Ambre Ribardière

Julia Centanni

Arnaud Dano

Jérôme Coudret

Claire Daguin-Thiébaut

Céline Houbin

Elise Kerdoncuff

Ségolène Jambut

Richard Cordaux

Thomas Broquet
email: thomas.broquet@sb-roscoff.fr

Claire Daguin-Thiebaut

Female-biased sex ratios unrelated to Wolbachia infection in European species of the Jaera albifrons complex (marine isopods)

Keywords: female biased sex ratio, Wolbachia endosymbionts, marine crustaceans, Jaera albifrons

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Introduction

Sex allocation theory predicts that frequency-dependent selection favours equal investments into male and female offspring [START_REF] Fisher | The genetical theory of natural selection: a complete variorum edition[END_REF]. If production costs are equivalent between offspring of the two sexes then the number of males and the number of females in a population are expected to be balanced. However, there are many constraints to the regulation of this equilibrium [START_REF] West | Constraints in the evolution of sex ratio adjustment[END_REF], and biased sex ratios are common in nature [START_REF] Hardy | Sex ratios, Concepts and research methods[END_REF]. Causes of departure from Fisher's null model include in particular local mate competition between individuals for access to sexual partners (e.g. [START_REF] Werren | Sex ratio evolution under local mate competition in a parasitic wasp[END_REF], meiotic drive on sex chromosomes (reviewed in [START_REF] Jaenike | Sex chromosome meiotic drive[END_REF] and cytoplasmic sex ratio distorters [START_REF] Cordaux | The impact of endosymbionts on the evolution of host sexdetermination mechanisms[END_REF][START_REF] Taylor | Evolutionary consequences of cytoplasmic sex ratio distorters[END_REF]) such as Wolbachia.

Wolbachia is a group of cytoplasmic endosymbiotic bacteria found in a large number of invertebrates [START_REF] Werren | Wolbachia: master manipulators of invertebrate biology[END_REF]. It is predominantly transmitted via female gametes [START_REF] Werren | Wolbachia: master manipulators of invertebrate biology[END_REF] and it often promotes its transmission by interfering in the process of reproduction of its host [START_REF] Rousset | Wolbachiae ndosymbionts responsible for various alterations of sexuality in arthropods[END_REF][START_REF] Werren | Biology of wolbachia[END_REF]. Wolbachia is notably known to be involved in the conversion of genetic males into functional phenotypic neo-females, a process called feminization [START_REF] Bouchon | Feminizing Wolbachia and the evolution of sex determination in isopods[END_REF][START_REF] Cordaux | Evolutionary Significance of Wolbachia-to-Animal Horizontal Gene Transfer: Female Sex Determination and the f Element in the Isopod Armadillidium vulgare[END_REF][START_REF] Rigaud | Wolbachia infection in the terrestrial isopod Oniscus asellus: sex ratio distortion and effect on fecundity[END_REF][START_REF] Werren | Wolbachia: master manipulators of invertebrate biology[END_REF]. It can also induce parthenogenesis in several otherwise sexually reproducing species, or specifically kill the male offspring of infected females [START_REF] Hurst | Male-killing Wolbachia in two species of insect[END_REF]. Therefore, in absence of compensatory mechanisms (which would be readily favoured by sex ratio selection), Wolbachia can cause an increase in the proportion of females in infected populations.

In addition, these bacteria can also play a role in speciation by inducing interspecific cytoplasmic incompatibilities [START_REF] Rousset | Wolbachiae ndosymbionts responsible for various alterations of sexuality in arthropods[END_REF][START_REF] Telschow | Wolbachia-induced unidirectional cytoplasmic incompatibility and speciation: mainland-island model[END_REF][START_REF] Werren | Biology of wolbachia[END_REF][START_REF] Werren | Wolbachia: master manipulators of invertebrate biology[END_REF]. For example, studies on wasps of the genus Nasonia [START_REF] Bordenstein | Wolbachia-induced incompatibility precedes other hybrid incompatibilities in Nasonia[END_REF][START_REF] Bordenstein | Effects of A and B Wolbachia and host genotype on interspecies cytoplasmic incompatibility in Nasonia[END_REF][START_REF] Bordenstein | Bidirectional incompatibility among divergent Wolbachia and incompatibility level differences among closely related Wolbachia in Nasonia[END_REF] have shown that Wolbachia can cause reproductive isolation between two closely related species by bidirectional incompatibility of two strain types. Furthermore, Wolbachia can also drive the reinforcement of behavioural isolation between infected and uninfected species [START_REF] Jaenike | Asymmetrical reinforcement and Wolbachia infection in Drosophila[END_REF].

Although Wolbachia is essentially maternally transmitted, its capacity to move into new hosts via horizontal transmission has promoted its spread to different invertebrate clades [START_REF] Cordaux | Wolbachia infection in crustaceans: novel hosts and potential routes for horizontal transmission[END_REF][START_REF] Duron | Arthropods and inherited bacteria: from counting the symbionts to understanding how symbionts count[END_REF][START_REF] Turelli | Rapid Global Spread of wRi-like Wolbachia across Multiple Drosophila[END_REF][START_REF] Vavre | Phylogenetic evidence for horizontal transmission of Wolbachia in host-parasitoid associations[END_REF]. Wolbachia is particularly frequent in arthropods, infecting mites [START_REF] Breeuwer | Wolbachia: intracellular manipulators of mite reproduction[END_REF], crustaceans [START_REF] Bouchon | Evidence for widespread Wolbachia infection in isopod crustaceans: molecular identification and host feminization[END_REF] and insects [START_REF] Werren | Wolbachia infection frequencies in insects: evidence of a global equilibrium?[END_REF]. Although the prevalence of Wolbachia is difficult to quantify, it was estimated to infect 20 to 60% of insects [START_REF] Sazama | Incidence of Wolbachia in aquatic insects[END_REF][START_REF] Werren | Wolbachia infection frequencies in insects: evidence of a global equilibrium?[END_REF]. Few species of marine crustaceans are known to be infected: Wolbachia was found in a handful of marine amphipods, isopods, and cirripedes [START_REF] Bouchon | Evidence for widespread Wolbachia infection in isopod crustaceans: molecular identification and host feminization[END_REF][START_REF] Cordaux | Widespread Wolbachia infection in terrestrial isopods and other crustaceans[END_REF].

In this study, we are interested in the Jaera albifrons complex, a group of small (2-5 mm) marine isopods where there are both (i) observations of strongly female-biased sex ratios and (ii) variations in the level of reproductive isolation between species. The Jaera albifrons complex includes five intertidal species that live on the shores of the temperate and cold waters of the North-Atlantic Ocean [START_REF] Bocquet | Recherches sur le polymorphisme naturel des Jaera Marina (Fabr.)(Isopodes Asellotes) : Essai de systématique évolutive[END_REF][START_REF] Bocquet | La speciation des Jaera albifrons. Etat présent des connaissances et des problèmes[END_REF][START_REF] Naylor | Habitat Preferences and Interspersion of Species within Superspecies Jaera Albifrons Leach (Crustacea . Isopoda)[END_REF]. Three of these species (J. albifrons, J. praehirsuta, and J. ischiosetosa) have an amphi-atlantic distribution, while the other two species are restricted either to the North-American East coast (J. posthirsuta) or the European coasts (J. forsmani).

Nearly all demographic analyses of the four species that are found on the European coasts have reported female-biased sex ratios in adults in natural populations (Cléret, 1966b;[START_REF] Jaźdźewski | Ecology and Biology of Species of the j aEra Albifrons Group (Isopoda Asellota) in the Bay of Puck, Polish Baltic Sea[END_REF][START_REF] Jones | Breeding and bionomics of the British members of the Jaera albifrons group of species (Isopoda: Asellota)[END_REF][START_REF] Naylor | Quantitative ecological distribution of the Jaera albifrons group of species in the Baltic[END_REF][START_REF] Naylor | Observations on the British species of Jaera (Isopoda: Asellota)[END_REF][START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF][START_REF] Solignac | Demographic Aspects of Interspecific Hybridization[END_REF] with male proportions locally as low as 0.07 (J. ischiosetosa in the UK, [START_REF] Jones | Breeding and bionomics of the British members of the Jaera albifrons group of species (Isopoda: Asellota)[END_REF]. To our knowledge no such estimations have been reported for J. posthirsuta.

Two studies examined the sex ratio in offspring reared in the laboratory (with low mortality, sex ratio at maturity is informative of sex-ratio at birth). In contradiction with the results from adults in natural populations, these two studies found unbiased offspring sex ratio in species J. albifrons (Cléret, 1966b;[START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF], J. forsmani, and J. ischiosetosa (Cléret, 1966b). Solignac (1978, p. 89) also reported that he did not observe a biased sex ratio in young adults reared in the laboratory. However, the figures reported by this author suggest a slight excess of females at birth in J. ischiosetosa (r=0.42, binomial test p=0.02, from table 4.1 in Solignac 1978: 89). In addition, a notable exception concerns a population from Normandy, France, where a subset of J. praehirsuta females were shown to produce an excess of female offspring (Cléret, 1966a). The author concluded that a genetic factor lethal for the males was segregating in this population.

