Thibaud Monnin
email: author.thibaud.monnin@upmc.fr

Florence Helft

Chloé Leroy

Patrizia D'ettorre

Claudie Doums

CHEMICAL CHARACTERIZATION OF YOUNG VIRGIN QUEENS AND MATED EGG-LAYING QUEENS IN THE ANT Cataglyphis cursor

Keywords: Queen pheromone, sex pheromone, cuticular hydrocarbons, Dufour's gland, random forest

Social insects are well known for their extremely rich chemical communication, yet their sex pheromones remain poorly studied. We analysed the cuticular hydrocarbon profiles and Dufour's gland contents of queens of different ages and reproductive statuses (sexually immature gynes, sexually mature gynes, mated and egg-laying queens) and of workers in the thermophilic and thelytokous ant Cataglyphis cursor. Random forest classification analyses show that the four groups of individuals were well separated for both chemical sources, except mature gynes that clustered with queens for cuticular hydrocarbon and with immature gynes for Dufour's gland. Analyses carried out with two groups of females only allowed identifying candidate chemicals for queen signal and for sexual attractant. In particular, gynes produce more undecane in the Dufour's gland. This chemical is both the sex pheromone and the alarm pheromone of the ant Formica lugubris. It may therefore possibly act as sex pheromone in C. cursor, and/or be involved in the restoration of monogyny that occurs rapidly following colony fission. Indeed, new colonies often start with several gynes and all but one are rapidly culled by workers, and this process likely involves chemical signals between gynes and workers. These findings open novel opportunities for experimental studies of inclusive mate choice and queen choice in C. cursor.

INTRODUCTION

Mate attraction and mate choice are essential features of living organisms [START_REF] Clutton-Brock | Female mate choice in mammals[END_REF]Mcauliffe 2009, Jennions and[START_REF] Jennions | Variation in mate choice and mating preferences: A review of causes and consequences[END_REF][START_REF] Stearns | Evolution. An introduction[END_REF]). They rely on different modalities of communication depending on species. For instance, birds predominantly rely on acoustic and visual signals (songs, plumage and courtship dances), mammals use acoustic, visual and chemical cues, and insects and arachnids mostly rely on tactile, acoustic and chemical signals. Social insects are well known for their extremely rich chemical communication. In ants, chemical trails often underline foraging, and cuticular hydrocarbon (CHC) profiles allow nestmate recognition [START_REF] Hefetz | The evolution of hydrocarbon pheromone parsimony in ants (Hymenoptera: Formicidae) -interplay of colony odor uniformity and odor idiosyncrasy. A review[END_REF][START_REF] Van Zweden | The role of hydrocarbons in nestmate recognition[END_REF] and the signalling of queen fertility [START_REF] Holman | Identification of an ant queen pheromone regulating worker sterility[END_REF][START_REF] Holman | The evolution of queen pheromones in the ant genus Lasius[END_REF][START_REF] Conte | Primer pheromones in social Hymenoptera[END_REF][START_REF] Monnin | Chemical recognition of reproductive status in social insects[END_REF][START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF].

However, although ant semiochemicals are well studied in many regards their sex pheromones remain poorly studied [START_REF] Ayasse | Mating behavior and chemical communication in the order Hymenoptera[END_REF].

Young, virgin, queens (hereafter gynes) attract males and advertise their sexual receptivity with volatile signals produced by the Dufour's gland, the venom gland or the pygidial glands (reviewed in [START_REF] Ayasse | Mating behavior and chemical communication in the order Hymenoptera[END_REF][START_REF] Hölldobler | The ants[END_REF]. To our knowledge, only two ant sex pheromones have been identified, in Formica lugubris [START_REF] Walter | Identification of the sex pheromone of an ant, Formica lugubris (Hymenoptera, Formicidae)[END_REF]) and in Polyergus breviceps [START_REF] Greenberg | Queen sex pheromone of the slave-making ant, Polyergus breviceps[END_REF]. The chemical bouquet produced by a queen changes once she is mated, as reflected in modifications of the relative abundances of cuticular hydrocarbons within hours or a few days from mating in several ant species [START_REF] Hora | Postmating changes in cuticular chemistry and visual appearance in Ectatomma tuberculatum queens (Formicidae: Ectatomminae)[END_REF][START_REF] Monnin | Chemical recognition of reproductive status in social insects[END_REF][START_REF] Oppelt | Mating is associated with immediate changes of the hydrocarbon profile of Leptothorax gredleri ant queens[END_REF] and in the honeybee [START_REF] Babis | Cuticular lipids correlate with age and insemination status in queen honeybees[END_REF]. This is because mated queens never re-mate [START_REF] Boomsma | Beyond promiscuity: mate-choice commitments in social breeding[END_REF] hence need not attract males anymore whereas they need to advertise their fertility to colony members [START_REF] Foitzik | Competition over workers: Fertility signalling in wingless queens of Hypoponera opacior[END_REF][START_REF] Hannonen | Queen reproduction, chemical signalling and worker behaviour in polygyne colonies of the ant Formica fusca[END_REF][START_REF] Holman | Identification of an ant queen pheromone regulating worker sterility[END_REF][START_REF] Holman | The evolution of queen pheromones in the ant genus Lasius[END_REF][START_REF] Keller | The role of queen pheromones in social insects: queen control or queen signal?[END_REF][START_REF] Conte | Primer pheromones in social Hymenoptera[END_REF][START_REF] Monnin | Chemical recognition of reproductive status in social insects[END_REF][START_REF] Ruel | Surface lipids of queen-laid eggs do not regulate queen production in a fission-performing ant[END_REF][START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF].

We address this scarcity of knowledge of ant sex pheromones by examining the production of chemicals by queens of different ages and reproductive statuses in the thermophilic and thelytokous ant Cataglyphis cursor. Identifying queen signals would be particularly rewarding in this species where inclusive sexual selection and culling of supernumerary queens occur and likely involve chemical signals. In C. cursor, gynes do not fly. They mate at the nest entrance, where foreign males gather [START_REF] Cronin | Opportunities for mate choice in the fissionperforming ant Cataglyphis cursor[END_REF][START_REF] Lenoir | Reproduction and dispersal in the ant Cataglyphis cursor (Hymenoptera, Formicidae)[END_REF]. Gynes show no mate choice, but workers harass males seeking to mate [START_REF] Helft | First evidence of inclusive sexual selection in the ant Cataglyphis cursor: worker aggressions differentially affect male access to virgin queens[END_REF][START_REF] Helft | No evidence of pre-copulatory mate choice by gynes in the facultatively parthenogenetic ant Cataglyphis cursor[END_REF]. How males are attracted to the nest entrance and how they identify sexually receptive gynes are unknown in C. cursor, but they likely rely on chemical signals. Newly mated gynes then disperse with workers to found new colonies (dependent colony foundation, Chéron et al. 2011a;[START_REF] Cronin | Recurrent evolution of Dependent Colony Foundation across eusocial Insects[END_REF][START_REF] Lenoir | Reproduction and dispersal in the ant Cataglyphis cursor (Hymenoptera, Formicidae)[END_REF]. Many new colonies are temporarily polygynous, but this state is transitory and monogyny is restored within a few days (Chéron et al. 2011a;[START_REF] Cronin | The influence of intraspecific competition on resource allocation during dependent colony foundation in a social insect[END_REF]). How monogyny is restored is unknown, but it likely entails some degree of competitive chemical signalling of newly-mated queens vying for colony ownership.

Identifying potential queen signals would therefore allow designing precise key bioassays and studies on inclusive sexual selection and queen competition in this interesting ant species.

Queen chemistry has not been studied in C. cursor and very little is known from other

Cataglyphis species [START_REF] Dahbi | Queen and colony odour in the multiple nest ant species, Cataglyphis iberica (Hymenoptera, Formicidae)[END_REF][START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF], even though worker chemistry has been studied in C. cursor [START_REF] Hefetz | Dufour's gland composition in the desert ant Cataglyphis -species specificity and population differences[END_REF][START_REF] Nowbahari | Individual, geographical and experimental variation of cuticular hydrocarbons of the ant cataglyphis cursor (Hymenoptera: Formicidae): Their use in nest and subspecies recognition[END_REF]) and in other Cataglyphis species [START_REF] Ali | Secretion of the dufour glands of two african desert ants, Camponotus aegyptiacus and Cataglyphis savignyi (Hymenoptera: Formicidae)[END_REF][START_REF] Dahbi | Chemotaxonomy of some Cataglyphis ants from Morocco and Burkina Faso[END_REF][START_REF] Gökçen | Dufour gland contents of ants of the Cataglyphis bicolor group[END_REF][START_REF] Hefetz | Dufour's gland composition in the desert ant Cataglyphis -species specificity and population differences[END_REF].

