C Tougard

F Justy

B Guinand

E J P Douzery

P Berrebi

Salmo macrostigma (Teleostei, Salmonidae): nothing more than a brown trout (S. trutta

Keywords: Conservation, mtDNA, North Africa, Sicily, syntype, taxonomic status

We examined specimens of the macrostigma trout Salmo macrostigma, which refers to big black spots on the flanks, to assess whether it is an example of taxonomic inflation within the brown trout Salmo trutta complex. Using new specimens, publicly available data and a mitogenomic protocol to amplify the control and cytochrome b regions of the mitochondrial genome from degraded museum samples, including one syntype specimen, the present study shows that the macrostigma trout is not a valid species. Our results suggest the occurrence of a distinct evolutionary lineage of S. trutta in North Africa and Sicily.

Accepted Article

| INTRODUCTION

All biological conservation is based on taxonomy and the central unit in taxonomy is the species. Since the advent of Linnaean binomial taxonomy, taxonomists have been describing, naming and classifying species, mainly based on morphological characters. During the past 3 decades, numbers of described species have increased in part due to the widespread use of advanced technologies, such as molecular phylogenetics, DNA barcoding, computed tomography, geographical information systems and various internet tools (Bickford et al., 2007;[START_REF] Padial | The integrative future of taxonomy[END_REF][START_REF] Zachos | Species inflation and taxonomic artefacts -A critical comment on recent trends in mammalian classification[END_REF]. The increased availability and selective use of these data have led to reinterpretations of species limits based only on changes in species concept rather than new discoveries (e.g. cryptic species). This process is known as "taxonomic inflation" [START_REF] Isaac | Taxonomic inflation: its influence on macroecology and conservation[END_REF][START_REF] Zachos | Species inflation and taxonomic artefacts -A critical comment on recent trends in mammalian classification[END_REF] and it has resulted in over-splitting in which numerous known subspecies are elevated to the species rank [START_REF] Isaac | Taxonomic inflation: its influence on macroecology and conservation[END_REF][START_REF] Zachos | Species inflation and taxonomic artefacts -A critical comment on recent trends in mammalian classification[END_REF]. Species elevated in this way have often been found to be invalid, with numerous subspecies boundaries based on discontinuities in the geographic distribution of phenotypic traits poorly aligning with described molecular lineages (Burbrink et al., 2000;[START_REF] Phillimore | Are subspecies useful in evolutionary and conservation biology[END_REF][START_REF] Newman | Phylogeographic analyses of the southern leopard frog: the impact of geography and climate on the distribution of genetic lineages vs. subspecies[END_REF][START_REF] Prie | Bad taxonomy can kill: molecular reevaluation of Unio mancus Lamarck, 1819 (Bivalvia: Unionidae) and its accepted subspecies[END_REF][START_REF] Deichmann | How many species and under what names? Using DNA barcoding and GenBank data for west Central African amphibian conservation[END_REF]. However, effective conservation and management rely on the proper definition of operational units (e.g. evolutionarily significant units, ESU; [START_REF] Moritz | Defining "Evolutionarily Significant Units" for conservation[END_REF]. Such units require that variation related to species status be appropriately assessed and considered before relevant taxonomic decisions are made [START_REF] Mace | The role of taxonomy in species conservation[END_REF][START_REF] Sites | Operational criteria for delimiting species[END_REF]). To gain support, operational conservation and management units also need congruent molecular and morphological patterns [START_REF] Fraser | Adaptive evolutionary conservation: towards a unified concept for defining conservation units[END_REF]Agapow et al., 2004;[START_REF] Sites | Operational criteria for delimiting species[END_REF]).

In the brown trout Salmo trutta L. 1758, natural diversity is notably characterized by complex patterns of phenotypically distinct geographic forms and considerable life-history variation (Bernatchez et al., 1992;[START_REF] Elliott | Quantitative Ecology and the Brown Trout[END_REF][START_REF] Kottelat | Hanbook of European freshwater fishes[END_REF][START_REF] Sanz | Phylogeography history of brown trout: a review[END_REF]. In addition to S. trutta and Salmo salar L. 1758, studies of biological variation during the last century have led to the description of several Salmo L. 1758 species, often having very restricted geographical ranges (Berrebi et al., 2013;Clavero et al., 2017;[START_REF] Ninua | Phylogeography and taxonomic status of trout and salmon from the Ponto-Caspian drainages, with inferences on European brown trout evolution and taxonomy[END_REF].

Depending on the source, the number of Salmo species ranges from around 25 [START_REF] Kottelat | Hanbook of European freshwater fishes[END_REF]IUCN, 2016) to nearly 50 (Froese & Pauly, 2018). Among these, a dozen were described during the past decade (Turan et al., 2009;[START_REF] Delling | Diversity of western and southern Balkan trouts, with the description of a new species from the Louros River, Greece (Teleostei: Salmonidae)[END_REF]Turan et al., 2011[START_REF] Turan | The trouts of the Mediterranean drainages of southern Anatolia, Turkey, with description of three new species (Teleostei: Salmonidae)[END_REF]Turan et al., , 2014)), such as Salmo akairos [START_REF] Delling | Systematics of the trouts endemic to Moroccan lakes, with description of a new species (Teleostei: Salmonidae)[END_REF] and Salmo viridis Doadrio, Perea, & Yahyaoui 2015 described from Morocco. As illustrated by the numerous references cited above, which are only a snapshot of the available literature, research in this area is very active and molecular data have already begun to show that some species are not valid [START_REF] Sanz | Phylogeography history of brown trout: a review[END_REF] provides a detailed list and references]. Apart from S. salar and few other valid species [e.g. Salmo obtusirostris (Heckel 1851); [START_REF] Snoj | DNA phylogeny supports revised classification of Salmothymus obtusirostris[END_REF], this diversity is subsumed within the Salmo trutta species complex [START_REF] Sanz | Phylogeography history of brown trout: a review[END_REF]. Hence, this complex represents an interesting case of possible taxonomic inflation that has confounding taxonomic ramifications, hampers the understanding of the species" evolutionary history and impedes the development of appropriate strategies to protect natural trout diversity (Bernatchez et al., 1992;Antunes et al., 2001;[START_REF] Fumagalli | Extreme genetic differentiation among the remnant populations of marble trout (Salmo marmoratus) in Slovenia[END_REF][START_REF] Snoj | Resolving taxonomic uncertainties using molecular systematics: Salmo dentex and the Balkan trout community[END_REF][START_REF] Crête-Lafrenière | Framing the Salmonidae family phylogenetic portrait: a more complete picture from increased taxon sampling[END_REF][START_REF] Gratton | Genetic differentiation and hybridization in two naturally occurring sympatric trout Salmo spp. forms from a small karstic lake[END_REF][START_REF] Ninua | Phylogeography and taxonomic status of trout and salmon from the Ponto-Caspian drainages, with inferences on European brown trout evolution and taxonomy[END_REF]. Furthermore, to our knowledge, no molecular phylogenetic study within this complex has included type specimens (e.g. holotype, isotype, syntype) to check the validity of taxa, even though these are the only objective link to the Linnean binomial [START_REF] Mutanen | One species in eight: DNA barcodes from type specimens resolve a taxonomic quagmire[END_REF].

