Olivier Teytaud

Sylvain Gelly

Stphane Lallich

Elie Prudhomme May

Quasi-random resamplings, with applications to rule extraction, cross-validation and (su-)bagging

Introduction

Resampling (typically, but not necessarily, bootstrapping) is a well-known stochastic technique for improving estimates in particular for small samples. It is known very efficient in many cases. Its drawback is that resampling leads to a compromise computational cost / stability through the number of resamplings. The computational cost is due to the study of multiple randomly drawn resamples. Intuitively, we want some more properly distributed resamples to improve the stability of resampling-based algorithms. Quasi-random numbers are a wellknown technique for improving the convergence rate of data-based estimates. We here consider quasi-random version of resamplings. We apply this technique to BSFD, a data-mining algorithm for simultaneous-hypothesis-testing, to crossvalidation, and to (su-)bagging, an ensemble method for learning. We present quasi-random numbers in section 2. We present bootstrap and a quasi-random version of bootstrap-sampling in section 3. We present experimental results in section 4.

Introduction to quasi-random numbers

If you are unlucky, random points can be distributed in a very non-uniform manner. Figure 1 (upper-left) is a pseudo-random independent sample (uniformly drawn in [0, 1] 2 ). Usually, you can not get by chance something as regular as other plots in figure 1. Therefore, in many areas of computer science, betterthan-random points have been studied (integration [START_REF] Niederreiter | Random Number Generation and Quasi-Monte Carlo Methods[END_REF], optimization [START_REF] Auger | Xse: quasi-random mutations for evolution strategies[END_REF], path planning [START_REF] Tuffin | On the use of low discrepancy sequences in monte carlo methods[END_REF], learning [START_REF] Cervellera | A deterministic learning approach based on discrepancy[END_REF]). In order to generate and check uniform point-sets, a measure of uniformity is useful. Consider a point set x 1 , . . . , [1,n]] d(x, x i ) (to be minimized), where d is some distance (e.g. L ∞ distance). Then, generating points as the lattice in figure 1 is easy, and it has been pointed out that for the criterion above, this is optimal for many values of the number of points ( [START_REF] Tuffin | On the use of low discrepancy sequences in monte carlo methods[END_REF]). However, this point set is not satisfactory. For example, it would be nice that the projection on any axis of a good point set is a good point set. This is not the case for the lattice in figure 1: the projection on some well-chosen axis leads to accumulations. Therefore, other criterions have been defined; the most well known is discrepancy. Among various discrepancies, the most well known is the following: sup r∈D [1,d]] r j . This formula has an immediate interpretation: it is the largest absolute difference between the area of a rectangle including 0 and the proportion of points in this rectangle. It is much more stable with respect to projection on an axis. However, it has various drawbacks (see [START_REF] Hickernell | A generalized discrepancy and quadrature error bound[END_REF]): (1) it only deals with rectangles with axis parallel to the canonical axis; (2) it only deals with rectangles; (3) it is not symmetric in the sense that the discrepancy of x 1 , . . . , x n is not the discrepancy of 1 -x 1 , . . . , 1 -x n ; (4) it is a worst case on r. The two first drawbacks are unclear drawbacks. Considering variables, in a non-rotation invariant manner, can be meaningful. The fourth drawback is probably the main trouble. Fortunately, extensions have already been defined. The main tool is the L 2 -star-discrepancy:

x n in D = [0, 1] d . An intuitive measure is sup x∈D inf i∈[
1 n Card{i ∈ [[1, n]]; ∀j(x i ) j ≤ r j } -π j∈[
r∈D 1 n Card{i ∈ [[1, n]]; ∀j(x i ) j ≤ r j } -π j∈[[1,d]] r j 2 .
This form of discrepancy (as well as others) verify inequalities similar to Koksma's inequality (see [START_REF] Hickernell | A generalized discrepancy and quadrature error bound[END_REF] on this topic). Many algebraic methods have been defined for generating sequences of points with low discrepancy ( [START_REF] Niederreiter | Random Number Generation and Quasi-Monte Carlo Methods[END_REF][START_REF] Tuffin | On the use of low discrepancy sequences in monte carlo methods[END_REF][START_REF] Owen | Quasi-Monte Carlo Sampling, A Chapter on QMC for a SIG-GRAPH 2003 course[END_REF][START_REF] Sobol | On the systematic search in a hypercube[END_REF][START_REF] Bratley | Algorithm 659: Implementing sobol's quasirandom sequence generator[END_REF]). We here consider scrambled-Halton-sequences. We now define this quasi-random sequence. Consider p a prime number. The following sequence generates the n th element x n,p ∈ [0, 1] of the Van Der Corput sequence [START_REF] Van Der Corput | Verteilungsfunktionen[END_REF] in basis p:

• write n in basis p: n = p k p k-1 . . . p 1 , i.e. n = k i=1 p i p i with p i ∈ [[0, p -1]];
• x n,p = 0.p 1 p 2 . . . p k in basis p, i.e. x n,p = k i=1 p i /p i . A classical improvement, termed scrambling consists in replacing this by x n,p = 0.π(p 1 )π(p 2 ) . . . π(p k ) where π is some permutation of 0, 1, . . . , p-1. The Halton sequence [START_REF] Halton | On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals[END_REF] generalizes the Van Der Corput sequence to dimension d. Consider p i the i th prime number. Then, x n , the n th element of a Halton sequence in dimension d, is x n = (x n,p1 , x n,p2 , . . . , x n,p d ) ∈ [0, 1] d . The scrambled-Halton sequence is the use of a randomly drawn permutation for each i ∈ [ [1, d]].

The applications of bootstrap in data mining and quasi-random bootstrap

Bootstrap has been first defined by Efron [START_REF] Efron | Bootstrap methods: Another look at the jacknkife[END_REF] and uniform versions appeared with the work of Giné and Zinn [START_REF] Gine | Bootstrapping general empirical measures[END_REF]. These works and many others are summarized in [START_REF] Vaart | Weak convergence and empirical processes[END_REF].

Often, we would like to know P , an unknown law of probability, but we only have a database which can be assumed i.i.d according to P . If this database is x 1 , . . . , x n , the traditional notation is P for the empirical measure, i.e. P =

i ∈ [[1, n]], x ′
i is equal to x ji , where the (j i ) i∈[ [1,n]] are independent and uniform on [ [1, n]]. We then note P = 1 n n i=1 δ x ′ i . So, bootstrap is based on the replacement of a random variable that can not be simulated ( P , the random part of which being the sampling) by one that can be simulated ( P , the random part of which being the resampling).