The CHC profile of three mature, egg-laying, C. iberica queens was compared with that of their workers. It revealed no qualitative differences but higher relative abundances of three linear alkanes (n-C 27 , n-C 28 , n-C 29 ) and one dimethylalkane (dimeC 29 ) and a lower relative abundance of two methylalkanes (11-and 13-meC 27 ) in queens [START_REF] Dahbi | Queen and colony odour in the multiple nest ant species, Cataglyphis iberica (Hymenoptera, Formicidae)[END_REF]. The treatment of orphaned workers with a mixture of linear alkanes and methylalkanes (n-C 27 , n-C 29 and 3-meC 29 ) repressed their ovarian development, suggesting that these chemicals function as queen pheromones [START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF]).

To our knowledge, no gyne (i.e. young virgin queen) has been studied in Cataglyphis. We analyse here the cuticular hydrocarbon (CHC) profiles and Dufour's gland (DG) contents of egg-laying queens, sexually receptive gynes, gynes too young to be sexually receptive and workers of C. cursor.

Our hypothesis is that chemicals over-expressed in egg-laying queens and in sexually receptive gynes may be candidate components of queen pheromones and sexual pheromones, respectively.

METHODS AND MATERIALS

Sixteen complete colonies of C. cursor were collected in Argelès-sur-Mer, Southern France (42.5722508°N, 3.043670°E), on the beginning of March 2014 (1 colony) and March 2015 (15 colonies) (Table 1). This is right after the end of hibernation and immediately prior the onset of sexual production in April-May, with mating taking place in May-June (Chéron et al. 2011a;Cronin et al. 2011). Colonies contained 642 ± 496 workers (mean ± SD, range 168-1857) and were set up in the laboratory within a week of the collection. Each colony was housed in a plaster nest contained in a 35

x 25 x 12 cm box as foraging arena, kept under a 12:12 day:night light cycle and 25-28°C, provided with sugar and water ad libitum, and fed mealworm and crickets twice to thrice a week. Three colonies were queenless by late April, when we started monitoring sexual production (Table 1). We retained them because C. cursor workers produce new queens by thelytokous parthenogenesis when orphaned [START_REF] Cagniant | La parthénogenèse thélytoque et arrhénotoque chez la fourmi Cataglyphis cursor Fonsc. (Hym. Form.). Cycle biologique en élevage des colonies avec reine et des colonies sans reine[END_REF]Chéron et al. 2011b).

Only four colonies, including the three orphaned colonies, produced sexuals in the laboratory (Table 1). These four colonies produced gynes, but only two colonies (one queenright and one orphaned) produced males. Note that orphaned colonies mainly produce diploid males who behave like haploid males and can mate and fertilise the queen (Doums et al. 2013b). Males were removed upon emergence to prevent them from dispersing to other colonies and mate, hence gynes remained virgin. We sampled 25 gynes between 11 th of May and 5 th of June 2015. Twelve were sampled when they were one to five days old (mean age of three days, hereafter gynes G0) while the remaining 13 were sampled at eight to 11 days old (mean age of 10 days, gynes G1). Gynes G0 and G1 are sexually immature and sexually mature, respectively, and this was confirmed by the shedding of wings and dissections (see results). They originated from four and three sexuals-producing colonies, respectively (Table 1). This introduces some pseudo replication in our dataset. This is common in chemical studies of social insect sexuals because of the difficulties for obtaining samples from many independent colonies. Our study focuses on chemicals involved in behaviours that are not expected to differ in any consistent way between colonies (mate attraction, competition between young queens for colony "ownership") hence these chemicals should not be affected by colony effects and our result should be robust. Gynes were immediately stored at -80°C when collected, until later dissection and chemical extraction. In addition, 13 queens (Q) and 16 workers (W) were collected on the 9 th of June hence totalling 54 individuals (Table 1).

Chemical extraction and dissections were carried out at the end of June. Each ant was individually retrieved from the freezer immediately before its chemical extraction and dissection. We recorded whether gynes were winged or dealated as a cue of sexual maturity independent from our age-based groups of Gynes G0 and G1. Wing loss is indicative of mating in the field where 83.5% of virgin gynes vs. 16% of mated gynes were winged (Doums et al. 2013a). We then separated the gaster from the rest of the body. The gasterless body was immersed in 200 µl of pentane for 5 min in order to extract the cuticular hydrocarbons. At the same time, we dissected the gaster to collect the Dufour's gland, which was extracted in 100 µl of pentane. Lastly, we dissected the reproductive apparatus and recorded mating status and ovarian development.

Chemical Analysis

Samples were analysed by gas chromatography-mass spectrometry (GC-MS). Each sample was evaporated at ambient temperature under an extractor hood and re-diluted with 70µl of pentane.

Two µl of the solution were injected using an Agilent G4513A Automatic Liquid Sampler into an Agilent Technologies 7890A gas chromatograph (capillary column: Agilent HP-5MS, 30 m × 0.25 mm × 0.25 μm; split-splitless injector; carrying helium gas at 1 mL/min) coupled with an Agilent 5975 C mass spectrometer with 70 eV electron impact ionization. The injector was set at 280°C and the temperature programme was as follows: an initial hold at 70°C for 1 min, then 70°C to 175°C at 10°C.min-1, and up to 320°C at 5°C.min-1 and hold for 3 min.

Peak areas were integrated with MSD ChemStation software version E.02.01.1177 (Agilent technologies). We used the best profile for each chemical source (CHC, DG) and each group of individuals (W, G0, G1, Q) to select and identify the peaks to include in our analyses. We identified chemical compounds by their retention time, fragmentation pattern and comparisons with published results on Cataglyphis species including C. cursor [START_REF] Ali | Secretion of the dufour glands of two african desert ants, Camponotus aegyptiacus and Cataglyphis savignyi (Hymenoptera: Formicidae)[END_REF][START_REF] Dahbi | Chemotaxonomy of some Cataglyphis ants from Morocco and Burkina Faso[END_REF][START_REF] Gökçen | Dufour gland contents of ants of the Cataglyphis bicolor group[END_REF][START_REF] Hefetz | Dufour's gland composition in the desert ant Cataglyphis -species specificity and population differences[END_REF][START_REF] Keegans | What do glands tell us about species? A chemical case study of Cataglyphis ants[END_REF][START_REF] Nowbahari | Individual, geographical and experimental variation of cuticular hydrocarbons of the ant cataglyphis cursor (Hymenoptera: Formicidae): Their use in nest and subspecies recognition[END_REF].

Statistical Analysis

The results were analysed separately for each chemical source (CHC, DG). We used random forest classification analysis (RF) [START_REF] Liaw | Classification and regression by randomForest[END_REF] to see whether the four groups (egg-laying queens, sexually mature gynes, sexually immature gynes, workers) could be discriminated and to identify peaks that best discriminate groups. RF is a method increasingly used in chemical studies, including the chemical ecology of social insects [START_REF] Jansen | Disentangling the effect of insemination and ovary development on the cuticular hydrocarbon profile in the bumblebee Bombus terrestris (Hymenoptera: Apidae)[END_REF][START_REF] Mitra | Nestmate discrimination in the social wasp Ropalidia marginata: chemical cues and chemosensory mechanism[END_REF][START_REF] Oliveira | Intraspecific worker parasitism in the common wasp, Vespula vulgaris[END_REF]. It is a tree-based machine learning tool for analysing multivariate dataset with more variables than individuals [START_REF] Goldstein | Random forests for genetic association studies[END_REF], and this is typically the case in chemical analyses. In addition, RF deals well with multicollinearity, assumes no specific distribution of the variables and does not require transformation of constrained data (such as chemical compounds) [START_REF] Ranganathan | Reducing the babel in plant volatile communication: using the forest to see the trees[END_REF].