Accepted Article

Considered to be distributed in southern Eurasia and North Africa (Tortonese, 1954;[START_REF] Geldiay | A study on trout (Salmo trutta L.) populations in the Kazdagi stream[END_REF]Geldiay & Balik, 1988;[START_REF] Kottelat | Hanbook of European freshwater fishes[END_REF], Salmo macrostigma [START_REF] Duméril | Note sur une truite d"Algérie (Salar macrostigma, A. Dum.)[END_REF] represents one interesting case study to test for taxonomic inflation within the Salmo genus. The term macrostigma was used by [START_REF] Duméril | Note sur une truite d"Algérie (Salar macrostigma, A. Dum.)[END_REF] to describe a trout with big black spots on the flanks named Salar macrostigma, found in the Oued-el-Abaïch 40 km west of Collo in Algeria. According to [START_REF] Duméril | Note sur une truite d"Algérie (Salar macrostigma, A. Dum.)[END_REF], two identical specimens, here considered syntypes, were brought to Paris, France, one for the collections of the National Museum of Natural History (MNHN) and the other for the French Zoological Society. The term macrostigma has subsequently been used at both the species (Salmo macrostigma) and subspecies (S. t. macrostigma) level to characterize other trout native to North Africa (Morocco: [START_REF] Vivier | Note sur les eaux douces du Maroc et sur leur mise en valeur[END_REF]Azeroual et al., 2000;[START_REF] Abba | Relation taille-poids et coefficient de condition de la truite commune (salmo trutta macrostigma dumeril[END_REF][START_REF] Lbadaoui | Les populations marocaines autochtones des truites du genre Salmo: variation allozymique et statut taxonomique[END_REF]), Turkey (Togan et al., 1995;Bardakci et al., 2006;[START_REF] Kara | Distribution of fish fauna on the upper and middle basin of Ceyhan River, Turkey[END_REF] and the Middle East (Berg, 1949;[START_REF] Derzhavin | A note on fishes of the River Karaj (North Persia)[END_REF][START_REF] Segherloo | Phylogenetic status of brown trout Salmo trutta populations in five rivers from the southern Caspian Sea and two inland lake basins, Iran: a morphogenetic approach[END_REF]. Macrostigma phenotypes have also been reported in Italy (including Sardinia and Sicily;Boulenger, 1901;[START_REF] Mola | Facies della fauna e della flora delle aque interne[END_REF][START_REF] Gandolfi | I pesci delle acque interne italiane[END_REF][START_REF] Patarnello | Cytochrome b and 16S rRNA sequence variation in the Salmo trutta (Salmonidae, Teleostei) species complex[END_REF][START_REF] Massidda | Salmo (trutta) macrostigma in Sardegna[END_REF][START_REF] Nonnis Marzano | Molecular evidence for introgression and loss of genetic variability in Salmo (trutta) macrostigma as a result of massive restocking of Apennine populations (Northern and Central Italy)[END_REF]Ciuffardi & Arillo, 2006;[START_REF] Querci | Molecular characterization and hybridization in Salmo (trutta) macrostigma morphotypes from central Italy[END_REF], Albania [START_REF] Rakaj | Conservation status of freshwater fish of Albania[END_REF][START_REF] Cullaj | The quality of Albanian natural waters and the human impact[END_REF], Greece [START_REF] Kattoulas | The fish fauna of the Mornos Rivers (Greece)[END_REF][START_REF] Karakousis | Genetic structure and differentiation among Greek brown trout (Salmo trutta L.) populations[END_REF] and Corsica, France, [START_REF] Guyomard | Diversité génétique de la truite commune[END_REF][START_REF] Roche | Les espèces animales introduites dans les eaux douces de Corse[END_REF][START_REF] Gauthier | La colonisation de l"île par différentes souches de truite[END_REF]. A macrostigma phenotype might be observed in Salmo cettii Raffinesque 1810, inhabiting Sicily [START_REF] Schöffmann | Phylogenetic origin of Salmo trutta L 1758 from Sicily, based on mitochondrial and nuclear DNA analyses[END_REF][START_REF] Kottelat | Hanbook of European freshwater fishes[END_REF] and [START_REF] Duchi | Flank spot number and its significance for systematics, taxonomy and conservation of the near-threatened Mediterranean trout Salmo cettii: evidence from a genetically pure population[END_REF] rightly reported that confusion still exists regarding how to distinguish S. macrostigma from S. cettii. Indeed, distribution of the macrostigma trout remains controversial and some authors assert that it should be exclusively used for Algerian populations [START_REF] Zouakh | Hydrosystèmes continentaux et valorisation des ressources ichtyologiques d"Algérie. D. Phil[END_REF]Turan et al., 2011). Thus, the use of macrostigma for populations beyond Algeria and evaluation of the taxonomic status of S. macrostigma itself within or outside the S. trutta complex required genetic comparison

Accepted Article

of the Algerian macrostigma syntypes with European, Asian and other North African trout populations.

Mitochondrial DNA markers are valued for phylogenetic reconstructions using both museum and fresh samples because nucleic acids degrade over time and mitochondrial genomes (mtDNA) are available at much higher copy numbers per cell compared with singlecopy nuclear DNA [START_REF] Höss | Neanderthal population genetics[END_REF][START_REF] Wandeler | Pattern of nuclear DNA degradation over time -a case study in historic teeth samples[END_REF] and because mtDNA has reliable barcoding properties across vertebrates, including fishes (Allio et al., 2017). Despite its uniparental inheritance, mtDNA remains an important marker in studies of the S. trutta complex partly because so much data are already available from previous salmonid studies (Bernatchez et al., 1992;[START_REF] Snoj | DNA phylogeny supports revised classification of Salmothymus obtusirostris[END_REF][START_REF] Verspoor | Restricted matrilineal gene flow and regional differentiation among Atlantic salmon (Salmo salar L.) populations within the Bay of Fundy, eastern Canada[END_REF]Sušnik et al., 2006;[START_REF] Crête-Lafrenière | Framing the Salmonidae family phylogenetic portrait: a more complete picture from increased taxon sampling[END_REF] and partly because a well-supported mtDNA-based hypothesis of phylogenetic relationships is available [START_REF] Fraser | Adaptive evolutionary conservation: towards a unified concept for defining conservation units[END_REF][START_REF] De Cortey | Historical biogeography of Mediterranean trout[END_REF][START_REF] Vera | Maintenance of an endemic lineage of brown trout (Salmo trutta) within the Duero river basin[END_REF][START_REF] Snoj | Phylogeographic structure and demographic patterns of brown trout in north-west Africa[END_REF][START_REF] Sanz | Phylogeography history of brown trout: a review[END_REF].