Simulating P is usually done in an i.i.d manner. However, there is a straightforward application of quasi-random numbers to this simulation. Precisely, we have to quasi-randomly draw the (x ′ 1 , . . . , x ′ n ). Each x ′ i is equal to x ji where the j 1 , . . . , j n are i.i.d uniformly in [ [1, n]]. Naively sampling the bootstrap distribution is therefore equivalent to:

• randomly draw z ∈]0, 1] n ; • for i ∈ [[1, n]], define x ′ i =
x ji where j i = ⌈n × z i ⌉. With this formalism, a quasi-random version is straightforward: we only have to quasi-randomly draw the z in dimension n. Therefore, we can use a quasirandom sequence in dimension n, where n is the number of instances. Unfortunately, this naive approach does not work. The reason is that strongly redundant results can appear, as the result of the second line above is the same when ordinates of z are permuted. Well distributed z's do not lead to well distributed samples. Therefore, we define a better approach. The indices j i are multinomially distributed. It is known that the multinomial distribution is still multinomial after the first components are observed. In algorithmic terms, this means that the following procedure works for generating correct bootstrap samples:

• randomly draw z ∈]0, 1] n ;

• set r = n (number of elements to be drawn in the database);

• for i ∈ [[1, n]], -define z ′ i minimal such that P (binomial(r, 1/(n + 1 -i)) ≤ z ′ i ) ≥ z i ; -set r ← r -z ′ i . • for i ∈ [[1, n]],
define the bootstrap sample such that x i appears in the x ′ j exactly z ′ i times. This generates independent bootstrap samples. We now just have to replace the random-drawing at the first line by a quasi-random sequence. Traditionally, the efficiency of quasi-random sequences is justified by Koksma-Hlawka's inequality. This inequality ensures a convergence in O(V log(b) n /b), where n is the dimension, b is the number of quasi-random samples, and V is the total variation in the sense of Hardy & Krause. In many cases, the quasi-random method indeed works, whenever V is infinite. Here, we are in a nice case: V is finite. Let's formalize this claim:

Theorem: finiteness of the Hardy&Krause total variation Consider f any mapping

[[0, n]] n → R. Consider the following application π f : z → f (z ′ ), π f : [0, 1] n → R,
where z ′ is defined as follows:

• set r = n (number of elements to be drawn in the database);

• for i ∈ [[1, n]], -define z ′ i minimal such that P (binomial(r, 1/(n + 1 -i)) ≤ z ′ i ) ≥ z i ; -set r ← r -z ′ i .
Then, π f has finite total variation in the sense of Hardy&Krause. Proof: π f is constant in each of finitely many hyperrectangles partitionning [0, 1] n . This is sufficient to imply the finiteness of the total variation.

Quasi-random points are often much more efficient than random points in low dimension, but quasi-random points must be adapted for huge dimension, in spite of strong improvements due in particular to scrambling. We need a dimension reduction. We perform this dimension reduction as follows for cases in which the dimensionality of the quasi-random sequence would be too high:

• group examples in the learning set in k clusters by k-means (including the label as supplementary ordinate);

• by quasi-random, choose the number of random draws in each of the k clusters, n 1 examples in cluster 1, . . . , n k examples in cluster k;

• then, randomly distribute the n i examples among the examples in cluster i.

This method is inspired by [START_REF] Diamantidis | Unsupervised stratification of cross-validation for accuracy estimation[END_REF] in a different context. It's likely that more sophisticated methods could be defined also. See [START_REF] Hickernell | A generalized and quadrature error bound[END_REF] for particular cases of derandomization in huge dimension that might be helpful.

Experimental results

More detailed results are available in http://www.lri.fr/ ∼ teytaud/ qrboutput.pdf. One can find there results about quasi-random-cross-validation also.

Results for information extraction

We refer to the url above for full results; we here only present in Figure 2 one of the tables of results, in the following setting: each variable is independent, normally distributed with variance one and mean 0. BSFD is applied for ex-tracting variables with mean > 0; therefore the best answer is the empty answer (no detection). The table presents for each dimensionality and for 16 examples the empirical probability of more than V 0 false detections, when the bootstrap-based evaluation (thanks to BSFD [START_REF] Lallich | Statistical inference and data mining: false discoveries control[END_REF]) of the selection threshold is based on 32 bootstrap-samples. The user provides δ = 0.25 and V 0 ; the goal of BSFD is to be as close as possible to a risk δ of selecting more than V 0 type-I errors.

Results for (su-)bagging with dimension-reduction

Bagging and subagging were applied in a setting detailed in http://www.lri. fr/ ∼ teytaud/qrboutput.pdf (18 examples, 25 bootstraps). A few results are presented in figure 3. The complete results in the url above show that QRBagging > Bagging > Weak learner, and QRSuBagging > SuBagging > Weak learner.

Conclusion

We experimented quasi-random-sequences of resamples. The standard quasirandom points in [[0, 1]] k could be used thanks to the decomposition of the multinomial law into k binomial laws. The convergence is faster and more stable, both theoretically and in various applications. As far as we know, it's the first time that quasi-random-sequences of bootstrap-samples and quasi-randomsequences of subsets are defined and applied.

Figure 1 :

 1 Figure 1: Random points, lattice points, Sobol points, scrambled-Halton points.

Figure 2 :

 2 Figure 2: Results of quasi-random-BSFD versus standard-BSFD. The variance is much lower in all but one case.

n n i=1 δ xi , where δ x is the Dirac measure located at x. A bootstrap sample consists in randomly drawing n elements, with replacement, among the x i : for

Method (mean standard

Error rate ± deviation of output) standard deviation 199 runs, 320 examples (


Kamil M Szafranski
email: km.szafranski@gmail.com

Bérénice Piquet

Bruce Shillito

François H Lallier

Sébastien Duperron

Relative abundances of methane-and sulfur-oxidizing symbionts in gills of the deep-sea hydrothermal vent mussel Bathymodiolus azoricus under pressure

Keywords: 3D FISH, hydrothermal vents, pressurized recovery, symbiosis, symbiont quantification, mussels

The deep-sea mussel Bathymodiolus azoricus dominates hydrothermal vent fauna in the the Azores region. The gills of this species house methane-and sulfur-oxidizing bacteria that fulfill most of the mussel's nutritional requirements. Previous studies suggested that the ratio between methane-and sulfur-oxidizers could vary in response to the availability of electron donors in their environment, and this flexibility is considered a key factor in explaining the ecological success of the species.