Observations of even numbers of males and females at birth are compatible with the genetic sex-determination system that was identified for the four European species (males ZZ, females ZW1W2, [START_REF] Staiger | Cytological demonstration of female heterogamety in isopods[END_REF][START_REF] Staiger | Les chromosomes de la super-espèce Jaera marina (F.) et de quelques autres Janiridae (Isopodes Asellotes)[END_REF], again to our knowledge this system

has not yet been confirmed in J. posthirsuta). Accordingly, all four European species of the Jaera albifrons group have long been proven to be strictly gonochoric (no sex-change, which is a strategy found in some other isopods, as reviewed in [START_REF] Policansky | Sex change in plants and animals[END_REF][START_REF] Poore | Global diversity of marine isopods (except Asellota and Crustacean symbionts)[END_REF]. Moreover, genetic sex determination has been confirmed through repeated karyotype studies [START_REF] Lécher | Cytogénétique de l'hybridation expérimentale et naturelle chez l'isopode Jaera (albifrons) syei Bocquet[END_REF][START_REF] Lécher | Caryologie et taxinomie de Jaera albifrons (crustacé, isopode), populations des côtes Bretonnes[END_REF]) and molecular linkage maps (AFLP: [START_REF] Mifsud | The genetic basis of speciation in the Jaera albifrons species group of intertidal isopods[END_REF], and RAD-seq genotyping: Ribardière et al. unpublished). One study also found sex determination in species J. albifrons to be unaffected by strong variations in temperature conditions [START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF].

Several ideas have been put forward to explain why adult females are systematically more abundant than adult males in natural populations. First, males are smaller and less conspicuous than females, meaning that they could simply be missed during collection in the field (Cléret, 1966b).

However, sex ratio investigations based on a careful dedicated sampling consistently found female biases [START_REF] Jaźdźewski | Ecology and Biology of Species of the j aEra Albifrons Group (Isopoda Asellota) in the Bay of Puck, Polish Baltic Sea[END_REF][START_REF] Naylor | Observations on the British species of Jaera (Isopoda: Asellota)[END_REF][START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF]. Second, it has been suggested that males have a shorter lifespan than females [START_REF] Jaźdźewski | Ecology and Biology of Species of the j aEra Albifrons Group (Isopoda Asellota) in the Bay of Puck, Polish Baltic Sea[END_REF][START_REF] Solignac | Demographic Aspects of Interspecific Hybridization[END_REF][START_REF] Steele | The biology of Jaera spp.(Crustacea, Isopoda) in the northwestern Atlantic. 1. Jaera ischiosetosa[END_REF], although the only data available, obtained in laboratory conditions, suggest otherwise [START_REF] Solignac | Demographic Aspects of Interspecific Hybridization[END_REF], J. albifrons and J. ischiosetosa males both had better survival than females). Finally, strong sex ratio biases could be driven by sex ratio distorters such as mitochondrial variants or cytoplasmic microorganisms (reviewed in [START_REF] Duron | The diversity of reproductive parasites among arthropods: Wolbachia do not walk alone[END_REF][START_REF] Duron | Arthropods and inherited bacteria: from counting the symbionts to understanding how symbionts count[END_REF][START_REF] Jaenike | Sex chromosome meiotic drive[END_REF][START_REF] Werren | Wolbachia: master manipulators of invertebrate biology[END_REF]. In isopods in particular, Wolbachia is the most frequent inherited bacterium that can manipulate reproduction of its host. Yet an effect of sex ratio distorters would be visible not only at the adult stage in natural populations but also in young adults reared in the laboratory. Such effects have not yet been observed (Cléret, 1966b;[START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF] except in some specific populations of J. praehirsuta (Cléret, 1966a) and perhaps J. ischiosetosa [START_REF] Solignac | Nature, déterminisme et origine des mécanismes d'isolement dans le complexe Jaera albifrons (Isopodes, Asellotes)[END_REF].

In summary, sex ratio biases in the Jaera albifrons complex are intriguing, and the causes of female excesses in adults and perhaps in some cases in offspring are unresolved. In addition to sex ratio biases, another reason to investigate whether Wolbachia endosymbionts are present in the Jaera albifrons complex is that they could play a role in reproductive isolation. Species in this complex are isolated by a combination of ecological isolation, sexual isolation, and genetic incompatibilities (reviewed in [START_REF] Mifsud | The genetic basis of speciation in the Jaera albifrons species group of intertidal isopods[END_REF][START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF][START_REF] Solignac | Isolating mechanisms and modalities of speciation in the Jaera albifrons species complex (Crustacea, Isopoda)[END_REF] so that they generally coexist without hybridization. But in some instances, local populations undergo hybridization (Solignac, 1969a, b;[START_REF] Solignac | Nature, déterminisme et origine des mécanismes d'isolement dans le complexe Jaera albifrons (Isopodes, Asellotes)[END_REF]. Species J. albifrons and J. praehirsuta are particularly interesting in this respect as replicate mixed populations show varying degrees of introgressive hybridization [START_REF] Ribardière | Isolement reproductif et architecture génomique de la différenciation chez deux espèces du complexe Jaera albifrons (isopodes marins) -Etude de populations mixtes présentant des niveaux d'isolement interspécifique contrastés[END_REF][START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF]. It would be important to know if Wolbachia may play any role in this variation. Interestingly, the J. praehirsuta broods showing aberrant sex ratios as observed by Cléret (1966a) came from a population with introgressive hybridization between J. praehirsuta and J. albifrons (Solignac 1969a, Ribardière et al. 2017). [START_REF] Bouchon | Evidence for widespread Wolbachia infection in isopod crustaceans: molecular identification and host feminization[END_REF] found no Wolbachia in J. albifrons, but it could have been due to sampling insufficiency (three individuals were tested). Recently, [START_REF] Wenzel | Microbiome composition within a sympatric species complex of intertidal isopods (Jaera albifrons)[END_REF] performed an analysis of the microbiome of the four European species of the Jaera albifrons complex using bacterial 16S rDNA sequencing in populations from Scotland. None of the bacterial 16S sequences that they identified belonged to the Wolbachia group. Here we had two objectives. Our first objective was to compare sex ratios at birth vs adult stage in the four European species of the Jaera albifrons complex. For that, we reanalysed data from a large number of broods reared in the laboratory as part of an ongoing project on speciation in the Jaera albifrons complex [START_REF] Ribardière | Isolement reproductif et architecture génomique de la différenciation chez deux espèces du complexe Jaera albifrons (isopodes marins) -Etude de populations mixtes présentant des niveaux d'isolement interspécifique contrastés[END_REF]. Although adult sex ratios have been well documented by others, for comparison with our brood data we also estimated sex ratios in natural populations using a dedicated sampling effort in the region where most of our brood data came from. Our second objective was to screen all five species of the complex with a targeted assay for the presence of Wolbachia endosymbionts using several gene targets and populations of various geographic origins. We focused particularly on the J. albifrons / J. praehirsuta pair in regions with varying degrees of reproductive isolation. With this, our overarching goal was to test whether Wolbachia may or may not be involved in sex ratio biases and reproductive isolation in the Jaera albifrons complex.

Methods

Study system and general strategy

The five species of the Jaera albifrons group are found mid-to upper-shore, where they can locally show some differential preferences in substrate (under pebbles or on seaweeds), position in the intertidal zone, salinity, and exposure [START_REF] Bocquet | Recherches sur le polymorphisme naturel des Jaera Marina (Fabr.)(Isopodes Asellotes) : Essai de systématique évolutive[END_REF][START_REF] Jones | Effects of salinity on the survival of the Jaera albifrons Leach group of species (Crustacea: Isopoda)[END_REF][START_REF] Naylor | Habitat Preferences and Interspersion of Species within Superspecies Jaera Albifrons Leach (Crustacea . Isopoda)[END_REF]. Individuals from the different species have the same general morphology, with males (2-3 mm) smaller than females (5 mm). Males from the five species differ only in the number and position of spines and setae that they use to court females [START_REF] Bocquet | Recherches sur le polymorphisme naturel des Jaera Marina (Fabr.)(Isopodes Asellotes) : Essai de systématique évolutive[END_REF], and females cannot be distinguished based on morphology. Development is direct, there is no pelagic larval stage, and offspring measure ca. 0.5 mm when they are released. Individuals become sexually mature within 4 to 5 weeks and can then be sexed based on praeoperculum differentiation (e.g. [START_REF] Solignac | Analyse expérimentale et variabilité de l'hybridation interspécifique dans le complexe d'espèces affines Jaera albifrons (crustacé isopode)[END_REF]. We define sex ratio (r) as the proportion of males in a sample.

Our sex ratio analyses are based on two classes of data. First, we determined the sex of adult individuals sampled in natural populations. These analyses, based on a small number of sampling sites, were used to check if our study populations conform to the well-described sex ratio biases reported in the literature. Second, we used a much larger dataset to analyse sex ratios in broods reared in the laboratory. When survival in the laboratory is high (see results and discussion), then the sex ratio measured at least five weeks after birth is a good proxy for the sex ratio at birth, which has been less well documented than adult sex ratios and brings complementary information. In addition to sex ratio analyses we used a multi-target molecular approach to search for Wolbachia in a large number of individuals from different species and geographic origins.