We used R v3.2.2 (R Core Team 2016) with Rstudio v1.0.44 (RStudio Team 2016). We used the relative abundances of peaks (i.e. proportions each peak represents relative to the sum of all peaks) computed from the raw dataset, including all the zero values. RF were ran using the package randomForest [START_REF] Liaw | Classification and regression by randomForest[END_REF]. We performed RF using 10,000 trees to determine the importance of each peak in classifying the individuals in the four groups. We used the default value for the number of input variables randomly selected to build each node of the tree (denoted by mtry), that is the squared root of the number of variables (seven in our case). We also used the default value (33%) for defining the set of observations not used for building the current tree, i.e. the out of bag sample (OOB sample). This OOB sample is used to generate the confusion matrix and OOB error rate (i.e. rate of unsuccessful assignment of the OOB samples to the correct group). A low OOB error rate indicates a high ability of the indicator variables to predict the group of origin of the individual. The separation of the groups was visualized using a multidimensional scaling plot based on a proximity matrix of the individuals on the RF (i.e. the number of times they end up on the same leaf in the trees) (function MDSplot).

For each chemical source, as a second step, we tried to identify the peaks that are the most important for queen recognition by comparing queens vs. workers, and for sexual attraction by comparing gynes G1 vs. gynes G0 and gynes G1 vs. queens. To do so, we ran three additional RF analyses, each contrasting only the two groups of interest, and used the package VSURF [START_REF] Genuer | VSURF: An R package for variable selection using random forests[END_REF] to identify the peaks important in discriminating the two groups. The measure of variable importance is based on the decrease of classification accuracy when the observed values of the given variable are randomly permuted in the OOB samples [START_REF] Genuer | VSURF: An R package for variable selection using random forests[END_REF]. The selection procedure is based on three steps. The first (thresholding step) ranks variables according to a score of importance, and eliminates variables with a score lower than a threshold value. The second selects the variables needed to best discriminate the groups of interest. Embedded RF models are grown, starting with a RF build with only the most important variable and finishing with a RF with all the variables retained in the previous step, and the best model is selected on the basis of the means OOB error. The third step refines the previous selection for a predictive purpose and was therefore not used here. As above, the RF models were run with 10,000 trees and a sample of seven peaks for each node. The selection procedure for each comparison was run 20 times to assess the stability of the variable selection process. For each comparison, the chemical compounds were therefore ranked by their level of importance in discriminating the two groups and we averaged their ranks over the 20 runs of the variable selection process.

RESULTS

The dissections confirmed that all gynes were virgin, as expected since males were removed from colonies to prevent mating. Gynes G0 were all winged and had inactive ovaries without oocytes or with a few small and non-yolky oocytes at most. Seven gynes G1 were dealated (three partially and four fully) and six were winged. Gynes G1 had slightly more developed ovaries than gynes G0: five had small non-yolky oocytes while the remaining eight had small but yolky oocytes. This supports our hypothesis that gynes G1 were sexually mature because dealation is a good indicator that a gyne is mated in nature (Doums et al. 2013a). All queens were mated and had active ovaries with yellow bodies, except the queen of colony 1268 which showed regressing ovaries indicative of aging.

Table S1 lists the compounds identified from the cuticle (60 peaks) and Figure S1 provides representative chromatograms for each group of individuals. Similarly, Table S2 lists the compounds from the Dufour's gland (36 peaks) and Figure S2 shows representative chromatograms. The compounds identified include alkanes, methylalkanes and alkenes. In addition, some acetates and alcohols were also found in the DG.

Cuticular Hydrocarbons

The RF analysis with the four groups of individuals shows that workers were clearly separated from sexual females (gynes and queens) along the first axis, while the three groups of sexual females were separated along the second axis (Figure 1). Gynes G0 were clearly separated from queens and most gynes G1 clustered with queens, although two clustered with gynes G0. That is, there was a gradual transition of the CHC profile from G0 to G1 and queens. The OOB error rate (i.e. individuals not correctly assigned to their group) was 12.96% and most misclassifications occurred between gynes G1 and either gynes G0 (2 errors) or queens (4 errors, Table S3).

In order to identify the compounds most important for differentiating two given types of females (Q vs. W; G1 vs. G0; G1 vs. Q), we ran three additional RF analyses considering only two groups of individuals at a time, for both CHC and DG. We selected the variables (compounds) of importance for the discrimination using the package VSURF and ran each variable selection process 20 times to assess the stability of the selection process (see Methods and Materials). The results show that the importance of chemical compounds was stable over the 20 runs. The first step of the variable selection procedure (thresholding step) retained 45 to 51 peaks out of 60 peaks (i.e. 75-85%). Most compounds were consistently ranked with the same importance, and when variation occurred it was small. The variable selection procedure was reliable for the three paired comparisons, and thus for the sake of clarity we present the 20 peaks with the highest averaged ranks over the 20 runs (Figure 2).

The Q/W comparison aimed at identifying chemicals that may be queen signals. The OOB error rate was much lower (3.45%) than when considering the four groups. The 20 peaks with the highest averaged rank of importance show a clear queen/worker difference in terms of the weight of their CHCs, with the heavier compounds being more abundant in queens than in workers (Figure 2A).

The second step of the variable selection procedure retained a single compound as needed for obtaining the best discrimination (Peak 26 = 3-meC 27 ). However, this chemical was more abundant in workers than in queens (Table S1) hence is unlikely to be a queen signal.

The comparison gynes G1 vs. gynes G0 aimed at identifying compounds differentiating sexually mature and sexually immature gynes. In agreement with the results obtained when considering the four groups of individuals (Figure 1), gynes G1 and G0 were well differentiated (OOB error rate of 8%). The second step of the selection procedure identified three chemicals as necessary for best discrimination (P35 = n-C 29 , P44 = 14-meC 30 + 8,12-dimeC 30 and P50 = 11,13-dimeC 31 ), among which one was more abundant in gynes G1 and two were more abundant in gynes G0 (Figure 2B). Last, we compared gynes G1 and queens. Again, in agreement with the results when considering the four groups of individuals (Figure 1), they were rather poorly differentiated (OOB error rate of 15%). Nine of the 20 peaks with the highest averaged rank of importance were more abundant in queens than in gynes G1, and these comprised the four heaviest and the five lightest compounds (Figure 2C). Three peaks were required for the best discrimination (P53 = n-C 33 , P47 = n-C 31 and P54 = 15+17-meC 33 ), and they were more abundant in queens and among the four heaviest compounds.

Dufour's Gland

The RF analysis with the four groups of individuals shows that the first axis separates workers from sexual females, and that the second axis separates sexual females (Figure 1). Gynes G0 and G1 clustered together and were well separated from queens. That is, there was a gradual transition of the DG content from G0 and G1 to queens, but while gynes G1 clustered with queens for CHC they clustered with gynes G0 for DG. The OOB error rate was 11.11%, and most misclassification occurred between gynes G0 and G1 (DG: 5 errors, Table S3).

We performed the same variable selection procedure than for CHC, using RF to identify the compounds most important in differentiating two given types of females. As for CHC, the variable selection procedure was stable over the 20 runs. The first step of the procedure (thresholding step) retained 24 to 35 peaks out of 36 peaks (67-97%) and for the sake of clarity we present the 20 peaks with the highest averaged ranks over the 20 runs (Figure 3).

The RF comparing queens and workers yielded a low OOB error rate of 3.45%, in agreement with the results obtained when including the four groups. As for CHC, there was a very clear queen/worker difference in terms of the weight of chemicals, with all but one of the heavier compounds being more abundant in queens than in workers (Figure 3A). The second step retained one compound only as needed for best discrimination, but this compound varied across runs (it was either peak 27 = C 27:1 , P31 = C 29:1 or P33 = C 31:2 ). This is because these three compounds were correlated hence the information they provide for discriminating the two groups was redundant. It is worth noticing that the three compounds are structurally related (alkene) and more abundant in queens than in workers (Table S2).

The comparison of gynes G1 and G0 yielded a high OOB error rate (20%), which is also in agreement with the results obtained when considering the four groups of individuals where G1 and G0 clustered together (Figure 1). The second step of the selection procedure showed that three peaks are needed for the best discrimination (P15 = C 19:2 , P12 = me-C 17 and P21 = C 23:1 ), including two more abundant in gynes G1 and one more abundant in gynes G0 (Figure 3B).