However, previous studies were based on non-isobaric recovery of specimens, with experiments at atmospheric pressure which may have induced artifacts. This study investigates the effect of pressure-related stress during recovery and experimentation on the relative abundances of bacterial symbionts. Mussel specimens were recovered for the first time using the pressure-maintaining device PERISCOP. Specimens were subsequently transferred into pressurized vessels and exposed to various chemical conditions. Using optimized fluorescence in situ hybridization-based approaches, relative abundance of symbionts were measured. Our results show that the recovery method (isobaric versus non-isobaric) does not influence the abundances of bacterial symbionts.

Significant differences occur among specimens sampled from two contrasting sites. Exposure of mussels from the deeper site to sulfide and bicarbonate, and to bicarbonate alone, both resulted in a rapid and significant increase in the relative abundance of sulfur-oxidizers. Results reported herein are congruent with those from previous reports investigating mussels originating from shallow sites and kept at ambient pressure. Isobaric recovery and maintenance allowed us to perform in vivo experiments in specimens from a deeper site that could not be maintained alive at ambient pressure, and will greatly improve the chances of identifying the molecular mechanisms underlying the dialogue between bathymodioline hosts and symbionts.

Introduction

Bathymodiolinae mussels (family Mytilidae) are part of the remarkable fauna colonizing ecosystems such as hydrothermal vents and cold seeps in the deep-sea [START_REF] Desbruyères | A review of the distribution of hydrothermal vent communities along the northern Mid-Atlantic Ridge: dispersal vs. environmental controls[END_REF][START_REF] Duperron | The diversity of deep-sea mussels and their bacterial symbioses[END_REF][START_REF] Duperron | Symbioses between deep-sea mussels (Mytilidae: Bathymodiolinae) and chemosynthetic bacteria: diversity, function and evolution[END_REF][START_REF] Cosel | Bathymodiolus (Bivalvia: Mytilidae) from hydrothermal vents on the Azores Triple Junction and the Logatchev Hydrothermal Field[END_REF][START_REF] Cosel | Vesicomyidae (Mollusca: Bivalvia) of the genera Vesicomya, Waisiuconcha, Isorropodon and Callogonia in the eastern Atlantic and the Mediterranean[END_REF]. These mussels rely upon sulfur-or methane-oxidizing (SOX and MOX) bacteria occurring in their gill epithelial cells for all or part of their nutrition [START_REF] Cavanaugh | prokaryotic cells in the hydrothermal vent tube worm Riftia pachyptila Jones: possible chemoautotrophic symbionts[END_REF][START_REF] Felbeck | Chemoautotrophic potential of the hydrothermal vent tube worm, Riftia pachyptila Jones (Vestimentifera)[END_REF]. The symbionts of mussels exploit compounds present in vent or seep fluids for their metabolism [START_REF] Van Dover | The ecology of deep-sea hydrothermal vents[END_REF][START_REF] Van Dover | Evolution and biogeography of deep-sea vent and seep invertebrates[END_REF]. Although sulfide is toxic to animals, symbiotic sulfur-oxidizers use hydrogen sulfide from the fluids as the source of energy for their metabolism and to fix inorganic carbon [START_REF] Cavanaugh | Immunochemical localization of ribulose-1,5-bisphosphate carboxylase in the symbiont-containing gills of Solemya velum (Bivalvia: Mollusca)[END_REF]. Methane-oxidizing bacteria use methane both as a carbon and an energy source [START_REF] Cavanaugh | Evidence for methylotrophic symbionts in a hydrothermal vent mussel (bivalvia: mytilidae) from the mid-atlantic ridge[END_REF][START_REF] Childress | A methanotrophic marine molluscan (bivalvia, mytilidae) symbiosis: mussels fueled by gas[END_REF]. Organic carbon compounds are subsequently transferred to their animal host and ultimately contribute to ecosystem productivity in habitats where only a small fraction of the photosynthetic primary production from upper layers of the oceans is brought in by sedimentation or advective transport [START_REF] Cavanaugh | Symbiotic chemoautotrophic bacteria in marine invertebrates from sulphide-rich habitats[END_REF][START_REF] Corliss | Submarine Thermal Sprirngs on the Galápagos Rift[END_REF][START_REF] Karl | Deep-Sea primary production at the galapagos hydrothermal vents[END_REF].

Bathymodiolus azoricus and its sister species B. puteoserpentis dominate several vent sites on the Mid-Atlantic Ridge (MAR). They possess both sulfur-and methane-oxidizing symbionts in their gill bacteriocytes, as demonstrated through ultrastructural studies, 16S rRNA-encoding gene sequence analyses, and enzyme assays [START_REF] Cavanaugh | Evidence for methylotrophic symbionts in a hydrothermal vent mussel (bivalvia: mytilidae) from the mid-atlantic ridge[END_REF][START_REF] Distel | Intracellular coexistence of methano-and thioautotrophic bacteria in a hydrothermal vent mussel[END_REF][START_REF] Duperron | A dual symbiosis shared by two mussel species, Bathymodiolus azoricus and Bathymodiolus puteoserpentis (Bivalvia: Mytilidae), from hydrothermal vents along the northern Mid-Atlantic Ridge[END_REF][START_REF] Fiala-Medioni | Ultrastructural, biochemical, and immunological characterization of two populations of the mytilid mussel Bathymodiolus azoricus from the Mid-Atlantic Ridge: evidence for a dual symbiosis[END_REF][START_REF] Fisher | The cooccurrence of methanotrophic and chemoautotrophic sulfur-oxidizing bacterial symbionts in a deep-sea mussel[END_REF]. Dual symbiosis is thought to increase the environmental tolerance of hosts because the distinct metabolism of the sulfur-and methaneoxidizing symbionts may help the holobiont adapt to varying availability of reduced sulfur and methane [START_REF] Distel | Intracellular coexistence of methano-and thioautotrophic bacteria in a hydrothermal vent mussel[END_REF][START_REF] Fiala-Medioni | Ultrastructural, biochemical, and immunological characterization of two populations of the mytilid mussel Bathymodiolus azoricus from the Mid-Atlantic Ridge: evidence for a dual symbiosis[END_REF]. Several studies point to a high flexibility of the symbiont populations [START_REF] Kádár | Experimentally induced endosymbiont loss and re-acquirement in the hydrothermal vent bivalve Bathymodiolus azoricus[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF]. Bacteria indeed disappear from B. azoricus gill bacteriocytes when subjected to starvation in sulfide-and methane-free sea-water, but can be recovered when mussels return to sulfide-enriched aquaria [START_REF] Kádár | Experimentally induced endosymbiont loss and re-acquirement in the hydrothermal vent bivalve Bathymodiolus azoricus[END_REF]. The relative volume occupied by each symbiont type in bacteriocytes of B. azoricus varies within vent sites, and between sites displaying different chemical signatures [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF]. Experiments using mussels maintained in controlled conditions at atmospheric pressure with one, both or none of the electron donors necessary for endosymbiont metabolism confirm that symbiont relative abundances can change rapidly in response to changes in the availability of their respective substrates [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Riou | Variation in physiological indicators in Bathymodiolus azoricus (Bivalvia: Mytilidae) at the Menez Gwen Mid-Atlantic Ridge deep-sea hydrothermal vent site within a year[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF].

