System evaluation

Our recommender systems are systematically compared with the performance of the "average recommender" (AR). The average recommender provides recommendations based on job board average rating (computed on all past postings) and does not take job features into account. p AR u,i , rating predicted by average recommender for user u and all items, is defined by:

p AR u = i∈Du r u,i |D u |
where D u is the set of items previously rated by user u.

To assess the capability of a system to provide good rating estimations, estimated values are usually compared to actual values thanks to MAE or RMSE. In our context, users have big differences in the number of rated items. This can bias our quality criterion because there is a high variability between average ratings of users (see figure 1). In this work, we will use M AE to compare system performances on the prediction task, which is the mean of users MAE:

M AE = 1 N u∈U i∈Du |p u,i -r u,i | |D u |
where U is the set of users, N = |U | the number of users, and p u,i the estimated rating for user u and item i.

As shown in figure 2, every learning step is made on a specific sample (learning sample), and predictive accuracy of algorithms is assessed on a test sample. Attribution is made randomly on the perimeter of job postings which are not reposts.

Experiments

Data description

Data are provided by Multiposting.fr, an online job posting distributor, and concern generalist and specialized job boards with an history of 80 postings at least. We decide to focus our attention on job boards with a mean return higher or equal to 2 because returns on other job boards are easy to predict and we don't want to take them into account when assessing system performance. This kind of application is quite unusual in recommender system literature because we are studying a small dataset: few users (30 job boards), and about 42 000 ratings. We are studying about 18 000 items, each one has 3 ratings in average (a job is posted on 3 job boards of the dataset in average).

Reposts are identified and will be considered seperately. Remaining dataset is affected to learning and test samples, with a 60% and 40% distribution respectively. In experiments, repost sample will be treated like the test sample.

Experiments on text representation method

We first want to compare TF, LSA with TF-IDF weighting, and CA representations and to identify which one provides the best result (the lowest M AE). To make this comparison, only textual features will be used in a first time. Different document representation techniques will be compared over three predictive algorithms: PLS-R (S1), hybrid recommender with naive similarity (or non-supervised recommender, S2) and hybrid recommender with supervised similarity (or semi-supervised recommender, S3). In S2 and S3 approaches, several similarity functions are compared (see section 3.3.1) and the optimal number of neighbors is studied. Cosine similarity is not relevant in S3 approach because the number of components kept is very small (less than 10 components) and sometimes equal to 1. Since S2 is a non-supervised system, the number of dimensions kept with LSA and CA can impact the recommender performance: preliminar experiments lead us to keep 50 dimensions for both methods.

PLS-R algorithm results are presented in table 1.

Approach AR PLS-R Representation method None TF LSA (TF-IDF) CA M AE
12.5 10.8 11.1 11.2

TAB. 1 -PLS-R (S1) results.

We first discuss the optimal standard deviation parameter in S2 and S3 approaches for gaussian and exponential similarity functions. The following sets of values are respectively used for gaussian and exponential function parameters: In S2 approach, lowest M AE for gaussian and exponential functions are reached respectively with σ opt,S2 g

σ g ∈ {σ d , 1 2 σ d , 1 3 σ d , 1 4 σ d , 1 6 σ d } and σ e ∈ {σ d , 1 3 σ d , 1 6 σ d , 1 8 σ d ,
∈ { 1 3 σ d , 1 4 σ d } and σ opt,S2 e ∈ { 1 6 σ d , 1 8 σ d }.
In S3 approach, decreasing initial value of standard deviation parameter does not allow to improve prediction accuracy.

We choose the best parameters in gaussian and exponential functions, and compare text representation methods for S2 and S3 approaches in figure 4. In the semi-supervised system, TF and LSA representations are equivalent whereas CA representation provides slightly lower quality. M AE is quite stable from 30 neighbors, except for estimation by mean on the neighborhood. In the non supervised system, all representation methods allow to reach a similar prediction quality, but LSA and CA methods are more stable with the number of neighbors. In the rest of the paper, we choose TF representation because it provides slightly better results for S1 and S2 approaches. However, we notice that LSA has allowed to reduce dimensionality and to preserve prediction accuracy.