Last, we compared gynes G1 and queens. They were perfectly differentiated (OOB error rate of 0%), in agreement with the comparison using the four groups of individuals (Figure 1). Most of the peaks more abundant in queens were heavy compounds (Figure 3C). The second step selected three peaks (P8 = tridecanol, P7 = dodecanyl acetate and P1 = n-C 11 ). All were more abundant in gynes G1 and among the light compounds (Figure 3C), which is consistent with their putative use as volatile attractants of foreign males for mating.

DISCUSSION

We examined the changes in chemical production that C. cursor sexual females undergo as they age and mate, by comparing virgin and sexually immature queens (gynes G0), virgin and sexually mature queens (gynes G1) and mated and egg-laying queens. We included workers as a control and analysed the chemical compounds from the cuticle and the Dufour's gland. As expected, the four groups of individuals were overall well discriminated, for the two chemical sources. Subsequent analyses contrasting two types of females each (queens vs. workers, gynes G1 vs. gynes G0 and gynes G1 vs. queens) pinpointed the chemical compounds that are good candidate as chemical signals.

Compounds that were of high importance for discriminating queens from workers and that were more abundant in the former may be queen signals. Similarly, compounds that were important in discriminating gynes G1 from G0 or from queens and that were more abundant in gynes G1 may be male attractants or chemicals involved in the restoration of monogyny.

The branched alkane 3-meC 27 was important in discriminating queen and worker CHC profiles. This is in apparent agreement with previous studies that have found 3-methylalkanes to be characteristic of queen vs. worker CHC profiles in several social insect species (3-meC 29 in C. iberica:

Oystaeyen et al. 2014; from 3-meC 25 to 3-meC 35 in several Lasius species: [START_REF] Holman | The evolution of queen pheromones in the ant genus Lasius[END_REF][START_REF] Oi | The origin and evolution of social insect queen pheromones: novel hypotheses and outstanding problems[END_REF]. However, 3-meC 27 was less abundant in C. cursor queens than workers, whereas in contrast 3methylalkanes are more abundant in C. iberica and Lasius queens than workers [START_REF] Holman | The evolution of queen pheromones in the ant genus Lasius[END_REF][START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF]. It is therefore doubtful that 3-meC 27 could be (a component of) the queen signal in C. cursor. Other compounds that were both important in discriminating queen and worker CHC profiles and more abundant in the former may constitute the queen signal. These include linear alkanes (n-C 31 and n-C 33 ), methylalkanes (13+15-meC 31 and 15+17-meC 33 ) and alkenes (C 23:1 , C 31:1 and C 33:1 ) (Figure 2 and Table S1). In addition, C. cursor queens also differed from workers by producing more alkenes (C 27:1 , C 29:1 and C 31:2 ) in the Dufour's gland. Chemicals of these types have been identified as putative queen signals in several other social insect species (e.g. Le [START_REF] Conte | Primer pheromones in social Hymenoptera[END_REF]Oi et al. 2016;[START_REF] Van Zweden | Queen signaling in social wasps[END_REF] including the congeneric C. iberica [START_REF] Dahbi | Queen and colony odour in the multiple nest ant species, Cataglyphis iberica (Hymenoptera, Formicidae)[END_REF][START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF]. It is now relatively consensual that queen signals are honest [START_REF] Heinze | Honest and dishonest communication in social Hymenoptera[END_REF][START_REF] Keller | The role of queen pheromones in social insects: queen control or queen signal?[END_REF], but whether they are largely conserved across social insect species ( Oi et al. 2016;[START_REF] Van Oystaeyen | Conserved class of queen pheromones stops social insect workers from reproducing[END_REF] or variable [START_REF] Amsalem | A conserved class of queen pheromones? Re-evaluating the evidence in bumblebees (Bombus impatiens)[END_REF][START_REF] Evison | Chemical signature and reproductive status in the facultatively polygynous ant Pachycondyla verenae[END_REF][START_REF] Smith | Comparative analysis of fertility signals and sex-specific cuticular chemical profiles of Odontomachus trap-jaw ants[END_REF]) remains debated. The activity of the queen-characteristic compounds presently identified in C. cursor should be determined with an adequate bioassay, such as whether they inhibit (delay or decrease) egg-laying by orphaned workers (e.g. Oi et al. 2016). The queen is multiply mated in C. cursor and it would also be worth investigating the sensitivity of worker patrilines to queen pheromones, to test for instance whether it correlates negatively with their propensity to reproduce in presence of their queen ( i.e. behave as cheaters, Doums et al. 2013b) or to enter foreign colonies and reproduce ( i.e. behave as social parasite, Chéron et al. 2011b).

CHC profiles also discriminated well gynes G0 from gynes G1, and this likely stems from the fact that gynes G0 had a callow-like chemical profile while gynes G1 had already started producing a queen profile given that they had started developing their ovaries. In contrast, DG contents did not differentiate between the two categories of gynes, which suggests that CHC and DG contents mature at different speeds. Complementary studies are necessary to get a better understanding of the maturation of gynes, for instance by using additional age groups of gynes to cover a larger range of age differences, or by sampling gynes performing sexual calling in the field (as in [START_REF] Walter | Identification of the sex pheromone of an ant, Formica lugubris (Hymenoptera, Formicidae)[END_REF].

Although the comparison between gynes G1 and gynes G0 did not allow identifying putative sex pheromones, the comparison of gynes G1 with queens was more informative. CHC profiles did not discriminate well these two types of females. This may be because gynes G1 had started developing their ovaries and producing queen pheromones. However, the Dufour's gland content allowed a perfect discrimination of gynes G1 and queens, in agreement with our expectation that virgin and sexually mature gynes G1 produce male attractants whereas mated and egg-laying queens do not. Undecane (n-C 11 ) was one of three components allowing this discrimination and it was more abundant in gynes G1 than in queens. Undecane is the main component of the sex pheromone of the ant Formica lugubris [START_REF] Walter | Identification of the sex pheromone of an ant, Formica lugubris (Hymenoptera, Formicidae)[END_REF], opening up the possibility that it may be (a component of) the sex pheromone of C. cursor. The effect of undecane could be experimentally tested by recording males' responses to synthetic chemical deposited on filter paper, dummies (e.g. glass beads or dead individuals) or live individuals (workers or non-receptive queens). C. cursor workers are involved in inclusive sexual selection [START_REF] Helft | First evidence of inclusive sexual selection in the ant Cataglyphis cursor: worker aggressions differentially affect male access to virgin queens[END_REF][START_REF] Helft | No evidence of pre-copulatory mate choice by gynes in the facultatively parthenogenetic ant Cataglyphis cursor[END_REF]) and it would be interesting to test their possible contribution to male attraction. Workers use DG secretions for marking the surroundings of the nest entrance [START_REF] Mayade | Home-range marking and territorial marking in Cataglyphis cursor (Hymenoptera, Formicidae)[END_REF] and by doing so they may release undecane and contribute to attract males. Indeed, although each worker harbours little undecane in her DG (Table S2), workers may collectively deposit significant amounts.

Another possibility is that undecane is involved in the restoration of monogyny during the process of colony fission. Indeed, undecane has two functions in F. lugubris: sex pheromone in queens and alarm pheromone in workers [START_REF] Walter | Identification of the sex pheromone of an ant, Formica lugubris (Hymenoptera, Formicidae)[END_REF]). In C. cursor new colonies are founded by colony fission. They often start with several gynes but monogyny is restored within a few days (Chéron et al. 2011a) by fights between young queens and by attacks by workers (pers. obs.).

Undecane could be a signal allowing physiologically more fertile gynes to mark less fertile gynes and thereby target worker attacks against the latter, as occurs in some other species in comparable contexts [START_REF] De Souza | The relationship between queen execution and cuticular hydrocarbons in stingless bee Melipona scutellaris (Hymenoptera: Meliponini)[END_REF][START_REF] Monnin | Pretender punishment induced by chemical signalling in a queenless ant[END_REF][START_REF] Smith | Queen-specific signals and worker punishment in the ant Aphaenogaster cockerelli: the role of the Dufour's gland[END_REF]. The involvement of undecane in intra-colonial aggressions could be experimentally tested by recording workers' response to the deposit of synthetic chemical on live individuals (workers or non-receptive queens). A preliminary study indeed suggests that undecane triggers worker aggressions against male. When a worker and a male from another colony were placed together in a small box containing a filter paper, the worker attacked the male in 6 out of 18 replicates when the filter paper contained undecane whereas she did not when the filter paper was blank (0 out of 18 trials, Fisher exact test: p = 0.019).

