Arielle Salmier

Sourakhata Tirera

Benoit De Thoisy

Alain Franc

Edith Darcissac

Damien Donato

Christiane Bouchier

Vincent Lacoste

Anne Lavergne
email: alavergne@pasteur-cayenne.fr

Virome analysis of two sympatric bat species (Desmodus rotundus and Molossus molossus) in French Guiana

Environmental disturbances in the Neotropics (e.g., deforestation, agriculture intensification, urbanization) contribute to an increasing risk of cross-species transmission of microorganisms and to disease outbreaks due to changing ecosystems of reservoir hosts. Although Amazonia encompasses the greatest diversity of reservoir species, the outsized viral population diversity (virome) has yet to be investigated. Here, through a metagenomic approach, we identified 10,991 viral sequences in the saliva and feces of two bat species, Desmodus rotundus (hematophagous), trapped in two different caves surrounded by primary lowland forest, and Molossus molossus (insectivorous), trapped in forest and urban habitats. These sequences are related to 51 viral families known to infect a wide range of hosts (i.e., bacteria, plants, insects and vertebrates). Most viruses detected reflected the diet of bat species, with a high proportion of plant and insect-related viral families for M. molossus and a high proportion of vertebrate-related viral families for D. rotundus, highlighting its influence in shaping the viral diversity of bats. Lastly, we reconstructed the phylogenetic relationships for five vertebrate-related viral families (Nairoviridae, Circoviridae, Retroviridae, Herpesviridae, Papillomaviridae). The results showed highly supported clustering with other viral sequences of the same viral family hosted by other bat species, highlighting the potential association of viral diversity with the host's diet. These findings provide significant insight into viral bat diversity in French Guiana belonging to the Amazonian biome and emphasize that habitats and the host's dietary ecology may drive the viral diversity in the bat communities investigated.

Introduction

Bats present a rich viral diversity as compared to other animals and their uniqueness as hosts of pathogenic viruses has animated debates in recent years [START_REF] Moratelli | Bats and zoonotic viruses: can we confidently link bats with emerging deadly viruses?[END_REF][START_REF] Olival | Are Bats Really "Special" as Viral Reservoirs? What We Know and Need to Know[END_REF][START_REF] Olival | Host and viral traits predict zoonotic spillover from mammals[END_REF]. Their ability to fly over long distances and their diverse feeding strategies seem to facilitate the acquisition and dispersal of viruses across remote regions, as well as cross-species transmissions [START_REF] Olival | Are Bats Really "Special" as Viral Reservoirs? What We Know and Need to Know[END_REF][START_REF] Brook | Bats as 'special' reservoirs for emerging zoonotic pathogens[END_REF][START_REF] Luis | Network analysis of host-virus communities in bats and rodents reveals determinants of cross-species transmission[END_REF]. Likewise, their wide variety of both social structures and behaviors contribute to viral transmissions and persistence of viruses in bat populations [START_REF] Olival | Are Bats Really "Special" as Viral Reservoirs? What We Know and Need to Know[END_REF][START_REF] Plowright | Ecological dynamics of emerging bat virus spillover[END_REF]. Studies have also highlighted that bats present long associations with numerous viral families and genera (e.g., Paramyxoviridae, Filoviridae, Lyssavirus, Henipavirus), with viruses detected in bats usually being older than those found in humans or other animals [START_REF] Schneeberger | Zoonotic Viruses and Conservation of Bats[END_REF]. To date, viral metagenomics in bats has almost exclusively focused on North American and Eurasian bat communities and many novel mammalian viruses have been reported, including some that are important to public health [START_REF] Donaldson | Metagenomic Analysis of the Viromes of Three North American Bat Species: Viral Diversity among Different Bat Species That Share a Common Habitat[END_REF][START_REF] Li | Bat Guano Virome: Predominance of Dietary Viruses from Insects and Plants plus Novel Mammalian Viruses[END_REF][START_REF] Canuti | Two Novel Parvoviruses in Frugivorous New and Old World Bats[END_REF][START_REF] Ge | Metagenomic Analysis of Viruses from Bat Fecal Samples Reveals Many Novel Viruses in Insectivorous Bats in China[END_REF][START_REF] Tse | Identification of a Novel Bat Papillomavirus by Metagenomics[END_REF][START_REF] Wu | Virome Analysis for Identification of Novel Mammalian Viruses in Bat Species from Chinese Provinces[END_REF][START_REF] He | Virome Profiling of Bats from Myanmar by Metagenomic Analysis of Tissue Samples Reveals More Novel Mammalian Viruses[END_REF][START_REF] Dacheux | A Preliminary Study of Viral Metagenomics of French Bat Species in Contact with Humans: Identification of New Mammalian Viruses[END_REF][START_REF] Hu | Virome analysis for identification of novel mammalian viruses in bats from Southeast China[END_REF][START_REF] Wu | Deciphering the bat virome catalog to better understand the ecological diversity of bat viruses and the bat origin of emerging infectious diseases[END_REF].

Amazonia encompasses a great diversity of bat species. Numerous studies, using conventional methods or high-throughput sequencing, have allowed the identification of a number of viruses in this region [START_REF] Calisher | Viruses in bats: a historic review[END_REF][START_REF] Cibulski | A Novel Anelloviridae Species Detected in Tadarida brasiliensis Bats: First Sequence of a Chiropteran Anellovirus[END_REF][START_REF] De S Lima | A Novel Chiropteran Circovirus Genome Recovered from a Brazilian Insectivorous Bat Species[END_REF][START_REF] De S Lima | Genomic Characterization of Novel Circular ssDNA Viruses from Insectivorous Bats in Southern Brazil[END_REF]. For instance, Drexler et al. detected and identified a diversity of paramyxoviruses in several New World bat species [START_REF] Drexler | Bats host major mammalian paramyxoviruses[END_REF], Tong et al. reported novel influenza A viruses in Peruvian flat-faced fruit bats (Artibeus planirostris) [START_REF] Tong | New World Bats Harbor Diverse Influenza A Viruses[END_REF], and Lima et al. proposed a new genus for two newly characterized polyomaviruses in Tadarida brasiliensis [START_REF] De S Lima | Genomic characterization of two novel polyomaviruses in Brazilian insectivorous bats[END_REF].

In French Guiana, an Amazonian region, 106 bat species have been listed [START_REF] Catzeflis | Liste des Mammifères de Guyane franc ¸aise[END_REF]. During the last few decades this region has undergone environmental changes (e.g., urbanization, agriculture intensification, deforestation), which have led to alterations in the composition and dynamics of bat communities [START_REF] Brosset | Bat communities and deforestation in French Guiana[END_REF][START_REF] Delaval | Edge effects on frugivorous and nectarivorous bat communities in a neotropical primary forest in French Guiana[END_REF]. Studies conducted in the Neotropics reported an overall decrease in species richness and relative abundance correlated with the urban influence, although species highly tolerant to environmental disturbances, such as insectivorous bats, tend to persist in large urban environments [START_REF] Jung | Urbanisation and Its Effects on Bats-A Global Meta-Analysis[END_REF]. Furthermore, the diversity of bat habitats may influence both microbe transmission and persistence in bat communities. For example, de Thoisy et al. [START_REF] De Thoisy | Bioecological Drivers of Rabies Virus Circulation in a Neotropical Bat Community[END_REF] showed that pristine forest habitats favored the circulation and maintenance of the rabies virus, compared to disturbed areas, and in Southeast Asian rainforests Gay et al. [START_REF] Gay | Parasite and viral species richness of Southeast Asian bats: Fragmentation of area distribution matters[END_REF] showed that fragmentation reduces both viral and endoparasite species richness.

The aim of our study was to characterize the virome in the feces and the saliva of two abundant and opportunistic Amazonian bat species: the common vampire bat, Desmodus rotundus (Phyllostomidae) and Pallas's mastiff bat, Molossus molossus (Molossidae). Both bat species are sympatric in the forest areas of French Guiana. They both have high plasticity and tolerance to perturbations but present distinct diet and social behavior.

D. rotundus bats are hematophagous and live in groups in highly complex social systems, for which Wilkinson et al. showed a strong association between the mating system and genetic structure of populations [START_REF] Wilkinson | The social organization of the common vampire bat[END_REF][START_REF] Wilkinson | The social organization of the common vampire bat[END_REF]. Studies on D. rotundus also highlighted that their diet associated with social interactions (especially social grooming and food sharing) within colonies contribute to the transmission and maintenance of viruses such as rabies [START_REF] De Thoisy | Bioecological Drivers of Rabies Virus Circulation in a Neotropical Bat Community[END_REF][START_REF] Johnson | Vampire Bat Rabies: Ecology, Epidemiology and Control[END_REF]. Furthermore, a modeling study of rabies transmission in a Desmodus population in Peru identified metapopulation dynamics as a major driver of rabies maintenance [START_REF] Blackwood | Resolving the roles of immunity, pathogenesis, and immigration for rabies persistence in vampire bats[END_REF]. Turmelle and Olival also pointed out that genetic spatial structure and the host's ecology and social behavior correlate with viral richness [START_REF] Turmelle | Correlates of Viral Richness in Bats (Order Chiroptera)[END_REF]. We investigated the virome of D. rotundus bats trapped in two caves (F and M) located in forest areas, for which no exchange of individuals was observed through a longitudinal mark-recapture study [START_REF] De Thoisy | Bioecological Drivers of Rabies Virus Circulation in a Neotropical Bat Community[END_REF].

M. molossus bats are insectivorous and live in stable social groups that practice social foraging over large spatial scales [START_REF] Dechmann | Group Hunting-A Reason for Sociality in Molossid Bats?[END_REF]. Studies on Molossidae also highlighted that members of this family tend to benefit from increased foraging resources in urban areas and persist in large urban environments for which they present high behavioral flexibility and heterogeneity [START_REF] Jung | Urbanisation and Its Effects on Bats-A Global Meta-Analysis[END_REF]. We investigated the virome of M. molossus bats trapped in urban and forest areas.

Lastly, focusing on viral families known to infect mammals, we investigated the phylogenetic relationships of viral sequences related to five viral families (Circoviridae, Herpesviridae, Nairoviridae, Papillomaviridae and Retroviridae (genus Spumavirus)), detected in either high proportion in both species and all habitats or only a distinct bat species and habitat. These findings allowed identifying novel vertebrate-related viral sequences and emphasize the importance of studying the role of habitats and dietary ecology in shaping viral diversity for these two Amazonian bat species.

Materials and methods

Ethics statement

All animals were captured, handled and sampled following ASM guidelines [START_REF] Sikes | Guidelines of the American Society of Mammalogists for the use of wild mammals in research[END_REF] under the supervision of researchers granted the French animal experimentation level 1 diploma. Bats are not protected by law in French Guiana.

Study areas

D. rotundus bats were sampled in two caves (F and M) located 25 km apart in pristine primary lowland forests, presenting differences in physical patterns, cave-inhabiting bat species as well as population size (Table 1 and S1 Fig) . Cave F is cohabited by four bat species (i.e., Anoura geoffroyi, Carollia perspicillata and Trachops cirrhosus), and the D. rotundus population ranges from 60 to 100 individuals [START_REF] De Thoisy | Bioecological Drivers of Rabies Virus Circulation in a Neotropical Bat Community[END_REF]. Cave M is larger and moister than cave F, suggesting different roost characteristics and carrying capacity. Cave M is cohabited by at least nine different bat species (i.e., Anoura geoffroyi, Artibeus spp., Carollia perspicillata, Pteronotus rubiginosus and P. sp3, Tonatia saurophila, Trachops cirrhosus and Xophostoma sylvicola), and the D. rotundus population ranges from 120 to 150 individuals [START_REF] De Thoisy | Bioecological Drivers of Rabies Virus Circulation in a Neotropical Bat Community[END_REF].