In this study, traditional mtDNA marker analyses were combined with a mitogenomic approach used to obtain sequence data from the damaged DNA of museum samples labelled as S. macrostigma, including the syntype catalogued at National natural history museum, Paris (MNHN). The aim of the present study was to characterize: phylogenetic relationships of this syntype with other Salmo mtDNA lineages or species; the taxonomic status of S. macrostigma and whether this name refers to a distinct phylogenetic lineage; the limits of the geographic distribution of this lineage.

| MATERIALS AND METHODS

| Sampling

Fin or DNA samples were obtained for 67 specimens belonging to European, Moroccan and Turkish populations of S. trutta (Supporting Information Table S1). To assess the phylogenetic position of the macrostigma trout, a small piece of muscle from the MNHN syntype specimen (MNHN_IC_A_7585) and three other museum samples attributed to the macrostigma trout (MNHN_IC_0000_1909_C, MNHN_IC_1977_272_A and NMW_67984) were analysed (Supporting Information Table S1).

| DNA extraction and sequencing

Total genomic DNA from 67 specimens was extracted from 96% ethanol-preserved fin tissue following standard procedures [START_REF] Sambrook | Molecular cloning: a laboratory manual[END_REF] The Illumina library preparation procedure thus followed the recommendations of Tilak et al.

(2015) for blunt-end repair, adapter ligation, adapter fill-in and indexing PCR steps. An equimolar mix including a library for each museum sample was handed over to GATC-Biotech (www.eurofinsgenomics.eu) for the sequencing step on a single Illumina HiSeq2000 lane. Mapping of short reads (≤ 100 bp) and annotation of the complete mitogenomes were carried out against a reference genome of S. trutta (JQ390057) using Geneious 7 [START_REF] Kearse | Geneious Basic: an integrated and extendable desktop software platform for the organization and analysis of sequence data[END_REF]. Reads were mapped as follows: a minimum of 24 contiguous nucleotides matched the reference genome; a 5% maximum of mismatches per read; a minimum of 95% overlap similarity with the reference genome; a 3% indel maximum not exceeding a gap size of 10 nucleotides.

| Quality control of mitogenomes

To evaluate the potential presence of nuclear pseudogenes in the assemblies, each annotated mitogenome was carefully inspected by eye to detect abnormal boundaries, frameshifts and premature stop codons in protein coding genes. Three other quality controls recommended by Botero-Castro et al. (2016) were also performed: detailed information on the origin of the samples used for mitogenome sequencing and the museum voucher of each sample was provided to ensure taxonomic identification and easier cross-referencing; a CR and cytb barcoding identification of the specimens through a phylogenetic tree based on the closest available sequences was done to avoid specimen misidentification; a phylogenetic analysis of the new mitogenomes in the context of closely related species was conducted to get a clear depiction of the evolutionary affinities of the new mitogenomes and their degree of divergence compared with close relatives.

| Phylogenetic analyses and genetic distances

Mitogenomes of the four museum samples and of several GenBank S. trutta (4) and S. salar

(2) were aligned using the Geneious aligner with default parameters. Control region and cytb sequences were extracted from these mitogenomes and aligned by hand using MEGA 6.06 (Tamura et al., 2013) with newly produced and GenBank sequences obtained for additional specimens (Supporting Information Table S1).

Phylogenetic analyses were performed on a dataset including 46 new sequences of the control region. As mtDNA lineages of S. trutta were previously identified from CR sequences, 71 GenBank sequences were added to identify these lineages in our dataset.

Sequences belonged to eight main recognized lineages of S. trutta: Atlantic; Danubian; Adriatic; Marbled or S. (trutta) marmoratus Cuvier 1829; Mediterranean; Duero; Tigris; Dades [START_REF] Maccrimmon | World distribution of brown trout, Salmo trutta[END_REF][START_REF] Elliott | Wild brown trout Salmo trutta an important national and international resource[END_REF]Bernatchez et al., 1992;Suárez et al., 2001;[START_REF] De Cortey | Historical biogeography of Mediterranean trout[END_REF][START_REF] Cortey | Northern and Southern expansions of Atlantic brown trout (Salmo trutta) populations during the Pleistocene[END_REF][START_REF] Vera | Maintenance of an endemic lineage of brown trout (Salmo trutta) within the Duero river basin[END_REF][START_REF] Snoj | Phylogeographic structure and demographic patterns of brown trout in north-west Africa[END_REF][START_REF] Özen | Türkiye"deki alabaliklarin (Salmo trutta L.) moleküler filogenisi[END_REF]. Thus, a total of 117 CR sequences were used for phylogenetic reconstructions. Phylogenetic analyses were also based on a dataset including 70 new and 49 GenBank sequences of cytb (i.e. 119 cytb sequences in total). The two datasets were concatenated in a single dataset when sequences for both markers were available for the same individual. This concatenated dataset included 89 new and GenBank sequences (Supporting Information Table S1). According to the cytb phylogeny from Crête-Lafrenière et al. (2012), these separated and concatenated datasets were completed with GenBank sequences of S. obtusirostris and Salmo ohridanus Steindachner 1892. Finally, the tree was rooted by designating S. salar, as an outgroup (Supporting Information Table S1).

Phylogenetic reconstructions were conducted on the mitogenomic dataset as well as on both separate and concatenated CR and cytb datasets through the technical facilities of the

Accepted Article

platform Montpellier bioinformatics biodiversity at ISEM. Phylogenetic trees were reconstructed using a maximum-likelihood approach (ML) in the program PhyML 3.0 [START_REF] Guindon | New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0[END_REF] and Bayesian inference (BI) using MrBayes 3.1.2 [START_REF] Ronquist | MrBayes3: Bayesian phylogenetic inference under mixed models[END_REF]. Best-fitting models of sequence evolution were identified for each marker dataset as well as the concatenated dataset using MrModeltest 2.3 [START_REF] Nylander | MrModeltest v2. Program distributed by the author[END_REF]. A generalized time reversible (GTR) model [START_REF] Yang | Estimating the pattern of nucleotide substitution[END_REF] with a proportion of invariable sites (I) and a gamma distribution (G) was selected for the concatenated dataset in ML and the mitogenomic dataset in both ML and BI. A mixed model was recommended for a concatenated BI analysis in which the CR region and cytb codon positions were separately partitioned: HKY [START_REF] Hasegawa | Dating the human-ape splitting by a molecular clock of mitochondrial DNA[END_REF] + I + G for CR; K80 [START_REF] Kimura | A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences[END_REF] for the first codon position of cytb; GTR + I + G for the second and third positions of the cytb. Nodal robustness was estimated by bootstrap percentage values (BP) after 1000 pseudo-replicates under ML optimization. Five independent runs of five Markov chain Monte-Carlo chains were simultaneously carried out for 5 000 000 generations under BI optimization. Bayesian posterior probabilities (PP) were obtained from the 50% majority rule consensus of trees sampled every 100 generations after a burn-in stage of 25 000 generations.