However, the previously mentioned results suffer numerous potential biases. First, specimen recovery from the MAR vent sites, which are located at depths between 800 m (Menez Gwen) and 3500 m (Logatchev), involved rapid (usually a few hours) and large de-pressurization of specimens (8 to 35 MPa). This results in high levels of stress, ultimately resulting in the death of specimens from the deepest sites [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF]. Second, specimens used in in vivo experiments are usually from shallower vent sites (Menez Gwen) and maintained in the laboratory at atmospheric pressure, i. e. ~80-fold lower than in situ conditions [START_REF] Kádár | Experimentally induced endosymbiont loss and re-acquirement in the hydrothermal vent bivalve Bathymodiolus azoricus[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF]. Results from these studies are thus potentially affected by artifacts associated with depressurization, and it remains to be confirmed whether observed symbiont dynamics were the consequence of these stresses or true biological responses. Another issue is with the quantification of symbionts itself.

Several studies are based on a 3D fluorescence in situ hybridization (FISH) approach, which measures the fraction of the total volume occupied by each type of symbiont within bacteriocytes [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF][START_REF] Duperron | Relative abundances of methane-and sulphur-oxidising symbionts in the gills of a cold seep mussel and link to their potential energy sources[END_REF]. Although reliable, this approach is time consuming because it involves the acquisition of 3D images of gill sections, manual cropping of individual bacteriocytes, and computing volumes using a dedicated ImageJ plugin [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF]. This has limited the number of specimens that could be analyzed, reducing the statistical power of comparisons [START_REF] Prosser | Replicate or lie[END_REF].

Several pressurized vessels for live maintenance and pressurized recovery that prevent or reduce pressure-related stress have become available in recent years [START_REF] Boutet | Molecular identification of differentially regulated genes in the hydrothermal-vent species Bathymodiolus thermophilus and Paralvinella pandorae in response to temperature[END_REF]. The first aim of the present study is to investigate relative symbiont abundances in B. azoricus mussels recovered from the Menez Gwen (800 m depth) and Rainbow (2300 m depth) vent sites using the pressuremaintaining PERISCOP sampling cell [START_REF] Shillito | Live capture of megafauna from 2300 m depth, using a newly designed pressurized recovery device[END_REF]. The second aim is to investigate these abundances in Rainbow specimens exposed to substrates used by the sulfide-oxidizing bacteria at their native pressure in the IPOCAMP vessel [START_REF] Shillito | The Ipocamp pressure incubator for deep-sea fauna[END_REF]. The percentage of total bacterial volume corresponding to methane-plus sulfur-oxidizing symbionts is measured by means of FISH and image analysis. In order to optimize the method, we compare results from three FISH-based approaches, and images acquired from the anterior and posterior regions of the gills. We then compare isobaric vs. non-isobaric recovery, Menez Gwen and Rainbow specimens, and the effect of treatments applied to live specimens from Rainbow. Results are discussed in relation to improvements of the methods used to investigate symbiont dynamics in animal tissue in light of previous reports, based on specimens from non-isobaric recoveries and exposed to various experimental conditions at atmospheric pressure.

Material and methods

Sampling sites

Bathymodiolus azoricus mussels (Bivalvia, Mytilidae) (von [START_REF] Cosel | Vesicomyidae (Mollusca: Bivalvia) of the genera Vesicomya, Waisiuconcha, Isorropodon and Callogonia in the eastern Atlantic and the Mediterranean[END_REF] were collected from two hydrothermal vent sites during the 2013 BioBaz cruise to the Mid-Atlantic Ridge aboard RV Pourquoi Pas? using the ROV Victor 6000. Specimens were sampled from the vicinity of active smokers at Menez Gwen (MG2 marker, 37°50.669' N 31°31.156' W, 830 m depth) and Rainbow (France5 marker, 36°13.766' N 33°54.117' W, 2270 m depth) (Figure 1). Active vents were colonized by fauna typical for MAR vents, including one bivalve (Bathymodiolus azoricus) and three shrimp species (Rimicaris exoculata, Mirocaris fortunata and Chorocaris chacei) [START_REF] Desbruyères | Variations in deep-sea hydrothermal vent communities on the Mid-Atlantic Ridge near the Azores plateau[END_REF].

Isobaric and non-isobaric recovery

At each sampling site, specimens were recovered in clean watertight BioBoxes, which were brought to the surface by the ROV or the shuttle within a few hours (non-isobaric sampling). Others were placed inside a "CROCO" sampling cell that was fit into the pressure-keeping vessel PERISCOP (isobaric recovery, [START_REF] Shillito | Live capture of megafauna from 2300 m depth, using a newly designed pressurized recovery device[END_REF]. PERISCOP was then closed and the shuttle to which it was attached was released within a few minutes, and surfaced within 45 minutes. Pressure was monitored during surfacing with autonomous pressure sensor (SP2T4000, NKE Instruments, France). Once onboard, PERISCOP was opened and mussels were recovered and either dissected and fixed, or transferred to the IPOCAMP pressure vessel within 10 minutes.

Exposure to bicarbonate and sulfide in pressurized vessels

Six mussels from Rainbow, recovered using the PERISCOP, were taken out and used in incubation experiments (shell length: 44.4-100.5 mm). Due to the limited volume of the IPOCAMP chamber and the size of specimens, only two specimens were transferred in each of three 1 liter Nalgene™ bottles filled with 11.8 µM NaHCO 3 and 36.4 µM Na 2 S; with 11.8 µM NaHCO 3 ; or with filtered sea-water alone (control). These concentrations were within the range of values recorded in mussel aggregates on the site, and similar to values used in previous studies [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF]. Bottles were tightly closed and re-pressurized in IPOCAMP aquariums within 5 minutes.

Mussels were incubated at 23MPa and 8°C for 5 h, then dissected immediately and fixed.

Sample fixation onboard

Anterior and posterior parts of mussel gill tissue were dissected at 4°C and fixed for fluorescence in situ hybridization (FISH). Gill fragments were transferred to 4% formaldehyde in twice-filtered seawater (TFSW) (4°C, 2-4 h), rinsed, and dehydrated in increasing ethanol (50, 70 80, and 96%, 15 min each). The density of gill filaments per millimeter was measured under a dissecting microscope.