M. molossus bats were sampled in two sites located in primary lowland rainforests and under the roofs of houses in two sites located in disturbed areas (Table 1 andS1

Bat sampling

Feces and saliva samples were collected in both dry and rainy seasons during a 2-year period (April 2012 to April 2014). All animals were trapped with mist nets erected inside roosts or in putative foraging courses. Species were identified on site, using external morphology. Prior to release, 138 saliva swabs were collected from M. molossus and D. rotundus, in cave M only (Table 1). Samples were preserved on ice with 500 μl of Dulbecco's modified Eagle Medium (DMEM, Sigma). Feces were collected in two ways: M. molossus bats were held in individual sacks secured to a rope line for at least 10 min, allowing enough time for the excretion of 19 fresh feces of about 100 mg each (n = 5 in urban habitats, n = 14 in forest habitats; Table 1), while clean plastic sheets were laid down on flat surfaces beneath known roosts for D. rotundus. Then 141 freshly produced feces of about 150 mg each were collected (n = 75 in cave F, n = 66 in cave M; Table 1) the following morning and temporarily preserved on ice. All samples were later stored at -80˚C.

Sample processing

Feces and saliva samples were pooled according to the habitats and the species regardless of the season and year, corresponding to four pools for M. molossus (urban saliva, urban feces, forest saliva, forest feces) and three pools for D. rotundus (cave F feces, cave M saliva, cave M feces) (Table 1).

Samples were processed as previously described by Victoria et al. [38]. Briefly, feces were vigorously homogenized with 5-10 mL DMEM. Samples were cleared of debris by low-speed centrifugation (5 min, 10,000 g, 4˚C). Eukaryotic and prokaryotic cell-sized particles were removed from supernatants through three successive filtrations (0.8 μm, 0.45 μm and 0.22 μm), using cellulose acetate membrane filters (Nalgene). A differential centrifugation procedure, described by Prescott et al. [START_REF] Prescott | Les virus : introduction et caractères ge ´ne ´raux[END_REF], was used to pellet the viral particles. Briefly, filtrates were cleared of smaller and less dense components through a 1-h ultracentrifugation (100,000 g, 4˚C) procedure. Then the pellets were resuspended in nuclease-free water and cleared of persistent high-density particles with a low-speed centrifugation (15 min, 10,000 g, 4˚C). Lastly, viral particles were pelleted with a 1-h ultracentrifugation step (100,000 g, 4˚C).

For saliva samples, swabs were vigorously resuspended and 200 μL of suspension from each collecting tube was used to constitute the pools. Samples were cleared of debris by low-speed centrifugation (5 min, 10,000 g, 4˚C). Eukaryotic and prokaryotic cell-sized particles were removed from supernatants through two successive filtrations (0.45 μm and 0.22 μm), using cellulose acetate membrane filters (Nalgene). The filtrates were cleared of persistent high-density particles with low-speed centrifugation (15 min, 10,000 g, 4˚C), then viral particles were pelleted with a 1-h ultracentrifugation step (100,000 g, 4˚C). All viral pellets were resuspended in 40 μL of nuclease-free water.

Nuclease treatment and viral acid nucleic extraction

Resuspended viral pellets from feces were treated with a mixture of DNases (Turbo DNase from Ambion and Benzonase from Novagen) and RNase One (Promega) to digest nonenveloped nucleic acids (i.e., those not in viral capsids) [START_REF] Allander | A virus discovery method incorporating DNase treatment and its application to the identification of two bovine parvovirus species[END_REF]. Resuspended viral pellets from saliva samples were treated with the mixture of DNases. All viral nucleic acids (RNA and DNA) were then extracted using the NucliSENS easyMAG 1 bio-robot (bioMe ´rieux).

Reverse transcription and amplification

For both feces and saliva samples, the RNA virus-only and DNA virus-only libraries were respectively constructed using a whole transcriptome (WTA) or a whole genome (WGA) amplification method previously described by Berthet et al. [START_REF] Berthet | Phi29 polymerase based random amplification of viral RNA as an alternative to random RT-PCR[END_REF].

For the RNA virus-only amplification, an aliquot of the extracted viral nucleic acid collected was treated with Turbo DNase to remove viral DNA. Persistent rRNA was depleted with the GeneRead™ rRNA depletion kit (Qiagen), following the manufacturer's recommendations. Then viral RNA amplification was performed as described in the protocol of the QuantiTect 1 Whole Transcriptome Kit (Qiagen) except for the reverse transcription step. cDNA was synthesized using SuperScript 1 III Reverse Transcriptase (Invitrogen) and random hexamers (Roche), following the manufacturers' recommendations.

For DNA virus-only amplification, an aliquot of the extracted viral nucleic acid collected was treated with RNase One to remove viral RNA. Then viral DNA amplification was performed as described in the protocol of the QuantiTect 1 Whole Genome Kit (Qiagen). To ensure homogeneity and blunt ends at the end of the strands produced, 10 U of Klenow polymerase (Roche) was added to the WTA-and WGA-amplified nucleic acids with 8 μL of random hexamers (Roche), incubated 1 h at 37˚C, followed by 10 min at 75˚C. Samples were assayed with a Qubit 1 fluorometric quantitation (Qiagen), using the dsDNA Broad Range and dsDNA High Sensitivity Qubit 1 assay kits, as recommended by the manufacturer.

High-throughput sequencing

For both feces and saliva samples, 1 μg of each viral library was pooled together, whenever possible, to construct RNA plus DNA viral libraries. High-throughput sequencing was carried out at the Genomics platform at the Institut Pasteur, Paris. Shotgun libraries were prepared by standard Illumina protocols using 1 μg of total genomic DNA. Each sample (feces or saliva) was indexed according to its provenance (species and habitats) using Illumina adaptor-specific primers. Samples were sequenced on a MiSeq sequencer in 300-base paired-end reads.

Bioinformatic pipeline

The Illumina sequencing reads were grouped according to their adaptor tags and were processed individually. Sequence files were stripped of their adapter sequences using Trimmomatic v.0.32 [START_REF] Bolger | Trimmomatic: a flexible trimmer for Illumina sequence data[END_REF]. Duplicate sequence reads were removed with FastqMcf v.1.04.676 and reads were quality-filtered using the fastq_quality_filter program from the Fastx toolkit v.0.0.13 (available at http://hannonlab.cshl.edu/fastx_toolkit/index.html), with a quality threshold of 30 and length criteria of 70%. All cleaned data sets were saved for further analysis. Simultaneously, a three-pass digital normalization was run on each sample file using the Khmer software library [START_REF] Brown | A Reference-Free Algorithm for Computational Normalization of Shotgun Sequencing Data[END_REF][START_REF] Crusoe | The khmer software package: enabling efficient nucleotide sequence analysis[END_REF]. Normalized files were saved for further analysis. Following Baker's contig consolidation strategy [START_REF] Baker | Metagenomic study of the viruses of African straw-coloured fruit bats: Detection of a chiropteran poxvirus and isolation of a novel adenovirus[END_REF], both normalized and non-normalized reads were de novo assembled using two assembly algorithms: Velvet [START_REF] Zerbino | Velvet: algorithms for de novo short read assembly using de Bruijn graphs[END_REF] and SPAdes [START_REF] Bankevich | SPAdes: A New Genome Assembly Algorithm and Its Applications to Single-Cell Sequencing[END_REF]. Three k-mer sizes (21, 55 and 99) were used for both assemblers. The contigs generated were compared (Fig 1) between k-mer sizes for each assembler (comparison 1), between assemblers (comparison 2) and between normalized and non-normalized data sets (comparison 3). A removal of duplicated contigs and a clustering, using USEARCH v.7.0.1090 (available at http://www.drive5.com/ usearch, [START_REF] Edgar | Search and clustering orders of magnitude faster than BLAST[END_REF]) with a 95% threshold identity value, were performed following each comparison. Clustered contigs from comparison 3 (centroids) were considered as consolidated contig sets with lengths ranging from 33 to 45,057 bp and low redundancy. Centroids were submitted to BLASTn comparison with both the NCBI nt and Institut Pasteur de Paris gbvrl databases (in March 2015), (Fig 1). The best-matched reference sequence was retrieved from both databases (cutoff value: 10 e-5 ). A length comparison between the results was performed using a bit score ratio (br = bitscore_blastn_nt/bitscore_blastn_gb_vrl), and only contigs with br > 0.90 were regarded as suspect-viral sequences and conserved for further analysis. Centroids not identified as suspect-viral underwent a BLASTx comparison against a custom-made database, which

Phylogenetic analysis

Contigs from five vertebrate-related viral families: Nairoviridae, Circoviridae, Retroviridae, Herpesviridae and Papillomaviridae were used for phylogenetic analysis. Reference genomes or nucleotide sequences of previously identified viruses were downloaded from GenBank. The accession number of viral sequences used to infer the phylogenetic trees are given in the respective analyses. Nucleotide and protein sequence editing were performed with GENEIOUS R9 (available at http://www.geneious.com, [START_REF] Kearse | Geneious Basic: An integrated and extendable desktop software platform for the organization and analysis of sequence data[END_REF]). Sequences were aligned using the MAFFT alignment tool [START_REF] Katoh | MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform[END_REF] included in the software. Nucleotide and protein sequences were trimmed and gap-stripped prior to phylogenetic analyses. For each analysis, the best-fitted model of nucleotide or amino acid substitution was selected using jModelTest 2 [START_REF] Darriba | jModelTest 2: more models, new heuristics and parallel computing[END_REF] and ProtTest 3 [START_REF] Darriba | ProtTest 3: fast selection of best-fit models of protein evolution[END_REF], respectively, under corrected Akaike information criteria (AICc). Bayesian phylogenetic analyses were performed using MRBAYES 3. The Markov chain Monte Carlo (MCMC) algorithm was run with four chains with 10 million generations each, with trees sampled every 500 generations and a burn-in of 25%. Validation of the inference was assessed based on the standard deviation of split frequencies, less than the expected threshold value of 0.01 in MRBAYES and by inspecting the effective sampling size (ESS > 500) criterion in TRACER version 1.6 [START_REF] Rambaut | Tracer v1.6[END_REF].

Nucleotide sequence accession numbers

All virus sequences reported in this study were deposited in the GenBank nucleotide database under accession numbers KX812440 to KX812444, KX812446, KX812447, KX821677 and KX954092. The data from Illumina sequencing were deposited in GenBank Sequence Reads Archive under accession numbers SAMN05725475-SAMN05725481.