Intra-and interlineage genetic distances were estimated by the uncorrected p-distance on the separate and concatenated datasets with MEGA.

| RESULTS

New sequences were deposited in the European Nucleotide Archive under the accession numbers LT617521-LT617587 for cytb, LT617588-LT617629 for CR and LT617630-LT617633 for the mitogenomes (Supporting Information Table S1). Alignments of the complete CR and cytb sequences were 1019 and 1140 nucleotides long with 108 and 128

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phylogenetically informative sites, respectively. Alignment of the mitogenomes comprised 16 683 positions with 907 phylogenetically informative sites (Supporting Information Table S2).

| TREE TOPOLOGIES

Phylogenetic analyses generated similar tree topologies in BI and ML (Figure 1 and Supporting Information Figures S1-S3 with PP and BP values). The monophyly of S. trutta was supported with high PP (1.00) values in the concatenated tree (Figure 1) and with high PP (1.00) and BP (100%) values in the mitogenome tree (Supporting Information Figure S3). In the other analyses, S. trutta formed a clade with S. ohridanus and S. obtusirostris (PP = 1.00; BP = 100%). The two latter species were always highly supported (PP = 1.00; 98% < BP < 100%) but were included in S. trutta in the CR and cytb gene trees (Supporting Information Figures S1,S2).

In the CR gene tree (Supporting Information Figure S2), the Mediterranean, Marbled, Danubian and Turkish mtDNA lineages were moderately to highly supported (0.93 < PP < 0.99; 57% < BP < 95%), whereas the Atlantic, Duero, Sicilian and Moroccan specimens were clustered together with weak support (PP ≤ 0.80; BP ≤ 50%). In the cytb gene tree (Supporting Information Figure S1), the Atlantic, Mediterranean, Dades, Danubian and Duero lineages had moderate to high support values (PP = 1.00; 71% < BP < 95%), whereas the Adriatic, Marbled and Turkish lineages were spread out in the tree. In the tree obtained from the concatenated dataset, all mitochondrial lineages were moderately to highly supported (0.99 < PP < 1.00; 55% < BP < 100%). In the separate and concatenated trees, relationships between these lineages remained unresolved.

| Genetic distances

Genetic distances from the separate and concatenated datasets were estimated within and between S. trutta lineages, S. obtusirostris, S. ohridanus and S. salar (Tables 1 andSupporting Information Tables S3, S4). In S. trutta, intragroup distances were as follows: 0.0 ± 0.0% to 0.6 ± 0.1% for cytb; 0.0 ± 0.0% to 0.4 ± 0.1% for CR (but distances rose to 5.4 ± 0.5% for the group including Atlantic, North African, Sicilian and Duero specimens); 0.1 ± 0.0% to 0.5 ± 0.1% for the concatenated dataset. The intergroup distances were as follows: 0.6 ± 0.2% to 1.7 ± 0.3% for cytb; 0.7 ± 0.2% to 1.3 ± 0.2% for CR (but 6.2 ± 0.5% for the group including Atlantic, North African, Sicilian and Duero specimens with the Danubian lineage); 0.5 ± 0.1% to 1.6 ± 0.3% for concatenated dataset. From the concatenated dataset, genetic distances between S. trutta and its closest related species were: 1.7 ± 0.2% with S. obtusirostris (2.1 ± 0.4% and 3.9 ± 0.4% for cytb and CR, respectively), 2.6 ± 0.3% with S. ohridanus (2.4 ± 0.4% and 5.6 ± 0.5% for cytb and CR, respectively) and 5.7 ± 0.5% with S. salar (5.9 ± 0.6% and 8.0 ± 0.7% for cytb and CR, respectively).

| Position of the macrostigma museum specimens

It clearly appears from the concatenated dataset that the three macrostigma MNHN samples originating from Northern Africa (Algeria and Morocco; Supporting Information Table S1) form a clade with new and GenBank specimens from Morocco and Sicily (PP = 0.99; BP = 55%) (Figure 1). This clade is closely related to the Atlantic lineage of S. trutta (PP = 1.00; BP = 76%; Figure 1) and not at all to the Dades lineage, endemic to Morocco [START_REF] Snoj | Phylogeographic structure and demographic patterns of brown trout in north-west Africa[END_REF]. The last museum sample attributed to a macrostigma trout (NMW 67984, originating from Albania; Supporting Information Table S1) clustered with the S. obtusirostris specimens from Bosnia and Herzegovina and Croatia in all trees (Figures 1and Supporting Information S2).

| DISCUSSION

The term macrostigma is widely used to phenotypically describe peri-Mediterranean trout samples from North Africa, Turkey, Middle East and Southern Europe. However, no phylogenetic study focused on this phenotype has previously been performed. Its recognition as a valid species may contribute to taxonomic inflation because morphological and meristic characters that strongly vary within the S. trutta complex are being erroneously used to diagnose an invalid taxon. Results showed that the existence of a single S. (t.) macrostigma (sub)species covering this very wide geographic area is unlikely as the four macrostigma trout considered in this study did not cluster together. No specimen from the Balkans, Turkey, Iran or France, where macrostigma is thought also to be distributed, was found to cluster with the MNHN syntype or with other macrostigma specimens considered in this study. They were all found to cluster within recognized S. trutta lineages (e.g. Danubian for Iranian samples; Adriatic for Albanian samples; Atlantic, Adriatic, Marbled and Mediterranean for Corsican samples).

