Dr Benjamin Gehres
email: benjamin.gehres@gmail.com

Dr Guirec Querré
email: guirec.querre@univ-rennes1.fr

Analysis of mica inclusions using LA-ICP-MS: a new approach for sourcing raw material of ceramics

Keywords: LA-ICP-MS, Sourcing, Ceramic, Raw material, Biotite 1

published or not. The documents may come

Analysis of mica inclusions using LA-ICP-MS: 1 a new approach for sourcing raw material of ceramics

Benjamin Gehres, Guirec Querré

Introduction

In archaeology, the study of the origin of objects and of the raw materials in which they were made provides invaluable information for tracking relationships between different human groups for a given region and period, as well as recording the evolution of procurement throughout time. This is particularly true for archaeological ceramics, for which typochronology, but also composition and fabrication techniques are provenance criteria. At the present time, the most frequently used analytical methods for determining ceramic raw material sources are mineralogical and petrographic analyses with polarized light microscopy, X-ray powder diffraction (XRD), elementary chemical analyses using several techniques: pXRF [START_REF] Hunt | Portable XRF analysis of archaeological sediments and ceramics[END_REF], INAA [START_REF] Speakman | Sourcing ceramics with portable XRF spectrometers? A comparison with INAA using Mimbres pottery from the American Southwest[END_REF], ICP-OES [START_REF] Tsolakidou | Comparative analysis of ancient ceramics by neutron activation analysis, inductively coupled plasma-optical-emission spectrometry, inductively coupled plasma-mass spectrometry, and X-ray fluorescence[END_REF], ICP-MS [START_REF] Kennett | Geochemical characterization of Lapita pottery via Inductively Coupled Plasma-mass Spectrometry (ICP-MS)[END_REF]. Other methods can be used and a more comprehensive list of these and their applications can be found in the literature [START_REF] Rice | Pottery analysis, a sourcebook[END_REF][START_REF] Quinn | Interpreting silent artefacts, petrographic approaches to archaeological ceramics[END_REF][START_REF] Quinn | Ceramic petrography: the interpretation of archaeological pottery and related artefacts in thin section[END_REF]. The development of spectrometric spot analysis methods over the past few years paves the way for new perspectives in archaeometry (Sourcing of fluviatile shell temper: [START_REF] Peacock | Using laser ablation-inductively coupled plasma-mass spectrometry to source shell in shell-tempered pottery: a pilot study from north Mississippi[END_REF]; elementary analyses of ceramics: [START_REF] Kennett | Geochemical characterization of Lapita pottery via Inductively Coupled Plasma-mass Spectrometry (ICP-MS)[END_REF][START_REF] Golitko | Mapping prehistoric social fields on the Sepik coast of Papua New Guinea: ceramic compositional analysis using laser ablation-inductively coupled plasma-mass spectrometry[END_REF]; U/Pb dating of inclusions of detrital zircons: [START_REF] Tochilin | Sourcing temper sands in ancient ceramics with U-Pb ages of detrital zircons: a southwest Pacific test case[END_REF]; distinction between fossil inclusions and shell temper: Gehres et al. 2015; characterization of archaeological materials: [START_REF] Speakman | Characterization of archaeological materials by laser ablation-inductively coupled plasma-mass spectrometry[END_REF][START_REF] Speakman | Sourcing ceramics with portable XRF spectrometers? A comparison with INAA using Mimbres pottery from the American Southwest[END_REF]. We used the laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) method to characterize mineral phases included in ceramic bodies in order to determine their origin. In archaeology, the study of ceramic bodies is particularly interesting for tracing where they were made, among other aspects. In this way, these objects can be used to better evaluate exchange networks. Apart from some organic tempers (ground bone, plants), the inclusions contained in ceramic bodies are mineral and these grains are characteristic of a specific geological source. The mineralogical and petrographic composition of archaeological ceramics generally reflects the geology of the place where they were produced, as workshops and production zones are generally close to raw materials sources. There are cases where the minerals, or assemblages of minerals from ceramic bodies are sufficiently rare and original to find their origin and define a presumably very restricted or even once-off production zone (Peacock 1988;[START_REF] Martineau | Clay resources and technical choices for neolithic pottery (Chalain, Jura, France): chemical, mineralogical and grain-size analyses[END_REF][START_REF] Quinn | Calcareous microfossils in Bronze Age aegean ceramics: illuminating technology and provenance[END_REF][START_REF] Ixer R | The provenance potential of igneous glacial erratics in Anglo-Saxon ceramics from Northern England[END_REF], or where is a contrast in the composition of the geological substratum and the mineralogical composition of the bodies [START_REF] Boileau | Pottery technology & regional exchange in Early Iron Age Crete[END_REF]). When we work on archaeological sites located on crystalline bedrock with granite-gneissic rocks, it is very difficult to determine the massif or the formation of the original crystalline rocks from the alteration clays used to made ceramics, as a whole complex of formations have identical or close mineralogical compositions. In the geological formations existing on Earth, ancient cratons are generally composed of granite-gneissic rocks: like for example the Canadian Shield or the Baltic Shield. This is the case in the Massif Central and the Armorican Massif in France (Fig. 1). There are numerous granite-gneissic formations in these cratons with very similar mineralogical composition, mainly made up of essential minerals such as quartz, plagioclase, potassium feldspar, micas such as biotite, muscovite) and at times smaller quantities of amphiboles and secondary minerals such as zircon, opaque minerals, rutile. In order to develop our methodology, we worked on archaeological ceramics discovered in occupation sites mainly located in the Armorican Massif (Fig. 1), dating from the Neolithic and protohistory, from the end of the 5 th millennium to the 1 st century before our era. We used the LA-ICP-MS technique on thin sections to chemically characterize the biotite inclusions in ceramics and different rocks from the Armorican Massif (Fig. 1), where weathered and decayed rocks are likely to have been used by potters. Indeed, chemical variations in the composition of these minerals are known to be very susceptible to the physico-chemical conditions of different magmas [START_REF] Wones | Stability of biotite: experiment, theory and application[END_REF][START_REF] Czamanske | Oxidation during magmatic differentiation, Finnmarka complex, Oslo Ara Norway--ll. Mafic silicates[END_REF][START_REF] Helz | Phase relation of basalts in their melting range at P HO2 = 5 kb as a function of oxygen fugacity-1 Mafic phases[END_REF][START_REF] Speer | Micas in igneous rocks[END_REF][START_REF] Haslam | The crystallization of intermediate and acid magmas at Ben Nevis, Scotland[END_REF].

2. Origins of the studied ceramics (Table 1 / Fig. 2) In order to test our method, we chose to work on ceramic productions issued from insular sites. By working on islands, we have access to local, slightly diversified geological formations, creating more favourable conditions than on the mainland. The studied ceramics are from two archipelagos in the south of Brittany, one in the region of Carnac in Morbihan (Table 1, Fig. 2), the other in Finistère near Pont-Aven (Table 1, Fig. 2). For the Houat-Hoedic archipelago, Belle-Île-en-Mer (Fig. 2), two ceramics from the Middle Neolithic I standing stone alignment (4700 -4300 BCE) from Douet [START_REF] Large | La file de pierres dressées du Douet, Hoedic[END_REF]) and one pottery from the salt fabrication workshop from the Second Iron Age (700 -1 st century BCE) from Port Blanc were used. A Bronze Age urn (850 -700 BCE) with a granitic body from Belle-Île-en-Mer, completes the corpus from this archipelago. This pot was used as a container for a deposit of metallic objects [START_REF] Audouard | Belle-Île-en-Mer du Mésolithique à l'âge du Bronze : Emergence d'une nouvelle dynamique de recherche[END_REF]. One Hoedic granite sample, which is the only rock type on this island, is used as a reference sample to define the geological source. The petrographic analysis of these ceramics enabled us to observe inclusions characteristic of clays derived from the alteration of granite: grains of quartz, potassium feldspar and plagioclase, but also biotite and muscovite tablets. Rock fragments combining quartz, potassium feldspar and micas and presenting a grainy texture were also detected. Therefore, these potteries were made from granitic clay. However, it is not possible to determine whether they were made from the same clay, or clay from different sources. For the Glénan Archipelago and Île aux Moutons (Fig. 2): three ceramics from the Middle Neolithic occupation II (4200 -3800 BCE) from Île aux Moutons, three from the Second Iron Age settlement from Île aux Moutons [START_REF] Daire | L'île aux Moutons (Fouesnant, Finistère) : un établissement gaulois dans son contexte atlantique[END_REF] and two pottery from the Recent Neolithic settlement (3800 -2800 BCE) from the Glénan Archipelago were used. These pots were made from clays with inclusions corresponding to the mineralogical composition of granitic rock. However, due to the marked similarity of the inclusions, it was not possible to differentiate the origin of these ceramics. Granite samples from Île aux Moutons and the Glénan Archipelago (one sample for each rock) were then used as local references and samples of granites from Beg Meil and Trégunc served as continental markers.

2.1. Geological context of the two archipelagos Hoedic Island is mainly made up of granite with muscovite and biotite belonging to the family of granites from the south of the Armorican Massif formed during variscan tectogenesis (340 -300 Ma) [START_REF] Audren | Notice explicative, Carte géologique de France (1/50000[END_REF]. The Belle-Île-en-Mer substratum is separated from the Houat-Hoedic complex by a NW-SE fault line, and is very different from the neighbouring islands. It is mainly made up of slightly metamorphic volcanic-sedimentary rocks: fine tuffs or porphyroids with a green schist facies (Table 2; [START_REF] Audren | Notice explicative, Carte géologique de France (1/50000[END_REF]. Île aux Moutons and the Glénan Archipelago are the most northern islands off the southern coast of Brittany. Île aux Moutons is formed of a granitic base characterized by coarse feldspar grains [START_REF] Delanoë | Littoraux et vallées holocènes submergés en Baie de Concarneau (Bretagne méridionale)[END_REF]. It is to highlight that this granite could be the same as the granite of Trégunc on the mainland, according to the 1/250000 e geological map [START_REF] Thinon | Carte géologique de la France à 1/250 000 e de la marge continentale[END_REF]. The Glénan Archipelago is made up of at least two types of rock: a porphyroid leucogranite carved by granitic rock with muscovite and granite with muscovite and biotite (Table 2; Béchennec et al. 1996).