Results

Illumina sequencing and assembly

Overall, we obtained 53,325,594 raw read sequences (Table A in S1 File). For M. molossus, 33,333,557 raw sequences were generated from both feces and saliva samples and 19,992,037 for D. rotundus. Following the data reduction steps, 10,339,752 non-digitally normalized reads and 4,117,544 digitally normalized reads were used for de novo assembly. SPAdes and Velvet assemblers generated a comparable number of contigs, even between normalized and nonnormalized data. Between 50.22% and 67.66% of the contigs were saved after comparison 1 (Table B in S1 File). Following comparison 2, between 68.09% and 73.19% of the contigs from comparison 1 were saved for further analyses (Table C in S1 File). Finally, between 50.61% and 56.30% of the contigs from comparison 2 were saved to generate the centroids (Table D in S1 File). Following our consolidation steps, a total of 3,722,219 contigs were used for the taxonomic assignment. Most of the contigs retained originated from feces (Fig 1). Eukaryota-, Bacteria-and Virus-associated contigs accounted for 1.02%, 3.82% and 0.30% of the total of

General virome information and phage-related sequences

More than half of the viral-associated contigs matched phage sequences (Fig 1 andTable 2), accounting for nine phage families belonging to the dsDNA, ssDNA and ssRNA positivestrand groups. These families were identified in both feces and saliva samples (Fig 2 andTable 2). Among the nine phage families, the Podoviridae family of the dsDNA order Caudovirales accounted for greatest number of phage sequences detected in D. rotundus while the Microviridae family accounted for most of the phage sequences identified for M. molossus (Fig 2 andTable 2). The eukaryotic viral sequences (insect, plant/protozoan and vertebrate viruses) accounted for about three-tenths of the total of the viral-associated contigs identified, representing 42 known viral families. A high proportion of these families reflected the diet of bats, especially for M. molossus trapped in urban areas where most of the eukaryote-associated viruses identified belonged to nonmammalian viruses (Fig 1

Eukaryotic viral sequences

Insect viruses. Fourteen insect-related viral families and a group of unclassified viruses were identified (Table 2). Positive single-stranded RNA (ssRNA (+)) viruses were predominant for M. molossus trapped in urban habitats, with most of the viral sequences identified related to the Dicistroviridae, Nodaviridae and Iflaviridae families. DNA viruses detected in this sample were related to viruses from the double-stranded DNA (dsDNA) Iridoviridae family and the single-stranded DNA (ssDNA) Parvoviridae family. In contrast, ssDNA viruses (mostly from Parvoviridae) were slightly more numerous for M. molossus trapped in forest habitats compared to RNA viruses mostly from the Dicistroviridae and Nodaviridae families. The four viral families (Baculoviridae, Iridoviridae, Nudiviridae and Iflaviridae) detected for the D. rotundus were likely related to insects flying around feces.

Plant and protozoan viruses. Sixteen plant-and protozoan-related viral families and a group of unassigned viruses were identified (Table 2). ssRNA viruses, mostly from the unassigned group followed by the Luteoviridae, Bromoviridae and Virgaviridae families, were predominant for M. molossus trapped in urban habitats. In contrast, dsDNA viruses (Phycodnaviridae) and ssDNA viruses (Geminiviridae) were predominant for M. molossus and D. rotundus trapped in forest habitats.

Vertebrate viruses. Fourteen vertebrate-related viral families were identified (Fig 1 and Table 2). The highest viral diversity was found in both feces samples and forest habitats, and DNA viruses were the most frequently found viruses for both species. The Anelloviridae, Circoviridae and Parvoviridae families accounted for the highest proportion of DNA viruses for both samples of D. rotundus, with variation in number according to the sampling sites.

The Circoviridae and Anelloviridae families were also the most abundant in the sample of M. molossus trapped in urban habitats, with very few viral sequences detected in saliva. In contrast, for M. molossus trapped in forest habitats, viral sequences related to the Herpesviridae, Papillomaviridae and Circoviridae families were the most numerous, with herpesviruses found for the most part in the saliva sample. We found viral sequences related to Poxviridae in both species, but only the D. rotundus trapped in cave M presented mammal-related poxviruses. These sequences presented high amino acid homology (>90%) with the bovine papular stomatitis virus, suggesting that this virus came directly from cattle and its presence was related to the dietary habit of D. rotundus (i.e., D. rotundus feeds off the blood of cattle).

RNA viruses were found in distinct bat species or habitats and belonged to the Astroviridae, Nairoviridae, Hepeviridae, Picornaviridae and Retroviridae families. Astroviruses were only found in D. rotundus trapped in cave F but in both habitats for M. molossus. In contrast, nairoviruses were only found in D. rotundus trapped in cave F and in M. molossus trapped in forest habitats. Hepeviruses were only found in M. molossus trapped in urban areas. Picornaviruses were found in both habitats for M. molossus, but the only sequence detected in forest habitats was different from those detected in urban habitats.

Viral characterization and phylogenetic relationships of selected viruses

Bat circoviruses. The family Circoviridae is known to infect birds, mammals and insects, and comprises two genera, Circovirus and Cyclovirus (ICTV 2016). Their transmission occurs primarily through the fecal-oral route [START_REF] Li | Multiple Diverse Circoviruses Infect Farm Animals and Are Commonly Found in Human and Chimpanzee Feces[END_REF]. Here, Circoviridae viruses were detected in both D. rotundus and M. molossus samples, whatever the environment, with a total of 545 contigs (Table 2). These viruses were essentially found in the feces, except for D. rotundus in cave M for which a small proportion of sequences was also detected in saliva. Four complete genomes of circoviruses (CVs) were obtained for M. molossus (n = 1 in urban habitats and n = 3 in forest habitats), and one partial sequence corresponding to the complete replication-associated protein gene for D. rotundus in cave M (n = 1) (Genbank acc. nb.: KX812440-KX812443 and KX954092). The complete genomes presented the archetypal genome organization of CVs, with the two inversely arranged ORFs encoding the Rep and Cap proteins (Fig 3). The intergenic region was variable in length, depending on the species as well as the habitat. The fulllength REP was used to perform evolutionary analyses. The phylogenetic tree revealed that CVs (identified in cave M for D. rotundus and forest habitats for M. molossus) formed two distinct monophyletic clades with other bat circoviruses detected in the gastrointestinal tract and feces samples of Chinese bat species [START_REF] Ge | Genetic diversity of novel circular ssDNA viruses in bats in China[END_REF] (Fig 3). In contrast, the CV identified in urban areas for M. molossus was closely related to CVs detected in birds, with a posterior probability of 0.84.

Bat spumaviruses. Spumavirus (ICTV 2016) constitutes the only genus of the Spumaretrovirinae subfamily, which belongs to the Retroviridae family. They are highly prevalent in several animal species (e.g., cats, cows, horses and nonhuman primates) and currently six species have been described in the genus. Transmission of spumaviruses between nonhuman primates and cross-species transmission to humans occurs mainly through saliva (e.g., by licking, aggressive contacts, bites) [START_REF] Murray | Foamy virus infection in primates[END_REF][START_REF] Voevodin | Spumaviruses. Simian Virology[END_REF][START_REF] ´a | Cross-Species Transmission of Simian Foamy Virus to Humans in Rural Gabon, Central Africa[END_REF]. Nevertheless, other routes of transmission, such as vertical transmission, are being studied [START_REF] Blasse | Mother-Offspring Transmission and Age-Dependent Accumulation of Simian Foamy Virus in Wild Chimpanzees[END_REF][START_REF] Liu | Molecular Ecology and Natural History of Simian Foamy Virus Infection in Wild-Living Chimpanzees[END_REF][START_REF] Muniz | An expanded search for simian foamy viruses (SFV) in Brazilian New World primates identifies novel SFV lineages and host agerelated infections[END_REF]. In this study, a 312-nt-length fragment (Genbank acc. nb.: KX812444), obtained with two contigs detected in the saliva sample of M. molossus in urban habitats, showed 54.88% and 48.48% nucleotide and amino acid identity, respectively, with the pol gene of Rhinolophus affinis foamy virus 1 (Genbank acc. nb.: JQ814855) detected in the feces of Chinese bats [START_REF] Wu | Virome Analysis for Identification of Novel Mammalian Viruses in Bat Species from Chinese Provinces[END_REF]. Phylogenetic analysis revealed that the foamy virus (FV) identified was close to Rhinolophus affinis foamy virus 1, with a high posterior probability value of 0.91 (Fig 4). Bat FVs seem to share a common origin with equine, bovine and feline FVs. In addition, this analysis shows that bat FVs are divergent from those infecting nonhuman primates. Bat herpesviruses. Mammalian herpesviruses (HVs) belong to the Herpesviridae family (order Herpesvirales). HVs are organized in three subfamilies-Alphaherpesvirinae, Betaherpesvirinae and Gammaherpesvirinae. HVs can infect a wide range of hosts, including humans. Most HV-related contigs were found in the saliva sample of M. molossus in forest habitats. We identified a 943-nt-length fragment covering the DNA polymerase gene (Genbank acc. nb.: KX812446). This fragment displayed from 62.46% to 71.31% and from 68.93% to 80.58% nucleotide and amino acid identities, respectively, with other bat HVs. The highest percentage of identity in amino acids was observed with Myotis ricketti herpesvirus 1 (Genbank acc. nb.: JN692429). Phylogenetic analysis showed that the HV identified belonged to the Gammaherpesvirinae subfamily and was related to the Tupaia belangeri gammaherpesvirus 1 and the Myotis ricketti herpesvirus 1, with a posterior probability of 0.68 (Fig 5).

Bat nairoviruses. The Nairoviridae family belongs to the order Bunyavirales (ICTV 2016). This family encompasses at least nine serogroups, including the Crimean-Congo hemorrhagic fever serogroup. Nairoviruses (NVs) are primarily tick-borne viruses capable of infecting different vertebrate hosts. Four contigs matching nairoviruses (NVs) were detected in the feces of M. molossus in urban areas (Table 2). The contigs covered 1 kb of segment L (Genbank acc. nb: KX821677) and showed a 43% pairwise homology in amino acids with the RNA-dependent RNA polymerase of the previously described Rhinolophus pearsoni bunyavirus (Genbank acc. nb.: KC154063). Phylogenetic analysis revealed that the NV identified clustered with Rhinolophus pearsoni bunyavirus, with a posterior probability of 0.74 (Fig 6). These NVs share a common ancestor with mosquito NVs, with whom they clustered with a posterior probability of 1.

Bat papillomaviruses. Papillomaviridae are nonenveloped dsDNA viruses. Currently, 49 genera have been identified in this family, including the most species-abundant genera Gammapapillomavirus. Papillomaviruses (PVs) are usually asymptomatic and thought to be rarely transmitted between species. In this study, a total of 235 contigs related to PVs were detected in M. molossus samples, with most of them identified in the feces collected in forest habitats (Table 2). The longest contig obtained covered the entire genome of known PVs and was named MmoPV1 (Genbank acc. nb.: KX812447). The MmoPV1 genome was 7,869 bp in length with a 40% G+C content. The MmoPV1 genome had the typical organization of PV ORFs (S2 Fig) . The phylogenetic tree indicated that MmoPV1 possessed a basal position of a cluster of PVs encompassing mupa PVs, kappa PVs, lambda PVs, sigma PVs, nupa PVs and novel unclassified bat PVs detected in Miniopterus schreibersii [START_REF] Tse | Identification of a Novel Bat Papillomavirus by Metagenomics[END_REF], Eidolon helvum (Germany), Eptesicus serotinus and Rhinolophus ferrumequinum [START_REF] Garcı ´a-Pe ´rez | Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination[END_REF], with a high posterior probability value of 0.98 (Fig 7).

Discussion

A wide spectrum of viruses capable of infecting a wide range of animals, plants, insects and bacteria was detected in bats. Since the 1950s, 28 viral families including more than 50 genera have been described in bats [START_REF] Calisher | Viruses in bats: a historic review[END_REF]. With the advent of new-generation technologies, the characterization of bat viromes and the discovery of related variants of known viruses and new batborne viruses continue to increase rapidly. The key purpose of the present work was to explore the viral composition of feces and saliva samples of Desmodus rotundus and Molossus molossus bat species, living in sympatry but using distinct microhabitats in French Guiana.