Adult sex ratio in natural populations

Because males of all four European species of the Jaera albifrons group are smaller than females and can thus be more easily missed during field sampling, we selected four sampling sites/habitats (Table 1) where we carefully sampled all individuals in a delimited area. In our primary study region (Brittany, western France), species J. albifrons, J. ischiosetosa, and J. forsmani live under rocks, while J. praehirsuta is found mainly on Fucus vesiculosus and Ascophyllum nodosum seaweeds [START_REF] Bocquet | Recherches sur le polymorphisme naturel des Jaera Marina (Fabr.)(Isopodes Asellotes) : Essai de systématique évolutive[END_REF], Ribardière et al. 2017). To estimate sex ratio we thus sampled all individuals found on a limited number of rocks or algae in each site (5-15 pebbles or stones of different sizes or a random sample of algae typically contained within 10 m 2 , depending on local density). All individuals were brought back to the laboratory where they were sexed and males were identified based on their secondary sexual characters. The four sampling site/habitat combinations were previously known to shelter a single species, meaning that there would be little risk that the females (for which species cannot be identified from morphological characters) could belong to two different species (see results). Binomial tests were used to test for a departure from even sex ratio (all analyses performed in R, R Core Team, 2016).

Sex ratio in broods reared in the laboratory.

Raising individuals from birth to sexual maturity in the laboratory gives access to sex ratio under controlled conditions, and, if survival has been high enough (see results), to estimate sex ratio at birth. In the course of an ongoing project on the Jaera albifrons complex we raised a large number of broods in standardized laboratory conditions. These data were used to count the number of males and females in each brood and compare sex ratio estimates across broods and populations. Rearing conditions are detailed in supplementary material.

All broods were produced by females maintained in the laboratory, but within two different experimental frameworks. First, we reared broods produced by females that came directly from the field. This is possible because females store sperm and can thus produce offspring in the laboratory in absence of males (each female was kept in an separate well and was thus never in contact with males). Within this framework, we have no information on the father of the offspring, the age of the mother, and little a priori information, if any, on the female's species (this was later determined from the morphological characters borne by male offspring of each female).

Second, we reared broods produced through controlled experimental crosses featuring parents that had been reared in captivity. In that case both the mother and father of each brood are known and identified, and the parents were virgin before the experiment (i.e. in most cases we analysed their first brood, or we knew how many broods were produced before). Such controlled crosses were run only with J. albifrons and J. praehirsuta. Since we did not detect any significant difference in sex ratio between the broods produced by females caught in the wild vs those from controlled experimental crosses (supplementary material Figure S1), we did not separate these two types of data for sex ratio analyses (unless stated otherwise).

Overall, we used data from 375 broods reared in the laboratory between 2013 and 2016. A large fraction of the data came from a region of France where we have been studying natural hybridization between J. albifrons and J. praehirsuta (region Normandy, [START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF]. These data (243 broods) were analysed separately (next section). The other fraction corresponds to 132 broods from four species that were originally sampled in region Brittany, where no hybridization has been detected [START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF]: J. albifrons (n = 72 broods), J. praehirsuta (n = 25), J. ischiosetosa (n = 12), and J. forsmani (n = 23). We used these data to estimate brood sex ratio and compare it with adult sex ratio estimated in natural populations from Brittany (as described above).

Sex ratio in case of introgressive hybridization between J. albifrons and J. praehirsuta

Two analyses were performed to investigate the consequences of introgressive hybridization on sex ratio in J. albifrons and J. praehirsuta. First, we compared the sex ratio in broods from each species in regions Brittany (no hybridization) vs Normandy (hybridization). For that we used broods from females sampled in the wild (J. albifrons in Brittany, n = 34 broods, Normandy, n = 22; J. praehirsuta in Brittany, n = 15, Normandy, n = 39). Second, we compared the sex ratio in broods resulting from controlled intra-and inter-specific crosses. For that we used intra-specific J. albifrons crosses (n = 131 broods), intra-specific J. praehirsuta crosses (n = 134), first-generation hybrids (n = 17), and backcrosses (F1 hybrid females crossed with either J. albifrons or J. praehirsuta males, n = 58). Generalized linear models with a logit link function and binomial errors were used to test for differences in sex ratio amongst categories.

PCR detection of Wolbachia

The presence of Wolbachia endosymbionts can be detected by PCR amplification using host DNA extracts (potentially containing co-extracted DNA from endosymbionts) with Wolbachia specific primers [START_REF] Simoes | Wolbachia detection: an assessment of standard PCR protocols[END_REF].

A total of 817 individuals belonging to the five species of the Jaera albifrons complex, including 321 females and 496 males, were tested. We used samples from 9 populations from France, 2 populations from Quebec (Canada), 1 population from the Isles of Scilly (United-Kingdom), and 1 population from Tromsø (Norway), as detailed in supplementary Table S1. The samples from France included J. albifrons and J. praehirsuta from sites with and without hybridization, as described above for the sex ratio analyses. In addition, because the presence of Wolbachia has been investigated in few marine species, we also analysed 34 individuals of 6 marine isopod and amphipod species (Table S2).

Total DNA (from Jaera spp. and potential Wolbachia sp.) was extracted using either a NucleoSpin Tissue kit (Macherey-Nagel) or a salt protocol (detailed in supplementary material). To check the general quality of DNA extracts, we used a subset of 90 randomly chosen individuals to amplify 24 Jaera albifrons microsatellites [START_REF] Ribardière | Microsatellite markers for the Jaera albifrons species complex (marine isopods)[END_REF]. In addition, a DNA extract from Oniscus asellus (common woodlouse) known to be infected by Wolbachia was used as positive control to check if Wolbachia was correctly detected by the different methods described below.

Three different loci were targeted to increase our detection ability and confidence (details in Table 2). First, we used the wsp gene (Wolbachia surface protein), which encodes a major cell surface coat protein and is one of the most common targets for Wolbachia PCR detection [START_REF] Braig | Cloning and Characterization of a Gene Encoding the Major Surface Protein of the Bacterial EndosymbiontWolbachia pipientis[END_REF][START_REF] Zhou | Phylogeny and PCR-based classification of Wolbachia strains using wsp gene sequences[END_REF]. We used four distinct wsp protocols (wsp-1, wsp-2, wsp-L, and wsp-J, Table 2) with three different pairs of primers, including newly developed primers JwspF 5' CGTTCGTTTACAATACAACGGTGA 3' and JwspR 5' AACCGAAGTAACGAGCTCCA 3'. These new primers were designed from a Wolbachia sequence that we obtained in this study from two individuals of the Jaera albifrons complex (see results). Second, the ribosomal 16S-2 marker was also chosen because it is a universal barcoding locus for bacteria identification that is expected to produce a strong signal [START_REF] Simoes | Wolbachia detection: an assessment of standard PCR protocols[END_REF]. Finally, we also used the fbpA primers that amplify a region of the fructose-bisphosphate aldolase gene [START_REF] Baldo | Multilocus sequence typing system for the endosymbiont Wolbachia pipientis[END_REF]. This method lacks specificity but it can be more sensitive [START_REF] Simoes | Wolbachia detection: an assessment of standard PCR protocols[END_REF]. Polymerase Chain Reaction (PCR) conditions are detailed in Tables S3 andS4. PCR products were electrophoresed in 1.5% agarose gels stained with ethidium bromide and visualized under UV light. Some individuals were tested several times with different primers, bringing the total number of tests to 1692 (or 2445 when including individuals tested several times with the same protocol). A re-amplification based on a subset of PCR products for the wsp gene was also performed for 423 samples to enhance detection ability. Details of analysed samples (primers used, species, sex, origin) are given in supplementary materials (Table S1).

The large majority of these tests produced no amplified products (see results), but all amplifications resulting in a single band around the expected size were directly sequenced. Overall, 98 PCR products (in addition to the positive control) were sent for sequencing to Eurofins Genomics (Ebersberg, Germany). The sequences obtained were assembled and checked with the CodonCode Nucleotide database using BLAST (Basic Local Alignment Search Tool, NCBI).

To determine the phylogenetic position of the Jaera-specific Wolbachia sequence that we found in this study (see results), we built a neighbour-joining phylogeny using a sample of related sequences deposited in GenBank (with a particular focus on strains found in marine crustaceans, [START_REF] Cordaux | Widespread Wolbachia infection in terrestrial isopods and other crustaceans[END_REF].

RESULTS

Adult sex ratio in natural populations

Between 64 and 115 adult individuals were sampled in each of the four populations chosen for sex ratio estimates. Three out of the four European species of the Jaera albifrons group presented a female-biased sex ratio (Table 1 and Figure 1), with J. ischiosetosa showing the strongest bias (20 males, 94 females, binomial test p-value < 0.001). J. albifrons and J. forsmani were also characterized by a significant excess of females, while J. praehirsuta did not reveal any bias (30 males, 34 females, p = 0.71). All males sampled in a site/habitat combination belonged to a single species, except for three J. praehirsuta males that were found in the J. albifrons sample (that is, under rocks), in agreement with the level of habitat overlap between these two species in the region sampled [START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF]. These males were removed from all analyses but there is a small possibility that some of the females used to estimate the J. albifrons sex ratio were in fact J. praehirsuta (see discussion).

Sex ratio in broods reared in the laboratory.

Using 132 broods from four species that were originally sampled in the French region Brittany (i.e. where species are reproductively isolated), we raised 1349 progenies (Table 4). The average survival rate in the laboratory (that is, from birth to the date when each individual was sexed) was 77.5%, meaning that 1046 individuals could be sexed successfully across the four species. We observed a strong bias towards females in J. ischiosetosa (r = 0.29, binomial test p-value < 0.001). The other three species did not show any significant sex bias (Table 3 and Figure 1). The distribution of sex ratio per brood is shown in supplementary material Figure S2.

In the case of J. ischiosetosa, we raised 130 offspring from 12 broods with a survival rate of 85%. With 20 dead out of 130 individuals, sex-biased mortality cannot account for the sex ratio bias that we observed. Even if all dead individuals were males, then the sex ratio at birth would still be significantly biased (52 theoretical males, 78 females, binomial test p-value = 0.028). The same reasoning applies to all four species and we consider laboratory sex ratio as a good proxy for sex ratio at birth (Figure 1).