Our results show that the complex chemical bouquet of C. cursor queens changes according to age, mating status and reproductive activity, as occurs in other species where mating triggers chemical switches [START_REF] Babis | Cuticular lipids correlate with age and insemination status in queen honeybees[END_REF][START_REF] Hora | Postmating changes in cuticular chemistry and visual appearance in Ectatomma tuberculatum queens (Formicidae: Ectatomminae)[END_REF][START_REF] Oppelt | Mating is associated with immediate changes of the hydrocarbon profile of Leptothorax gredleri ant queens[END_REF]. These changes are related to mate attraction and to queen signalling towards workers, and the identification of candidate chemicals is a first step towards identifying pheromones. These would in turn allow exciting studies of the chemical determinants of mating site selection by males, restoration of monogyny (i.e. queen choice) by workers, and the link between sensitivity to queen pheromone and cheating and social parasitism. S1). Peaks importance for discriminating the two groups of females decrease from rank 1, the most important peak, to rank 20, the least important peak. Peaks needed to obtain the best discrimination (i.e. retained by the second selection step, see M&M) are encircled. Peak identification is given in Table S1. S2. Fig. 3 WQ G0G1 G1Q

Fig. 1

 1 Fig.1MDS plots of the proximity distance estimated from the Random Forest analysis including the

Fig. 2

 2 Fig. 2 Random forest analyses for cuticular hydrocarbons, comparing queens and workers (a), gynes

Fig. 3

 3 Fig. 3 Random forest analyses for Dufour's gland content, comparing queens and workers (a), gynes

  Fig.2

Table 1

 1 Colony origin of the 54 individuals analysed. Three colonies were queenless (QL) at the time 568 of gyne production, and two colonies produced males in addition to gynes

	569
	570
		COLONY CODE	COLONY SIZE	MALES PRODUCED INDIVIDUALS SAMPLED
					QUEEN	GYNES G0	GYNES G1	WORKER
		1206 QL*	606			2
		1250	254		1
		1251	1561		1
		1252	877		1
		1254	217		1
		1257	430		1
		1258 QL	459	4		5	6
		1259 QL	1857			2	4
		1260	168		1
		1262	867		1
		1263	299		1
		1264	912		1
		1265	185		1
		1266	361		1
		1267	883		1
		1268	340	23	1	3	3
		TOTAL			13	12	13	16
	571	* collected in March 2014
	572

Table S2

 S2 Relative abundance (percentage of total area) of peaks in extracts of Dufour's gland (DG) of workers, gynes G0 and G1, and queens Fig.S1Representative chromatograms of cuticular hydrocarbon extracts for the four groups of individuals. X and y-axes are retention time and abundance, respectively. Representative chromatograms of Dufour's gland extracts for the four groups of individuals. X and yaxes are retention time and abundance, respectively.

	PEAK NUMBER P1 P2 P3 P4 P5 P6 P7 P8 P28 P29 P30 P31 P32 P33 P34 P35 P36 1000000 2000000 3000000 4000000 5000000 6000000 2000000 4000000 6000000 8000000 1e+07 1.2e+07 1.4e+07 1.6e+07 4000000 8000000 1.2e+07 1.6e+07 2e+07 2.4e+07 2.8e+07 3.2e+07 3.6e+07 Fig. S2 10.00 PEAK IDENTIFICATION n-C 11 n-C 12 n-C 13 Dodecyl acetate 9.98 RETENTION TIME 5.72 7.15 8.54 Dodecanol 10.82 n-C 15 11.09 Dodecanyl acetate 12.46 Tridecanol 12.78 Dodecyl myristate 29.91 Tetracosanal 30.22 Tetracosyl acetate 30.55 C 29:1 31.45 C 30 32.96 C 31:2 34.00 ? 35.44 ? 37.79 ? 40.11 20.00 22.00 24.00 26.00 PEAK RELATIVE ABUNDANCE (MEAN % ± SD) WORKERS GYNES G0 GYNES G1 0.08 ± 0.22 5.39 ± 2.63 2.79 ± 0.94 0.01 ± 0.02 0.26 ± 0.18 0.13 ± 0.05 4.53 ± 3.80 15.84 ± 6.29 12.24 ± 3.42 0.02 ± 0.03 0.29 ± 0.24 0.23 ± 0.14 0.27 ± 0.43 0.93 ± 1.45 0.31 ± 0.35 2.56 ± 1.68 2.13 ± 1.32 2.10 ± 0.42 21.76 ± 8.46 20.72 ± 5.23 14.41 ± 3.63 0.20 ± 0.20 0.36 ± 0.23 0.41 ± 0.10 4.24 ± 2.578 0.89 ± 1.23 0.28 ± 0.28 0 0.32 ± 0.23 0.53 ± 0.18 0 0.60 ± 0.54 0.86 ± 0.41 0 3.36 ± 1.98 4.27 ± 1.09 0.09 ± 0.24 0.28 ± 0.25 0.49 ± 0.25 0 0.51 ± 0.37 1.00 ± 0.54 0 0.40 ± 0.30 0.63 ± 0.25 0.06 ± 0.25 1.81 ± 0.88 2.07 ± 0.65 0 4.60 ± 11.07 1.48 ± 0.51 28.00 30.00 32.00 34.00 36.00 38.00 Worker 15.00 20.00 25.00 30.00 35.00 Worker 10.00 15.00 20.00 25.00 30.00 35.00 Gyne G1 Queen	QUEENS 0.64 ± 0.49 0.11 ± 0.07 10.41 ± 3.48 0.00 ± 0.00 0.09 ± 0.13 3.24 ± 0.67 5.21 ± 3.32 0.08 ± 0.06 0.31 ± 0.27 0.83 ± 0.32 0.74 ± 0.38 3.56 ± 0.95 0.74 ± 0.43 0.62 ± 0.24 0.93 ± 0.45 2.66 ± 1.44 1.51 ± 0.95 40.00 40.00 40.00
	P9 4.8e+07	n-C 17		13.67	6.78 ± 1.23	1.49 ± 0.96		2.02 ± 0.36		2.69 ± 0.95
	P10 P11 P12 2.8e+07 3.2e+07 1e+07 3.6e+07 4e+07 1.2e+07 4.4e+07	? (fatty acid) meC 17 meC 17 Gyne G0 Gyne G0	13.80 13.84 14.44	0.32 ± 0.16 0.72 ± 1.13 1.29 ± 2.05	0.89 ± 0.47 0.97 ± 2.03 1.77 ± 3.46		1.10 ± 0.19 0.05 ± 0.05 0.21 ± 0.31		0.76 ± 0.32 0.09 ± 0.07 0.06 ± 0.04
	P13 2.4e+07 8000000 2.4e+07 2.8e+07	Tetradecanol acetate	15.22	1.42 ± 0.66	3.25 ± 2.21		4.21 ± 1.35		4.29 ± 2.22
	P14 1.6e+07 1.6e+07 6000000 2e+07 2e+07	Farnesol acetate		15.75	0	0.14 ± 0.15		0.26 ± 0.11		0.06 ± 0.06
	P15 P16 4000000 8000000 1.2e+07 1.2e+07	C 19:2 C 19:1		16.14 16.25	2.90 ± 0.98 44.39 ± 9.89	0.19 ± 0.18 4.90 ± 2.83		1.10 ± 0.82 9.86 ± 3.10		0.93 ± 0.43 17.62 ± 6.49
	P17 2000000 8000000 4000000	n-C 19		16.60	1.32 ± 0.31	2.92 ± 1.80		3.71 ± 1.04		3.59 ± 1.01
	P18 4000000	C 21:2	10.00	19.27 15.00	1.20 ± 0.55 20.00	0.51 ± 0.49 25.00	30.00	1.94 ± 1.34 35.00	1.88 ± 0.52 40.00
	P19	C 21:1 20.00	22.00	19.36 24.00	2.76 ± 0.96 26.00 28.00	1.17 ± 0.75 30.00 32.00	34.00	2.44 ± 0.80 36.00	38.00	4.41 ± 0.87 40.00
	P20	n-C 21	10.00	19.77 15.00	0.07 ± 0.11 20.00	2.41 ± 1.48 25.00	30.00	2.87 ± 1.33 35.00	2.13 ± 0.70 40.00
	P21	C 23:1		22.57	0.23 ± 0.21	4.30 ± 1.11		5.29 ± 0.71		6.15 ± 1.54
	P22	n-C 23		23.00	0	4.85 ± 2.98		5.31 ± 2.05		4.21 ± 1.41
	P23	Eicosenol	24.29	2.67 ± 0.89	0.91 ± 1.02		2.37 ± 1.45		5.52 ± 1.83
	P24	Eicosyl acetate	24.68	0.02 ± 0.05	0.38 ± 0.37		0.56 ± 0.25		0.83 ± 0.43
	P25	C 25:1		25.81	0	6.39 ± 1.79		7.56 ± 1.00		7.98 ± 2.26
	P26	n-C 25		26.03	0.08 ± 0.13	0.59 ± 0.53		0.48 ± 0.35		0.42 ± 0.29
	P27	C 27:1		28.60	0.01 ± 0.04	3.24 ± 1.68		4.41 ± 0.55		4.69 ± 0.80