Fluorescence in situ hybridization (FISH)

Fragments of gills were embedded in polyethylene glycol distearate (PEG):1-hexadecanol (9:1), cut into 8 µm-thick sections and deposited on SuperFrost Plus slides (VWR International, USA). Wax was removed and tissue rehydrated in decreasing ethanol series (96% to 70%). Sections were hybridized using 40% formamide for 1-3 h at 46°C as previously described [START_REF] Duperron | Sulphur-oxidizing extracellular bacteria in the gills of Mytilidae associated with wood falls[END_REF], rinsed, and mounted in DAPI-containing "Slow Fade" (Life Technologies) under a coverslip. Three 16S rRNA-specific probes were applied simultaneously on every section. FISH probes used are summarized in Table 1.

Image acquisition and analysis

Slides were observed under a BX61 epifluorescence (Olympus, Japan) or a SP5 confocal (Leica, Germany) microscope, and images were acquired at 400x magnification using ImagePro 6.0 (Olympus, Japan). On each section, a 2D image was first acquired by overlaying signals from the three probe-associated fluorochromes (2D acquisition). Second, an image stack was built by acquiring images every 0.3 µm over the thickness of the section (3D acquisition). Images were analyzed using ImageJ [START_REF] Abramoff | Image Processing with ImageJ[END_REF] and the total volume occupied by bacteria and respective proportions of the sulfur-and methane-oxidizing symbionts were computed for 2D and 3D images using the SymbiontJ plug-in as previously described, but applying the procedure to the whole field of view without isolating individual bacteriocytes [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF]. SymbiontJ applies filters and thresholds to the different color channels and computes the number of voxels corresponding to each symbiont type. Finally, ten bacteriocytes were manually cropped from each 3D acquisition, analyzed using SymbiontJ, and the mean percentage of volume occupied by each bacterial type was computed (bacteriocyte acquisition).

Statistical analyses

The percentage of bacterial volume occupied by methane-oxidizing bacteria was used for all analyses, after an Arcsine transformation [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF]. Values were then used for transformation-based redundancy analyses (tb-RDA). Sampling site (Menez Gwen versus Rainbow), recovery mode (isobaric versus non-isobaric), acquisition method (2D, 3D or bacteriocyte), gill region (anterior versus posterior), and specimen were used as factors into the constrained redundancy analysis (RDA), in order to estimate their contribution to the global variance. Significance was assessed using permutation tests (n=9999) using a full model, with separate test for each term (constraining variable). Shapiro-Wilk tests revealed non-normal distribution of the data, and non-parametric tests were thus applied for inter-groups comparisons.

The Mann-Whitney-Wilcoxon (MWW, for 2 class factors) and Kruskal-Wallis (KW, for 3 or more class factors) tests were used to compare percentages of methanotrophs. All statistical analyses were performed using R (R Development Core Team, 2013); 'vegan' package was used for the constrained redundancy analysis.

Results

In order to optimize the 3D FISH method [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF], three types of images were acquired and compared. For each mussel specimen, 10 acquisitions in 2D and 10 in 3D were obtained. From each of the later 3D acquisitions, 10 randomly chosen bacteriocytes were analyzed, resulting in 100 bacteriocytes per specimen. These acquisitions were obtained from at least 5 different sections, each containing 10-20 filaments. Results are summarized in Table 2, and a micrograph showing gill tissue with bacteriocytes containing the two symbionts is presented on Figure 2. The analyses of 2D, 3D, and bacteriocytes did not yield significantly different results (KW test on all measurements including anterior and posterior gill regions, p-value = 0.09).

The filament density per mm gill length along the anterior-posterior axis decreased significantly with increasing shell length (R 2 =65%, Pearson"s correlation test: p-value < 0.001, Figure 3). Gills form and grow from the posterior end. Percentages of methanotrophs (MOX) in the anterior and posterior regions of gill from 3 specimens per treatment (12 specimens) were computed using 2D and 3D methods, yielding in total 480 measurements (Table 2, Table S1). The percentage of volume occupied by methanotrophs was not significantly different between anterior and posterior regions of the gills (MWW test, p-value = 0.64). Subsequent analyses were thus made only on the anterior part of gills, for which more specimens were available.

When recovered in BioBoxes, mussels from Menez Gwen and Rainbow experienced pressure loss of around 8.3 and 23 MPa, respectively. The use of PERISCOP prevented that, and mussels arrived onboard at pressures close to those of the deep waters (Table 2). Percentages of volume occupied by methanotrophs were 46.5% ± 5.8 and 56.3% ± 6.4 in Menez Gwen and Rainbow mussels recovered in BioBoxes, and 44.3% ± 5.7 and 56.3% ± 8.3 in mussels recovered using PERISCOP (Figure 4, Table 2). A MWW test based on 1140 values from the anterior and posterior regions of the gills indicated no significant difference between the two types of recovery (p-value = 0.12). Mussels from Menez Gwen and Rainbow sites displayed significantly different percentages of methanotrophs in their gills (MWW test, W = 36185.5, p-value < 2.2e-16). A unilateral test confirmed that methanotrophs occupied a higher fraction of the overall volume in bacteriocytes of B. azoricus from the deeper Rainbow site (Figure 4, Table 2, Table S1).

The influence of each aforementioned factor was estimated by constrained redundancy analysis (RDA) and ANOVA permutation tests. Overall, our model could explain 56% of the total variance. Sampling site was the most influential factor (41%; df = 1; F = 1026.1), followed by interindividual differences, which accounted for more than 14% (df = 27; F = 13.3) of the total variance.

Other factors explained much lower fractions of the variance: recovery mode (0.3%; df = 1; F = 7.7), acquisition method (0.3%; df = 2; F = 3.8) and gill region (0.04%; df = 1; F = 0.1) (Table S2).

Each experimental condition could be applied to 2 specimens only from Rainbow because of the limited volume of bottles and the limited number of bottles that could be incubated at once in pressurized vessels. Nevertheless, 2 different treatments (NaHCO 3 + Na 2 S or NaHCO 3 alone) and 2 control experiments (10 mussels fixed immediately after recovery using PERISCOP and 2 incubated in filtered sea-water in the same conditions as above) were applied, and 320 measurements were made using 2D and 3D methodologies (Figure 5, Table S3). There was no significant difference between 2D and 3D FISH acquisition methods in this dataset (MWW test, pvalue = 0.54). The different treatments under pressure resulted in significant differences in percentages of methanotrophs (KW test, p-values < 0.011). The percentage of sulfur-oxidizers was twice higher in specimens exposed to sulfide and bicarbonate than in the sea-water treatment, with 90.1% ± 17.6 versus 38.5% ± 4.9 (Figure 5, Table S3). Specimens exposed to bicarbonate alone also displayed a markedly higher percentage of sulfur-oxidizers (SOX) than in the sea-water treatment. SOX in the bicarbonate treatment occupied 76.0% ± 23.0 of the bacterial volume. The percentage of SOX was slightly lower in mussels incubated in filtered seawater than prior to treatments (38.5 ± 4.9 versus 42.5% ± 7.6). Constrained RDA indicated that the overall variance was mainly explained by the 'treatment' factor (68.5%; df = 3; F = 506.7) and by inter-individual variability (18%; df = 12; F = 32.8), while 0.4% (df = 1; F = 0.9) was due to the method of image acquisition (Table S4).