3. Method Spot chemical analyses were carried out with a quadrupole mass spectrometer with plasma source (Agilent Technologies, 7700 Series) coupled with a laser ablation system Nd:YAG of 213 nm (Cetac Technologies, LSX-213, G2). Laser ablation system conditions are the following: analysis time 180s, spot diameter: 20 μm, force ≈ 2.5 mJ/pulse, pulse width ≈ 5 ns, pulse frequency 20 Hz, ablation speed of 20 μm/s. Ablations are carried out on thin sections for archaeological pottery and directly on rock fragment references. After the drawing of the ablation layout, a quick ablation is made, with low energy and high speed, in order to homogenize the layout and remove possible pollution on the sample. 5 to 10 biotite tablets are analyzed per sample. The depth of the ablation is less than 30 μm and the inclusions can still be observed. The analysis of the average composition of each of the biotite inclusions with an average size generally ranging from 200 to 500 μm was obtained by laser scan on the whole inclusion. The instrument is calibrated using international geological standards: DR-N, DT-N, UB-N (Govindaraju and Roelandts 1989) and MICA-Fe (Govindaraju and Roelandts 1988). Altogether, 46 elements were measured: Na, Mg, Al, Si, K, Ca, Ti, Mn, Fe, Li, Sc, V, Cr, Co, Ni, Cu, Zn, As, Rb, Sr, Y, Zr, Nb, Cd, Sb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, Tl, Pb, Th, U. The analysis results from biotite inclusions (Tables 3 and4) contained in rocks and ceramics reveal several elements enabling us to differentiate biotites depending on their origin. Indeed, the internal variation of the chemical composition within sources is low and allow to determine the origin of each rocks and ceramics. The major element have been converted into oxide forms (Na 2 O, MgO, Al 2 O 3 , SiO 2 , K 2 O, CaO, TiO 2 , MnO, and Fe2O3) and the REE have been chondrite-normalized [START_REF] Mcdonough | The composition of the Earth[END_REF].

Results and discussion

To identify the elements who allowed us to distinguish the different granites, the results of the different analysis of biotites from the granites from Île aux Moutons, the Glénan Archipelago and also from Beg Meil and Trégunc on the mainland, have been grouped using the principal component analysis (Fig. 3). Thus, we can observe that the granite from Île aux Moutons and Trégunc are not differentiable, but the granites from the Glénan Archipelago and from Beg Meil are clearly distinguishable from the other rocks (Fig. 3). A cluster analysis of the measured elements allow us to determine the main elements that can distinguish the different sources: Li, V, Zn, Sr (Fig. 4). Two elements are particularly relevant; lithium -known for fixing mainly in mica tablets [START_REF] Siroonian | Lithium geochemistry and the source of the spodumene pegmatites of the Pressac-Lamotte-Lacorne region of western Quebec[END_REF]Kuts and Mishchenko 1963) -and vanadium. 4.1. Houat-Hoedic-Belle-Île-en-Mer complex (Fig. 2) The analyses of the biotite inclusions in four ceramics from the sites of Hoedic and one from Belle-Îleen-Mer show dispersed composition (Fig. 5; Table 3). In the V versus Li diagram, the representative points of the analyses are placed along two lines corresponding to very different Li/V ratios.

The first group of analyses presents a very high Li/V ratio with biotites with low vanadium contents; these analyses correspond to the pottery from Belle-Île-en-Mer. The second group of analysis presents a much lower Li/V ratio with low lithium values. These analyses correspond to the pottery from Hoedic. These variations in Li concentration in biotites are generally linked to the intensity of hydrothermal granite alterations [START_REF] Konings | Chemistry of biotites and muscovites in the Abas granite, northern Portugal[END_REF]. Therefore, this technique enables us to differentiate compositions of trace elements in two types of ceramic productions with similar petrographic characteristics. Moreover, the two composition groups probably correspond to two different geological origins (Fig. 5). No granitic rocks outcrop on Belle-Île-en-Mer, where the geological formations are largely dominated by green schists [START_REF] Audren | Notice explicative, Carte géologique de France (1/50000[END_REF]. Thus the analyzed urn can only correspond to an imported vessel. According to biotite analyses by LA-ICP-MS, the hypothesis of the importation of this urn to Belle-Île-en-mer from Hoedic or Houat must be rejected. Therefore, the urn was made on the mainland from clay derived from the alteration of granitic rock. However, the production zone has yet to be more accurately defined. Biotite analyzes of the Hoedic granite follow the same line as those of the biotites included in the ceramics discovered on this same island (Fig. 5). Furthermore, all the analyzed biotites in a single sample have the same composition range, who is broader for the rock than for ceramics, but always with the same Li/V ratio for both of them. The ceramics were thus probably made from clay derived from the alteration of local rock. Consequently, this is a local non-imported production.

4.2. Glénan Archipelago -Île aux Moutons complex (Fig. 2) Eight ceramics discovered on these different islands were selected for chemical LA-ICP-MS spot analyses on the basis of the presence of biotite inclusions in ceramic raw materials from the Île aux moutons and the Glénan Archipelago sites. Furthermore, by comparing the analyses of biotites from local and continental granites, it should be possible to find the rocks that formed these clays by alteration. The results show that biotite compositions of ceramic bodies are not homogeneous, but develop around regression lines (Fig. 6; Table 4). Biotite analyses are recorded in the same V versus Li diagram as for the previous case. The points are distributed in composition groups defining the lines with different V/Li ratios. The Li/V ratio is between 1.84 and 7.34 for biotites from ceramics for which the raw material comes from Île aux Moutons, whereas the Li/V ratio of biotites from pottery made with clays derived from the alteration of the Beg Meil granite ranges between 0.06 and 2.12. Lastly, the Li/V ratio of biotites from the Glénan Archipelago granite is between 73.51 and 242.22. Three sets of points can be differentiated (Fig. 6). Two are made up of ceramic and granite biotite and the other only of granite biotite. The first group corresponds to biotite inclusions with little Li, between 0 and 300 ppm and very dispersed V values, ranging from several tens of ppm to nearly 800 ppm. These inclusions correspond to Neolithic ceramics from Île aux Moutons and the Glénan Archipelago, as well as vessels from the Second Iron Age from Île aux Moutons. The Beg Meil continental granite, located 10 km to the north of the archaeological sites is also in this group. Indeed, biotites from ceramics and rock sample have the same Li/V range ratio. However, it is possible to observe that the Li concentrations is higher in the rock, because of the alteration of the biotite crystals. A second set groups is composed by Neolithic ceramics discovered on the Glénan Archipelago and Iron Age ceramics on the Île aux Moutons, as well as to the Île aux Moutons granite and the continental granite from B, situated 12 km northwest of the archaeological sites. This observation confirm that the granites from Trégunc and Île aux Moutons are the same. The last set only contains granite biotites from the Glénan Archipelago. Therefore, the LA-ICP-MS analyses confirm the utilization of two clay sources on these islands. By extension, it is now possible to deduce the origin of the other ceramics discovered on these islands. In this way, we observe that exchanges with the mainland took place during the Neolithic, but also that pottery was produced on Île aux Moutons and exported into the Glénan Archipelago. During the Second Iron Age, this production no longer exists and all the vases are imported from the continent to Île aux Moutons. Lastly, we note that no vessels appear to have been made from the clays derived from granite alteration in the Glénan Archipelago during these periods. These conclusions raise questions as to the type of occupations on these islands. They may have consisted of seasonal occupations by mainland populations, during the harvesting of certain marine products.

Conclusions

The chemical spot analysis of mineral inclusions in archaeological ceramic bodies using LA-ICP-MS opens new prospects in terms of sourcing. The comparison of the analyses of biotite inclusions in ceramics and the granitic rocks liable to have supplied pottery clays by alteration, using Armorican samples, validates the method. The possibility of simultaneously analyzing very light elements like lithium with this technique, which is generally difficult to measure, and heavier elements on very small volumes of the size of an infra millimetric inclusion, is particularly potent. This is not the case with commonly used techniques, such as Castaing electron microprobe [START_REF] Froh | Archaeological ceramics studied by scanning electron microscopy[END_REF]), ICP-AES (Bruno et al. 2000) or PIXE, for example [START_REF] Roumié | Provenance study of excavated pottery from Beirut using PIXE cluster analysis. Ion Beam Analysis[END_REF]. This is a rapid method that requires little sample preparation: ablation is carried out directly on ceramics, rocks or uncovered thin sections, unlike methods such as ICP-AES, which necessitates Frantz magnetic separation [START_REF] Konings | Chemistry of biotites and muscovites in the Abas granite, northern Portugal[END_REF]) and which can do spot analyses, in contrast to PIGE [START_REF] Calligaro | PIXE/PIGE characterisation of emeralds using an external microbeam[END_REF][START_REF] Bugoi | Compositional studies on Transylvanian gold nuggets: advantages and limitations of PIXE-PIGE analysis[END_REF]. Results are obtained rapidly; analysis time is 180s for measuring 46 elements. The measurement of limited quantities of elements improves the analysis results and leads to the analysis of more biotite inclusions.

In those examples, we didn't find biotites with more than one geochemical composition in a single sherd. This can be explain by the utilization of non-mixed clays, coming from a unique mother rock. However, it can be possible that potters used mixed clays from alluvial deposits or have added crushed rocks. In this case, it is possible to obtain several geochemical composition and different Li/V ratios that represent each origins [START_REF] Gehres | Connaissances des sociétés insulaires armoricaines par l'étude archéométrique du mobilier céramique. Les réseaux d'échanges îles-continent : évolution du Néolithique à la période gallo-romaine[END_REF]. The application of this new method to archaeological ceramics could be extended to minerals other than biotite from granitic rocks when this material is not sufficiently abundant in ceramic bodies and source rocks. Indeed, our work have been extended to the gabbroic clay with the analyses of amphibole grains and ultrabasic clay with the studies of opaque mineral [START_REF] Gehres | Connaissances des sociétés insulaires armoricaines par l'étude archéométrique du mobilier céramique. Les réseaux d'échanges îles-continent : évolution du Néolithique à la période gallo-romaine[END_REF]Gehres and Querré, under press).