Ali Bourega

Bendouma Doumi
email: bdoummi@yahoo.fr

Allel Mokaddem
email: mokaddem.allel@gmail.com

Adlane Sayede

Abdelkader Tadjer

Electronic structures and magnetic performance related to spintronics of Sr 0

Keywords: Ali Bourega, Bendouma Doumi, Allel Mokaddem, Adlane Sayede, Abdelkader Electronic structures, Half-metallic ferromagnetism, Ti-substituted SrS, TB-mBJ

may come

Electronic structures and magnetic performance related

to spintronics of Sr0.875Ti0.

Introduction

The diluted magnetic semiconductors (DMS) have been the subject of several experimental and theoretical studies to improve the performance of their properties for magneto-electronics applications [START_REF] Cui | Magnetic properties of diluted magnetic semiconductors Li (Zn, TM) N with decoupled charge and spin doping (TM: V, Cr, Mn, Fe, Co and Ni)[END_REF][START_REF] Berriah | Theoretical investigation of electronic performance, half-metallicity, and magnetic properties of Cr-substituted BaTe[END_REF][START_REF] Lakhdari | Investigation of the substituting effect of chromium on the electronic structures and the half-metallic ferromagnetic properties of BaO[END_REF][START_REF] Yunusov | Band gap engineering of ZnMnO diluted magnetic semiconductor by alloying with ZnS[END_REF][START_REF] Torquato | Synthesis and structural, magnetic characterization of nanocrystalline Zn1-xCoxO diluted magnetic semiconductors (DMS) synthesized by combustion reaction[END_REF][START_REF] Miyagawa | Origin of magnetization in diluted magnetic semiconductor GaGdAs monolayer and superlattice[END_REF][START_REF] Emam-Ismail | Spectroscopic ellipsometry and morphological characterizations of nanocrystalline Hg1-xMnxO oxide diluted magnetic semiconductor thin films[END_REF]). These compounds are potential candidates for modern spintronics due to their magnetic and semiconductor characters, which can be generated by the doping magnetic transitions or rare earths ions in the host semiconductors. In the spintronics devices, the spin (magnetic moment) of the electron in addition to its charge is explored as another degree of freedom. However, the DMS are used in logic function gates and storage devices due to these particular features (Ghosh et al. 2019b). It is necessary to understand the importance of high Curie temperature (TC) of half-metallic materials for spintronics [START_REF] Lei | First-principle study of half-metallic ferromagnetism in rocksalt XO (X = Li, K, Rb, Cs)[END_REF]. The wide-band gap semiconductors based half-metallic DMS are suitable materials for applications of spintronics devices because they show the stability of the ferromagnetism at temperatures higher than the room temperature [START_REF] Sato | Material design of GaN-based ferromagnetic diluted magnetic semiconductors[END_REF][START_REF] Wu | Synthesis, characterization, and modeling of high quality ferromagnetic Cr-doped AlN thin films[END_REF]. [START_REF] Dietl | Zener model description of ferromagnetism in zinc-blende magnetic semiconductors[END_REF] have predicted high-TC ferromagnetism in the GaN doped Mn, using a mean field approximation of Zener carrier-mediated model. Recently, [START_REF] Wang | Determining Curie temperatures in dilute ferromagnetic semiconductors: high Curie temperature (Ga, Mn) As[END_REF] have obtained an accurate TC of 178 ± 1 K for (Ga, Mn)As DMS using experimental simultaneous magnetometry and transport measurements. Although, the high TC can be estimated in the half-metallic materials with wide half-metallic gaps [START_REF] Saini | Emergence of half metallicity in Cr-doped GaP dilute magnetic semiconductor compound within solubility limit[END_REF].

The SrS is one of the II-VI strontium chalcogenides such as SrX (X = S, Se and Te), they shape closed-shell ionic compounds crystallized in rock-salt NaCl (B1) structure under ambient conditions [START_REF] Dadsetani | Optical properties of strontium monochalcogenides from first principles[END_REF]Bhattacharjee and Chattopadhyaya 2017a;[START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF]). These materials are important semiconductors owing to their large band gaps and valence-band widths with significant technological applications in the field of microelectronics, catalysis, radiation dosimetry, luminescent and infrared sensitive devices, and fast high resolution optically stimulated luminescence imaging (Ruoff a nd G rzybowski 1985;Pandey a nd S ivaraman 1991;Y amashita et al. 1984;[START_REF] Varshney | High pressure structural (B1-B2) phase transition and elastic properties of II-VI semiconducting Sr chalcogens[END_REF].

Recently, the electronic structures and magnetism in the II-VI semiconductors based DMS have been extensively studied experimentally and theoretically [START_REF] Berriah | Theoretical investigation of electronic performance, half-metallicity, and magnetic properties of Cr-substituted BaTe[END_REF][START_REF] Yang | Effects of epitaxial strains on spontaneous polarizations and band gaps of alkaline-earth-metal oxides MO (M = Mg, Ca, Sr, Ba)[END_REF][START_REF] Addadi | Electronic and ferromagnetic properties of 3d (V)-doped (BaS) barium sulfide[END_REF][START_REF] Linneweber | Exchange couplings for Mn ions in CdTe: validity of spin models for dilute magnetic II-VI semiconductors[END_REF][START_REF] Shahjahan | Numerical study of magnetic states and magnetic properties of transition metal doped II-VI oxide semiconductors[END_REF][START_REF] Salam | First principles study of structural, elastic and electronic structural properties of strontium chalcogenides[END_REF]Ghosh et al. 2019a). Among these materials, the SrX strontium chalcogenides are considered as potential DMS candidates according to the theoretical predictions of electronic structures, half-metallic behavior and the existence of ferromagnetism in vanadium (V)-and chromium (Cr)-substituted SrS, SrSe and SrTe (Doumi et al. 2015a¸d). Recently, [START_REF] Lin | Magnetism in the p-type Monolayer II-VI semiconductors SrS and SrSe[END_REF] have used first-principle calculations to predict that the hole doping can induce ferromagnetism in SrS and SrSe monolayer sheets.

The objective of this study is to investigate the structural, electronic and half-metallic ferromagnetic properties of Ti-substituted SrS such as Sr 1-x Ti x S compound at concentration x = 0.125. We have used in our calculations the generalized gradient approximation functional (GGA-WC) [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF] and the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential [START_REF] Tran | Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential[END_REF][START_REF] Becke | A simple effective potential for exchange[END_REF] based on full-potential linearized augmented plane-wave method within first-principle approaches of density functional theory [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF].

The SrS belongs to the II-VI strontium chalcogenides, crystallizing in the rock-salt NaCl (B1) phase. The conventional structure of SrS has space group of ( Fm3m ) No. 225, which Sr and S atoms are situated at the (0, 0, 0) and (0.5, 0.5, 0.5) sites, respectively. The Sr 1-x Ti x S (1 × 1 × 2) supercell of 16 atoms with concentration x = 0.125 is created by substituting of Sr atom by the Ti impurity at (0, 0, 0) position. We have obtained the tetragonal structure of Sr 0.875 Ti 0.125 S with space group of (P4/mmm) No. 123. The supercell of Sr 0.875 Ti 0.125 S is described by a structure closed to the stoichiometric ordered structure in order to avoid side effects as defects on this ordered structure. We have employed the fullpotential linearized augmented plane-wave (FP-LAPW) method based on density functional theory (DFT) [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF] as implemented in the WIEN2 K package [START_REF] Blaha | WIEN2K: an augmented plane wave and local orbitals program for calculating crystal properties[END_REF] to determine the structural, electronic and halfmetallic ferromagnetic properties of Sr 0.875 Ti 0.125 S. The augmented plane wave (APW) method supposes that the crystalline potential is replaced by its spherical average in the Muffin-tin spheres and it is constant in the interstitial zone between the spheres. However, the full-potential FP-LAPW improves the APW method, which provides continuity of potential at the surfaces of Muffin-tin spheres [START_REF] Singh | Planewaves, Pseudopotentials, and the LAPW method[END_REF].