The macrostigma syntype from MNHN and two other macrostigma trouts clustered with specimens from Moroccan and Sicilian populations that were grouped in a wellsupported clade in the concatenated tree (Figure 1). The geographical origin of these three museum specimens matched with the location from where S. macrostigma was originally described (Oued-el-Abaïch, Algeria;[START_REF] Duméril | Note sur une truite d"Algérie (Salar macrostigma, A. Dum.)[END_REF]. However, results did not support the existence of a monophyletic S. macrostigma restricted to North Africa, but rather showed that these specimens with alternative phenotypes are included in the S. trutta complex. Individuals of this well-supported Siculo-North African clade are distributed in four more-or-less geographically restricted groups with unresolved relationships (Figure 1) and with low intergroup genetic distances (0.2 to 0.6% for cytb and 0.2 to 0.5% for CR in [START_REF] Doadrio | Two new species of Atlantic trout (Actinopterygii, Salmonidae) from Morocco[END_REF]. Such distances compared with the intergroup genetic distances between S. trutta and other species considered (S. obtusirostris, S. ohridanus and S. salar, always > 2% for cytb, > 3.5% for CR) do not support the definition of valid Salmo species. According to [START_REF] Snoj | Phylogeographic structure and demographic patterns of brown trout in north-west Africa[END_REF], the evolutionary legacy of Salmo diversification in Northern Africa is probably the result of several waves of colonisation in North Africa during the Pleistocene. It may have occurred that S. trutta mtDNA haplotypes replaced undetected macrostigma, and possibly other (e.g. similarity of cytochrome oxidase I haplotypes among Mediterranean trout; Figure S1 in [START_REF] Geiger | Spatial heterogeneity in the Mediterranean biodiversity hotspot affects barcoding accuracy of its freshwater fishes[END_REF], mtDNA haplotypes during this process. However, samples that grouped with the three macrostigma trout are all Sicilian (T250009, T25010 and T25011) and Moroccan samples from Lake Ifni (I1, MNCN85764 and MNCN85765) in the concatenated tree (Figure 1). This suggests that at least one wave of mtDNA replacement would had to have been strong enough and relatively uniform throughout the range covered by those samples, from western Morocco (Lake Ifni) to Sicily. Additionally, some authors have reported that the so-called S. macrostigma is restricted to Mediterranean drainages of Morocco and Algeria [START_REF] Delling | Systematics of the trouts endemic to Moroccan lakes, with description of a new species (Teleostei: Salmonidae)[END_REF][START_REF] Zouakh | Hydrosystèmes continentaux et valorisation des ressources ichtyologiques d"Algérie. D. Phil[END_REF][START_REF] Doadrio | Two new species of Atlantic trout (Actinopterygii, Salmonidae) from Morocco[END_REF], while Lake Ifni is located in the Atlantic slope of Morocco. Thus, a multi-replacement scenario over a wide North African geographic area does not appear to be very parsimonious. This has to be investigated further but, at this stage, the North African S. macrostigma appears to be more of a myth than a well-supported reality. Nuclear data are necessary to address the relevance of S. macrostigma and other described Salmo species as valid species. Phylogenomic methods to delimit taxon boundaries are challenging but have greatly improved in the past few years.

Such methods can distinguish between structure associated with intraspecific variation and introgression from that resulting from speciation [START_REF] Wagner | Genome-wide RAD sequence data provide unprecedented resolution of species boundaries and relationships in the Lake Victoria cichlid adaptative radiation[END_REF][START_REF] Mutanen | One species in eight: DNA barcodes from type specimens resolve a taxonomic quagmire[END_REF][START_REF] Zarza | Hidden histories of gene flow in highland birds revealed with genomic markers[END_REF]Baumsteiger et al., 2017) and sometimes allow for a deep taxonomic reassessment of evolutionary units in challenging taxa [START_REF] Papakostas | Integrative taxonomy recognizes evolutionary units despite widespread mitonuclear discordance: evidence from a rotifer cryptic species complex[END_REF], or even reconciliation of morphological and molecular taxonomies in integrative studies [START_REF] Dejaco | Taxonomist"s nightmare … evolutionist"s delight: an integrative approach resolves species limits in jumping bristletails despite widespread hybridization and parthenogenesis[END_REF][START_REF] Morard | Nomenclature for the nameless: a proposal for an integrative molecular taxonomy of cryptic diversity exemplified by planktonic Foraminifera[END_REF]. The Salmo genus is certainly one interesting case to consider because large scale integrative taxonomic studies are currently lacking. Consideration of type specimens certainly remains crucial [START_REF] Mutanen | One species in eight: DNA barcodes from type specimens resolve a taxonomic quagmire[END_REF][START_REF] Schultz | A barcode analysis of the genus Lobophora (Dictyotales, Phaeophyceae) in the western Atlantic Ocean with four novel species and the epitypification of L. variegata (J. V. Lamouroux)[END_REF]. New techniques may facilitate the retrieval of more complete mitochondrial [START_REF] Van Der Valk | Whole mitochondrial genome capture from faecal samples and museum preserved specimens[END_REF] and nuclear data (e.g. [START_REF] Grandjean | Rapid recovery of nuclear and mitochondrial genes by genome skimming from Northern Hemisphere freshwater crayfish[END_REF] from museum specimens.

Conversely, it is clear from Figure 1 that North African macrostigma specimens and other samples probably belong to a previously undescribed North African mtDNA lineage in S. trutta, with the well-known Atlantic lineage as its sister clade. This confirms previous results based on partial and complete CR that have already underlined the close phylogenetic relationships between native Moroccan and Sicilian populations [START_REF] Schöffmann | Phylogenetic origin of Salmo trutta L 1758 from Sicily, based on mitochondrial and nuclear DNA analyses[END_REF][START_REF] Snoj | Phylogeographic structure and demographic patterns of brown trout in north-west Africa[END_REF][START_REF] Fruciano | Phylogeographical relationships of Sicilian brown trout and the effects of genetic introgression on morphospace occupation[END_REF].

However, if S. macrostigma is not a valid species based on our mtDNA data, native populations of the so-called North African lineage are currently threatened by human activities (e.g. increased water use, environmental degradation due to deforestation) and by introgression with domestic S. trutta from hatcheries [START_REF] Snoj | Phylogeographic structure and demographic patterns of brown trout in north-west Africa[END_REF][START_REF] Fruciano | Phylogeographical relationships of Sicilian brown trout and the effects of genetic introgression on morphospace occupation[END_REF].

To manage native biodiversity better, [START_REF] Zachos | Species inflation and taxonomic artefacts -A critical comment on recent trends in mammalian classification[END_REF] particularly discouraged both species-splitting based on gene trees inferred from mtDNA and phenetic analyses aimed at diagnosability. These authors recommend the use of concepts such as ESUs (considering the spatial distribution of the genetic diversity; [START_REF] Moritz | Defining "Evolutionarily Significant Units" for conservation[END_REF]Almodóvar et al., 2006), or alternatives [e.g. operational conservation units (OCU), reflecting interaction with socioeconomic issues [START_REF] Dodson | Elements in the development of conservation plans for Atlantic salmon (Salmo salar)[END_REF][START_REF] Machordom | Mitochondrial haplotype variation and phylogeography of Iberian brown trout populations[END_REF]], which highlight intraspecific diversity without promoting taxonomic inflation and the arbitrary concept of subspecies [START_REF] Freudenstein | Biodiversity and the species concept -lineages are not enough[END_REF]. The North African lineage described in this study and probably more local groups within this lineage certainly must be managed in a more adaptive and integrated evolutionary framework, such as with ESUs, to be more effective [START_REF] Fraser | Adaptive evolutionary conservation: towards a unified concept for defining conservation units[END_REF].

  . The entire control region (CR) and cytochrome b (cytb) gene were amplified by PCR with the following primer sets, respectively: Str-DL1F (5'-GCACCGACTACACTATCATT-3') and StrDL1R (5'-TTTATATGTTTGATTGAGA-3') designed for this study; SalmoCBF (5'-CATAATTCCTGCCCGGACTCTAACC-3') and Salmo-CBR (5'-TTTAACCTCCGATCTCCGGATTACA-3') corresponding to the cytb primers mentioned in Crête-Lafrenière et al. (2012). Direct sequencing was carried out in both directions at the technical facilities of the genotyping and sequencing platform of the Institute for Evolutionary Sciences Montpellier (ISEM). For the museum samples, DNA retrieval was optimized using a protocol recently developed by Tilak et al. (2015) to build and sequence shotgun Illumina (www.illumina.com) libraries from small quantities of degraded genomic DNA. First, DNA extraction with blank controls was performed in the ADN dégradé platform of ISEM dedicated to damaged DNA experiments, with the DNeasy Blood and Tissue kit (QIAGEN; www.qiagen.com) following the recommendations of the manufacturer, except decreasing the elution volume to 100 µl.