Acknowledgments

The authors would like to thank J.-C Le Bannier for his technical assistance, M.-Y. Daire, G. Hamon, J.-M Large, G. Musch, for the lending of the archaeological collections.  Biotite tablets from the ceramic (Saint Nicolas 10) of the Recent Neolithic site of Saint Nicolas (Glénan Archipelago)  Biotite tablets from the ceramic (Île aux Moutons Iron Age 2) of the Second Iron Age site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Iron Age 4) of the Second Iron Age site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Iron Age 17) of the Second

CaptionsFig. 1 Fig. 2 Fig. 3 

 123 Fig.1 Simplified geological map of the Armorican massif

Fig. 5

 5 Fig.5 Scatterplot of the concentrations obtained by LA-ICP-MS of Li and V (in ppm) of the analyzed biotites. Each point corresponds to an analyzed inclusion. The ellipses represent the 95% confidence ellipses.  Biotite tablets from the granite of the Hoedic island.  Biotite tablets from the ceramic (Douet 23) of the Middle Neolithic II site of Douet (Hoedic island)  Biotite tablets from the ceramic (Douet 32) of the Middle Neolithic II site of Douet (Hoedic island)  Biotite tablets from the ceramic of the Second Iron Age site of Port-Blanc (Hoedic island)  Biotite tablets from the Bronze Age urn (Belle-Île-en-Mer).

Fig. 6 Fig. 1

 61 Fig.6 Scatterplot of the concentrations obtained by LA-ICP-MS of Li and V (in ppm) of the analyzed biotites. Each point corresponds to an analyzed inclusion.  Biotite tablets from the granite of Beg Meil  Biotite tablets from the granite of Île aux Moutons  Biotite tablets from the granite of Glénan Archipelago  Biotite tablets from the granite of Trégunc  Biotite tablets from the ceramic (Île aux Moutons Neo 4) of the Middle Neolithic II site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Neo 3) of the Middle Neolithic II site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Neo 9) of the Middle Neolithic II site of Île aux Moutons Biotite tablets from the ceramic (Saint Nicolas 3) of the Recent Neolithic site of Saint Nicolas (Glénan Archipelago)  Biotite tablets from the ceramic (Saint Nicolas 10) of the Recent Neolithic site of Saint Nicolas (Glénan Archipelago)  Biotite tablets from the ceramic (Île aux Moutons Iron Age 2) of the Second Iron Age site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Iron Age 4) of the Second Iron Age site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Iron Age 17) of the Second Iron Age site of Île aux Moutons

Fig. 3

 3 Fig.3 Results of the Principal Component Analysis of the dataset (44 elements). The percentage of the total variance that is explained by the two principal components is 26.3 % and 17.5 %, respectively. The biotites from the five different granites analysed in the article are represented. The ellipses represent the 95% confidence ellipses. Each point corresponds to an analysed inclusion from mother rocks.  Biotite tablets from the granite of Beg Meil  Biotite tablets from the granite of Île aux Moutons  Biotite tablets from the granite of Glénan Archipelago  Biotite tablets from the granite of Trégunc  Biotite tablets from the granite of Hoedic

Fig. 4

 4 Fig.4 Hierarchical cluster analysis of the dataset with the Ward's method: Dendrogram displaying rescaled distance among the different element of the biotites from the five granites analyzed.

Fig. 5

 5 Fig.5 Scatterplot of the concentrations obtained by LA-ICP-MS of Li and V (in ppm) of the analyzed biotites. Each point corresponds to an analyzed inclusion. The ellipses represent the 95% confidence ellipses.  Biotite tablets from the granite of the Hoedic island.  Biotite tablets from the ceramic (Douet 23) of the Middle Neolithic II site of Douet (Hoedic island)  Biotite tablets from the ceramic (Douet 32) of the Middle Neolithic II site of Douet (Hoedic island)  Biotite tablets from the ceramic of the Second Iron Age site of Port-Blanc (Hoedic island)  Biotite tablets from the Bronze Age urn (Belle-Île-en-Mer).

Fig. 6

 6 Fig.6 Scatterplot of the concentrations obtained by LA-ICP-MS of Li and V (in ppm) of the analyzed biotites. Each point corresponds to an analyzed inclusion.  Biotite tablets from the granite of Beg Meil  Biotite tablets from the granite of Île aux Moutons  Biotite tablets from the granite of Glénan Archipelago  Biotite tablets from the granite of Trégunc  Biotite tablets from the ceramic (Île aux Moutons Neo 4) of the Middle Neolithic II site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Neo 3) of the Middle Neolithic II site of Île aux Moutons  Biotite tablets from the ceramic (Île aux Moutons Neo 9) of the Middle Neolithic II site of Île aux Moutons  Biotite tablets from the ceramic (Saint Nicolas 3) of the Recent Neolithic site of Saint Nicolas (Glénan Archipelago)

Table 1

 1 Iron Age site of Île aux Descriptions of the geographic origin of the archaeological sites and their occupation periods and location of the different granites mentioned

	Moutons

Table 2

 2 Geological description of the mentioned insular complexes

			Port Blanc	Standard deviation	Douet 23	Standard deviation	Douet 32	Standard deviationv	Belle-Ile	Ecart type	Granite Hoedic	Standard deviation
	Na2O	%	0,42	0,18	0,66	0,2	0,89	0,11	0,8	0,17	5,55	9,03
	MgO	%	2,72	2,07	3,43	0,48	3,09	0,24	2,68	0,3	4,23	1,62
	Al2O3	%	50,53	7,23	46,41	3,21	45,38	1,31	48,31	2,5	45,35	6,29
	SiO2	%	38,35	3,89	39,43	2,62	39,1	0,74	37,9	1,56	35,42	9,99
	K2O	%	1,87	0,35	1,5	0,41	1,83	0,32	1,54	0,19	1,11	0,53
	TiO2	%	0,98	0,63	1,34	0,5	1,47	0,21	1,1	0,22	1,01	0,63
	MnO	%	0,07	0,05	0,1	0,06	0,1	0,05	0,09	0,03	0,06	0,05
	Fe2O3	%	5,07	4,11	7,13	0,91	8,13	0,85	7,58	1,05	4,79	2,08
	Li	ppm	560	503,9	406	208,35	351	90,69	1476	482,39	627	283,29
	V	ppm	126	62,36	215	122,86	163	50,6	71	28,27	302	110,14
	Co	ppm	23	19,68	38	15,2	34	6,05	45	19,22	43	19,6
	Ni	ppm	30	15,65	47	12,98	48	5,54	45	13,93	29	29,54
	Cu	ppm	3	0,33	9	7,11	4	1,64	1304	1771,55	53	38,32
	Zn	ppm	257	247,17	425	188,54	371	140,9	621	237,41	502	232,59
	As	ppm	1	1,23	4	2,88	2	1,37	38	56,35	21	14,14
	Rb	ppm	664	450,74	911	398,01	700	229,05	1019	316,43	677	490,46
	Sr	ppm	158	63,62	323	227,33	189	95,51	366	307,15	1039	1741,94
	Y	ppm	6	12,36	76	98,51	12	7,57	21	19,54	41	53,85
	Zr	ppm	34	45,57	1089	2375,9	26	16,9	430	594,9	1963	3298,49
	Nb	ppm	60	42,19	73	35,94	84	28,08	91	25,4	56	33
	Sb	ppm	0	0,03	0	0,1	0	0,32	1	0,71	1	1,6
	Ba	ppm	403	127,13	952	1389,3	704	669,25	333	203,26	450	312,65
	La	ppm	2	2,29	400	550,92	17	15,99	30	28,1	118	205,31
	Ce	ppm	6	8,36	1191	1754,14	58	49,22	62	54,28	177	350,1
	Pr	ppm	1	1,05	93	133,14	7	5,72	7	6,94	20	37,93
	Nd	ppm	4	6,82	388	526,41	17	14,35	25	20,66	101	183,95
	Sm	ppm	1	1,13	66	93,51	4	2,94	4	3,22	21	33,1

Table 3

 3 Average chemical composition and standard deviation of biotite in potteries and granite from Hoedic and Belle-Île-en-Mer