Overall, this study identified 10,991 viral-associated contigs distributed within 51 known viral families of which 14 are known to infect mammals. New mammalian-related viral sequences/variants were discovered, adding knowledge on the bat-borne viral population. The proportion of eukaryote-and prokaryote-related sequences was low (less than 2% and 20%, respectively). About 0.30% of total contigs were virus-related sequences, with differences in composition depending on the type of sample, the investigated species, habitats, and fine-scale ecological heterogeneity (Table E in S1 File). For instance, of the 30 viral families detected in D. rotundus, only 20 were common to both sampling sites (cave F vs. cave M). Likewise, focusing on vertebrate-related viral families, eight of the 11 viral families detected for this species Focusing on vertebrate-related viral families, ten of the 12 viral families detected in this species were common to both habitats. Furthermore, we observed differences in the viral genera and species detected, depending on the sampling sites for both species. These results suggest that habitats may play a role in shaping the viral diversity harbored by the bats investigated. This observation was also supported by Hu et al. [START_REF] Hu | Virome analysis for identification of novel mammalian viruses in bats from Southeast China[END_REF], who showed that the metagenomic approach can reflect differences in viral diversity carried by different bats in different regions. However, a verification of confounding factors (e.g., sampling size, type of sample, capture effort, species, feeding strategies) will be necessary to confirm these results. Likewise, population structure analysis at the species level and studies on interactions with other bat species using the same habitat are needed to determine their respective roles in shaping viral diversity.

Regardless of the bat species and the habitat studied, phage-related sequences represented a significant proportion of the viral-associated sequences identified (Table 2 and Table F in S1 File). Sequences related to the order Caudovirales and the Microviridae family were the most frequent. Phage-related sequences detected in the feces accounted for most of this proportion, as could be expected considering the type of sample. Despite the constant and rapid expansion of existing databases, sequences lacking counterparts remained the largest part of the data. These global results are in agreement with previous virome studies conducted on North American and Eurasian bat species [START_REF] Donaldson | Metagenomic Analysis of the Viromes of Three North American Bat Species: Viral Diversity among Different Bat Species That Share a Common Habitat[END_REF][START_REF] Li | Bat Guano Virome: Predominance of Dietary Viruses from Insects and Plants plus Novel Mammalian Viruses[END_REF][START_REF] Ge | Metagenomic Analysis of Viruses from Bat Fecal Samples Reveals Many Novel Viruses in Insectivorous Bats in China[END_REF][START_REF] Tse | Identification of a Novel Bat Papillomavirus by Metagenomics[END_REF][START_REF] He | Virome Profiling of Bats from Myanmar by Metagenomic Analysis of Tissue Samples Reveals More Novel Mammalian Viruses[END_REF][START_REF] Dacheux | A Preliminary Study of Viral Metagenomics of French Bat Species in Contact with Humans: Identification of New Mammalian Viruses[END_REF] and highlight the need to pursue investigations and taxonomic assignments on microorganism communities. Therefore, the underestimation of the total number of bat-borne viruses present in the samples, including highly divergent viruses, cannot be excluded.

Despite a smaller number of samples for M. molossus, the number of viral-associated contigs detected in these samples was higher than that found in D. rotundus, suggesting a higher number of viruses passing through this species. However, these viruses are likely related to nondigested viruses associated with the diet of their prey but not directly to the host. Indeed, as highlighted in Li et al., insect and plant viruses were mostly represented in the insectivorous species, while they accounted for less than 5% in the vampire species [START_REF] Li | Bat Guano Virome: Predominance of Dietary Viruses from Insects and Plants plus Novel Mammalian Viruses[END_REF]. The diet of the vampire bat (vertebrate blood) may also be reflected in the high proportion of vertebrate-related viral sequences found. Likewise, the divergence observed in the distribution of phage-related viruses might be associated with the diets of the species investigated and/or to their phylogenetic position, Molossidae vs. Phyllostomidae. For instance, Podoviridae species were the most frequent in D. rotundus, whatever the sampling site, while Microviridae species were the most often found in M. molossus. In bats, former studies highlighted a strong association between the microbiota, host phylogeny, life history, physiology as well as locality [START_REF] Phillips | Microbiome analysis among bats describes influences of host phylogeny, life history, physiology and geography[END_REF][START_REF] Carrillo-Araujo | Phyllostomid bat microbiome composition is associated to host phylogeny and feeding strategies[END_REF]. Given that gut microbiota is known to be highly dependent on diet, these results may reflect differences between the dietary ecology of D. rotundus and M. molossus species.

We found several novel mammalian-related viral sequences/variants from the Anelloviridae, Nairoviridae, Circoviridae, Hepeviridae, Herpesviridae, Retroviridae and Papillomaviridae families. These viral sequences were closely related to sequences detected in Old World bat species [START_REF] Wu | Deciphering the bat virome catalog to better understand the ecological diversity of bat viruses and the bat origin of emerging infectious diseases[END_REF][START_REF] Garcı ´a-Pe ´rez | Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination[END_REF][START_REF] Drexler | Bats Worldwide Carry Hepatitis E Virus-Related Viruses That Form a Putative Novel Genus within the Family Hepeviridae[END_REF][START_REF] Ge | Metagenomic Analysis of Viruses from the Bat Fecal Samples Reveals Many Novel Viruses in Insectivorous Bats in China[END_REF][START_REF] Tse | Identification of a Novel Bat Papillomavirus by Metagenomics[END_REF][START_REF] Wu | Virome Analysis for Identification of Novel Mammalian Viruses in Bat Species from Chinese Provinces[END_REF]. Furthermore, most of the families identified in Old World bat species were identified here, even for non-mammalian viruses. Moreover, where divergence could be expected due to geographical isolation, we observed highly supported phylogenetic proximity between Old and New World bat viruses in their respective continents, revealing the existence of common evolutionary processes and supporting the long evolutionary hypothesis of bats and their viruses [START_REF] Schneeberger | Zoonotic Viruses and Conservation of Bats[END_REF]. For example, most of the circovirus (CV) sequences detected in the present study shared high sequence identities with bat CVs detected in several bat species trapped in different Chinese provinces [START_REF] Wu | Deciphering the bat virome catalog to better understand the ecological diversity of bat viruses and the bat origin of emerging infectious diseases[END_REF][START_REF] Ge | Genetic diversity of novel circular ssDNA viruses in bats in China[END_REF] and clustered in highly supported monophyletic groups. The results reported herein suggest that the associated viruses may be hosted by bats. Conversely, the highly supported clustering of M. molossus CV (KX812443) with avian CVs may result from a cross-species jump from birds to bats, as reported by Hu et al. [START_REF] Hu | Virome analysis for identification of novel mammalian viruses in bats from Southeast China[END_REF] and Lima et al. [START_REF] De S Lima | Genomic Characterization of Novel Circular ssDNA Viruses from Insectivorous Bats in Southern Brazil[END_REF]. Likewise, foamy virus (FV) sequences, also called spumaviruses, detected in saliva swab samples of M. molossus showed a high genomic similarity with the FVs detected in pharyngeal and rectal swab samples of Rhinolophus affinis reported by Wu et al. [START_REF] Wu | Virome Analysis for Identification of Novel Mammalian Viruses in Bat Species from Chinese Provinces[END_REF], but low similarity with other spumaviruses infecting other hosts (e.g., equines, felines, bovines, nonhuman primates). Our findings indicate that FVs can indeed infect bats, which could be considered as potential reservoirs and dispersers of this viral genus.

Several studies reported the detection of herpesviruses (HVs) of the three subfamilies (Alpha-, Beta-and Gammaherpesvirinae) in feces, anal swabs, digestive tract and saliva samples of bats [START_REF] Hu | Virome analysis for identification of novel mammalian viruses in bats from Southeast China[END_REF][START_REF] Wu | Deciphering the bat virome catalog to better understand the ecological diversity of bat viruses and the bat origin of emerging infectious diseases[END_REF][START_REF] Wu | Virome Analysis for Identification of Novel Mammalian Viruses in Bat Species from Chinese Provinces[END_REF][START_REF] Wibbelt | Discovery of herpesviruses in bats[END_REF][START_REF] Molna ´r | Detection of a novel bat gammaherpesvirus in Hungary[END_REF][START_REF] Razafindratsimandresy | Partial molecular characterization of alphaherpesviruses isolated from tropical bats[END_REF][START_REF] Watanabe | Detection of a new bat gammaherpesvirus in the Philippines[END_REF][START_REF] Sano | Detection of a novel herpesvirus from bats in the Philippines[END_REF][START_REF] Host | Discovery of a Novel Bat Gammaherpesvirus[END_REF][START_REF] Zheng | High prevalence and diversity of viruses of the subfamily Gammaherpesvirinae, family Herpesviridae, in fecal specimens from bats of different species in southern China[END_REF]. These findings suggested that the oral-fecal transmission route may be important for the transmission of HVs in bats. Furthermore, cases of cross-species transmission of HVs were also reported in bats, but their mode of transmission is still unclear [START_REF] Zheng | High prevalence and diversity of viruses of the subfamily Gammaherpesvirinae, family Herpesviridae, in fecal specimens from bats of different species in southern China[END_REF]. In this study, we found a high diversity of HVs in the feces and saliva samples of both species investigated. Moreover, some sequences detected in the saliva samples of M. molossus from forest habitats were also found in the feces samples, which showed the capacity of these bats to shed HVs in the environment and supported the hypothesis of a potential oral-fecal transmission route. Detected HV-related sequences were novel and showed a high sequence similarity with other bat HVs. Nevertheless, the phylogenetic tree constructed using a Bayesian method revealed that M. molossus herpesvirus 1 (KX812446) did not cluster in a unique group with other known bat gamma-HVs. Rather, it shares a common ancestor with Myotis ricketti and Tupaia belangeri gamma-HVs, stressing the need for further characterization of M. molossus herpesvirus 1 to confirm its taxonomic assignment.

Nairoviruses (NVs) naturally infecting bats were reported in a few studies, with some capable of causing intestine and hepatic disorders in other mammals [START_REF] Dacheux | A Preliminary Study of Viral Metagenomics of French Bat Species in Contact with Humans: Identification of New Mammalian Viruses[END_REF][START_REF] Ishii | A nairovirus isolated from African bats causes haemorrhagic gastroenteritis and severe hepatic disease in mice[END_REF][START_REF] Walker | Genomic Characterization of Yogue, Kasokero, Issyk-Kul, Keterah, Gossas, and Thiafora Viruses: Nairoviruses Naturally Infecting Bats, Shrews, and Ticks[END_REF][START_REF] Lvov | Issyk-Kul" virus, a new arbovirus isolated from bats and Argas (Carios) vespertilionis (Latr., 1802) in the Kirghiz S.S.R. Brief report[END_REF]. Evidence of neutralizing antibodies against Crimean-Congo hemorrhagic fever (CCHF) was reported by Mu ¨ller et al. [START_REF] Mu ¨ller | Evidence for widespread infection of African bats with Crimean-Congo hemorrhagic fever-like viruses[END_REF], but the role of bats regarding the cycle and dispersal of this virus is not clear. Here, we found a novel NV-related sequence in the feces of M. molossus sampled in urban areas. Phylogenetic relationships based on the partial segment L sequence showed a highly supported clustering with another NV-related sequence detected from the feces of Rhinolophus pearsoni. This analysis also revealed that the detected NV was related to the genus Phlebovirus, primarily constituted of tick-, mosquito-and phlebotomine-borne viruses. These findings suggest that this sequence may be related to undigested viruses associated with the bats' diet rather than viruses hosted by bats. However, screening of other organs will be necessary to rule out the role of bats in the virus cycle and dispersal.