Figures S1,

  Figures S1, S2).

FIGURE 1

 1 FIGURE 1Bayesian phylogenetic tree reconstructed from a concatenated alignment of the

TABLE 1

 1 Genetic distances between lineages and the most closely related species of Salmo trutta based on the concatenated dataset. Genetic distances (with S.E. in brackets) in the diagonal are intragroup distances (in bold), while the genetic distances below the diagonal (with their S.E.

	above the diagonal) are intergroup distances
		1	2	3	4	5	6	7	8	9	10	11	12
	Adriatic	0.004	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.003	0.003	0.005
		(0.001)
	Atlantic	0.011	0.001	0.002	0.002	0.002	0.001	0.002	0.002	0.002	0.003	0.003	0.005
			(0.000)
	Dades	0.009	0.009	0.002	0.002	0.002	0.002	0.002	0.001	0.002	0.003	0.003	0.005
				(0.001)
	Danubian	0.012	0.013	0.011	0.005	0.003	0.002	0.002	0.002	0.002	0.004	0.003	0.005
					(0.001)
	Duero	0.011	0.009	0.011	0.016	0.001	0.002	0.002	0.002	0.002	0.003	0.002	0.005

This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

This article is protected by copyright. All rights reserved.

ACKNOWLEDGEMENTS

Thanks to A. Dettai (Collections of Ichthyology, Museum National d"Histoire Naturelle, Paris, France) and H. Wellendorf (Naturhistorisches Museum Wien, Vienna, Austria) for providing trout museum samples, especially the macrostigma syntype specimen. The authors are also grateful to A. Snoj, M. Arculeo, A. Crivelli, D. Doucende, M. Geiger, D. Jesensek, J.-L. García-Marín, S. Muracciole, V. Peyronnet, G. Pustovrh, A. Sabatini, H. Watt and to the GENESALM project for providing trout samples or DNA. We also thank the teams of the ISEM platforms shared with the LabEx CeMEB (Centre Méditerranéen de l"Environnement et de la Biodiversité, Montpellier, France) for their technical help, as well as two anonymous reviewers for helpful comments. Publication ISEM n°201X-XXX.

l'Oued Sidi Rachid (Moyen Atlas) Maroc. Afrique Science 6, 60-70.

This article is protected by copyright. All rights reserved.

Accepted Article

Agapow, P.-M., Bininda-Edmonds, O. R. P., Crandall, K. A., Gittleman, J. L., Mace, G. M., Marshall, J. C. & Purvis, A. (2004). The impact of species concept on biodiversity studies.

The

Quarterly Review of Biology 79, 161-179. Allio, R., Donega, S., Galtier, N. & Nabholz, B. (2017). Large variation in the ratio of mitochondrial to nuclear mutation rate across animals: implications for genetic diversity and the use of mitochondrial DNA as a molecular marker. Molecular Biology and Evolution 34, 2762-2772. Almodóvar, A., Nicola, G. G., Elvira, B. & García-Marín, J. L. (2006). Introgression variability among Iberian brown trout evolutionary significant units: the influence of local management and environmental features. Freshwater Biology 51, 1175-1187. Antunes, A., Faria, R., Weiss, S. & Alexandrino, P. (2001). Complex evolutionary history in the brown trout: insights on the recognition of conservation units. Conservation Genetics 2, 337-347. Azeroual, A., Crivelli, A. J., Yahyaoui, A. & Dakki, M. (2000). The ichthyofauna of the inland waters of Morocco. Cybium 24, 17-22. Bardakci, F., Degerli, N., Ozdemir, O. & Basibuyuk, H. H. (2006). Phylogeography of the Turkish brown trout Salmo trutta L.: mitochondrial DNA PCR-RFLP variation. Journal of Fish Biology 68, 36-55. Baumsteiger, J., Moyle, P. B., Aguilar, A., O"Rourke, S. M. & Miller, M. R. (2017). Genomics clarifies taxonomic boundaries in a difficult species complex. PLoS ONE 12, e0189417. Berg, L. S. (1949). Presnovodnye ryby Irana i sopredel"nykh stran. Trudy Zoologicheskogo Instituta Akademii Nauk SSSR 8, 783-858. This article is protected by copyright. All rights reserved. Accepted Article Bernatchez, L., Guyomard, R. & Bonhomme, F. (1992). DNA sequence variation of the mitochondrial control region among geographically and morphologically remote European brown trout Salmo trutta populations. Molecular Ecology 1, 161-173. Bernatchez, L. (2001). The evolutionary history of brown trout (Salmo trutta L.) inferred from phylogeographic, nested clade and mismatch analyses of mitochondrial DNA variation. Evolution 55, 351-379. Berrebi, P., Tougard, C., Dubois, S., Shao, Z., Koutseri, I., Petkovski, S. & Crivelli, A. J. (2013). Genetic diversity and conservation of the Prespa trout in the Balkans. International Journal of Molecular Sciences 14, 23454-23470. Bickford, D., Lohman, D. J., Sodhi, N. S., Ng, P. K. L., Meier, R., Winker, K., Ingram, K. K. & Das, I. (2007). Cryptic species as a window on diversity and conservation. Trends in Ecology and Evolution 22, 148-155. Botero-Castro, F., Delsuc, F. & Douzery, E. J. P. (2016). Thrice better than once: quality control guidelines to validate new mitogenomes. Mitochondrial DNA Part A 27, 449-454. Boulenger, G. A. (1901). IV On the Occurrence of Salmo macrostigma in Sardinia. Annals and Magazine of Natural History 8, 14-14. Burbrink, F. T., Lawson, R. & Slowinski, J. B. (2000). Mitochondrial DNA phylogeography of the polytypic North American rat snake (Elaphe obsolete): a critique of the subspecies concept. Evolution 54, 2107-2118. Ciuffardi, L. & Arillo, A. (2006). La fauna ittica d"acqua dolce della Liguria: composizione attuale e categorie regionali IUCN. Journal of Freshwater Biology 34, 1-5. Clavero, M., Calzada, J., Esquivias, J., Veríssimo, A., Hermoso, V., Qninba, A. & Delibes, M. (2017). Nowhere to swim to: climate change and conservation of the relict Dades trout Salmo multipunctata in the high Atlas Mountains, Morocco. Oryx doi:10.1017/S0030605316001551.