			Ile aux Moutons Neo 4	Standard deviation	Ile aux Moutons Neo 3	Standard deviation	Ile aux Moutons Neo 9	Standard deviation	Ile aux Moutons Iron age 2	Standard deviation	Ile aux Moutons Iron age 4	Standard deviation	Ile aux Moutons Iron age 17	Standard deviation	Saint Nicolas 3	Standard deviation	Saint Nicolas 10	Standard deviation	Granite Ile aux Moutons	Standard deviation	Granite Archipel des Glénan	Standard deviation	Granite contiental (Beg Meil)	Standard deviation	Granite contiental (Trégunc)	Standard deviation
	Na2O	%	1,6	0,81	0,28	0,26	0,48	0,17	2,37	2,8	0,3	0,09	2,48	1,63	1,2	0,66	0,61	0,48	0,16	0,10	0,37	0,11	0,20	0,09	0,11	0,08
	MgO	%	3,35	1,1	2,39	1,04	3,15	1,17	1,11	1,47	4,21	0,61	2,84	1,07	3,21	1,69	0,96	0,44	5,77	0,66	1,47	0,19	5,69	0,60	5,51	0,20
	Al2O3	%	44,63	5,31	44,86	3,41	42,74	2,69	48,96	8,47	39,48	2	46,52	5,07	47,3	8,63	27,77	12,56	19,38	1,63	23,38	1,60	19,07	0,86	19,11	0,95
	SiO2	%	41,58	5,67	36,52	3,67	42,84	2,73	42,27	5,02	40,55	3,94	37,9	2,9	39,99	5,81	31,47	7,43	44,16	2,57	42,47	4,94	44,18	1,59	42,06	0,85
	K2O	%	1,15	0,21	1,83	0,87	1,48	0,5	1,3	0,72	1,74	1,1	1,38	0,58	1,41	0,68	1,6	0,8	3,71	0,76	1,96	0,84	4,11	0,21	3,50	0,80
	TiO2	%	0,06	0,02	1,24	0,42	1,36	0,37	0,45	0,51	1,26	0,77	1,03	0,49	0,88	0,56	9	17,68	1,65	0,46	1,09	0,41	1,27	0,14	1,83	0,21
	MnO	%	6,49	1,75	0,07	0,03	0,09	0,07	0,06	0,08	0,06	0,01	0,04	0,02	0,12	0,08	0,41	0,77	0,25	0,06	0,69	0,15	0,20	0,05	0,47	0,04
	Fe2O3	%	645,8	286,1	12,26	2,16	7,86	2,38	3,49	3,1	12,4	5,26	7,81	1,62	5,9	2,64	13,15	4,89	24,72	2,85	28,51	4,35	25,25	1,68	27,34	0,98
	Li	ppm	646	286,02	1409	1196,59	179	65	131	103,76	58	24,86	85	47,91	596	419,52	1568	1564,14	743	267,65	6144	1995,01	128	26,37	975	151,74
	V	ppm	214	62,43	217	187,43	222	88,53	73	37,72	488	219,23	243	100,99	202	121,29	492	325,7	299	106,72	50	15,08	488	101,56	319	68,54
	Co	ppm	16	4,39	16	2,73	10	3,06	5	4,11	16	6,58	17	5,86	21	12,47	77	39,35	43	13,29	17	4,60	60	12,59	48	7,64
	Ni	ppm	37	15,06	29	13,98	35	22,51	11	14,91	44	9,19	27	14,57	44	29,33	59	30,91	45	14,14	24	7,19	130	25,81	45	7,63
	Cu	ppm	75	23,75	49	15,49	44	14,85	21	13,01	72	38,55	40	14,61	54	21,55	272	180,13	17	16,19	14	9,13	54	27,35	8	7,86
	Zn	ppm	8	3,57	98	58,93	53	23,74	48	24,04	40	34,98	4	2,03	49	65,88	9	3,89	397	128,38	527	149,41	199	33,46	564	76,81
	As	ppm	285	128,52	927	547,62	148	97,15	109	134,47	215	97,4	73	72,75	413	285,73	1597	2523,75	8	7,71	31	11,10	10	12,08	6	5,09
	Rb	ppm	6	4,82	27	20,2	29	16,58	6	4,83	39	48,91	13	3,28	6	3,97	31	24,91	527	193,60	418	209,32	291	51,18	1146	799,43
	Sr	ppm	609	168,89	845	542,19	400	281,49	287	269,02	357	242,33	252	154,32	709	514,74	954	1320,08	99	65,52	65	16,18	22	8,59	21	11,33
	Y	ppm	139	94,79	179	126,58	227	204,37	513	819,65	88	62,95	368	484,84	428	263,06	3125	3611,85	10	11,69	24	25,57	37	113,81	37	48,04
	Zr	ppm	21	28,78	6	4,43	16	7,07	5	0,91	36	48,57	21	10,79	52	97,89	186	181,71	174	445,94	183	361,12	210	611,84	79	269,92
	Nb	ppm	322	247,22	109	94,46	225	397,29	157	166,88	51	28,37	98	50,11	1264	2888,86	840	1101,5	66	23,20	218	142,51	59	12,94	118	27,58
	Sb	ppm	56	20,11	104	51,62	30	12,87	32	39,74	33	20,75	32	16,88	72	48,63	243	276,61	0	0,15	1	0,32	0	0,10	0	0,10
	Ba	ppm	0	0,18	1	0,26	1	0,46	0	0,06	1	0,42	0	0,04	0	0,08	0	0,17	430	275,23	167	223,70	1163	247,07	694	816,35
	La	ppm	294	173,27	240	139,32	301	101,55	169	59,2	295	225	155	45,08	856	815,45	666	537,74	196	589,59	216	613,78	611	1010,96	547	1208,48
	Ce	ppm	11	9,86	16	19,69	29	11,36	19	20,99	72	102,69	40	24,65	50	77,49	148	138,7	127	335,39	166	514,72	302	525,85	352	799,46
	Pr	ppm	21	18,83	29	34,37	57	22,2	29	28,08	147	214,93	104	85,14	109	140,78	497	539,11	68	148,44	91	244,18	159	255,39	216	387,07
	Nd	ppm	2	1,79	4	4,35	8	3,31	5	2,67	24	35,77	9	5,58	11	14,24	60	67,45	59	125,93	64	160,79	123	200,56	170	275,61

Table 4

 4 Average chemical composition and standard deviation of biotite in potteries and granites from the Glénan


Kevin Tougeron
email: tougeron.kevin@gmail.com

George Hraoui

Cécile Le Lann

Joan Van Baaren

Jacques Brodeur

Intraspecific maternal competition induces summer diapause in insect parasitoids

Keywords: aestivation, bet-hedging, host density, intraspecific competition, superparasitism

Organisms often live in unpredictable environments and have to adopt life history strategies that optimize their fitness under these conditions. According to bet-hedging theory, individuals can reduce variation in fitness outcomes by investing in different strategies at the same time. For arthropods, facultative summer diapause enables survival during dry and hot periods of the year, and can be triggered by a decrease in resource abundance. However, the . effect of resource depletion on diapause induction has never been disentangled from the effect of the perception of the presence of competitors. Using two solitary parasitoid species of cereal aphids as a model system, Aphidius avenae (Haliday) and Aphidius rhopalosiphi (De Stefani-Perez) (Hymenoptera: Braconidae), we tested whether (i) low absolute host density and/or (ii) high levels of parasitoid females' competition lead to maternal-induced summer diapause in parasitoid offspring. Under summer-like climatic conditions, emerging parasitoid females were (i) reared alone and exposed to different host densities (from 5 to 130 aphids), or (ii) reared together with competing females (from 2 to 20 females) and then exposed individually to 50 aphids. For both parasitoid species, low aphid densities did not induce summer diapause. However, the incidence of summer diapause increased up to a maximum of 11% with increasing levels of competition experienced by female parasitoids.

More than 60% of the females produced both diapausing and non-diapausing offspring after being kept at the two highest competition densities. Such a -spreading-the-risk‖ strategy has likely evolved to optimize parasitoid fitness by preventing the following generation from exposure to low populations of suitable hosts and high mortality from superparasitism. These results provide the first experimental evidence of direct maternal competition-induced diapause in insects, and may change the way we apprehend the evolution of arthropod seasonal ecology, by considering intraspecific competition.

Introduction

Phenotypic plasticity allows a given genotype to produce a range of phenotypes in response to variable environmental conditions [START_REF] Auld | Re-evaluating the costs and limits of adaptive phenotypic plasticity[END_REF]. For example, alternative lifehistories can arise from maternal effects (i.e. transgenerational plasticity), whereby the proportion of individuals expressing a given phenotype depends on the conditions experienced by the preceding generation [START_REF] Mousseau | Maternal effects in insect life histories[END_REF]. In insects, facultative diapause, a period of deferred development, can be induced by environmental cues perceived either by the diapausing individual or by its mother [START_REF] Saunders | Larval diapause of maternal origin: induction of diapause in Nasonia vitripennis (Walk.) (Hymenoptera: Pteromalidae)[END_REF][START_REF] Tauber | Seasonal Adaptations of Insects[END_REF][START_REF] Brodeur | Biotic and abiotic factors involved in diapause induction of the parasitoid, Aphidius nigripes (Hymenoptera: Aphidiidae)[END_REF]. In the latter case, the female can change carbohydrates and polyols contents of the egg through hormonal regulation which acts on the egg's development [START_REF] Yamashita | Insights for future studies on embryonic diapause promoted by molecular analyses of diapause hormone and its action in Bombyx mori. Insect Timing: Circadian Rhythmicity to Seasonality[END_REF][START_REF] Denlinger | Regulation of diapause[END_REF]. Such ‗anticipatory' maternal effects allow the mother to alter the phenotype of her offspring to increase their survival in the future environment by buffering against anticipated environmental stressors [START_REF] Burgess | Adaptive parental effects: the importance of estimating environmental predictability and offspring fitness appropriately[END_REF]. However, when a female cannot exactly assess which phenotype would be favored in the future environment, she may produce a range of offspring phenotypes to optimize her fitness (i.e. she -hedges her bets‖). The proportion of each offspring phenotype may be adjusted to the probability of encountering a given environment, when biotic or abiotic cues make it partially predictable [START_REF] Hopper | Risk-spreading and bet-hedging in insect population biology[END_REF][START_REF] Menu | Bet-Hedging diapause strategies in stochastic environments[END_REF][START_REF] Marshall | When is a maternal effect adaptive?[END_REF].

Summer diapause is a phase of dormancy that is followed by an active phase in fall and occurs either at the same developmental stage as winter diapause, or at a different one [START_REF] Masaki | Summer diapause[END_REF]. Summer diapause should be distinguished from aestivation which is a form of dormancy mostly expressed in tropical insects during the dry season [START_REF] Navas | Aestivation, Molecular and Physiological Aspects[END_REF][START_REF] Denlinger | Mosquito diapause[END_REF]. Although overlooked, summer diapause is likely to be as widespread as winter diapause among insects [START_REF] Masaki | Summer diapause[END_REF], and has been observed in few hymenopterous parasitoid species from temperate regions (He et al., 2010, and references therein). Whereas the developmental, physiological and hormonal syndrome associated with summer diapause is quite similar to winter diapause syndrome (i.e. metabolic depression, developmental arrest and increasing resistance to adverse conditions) [START_REF] Masaki | Summer diapause[END_REF][START_REF] Denlinger | Mosquito diapause[END_REF], there is still a black-box in insect ecology and physiology concerning diapause induction, maintenance and termination stimuli [START_REF] Koštál | Eco-physiological phases of insect diapause[END_REF]. It has been shown that summer diapause is predominantly induced by overcrowding on a resource patch, by a decrease in food resource availability and/or by dry and warm environmental conditions [START_REF] Masaki | Summer diapause[END_REF][START_REF] Tauber | Moisture, a vital but neglected factor in the seasonal ecology of insects: hypotheses and tests of mechanisms[END_REF]. In the leaf-curling midge parasitoid Platygaster demades Walker (Hymenoptera: Platygastridae), there is a bet-hedging strategy on embryonic summer diapause levels and duration to match expected periods of host-shortage, thus avoiding fitness impairment and asynchronism with hosts [START_REF] He | A sophisticated life history strategy in a parasitoid wasp: producing univoltine and multivoltine phenotypes in a local population[END_REF]. In addition to limited food resources, competition avoidance has been proposed as a factor selecting for diapause evolution in insects because competition may also lead to a reduction in resource availability [START_REF] Danks | Insect Dormancy: an Ecological Perspective. Biological Survey of Canada (Terrestrial Arthropods)[END_REF][START_REF] Lalonde | Some dynamical consequences of parasitoid diapause[END_REF]. Induction of diapause through competition (i.e. due to overcrowding on a resource patch) has been reported in rotifers [START_REF] Gilbert | Population density, sexual reproduction and diapause in monogonont rotifers: new data for Brachionus and a review[END_REF] and some insects among the Lepidoptera, Hemiptera, Coleoptera and Hymenoptera [START_REF] Brown | Density-dependent induction of diapause in the codling moth, Laspeyresia pomonella (Lepidoptera: Olethreutidae)[END_REF][START_REF] Hagstrum | Diapause induction in Ephestia cautella: an interaction between genotype and crowding[END_REF][START_REF] Harada | Nymphal density and life histories of two water striders (Hemiptera: Gerridae)[END_REF][START_REF] He | A sophisticated life history strategy in a parasitoid wasp: producing univoltine and multivoltine phenotypes in a local population[END_REF][START_REF] Togashi | Effects of crowding on larval diapause and adult body size in Monochamus alternatus alternatus (Coleoptera: Cerambycidae)[END_REF]. However, to our knowledge, the influence of resource scarcity due to competition was never disentangled from the influence of competition perception by itself on diapause induction, and increasing maternal competition was never shown to induce diapause in their offspring. Separating these effects would bring new evolutionary insights on intraspecific interactions theories, on arthropods' seasonal ecology in response to varying environments and in the face of climate change, as well as on still overlooked token stimuli that control dormancy in insects.