The three approaches are finally compared in figure 5. We retain max(d) -d similarity measure for the non-supervised hybrid system, and gaussian similarity for the semi-supervised hybrid system. The three approaches are better than average recommender, but the semisupervised system allows to reach the lowest M AE.

Improving job posting description

We now add structured variables to the set of descriptive variables. S2 approach is based on textual similarity and can't support the adding of qualitative and quantitative variables.

We lead the same experiments as previously to identify the best standard deviation parameters in gaussian and exponential similarity functions: σ opt g = 1 3 σ d and σ opt e = 1 3 σ d . Results for S1 and S2 approaches with or without the adding of job descriptive variables are presented in figure 6. Curve pattern is similar but adding job posting characteristics has improved the quality of predictive algorithm.

Relevance feedback

We now consider the sample of reposted jobs. These jobs have already been posted on one or several job boards by the past, and our objective is to exploit previously observed returns to improve the quality of prediction on the sample of reposts. In relevance feedback (RF) approach, learning is made on all other postings described with the enriched vector (see section 3.3.3), including first postings associated with reposts. Approach without relevance feedback requires only textual features and other descriptive variables. As previously, enriched descriptive vector can only be used in supervised and semi-supervised approaches, S1 and S3. Figure 7 shows the comparison of results for the two approaches, with or without the use of relevance feedback. Thanks to relevance feedback, the prediction for a job repost will be more accurate (M AE is reduced by 1.5).

Discussion

Strengths and weaknesses of approaches proposed are summarized in table 3. PLS-R implies a linear relation between components and dependent variable, whereas other approaches are nonlinear with an estimation on the job posting neighborhood. In addition, the risk of overfitting is higher in PLS-R (because of the high number of input variables) than in other approaches. We appreciate the ability of S1 and S3 systems to provide interpretation tools of variable impact during the PLS modeling step. These systems also allow to give more important weigths to relevant features regarding to return estimation. On the contrary, S2 system does not allow neither explainability nor control on the weights of posting features.

Conclusions and future work

In this article, we have introduced three different approaches to predict job posting returns on job boards. We propose an innovative application of recommender systems by introducing two hybrid systems adapted to the new item problem. In the main case, systems are only based on posting features (no use of rating knowledge). The semi-supervised hybrid system outperforms other approaches by combining the understanding of posting feature impact on job board return and the usage of collaborative knowledge. This system also allows the adding of descriptive data to improve prediction accuracy and ensure algorithm stability with the number of neighbors. In this approach, TF and LSI representation methods provide similar results, just as max(d) -d, gaussian and exponential similarity functions. In case of repost, learning on an enriched descriptive vector allows to improve algorithm efficiency. Since our recommender system is dependent from a content-based approach, we need a sufficient number of postings on a job board to understand returns and give reliable recommendations. In a future work, we will extend this research to the case of new job boards (new users), with the introducing of job board features and the understanding of their impact on posting performance.

FIG. 1 -

 1 FIG.1-Job boards represented in the maps (number of job postings, standard deviation of return) and (number of job postings, average return).

FIG. 2 -

 2 FIG. 2 -Recommender system overview.

  FIG.3 -M AE with S2 and S3 systems, according to standard deviation parameter (sd) in gaussian and exponential similarity functions (TF representation).

  FIG.4-M AE with S2 and S3 systems, according to the representation method and similarity measure.

FIG. 6 -

 6 FIG. 5 -Comparison of best algorithms.

  FIG. 7 -Prediction improvement by relevance feedback.

  1 10 σ d }. Results are illustrated in figure 3, for TF representation (same "pattern" for LSA and CA representation methods). Best parameter values are reported in table 2.

	Approach		S2			S3
	Representation method	TF	LSA	CA	TF	LSA	CA
	Gaussian function	1/3	1/3	1/4	1, 1/2 1, 1/2 1, 1/2
	Exponential function	1/6, 1/8 1/6, 1/8 1/6, 1/8 1, 1/3	1	1/3
	TAB. 2 -Best parameter value(s) (×σ d ) for gaussian and exponential functions in S2 and S3
	approaches.