Vanina Guernier

Kathryn J Allan

Cyrille Goarant
email: cgoarant@pasteur.nc

Advances and challenges in barcoding pathogenic and environmental Leptospira

Keywords: Leptospira, epidemiology, zoonotic reservoir, barcoding, genotyping

Leptospirosis is a zoonotic bacterial disease of global importance. A large spectrum of asymptomatic animal hosts can carry the infection and contribute to the burden of human disease. Environmental sources in human contaminations also point to the importance of a hydro-telluric reservoir. Leptospirosis can be caused by as many as 15 different pathogenic or intermediate Leptospira species. However, classification of these bacteria remains complicated through the use of both serological and genetic classification systems that show poor correlation. With the advent of molecular techniques, DNA-based barcoding offers a conceptual framework that can be used for leptospirosis surveillance as well as source tracking. In this review, we summarize some of the current techniques, highlight significant successes and weaknesses and point to the future opportunities and challenges to successfully establish a widely applicable barcoding scheme for Leptospira.

INTRODUCTION

Leptospirosis is a zoonotic disease with a worldwide distribution. An estimated 1.03 million human cases and almost 60,000 deaths occur annually [START_REF] Costa | Global Morbidity and Mortality of Leptospirosis: A Systematic Review[END_REF]. Human leptospirosis is caused by infection with pathogenic Leptospira spp. bacteria through indirect exposure to water or moist environments contaminated with the urine of infected animals, or through direct contact with infected animals or their tissues. Although it is recognized as an emerging infectious disease, leptospirosis is also considered a neglected disease that places its greatest burden on impoverished populations from developing countries and tropical regions [START_REF] Mcbride | Leptospirosis[END_REF]. Human leptospirosis is often diagnosed late, due to its broad spectrum of signs and symptoms that range from a flu-like syndrome to multi-organ failure, and because the clinical presentation of leptospirosis mimics that of many other diseases, including dengue fever, chikungunya and malaria. Laboratory confirmation of a clinical suspicion of leptospirosis is therefore essential to ensure optimal patient care [START_REF] Goarant | Leptospirosis: risk factors and management challenges in developing countries[END_REF][START_REF] Hartskeerl | The role of leptospirosis reference laboratories[END_REF].

The genus Leptospira belongs to the phylum of Spirochaetes, order Spirochaetales, family Leptospiraceae [START_REF] Paster | Phylogenetic analysis of the Spirochetes[END_REF]. Two classification schemes are used for leptospires, one of which is based on serology with the serovar as the basic taxon, and another which uses molecular taxonomy to identify the Leptospira species, sometimes referred to as genomospecies [START_REF] Levett | Leptospirosis[END_REF]. Serological classification is based on antigenic determinants related to the structural heterogeneity of the lipopolysaccharide (LPS), the major component of the outer membrane of Gram-negative bacteria (Bharti et al., 2003). Leptospira have been classified serologically into 26 serogroups and over 300 serovars (both saprophytic and pathogenic) using Microscopic Agglutination Test (MAT) and Cross Agglutination Absorption Test (CAAT) respectively [START_REF] Cerqueira | A century of Leptospira strain typing[END_REF][START_REF] Hartskeerl | The role of leptospirosis reference laboratories[END_REF].

Phylogenetically, 22 species of the Leptospira genus have been described so far, based on 16S rRNA phylogeny and DNA-DNA hybridization (until recently the gold-standard for defining bacterial species) [START_REF] Fouts | What Makes a Bacterial Species Pathogenic?:Comparative Genomic Analysis of the Genus Leptospira[END_REF]. Those species are arranged into three large groups based on their pathogenicity: pathogenic species (Leptospira interrogans, L. kirschneri, L. borgpetersenii, L. mayottensis, L. santarosai, L. noguchii, L. weilii, L. alexanderi, L. kmetyi, and L. alstonii), intermediate (i.e. species of unclear or low pathogenicity: L. broomii, L. fainei, L. inadai, L. licerasiae, L wolffii), and saprophytic species (i.e. free-living organisms found in water and soil and generally considered not to infect animal hosts: L. biflexa, L. idonii, L. meyeri, L. terpstrae, L. vanthielli, L. wolbachii, L. yanagawae) [START_REF] Faine | Leptospira and Leptospirosis, Second Edition[END_REF]. Intermediate leptospires cause predominantly mild selfresolving illnesses without fatal complications, while pathogenic species produce disease of varying severity in both humans and animals, ranging from subclinical infections to severe disease and death. The most severe forms are frequently caused by pathogenic strains belonging to the evolutionarily-related species L. interrogans, L. kirschneri, and L. noguchii [START_REF] Lehmann | Leptospiral Pathogenomics[END_REF][START_REF] Xu | Whole genome sequencing revealed host adaptation-focused genomic plasticity of pathogenic Leptospira[END_REF], although severe diseases might involve any other species [START_REF] Levett | Leptospirosis[END_REF].