Sex ratio in case of introgressive hybridization between J. albifrons and J. praehirsuta

First, we compared the sex ratio in broods produced by females J. albifrons and J. praehirsuta in Brittany (no hybridization) and Normandy (introgressive hybridization). For this analysis we had the sex of 798 individuals (out of 1070 offspring isolated) and found no significant bias in sex ratio within each species in each region (all binomial test p-values > 0.05) and no significant differences across species and regions (GLM p-values > 0.05 for both factors and their interaction). These results are shown in supplementary material Figure S3.

We came to the same conclusion when analysing broods from experimental crosses featuring J. albifrons, J. praehirsuta, F1 hybrids, and backcross hybrids (Figure 2, 1902 sexed individuals out of 2744 reared offspring). Again we found no significant deviation from even sex ratio within each class (all binomial test p-values > 0.05) and no significant difference between classes (GLM p-value > 0.05).

PCR detection of Wolbachia

We searched for Wolbachia in the Jaera albifrons complex by conducting 2,445 tests involving 817 individuals (see supplementary material, Table S1). Overall, 731 individuals were tested more than once, among which 232 have been tested with at least 2 different protocols. None of our negative controls showed amplification signals, whilst our positive control (DNA extract from a Wolbachia-infected woodlouse) was correctly and constantly amplified by all methods. Our Jaera microsatellite markers amplified well, suggesting that there was no obvious problem with the general quality of the DNA extraction protocols (linked e.g. with PCR inhibitors).

With the fbpA and 16S-2 protocols no amplification of expected size was detected for any of the tested individuals (n=47 individuals tested for each marker). The wsp-1 and wsp-2 protocols produced a weak amplification signal for 6% (n= 6 out of 95) and 3% (n=8 out of 252) of the tested individuals, respectively. Re-amplification attempts for 272 of these PCR products (details in Table S1) did not produce any amplicon corresponding to a Wolbachia sequence. By contrast, the sequence obtained with our positive control hit the expected Wolbachia sequence (accession number

AJ276601.1).

The more sensitive wsp-L protocol, tested on 615 individuals, produced 62 PCR products showing a single band with amplification size close to that expected. These 62 PCR products were directly sequenced, and two of them were identical and showed >99% identity with the top Wolbachia wsp hit in Genbank (3 differences out of 540 nucleotides). We deposited this new Wolbachia sequence in Genbank with accession number MH121068. Here again, re-amplification attempts of 102 individuals did not lead to the discovery of further Wolbachia hosts.

The new primers specifically designed from the Wolbachia sequence that we isolated as described above were used with 129 individuals (protocol wsp-J). None of them produced amplification signals (including the two individuals that were previously found to be infected with Wolbachia). Re-amplification of a subset of 40 PCR products did not yield any additional result.

Finally, we used the newly designed primers to re-amplify 53 PCR products previously amplified with the wsp-L primers (chosen because they produced a signal of expected size). Twelve of these re-amplifications produced a strong band at the expected size, and eight of them appeared to be Wolbachia sequences, including the 2 individuals previously detected as positives. All eight individuals shared the same Wolbachia sequence (accession number MH121068). They were all females: 1 supposed J. praehirsuta (because found on seaweeds in region Brittany, [START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF], and 4 J. albifrons, 2 J. praehirsuta and 1 female of unknown species from French region Normandy.

The phylogeny that we built using closely related sequences indicated that our discovered Wolbachia strain belongs to the Rug group of Wolbachia, within the B supergroup (Figure 3, Cordaux et al., 2001). Interestingly, the Rug group happens to be the main Wolbachia group known to include strains infecting marine arthropods [START_REF] Cordaux | Widespread Wolbachia infection in terrestrial isopods and other crustaceans[END_REF].

Finally, the presence of Wolbachia was not detected in any of the other isopod and amphipod species that were tested in this study (Table 3).

DISCUSSION

Unexpectedly, the four European species of the Jaera albifrons complex followed one of three distinct sex ratio regimes. Two species (J. albifrons and J. forsmani) were found to have balanced sex ratios at birth (as deduced from the sex ratio in young adults and low mortality in laboratory conditions), but a female-biased adult sex ratio in natural populations (Table 1 and Figure 1). This result confirms previous findings for these two species (Cléret, 1966b;[START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF].

More surprising results came from J. ischiosetosa, which showed a strong bias towards females both at the offspring and adult stages, and J. praehirsuta, which showed no bias at any stage (Table 1 and Figure 1).

The case of J. ischiosetosa is the most interesting, as it indicates that there is a mechanism in this species that drives a female-biased sex ratio very early in the life cycle. Moreover, this result disagrees with the only other report of sex ratio at birth in this species (Cléret, 1966b), suggesting that there is variation in the sex ratio at birth between populations, or through time (see also Solignac, 1978, p. 89). This points towards endogenous factors such as mitochondrial variants, meiotic drive sex ratio distorters, or reproductive parasites. Here we have performed an intensive survey for the presence of Wolbachia endosymbionts, which were an obvious candidate for reproductive manipulation in isopods showing an excess of females. We did not find any trace of Wolbachia in 77 J. ischiosetosa individuals using several different protocols that targeted the wsp region (Table S1). This targeted assay involved the mothers of seven of the 12 broods that were analysed for that species (brood sex ratio from 0.08 to 0.43, Figures 1 andS2). We conclude from these observations that Wolbachia is either absent or has a low prevalence in J. ischiosetosa and thus cannot be accountable for the excess of females observed in this species.

Other endosymbiotic manipulators of sex (such as bacteria from groups Cardinium, Rickettsia, and Spiroplasma, or microsporidia) could be involved. In their microbiome study, [START_REF] Wenzel | Microbiome composition within a sympatric species complex of intertidal isopods (Jaera albifrons)[END_REF] found evidence for the presence of Rickettsiacea in J. ischiosetosa females (and not in males), but in minute quantities (1.16% of the 16s sequences obtained for a sample of J. ischiosetosa females, M. Wenzel pers. comm.). The best way to test for this hypothesis will be to estimate sex ratio in broods reared in laboratory with and without broad-spectrum antibiotic treatment [START_REF] Bordenstein | Wolbachia-induced incompatibility precedes other hybrid incompatibilities in Nasonia[END_REF][START_REF] Breeuwer | Wolbachia: intracellular manipulators of mite reproduction[END_REF]. Alternatively, the hypothesis of sex ratio distorters borne on the sex chromosomes could be tested using controlled crossing experiments. Finally, although it seems an unlikely hypothesis (ruled out in species J. albifrons, [START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF], an effect of the environment on sex determination could be further checked specifically in species J. ischiosetosa.

The three other species analysed here did not show any bias in sex ratio at birth, but two of them (J. albifrons and J. forsmani) had female-biased sex ratios at the adult stage in natural populations, in agreement with all previous sex ratio reports for these two species. Hence for these two species at least, males must have lower survival than females in nature. This sex-linked difference in survival is not seen in the laboratory [START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF]Solignac, 1978, p. 89), which suggests that it depends on environmental conditions encountered in natural settings.

Excluding environmental effects on sex determination [START_REF] Piertney | Sex ratio variation in the intertidal isopod, Jaera albifrons[END_REF], the earlier mortality of males could be due to a difference in costly activities between males and females. In particular, one can imagine that males wander more than females to search for potential mates.

Moving from one shelter to another could be a risky business in species that live under pebbles and stones on coarse sand or gravel. This sex-specific behaviour could also be linked to a more general pattern of male-biased dispersal. In both cases, it could result in a higher mortality of males seen in nature but not in the laboratory. Mortality risks associated with sex-specific behaviours such as mate seeking or dispersal have been found to impact adult sex ratios in other animal groups (e.g. reviewed in [START_REF] Donald | Adult sex ratios in wild bird populations[END_REF][START_REF] Székely | Adult sex ratio variation: implications for breeding system evolution[END_REF]. Interestingly, J. ischiosetosa not only showed a female bias at birth but it was also the species with the strongest bias in adults from natural populations in this study (Table 1 and Figure 1) and other works (e.g. [START_REF] Jones | Breeding and bionomics of the British members of the Jaera albifrons group of species (Isopoda: Asellota)[END_REF]). Here we found that the bias in adults (r=0.18) was significantly stronger than in offspring reared in the laboratory (r=0.29, binomial proportions test p=0.03), suggesting that the factor that causes the female bias at the adult stage in other species may also be acting in J. ischiosetosa.

Finally, the fourth species studied here (J. praehirsuta) did not show any bias at the offspring and adult stages (Table 1 and Figure 1). The most obvious difference between this species and others is that it lives essentially on seaweeds (in our study area). It is thus possible that the male-biased mortality discussed above is habitat-dependent. Since ecological conditions vary widely across the distribution of all species of the Jaera albifrons complex, one straightforward way to test this hypothesis is to compare sex ratios in populations in different ecological contexts (especially different substrate types where one can hypothesize that exploratory movements are more or less facilitated). For instance, while J. praehirsuta is dwelling on seaweeds in our study area (French region Brittany), it is found under pebbles in other areas such as region Normandy. There, this species is found mixed with J. albifrons, with which it hybridizes [START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF], making it more difficult to estimate specific sex ratios in nature (also because females cannot be identified unless they are kept in the laboratory until they produce offspring and these offspring are reared for long enough that the males can be identified based on their secondary sexual traits). Nonetheless, the available data for such mixed populations occupying stones and pebbles strongly suggest that the sex ratio is female-biased in J. praehirsuta (e.g. 61 males for 138 females of a mixed J. albifrons/J. praehirsuta population, [START_REF] Ribardière | Geographically distinct patterns of reproductive isolation and hybridization in two sympatric species of the Jaera albifrons complex (marine isopods)[END_REF], and the same type of observation was made in populations from the UK where there seems to be no hybridization, M. Wenzel pers. comm.). Hence it seems that the adult female excess is dependent upon ecological conditions, at least in species J. praehirsuta.