Discussion

Image based quantification of volumes occupied by symbionts

Three FISH approaches were applied in this study, based on acquisition of 2D (Figure 2A) and 3D images, and of individual bacteriocytes (Figure 2B). They did not yield significantly different results. Although the results are similar, the bacteriocyte-based method used in previous studies [START_REF] Riou | Variation in physiological indicators in Bathymodiolus azoricus (Bivalvia: Mytilidae) at the Menez Gwen Mid-Atlantic Ridge deep-sea hydrothermal vent site within a year[END_REF] is by far the most time-consuming, because it involves manually cropping and computing percentages of methanotrophs in at least 10 bacteriocytes from each 3D image. If the aim is to maximize the number of acquisitions, the 2D or 3D approaches are equally suitable and far less time-consuming. In this study we managed to analyze a total of 36 specimens with two to three of these methods (Table 2), while previous studies using 3D-FISH were based 20 or fewer individuals [START_REF] Duperron | Relative abundances of methane-and sulphur-oxidising symbionts in the gills of a cold seep mussel and link to their potential energy sources[END_REF][START_REF] Duperron | Diversity, relative abundance and metabolic potential of bacterial endosymbionts in three Bathymodiolus mussel species from cold seeps in the Gulf of Mexico[END_REF][START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Lorion | Evolutionary history of Idas sp. Med (Bivalvia: Mytilidae), a cold seep mussel bearing multiple symbionts[END_REF][START_REF] Riou | Variation in physiological indicators in Bathymodiolus azoricus (Bivalvia: Mytilidae) at the Menez Gwen Mid-Atlantic Ridge deep-sea hydrothermal vent site within a year[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF].

Sampling methodology

The density of gill filaments was negatively related to shell length, i.e. the longer the shell was, the less dense gill filaments were (Figure 3). Similar filament densities and size-related trend are reported for the mussel Mytilus edulis [START_REF] Jones | Gill dimensions, water pumping rate and body size in the mussel Mytilus edulis L[END_REF]. The gill forms and grows from the posterior end in bivalves [START_REF] Cannuel | Gill development and its functional and evolutionary implications in the blue mussel Mytilus edulis (Bivalvia: Mytilidae)[END_REF][START_REF] Wentrup | Forever competent: Deep-sea bivalves are colonized by their chemosynthetic symbionts throughout their lifetime[END_REF]; this process could result in differences in symbiont relative abundances between the "young' posterior part and 'old' anterior one, but this was not confirmed by our data. It is likely that the absolute number of symbionts in each filament, which was not computed here, is different in the respective gill regions, in particular in the posterior-most budding zone [START_REF] Wentrup | Forever competent: Deep-sea bivalves are colonized by their chemosynthetic symbionts throughout their lifetime[END_REF]. Measuring absolute numbers of symbionts would be necessary, but a reliable method still remains to be implemented [START_REF] Boutet | Conjugating effects of symbionts and environmental factors on gene expression in deep-sea hydrothermal vent mussels[END_REF].

The two sites analyzed differed in depth (850 m at Menez Gwen and 2300 m at Rainbow) but nonisobaric recovery in BioBoxes involved significant pressure loss and potential physiological stress in both cases. Recovery stress is a major criticism often addressed to deep-sea biologists and physiologists by many colleagues who are dubious about reports from ex situ experiments. In the present study, mussels were for the first time recovered under their natural pressure until opening of the PERISCOP vessel on board, and compared with specimens recovered using classical, nonisobaric BioBoxes. Results indicate that, as far as symbiont relative abundances in gills are concerned, the recovery mode did not have any significant influence, not even for the deeper Rainbow site (Figure 4). This major finding validates a posteriori previous studies dealing with symbiont relative abundances that did use classical non-isobaric recovery methods involving pressure loss [START_REF] Duperron | Relative abundances of methane-and sulphur-oxidising symbionts in the gills of a cold seep mussel and link to their potential energy sources[END_REF][START_REF] Duperron | A dual symbiosis shared by two mussel species, Bathymodiolus azoricus and Bathymodiolus puteoserpentis (Bivalvia: Mytilidae), from hydrothermal vents along the northern Mid-Atlantic Ridge[END_REF][START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Lorion | Evolutionary history of Idas sp. Med (Bivalvia: Mytilidae), a cold seep mussel bearing multiple symbionts[END_REF][START_REF] Riou | Variation in physiological indicators in Bathymodiolus azoricus (Bivalvia: Mytilidae) at the Menez Gwen Mid-Atlantic Ridge deep-sea hydrothermal vent site within a year[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF]. However, although non-isobaric sampling is appropriate for studies focusing on symbiont relative abundances, isobaric recovery probably makes a difference when dealing with physiological parameters such as host and symbiont activities and gene expression. FISH signal intensities (but not areas and volumes) were indeed usually higher in specimens recovered using PERISCOP, suggesting that ribosomes to which FISH probes attach were less abundant in the latter (unpublished data).