Overall, there is poor correlation between the two Leptospira classification schemes, serological classification cannot be used to reliably predict the species of Leptospira isolates. For example, a single serogroup may contain serovars from different Leptospira species and similarly, a single genomic species may also contain representatives from several different serogroups [START_REF] Levett | Leptospirosis[END_REF]. Furthermore, a number of Leptospira serovars are found in more than one Leptospira species [START_REF] Levett | Systematics of leptospiraceae[END_REF]. Although serological classification is still essential to support clinical diagnostics and surveillance, the development of Leptospira genomics is revealing new insights into the biology and pathogenesis of Leptospira infection [START_REF] Fouts | What Makes a Bacterial Species Pathogenic?:Comparative Genomic Analysis of the Genus Leptospira[END_REF][START_REF] Lehmann | Leptospiral Pathogenomics[END_REF]. Increasingly, genetic typing approaches for leptospires are being used to further understand the epidemiology of Leptospira infection in a range of clinical and research settings.

In the same way that the black stripes of the "Universal Product Code" or "barcode" distinguish products in a supermarket, DNA barcoding was developed as a molecular identification technique in which a single short DNA sequence can be used for species identification [START_REF] Hebert | Biological identifications through DNA barcodes[END_REF]. DNA barcoding was originally proposed as an identification tool for animals, and used PCR amplification and sequence analysis of a ~650 bp (conserved) region of the mitochondrial cytochrome c oxidase subunit 1 (CO1) gene as a universal target. Barcoding has been very largely used in Arthropods, notably Lepidopterans, but was also developed in many other animals, as well as (frequently with other gene targets) in plants, algae, Protists, Fungi and Eubacteria. In Prokaryotes, sequencing of the small ribosomal 16S rRNA subunit gene (rrs) has been regarded as a standard for bacterial species identification for some time, and is analogous to the barcoding approach used in higher species. Unique sequence types could not always be attributed to a single bacterial species though, and reversely, some bacterial species could display sequence variations within the barcode. The term "molecular Operational Taxonomic Unit" or mOTU was therefore created to describe unique sequence types when studying complex communities. Prokaryote barcoding has been most notably used to describe microbial assemblages by directly amplifying rrs genes from environmental DNA extracts, cloning the PCR product and sequencing as many clones as possible [START_REF] Pace | A molecular view of microbial diversity and the biosphere[END_REF], an ancestor form of what became "metabarcoding", aimed at barcoding every individual from a complex community.

DNA-barcoding of a group of organisms requires a good understanding of the diversity of the genome in question, and the identification of suitable gene targets that can be used to discriminate between different species within the group. For Leptospira species, the genomes range from 3.9 to 4.7 mega-bases (MB) in size and consist of two circular chromosomes: a large chromosome CI (~3.6 to 4.3 MB) and a smaller chromosome CII ~350 kilo-bases (KB) in length [START_REF] Picardeau | Genomics, proteomics, and genetics of leptospira[END_REF]. Some saprophytic species such as

Leptospira biflexa also have an extra-chromosomal element p74 of around 74 KB that has not been detected in any of the pathogenic Leptospira species [START_REF] Fouts | What Makes a Bacterial Species Pathogenic?:Comparative Genomic Analysis of the Genus Leptospira[END_REF][START_REF] Picardeau | Genome Sequence of the Saprophyte Leptospira biflexa Provides Insights into the Evolution of Leptospira and the Pathogenesis of Leptospirosis[END_REF]. Comparative genomic analysis suggests that pathogenic species have a common progenitor with a genome resembling that of L. biflexa. Many of the essential housekeeping genes are located on CI, as are most of the genes encoding virulence factors, such as lipL32 and ligB [START_REF] Picardeau | Genome Sequence of the Saprophyte Leptospira biflexa Provides Insights into the Evolution of Leptospira and the Pathogenesis of Leptospirosis[END_REF]. In saprophytic species (e.g. L. biflexa), some housekeeping genes are also located on the p74 extra-chromosomal replicon.