Diverse sequences related to papillomaviruses (PVs) were reported in bats [START_REF] Hu | Virome analysis for identification of novel mammalian viruses in bats from Southeast China[END_REF][START_REF] Wu | Deciphering the bat virome catalog to better understand the ecological diversity of bat viruses and the bat origin of emerging infectious diseases[END_REF][START_REF] Garcı ´a-Pe ´rez | Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination[END_REF][START_REF] Ge | Metagenomic Analysis of Viruses from the Bat Fecal Samples Reveals Many Novel Viruses in Insectivorous Bats in China[END_REF][START_REF] Tse | Identification of a Novel Bat Papillomavirus by Metagenomics[END_REF][START_REF] Donaldson | Metagenomic Analysis of the Viromes of Three North American Bat Species: Viral Diversity among Different Bat Species That Share a Common Habitat[END_REF][START_REF] Baker | Metagenomic study of the viruses of African straw-coloured fruit bats: Detection of a chiropteran poxvirus and isolation of a novel adenovirus[END_REF]. Here, we detected 235 PV-like sequences related to members of genetically diverse genera within the Papillomaviridae, indicating that bat species might be associated with a wide diversity of PVs. We described the complete genome of a novel bat PV, MmoPV1 (KX812447), detected in the feces and saliva samples of M. molossus sampled in forest and urban habitats. This is the first detection of PV in this species to date. Comparing MmoPV1 with other PVs showed that it contains the typical PV ORFs coding for four putative early proteins (E6, E7, E1, E2) and two putative late capsid proteins (L2 and L1). The putative early protein E4 -present in other phylogenetically closely-related bat PVs (JQ692938 [START_REF] Tse | Identification of a Novel Bat Papillomavirus by Metagenomics[END_REF], JX123128 [START_REF] Baker | Metagenomic study of the viruses of African straw-coloured fruit bats: Detection of a chiropteran poxvirus and isolation of a novel adenovirus[END_REF], KC858263, KC858265, KC858266 [START_REF] Garcı ´a-Pe ´rez | Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination[END_REF])-was absent in MmoPV1. Furthermore, the phylogenetic tree revealed that MmoPV1 may be more ancient than these bat PVs, suggesting that they may either have undergone a divergent evolution that allowed them to acquire the early protein or represent different host-specific and area-specific lineages [START_REF] Garcı ´a-Pe ´rez | Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination[END_REF].

This study is the very first to explore the virome of fecal and saliva samples obtained from the two common Amazonian bat species, M. molossus and D. rotundus, with overlapping distribution but using distinct microhabitats in French Guiana. It provides important insight into the feces and saliva viromes of the two bat species investigated within contrasting habitats.

However, to fully understand how viral diversity is shaped in D. rotundus and M. molossus, further characterization of their geographic range, foraging-induced interactions, species distribution and gregariousness will be necessary. Indeed, larger geographic ranges encompass greater diversity of ecosystems/habitats, which could lead to a spatial population substructure [START_REF] Turmelle | Correlates of Viral Richness in Bats (Order Chiroptera)[END_REF]. The overlapping distribution of reservoirs and recipient hosts, the social complexity of bats as well as species-specific evolutionary and life-history traits are known as predictors of viral richness in wildlife [START_REF] Plowright | Ecological dynamics of emerging bat virus spillover[END_REF][START_REF] Turmelle | Correlates of Viral Richness in Bats (Order Chiroptera)[END_REF]. Likewise, the contact and proximity between individuals influence the presence, abundance and diversity of the pathogens harbored [START_REF] Duboscq | Pathogènes, parasites et re ´seaux dans les socie ´te ´s animales. Analyse des re ´seaux sociaux applique ´e à l'e ´thologie et l'e ´cologie[END_REF]. Consequently, deciphering the virome of bats should consider the size of the whole community of bats, the genetic structure of populations in a given habitat and the rates of interactions among them, all parameters contributing to the viral diversity observed for bat species.

  Fig). M. molossus individuals trapped in forest habitats formed monospecific colonies, whereas individuals trapped in urban habitats shared artificial roosts with a congener, Molossus coibensis.

Fig 1 .

 1 Fig 1. Bioinformatic analysis pipeline for the 3,722,219 assembled contigs, based on Baker et al. [45]. (A) Contigs assembled from both normalized and non-normalized sequence reads by two de novo assemblers (SPAdes and Velvet) were consolidated by sequential comparisons (numbered shadowed areas) and removal of duplicate sequences (red arrows). (B) Centroids subjected to sequential BLAST comparison and manually controlled taxonomic classification to identify viral sequences. Proportion of sequences assembled from feces (red) and saliva swabs (blue) are shown in the stacked chart for each species

  depending on habitats (caves F and M for D. rotundus and Urban and Forest for M. molossus). (C) Column charts represent the distribution of contig matches (per pooled samples and overall) and the distribution of vertebrate-related viral families by bat species and habitats. https://doi.org/10.1371/journal.pone.0186943.g001 consolidated contigs, respectively (Table E in S1 File). A total of 10,991 viral-associated sequences related to 51 known viral families were identified based on their most significant BLAST matches (Fig 2). The total number of virus-associated contigs ranged from 1,930 for D. rotundus in cave F to 3,768 for M. molossus in forest areas (Table F in S1 File).

Fig 2 .Total

 2 Fig 2. Heatmap based on the viral-associated contigs of 51 families of insect, phage, plant/protozoan and vertebrate viruses in each pooled sample. Location information is provided above each column (Caves F and M for D. rotundus, Urban and Forest for M. molossus). The names of the viral families are presented in alphabetical order in the middle. The boxes colored from green to dark red represent the number of contigs observed. Contigs varied between 1 and 450 for the saliva samples and between 1 and 1465 for feces. The scales are given for each type of sample. https://doi.org/10.1371/journal.pone.0186943.g002

Fig 3 .

 3 Fig 3. Circular genome maps of five putative circoviruses directly recovered from metagenomic data of M. molossus and D. rotundus bat feces and their phylogenetic relationships with other representative members of the Circoviridae family. (A) The inversely arranged open-reading frames encoding the putative replication-associated protein (REP) and capsid protein (CAP) are shown in green and blue boxes, respectively. The genome organization was determined with GENEIOUS R9. (B) The phylogenetic analysis is based on the REP protein sequences (alignment of 109 amino acids). The blue arrows indicate the five REP sequences of bat-sourced circoviruses obtained in the present study. The tree was inferred using the Bayesian method with the blosum62 model. Sequence identifiers include the NCBI accession number and the isolate name. Posterior probabilities of the Bayesian analysis (>50%) are shown next to each node. The scale bar indicates amino acid substitutions per site. https://doi.org/10.1371/journal.pone.0186943.g003

Fig 4 .

 4 Fig 4. Phylogenetic analysis of partial sequences of the pol s region (alignment of 107 amino acids) directly obtained from the metagenomic data of pooled fecal samples of M. molossus with other representative members of the Spumavirus genus. The tree was inferred using the Bayesian method with the WAG + G model. Sequence identifiers include the NCBI accession number and the isolate name. The blue arrows indicate the sequence of bat-sourced spumavirus obtained in the present study. Posterior probabilities of the Bayesian analysis (>50%) are shown next to each node. The scale bar indicates amino acid substitutions per site. https://doi.org/10.1371/journal.pone.0186943.g004

Fig 5 .

 5 Fig 5. Phylogenetic analysis of partial pol gene sequences (alignment of 951 nucleotides) directly obtained from the metagenomic data of pooled fecal samples of M. molossus with other representative members of the Herpesviridae family. The tree was inferred using the Bayesian method with the GTR + G + I model. Sequence identifiers include the NCBI accession number and the isolate name. The blue arrows indicate the bat-sourced herpesvirus obtained in the present study. Posterior probabilities of the Bayesian analysis (>50%) are shown next to each node. The scale bar indicates amino acid substitutions per site. https://doi.org/10.1371/journal.pone.0186943.g005

Fig 6 .Fig 7 .

 67 Fig 6. Phylogenetic analysis of partial RdRp protein sequences (alignment of 341 amino acids) directly obtained from the metagenomic data of pooled fecal samples of M. molossus with other representative members of the Nairoviridae family. The tree was inferred using the Bayesian method with the WAG + G model. Sequence identifiers include the NCBI accession number and the isolate name. The blue arrows indicate the bat-sourced nairovirus sequence obtained in the present study. Posterior probabilities of the Bayesian analysis (>50%) are shown next to each node. The scale bar indicates amino acid substitutions per site. https://doi.org/10.1371/journal.pone.0186943.g006

  Bayesian analysis (>50%) are shown next to each node. The scale bar indicates amino acid substitutions per site. https://doi.org/10.1371/journal.pone.0186943.g007

  The project was nevertheless submitted to and approved by the Conseil Scientifique Re ´gional pour le Patrimoine Naturel de la Guyane. Captures that occurred within protected areas (nature reserves) received approval by the Conseil Scientifique Re ´gional du Patrimoine Naturel on 26 January 2010 and ad hoc authorizations (No. 2011-35 dated 05/30/2011, No. 35 and 59 obtained 03/21/2013 and 04/17/2013, respectively, and delivered by the Prefecture of French Guiana).

Table 1 . Characteristics of the sampling sites and number of collected feces and saliva samples for Molossus molossus and Desmodus rotundus.

 1

	Species	Habitats	Sites	GPS coordinates	n saliva swabs	n feces
				Latitude (N)	Longitude (W)	Per site	Total	Per site	Total
	D. rotundus	Forest	Cave F	4˚38 0 59.144@	52˚17 0 35.441@	0	0	75	75
			Cave M	4˚32 0 6.82@	52˚9 0 6.239@	50	50	66	66
						Total	50	Total	141
	M. molossus	Forest	Paracou	5˚14 0 21.282@	52˚55 0 24.218@	17	58	4	14
			Saut Athanase	4˚11 0 14.706@	52˚19 0 11.21@	41		10
		Urban	Cacao	4˚34 0 33.771@	52˚28 0 4.926@	18	30	0	5
			La Chaumière	4˚53 0 5.419@	52˚21 0 4.124@	12		5
						Total	88	Total	19

https://doi.org/10.1371/journal.pone.0186943.t001

  and Table2). Contigs matching unclassified viral sequences accounted for one-tenth of the total of viral contigs (Fig1and Table2).

PLOS ONE | https://doi.org/10.1371/journal.pone.0186943November 8, 2017

Acknowledgments

We acknowledge Franc ¸ois Catzeflis and Marguerite Delaval for useful discussions on the biology, ecology and dynamics of bats. All field volunteers and owners and/or managers of capture sites are warmly acknowledged for their assistance in captures. We thank the INDA and C3BI teams at the Institut Pasteur and UMR BIOGECO for their technical support and access to the clusters. We thank L. Ma and M. Tichit for technical assistance.