Site-related differences in symbiont abundances

Besides depth, the Menez Gwen and Rainbow sites differ by several characteristics, including the chemical composition of end-member fluids. Fluids at Menez Gwen indeed display slightly lower concentrations of methane compared to Rainbow [START_REF] Charlou | Geochemistry of high H 2 and CH 4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14′N, MAR)[END_REF]. Sulfide concentrations are similar, but sulfide interacts with the high concentrations of iron at Rainbow, and is thus not readily available to organisms [START_REF] Desbruyères | A review of the distribution of hydrothermal vent communities along the northern Mid-Atlantic Ridge: dispersal vs. environmental controls[END_REF][START_REF] Bris | Chemosynthetic communities and biogeochemical energy pathways along the Mid-Atlantic Ridge: the case of Bathymodiolus azoricus[END_REF]. Geochemical modeling applied to the mixing zone where mussels actually live indicate that more energy can be gained from sulfide at Menez Gwen compared to methane, while the opposite situation is encountered at Rainbow (Le [START_REF] Bris | Chemosynthetic communities and biogeochemical energy pathways along the Mid-Atlantic Ridge: the case of Bathymodiolus azoricus[END_REF]. The result at Rainbow is however less clearcut when including hydrogen, an alternative energy source for sulfur-oxidizing symbionts [START_REF] Petersen | Hydrogen is an energy source for hydrothermal vent symbioses[END_REF]. The ratio between sulfide and methane has been shown to influence the relative abundance of sulfur-versus methane-oxidizers in mussel gills, and methanotrophs are more abundant than thiotrophs at Rainbow [START_REF] Duperron | A dual symbiosis shared by two mussel species, Bathymodiolus azoricus and Bathymodiolus puteoserpentis (Bivalvia: Mytilidae), from hydrothermal vents along the northern Mid-Atlantic Ridge[END_REF]. Previous estimations of symbiont relative abundances indicated that sulfur-oxidizers represented 53.1% ± 10.3 of the total volume of symbionts at Menez Gwen, compared to 39.4% at Rainbow [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Bris | Chemosynthetic communities and biogeochemical energy pathways along the Mid-Atlantic Ridge: the case of Bathymodiolus azoricus[END_REF]. Our results from PERISCOP-recovered specimens were remarkably close (52.6% ± 4.9 and 43.7% ± 6.4 respectively; Table 2). This is in line with the hypothesis that symbiont relative abundances depend on the availability of their respective substrates [START_REF] Fiala-Medioni | Ultrastructural, biochemical, and immunological characterization of two populations of the mytilid mussel Bathymodiolus azoricus from the Mid-Atlantic Ridge: evidence for a dual symbiosis[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF][START_REF] Trask | Site-specific and ontogenetic variations in nutrition of mussels (Bathymodiolus sp.) from the Lucky Strike hydrothermal vent field, Mid-Atlantic Ridge[END_REF]. Furthermore, the unexpected similarity between measurements made on specimens sampled in 2006 and 2013 suggests a certain level of long term stability in site-related differences, although short-term fluctuations certainly have occurred [START_REF] Duperron | A dual symbiosis shared by two mussel species, Bathymodiolus azoricus and Bathymodiolus puteoserpentis (Bivalvia: Mytilidae), from hydrothermal vents along the northern Mid-Atlantic Ridge[END_REF][START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF].

Symbiont response to bicarbonate and sulfide pulses under pressure

Starvation experiments and exposure to increased concentrations of different chemosynthesis substrates have already been performed by several groups [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF][START_REF] Kádár | Experimentally induced endosymbiont loss and re-acquirement in the hydrothermal vent bivalve Bathymodiolus azoricus[END_REF][START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF], but most often on B. azoricus from the shallower Menez Gwen site and at ambient pressure. Here, we tested the effect of sulfide and bicarbonate exposure on pressurized B. azoricus from the deeper Rainbow site (2300 m depth). Mussels from this site are not easily maintained in the lab at ambient pressure (authors' personal observation). PERISCOP-recovered mussels were transferred to pressure vessels and maintained at 8°C and 23 MPa. A 5h incubation period with bicarbonate and sulfide resulted in doubling of the relative abundance of thiotrophs in the gills (Figure 5). Exposure to bicarbonate alone also significantly increased the relative abundance of thiotrophs (Figure 5). These rapid changes confirm that observations reported in [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF] and other works on mussels from Menez Gwen were not artifacts, and not linked to recovery stress or experimentation at atmospheric pressure. The increase in thiotroph relative volume observed in the present study is even more spectacular (65.0% in [START_REF] Halary | 3D FISH for the quantification of methane-and sulphur-oxidizing endosymbionts in bacteriocytes of the hydrothermal vent mussel Bathymodiolus azoricus[END_REF]. In another study, mussels subjected to a one-month starvation followed by 4 days of constant sulfide supply showed a 96% bacterial volume occupation by thiotrophs [START_REF] Riou | Influence of CH 4 and H 2 S availability on symbiont distribution, carbon assimilation and transfer in the dual symbiotic vent mussel Bathymodiolus azoricus[END_REF]. Here, we show that non-starved B. azoricus can shift to an almost thiotrophic symbiosis within 5 hours of exposure to sulfide and bicarbonate (Figure 5). Unfortunately, only two specimens could be subjected to each treatment because of space limitations in IPOCAMP. So although the trend is clear, data from more specimens is needed to reliably estimate the true amplitude of this effect. Thiotrophic symbionts fix inorganic carbon using ribulose-1,5-bisphosphate Carboxylase Oxygenase (RubisCO) in the Calvin cycle [START_REF] Cavanaugh | Immunochemical localization of ribulose-1,5-bisphosphate carboxylase in the symbiont-containing gills of Solemya velum (Bivalvia: Mollusca)[END_REF]. This process requires energy from the oxidation of reduced sulfur compounds [START_REF] Cavanaugh | Immunochemical localization of ribulose-1,5-bisphosphate carboxylase in the symbiont-containing gills of Solemya velum (Bivalvia: Mollusca)[END_REF]. The less spectacular increase in relative abundance of thiotrophs when only bicarbonate was available also suggests that another source of energy may have been used for chemosynthesis. Over a short period, bacteria might have used sulfur stored in compounds such as taurine or thiotaurine [START_REF] Pruski | Stimulatory effect of sulphide on thiotaurine synthesis in three hydrothermal-vent species from the East Pacific Rise[END_REF]. Alternatively, hydrogen, not measured in our study, has been demonstrated to be an alternative energy source for hydrothermal vent symbioses [START_REF] Amend | Energetics of overall metabolic reactions of thermophilic and hyperthermophilic Archaea and Bacteria[END_REF][START_REF] Petersen | Hydrogen is an energy source for hydrothermal vent symbioses[END_REF]. Although the increase in thiotrophs relative abundance could result directly from an actual increase in their number, it could alternatively result from a decrease in methanotrophs, whose substrate was absent and which may have been digested by host bacteriocytes before thiotrophs. Methanotrophs are indeed located more basally within bacteriocytes, closer to phagolysosome-like bodies [START_REF] Distel | Intracellular coexistence of methano-and thioautotrophic bacteria in a hydrothermal vent mussel[END_REF][START_REF] Duperron | Dual symbiosis in a Bathymodiolus sp. mussel from a methane seep on the Gabon continental margin (southeast Atlantic): 16S rRNA phylogeny and distribution of the symbionts in gills[END_REF]. It is not known which mechanisms on the host and symbionts sides control the dynamics of bacterial populations within bacteriocytes. Mussel symbionts have been shown to divide and to be digested within bacteriocytes, but additional mechanisms may explain their variations, including symbiont uptake from the environment by adults, as suggested in B.

brevior, and symbiont release as documented in corals [START_REF] Dubilier | Ultrastructure and stable carbon isotope composition of the hydrothermal vent mussels Bathymodiolus brevior and B. sp. affinis brevior from the North Fiji Basin, western Pacific[END_REF][START_REF] Lesser | Coral Bleaching: Causes and Mechanisms[END_REF][START_REF] Thurber | Metagenomic analysis of stressed coral holobionts[END_REF]. Whatever the underlying mechanisms, the symbiont population as a whole seems to be rapidly and significantly affected by changes in the availability of energy and carbon sources, although results from more specimens are necessary.