For insect parasitoids, the quality of their environment depends on both the suitability and abundance of hosts which vary throughout the seasons [START_REF] Vercken | Temporal autocorrelation in host density increases establishment success of parasitoids in an experimental system[END_REF]. Parasitoids have evolved behavioral responses to cope with both intra-and interspecific competition for hosts which can be used as a proxy for measuring resource availability and the risk of superparasitism [START_REF] Boivin | Intra-and interspecific interactions among parasitoids: mechanisms, outcomes and biological control. Trophic and Guild in Biological Interactions Control[END_REF][START_REF] Cusumano | Interspecific competition/facilitation among insect parasitoids[END_REF]. Superparasitism is repeated parasitism of a host by female parasitoids of the same species. It is typically deleterious for solitary parasitoids [START_REF] Van Alphen | Superparasitism as an adaptive strategy for insect parasitoids[END_REF][START_REF] Harvey | Intrinsic inter-and intraspecific competition in parasitoid wasps[END_REF] and increases with the level of competition between females in a population. Competition should thus be avoided in order to reduce the probability of both resource (host) scarcity and superparasitism. In aphid parasitoids, competing females have the capacity to modify their foraging behaviour in response to the presence of competitors, mostly detected through visual and chemical cues [START_REF] Mackauer | Host discrimination and larval competition in solitary endoparasitoids[END_REF][START_REF] Barrette | Testing competing measures of profitability for mobile resources[END_REF][START_REF] Van Baaren | How could host discrimination abilities influence the structure of a parasitoid community[END_REF]. For instance, Aphidius ervi Haliday (Hymenoptera: Braconidae) increase their patch residence time when exploiting an aphid colony in presence of competitors (direct perception of competition) or foraging on a patch previously exploited by competitors (indirect perception of competition) (Le Lann et al., 2011a).

We aimed to disentangle the effect of low host availability from the effect of maternal perceived competition (i.e. low relative host availability) on the incidence of summer diapause. We also measured the duration of summer diapause, which remains un-documented in most parasitoid species. We conducted experiments under laboratory conditions using two sympatric parasitoid species of the grain aphid Sitobion avenae (Fabricius) (Hemiptera: Aphididae); Aphidius avenae (Haliday) and Aphidius rhopalosiphi (De Stefani-Perez) (Hymenoptera: Braconidae). In cereal fields, these parasitoid species experience rapid decrease in host availability in summer [START_REF] Rabasse | Biologie des pucerons des céréales dans l'Ouest de la France. III. Action des hyménoptères parasites sur les populations de Sitobion avenae F., Metopolophium dirhodum Wlk[END_REF], especially because host-plants are drying and aphids are subject to deleterious heat shocks [START_REF] Alford | Effect of latitude and acclimation on the lethal temperatures of the peach-potato aphid Myzus persicae[END_REF]. Previously observed levels of summer diapause were relatively low in A. avenae and A. rhopalosiphi under natural conditions (< 5% of the population), when aphid abundance was low in the field [START_REF] Starý | The Aphidiidae of Italy (Hym., Ichneumonidae)[END_REF][START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF]. The cues responsible for triggering summer diapause in these species were not identified. In cereal fields of Western France, A. avenae is most abundant from spring to fall while A. rhopalosiphi presents higher abundance from autumn to spring [START_REF] Krespi | Etude de la biocénose parasitaire des pucerons des céréales dans le bassin de Rennes: cas particulier d'Aphidius uzbekistanicus Luz[END_REF][START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF]Tougeron et al., 2016b). The two species differ in their capacity to enter winter diapause; A. rhopalosiphi does not produce diapausing individuals whereas A. avenae enters winter diapause at low levels (Tougeron et al., 2016a).

Aphidius avenae is about 1 °C more resistant to high temperatures than A. rhopalosiphi (Le Lann et al., 2011b) which may imply lower summer diapause incidence in the former species.

Hence, the following hypotheses were tested: the incidence of summer diapause in parasitoid offspring is higher (i) when females encounter low aphid densities, (ii) when females experience high levels of conspecific competition, and (iii) in A. rhopalosiphi than in A. avenae, considering differences in their heat tolerance and seasonal occurrence.

Material and methods

Biological material

Aphidius avenae and A. rhopalosiphi were collected from cereal fields in Western France (Long Term Ecological Research area ZA Armorique, 48 °08′N, 1 °80′W) in 2014 and 2015 (details in Tougeron et al., 2016a) and have since been reared on a colony of the grain aphid S. avenae established from a single female collected at Le Rheu, France, in 1990. Parasitoids were reared at 20°C, 70% relative humidity (RH), and under 16 h∶ 8 h light∶ dark (LD) photoperiod while aphids were reared at 24°C, 55% RH, and 16 h∶ 8 h LD on winter wheat (Triticum aestivum var. Mégantic).

General experimental conditions

Experiments were conducted at 24°C, 55% RH, and 16 h : 8 h LD. These conditions simulate those that are typically encountered in the study area when aphid parasitoid summer diapause is assumed to occur, between 20th June and 31st August [START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF]Météo France, 2015). Ten days prior to a test, apterous parthenogenetic aphids were placed on sprouted wheat (about 2 cm high) in experimental arenas (plastic pots Φ10 cm) to produce aphid cohorts of 2nd or 3rd instar larvae. When necessary, aphids of the same age from the aphid colony were added to the infested wheat plants to reach the required density.

Last larval instars of Aphidiinae parasitoids make a cocoon and pupate inside the dead aphid host; the resulting structure is called a ‗mummy'. Aphid mummies were taken from the parasitoid colonies, isolated in small gelatin capsules (Φ 5 mm), and acclimated to the experimental abiotic conditions until adult emergence (3 to 5 days). Following emergence, each parasitoid female was placed in the presence of 2 males for mating and provided a honey solution (70% dilution) for 36 h. This duration allows females to reach their maximum egg-load [START_REF] Le Lann | Comparing resource exploitation and allocation of two closely related aphid parasitoids sharing the same host[END_REF]. Parasitoid females were then held along with aphids and honey in the experimental arenas for 48 hours, following the two protocols described below.

Mummy formation in the arenas was checked every day, beginning one week after oviposition. Mummies were kept individually in gelatin capsules at 20°C and adult emergence was checked daily. Twenty days after the first adult emergence within a single female offspring, the remaining mummies in the cohort were dissected, except for the diapause duration experiment (see below), and the content was recorded as being a dead individual or a diapausing golden-yellow prepupa (Tougeron et al., 2016a).

Effect of host density on offspring diapause incidence

To test the effects of host density on summer diapause incidence, we exposed parasitoids to the following host densities: 5, 20, 50, 65 and 130 aphids. These densities are encountered in the fields on wheat shoots [START_REF] Roschewitz | The influence of landscape context and farming practices on parasitism of cereal aphids[END_REF] and encompass the realized fecundities for 48 hours of both parasitoid species. Aphidius avenae and A. rhopalosiphi are able to produce about 62 and 31 mummies in two days, respectively [START_REF] Le Lann | Comparing resource exploitation and allocation of two closely related aphid parasitoids sharing the same host[END_REF]. Naive mated females (i.e. without oviposition experience or contact with other females) were individually introduced into experimental arenas to parasitize aphids. This experiment was replicated using four different females for each parasitoid species and aphid density modality (for a total of 20 females per species).

Effect of competition between females on offspring diapause incidence

To test the effect of competition among parasitoid females on summer diapause incidence, mated females were placed in plastic tubes (Φ = 4 cm, L = 9 cm) for 48 hours at the following densities: 2, 5, 10 and 20 females. These densities were chosen to represent the range of direct competition a female might experience in either natural (as indicated by natural parasitism rates , [START_REF] Roschewitz | The influence of landscape context and farming practices on parasitism of cereal aphids[END_REF] or laboratory rearing settings; with two and twenty females competing being highly credible in the field and in mass-rearing condition, respectively. Females were individually introduced in an experimental arena containing 50 aphids. This experiment was replicated using fifteen different females for each parasitoid species and competition treatment (for a total of 60 females per species).

Diapause duration in the offspring after mothers' competition experience

To measure the duration of summer diapause, four additional females of each parasitoid species from the 20-females-competition treatment were allowed to parasitize 50 aphids each.

Following parasitoid development, mummies were placed in gelatin capsules and parasitoid emergence was checked every day. Data are accurate to ± 2 days since parasitoids that emerged during the weekend were pooled with those emerging on Monday. Parasitoids with a delay of emergence > 20 days after first adult emergence were considered to be in diapause. This 20-days threshold was determined a priori since egg-to-adult development in nondiapausing Aphidius sp. usually lasts from 12 to 16 days at 20°C [START_REF] Zamani | Effect of temperature on life history of Aphidius colemani and Aphidius matricariae (Hymenoptera: Braconidae), two parasitoids of Aphis gossypii and Myzus persicae (Homoptera: Aphididae)[END_REF], and confirmed a posteriori following the distribution of emergence data. The remaining mummies were dissected 30 days after no emergence had been recorded in a given cohort to determine the status (dead or in diapause) of the parasitoid.