Our Wolbachia survey involved a large number of individuals (n=817) from the five species of the Jaera albifrons complex sampled in different geographic regions and tested with a variety of protocols (11 protocols involving 5 different primer pairs). This effort led to the discovery of a new Wolbachia strain (wsp sequence deposited in Genbank under accession number MH121068) that was detected in J. albifrons and J. praehirsuta. This adds these two species to the limited list of marine crustaceans known to be infected by Wolbachia [START_REF] Bouchon | Evidence for widespread Wolbachia infection in isopod crustaceans: molecular identification and host feminization[END_REF][START_REF] Cordaux | Widespread Wolbachia infection in terrestrial isopods and other crustaceans[END_REF].

Our negative controls always came back negative, no Wolbachia gene amplification was carried in our laboratory before this study, and the new sequence that we found was different from that of our positive control and related to other known marine arthropod-infecting strains. Yet this result must be considered with caution, as this new Wolbachia sequence was amplified from only eight DNA extracts, nearly only using a double amplification protocol (wsp-L followed by wsp-J, see Tables 2 andS1), and could not be replicated using simple-amplification protocols (even using newly designed primers). We conclude that Wolbachia bacteria are present in at least two species of the Jaera albifrons complex in French regions Brittany and Normandy, but most likely with a very small prevalence (both in terms of the number of individuals infected and the concentration of bacteria within infected individuals). This finding consolidates the simultaneous result obtained by [START_REF] Wenzel | Microbiome composition within a sympatric species complex of intertidal isopods (Jaera albifrons)[END_REF], where bacterial 16s rDNA sequencing did not reveal any trace of Wolbachia in Scottish populations from the four European species of the Jaera albifrons complex.

Taken together, our observations that i) Wolbachia was not found in the only population showing a female-biased sex ratio at birth (J. ischiosetosa), ii) it was detected in very few individuals in other species, and iii) a single strain was detected in species J. albifrons and J. praehirsuta based Tables Table 1. Number of males and females in natural populations of the four European species of the Jaera albifrons complex. Departure from an even sex ratio (proportion of males) was tested using a binomial test within each site (* p< 0.05, ** p<0.01, *** p<0.001). S3 andS4). Grey bars indicate 95% binomial confidence intervals around the observed sex ratio. All species but J.

Species

praehirsuta were found to be significantly female-biased at the adult stage in natural populations (sample sizes in tables 1 and 6). Only J. ischiosetosa presented a female-biased sex ratio in young adults reared in the laboratory (a good proxy for the sex ratio at birth when mortality is low, as in this study). sequence that we found in J. albifrons and J. praehirsuta is highlighted. Other Wolbachia sequences identified in non-marine hosts are represented in grey. The strain that we used as a positive control is identified with an asterisk. The definition of the "RUG" group follows [START_REF] Cordaux | Widespread Wolbachia infection in terrestrial isopods and other crustaceans[END_REF].

Bootstrap support inferred from 1000 replicates is shown when it is greater than 50%. Sexe-ratio (proportion de mâles)

Figure 1 :

 1 Figure1: Sex ratio (proportion males) in the four European species of the Jaera albifrons complex.

Figure 2 :

 2 Figure 2: Distribution of offspring sex ratio per brood in Jaera albifrons (n=131 broods), J. praehirsuta

Figure 3 :

 3 Figure 3: Neighbour joining tree of some Supergroup-B Wolbachia sequences, based on Kimura 2-

  Figure 1

Table 2 .

 2 Primers used in the six protocols tested in this study. Protocols Wsp-1 and -2 use the same primers with different PCR conditions (see supplementary Tables

		Site	Habitat Coordinates	Males Females Sex ratio
	J. albifrons	Lingoz	rocks 48°39ʹ12.31"N	15	49	0.23***
			3°57ʹ0.43ʺW
	J. praehirsuta Lingoz	algae 48°39ʹ12.31"N	30	34	0.47
			3°57ʹ0.43ʺW
	J. ischiosetosa Pempoul	rocks 48°41'16.9"N	20	94	0.18***
			3°57'27.6"W
	J. forsmani	Pointe Grande Grève	rocks 48°42'22.6"N	41	74	0.36**
			3°58'18.7"W

Acknowledgements

We thank Marius Wenzel for sharing ideas and submitted or unpublished results. We thank Elsa Pabion for her help with the maintenance of animals in the laboratory, and Olivier Timsit and Caroline Broudin for helping us collecting individuals in the field. This work benefited from access to the Biogenouest genomic platform at Station Biologique de Roscoff and was supported by the French Agence Nationale de la Recherche (grant ANR-13-JSV7-0001-01 to TB).

Research data

All data used for the brood sex ratio analyses presented in this article will be available on Dryad upon acceptance

on the wsp locus (and in regions with and without hybridization) lead to the conclusion that Wolbachia bacteria most likely have no feminization or male killing effects in the Jaera albifrons complex, and that they have also no bearing upon reproductive isolation between species within the complex. Sex ratio analyses prompted us to hypothesize that some other sex ratio distorter is acting in a subset of populations (such as the J. ischiosetosa population studied here, and perhaps the J. praehirsuta population reported by Cléret 1966b), and that the ubiquitous excess of adult females in nature may be due to substrate-dependent male-biased mortality.

Author contributions

Conceptualization and methodology: AR, CD-T, RC, and TB. Sex ratio data acquisition: AR, JC, JeC, CH, EK, SJ and TB. Molecular investigations: AR, JC, AD, and CD-T. Data curation: AR, JC, and TB. Writingoriginal draft: AR, CD-T and TB. Writing -review and editing: AR, CD-T, RC, and TB. Supervision, project administration and funding acquisition: TB. All authors have approved the final article.

Declarations of interest: none

Supplementary material

Rearing conditions

Lab conditions were as follows. All individuals were reared individually in 6-well plates (one individual per well, each well has a diameter of approximately 3.5 cm and contains ca. 10 mL of 3 μm-filtered seawater). Following the conditions described in Bocquet (Bocquet 1953: 212-213), each well contained small pieces of green algae (Enteromorpha sp.) and a small piece of elm leaf (elm leaves provide shelter and food, and have been used successfully for several decades by previous researchers). The plates were kept in thermostat cabinets at 17°C with an 11h/13h light/obscurity cycle and seawater was changed once a week (together with algae and leaves when needed).

Embryos develop in a marsupium (brood pouch containing typically around 15 offspring) until the female releases them. At that stage the offspring measure approximately half a millimetre and closely resemble the adults (direct development, no pelagic larval stage). Offspring were isolated one by one within a few days after their release and reared individually in the same conditions as the adults, with two exceptions: seawater was not changed during the first week, and elm leaves were added only during the second week. Under these conditions, individuals can usually be sexed around the age of 4 to 5 weeks but all experiments lasted for a longer time. Since each individual was reared individually (and thus the number of offspring per brood was counted) the survival rate could be estimated for each brood.

Salt extraction protocol

Entire individuals were mashed then tissues were soaked into 500 µl of NaCl buffer (containing 1% SDS, 150 mM NaCl, 1 mM EDTA and 20 mM TRIS) with 1 mg of proteinase-K (Macherey-Nagel, Duren, Germany) and incubated at 56°C during 3h30 under agitation at 120 rpm. 0.5 mg of ribonuclease A (Macherey-Nagel, Duren, Germany) was added to each tube and incubated for 20 min under agitation at room temperature. 200 µl of NaCl buffer (5M) was then added and the tubes were centrifuged at 16,000 g for 10 min. Supernatant was pipeted and mix to an equal volume of cold isopropanol and stored overnight at -20 °C. After centrifugation at 16,000 g for 15 min, the DNA pellet was washed with 500 µl of 80% cold ethanol and with 70% cold ethanol subsequently. DNA pellets were then dried and again suspended in 100 µl of TE 0.1X. . praehirsuta (47 and 87). Each brood was reared in the lab until indiv were sexed, but the brood came either from a female sampled in the wild ("Natural") or fr female that was itself born and reared in the lab until maturity and used in a controlled cro experiment ("Experimental"). This figure combines data from the two regions where J. alb J. praehirsuta were studied (Brittany and Normandy, see maintext). where the two species are reproductively isolated (Brittany, n albifrons = 34 broods, n praehirsuta = 15) and in a region with introgressive hybridization (Normandy, n albifrons = 22, n praehirsuta = 39). These broods were produced by mothers sampled from natural populations (i.e. uncontrolled mating, fathers unknown). [START_REF] Bocquet | Recherches sur le polymorphisme naturel des Jaera Marina (Fabr.)(Isopodes Asellotes) : Essai de systématique évolutive[END_REF] Recherches sur le polymorphisme naturel des Jaera Marina (Fabr.)(Isopodes Asellotes) : Essai de systématique évolutive. Centre national de la recherche scientifique.