Conclusions

In this study, a FISH-based method was used to quantify relative abundances of endosymbionts in gills of Bathymodiolus azoricus. Abundances in the anterior and posterior regions of the gill were similar. Mussels sampled in isobaric and non-isobaric recovery devices displayed similar relative volumes of the two types of symbionts indicating that non-isobaric recovery does not induce a major bias in measured volume occupation. However, the physiological status of mussels and their endosymbionts is probably not the same and isobaric recovery is certainly to be recommended for physiological or expression studies of specimens from the deepest sites. Symbiont relative volumes were different between the Menez Gwen and Rainbow sites, and similar to those previously measured on specimens sampled 7 years ago. On the other hand, symbiont populations displayed high flexibility in exposure experiments performed in pressurized aquaria. As postulated previously, this flexibility is certainly an advantage because physico-chemical micro-environments at hydrothermal vents are highly variable in time and space [START_REF] Chevaldonné | Time-series of temperature from three deepsea hydrothermal vent sites[END_REF][START_REF] Johnson | Biogeochemistry of hydrothermal vent mussel communities: the deep-sea analogue to the intertidal zone[END_REF][START_REF] Johnson | In situ measurements of chemical distributions in a deep-sea hydrothermal vent field[END_REF][START_REF] Bris | Processes controlling the physico-chemical microenvironments associated with Pompeii worms[END_REF], and maybe the key for the domination of Bathymodiolus azoricus at various hydrothermal vent sites of the Mid-Atlantic Ridge [START_REF] Desbruyères | Variations in deep-sea hydrothermal vent communities on the Mid-Atlantic Ridge near the Azores plateau[END_REF][START_REF] Desbruyères | A review of the distribution of hydrothermal vent communities along the northern Mid-Atlantic Ridge: dispersal vs. environmental controls[END_REF][START_REF] Cosel | Bathymodiolus (Bivalvia: Mytilidae) from hydrothermal vents on the Azores Triple Junction and the Logatchev Hydrothermal Field[END_REF]. More experiments involving methane, hydrogen, toxic compounds, but also thermal stress and symbiont release experiments will be necessary to further explore this flexibility.

The next step will then be to unravel the mechanisms that control this flexibility by exploring cell division patterns, genes and protein expressions of host and symbionts in various conditions.

(

  SOX), standard deviation (SD) measured using the 2D, 3D, and bacteriocyte-based FISH methods in the anterior region of the gill. Maintained pressure during recovery has been calculated as follow: P min /P max ×100%, where P max is the pressure at sampling site, P minthe minimal pressure during recovery.TableS1: Sites, number of individuals, and percentages of methane-(MOX), and sulfur-oxidizers (SOX), standard deviation (SD) measured using the 2D and 3D -based FISH methods in the posterior region of the gill.TableS2: Redundancy analysis estimating the contribution of factors site (SITE), recovery method (REC), FISH method (METH), localization in the gill (GILL), and inter-individual variability (IND) to the variability observed in percentages of methane-oxidizers in gills among Menez Gwen and Rainbow specimens.TableS3: Percentages of methane-(MOX), and sulfur-oxidizers (SOX) and standard deviation (SD) measured using the 2D-and 3D -based FISH methods in the anterior region of the gill of Rainbow specimens upon recovery using PERISCOP (T0) and those exposed to 5-hours experimental treatments in pressurized vessels at 23 MPa.TableS4: Redundancy analysis estimating the contribution of factors treatment (TREAT), FISH method (METH), and inter-individual variability (IND) in the variance observed in percentages of methane-oxidizers in gills among Rainbow specimens exposed to chemical treatments in pressurized vessels.

Figure 1 :

 1 Figure 1: Localization of sampling sites on the Mid-Atlantic Ridge. MG -Menez Gwen site (830 m depth); Rb -Rainbow site (2270 m depth).

Figure 2 :

 2 Figure 2: Overview (A) and detail (B) of transverse sections through B. azoricus gill filaments observed at 400× magnification. Filaments were cut parallel to the plane defined by the animals anterior-posterior and left-right axes, and perpendicular to its dorso-ventral axis. Nuclei from host tissue are labeled with DAPI (blue). FISH-labeled bacterial symbionts appear in pink (sulfuroxidizers) and green (methanotrophs).

Figure 3 :

 3 Figure 3: Density of gill filaments versus antero-posterior length of the shell. Fitted line is a linear regression (R 2 =65%, Pearson"s correlation test: p-value < 0.001).

Figure 4 :

 4 Figure 4: Mean percentage and standard deviation of total bacterial volume occupied by methaneoxidizers in gill tissue of B. azoricus specimens from Menez Gwen and Rainbow recovered in BioBoxes (non-isobaric) and PERISCOP vessels (isobaric). Shades of grey correspond to the three FISH methods as indicated (see text for details).

Figure 5 :

 5 Figure 5: Mean percentage and standard deviation of total bacterial volume occupied by sulfuroxidizers in gill tissue of B. azoricus specimens from Rainbow upon recovery using PERISCOP (T0) and exposed to experimental treatments in pressurized vessels (NaHCO 3 + Na 2 S, NaHCO 3 , filtered sea-water). Shades of grey correspond to the two FISH methods as indicated (see text for details).

Table legends Table 1 :

 legends1 Probes, target groups, and labels used in FISH experiments.

Table 2 :

 2 Sites, number of individuals, and percentages of methane-(MOX), and sulfur-oxidizers

Acknowledgments

We thank the captain and crew of RV "Pourquoi Pas?" and ROV "Victor 6000" for their invaluable help onboard. We are grateful to M. Zbinden, J-Y. Collet, J-B. Collet and A. Tanguy for their help with samples and aquaria onboard, and V. Le Layec for his help in the lab. This research was supported by CNRS, UPMC, UCBN and ITN Symbiomics. K. Szafranski was funded through a Ph.D. grant from the Marie Curie Actions Initial Training Network (ITN) SYMBIOMICS (contract number 264774). The authors would like to thank the reviewers and editors for their comments that helped to improve the manuscript.