Statistical analyses

No diapausing individuals were produced following the host density experiment (see results section) and therefore no statistical analysis was conducted on this dataset. To test for the effects of female competition (categorical effect), Generalized Linear Models (GLMs) with a quasi-binomial error distribution (to account for overdispersion) and a logit-link function were fitted to the data separately for each parasitoid species. The response variable was the number of diapausing and non-diapausing individuals, including dead ones, for each replicate (ovipositing female). Another GLM with a quasi-binomial error distribution was fitted to the data to test for differences in diapause induction between parasitoid species, competition treatment as well as their interaction. The significance of each factor was tested by implementing an iterative procedure with the ‗Anova' function from the package car, using F-tests for quasi-binomial data [START_REF] Fox | An R Companion to Applied Regression[END_REF]. Differences between competition levels were compared with Tukey Contrasts [START_REF] Hothorn | Simultaneous inference in general parametric models[END_REF]. Data for diapause duration within a species was pooled and thus was not compared among the offspring of different females. Statistical analyses were carried out with R software (R Development Core Team, 2015).

Results

Effect of host density on offspring diapause incidence

Aphid density (5, 20, 50, 65 and 130 individuals) had no effect on summer diapause expression; none of the mummies contained diapausing individuals for either A. avenae (n = 219 total mummies formed) or A. rhopalosiphi (n = 205). Parasitism rates (i.e. number of mummies formed / total number of aphids proposed to parasitoids) varied between aphid density treatments but were constant within a given density. They ranged between 80% and 100% depending on the female parasitoid at the density of 5 aphids and between 10% and 30% at the density of 130 aphids.

Effect of competition between females on offspring diapause incidence

Increasing competition between females led to increasing summer diapause induction in their offspring for both A. avenae (GLM, F = 76.8, df = 3, P < 0.001, n = 1327) and A. rhopalosiphi (F = 89.2, df = 3, P < 0.001, n = 1174) (Fig. 1). In the competition treatment of 20 females, diapause incidence reached maximums of 11.22 ± 1.5% and 9.92 ± 1.3% (mean ± SE) for A. avenae and A. rhopalosiphi, respectively. The 20-female competition treatment showed significantly higher proportions of parasitoids in summer diapause than the competition treatment of 10 females in A. avenae (Tukey Contrasts; z = 3.73, P < 0.005) but not in A. rhopalosiphi (z = 1.10, P = 0.69). There was no summer diapause in the other two competition treatments (2 and 5 females) for either parasitoid species. There was no significant difference in summer diapause incidence between species (GLM, F = 0.75, df = 1, P = 0.39) and no significant interaction between species and competition level (F = 2.28, df = 3, P = 0.08). Not all females produced diapausing offspring; in the competition treatment with 20 females, for both parasitoid species, 93.3% of the tested females (14 out of 15) produced a minimum of one offspring in diapause. In the competition treatment with 10 females, the proportion of females inducing summer diapause in their offspring decreased to 60% (9 out of 15) and 86.7% (13 out of 15) for A. avenae and A. rhopalosiphi, respectively. Moreover, there was high variability in the diapause incidence within each female offspring for females that produced diapausing individuals; from 2.9% to 20% in A. avenae and from 4.8% to 20% in A. rhopalosiphi (in the 20-female competition treatment for both species). In the 10-female competition treatment this proportion ranged from 2.6% to 14.3% in A. avenae and from 3.0% to 20% in A. rhopalosiphi.

Diapause duration in the offspring after mothers' competition experience

Most parasitoids did not enter diapause, emerging from 12 to 27 days after oviposition (80.5%, n = 62 for A. avenae; 75%, n = 54 for A. rhopalosiphi). Nine (11.7%) A. avenae and seven (9.7%) A. rhopalosiphi individuals emerged more than 32 days after oviposition (i.e. more than 20 days after the first emergence in their cohort) and were considered to be in summer diapause. The mean summer diapause duration was similar for both parasitoid species (A. avenae, 55.6 ± 5.2 days; A. rhopalosiphi, 54.7 ± 4.3 days), although emergences spread over a longer period in A. avenae (Fig. 2). All remaining mummies dissected 113 days after oviposition (last adult emergence occurred at day 83 after oviposition + 30 days without any emergence) contained dead, non-diapausing individuals (15 adults and 2 pupae).

Discussion

In addition to its other functions, diapause allows species exploiting the same ecological niche to avoid competition [START_REF] Danks | Insect Dormancy: an Ecological Perspective. Biological Survey of Canada (Terrestrial Arthropods)[END_REF][START_REF] Alekseev | Types of diapause in Crustacea: definitions, distribution, evolution[END_REF][START_REF] Tauber | Moisture, a vital but neglected factor in the seasonal ecology of insects: hypotheses and tests of mechanisms[END_REF][START_REF] Lalonde | Some dynamical consequences of parasitoid diapause[END_REF]. Although competition avoidance has been invoked as a potential biotic factor selecting for the evolution of diapause [START_REF] Danks | Insect Dormancy: an Ecological Perspective. Biological Survey of Canada (Terrestrial Arthropods)[END_REF], perception of competition has not been identified as a cue per se for summer or winter diapause induction in insectsprobably because it has never been decoupled from the influence of resource scarcity due to overcrowding. We report no effect of resource scarcity (host density), but we did observe a clear effect of increasing maternal competition on summer diapause induction in the progeny of two Aphidius parasitoids. This is the first evidence, to our knowledge, of maternal perception of competition for resources being identified as a biotic cue for summer diapause induction in insects. Summer diapause was triggered by the same cues and expressed in a similar way (i.e. incidence and duration) in both A. avenae and A. rhopalosiphi. Summer diapause led to a developmental arrest occurring at the same developmental stage (prepupa) as for winter diapause [START_REF] Brodeur | Biotic and abiotic factors involved in diapause induction of the parasitoid, Aphidius nigripes (Hymenoptera: Aphidiidae)[END_REF]Tougeron et al., 2016a). Although only expressed in a part of the population, summer diapause can have important consequences for parasitoids' life-cycle, population dynamics and interactions with their hosts.

Although the syndrome associated with summer and winter diapause is similar [START_REF] Masaki | Summer diapause[END_REF][START_REF] Denlinger | Mosquito diapause[END_REF], their inducing environmental cues differ as suggested by [START_REF] Masaki | Summer diapause[END_REF], [START_REF] Tauber | Seasonal Adaptations of Insects[END_REF] and [START_REF] Koštál | Eco-physiological phases of insect diapause[END_REF], mostly because summer diapause serves different ecological functions from winter diapause. Maternal effects on winter diapause expression in Aphidius sp. can be significant but remains marginal compared to other environmental stimuli, mainly photoperiod and temperature [START_REF] Brodeur | Biotic and abiotic factors involved in diapause induction of the parasitoid, Aphidius nigripes (Hymenoptera: Aphidiidae)[END_REF][START_REF] Langer | Overwintering strategies and cold hardiness of two aphid parasitoid species (Hymenoptera: Braconidae: Aphidiinae)[END_REF]. In the genus Aphidius, conditions directly encountered by the early sensitive stage (egg, young larva) represent the main cues initiating diapause [START_REF] Brodeur | Biotic and abiotic factors involved in diapause induction of the parasitoid, Aphidius nigripes (Hymenoptera: Aphidiidae)[END_REF]Tougeron et al., 2016a). In contrast, for other parasitoid species such as Nasonia vitripennis, winter diapause is triggered only by maternal environmental perception [START_REF] Saunders | Larval diapause of maternal origin: induction of diapause in Nasonia vitripennis (Walk.) (Hymenoptera: Pteromalidae)[END_REF] and is linked to seasonal patterns of host availability [START_REF] Saunders | The effect of host species on diapause induction in Nasonia vitripennis[END_REF].

In contrast to winter diapause, our results suggest that summer diapause has a strong maternal component in Aphidius species.

Summer diapause induction in Aphidius offspring appears to arise from the perception of direct conspecific competition among females, when no hosts are available. This perception may be a proxy for measuring the risk of both host shortage and superparasitism in the future offspring environment. Our results also suggest that solitary parasitoids may respond differently to the risk of self-superparasitism (i.e. by a single female; host-density experiment) which can be neutral or beneficial [START_REF] Van Alphen | Superparasitism as an adaptive strategy for insect parasitoids[END_REF], than to the risk of conspecific superparasitism (competition experiment), which is typically detrimental.

Indeed, in the experiment on host density, transgenerational diapause induction was not observed, even when only 5 aphids were offered for 48 hours, which strengthens the idea that increasing competition alone induces summer diapause. Not all parasitoid females produced diapausing offspring, and individual mothers that did lay diapausing offspring did so in only a subset of their progeny. This variability could be explained either by differing sensitivity to competition among mothers (i.e. high genetic polymorphism in the population) or high degrees of plasticity in parasitoid females. Because the offspring's environment cannot be fully predicted from the conditions experienced by the mother, evolution can select for maternal genotypes that produce both diapausing and nondiapausing offspring, and modify the frequency of each phenotype regarding relevant environmental cues [START_REF] Hopper | Risk-spreading and bet-hedging in insect population biology[END_REF], such as the level of competition for host resources. In this context, summer diapause expression induced by parasitoid mothers could be viewed as a type of ‗conditional diversified bet-hedging' strategy (sensu [START_REF] De Jong | Bet hedging or not? A guide to proper classification of microbial survival strategies[END_REF]. In the light of the above, we hypothesize that risks may be spread both among mothers at the population scale (not all mothers produced diapausing offspring) and at the progeny scale (individual mothers induced diapause in only a part of their offspring).

The highest female density we tested (n = 20) is likely to occur in laboratory or industrial mass-rearing but are less credible in field conditions. In cereal fields, Aphidius sp. abundances per aphid patch are relatively low, greatly vary between years [START_REF] Roschewitz | The influence of landscape context and farming practices on parasitism of cereal aphids[END_REF], and high levels of direct intraspecific competition may rarely occur among solitary parasitoids [START_REF] Vollhardt | Diversity of cereal aphid parasitoids in simple and complex landscapes[END_REF][START_REF] Wajnberg | Behavioral Ecology of Insect Parasitoids: from Theoretical Approaches to Field Applications[END_REF]. It may however occur for interspecific competition (e.g. host-patches exploited by different parasitoid females at the same time leading to high multiparasitism levels) or in other parasitoid species (e.g. gregarious parasitoids). The incidence of summer diapause induced by maternal competition under natural conditions nevertheless remains unknown. Our results are likely to translate to other parasitoids, including those released in inundative biological control programs. In the context of biological control, improving knowledge of factors inducing diapause is also of great importance if we aim at improving conditions of mass-rearing [START_REF] Boivin | Aphid parasitoids in biological control[END_REF].