A. Salmier was funded by a grant from European funds (PO FSE 2007-2013) and "Investissement d'Avenir" managed by Agence Nationale de la Recherche (CEBA, Ref. ANR-10-LABEX-25-01). This study was conducted within the CAROLIA program supported by European funds (ERDF/FEDER) and assistance from Re ´gion Guyane and Direction Re ´gionale pour la Recherche et la Technologie. It also received a European Commission "REGPOT-CT-2011-285837-STRonGer" grant within the FP7 and "Investissement d'Avenir" grants managed by the Agence Nationale de la Recherche (CEBA, Ref. ANR-10-LABEX-25-01). The Genomics Platform is a member of the France Ge ´nomique consortium (ANR10-INBS-09-08). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

All relevant data are within the paper and its Supporting Information files. All virus sequences reported in this study have been deposited in the GenBank nucleotide database under accession numbers KX812440 to KX812444, KX812446, KX812447, KX821677 and KX954092. The data from Illumina sequencing were deposited in GenBank Sequence Reads Archive under accession numbers SAMN05725475 -SAMN05725481.

Methodology: Sourakhata Tirera, Alain Franc, Christiane Bouchier.

Project administration: Anne Lavergne.

Supervision: Anne Lavergne.

Writing -original draft: Arielle Salmier, Sourakhata Tirera, Benoit de Thoisy, Alain Franc, Edith Darcissac, Damien Donato, Christiane Bouchier, Vincent Lacoste, Anne Lavergne.

Writing -review & editing: Arielle Salmier, Benoit de Thoisy, Alain Franc, Vincent Lacoste, Anne Lavergne.


Henning Fernau
email: fernau@uni-trier.de

Rudolf Freund

Rani Siromoney
email: siromoney@cmi.ac.in

K G Subramanian

Contextual Array Grammars with Matrix and Regular Control

We investigate the computational power of d-dimensional contextual array grammars with matrix control and regular control languages. For d ≥ 2, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages. Yet in the 1-dimensional case, for a one-letter alphabet, the family of 1-dimensional array languages generated by contextual array grammars with regular control languages coincides with the family of regular 1-dimensional array languages, whereas for alphabets with more than one letter, we obtain the array images of the linear languages.

Introduction

Contextual string grammars were introduced by Solomon Marcus [START_REF] Marcus | Contextual grammars[END_REF] with motivations arising from descriptive linguistics. A contextual string grammar consists of a finite set of strings (axioms) and a finite set of productions, which are pairs (s, c) where s is a string, the selector, and c is the context, i. e., a pair of strings, c = (u, v), over the alphabet under consideration. Starting from an axiom, contexts iteratively are added as is indicated by the productions, which yields new strings. In contrast to usual sequential string grammars in the Chomsky hierarchy (e.g., see [START_REF]Handbook of Formal Languages[END_REF]), these contextual string grammars are pure grammars where new strings are not obtained by rewriting, but by adjoining strings. Several classes of contextual grammars have been introduced and investigated, e.g., see [START_REF] Ehrenfeucht | Contextual grammars and formal languages[END_REF] and [START_REF] Pȃun | Marcus contextual grammars[END_REF] for surveys on the area.

The idea of contextual productions then was also introduced for multidimensional array grammars, for instance, to carry over ideas from formal languages to the processing of digital images. In the area of two-dimensional picture languages, e.g., see [START_REF] Giammarresi | Two-dimensional languages[END_REF][START_REF] Pradella | A unifying approach to picture grammars[END_REF][START_REF] Rosenfeld | Picture Languages[END_REF][START_REF] Rosenfeld | Picture languages -a survey[END_REF], different kinds of array grammars, both isometric and non-isometric ones, have been proposed, motivated by many applications such as character recognition (also confer [START_REF] Fernau | Bounded parallelism in array grammars used for character recognition[END_REF]), cluster analysis of patterns, and so on. Isometric contextual array grammars were introduced in [START_REF] Freund | Contextual array grammars[END_REF].

Regulated rewriting with different control mechanisms has been studied extensively especially for string grammars (e.g., see [START_REF] Dassow | Regulated Rewriting in Formal Language Theory[END_REF]), for example, grammars with control languages and matrix grammars, but then also for array grammars, e.g., see [START_REF] Freund | Control mechanisms on #-context-free array grammars[END_REF]. Non-isometric contextual array grammars (with regulation) were considered in [START_REF] Fernau | Non-isometric contextual array grammars with regular control and local selectors[END_REF][START_REF] Fernau | Contextual array grammars with matrix and regular control[END_REF][START_REF] Krithivasan | Array contextual grammars[END_REF].

In this paper we consider matrix contextual array grammars and contextual array grammars with regular control and examine their generative power. In the 1-dimensional case, we obtain special results: the family of 1-dimensional array languages generated by contextual array grammars with regular control languages coincides with the family of regular 1-dimensional array languages over unary alphabets and with array images of the linear languages over alphabets with more than one letter; already for binary alphabets, regular control is strictly more powerful than matrix control, a phenomenon rarely observed in regulated rewriting (confer [START_REF] Freund | A general framework for regulated rewriting based on the applicability of rules[END_REF]).

Definitions

For notions and notations as well as results related to formal language theory we refer to books like [START_REF] Dassow | Regulated Rewriting in Formal Language Theory[END_REF]. The families of λ-free (λ denotes the empty string) regular string languages (over a k-letter alphabet) is denoted by L (REG) (L REG k ). For the definitions and notations for arrays and sequential array grammars we refer to [START_REF] Freund | Control mechanisms on #-context-free array grammars[END_REF][START_REF] Rosenfeld | Picture Languages[END_REF][START_REF] Wang | Some new results on isotonic array grammars[END_REF].

Let Z be the set of integers and N be the set of positive integers. Let d ∈ N. A d -dimensional array A over the alphabet V is a mapping A :

Z d → V ∪ {#} where shape (A) = v ∈ Z d | A (v) = # is finite and # / ∈ V is called the blank symbol. We usually write A = {(v, A (v)) | v ∈ shape (A)}. The set of all d-di- mensional arrays over V is denoted by V * d . The empty array Λ d in V * d satisfies shape(Λ d ) = ∅. Moreover, we define V +d = V * d \ {Λ d } . Let v ∈ Z d . Then the (linear) translation τ v : Z d → Z d is defined by τ v (w) = w + v for all w ∈ Z d ,

and for any array

A ∈ V * d we define τ v (A), the corresponding d-dimensional array translated by v, by (τ v (A)) (w) = A (w -v) for all w ∈ Z d . The vector (0, ..., 0) ∈ Z d is denoted by Ω d .
Usually (see [START_REF] Rosenfeld | Picture Languages[END_REF]) arrays are regarded as equivalence classes of arrays with respect to linear translations.

The equivalence class [A] of an array

A ∈ V * d satisfies [A] = B ∈ V * d | B = τ v (A) for some v ∈ Z d .
The set of all equivalence classes of d-dimensional arrays over V with respect to linear translations is denoted by V * d , and this bracket notation carries over to classes of array languages, as well.

As many results for d-dimensional arrays for a specific d can be taken over immediately for higher dimensions, we introduce special notions:

Let n, m ∈ N with n ≤ m. For n < m, the natural embedding i n,m : Z n → Z m is defined by i n,m (v) = (v, Ω m-n ) for all v ∈ Z n ; for n = m we define i n,n : Z n → Z n by i n,n (v) = v for all v ∈ Z n . To an n-dimensional array A ∈ V +n with A = {(v, A (v)) | v ∈ shape (A)} we assign the m-dimensional array i n,m (A) = {(i n,m (v) , A (v)) | v ∈ shape (A)} .
We can use the well-known graph-theoretic notion of a connected graph to define connected arrays. Let W be a non-empty finite subset of Z d . We associate a graph g(W ) to W with vertex set W and an edge between v, w ∈ W if and only if v -w = 1, where the norm u of a vector

u ∈ Z d , u = (u (1) , ..., u (d)), is defined by u = max {|u (i)| | 1 ≤ i ≤ d} . Then W is said to be connected if g(W ) is connected.
There is a natural bijection between the (equivalence classes of) 1-dimensional connected arrays and strings: for any equivalence class of 1-

dimensional arrays A = [{((i -1), a i ) | 1 ≤ i ≤ n}]
we define its string image as str(A) = a 1 . . . a n ; the string w = a 1 . . . a n can be interpreted as the array arr (w) = {{((i -1), a i )} | 1 ≤ i ≤ n}. In the standard way, these notions are extended from strings and arrays to sets of strings and arrays.

Example 1. Consider the language L 1 of connected 2-dimensional arrays The following results for 1-dimensional array languages are folklore:

L 1 = ((0, i) , a) | 0 ≤ i ≤ n ∪ ((j, 0) , a) | 1 ≤ j ≤ m n, m ∈ N .
Theorem 1. For all k ≥ 1, L 1-REGA k = arr L REG k and str L 1-REGA k = L REG k .
Let us mention the close similarities of the work of 1-dimensional regular array grammars and Lindenmayer systems with apical growth [START_REF] Subramanian | A note on regular controlled apical growth filamentous systems[END_REF]. Another similar development can be found within Watson-Crick systems [START_REF] Nagy | On a hierarchy of 5 → 3 sensing Watson-Crick finite automata languages[END_REF].

Contextual Array Grammars

We now turn our attention to the main variants of contextual array grammars considered in this paper. Definition 2. A d-dimensional contextual array grammar (d ∈ N) is a construct G = (d, V, #, P, A) where V is an alphabet not containing the blank symbol #, A is a finite set of axioms, i. e., of d-dimensional arrays in V +d , and P is a finite set of rules of the form (U α , α, U β , β) where

(i) U α , U β ⊆ Z d , U α ∩ U β = ∅,
and U α , U β are finite and non-empty;

(ii) α : U α → V and β : U β → V.
(U α , α) corresponds with the selector and (U β , β) with the context of the production (U α , α, U β , β) ; U α is called the selector area, and U β is the context area. As the sets U α and U β are uniquely determined by α and β, we will also represent

(U α , α, U β , β) by (α, β) only. For C 1 , C 2 ∈ V +d we say that C 2 is directly derivable from C 1 by the contextual array production p ∈ P , p = (U α , α, U β , β) (we write C 1 =⇒ p C 2 ), if there exists a vector v ∈ Z d such that -C 1 (w) = C 2 (w) = α (τ -v (w)) for all w ∈ τ v (U α ) , -C 1 (w) = # for all w ∈ τ v (U β ) , -C 2 (w) = β (τ -v (w)) for all w ∈ τ v (U β ) , -C 1 (w) = C 2 (w) for all w ∈ Z d \ τ v (U α ∪ U β ) .
Hence, if in C 1 we find a subpattern that corresponds with the selector α and only blank symbols at the places corresponding with β, we can add the context β thus obtaining C 2 . For every B 1 , B 2 ∈ V +d we say that B 2 is directly derivable from B 1 by the contextual array production p ∈ P , p = (U α , α, U β , β), denoted

B 1 =⇒ p B 2 , if and only if C 1 =⇒ p C 2 for some C 1 ∈ B 1 and C 2 ∈ B 2 . C 1 =⇒ G C 2 (B 1 =⇒ G B 2 ) means that C 1 =⇒ p C 2 (B 1 =⇒ p B 2 ) for some p ∈ P .
The array language generated by G is defined as

L (G) = C ∈ V +d | A =⇒ * G C for some A ∈ A .
G = (d, V, #, P, A) with A = {A i | 1 ≤ i ≤ n} will be specified by writing [G] = (d, V, #, P, A ) where A = {A i | 1 ≤ i ≤ n} such that A i ∈ [A i ] , 1 ≤ i ≤ n,
which means specifying an axiom A i by one array from [A i ].