The structural properties are calculated by using of the generalized gradient approximation functional (GGA-WC) [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF], whereas the electronic structures and magnetic moments are calculated with Tran-Blaha modified Becke-Johnson (TB-mBJ) exchange potential combined with local density correlation potential [START_REF] Tran | Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential[END_REF][START_REF] Becke | A simple effective potential for exchange[END_REF]. The average radii of Muffin-tin spheres of the Sr, S and Ti atoms have been taken in condition that the spheres do not overlap. The cutoff of -6 Ry is employed to describe the separation between the valence and the core states. In the interstitial site of crystal, the wave functions have expanded to plane waves by means of a cut-off K max = 9.0/R MT . The K max defines the average radius of the muffin-tin sphere and the K max represents the size of the largest K vector in the plane wave. We have performed the Brillouin-zone sampling by the use of the Monkhorst-Pack mesh [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF][START_REF] Pack | Special points for Brillouin-zone integrations"-a reply[END_REF] of (4 × 4 × 4) k-points for SrS and (4 × 4 × 2) k-points for Sr 0.875 Ti 0.125 S. The Self-consistent was obtained when the total energy converges towards 0.1 mRy.

Results and discussions

Structural properties

We have employed the empirical Murnaghan equation of state [START_REF] Murnaghan | The compressibility of media under extreme pressures[END_REF] to adjust the curves of the total energies as a function of the volumes in order to calculate the structural parameters. The results of the lattice constants (a), bulk modules (B) and their pressure derivatives (B') for the SrS and the Sr 0.875 Ti 0.125 S with other experimental [START_REF] Syassen | Pressure-induced structural transition in SrS[END_REF] and theoretical (Bhattacharjee and Chattopadhyaya 2017a;[START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF] data are given in Table 1. The structural parameters a and B of binary SrS have good concordance with the experimental data [START_REF] Syassen | Pressure-induced structural transition in SrS[END_REF] and they are close to the theoretical calculations (Bhattacharjee and Chattopadhyaya 2017a;[START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF] found by the same GGA-WC potential. This is due to the better performance of the GGA-WC for calculating structural properties of solids [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF]Doumi et al. 2015b, c;[START_REF] Sajjad | The half-metallic ferromagnetism character in Be1 -xVxY (Y = Se and Te) alloys: An ab initio study[END_REF]. The lattice constant of Sr 0.875 Ti 0.125 S decreased due to the difference between the Ti and Sr ionic radii, meaning that the Sr 0.875 Ti 0.125 S is harder compared to the SrS. We haven't found any experimental and theoretical studies on the Sr 0.875 Ti 0.125 S in order to compare them with our results.

Electronic structures and half-metallic behavior

The electronic structures are performed by the use of TB-mBJ semi-local exchange-correlation potential due to its performance for calculating band structures [START_REF] Tran | Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential[END_REF][START_REF] Becke | A simple effective potential for exchange[END_REF]. The plots of band structures at the high symmetry points and2, respectively. The compound Sr 0.875 Ti 0.125 S is created from the substituting Ti atom in the supercell of 8 atoms of SrS wide-gap semiconductor. The magnetic Ti atom is placed at Sr cationic site in such a way that the magnetic spins of the 3d-Ti states are injected into SrS, which influence the electronic structures and induce the magnetism in the Sr 0.875 Ti 0.125 S compound. As result, the majority spins become metallic owing to localized electrons of 3d-Ti majority-spin states in the gap, while the minority spins keep semiconductor behavior of SrS because the 3d-Ti empty minority-spin states are located into bottom of conduction band far than Fermi level. Consequently, the Sr 0.875 Ti 0.125 S compound becomes halfmetallic ferromagnetic with spin polarization of 100%. The Fig. 1 shows similar band structures for two spins directions of SrS. The SrS depicts an indirect band gap (E Γ Χ ), which occurs between the valence band maximum (VBM) and the conduction band minimum (CBM) situated at Γ and Χ high symmetry points, respectively. The majority-spin bands of Sr 0.875 Ti 0.125 S compound are metallic due to localized partially filled 3d-Ti majority-spin levels in the gap around Fermi level (E F ). For the minority-spin bands of Sr 0.875 Ti 0.125 S, the valence band minimum is located at the Γ high symmetry point like SrS, whereas the conduction band minimum occurs at Γ high symmetry, which is formed by the 3d-Ti empty anti-bonding states far than E F , generating a direct band gap at Γ high symmetry. Consequently, the SrS shifts from indirect band gap Γ X to direct band gap Γ Γ for Sr 0.875 Ti 0.125 S.

E F Κ W L Λ Γ ∆ X Z W K (
The Sr 0.875 Ti 0.125 S compound has a gap for minority spin, while its majority spin exhibits metallic feature (see Fig. 2). The minority-spin bands of Sr 0.875 Ti 0.125 S are characterized by two important factors; the half-metallic ferromagnetic (HMF) gap (G HMF ) and the half-metallic (HM) gap (G HM ). The first determines the fundamental band gap, whereas the second defines the minimal energy band gap for a spin-flip of minority spin (Doumi et al. 2015a, d;[START_REF] Cherfi | A novel theoretical investigation of electronic structure and half-metallic ferromagnetism in 3d (V)-doped InP for spintronic applications[END_REF]. The HMF and HM gaps features have been observed in the V-and Cr-doped SrS materials such as Sr 0.875 V 0.125 S (Doumi et al. 2015a) and Sr 0.875 Cr 0.125 S (Doumi et al. 2015d). The half-metal gaps are 0.937 and 0.815 eV respectively for Sr 0.875 V 0.125 S and Sr 0.875 Cr 0.125 S, which are located between the valence band maximum and Fermi level (E F ). In distinguish, the d-Ti anti-bonding states of minority spin shift towards low energies, moving the conduction band minimum towards E F and valence band minimum far than E F. Therefore, the half-metal gap of Sr 0.875 Ti 0.125 S changes its position with respect to E F , which occurs between E F and the conduction band minimum. In this case, the half-metal gap of 1.245 eV for Sr 0.875 Ti 0.125 S is better than that of Sr 0.875 V 0.125 S and Sr 0.875 Cr 0.125 S. The wide HM gap makes the Sr 0.875 Ti 0.125 S compound potential candidate for spin-injection applications in semiconductor spintronics. Table 2 summarizes the results of indirect gap (E Γ Χ ) of SrS, and the G HMF and G HM of Sr 0.875 Ti 0.125 S with other theoretical (Bhattacharjee and Chattopadhyaya 2017a, b;[START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF] and experimental [START_REF] Kaneko | New developments in IIa-VIb (alkaline-earth chalcogenide) binary semiconductors[END_REF] values. The indirect gap of 3.59 eV of SrS is in good agreement with theoretical calculations (Bhattacharjee and Chattopadhyaya 2017a, b;[START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF] found with TB-mBJ, and it is better than that of the values of Refs. Bhattacharjee and Chattopadhyaya (2017a, b), [START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF] obtained by the GGA-WC [START_REF] Wu | More accurate generalized gradient approximation for solids[END_REF] and the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] because the TB-mBJ potential is suitable to improve the gaps of band structures with respect to the local density approximation and all forms of the generalized gradient approximation functional (Bhattacharjee and Chattopadhyaya 2017a, b;[START_REF] Tran | Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential[END_REF][START_REF] Chattopadhyaya | Theoretical study of structural, electronic and optical properties of BaxPb1-xS, BaxPb1-xSe and BaxPb1-xTe ternary alloys using FP-LAPW approach[END_REF]. The Fig. 2 revealed that the majority spins are metallic because some bands dominate the Fermi level (E F ), while a gap arises around E F for minority spins. Consequently, the Sr 0.875 Ti 0.125 S compound is a half-metallic ferromagnetic with a spin polarization of 100%. The minority spin bands show that Sr 0.875 Ti 0.125 S compound has a direct HMF gap of 2.844 eV situated at Γ high symmetry point between the VBM and CBM. In addition, the half-metallic gap is defined as the minimum energy gap of a spin excitation with respect to the Fermi level required to create a hole in the valence band maximum or to generate an electron in the [START_REF] Yao | Half-metallic ferromagnetism of zinc-blende CrS and CrP: a first-principles pseudopotential study[END_REF]. In Sr 0.875 Ti 0.125 S minority-spin bands, the minimum energy gap for a spin excitation is located between the conduction band minimum and the Fermi level. Thus, the half-metallic gap of 1.245 eV describes the minimal energy gap of a spin excitation to generate an electron in the conduction band minimum (Doumi et al. 2015a). The Fig. 3 shows the contribution of partial and total densities of states (DOS) of majority-spin and minority-spin states of Sr 0.875 Ti 0.125 S with respect to the Fermi level (E F ). In the Sr 0.875 Ti 0.125 S supercell, the Ti atom is situated in the crystal field originated from the octahedral environment of S ions, leading to split of 3d-Ti states into two levels such as the three low-lying t 2g d xy , d xz , and d yz states and two high-lying e g d z 2 and d x 2 -y 2 states (Doumi et al. 2015a, d). From the partial DOS of 3d-Ti states, we have depicted that the t 2g are lower than that e g states, confirming that Ti atom is positioned in the octahedral surrounding. The densities of states of two spin directions of Sr 0.875 Ti 0.125 S are symmetric in the range of -4.2 to -1.6 eV of valence bands, which are originated from the main contributions of p states of S atom and by the small contributions of the 3d-Ti and p-Sr states. Also, the DOS of the two spin channels are mainly dominated by the 3d-Ti states in the range of 1.3 to 4 eV of bottom of conduction bands. From the total DOS, we can clearly see that the density of states are metallic for majority spins and they have a band gap for minority spins, leading to a half-metallic behavior for Sr 0.875 Ti 0.125 S compound with a spin polarization of 100%.