Renzo E Navas
email: renzo.navas@imt-atlantique.fr

Laurent Toutain
email: laurent.toutain@imt-atlantique.fr

LATe: A Lightweight Authenticated Time Synchronization Protocol for IoT

Keywords: time, synchronization, secure, authenticated, protocol design, ietf, formal method, verification, Scyther

Time synchronization is fundamental for a wide variety of IoT applications. Time is also fundamental to provide security services such as certificates or OAuth-token validation. Having a secure source of time is a fundamental problem, and the first step to provide other services for applications. There is no standardized lightweight and secure time synchronization solution suitable for IoT. We propose a Lightweight Authenticated Time (LATe) Synchronization Protocol. Our proposal is based on IETF open standards and is agnostic to underlying communication technologies. We also provide a computer-aided proof of the security claims using the Scyther tool.

I. INTRODUCTION

Synchronized time is needed in several Internet of Things (IoT) applications, from time-stamping of sensor data to the establishment of authenticated secure channels. However, many time synchronization protocols are not secure: they assume existing secured communication channels. The establishment of secure channels, in most cases, assumes a secure source of time e.g. to assure freshness of transactions. This creates a circular dependence problem that has already been spotted on the standardization community. Time protocols are being designed to overcome this, such as the Internet Engineering Task Force (IETF) work-in-progress Network Time Security (NTS) [START_REF] Franke | Network Time Security for the Network Time Protocol[END_REF]. However, NTS or secure-versions of existing time protocols, are not designed for the IoT constraints, e.g. in NTS the simplest time synchronization takes at least six messages, including a Datagram Transport Layer Security (DTLS) handshake, and the format of each of the message is not optimized in terms of size.

Our study provides a solution for a coarse-grained secure time synchronization problem in a lightweight manner, i.e. requiring the least possible messages at the synchronizing node, minimizing the number of cryptographic operations and optimizing the traffic sent on the network. It is not a goal to provide precise time synchronization; we also use open standards to encode the messages, and the proposed protocol is agnostic to the underlying technologies (e.g. a packet switched network), guaranteeing end-to-end security properties among heterogeneous networks and in the presence of untrusted nodes.

The rest of this paper is structured as follows: Section II briefly discuss state of the art and related work on time syn-chronization. Sections III-IV describe our proposed solution. Section V presents a formal proof of the protocol and Section VI analyses possible attacks. On Section VII we compare our solution against different protocols. Finally, Sections VIII-IX offer some perspectives and a final conclusion for our work.

II. STATE OF THE ART FOR SECURE TIME SYNCHRONIZATION

Prominent standardized time synchronization protocols are the IETF Network Time Protocol (NTP) [START_REF] Burbank | Network Time Protocol Version 4: Protocol and Algorithms Specification[END_REF], IEEE 1588 Precision-Time-Protocol (PTP), and satellite-based Global Navigation Satellite System (GNSS). An excellent overview of time synchronization protocols over packet-switched networks is done in [START_REF] Lévesque | A Survey of Clock Synchronization Over Packet-Switched Networks[END_REF], it also analyses security threats and solutions. Moussa et al. [START_REF] Moussa | Security Assessment of Time Synchronization Mechanisms for the Smart Grid[END_REF] focus on time synchronization for the smart grid and its security requirements. Current standardized solutions to achieve secure time synchronization include Annex K of PTP, and authenticated mode of NTP. Design of secure time synchronization protocols from scratch is an active topic, such as the aforementioned Network Time Security for NTP [START_REF] Franke | Network Time Security for the Network Time Protocol[END_REF]. The IETF has released a document [START_REF] Mizrahi | Security Requirements of Time Protocols in Packet Switched Networks[END_REF] that specifies the threats and security requirements for future time protocols. Current standardization efforts do not deal with the specific constraints of IoT, and focus mostly on precision and robustness at the expense of increased requirements at the node and network. A standard suitable for IoT is an unsolved problem.

Outside standardization bodies the secure time synchronization problem has been prominently studied for wirelesssensor-networks (WSN) [START_REF] Ganeriwal | Secure Time Synchronization in Sensor Networks[END_REF][7][8] [START_REF] Benzaid | An Enhanced Secure Pairwise Broadcast Time Synchronization Protocol in Wireless Sensor Networks[END_REF]. WSN share many of IoT constraints. However the aforementioned solutions either require already loose time synchronization, use asymmetric cryptography, or they use nonces but requiring more messages exchanges than our proposed solution. On Section VII we will compare them to our proposed solution. To our knowledge none of the proposed lightweight time synchronization methods have been formally proved with computer-aided cryptographic tools.

III. LIGHTWEIGHT AUTHENTICATED TIME (LATE) SYNCHRONIZATION PROTOCOL: SEMANTICS

A. Background and justification

The non-cryptographic part of the proposed protocol can be traced to Cristian's time synchronization protocol [START_REF] Cristian | Probabilistic clock synchronization[END_REF].

However, the problem that needs to be solved concurrently is related to security and is how to assure the freshness and authentication of an exchange of information in the absence of time-awareness. The concept of authenticated and fresh exchange of information is generalized by Bauer et al. [START_REF] Bauer | A key distribution protocol using event markers[END_REF] with the concept of event-markers.

The proposed solution is intended to be the simplest possible to the secure time synchronization problem: namely using an event-marker for a two-message protocol; but our contribution also has the added value of using open standards suitable for the IoT and presenting a computer-aided security proof.

B. LATe Synchronization Protocol Entities

The nonce-based Lightweight Authenticated Time (LATe) Synchronization Protocol is our solution that allows to securely bootstrap time. The protocol involves two entities. Time Client (TC): the entity that attempts to update its local time representation. Time Server (TS): the entity that provides its local time representation. TC and TS have valid pre-shared cryptographic material. The messages are transported over unsecured communication channels.

C. Protocol Goals

Functional Goal: Provide an entity, i.e. the Time Client, with the time representation from a trusted party, i.e. the Time Server.

Security Goals: (1) Data Authentication: The time representation must be authenticated, data origin-authentication: coming from the intended party. (2) Data Integrity: The time representation must be integrity-protected, an alteration of the original information must be detected. (3) Freshness: The time representation must be fresh, it corresponds to the current run of the protocol and not replayed from an earlier run.

Design Goals: (1) Lightweight: Minimize the number of messages to exchange; minimize the cryptographic operations to execute (in terms of complexity, that will be equivalent to minimize CPU processing power-time needed at the entities); minimize the information to exchange and provide a compactrepresentation of the information over the channel 1 . (2) Agnostic to underlying communication technologies: The protocol messages should be easily transported over any underlying communication technology (wired, wireless, Ethernet, IP, non-IP, datagram oriented, etc) 2 . (3) Cryptographic agility: The crypto-primitives used by the protocol must be easily interchangeable, e.g. ready for future algorithms, or if an attack is discovered in current one easily to replace with other.

Non-goal: Precise, fine-grained, time synchronization its not a goal. e.g. not synchronize at the order of µs but rather at ms (will be determined by round-trip delay time of the network).

D. The LATe Synchronization Protocol

The Lightweight Authenticated Time (LATe) Synchronization Protocol consists of two messages exchanged between a Time Client (TC) and a Time Server (TS). K CS is a symmetric 1 Not a semantic goal but strictly related with the syntax of the protocol. 2 Idem footnote 1.

Time Client

K CS Time Server K CS fresh N C ID C , N C N C , T ime S , M AC K CS (N C , T ime S ) sync T ime
protocol LATe synchronization protocol

E. Time Synchronization Calculation

The Time Client (TC) will have to run the following steps to achieve authenticated time synchronization:

1) Timestamp when it sends Message 1: T 1 .

2) Validate Message 2:

• of the protocols that are in use on the Internet (e.g. IP and TCP). We use the CBOR and COSE IETF standards to encode the LATe messages. The Concise Binary Object Representation (CBOR) [START_REF] Bormann | Concise Binary Object Representation (CBOR)[END_REF] is a binary data format inspired by JSON and provides a compact representation of most common data types used at Internet standards; it also has the explicit goals of a lightweight implementation in terms of code and RAM needed. For the security services of the messages we use CBOR Object Signing and Encryption (COSE) [START_REF] Schaad | CBOR Object Signing and Encryption (COSE)[END_REF]. COSE describes how to create and process encryption, signatures and message authentication codes using CBOR for serialization. Security using COSE is at the application-layer of the network it is also referred as object security, the security properties can be maintained end-to-end (even if different technologies are used at lower layers, and -untrusted-intermediate nodes are involved) and can be set on a per-message basis (as opposed to session oriented security, e.g. IPSec, D-TLS).

B. LATe Message Encodings

The protocol consists of two messages encoded with CBOR. COSE is used to cryptographically protect the second message. We define two new CBOR objects: TIC Information and TOC Response. Those objects are CBOR Maps which consist of key-value pairs of information. Additionally, to give semantic meaning to the objects without relying on external information we assign a CBOR Tag to each of the objects. CBOR Tag values range between ±65536, and are registered on the Internet Assigned Numbers Authority, tags on the 1-23 range take one byte when encoded -but all are allocated-; tags in the 24-255 range take two bytes: we chose values in this range.