Accepted Article

Suárez, J., Bautista, J. M., Almodóvar, A. & Machordom, A. (2001). Evolution of the mitochondrial control region in Palaearctic brown trout (Salmo trutta) populations: the biogeographical role of the Iberian Peninsula. Heredity 87, 198-206. Sušnik, S., Knizhin, I., Snoj, A. & Weiss, S. (2006). Genetic and morphological characterization of a Lake Ohrid endemic, Salmo (Acantholingua) ohridanus with a comparison to sympatric Salmo trutta. Journal of Fish Biology 68, 2-23. Ichthyological Exploration of Freshwaters 20, 333-364.

Supporting Information

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domain: math shs

text:
Céline Vendeira

Sylvia Coutat
email: sylvia.coutat@unige.ch

Shapes recognition in early school: How to develop the dimensional deconstruction?

Keywords: Shape recognition, visualization, dimensional deconstruction, way of thinking

In primary school there is, in geometry, an important rupture between primary (age 4 to 12) and secondary school. Some activities are already proposed for students from 8 to 12 years old to help to prepare for this rupture. Our research has the same aims, but for students from 4 to 6 years old by developing some pre-geometrical activities around shape recognition using dimensional deconstruction.

Context

In all French speaking Switzerland we have a common program for all compulsory education. For the geometry curriculum, in the elementary division (from 4 to 8 years old), students use a physical space where «the shape is linked to the visual perception of the object» 1 . Then, from 8 years old, they use a conceptual space where objects are associated with figures as «unchangeable and ideal». These figures are independent of their graphical representation. We consider that there is an important gap between these two divisions, and we need to help students to overcome it.

Theoretical framework

Some researches like [START_REF] Berthelot | L'enseignement de la géométrie à l'école primaire[END_REF][START_REF] Berthelot | L'enseignement de la géométrie à l'école primaire[END_REF], [START_REF] Houdement | Paradigmes géométriques et enseignement de la géométrie[END_REF], [START_REF] Parzysz | Articulation entre perception et déduction dans une démarche géométrique en PE1[END_REF], [START_REF] Braconne-Michoux | Evolution des conceptions et de l'argumentation en géométrie chez les élèves : paradigmes et niveaux de Van Hiele à l'articulation CM2-6ième[END_REF] show a rupture, in geometry teaching, between primary and secondary school where the focus is put on reasoning and deduction. Without reaching the theoretical level of the geometric objects and therefore of their properties, an intermediate work on the elements which compose the forms is possible and constitutes the heart of this research with students of cycle 1 and beginning of cycle 2. As [START_REF] Duval | Les différents fonctionnements d'une figure dans une démarche géométrique[END_REF] says, one of the aims of geometry in primary school is to emerge the operative apprehension of a figure parallel to the one, first and naturel, more perceptive. Therefore, to help, it "presupposes the dimensional deconstruction of the visual representations" 2 (Duval & Godin, 2005, p.11). The first visualization is global; the perception is centered on the closed contours of the shape. This visualization is called two dimensional visualization (2D element), which is referred to by [START_REF] Duval | Les conditions cognitives de l'apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements[END_REF] as the iconic way of seeing. The dimensional deconstruction considers the elements of the shape like the sides and the lines, which are one dimensional elements (1D element) and the vertices and the points, the zero dimensional elements (0D elements). This is what [START_REF] Duval | Les conditions cognitives de l'apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements[END_REF] distinguishes as the non-iconic way of seeing. The decomposition of shapes into figural unities is an essential stage prior to building the non-iconic visualization. Having as objective to evolve the students' visualization of geometrical shapes, we rely on the work of the Lille group [START_REF] Duval | Les différents fonctionnements d'une figure dans une démarche géométrique[END_REF]), Duval, Godin & Perrin-Glorian (2004), Duval & Godin (2005), Keskessa, Perrin-Glorian, Delplace (2007), [START_REF] Godin | De la restauration de figure à la rédaction d'un programme de construction[END_REF], Perrin-Glorian, Mathé & Leclercq (2013), Perrin-Glorian, [START_REF] Perrin-Glorian | De la reproduction de figures géométriques avec des instruments vers leur caractérisation par des énoncés[END_REF][START_REF] Perrin-Glorian | Jouer avec des formes en maternelle: Premiers pas vers la géométrie[END_REF], [START_REF] Bulf | Essai d'une progression sur le cercle pour l'école primaire. Une transition clé : du gabarit au compas[END_REF]) which consider the transition between the recognition of a form by global perception and the deduction from its axioms as the "identification of properties that are verified or produced with instruments"3 (Houdement and Godin, 2014, p.28). Most of those researchers propose tasks of reproduction of figures in particular the reproduction problems called "restoration of figures (define by Perrin-Glorian and [START_REF] Godin | De la restauration de figure à la rédaction d'un programme de construction[END_REF]). In our case, we work on tasks of forms recognition. To prepare students to the rupture pointed out between primary and secondary school, we introduce two new levels between the global perception and the non-iconic way of seeing. We call them the "hybrid thinking" and "thinking by characteristics". Below, we associate each thinking according to the ways of seeing of Duval. We give an example based on the following shape: Those levels focus 1) on a global vision of the shape (2D) 2) on a hybrid vision of the shape (using the global vision and some characteristics of the shape (0-1-2D) 3) on the vison of only some localised areas of the global form (as the types of lines (straight or not, etc.)) considering therefore some of the characteristics of the shape (0-1D). This third level corresponds to pre-geometrical work. The last level "non-iconic visualization" relates to the definition of the properties of geometric figures. So, to think by the characteristics is more than a perceptive vision but does not yet correspond to the geometric properties. As for the hybrid thinking, it mobilizes in the same time the global vision of the shape, through its surface, and a more expert vision from its elements.

This table shows a wider process of dimensional deconstruction than usual. Thus, our goal, in this research, is to develop some pre-geometrical activities around shape recognition using these two new levels to provide students with a more harmonious transition in order to overcome the gap between primary and secondary school.

The developed material

In order to help 4 to 6-year-old students to pass from the perception of the shapes as they are worked in primary school to what is expected in secondary school, we propose to work on shapes recognition tasks with a collection of 36 shapes. Very often, the most common use of characteristics concerns the number of sides of the shape. However, students at this age are precisely building the concept of number which is therefore "fragile". Other characteristics of shapes are nevertheless affordable and interesting from Cycle 1. For example, the presence of straight or curved edges, symmetries, parallel opposite sides or the convex or concave character of the shape. Of course, students are not expected to use the correct mathematical terms. What is important is that they identify these characteristics, whatever the vocabulary used. The collection of 36 shapes takes into account the different characteristics cited. Figure 1 presents the collection of the 36 shapes. All the different tasks are built around this collection (tasks of classifications, associations and housing). The chosen shapes are not nameable, at least not using "classical" shape names such as triangles, squares, rectangles, circles. To identify them, students have to focus on other aspects than their name. Either students recognize, in the shape, a resemblance to a well-known object (for example the fish mentioned above), or they are obliged to refer to its characteristics. This last point promotes dimensional deconstruction with the components of shapes. Thus, the main objective aimed through the developed activities is that the student constructs a thinking of the objects based on their characteristics. This does not mean that it is necessary to replace the global thinking, but to supplement it. The joint use of the hybrid thinking and the thinking by characteristics is therefore also necessary. For example, in many activities, students can first classify the shape by global perception (we put together shapes perceptually close), and then only need to distinguish them through their characteristics.