Magnetic moments

In the Sr 0.875 Ti 0.125 S compound, the Ti atom is substituted at the Sr site, which contributes two electrons to S atoms. Therefore, the 3d states of Ti ion become partially occupied with two electrons, which generate a total magnetic moment of 2 μ B (μ B is the Bohr magneton). This value of total magnetic moment is mainly formed by the partial magnetic moment of Ti atom and minor local magnetic moments are induced in the non magnetic Sr and S sites due to the strong p-d exchange interaction between the p-S and 3d-Ti levels. The crystal field of surrounding S ions split d-Ti states into t 2g and e g states, which create bonding and anti-bonding states. For minority-spin states, a large p-d exchange interaction is responsible for the separation of bonding and anti-bonding states owing to the strong p-d hybridization between p-S and d-Ti states. This mechanism is responsible for attribution of different electrons densities in Sr, S and Ti atoms of Sr 0.875 Ti 0.125 S compound, and hence the ferromagnetism emerges in this system [START_REF] Saini | Emergence of half metallicity in Cr-doped GaP dilute magnetic semiconductor compound within solubility limit[END_REF].

Comparing to our result of total magnetic moment of 2 μ B of Sr 0.875 Ti 0.125 S, the calculations of Sr 0.875 V 0.125 S (Doumi et al. 2015a) and Sr 0.875 Cr 0.125 S (Doumi et al. 2015d) show total magnetic moments of 3 and 4 μ B arising from the partially occupied d-V and d-Cr states, respectively. The d states are partially filled by three electrons for V and four electrons for Cr because the V and Cr ions have one and two extra electrons than Ti. Consequently, the unpaired electrons of d states such as two for Ti, three for V and four for Cr ions generate total magnetic moments of 2, 3 and 4 μ B for Sr 0.875 Ti 0.125 S, Sr 0.875 V 0.125 S and Sr 0.875 Cr 0.125 S compounds, respectively.

The partial and total magnetic moments of relevant atoms and in the interstitial site of Sr 0.875 Ti 0.125 S material are given in Table 3. The positive magnetic moments of Ti, Sr and S atoms describe the ferromagnetic interaction between the magnetic spins of these atoms. In conclusion, the results of magnetic moments confirm the ferromagnetic feature of Sr 0.875 Ti 0.125 S compound.

Conclusion

The structural, electronic and ferromagnetic properties of SrS and Sr 0.875 Ti 0.125 S compound were investigated by employing the first-principle calculations of density functional theory. The results of structural parameters with GGA-WC and band gap with TB-mBJ of SrS are in good agreement with other theoretical calculations using the same exchange potentials. The lattice parameter of Sr 0.875 Ti 0.125 S is lower than that of SrS owing to the difference between Sr and Ti ionic radii. The electronic structures of Sr 0.875 Ti 0.125 S exhibit a half-metallic ferromagnetic behavior with a half-metallic gap of 1.245 and spin polarization of 100%. The ferromagnetic nature of Sr 0.875 Ti 0.125 S is confirmed by the ferromagnetic interaction between magnetic moments of Ti, Sr and S atoms. The integral total magnetic

Fig. 1

 1 Fig. 1 Spin-polarized band structures for SrS. a Majority spins (up) and b Minority spins (dn). (Fermi level (E F ) is set to zero)

Fig. 2

 2 Fig. 2 Spin-polarized band structures for Sr 0.875 Ti 0.125 S. a Majority spins (up) and b Minority spins (dn). (Fermi level (E F ) is set to zero)

Fig. 3

 3 Fig. 3 Spin-polarized total and partial densities of states (DOS) of Sr 0.875 Ti 0.125 S. (Fermi level (E F ) is set to zero)

Table 1

 1 Computed lattice constants (a), bulk modules (B) and their pressure derivatives (B') for SrS and Sr 0.875 Ti 0.125 S compounds

	Compound	a (Å)	B (GPa)	B'	Method
	This work
	SrS	5.973	52.90	4.36	GGA-WC
	Sr 0.875 Ti 0.125 S	5.873	55.78	4.32	GGA-WC
	Other calculations
	SrS	5.976 a	52.54 a	4.335 a	GGA-WC
		5.976 b	53.049 b	4.734 b	GGA-WC
		6.024 c	58.0 c		Experimental
	a Bhattacharjee and Chattopadhyaya (2017a)
	b Debnath et al. (2018)
	c Syassen (1985)

Table 2

 2 Computed indirect band gap (E Γ Χ ) for SrS, half-metallic ferromagnetic gap (G HMF ) and halfmetallic gap (G HM ) of minority-spin bands for Sr 0.875 Ti 0.125 S

	Compound	G HMF (eV)	G HM (eV)	E Γ Χ (eV)	Method
	This work
	SrS			3.62	TB-mBJ
	Sr 0.875 Ti 0.125 S	2.844	1.245		TB-mBJ
	Other calculations
	SrS			2.303 a , 2.305 b	GGA-WC
				2.3 c	GGA-PBE
				3.798 a , 3.686 b 3.798 c	TB-mBJ
				4.32 d	Experimental

a

Bhattacharjee and Chattopadhyaya (2017a)

b

[START_REF] Debnath | Tuning of electronic band gaps and optoelectronic properties of binary strontium chalcogenides by means of doping of magnesium atom (s)-a first principles based theoretical initiative with mBJ, B3LYP and WC-GGA functionals[END_REF]

c

Bhattacharjee and Chattopadhyaya (2017b)

d

[START_REF] Kaneko | New developments in IIa-VIb (alkaline-earth chalcogenide) binary semiconductors[END_REF]

Table 3

 3 Computed total and partial magnetic moments of Ti, Sr and S atoms and in the interstitial site (in Bohr magneton μ B ) for Sr 0.875 Ti 0.125 S B and the wide half-metallic gap suggest that the Sr 0.875 Ti 0.125 S is a right half-metal. Therefore, the Sr 0.875 Ti 0.125 S is promising material for possible spin-injection applications in semiconductor spintronics.

	Compound	Total (μ B )	Ti (μ B )	Sr (μ B )	S (μ B )	Interstitial (μ B )
	Sr 0.875 Ti 0.125 S	2	1.656	0.003	0.008	0.334