The emergence of A. avenae and A. rhopalosiphi individuals following summer diapause was spread over a long period of time (up to 11 weeks after oviposition). This pattern could represent a form of temporal risk-spreading to avoid parasitoid overcrowding on a resource patch and would also be beneficial when extreme climatic events could impair parasitoid survival. However, summer diapause duration, maintenance and termination mechanisms remain to be measured in field conditions. This pattern contrasts with other aphid parasitoid species, such as Aphidius nigripes (Ashmead), in which spring emergence after winter diapause is highly synchronized and occurs within three weeks [START_REF] Brodeur | Seasonal Ecology of Aphidius nigripes (Hymenoptera: Aphidiidae), a parasitoid of Macrosiphum euphorbiae (Homoptera: Aphididae)[END_REF].

We also showed that development from egg to adult emergence extended to a maximum of 83 days for parasitoids entering summer diapause. This is substantially less than winter diapause, which lasts for several months in overwintering aphid parasitoids from temperate areas [START_REF] Brodeur | Seasonal Ecology of Aphidius nigripes (Hymenoptera: Aphidiidae), a parasitoid of Macrosiphum euphorbiae (Homoptera: Aphididae)[END_REF]. These findings strengthen the idea that summer diapause has evolved in insects to cope with short-term deleterious conditions such as high competition for hosts -which are ephemeral resources -rather than predictive, long-term environmental fluctuations.

Parasitoid pupae developing inside the aphid mummy are highly vulnerable to natural enemies and adverse climatic conditions [START_REF] Brodeur | Intraguild interactions in aphid parasitoids[END_REF]. The optimal proportion of offspring entering summer diapause might be selected to balance risks of competition for hosts and mortality from, disease, extreme climatic events, predation or hyperparasitism (which levels can be high at the end of the summer , [START_REF] Holler | The relationship between primary parasitoids and hyperparasitoids of cereal aphids: an analysis of field data[END_REF].

There are, for instance, a few examples of predator-induced diapause in arthropods [START_REF] Slusarczyk | Predator-induced diapause in Daphnia[END_REF][START_REF] Kroon | Sleeping with the enemy‖-predator-induced diapause in a mite[END_REF]. [START_REF] Rausher | Competition, frequency-dependent selection, and diapause in Battus philenor butterflies[END_REF] also argued that a female butterfly's decision to induce diapause or not in a given proportion of its offspring may also depend on the ‗decision' taken by its competitors. In this regard, intra-and interspecific interactions between insects as well as predation and hyperparasitism levels must be considered in future research when studying summer diapause as a density-dependent process. However, the underlying ecological processes behind summer diapause induction and duration are poorly understood for insects from temperate regions and substantially more knowledge is needed concerning the multiple biotic and abiotic factors other than competition, and their interactions, that modulate summer diapause.

Fig. 1

 1 Fig. 1 Percentages ( ± CI 95%) of aphid mummies containing parasitoid prepupae in summer

Fig. 2

 2 Fig. 2 Distribution over time of parasitoid (Aphidius avenae and Aphidius rhopalosiphi)

Acknowledgments

KT was supported by the French Région Bretagne and the Canada Research Chair in Biological Control awarded to JB. The study was supported by the LTER France Zone Atelier Armorique. We thank P. Abram for insightful comments on an earlier version of the manuscript and for revising the use of English, three anonymous reviewers for helpful comments and J. Doyon and M. Gaudreau for technical support.

Disclosure

The authors declare no conflict of interest.

Author contributions

KT, CLL, JVB and JB conceived the experiments. KT and GH performed the experiments.

KT analyzed the data and wrote the manuscript. All co-authors contributed substantially to revisions.


F Chiaroni
email: florent.chiaroni@vedecom.fr

M-C Rahal

N Hueber

F Dufaux

LEARNING WITH A GENERATIVE ADVERSARIAL NETWORK FROM A POSITIVE UNLABELED DATASET FOR IMAGE CLASSIFICATION

Keywords: Deep Learning, Image classification, Positive Unlabeled Learning, Representation Learning, Generative Models

In this paper, we propose a new approach which addresses the Positive Unlabeled learning challenge for image classification. Its functioning is based on GAN abilities in order to generate fake images samples whose distribution gets closer to negative samples distribution included in the unlabeled dataset available, while being different to the distribution of the unlabeled positive samples. Then we train a CNN classifier with the positive samples and the fake generated samples, as it would be done with a classic Positive Negative dataset. The tests performed on three different image classification datasets show that the system is stable up to an acceptable fraction of positive samples present in the unlabeled dataset. Although very different, this method outperforms the state of the art PU learning on the RGB dataset CIFAR-10.

INTRODUCTION

Deep learning methods using convolutional kernel filters have demonstrated good prediction performances in the field of computer vision and especially for the task of image classification. To achieve such performance, large fully labeled datasets are required. Nowadays, multiple datasets can be merged to increase the generalization capacity of learning model as described in YOLO9000 [START_REF] Redmon | YOLO9000: Better, Faster, Stronger[END_REF].

Nevertheless, to mitigate this need of large labeled datasets, an idea is to focus mainly on data of interest. This is the case in One-Class Classification methods (OCC) [START_REF] Shehroz | One-class classification: taxonomy of study and review of techniques[END_REF], novelty detection [START_REF] Marco | A review of novelty detection[END_REF] where they only use during the training the samples of the class of interest; the positive class. To our knowledge, OCC methods have a limited performance when applied to large data tensors such as images. Besides, it is often easy to acquire unlabeled samples that may contain relevant information especially about the counter-examples of the class of interest.

In this way, we address a Positive Unlabeled learning problem. It turns out that PU learning methods have been applied recently to image data type such as the Rank Pruning method (RP) [START_REF] Northcutt | Learning with confident examples: Rank pruning for robust classification with noisy labels[END_REF]. RP method consists in consecutively carrying out several trainings of the classifier on a noisy labeled dataset, by removing the least relevant samples after each training stages. Furthermore, according to [START_REF] Niu | Theoretical comparisons of positive-unlabeled learning against positive-negative learning[END_REF], PU learning methods become competitive when the number of unlabeled samples in the dataset considerably increases. This is an advantage when we can easily get unlabeled data.

In addition, the generative adversarial networks (GANs) have drawn our attention because of their ability to generate fake samples x F that have a distribution p G (x F ) that tends towards the distribution p data (x R ) of the real samples x R used during its training. The original GAN [START_REF] Goodfellow | Generative adversarial nets[END_REF] contains a generative model G and a discriminative model D. Both models have a multilayer perceptron structure. A noise vector z with a distribution p z (z), composed of continuous random variables, is placed at the input of G. D is trained to distinguish real samples from fake samples generated by G, while the latter is trained to produce fake samples that seem as real as possible. This adversarial training consists in using a minimax function value V (G, D):

min G max D V (D, G) = E x R ∼p data (x R ) [logD(x R )] +E z∼pz(z) [log(1 -D(G(z)))]. (1)
When D can no longer distinguish real samples from fake samples, we have the following property for its scalar predicted output y D :

p G (x F ) -----→ y D →0.5 p data (x R ). (2)
Other variants of GAN have emerged such as the DCGAN [START_REF] Radford | Unsupervised representation learning with deep convolutional generative adversarial networks[END_REF], which adapts its structure to image processing by incorporating convolutional layers. The Wasserstein GAN (WGAN) [START_REF] Arjovsky | Wasserstein generative adversarial networks[END_REF] integrates the distance Earth -M over (EM ) into its cost function in order to rectify the instability problem of these early versions of GANs.

Because of their ability to learn relevant semantic representations, we decided to exploit their advantages for a PU learning application. The approach [START_REF] Hou | A generative adversarial framework for positive-unlabeled classification[END_REF] also appeared to answer the same problematic by the use of a GAN learning model. But their study stops at the functional description of their model. Moreover, the latter requires to train simultaneously five neural networks against only two in our method. Here, our proposed approach that we called Positive-GAN (hereafter "PGAN") has been tested on three different datasets and whose results are very promising in terms of prediction performance and robustness. It outperforms the state of the art on the most challenging image dataset that we tested.

The paper is organized as follows. In the next section we present the method. The experimentations and results are presented in the third section. In the end, a conclusion is drawn on our approach and future research directions are suggested.

POSITIVE-GAN LEARNING METHOD

In this section, we describe our PU learning framework as generically as possible and focus the description on the training method. The Positive-GAN learning method (PGAN) consists in substituting the absence of labeled negative samples x N with fake samples x F generated by our GAN, and so that whose distribution is as close as possible to that of x N , while being different from that of positive samples x P . Fig. 1 illustrates the structure of the system. • The discriminative model D U is trained to distinguish real unlabeled samples x U from fake generated unlabeled samples x F , with y D U ∈ (0, 1) its scalar output prediction.

• The generative model G takes in input a noise vector z of continuous random variables with a uniform distribution in this case and outputs, in the same format as x U , the fake image samples x F (⇔ G(z)) which can be either positive x F P or negative x F N . G is trained in an adversarial way with D U in order to generate fake samples such that their distribution p(x F ) tends towards p(x U ). At the same time it gets away from positive labeled samples distribution p(x P ) as explained below.

• In Step 2, once the GAN training is completed, the convolutional classifier D B , designed for binary image classification task, is trained to distinguish the real positive samples x P from fake samples x F .