1) Message 1 -TIC Information: The message will consist of a new CBOR MAP TIC Information as defined on Table I, we propose the CBOR Tag 59 to describe a TIC Information object. About the nonce generation: Nonce must be at least 64-bits and cryptographically secure randomness is needed, a pseudo-random number generator may be used if the seed has sufficient entropy, for details see [START_REF] Crocker | Randomness Requirements for Security[END_REF]. The Key-ID is an opaque identifier of the key to be used by the server, it is the equivalent of the client's identity. The Alg field allows cryptoagility, some recommended algorithms are HMAC w/SHA-256 truncated to 64 bits (using a 256-bit pre-shared-key), AES-CBC-MAC or AES-CMAC (for both, 128-bit key will suffice). Listing 3: TOC Information on CBOR diagnostic notation.

V. FORMAL METHOD VERIFICATION USING SCYTHER A. Security protocols verification

There are currently two main approaches to verify security protocols: the provable security and the formal method approach. Provable security defines a rigorous framework to define and prove (theorem-proof ) cryptographic properties from a mathematical point of view, proving a protocol secure is hard on the provable security approach, and although there is criticism to this approach [START_REF] Koblitz | Another look at "provable security[END_REF] it is still regarded as the most sound proof possible for a protocol. The formal method approach proposes a simpler model to describe an analyze cryptographic protocols, by abstracting basic properties (e.g: encryption), it assumes perfect cryptography (e.g. the cryptoprimitives can not be broken), and the attacker capabilities need to be modeled also (and restricted), then logical flaws can be found on such model. Several formal methods exists; the most known is the Burrows-Abadi-Needham (BAN) logic or logic of beliefs, and is deprecated: flaws have been found on protocols that have been proved secure on the BAN logic.

State-of-the-art approaches include the automatic falsification or verification of protocols with computer-aided tools like: Coq, CertiCrypt, EasyCrypt and CryptoVerif, all these aimed at achieve or help to manually achieve computational security -a subset of provable security-, in which the proof of security is reduced to the computational infeasibility of solving some mathematical problems for an adversary e.g. semi-prime factorization-(these methods cannot find particular attacks just prove they exist); on the other hand, tools like ProVerif, Scyther, and Tamarin are all three on a higher abstraction level (formal methods assuming a particular attacker model, e.g. the Dolev-Yao and perfect cryptography), they provide a weaker proof than a computational security one, but is easier to model complex cryptosystems.

B. The Scyther tool and a formal proof of LATe

The choice of the formal proof method for this paper is using the Scyther tool [START_REF] Cremers | The Scyther Tool: Automatic Verification of Security Protocols[END_REF]. The reasoning behind is its simplicity to model cryptosystems, the attacker model found adequate to our setting, and the possibility to find concrete attacks. Scyther assumes perfect (or black-box) cryptography: the cryptoprimitives can not be broken. Another important assumption is the Dolev-Yao adversary model [START_REF] Dolev | On the security of public key protocols[END_REF]. In Dolev-Yao an adversary has complete control over the communication channel: it can eavesdrop, intercept; modify, delete, and insert any message; the adversary is a legitimate user of the network.

To prove LATe security claims using the Scyther tool and its model we needed notably two additional tasks not straightforward: (1) express a message authentication code (MAC) function (the primitive does not exist); (2) express properly the security-authentication goals claimed.

To represent a MAC function over message m we use two primitives: Enc k (m) symmetric encryption of message m using key k, and a non-cryptographic hash function H(m) (a hash function on Scyter is a one-way-function and known to every agent); then to obtain the keyed M AC k (m) of a message m we chose to encrypt-then-hash as follows H(Enc k (m)), the captured semantical meaning is that only an agent in possession of the key k will be able to produce this one-way function over m.

Regarding the modeling of the authentication and freshness claims, Scyther offers the check of secrecy of a variable m, and the following notions of authentication: aliveness, weak agreement, non-injective agreement and non-injective synchronization. Non-injective synchronization requires that all protocol messages occur in the expected order with the expected values. Proving non-injective synchronization will implicitly include aliveness, weak agreement and non-injective agreement. For a deep analysis on authentication hierarchies and precise definitions see [START_REF] Lowe | A hierarchy of authentication specifications[END_REF] and [START_REF] Cremers | Injective synchronisation: An extension of the authentication hierarchy[END_REF].

1) The LATe Protocol Description: The LATe Synchronization Protocol defined on the Security Protocol Description Language (SPDL) from Scyther is shown on Listing 4.

C. Verify Results

We verify our protocol using Scyther v1.1.13 compiled from source running on OS Ubuntu 17.04 x64. The Scyther settings are: Maximum number of runs 0 (unbounded), Matching type "find all type flaws", advanced parameters were left to default values. The results are the following: all claims have been verified (Nisynch, Niagree, Alive and Weakagree).

Notably we achieved non-injective synchronization for the protocol. Secrecy of the server time was not a goal. The data authentication-integrity claims are satisfied by these results. However, the non-injective synchronization does not guarantee, by itself, the freshness goal of the LATe protocol, we will discuss this on Section VI.

VI. ATTACKS, MITIGATIONS AND REAL-WORLD ISSUES

This section studies possible attacks, its mitigations, and discuss other real-world issues that affect the LATe protocol.

A. Replay-attack, Injectivity and the Freshness claim

Our protocol satisfies the notion of non-injective synchronization, however, this is not enough to claim resilience to replay-attacks. This kind of attacks can be formally ruled out by the notions of injective agreement and injective synchronization. Injective-synchronization is the strongest notion of authentication on the model we are using and -informallyis defined as follows: "an Initiator I considers a protocol injectively synchronizing if the protocol (non-injective) synchronizes and each run of I corresponds to a unique run of Responder R.". The freshness goal of our protocol is strictly related to the injectivity property. The question arises if our protocol satisfies injective synchronization, while we will not make a formal proof, that will involve to prove the LOOP property proposed in [START_REF] Cremers | Injective synchronisation: An extension of the authentication hierarchy[END_REF], but an affirmative response can be done, informally justified by observing that every client run will have a unique and unpredictable Nonce N i which is used in all the messages exchanges with the Server in that run. This guarantees a one-to-one correspondence between all the messages of the same run, and message from others runs will not be able to be injected. On the formal model, a response that matches the nonce on the request, corresponds to the current run of the protocol and not another, it is fresh.

B. Real nonces and pre-play attack

The injective synchronization claim, who assure freshness, relies on the (idealized) properties of the Nonce as being unique and unpredictable. On practice this will not be the case, and the guarantees will be limited by the randomness quality of the nonce generation and by its length (not infinite). Shorter nonces will be more prone to collisions and pre-play attacks e.g. an attacker obtaining all possible nonce responses from the server, will be able to reply these responses -with old values of time-to any future client run of the protocol. To mitigate this risk one straightforward solution is to use longer nonces: e.g. 128-bits (the MAC-tag should also be increased accordingly). To make pre-play attacks infeasible (i.e. an attacker will not be able to obtain responses from the server to inject on the client) we define a stronger version of the protocol that includes the authentication of the first message as shown on Listing 5. Avoiding randomness: Authentication of the first message allows another refinement, the nonce does not need to be random and a counter (i.e. a sequence number) will suffice; the counter value must be stored on persistent memory to avoid being reset by an attacker.

C. Reflection Attack

Another attack can be done if the Time Client also acts as a Time Server: on the original LATe protocol an attacker can use a message generated by the actor in the Time Server role, to be injected in another run of the protocol with the same actor acting as a Time Client. The modified version on Listing 5 does not suffer from this attack. This can also be avoided if the second message includes the recipient ID in the MAC.

D. Symmetric cryptography: server key management issues

The use of symmetric cryptography comes at a burden at the server: it has to keep a copy of all clients' keys. We assume an IoT setting where the constrained node (i.e. Time Client) has a well-known trusted party which it uses for many purposes e.g. an Authorization Server (AS) as defined on IETF Authentication and Authorization for Constrained Environments [START_REF] Seitz | Authentication and Authorization for Constrained Environments (ACE) using the OAuth 2.0 Framework (ACE-OAuth)[END_REF] framework. On such a setting the AS can also act as a Time Server. LATe has also the flexibility to use asymmetric crypto to relieve the Time Server key management issues if fits better the envisioned IoT use case.

E. Protocol refinement

Using the Scyther tool we verified that the same security claims from the original LATe synchronization protocol are hold true in a protocol using a more compact Message 2. By omitting the Nonce in the response, but still using it to calculate the MAC, all the security claims hold still true, but we achieve a non-negligible gain in message size. This can be done only if we assume that a client can run only one concurrent run of the protocol (i.e. when receiving a response it can assume implicitly the nonce to use to calculate the MAC), this assumption is reasonable.

To conclude this section we gather all the mitigations proposed for attack plus this optimization to propose a stronger version of the LATe Synchronization Protocol on Listing 6.

The authentication of the first message that mitigates completely pre-play attacks, can also be used to mitigate Denial-of-Service attacks at the server-side. A version that does not authenticate the first message is still useful on real environments if the users are aware of the pre-play and nonce considerations of section VI-B.

VII. COMPARISON OF TIME SYNC. PROTOCOLS

To define a common baseline to compare several time synchronization protocols we do not take in account underlying layers overhead (e.g. IEEE 802.15.4), but only application data. We also simplify the encoding of the messages, assuming no overhead for metadata, and we assume the following data At the IoT constrained node energy is the scarcest resource and, simplifying, the total bytes to be exchanged is the most important factor to be minimized. LATe minimizes both the number of messages and the total bytes count, needing ≈ 25% less application data exchange than the second-lowest Secure Pairwise Synchronization Protocol (SPS). This percentage will vary if we include other protocols' overhead, or change the application data representation estimations, however LATe will still be strictly inferior. In terms of cryptographic burden LATe is also the lightest, with one MAC operation and one nonce generation.