Example 2. Any finite d-dimensional array language of connected arrays

L ⊂ T +d is in L (d-ContA) as L = L (G L ) where G L = (d, T, #, ∅, L).
Example 3. We now show how the language L 1 from Example 1 can be generated by the contextual array grammar G 1 , i.e.,

L 1 ∈ L 2-ContA 1 : G 1 = (2, {a} , #, P 1 , {A 1 })
where A 1 = {((0, 0) , a) , ((0, 1) , a) , ((1, 0) , a)} is the only axiom and P 1 consists of the two productions p u and p r :

p u = ({(0, 0) , (0, 1)} , {((0, 0) , a) , ((0, 1) , a)} , {(0, 2)} , {((0, 2) , a)}) , p r = ({(0, 0) , (1, 0)} , {((0, 0) , a) , ((1, 0) , a)} , {(2, 0)} , {((2, 0) , a)}) .
As the selector area U α and the context area U β in a contextual array production of the form (U α , α, U β , β) are disjoint, both α and β can be represented within only one pattern, i. e., p u and p r can be represented in a more depictive way by the patterns shown on the right (the symbols of the selector are enclosed in boxes).

p u = a a a , p r = a a a .
The example of the L-shaped array for n = 3 and m = 4 then is generated by twice applying rule p u and three times applying rule p r , in any order. We also observe that every intermediate array obtained by applying these rules is in L 1 , too. Obviously, by the definition of equivalence classes of arrays, we also have

[L (G 1 )] = [L 1 ] ∈ L 2-ContA 1 .
[A 1 ] can be described in a more depictive way by a a a , i.e., the contextual array grammar [G 1 ] for [L (G 1 )] can also be written as [G 1 ] = 2, {a} , #, P 1 , a a a (see Remark 1). In the following, the axiom(s) often will just be given in such a pictorial variant.

Example 4. For the singleton language

L ⊥ =    a a a a a a a    ⊂ {a} +2 , we have L ⊥ ∈ [L (2-ContA)] \ [L (2-REGA)].
As we can take L ⊥ (as any finite language) as a set of axioms, containment in [L (2-ContA)] is clear. Conversely, any regular array grammar has to scan the non-blank symbols of the array A, which is impossible, as the underlying graph g(shape(A)) is not Hamiltonian.

Theorem 2. L 1-REGA 1 ⊆ L 1-ContA 1 .
Proof. Due to the results from Theorem 1, it only remains to show that arr L REG 1 ⊆ L 1-ContA 1 . From [1, Theorem 4.4], we deduce that any infinite language L ⊆ {a} + in L REG 1 can be written in the form L = {a s1 , a s2 , . . . , a st }∪

m i=1 {a k•n+di | n ≥ 0} for some numbers k, k ≤ d 1 < d 2 < ... < d m < 2k, 0 ≤ s 1 < s 2 < ... < s t < k.
The 1-dimensional contextual array grammar now is constructed using a context of length k and putting the words a sj , 1 ≤ j ≤ t, and a di , 1 ≤ i ≤ m, into the set of axioms, i.e., we define the 1-dimensional contextual array grammar

G (L) = (1, {a} , #, P, A) with A = {arr (a sj ) | 1 ≤ j ≤ t} ∪ arr a di | 1 ≤ i ≤ m and P = a k a k . Obviously, [L (G (L))] = [arr (L)]. The 1-dimensional contex- tual array grammar [G (L)] for [L (G (L))] can also be written as [G (L)] = (1, {a} , #, P, A ) with A = {a sj | 1 ≤ j ≤ t} ∪ a di | 1 ≤ i ≤ m (compare with Remark 1).
For the sake of completeness we mention that every finite array language A = {arr (a sj ) | 1 ≤ j ≤ t} is generated by the 1-dimensional contextual array grammar G (L) = (1, {a} , #, P, A) with P = ∅.

Remark 2. Following the definition already given in [START_REF] Freund | Contextual array grammars[END_REF], our d-dimensional extension of (external) contextual grammars only appends at one location, while external contextual string grammars as originally defined by Solomon Marcus, see [START_REF] Marcus | Contextual grammars[END_REF], append to both ends of a string at the same time. This design decision has two main reasons. First, it is not quite clear what the d-dimensional counterpart of external contextual grammars would really mean: for instance, for d = 2, should we allow appending on both ends of a row or column at the same time, as we did in [START_REF] Fernau | Non-isometric contextual array grammars with regular control and local selectors[END_REF] for the case of non-isometric contextual array grammars? Or, should we rather append on 'all ends' ? Obviously, this situation becomes even more intricate for higher dimensions. Yet second and even more important, appending at both sides of a string, i.e., a 1-dimensional array, in parallel can easily be simulated sequentially by a matrix with two components. It is therefore easy to see that in the 1-dimensional case, the string images of the arrays generated by contextual array grammars with matrix control exactly correspond with the string languages generated by external contextual string grammars. This means that for the regulated variants discussed in the following, any variant that can be conceivably defined for the d-dimensional analogue of external contextual grammars, in the 1-dimensional case should lead to the same results as the original variant of contextual array grammars defined in [START_REF] Freund | Contextual array grammars[END_REF] and taken as the basis in this paper, too.

a a a =⇒ G M a a a a a =⇒ G M a a a a a a a =⇒ G M • • •
The single matrix p u , p r , p u = a a a

, p r = a a a , guarantees that both arms of the array grow in a synchronized way. In the 1-dimensional case, the situation is different: as we shall prove later, see Theorem 6, L 1- Even more, there is no 1-dimensional contextual array grammar for L n . Namely, if this would be the case, then first observe that there must be rules that append something to the right, as well as to the left of the array, and this should be possible infinitely often. Otherwise, the sequence of context additions would happen (finally) only on one side, which means that this behavior can again be simulated by some regular array grammar, contradicting our previous reasoning. Hence, there must be a rule that contains a sequence of a's as its selector, say, arr(a rs ), and also a sequence of a's, say, arr(a rc ) as its context in order to append a rc to the right of the current array, and likewise, there must be a rule that contains a sequence of a's as its selector, say, arr(a s ), and also a sequence of a's, say, arr(a c ) as its context in order to append a lc to the left of the current array. For sufficiently long arrays arr(a n ba n ), both rules can be applied, and arrays like arr(a n ba n+rc ) can generated that do not belong to L n . Hence, L n / ∈ L(1-ContA).

ContA 1 = L 1-M ContA 1 , but for k ≥ 2, we still have L 1-ContA k L 1-M ContA k ,

Yet for the 1-dimensional matrix contextual array grammar [G

M ] = (G n , M n ) with [G n ] = (1,
{a, b} , #, P, {aba}) where p l = a a , p r = a a , and

M n = { p l , p r }, we have [L (G n )] = [arr (L n )].
The single matrix p l , p r guarantees that the number of symbols a grows to the left and to the right in a synchronized way.

In addition, the following example even yields that for any k

≥ 2, L 1-M ContA k is incomparable with L 1-REGA k .

Contextual Array Grammars with Regular Control

Definition 4. A d-dimensional contextual array grammar with regular control is a pair G C = (G, L) where G = (d, V, #, P, A) is a d-dimensional contextual array grammar and L is a regular string language over P . Derivations in a d-dimensional contextual array grammar with regular control are defined as in the contextual array grammar G except that in a successful derivation the sequence of applied rules has to be a word from L. The array language generated by G C is the set of all d-dimensional arrays which can be derived from any of the axioms in A following a control word from L. The family of d-dimensional array languages of arrays generated by d-dimensional contextual array grammars over a k-letter alphabet with regular control is denoted by L ((d-ContA, REG)). The corresponding family of array languages of equivalence classes of arrays is denoted by using brackets in the notations.

As a general result (following [START_REF] Freund | A general framework for regulated rewriting based on the applicability of rules[END_REF]) we can state: Theorem 4. For any d ≥ 1 and any k ≥ 1,

L d-ContA k ⊆ L d-M ContA k ⊆ L d-ContA k , REG . Example 8. Consider the regular string language L r = {ba n b | n ≥ 1} from Ex- ample 7. We have shown that [arr (L r )] ∈ L 1-REGA 2 \ L 1-M ContA 2 . Moreover, [arr (L r )] ∈ L 1-ContA 1 , REG \ L 1-M ContA 2 : Consider G r = (G r , C r ) with G r = (1,
{a, b} , #, P, {arr (ba)}) and P = {p aa , p ab } with p aa = a a , and p ab = a b , as well as

C r = {p aa } * {p ab }. It is easy to see that [L (G r )] = [arr (L r )].
Theorem 5. For any d ≥ 1 and any k ≥ 2, we have:

L d-ContA k L d-M ContA k L d-ContA k , REG .
Proof. The inclusions directly follow from Theorem 4. The strictness of the first inclusion follows from Example 6 by taking the non-regular string language

L n = {a n ba n | n ≥ 1}. Then [i 1,d (arr (L n ))] ∈ L d-M ContA 2 \ L d-ContA k .
The strictness of the second inclusion follows from Example 8 by taking

[i 1,d (arr (L r ))].
On the other hand, in the 1-dimensional case, the following theorem says that even with the regulating mechanisms of matrix control or regular control languages, with 1-dimensional contextual array grammars over a one-letter alphabet we cannot go beyond regularity, i.e., beyond L 1-REGA 1 .

Theorem 6. L 1-REGA 1 = L 1-ContA 1 , REG = L 1-M ContA 1 = L 1-ContA 1 .
Proof. (Sketch) According to Theorems 4 and 2, we only have to show that L 1-REGA 1 ⊇ L 1-ContA 1 , REG . The main ideas of the corresponding technically non-trivial proof can be described as follows:

-Without loss of generality, right-hand sides of rules have the form a m a n . -Context information is irrelevant for the unary 1-dimensional case, assuming that the set of axioms collects all arrays of sufficient size. -The state information of the regular control is then encoded in the nonterminals of the regular array grammar.

Allowing for more than one symbol, 1-dimensional contextual array grammars can generate exactly the array images of linear languages. The proof is based on the following normal form: Lemma 1. For any 1-dimensional contextual array grammar with regular control G C = (G, L), where G = (1, V, #, P, A), L ⊆ P * , we can construct an equivalent 1-dimensional contextual array grammar with regular control G C = (G , L ) with G = (1, V, #, P , A ), L ⊆ P * , such that for P we have:

-All rules in P are of the form a b or b a for some a, b ∈ V , i.e., we only have the minimal non-empty size of selectors and minimal contexts of size 1.

-If there is a rule of the form a b / b a in P , then also all rules of the form c b or b c are in P , for any c ∈ V , i.e., the selector contents is irrelevant, only direction of growth of the array is important.

The rules in this normal form nicely correspond with the operations of left and right insertions for strings, which operations together with regular control languages also characterize the family of linear languages. Proof. (Sketch) The main ideas of the proof can be described as follows:

-Adding strings in a controlled way "on both ends" corresponds to applying linear rules, but in reverse order. -The information about the finitely many selectors possible can be stored in the nonterminal; on the other hand, the nonterminal can be stored in the state of the finite automaton of the control language.