Below is an example of strategy to find a shape in a collection of eight shapes :

Starting Collection Reduced collection Identified shape in the reduced collection I observe and manipulate the assortment of forms I extract all "bow ties" (or "vases") of the assortment.

I then focus on the characteristics "it is the one that is not regular (=symmetrical) and with rounds (=curved edges)". I select then the corresponding shape.

Table 2

Thematic Working Group 04

The choice of the selected shapes is essential because it can directly influences the way of thinking that the students will mobilize.

Perceptive thinking Hybrid thinking Thinking by characteristics

Table 3 Thus, if the selected shapes are perceptively distant, the overall vision is promoted. Conversely, if the shapes are perceptively close, an entry through the characteristics is necessary. These shapes are cut out from "translucent" Plexiglas. The choice of a circle does not favour any particular orientation. With this material, we can work on the shape using the edging by the exterior or the interior of the shape. Depending on the activity, we may choose to present one or both of these supports (or both). The interest of this material is that it can be embedded providing direct feedback for students.

The inside form the empty circular part

With this collection of shapes we then create activities working on shape recognition with different kinds of tasks, classifications, associations and housing.

Methodology

For one school year we have worked with six classes including four classes in a downtown Geneva school, a class in the Geneva countryside and a class in neighbouring France. This diversity makes it possible to confront our material and our activities in different contexts (without pretending any generalization). In total there were 112 students aged from 4 to 6. At the beginning and the end of the year all the students took a test. We do not develop the results of the tests in this article. The students worked in small groups with the researchers from 2 to 4 periods in total. Each period lasts 45 minutes. In every class, except one, we realized, among the proposed periods, a session with big shapes in the "meso-space".

Photo 1: Work with big shapes

In each class we have: 1) One individual pretest at the beginning of our research in which we use the activity « families to build ». This test has been passed by the teachers and was not filmed. 2) Many activities using the developed material. Each session was filmed by one or even two cameras.

3) One activity with big forms. 4) One « concluding activity » at the end of the year. 5) One post-test at the end of the school year (exactly the same as the pretest). 6) One pretest at the beginning of the following year (exactly the same as the previous ones). This test was filmed and students were systematically asked about their production.

We thus have many hours of observations that allow us to verify if students of this age can mobilize the characteristics of the shapes.

Presentation of an activity for 4 to 6 year old students: Families to build5

The activity is done in groups of 2 to 5 students. The teacher selects an assortment of 8 to 16 pieces from the collection (the inside form or the empty circular part). Below is an example of an assortment that has been frequently used in classrooms with students. In this activity students must build families (with a number of families imposed or not). The pieces are scattered on a table. Students must create families by putting the pieces "that fit well together".

Students must agree and be able to explain their choice, possibly giving a name to the families created. Various objectives can be identified for this activity: 1) classification of shapes based on characteristics 2) emergence of a common lexicon that can be reinvested in other activities 3) peer collaboration with the need to agree and to argue. Thus, according to the assortment of selected pieces, students can use global or hybrid thinking or thinking by characteristics. The choice of perceptively close shapes or not is therefore an important didactic variable for this activity as well as the number of families (imposed or free).

In the pooling phase the teacher can introduce new pieces to check the solidity of students' family choices. Either they manage to integrate the new pieces within the existing families, or they need to question their classification criteria and maybe modify them. Photo 2: An example of three families built by a group of students: 1) "the mountains" 2) "the pebbles" 3) "the fish" (vision according to the resemblance of the shapes to well-known objects)

Some results

In this section we look at the productions of three students which reveal three different ways of thinking that the students mobilize about the shapes following our interventions in class. These are outcomes from the activity "families to build" carried out during the pretest (done at the beginning of our research) and the same test realized a year later.

Concerning the case of Luce, almost no change is noticable between the two productions at one year interval. During the first run, it is found that very perceptively similar objects are associated in order to create three families. A year later, the student explained that he had formed a family of mountains, trumpets, teapots and lamps and could not say more. It is possible to relate these objects to some of their characteristics as the sharp peaks for the mountains, the symmetry for the lamps or the asymmetrical spout for the teapot. However, this remains implicit and the primarily mobilized vision is, in this case, global. Lea's productions at the same task are identical to those of Luce for the first test. Her vision is essentially global. On the other hand, the two families created the following year are quite distinct. She chose only two families by mobilizing hybrid thinking. Indeed, the global perception is partially used with the second family where Lea recognizes thunder thanks to their "peaks in". As for the first family, it only possesses "rounded in" and does not belong to the family of the thunders. The first production of David is distinct from those of these two classmates. However, without a trace of his activity, it is difficult to understand how this student proceeded. It is conceivable (1) that devolution has not taken place;

(2) that David mobilizes hybrid thinking but it is impossible for us to interpret. This is why we focus directly on the second production made the following year. The first family of David is justified according to two characteristics common to the three forms, namely "rounded and sharp". As for the second family, the forms are "all sharp", but have no rounding. This student thus mobilizes some characteristics of the forms.

Conclusion

The task "build families" is very interesting for the researcher because it gives a lot of information about the student's perception of the shape such as the visualization to build the families (global or not), the use of characteristics to build the families, the use of a pertinent language for oral interactions.

The various tasks created with the developed material and experimented in classrooms allow a progressive change of the visualization of geometrical shapes. It is important to note that students do not replace their perceptual way of thinking with a new way of thinking by the characteristics of the forms. Indeed, these ways of thinking must coexist and intertwine, sometimes giving rise to a hybrid way. It remains to be defined 1) whether the work undertaken allows all students to change their eyesight and 2) whether they are able to mobilize the appropriate thinking according to the situation.

«

  It looks like a fish» « It looks like a fish with a flat nose and a curved body » « It is a shape with holes (the convex character). It as rounds and straights (straight and curved edges) »

Figure 1 :

 1 Figure 1: The collection of the 36 shapes

Figure 2 :

 2 Figure 2: An assortment frequently used in classrooms

Table 1 : Levels of the different visions of the shapes

 1

Table 4 : the two productions of Luce at one year interval

 4

Table 5 : the two productions of Léa at one year interval

 5

Table 6 : the two productions of David at one year interval

 6

Our translation.

In the next steep of our research we will also consider the "associated action".Thematic Working Group 04Proceedings of CERME10

Proceedings of CERME10

For more activities see[START_REF] Coutat | Des pointes, des pics et des arrondis en 1P-2P[END_REF].Thematic Working Group 04Proceedings of CERME10

Currently we are experimenting with new tasks with students from 6 to 8 years old and still analyzing the data collected with students from 4 to 6 years old. In addition, the developed material is currently tested in five schools. We look forward to the feedback from the teachers.