VIII. PERSPECTIVES

Two main topics have been highlighted on this work: the need for a lightweight secure time synchronization protocol in the context of IoT, and the use of computer-aided tools to prove the security claims of protocols. The first issue needs to be solved, WSN time solutions aim at homogeneous one-hop precise time synchronization, and the end-to-end NTP-based IETF solution is not lightweight in any way; meanwhile IoT nodes need to securely bootstrap time, and we assume realworld implementations are using home-brew solutions. This paper has shown how difficult is to prove secure even a simple protocol like LATe, and this reinforces the need for an open standardized effort that will benefit from the scrutiny of experts and the academic community.

IX. CONCLUSION

Secure time synchronization is a fundamental service for many IoT applications. Notably, security services need a secure source of time. We proposed a nonce-based lightweight authenticated time synchronization protocol, which allows a client to securely bootstrap time with a trusted server. The proposed protocol guarantees end-to-end security among heterogeneous networks. We provided a specification of the protocol using state-of-the-art IETF standards suitable for IoT. We used the computer-aided tool Scyther to prove some security claims of our protocol on a formal model.

Fig. 1 .

 1 Fig. 1. LATe Synchonization Protocol Diagram. K CS is a symmetric preshared key between the Time Client (TC) and the Time Server (TS). ID C is the identity representation of T C. N C is a nonce generated by T C.

4 )

 4 Verify nonce N C on Message 2 matches N C sent on Message 1. (Freshness) • Verify data authentication and integrity: C Calculates M AC K CS (N C , T ime S ) and compares with the received value on Message 2. 3) Calculate Round Trip Time (RTT) as RT T = T 2 -T 1 , where T 2 is the local time of T C when performing this calculation. Set the internal time representation T C as T C = T ime S + RT T 2 , the associated uncertainty is ± RT T 2 IV. LATE SYNCHRONIZATION PROTOCOL: SYNTAX A. IETF standards: CBOR and COSE The Internet Engineering Task Force (IETF) is an open standards organization that has developed and published many

Listing 4 :

 4 ,R,I,Na); recv_2(R,I,Na,T,H1({Na,T}k(I,R)));#encrypt-then-hash claim_I1(I,Nisynch); #encrypt-then-hash claim_I2(I,Niagree); claim_I3(I,Alive); claim_I4(I,Weakagree); } role R # Time Server -Responder { var Na : Nonce; fresh T : TimeStamp; recv_1(I,R,I,Na); send_2(R,I,Na,T,H1({Na,T}k(I,R)));#encrypt-then-hash } } LATe Protocol on Scyther's SPDL

1 :

 1 C → S : IDC , NC , M ACK CS (IDC , NC ) 2 : S → C : NC , T ime, M ACK CS (NC , T ime) Listing 5: LATe w/MAC of first message: N C can be a counter 1 : C → S : IDC , NC , M ACK CS (IDC , NC ) 2 : S → C : T ime, M ACK CS (IDC , NC , T ime) Listing 6: LATe Synchronization Protocol v2

TABLE I CBOR

 I MAP "TIC INFORMATION" OBJECT DEFINITION

	Parameter name	CBOR Key	Value Type	Description
	nonce	4	binary string	A random nonce
				Key-ID is an opaque
	kid	5	binary string	value and identifies the cryptographic key to be
				used in the response
	alg (optional)	6	int	Identifies the crypto-graphic algorithm to be used in the response
				Identifies the intended
	server (optional)	7	string	Server for time syn-chronization
				(Absulute URI)

  The client can explicitly request for a time server, e.g. in cases where the message is dealing with intermediate nodes. On Listing 1 we show a TIC Information object on human-readable CBOR diagnostic notation.Listing 1: TIC Information on CBOR diagnostic notation.The binary representation of the same TIC Information object is found on Listing 2 the size of the message is 19 bytes. The message consists of a new CBOR MAP TOC Information as defined in TableII, we propose the CBOR Tag 60 to describe a TOC Information object. The TOC Information object contains the representation of the time from the server and a nonce.The TOC Response object needs to include a Message Authentication Code, this security service will be provided by COSE using a COSE_Mac0 object. A TOC Response authenticated and wrapped in COSE can be found on Listing 3 on CBOR diagnostic notation.

	{ nonce:h'73616E206C6F7265', kid :h'0001', alg :4/ * HMAC w/SHA-256 truncated to 64 bits * /} D83B # tag(59) (TIC Info.) A3 # map(3) 04 # unsigned(4) (=nonce) 48 # bytes(8) 73616E206C6F7265 # Nonce Value 05 # unsigned(5) (=kid) 42 # bytes(2) 0001 # Key-ID Value 06 # unsigned(6) (=alg) 04 # unsigned(4) Listing 2: TIC Information CBOR object (19 Bytes). 2) Message 2 -TOC Response: {protected: { / * Protected header of COSE_Mac0 Object * / kid: h'0001', alg: 4 / * HMAC w/ SHA-256 truncated to 64 bits * / }, payload : { / * TOC Response CBOR MAP * / time : 1477307841, nonce : h'73616E206C6F7265' }, tag : h'36f5afaf0bab5d43' / * MAC Code * /}

  Timestamp representation is 4 bytes, Node Identity is 2 bytes, a Nonce is 8 bytes, and a MAC is 8 bytes. In E-SPBS[START_REF] Benzaid | An Enhanced Secure Pairwise Broadcast Time Synchronization Protocol in Wireless Sensor Networks[END_REF] an ECDSA signature is 48 bytes; In Guo et al.[START_REF] Guo | A Lightweight Secure Time Synchronization Mechanism for ISO/IEC/IEEE 21451 Sensor Networks[END_REF] we assume an Unspecified Signature being of 16 bytes, and noncryptographic hash 16 bytes; In[START_REF] Ganeriwal | Secure Time Synchronization in Sensor Networks[END_REF][7] syn-ack information of 1 byte. On TableIIIwe can se the results.We also calculated values for NTS Extensions for NTPv4 after Key Establishment[START_REF] Franke | Network Time Security for the Network Time Protocol[END_REF]: 2 Messages; 134 bytes avg. msg. size; 268 total bytes; 2 AEAD (symmetric) operations. And for PTP with Annex-K after Security Association: 4 Messages; 128 bytes avg. msg. size; 512 total bytes; 4 × M AC. Both are one order of magnitude greater due to the calculations taking in account real applicative messages and not simplified encoding.

			TABLE III
	SECURE TIME SYNCHRONIZATION PROTOCOLS BASELINE COMPARISON
			Avg.
	Protocol	Nr. of Msg.	msg. size	Total Bytes	Crypto Ops. at Node
			(Bytes)
	SPS [6]	2	21	41	1 × M AC 1 × N once
	E-SPS [6]	3	17	50	1 × M AC 1 × N once
	TinySeRSync [7]	2	21	42	2 × M AC
	Guo et al. [8]	3	39	116	2 × Signature 1 × M AC
	E-SPBS [9]	3	35	104	1 × Signature 1 × N once
	LATe	2	15	30	1 × M AC 1 × N once
	LATe v2	2	15	30	2 × M AC 1 × N once
	sizes:

ACKNOWLEDGMENT

The authors would like to thank Göran Selander and Ludwig Seitz for its contributions on the design of the LATe protocol and his efforts on the IETF community.


Emersion Project (AO2015) : Nanoscale assembly of non-miscible metals by numerical engineering of their interfaces.

Emersion Project (AO2015): Nanoscale assembly of non-miscible metals by numerical engineering of their interfaces.

Scientific case

Cohesion model using semi-empirical potentials.

Benchmark the interatomic potentials against DFT and experiments.

.

Semi-coherent interfaces

Teaming up thermodynamic and kinetics in immiscible metals to describe interfaces at the nanoscale.

The modeling of the effects related to the existing interactions between defects and interfaces of ultra-thin heterophase layers composed of two metals with positive enthalpy of mixing is the key to improve the understanding of the fundamental mechanisms that modify the physics of these systems in the region surrounding the interface. The objective of the project is to capitalize this knowledge to eventually develop systems with well defined interface characteristics, exceeding the performance of current materials (thermal barriers, coatings, ...). We team up theoretical models, numerical and experimental approaches to solve this problem, to accelerate the discovery of the most promising metal couples, to predict their behavior in deployment conditions (these conditions are intrinsically out-of-equilibrium), and to develop and validate predictive models that ultimately help us designing advanced materials that exploit the metastability of particular architectures and microstructures.

Tight-binding 2nd moment approximation

Assessment of the potential of the chemical elements of the binary systems

U i R = A αβ exp -p αβ r ij d αβ -1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ j≠i α ≠β ∑ α,β = Ag,Cu U i B = ξ αβ 2 exp -2q αβ r ij d αβ -1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ j≠i α ≠β ∑ 0 1 2 3 4 5 6 7 8 ω (THz) Γ Γ X L 0 1 0 0.5 [ζ00] [ζζ0] [ζζζ]

  undergo non-equilibrium phase separation in which domains of two stable phases grow from a thermodynamically unstable homogeneous phase as a result of quenching below a critical temperature.

•

  Mixing occurs over several atomic layers at the interface • Segregation proceeds in the absence of bulk diffusion (no vacancies) and is favored near the misfit dislocations • The composition at the interface is asymmetric Ag :23x 23x 5(100)cells -N Ag = 10580 atoms Cu :26 x 26 x 5(100)cells -N Cu = 13520 atoms σ zz = 0