For d ≥ 2, i.e., in the case of at least two symbols, we can prove the incomparability of the families of array languages generated by contextual array grammars and those equipped with control mechanisms: Proof. For the singleton language L ⊥ from Example 4, we have i

2,d (L ⊥ ) ∈ L d-ContA 1 ∩ L d-M ContA 1 ∩ L d-ContA 1 , REG \ L d-REGA 1 .
On the other hand, for L r from Example 7 we have i

2,d ([arr (L r )]) ∈ L 1-REGA 2 \ L d-ContA 1 ∪ L d-M ContA 1 ∪ L d-ContA 1 , REG .
Yet even for the case of one-letter alphabets we can find an array language of 2-dimensional arrays in L 2-REGA 1 \ L 2-ContA 1 , REG : we consider -shaped arrays with the left vertical line having a length being a multiple of 3 and the right vertical line having a length being a multiple of 5. These arrays can easily be generated by a regular array grammar by first generating the left vertical line from up to down, followed by the horizontal line, finally generating the right vertical line upwards. On the other hand, this set of 2-dimensional arrays cannot be generated by a contextual array grammar even when using regular control: as soon as the vertical lines have become long enough, we cannot distinguish any more between the left and the right one, so either the lengths will not necessarily fulfill the constraints of being a multiple of 3 and 5, respectively, any more, or even worse, the lines might even be prolonged below the horizontal line yielding arrays of the shape of an H.

Decidability Questions

As the size of the arrays generated by contextual array grammars (even with any control mechanism) increases with every derivation step, the generated array languages are computable (i.e., recursive).

As an immediate consequence of Theorem 7, we obtain:

Corollary 1. Emptiness is decidable for L (1-ContA, REG).

Yet for higher dimensions, we obtain a completely different situation:

Theorem 9. Emptiness is not decidable for L d-ContA k , REG for d ≥ 2, even for k = 1.

Proof. (Sketch) As, for example, described in [START_REF] Fernau | Representations of recursively enumerable array languages by contextual array grammars[END_REF], the derivation carpet of a Turing machine can be described using 2-dimensional contextual array productions in the t-mode of derivation, i.e., a derivation only stops if no rule can be applied any more. The goal of only halting with specific conditions being fulfilled can also be obtained using suitable regular control languages, as we can require specific final rules to be applied. Hence, we will obtain a non-empty array language if and only if there is a derivation simulating the acceptance of a string by the given Turing machine. The proof given in [START_REF] Fernau | Representations of recursively enumerable array languages by contextual array grammars[END_REF] does not bound the number of symbols used. Yet m symbols can be encoded by 2 × m rectangles with the k-th of these m symbols being encoded by leaving the k-th position in the second vertical line free, which then can be checked by the selector in the contextual array productions. Hence, simulating successful computations of the given Turing machine will result in the generation of 2k × mn rectangles for accepting computations.

Picture Generation

Another interesting topic is to consider the generation of geometric objects such as solid rectangles and squares, which has been used to exhibit the generative power of various array grammar variants. Both of them, i.e., the 2-dimensional array language L rect of all solid rectangles of size m × n, m, n ≥ 2, made of a single symbol a and the 2-dimensional array language L square of all solid squares of side length n, n ≥ 2, made of a single symbol a are well-known to be in L 2-REGA 1 , see [START_REF] Yamamoto | Context-sensitivity of two-dimensional regular array grammars[END_REF], but as we are able to show they can also be generated by 2-dimensional contextual array grammars with regular control, i.e., {L rect , L square } ⊂ L 2-ContA 1 , REG . We now only exhibit the contextual array grammar with regular control for the squares. The rules are listed in the following: Notice that the rules s ur and s dl check if a complete new border layer was actually generated, so they provide "keystones" as used in architecture, and it somehow replaces the t-mode of derivation, e.g., see [START_REF] Fernau | Contextual array grammars and array P systems[END_REF].

s ul =
As already with the t-mode of derivation, e.g., see [START_REF] Fernau | Contextual array grammars and array P systems[END_REF], only eight contextual array rules were needed in Example 9 to generate the squares. This shows that the ability of contextual array grammars to insert new parts on different positions in the current array allows for a significantly smaller number of rules when using specific control mechanisms as the t-mode of derivation or regular control languages, in comparison with the construction of an extended regular array grammar as described in [START_REF] Yamamoto | Context-sensitivity of two-dimensional regular array grammars[END_REF], where the construction has to be carried out along a Hamiltonian path. The inserted pieces used in [START_REF] Yamamoto | Context-sensitivity of two-dimensional regular array grammars[END_REF] in fact could also be used as arrays inserted by a contextual array grammar with regular control, yet even for the subset of squares of side lengths 5k + 16, k ≥ 0, as exhibited in [START_REF] Yamamoto | Context-sensitivity of two-dimensional regular array grammars[END_REF], 27 rules (arrays) were used. As these are in fact a kind of macro-rules, a complete list of regular array rules based on [START_REF] Yamamoto | Context-sensitivity of two-dimensional regular array grammars[END_REF] would correspond to about one thousand rules. This is an example showing that contextual array grammars may allow for a succinct description of specific picture languages with rather small descriptional complexity.

  An example of these L-shaped arrays (for n = 3 and m = 4) from [L 1 ] can be depicted as shown on the left. Observe that both arms of these arrays can have arbitrary lengths. Definition 1. A regular d-dimensional array grammar is specified as G = (d, N, T, #, P, {(v S , S})) where N is the alphabet of non-terminal symbols, T is the alphabet of terminal symbols, N ∩ T = ∅, # / ∈ N ∪ T ; P is a finite non-empty set of regular d-dimensional array productions over N ∪ T, as well as v S ∈ Z d and S ∈ N is the start symbol. A regular d -dimensional array production either is of the form A → b, A ∈ N , b ∈ T , or Av# → bC, A, C ∈ N , b ∈ T , v ∈ Z d with v = 1. The application of A → b means replacing A by b in a given array. Av# → bC can be applied if in the underlying array we find a position u occupied by A and a blank symbol at position u + v; A then is replaced by b, and # by C. The array language generated by G is the set of all d-dimensional arrays derivable from the initial array {(v S , S)}. The family of Λ-free d-dimensional array languages (of equivalence classes) of arrays over a k-letter alphabet generated by regular d-dimensional array grammars is denoted by L d-REGA k ( L d-REGA k ). For arbitrary alphabets, we omit the superscript k.

Remark 1 .

 1 The special type of d-dimensional contextual array grammars where axioms are connected and rule applications preserve connectedness is denoted by d-ContA, the corresponding family of d-dimensional array languages by L (d-ContA); by L d-ContA k we denote the corresponding family of d-dimensional array languages over a k-letter alphabet. As we mostly are interested in (families of) equivalence classes of arrays, a d-dimensional contextual array grammar [G] for generating [L] for L ∈ L (d-ContA) being generated by a d-dimensional contextual array grammar

3. 1 Example 5 .

 15 Matrix Contextual Array Grammars Definition 3. A d-dimensional matrix contextual array grammar is a pair G M = (G, M ) where G = (d, V, #, P, A) is a d-dimensional contextual array grammar and M is a finite set of sequences, called matrices, of rules from P , i.e., each element of M is of the form p 1 , • • • , p n , n ≥ 1, where p i ∈ P for 1 ≤ i ≤ n. Derivations in a matrix contextual array grammar are defined as in a contextual array grammar except that a single derivation step now consists of the sequential application of the rules of one of the matrices in M, in the order in which the rules are given in the matrix. The array language generated by G M is the set of all d-dimensional arrays which can be derived from any of the axioms in A. The family of d-dimensional array languages of arrays generated by d-dimensional matrix contextual array grammars (over a k-letter alphabet) is denoted by L (d-M ContA) (L d-M ContA k ). Consider the language L 2 of connected arrays given byL 2 = ((0, 0) , a) ∪ ((0, i) , a) , ((i, 0) , a) | 1 ≤ i ≤ n n ∈ N ,which contains L-shaped arrays as L 1 from Example 1, but now with both arms having the same length. L 2 ∈ L 2-M ContA 1 , as it can be generated by the 2-dimensional matrix contextual array grammar G M = (G 1 , M ) where G 1 is the 2-dimensional contextual array grammar from Example 3 and M = { p u , p r }. The only derivations possible in G M for [L 2 ] ∈ L 2-M ContA 1 (see Remark 1) are:

Theorem 3 .

 3 For any d ≥ 2 and any k ≥ 1, we have L d-ContA k L d-M ContA k and L d-ContA k L d-M ContA k . Proof. The inclusion L d-ContA k ⊆ L d-M ContA k and therefore also L d-ContA k ⊆ L d-M ContA k is obvious from general results for grammars working on various kinds of objects and with specific regulating mechanisms, see [10]. For showing the strictness of the inclusion, we prove that the array language L 2 from Example 5 cannot be generated by a 2-dimensional contextual array grammar; for dimensions d > 2, we just take [i 2,d (L 2 )] . Now assume we could find a 2-dimensional contextual array grammar [G = (2, {a} , #, P, A)] that generates [L 2 ]. As contextual grammars are pure grammars, [A] is a finite subset of [L (G)]. As [L (G)] is infinite, we would need an infinite number of rules to get [L 2 ] which resembles the case of external contextual string grammars; in fact, as soon as the arms get long enough, we have to apply a rule which only grows the arm going up or only grows the arm going to the right, resulting in an array which contradicts the definition of [L 2 ]. It is obvious that we also have [i 2,d (L 2 )] ∈ L d-M ContA k \ L d-ContA k ; this observation completes the proof.

as the following example shows. Example 6 .

 6 Consider the non-regular language L n = {a n ba n | n ≥ 1}. By Theorem 1, there cannot exist an array grammar G of type 1-REGA 2 such that [L (G)] = [arr (L n )].

Example 7 .

 7 Consider the regular string language L r = {ba n b | n ≥ 1}. Due to Theorem 1, there exists an array grammar of type 1-REGA 2 G r such that [L (G r )] = [arr (L r )]. Yet on the other hand, there cannot exist an array grammar of type 1-M ContA 2 [G] such that L ([G]) = [arr (L r )], which can be proved by a simple pumping argument: The number of symbols a between the two symbols b can become arbitrarily large, but we only have a finite set of axioms A; as [G] is a pure grammar, [A] ⊂ [L]; yet [G] can only grow these arrays in an external way, i.e., by adding symbols on the left or on the right, but in this way we are not able to grow the number of symbols a in the middle.

Theorem 7 .

 7 [L (1-ContA, REG)] = arr (L (LIN )).

Theorem 8 .

 8 For any d ≥ 2 and any k ≥ 1, all the three families L d-ContA k , L d-M ContA k , and L d-ContA k , REG are incomparable with L d-REGA k .

Example 9 .

 9 L square is generated by the 2-dimensional contextual array grammar with regular control G squareRC = (G square , C square ) with G square = ({a}, P square , A square ), where A square collects the 2 × 2 and 3 × 3 squares, P square = {s ul , s dr , s ur , s dl , r ul , r uu , r dr , r dd } , and C square = ({s ul s dr } {r ul r dr } * {r uu r dd } * {s ur s dl }) + .

  How to derive a 4 × 4 square is shown below:

	a a a a	⇒s ul	a a a a a a a	⇒s dr	a a a a a a a a a a	⇒s ur	a a a a a a a a a a a a a	⇒s dl	a a a a a a a a a a a a a a a a
		a a			a				a a a	a a
		a a a		a a a			a a a	a a a
		a	, s dr =	a a , sur =	a a , s dl =	a a a ,
					a a				a
		a a		a a			a a a	a a
	r ul =	a a a , ruu =	a , r dr =	a a , r dd =	a a .