We remember that the untagged dataset is composed of a fraction π of positive samples x P and a fraction 1 -π of negative samples x N . So if the GAN is correctly trained on the unlabeled samples x U , we can deduce that:

p(x F ) ------→ y D U →0.5 p(x U ) (3) ⇔ p(x F P ), p(x F N ) ------→ y D U →0.5 p(x P ), p(x N ). (4)
It is also known that a GAN is not perfect in its operation when it is applied to high dimensional data, therefore:

p(x F P ) = p(x P ), and p(x

F N ) = p(x N ). ( 5
)
Thus it is possible to estimate the non-zero distance d computed into the cost function of D B such that:

d(p(x P ), p(x F )) ⇔ d(p(x P ), p(x F P )) d(p(x P ), p(x F N )). (6)
But, the distance d(p(x P ), p(x F P )) will not be exploited for the final application where we treat only real samples with the classifier. This means that when p(x F N ) ------→

y D U →0.5 p(x N ),
we get the equivalence:

d(p(x P ), p(x F N )) ⇔ d(p(x P ), p(x N )). (7)
We are thus able to calculate the distance that interests us. By transposing this reasoning in the PU framework, this amounts to asserting the following equivalences at the output loss function L D B of the classifier D B when y D U → 0.5:

L D B = E x P ∼p(x P ) [logD B (x P )] +E z∼pz(z) [log(1 -D B (G(z)))] (8)
⇔ L D B = E x P ∼p(x P ) [logD B (x P )] +E x N ∼p(x N ) [log(1 -D B (x N ))]. (9)
Thus, from the assumptions made above we can assume that the PGAN method is getting closer to a Positive Negative training while moving away from a Positive Unlabeled training despite the fact that the training dataset we have contains only positive labeled samples and unlabeled samples. However, two risks can occur with this method:

• If the untagged samples x U contain mostly positive samples x P , then it is possible that G no longer generates enough fake samples similar to the samples x N .

• If G generates false samples with a distribution equal to that of the real samples, unlike in the inequality 5, then PGAN would become equivalent in terms of performance to a classical Positive Unlabeled training. But when the dimensionality of images to be processed is large, this risk disappears.

EXPERIMENTS

Settings

Experiments have been realized on the three datasets MNIST [START_REF] Lecun | Gradient-based learning applied to document recognition[END_REF], Fashion-MNIST [START_REF] Xiao | Fashionmnist: a novel image dataset for benchmarking machine learning algorithms[END_REF] and CIFAR-10 [START_REF] Krizhevsky | Learning multiple layers of features from tiny images[END_REF]. We have compared our approach to RP [START_REF] Northcutt | Learning with confident examples: Rank pruning for robust classification with noisy labels[END_REF], which is the best PU learning method to the best of our knowledge. Author's implementation is available 1 . We also report the performance of the classifier trained on the entire Positive Negative initial training dataset, and we call naturally this method PN. We also compare our method to a training named PU which is equivalent to PN but with the PU dataset.

For these experiments, PN, PU, PGAN (ours) and RP methods are tested with exactly the same CNN classifier in order to stay impartial. The classifier has the same structure as in 2 to remain generic. It contains two convolutional layers, two corresponding maxpooling steps, and then two consecutive fully connected layers. Activation function after each layer is ReLU except the last one where softmax is applied. We only changed its last layer from 10 to 2 neurons to adapt it for binary classification. The classifier is trained on 20 epochs iterations. For the CIFAR-10 dataset images 32*32*3, the input and output tensors of the two convolutional layers are adapted and the depth of the first convolutional kernel filters is 3 to correspond to the 3 channels of the RGB images. But the number of kernel filters and their remaining height*width remain unchanged.

Because of the WGAN [START_REF] Arjovsky | Wasserstein generative adversarial networks[END_REF] abilities, we use its training method for these experiments. The training duration for the generative model depends on the dataset complexity: 10 epochs for MNIST, 20 for Fashion-MNIST, and 100 for CIFAR-10. For the latter, we do the same modifications in the structures of D U and G as explained before for the classifier.

Regarding the PU training dataset, ρ corresponds to the fraction of positive samples P from the total of positive samples in the initial training dataset which contains n P samples. These collected samples are then introduced into the U train unlabeled dataset, which initially contains only negative samples N whose total number is n N . π is the fraction of positive samples P present in the unlabeled training dataset U train . U train 1 https : //github.com/cgnorthcutt/rankpruning 2 https : //github.com/tensorf low/tensorf low/blob/master/ tensorf low/examples/tutorials/mnist/mnist sof tmax.py then contains both negative and positive samples according to the ρ and π parameters. We establish that if π ∈ [

U train = {ρ × n P P ; 1 -π π ρ × n P N }. ( (10)
) 11
The results presented below are all performed with ρ = 0.5 and for several values of π.

Results

In Fig. 2, we present some of the fake images generated, respectively from MNIST, Fashion-MNIST and CIFAR-10. We can notice that the images generated by G seem visually real, which indicates from a qualitative point of view the proper functioning of the generative model. In order to get such a rendering, the more complex and large the images are, the more the generative model requires a large number of training epochs.

To compute the F1-Scores, the ArgMax function is applied to the two output neurons of the classifier. Thus, if the index of the first neuron is returned by ArgMax, then the treated sample is considered as negative. Otherwise, the sample is considered as positive. Table 1 shows some of the average F1-Score3 comparative results.

In Fig. 3, it can be observed that the PN method is a good reference for the MNIST and Fashion-MNIST datasets. We find that the efficiency of the PGAN learning method is equivalent to that of the RP method up to π = 0.5 on MNIST and π = 0.3 on Fashion-MNIST. Its efficiency then declines a little bit faster than for RP, while keeping a correct F1-Score. On CIFAR-10 from end to end, the F1-Score is better for PGAN than for RP. Note that the PGAN method also presents better results than the reference PN up to π = 0.8, which is quite surprising. This is probably because the generated samples represent a larger field of negative sample distributions than the real negative samples present in the initial Positive Negative dataset. Moreover, the PGAN F1-Score is consistently higher than the PU method on the three datasets.

Figure 4 presents the study of the robustness of PGAN approach. Figures 4.a and 4.b show that PGAN method has a comparatively more robust behavior such that we can predict more easily the F1-Score evolution as a function of π for each dataset class. Figure 4.c shows us that the classifier stabilizes and converges after about 10 training epochs. To make the histogram in Fig. 4.d, we have retrieved the scalar of the second output neuron of the classifier which corresponds to the predicted probability for a input image of belonging to the positive class. It can be seen that the distribution of the negative and positive test samples processed by the PGAN is of the Gaussian type, which is an interesting characteristic for real applications.

CONCLUSION

Thereby, we demonstrated that the proposed PU learning approach provides state of the art prediction performances and has a steady behavior on small image datasets up to an acceptable fraction π of positive samples in the unlabeled training dataset. In addition, our method outperforms the state of the art on challenging RGB images of CIFAR-10. System optimization can be carried on testing other generative models instead of the WGAN [START_REF] Arjovsky | Wasserstein generative adversarial networks[END_REF], like BEGAN [START_REF] Berthelot | Began: Boundary equilibrium generative adversarial networks[END_REF], WGAN-GP [START_REF] Gulrajani | Improved training of wasserstein gans[END_REF]. Another orientation can be to exploit the z latent space of GANs to perform linear arithmetic operations, as in [START_REF] Bojanowski | Optimizing the latent space of generative networks[END_REF], in order to generate more relevant fake samples.

Considering the promising performances obtained on the CIFAR-10 dataset, a future direction is to extend this method to the analysis of larger images and thus to allow the realization of more complex tasks such as object detection [START_REF] Shaoqing Ren | Faster R-CNN: Towards real-time object detection with region proposal networks[END_REF], [START_REF] Liu | SSD: Single shot multibox detector[END_REF], [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] or semantic segmentation [START_REF] Badrinarayanan | Segnet: A deep convolutional encoder-decoder architecture for image segmentation[END_REF].

Fig. 1 .

 1 Fig. 1. Proposed Positive Unlabeled system: Positive-GAN Learning model.

  and ρ ∈ (0, 1), then we can obtain consecutively the two following training sets: P train = {(1 -ρ)n P P ; 0 N }, with P train the set of positive training samples, and

Fig. 2 .

 2 Fig. 2. Images generated by G trained with ρ = 0.5 and π = 0.5 after 10 epoch itterations on MNIST(a), 20 on Fashion-MNIST(b), and 100 on CIFAR-10(c). Respective positive classes are "5", "trouser" and "automobile".

Fig. 3 .

 3 Fig. 3. Average F1-Scores after 20 training epoch iterations of the classifier in fonction of the rate π that is varied between 0 and 1 with a step of 0.1, for PN (green), PU (red), RP (blue) and PGAN (orange) on MNIST (a), Fashion-MNIST (b) and CIFAR-10 (c).

Fig. 4 .

 4 Fig. 4. Robustness analysis on MNIST. F1-Score evolution for each class as a function of π for PGAN (a), and for RP [4] (b). (c) shows the Accuracy evolution during the PGAN training with the positive class "5" and π = 0.5. (d) is the histogram of the output distributions of the classifier at its 20th epoch iteration of (c) for positive (green) and negative (blue) test samples.

Table 1 .

 1 F1-Score averages results comparisons on MNIST, Fashion-MNIST and CIFAR-10 after 20 epochs of the classifier.

											PU PGAN RP	PU PGAN RP	PU PGAN RP	PU PGAN RP
						Dataset				ρ = 0.5, π = 0.1	ρ = 0.5, π = 0.3	ρ = 0.5, π = 0.5	ρ = 0.5, π = 0.7
					AV G MNIST		0.66		0.97		0.97 0.60	0.96	0.97 0.65	0.95	0.95 0.70	0.87	0.93
				AV G Fashion-MNIST 0.68		0.94		0.92 0.33	0.93	0.95 0.82	0.90	0.95 0.65	0.86	0.94
					AV G CIFAR-10		0.31		0.75		0.62 0.42	0.76	0.73 0.28	0.75	0.72 0.54	0.70	0.68
		1.0		mnist mean F1-Score in function of rate				1.0	fashion-mnist mean F1-Score in function of rate
		0.8												0.8
	F1-Score	0.4 0.6											F1-Score	0.4 0.6
		0.0 0.2	0.1	0.2	0.3	0.4	0.5 rate	0.6	0.7	0.8 PN PU PGAN (ours) 0.9 RP			0.0 0.2	0.1	0.2	0.3	0.4	0.5 rate	0.6	0.7	0.8 PN PU PGAN (ours) 0.9 RP
							(a)												(b)
								1.0		cifar-10 mean F1-Score in function of rate
								0.8
							F1-Score	0.4 0.6
								0.0 0.2	0.1	0.2	0.3	0.4	0.5 rate	0.6	0.7	0.8 PN PU PGAN (ours) 0.9 RP

Average F1-Score represents the mean of F1-Score mesured for each class in a given dataset.