Leptospira show unusual mechanisms of gene regulation and patterns of genetic organization [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF][START_REF] Saint Girons | Genome structure of spirochetes[END_REF]. In contrast to most bacteria where the rRNA genes are clustered and co-transcribed, in the Leptospira genome these genes are not linked to one another and are widely scattered along the CI chromosome [START_REF] Picardeau | Genomics, proteomics, and genetics of leptospira[END_REF]. There also appears to be substantial amount of functional gene redundancy in Leptospira, particularly in pathogen-specific genes notably through gene duplication [START_REF] Adler | Pathogenesis of leptospirosis: The influence of genomics[END_REF][START_REF] Xu | Whole genome sequencing revealed host adaptation-focused genomic plasticity of pathogenic Leptospira[END_REF], and little synteny between pathogenic Leptospira species despite the short evolutionary distance between them [START_REF] Picardeau | Genome Sequence of the Saprophyte Leptospira biflexa Provides Insights into the Evolution of Leptospira and the Pathogenesis of Leptospirosis[END_REF]. Pseudogenes and insertion sequences (IS) are common features in the Leptospira genomes [START_REF] Picardeau | Genomics, proteomics, and genetics of leptospira[END_REF]. Comparative genomics revealed both overall genetic similarities and significant structural differences at the genus level, confirming genomic plasticity [START_REF] Xu | Whole genome sequencing revealed host adaptation-focused genomic plasticity of pathogenic Leptospira[END_REF]. IS-mediated sequence disruption and large chromosomal inversion or deletion are thought to be an important mechanisms in the evolution of Leptospira, and the number of IS-elements varies between species and serovars [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF]. In general however, the Leptospira genome is considered relatively stable and Leptospira serovar identity can be maintained during in vitro cultures for more than 80 years in the absence of selective pressure [START_REF] Picardeau | Genomics, proteomics, and genetics of leptospira[END_REF].

In this article, we review the use of DNA-based 'barcoding' approaches to identify and explore the diversity of pathogenic Leptospira from clinical and environmental samples.

UTILITY OF LEPTOSPIRA BARCODING

Barcoding Leptospira in clinical and environmental samples is essential for a better understanding of the local epidemiology of infection and can provide information to inform the development of disease control strategies. Routine barcoding of infecting Leptospira supports surveillance of predominant strains and genotypes of Leptospira in local human and animal populations and may indicate of changing trends of Leptospira infection within populations, such as new or atypical sources of infection or the emergence of a novel genotype. Studies of circulating Leptospira types can prove useful to monitor the evolution of the disease on a long-term perspective within a specific area and are of particular interest in countries where the disease is endemic and/or where recurrent epidemic outbreaks occur.

As an example, a prospective study conducted in northern Thailand between 2000 and 2005, identified the emergence of a dominant clone of L. interrogans serovar Autumnalis which was a major cause of human disease during the outbreak unfolding in the early 2000s and has since diminished [START_REF] Thaipadungpanit | A Dominant Clone of Leptospira interrogans Associated with an Outbreak of Human Leptospirosis in Thailand[END_REF].

Characterization of Leptospira spp. detected in different animal hosts or environmental sources is now a prerequisite for epidemiological and source attribution studies as it allows human Leptospira infection to be traced back to the probable source of contamination. A wide variety of mammals may become infected with pathogenic Leptospira and act as reservoirs of infection for people and other animals through excretion of infectious bacteria in their urine [START_REF] Levett | Leptospirosis[END_REF]. Rodents are considered to be one of the main sources of Leptospira infection [START_REF] Adler | History of Leptospirosis and Leptospira[END_REF] but livestock, other domestic animals and many wild animal species can also carry and transmit pathogenic leptospires through urinary shedding [START_REF] Gay | Though not reservoirs, dogs might transmit Leptospira in New Caledonia[END_REF][START_REF] Weekes | Seroepidemiology of canine leptospirosis on the island of Barbados[END_REF]. Notable associations between animal reservoir host species and specific Leptospira serovars have been reported and are considered as a hallmark of leptospirosis epidemiology. Most of the knowledge of which animal hosts carry different Leptospira serovars relies on data from serological typing of isolates and seroprevalence surveys acquired over several decades. However, since the advent of the molecular taxonomy, studies that have used molecular analysis to explore host: pathogen relationships have revealed new insights into trends in host specificity (e.g. in bats and small mammals in the Western Indian Ocean islands [START_REF] Dietrich | Diversification of an emerging pathogen in a biodiversity hotspot: Leptospira in endemic small mammals of Madagascar[END_REF][START_REF] Gomard | Malagasy bats shelter a considerable genetic diversity of pathogenic Leptospira suggesting notable host-specificity patterns[END_REF]).

Publicly available databases also allow the comparison of genotypes between regions and are important to trace the movement of different Leptospira types from a phylogeographic perspective.

Identifying sources of Leptospira infection is essential to develop evidence-based infection control and prevention strategies for both human and animal infection. Detecting animal or environmental reservoirs of infection can prove particularly useful to infer transmission routes, and identify 'at-risk' groups of people and high-transmission settings [START_REF] Ganoza | Determining risk for severe leptospirosis by molecular analysis of environmental surface waters for pathogenic Leptospira[END_REF][START_REF] Viau | Quantitative PCR-based detection of pathogenic Leptospira in Hawai'ian coastal streams[END_REF]. Vaccinations against Leptospira are available but are serovar-(or at very best serogroup-) specific. Vaccine design and implementation policies require a good characterisation of predominant Leptospira in the target human or animal population and have been used in some settings as an effective method to reduce infection in animal reservoirs of infection (e.g. vaccination of dairy cattle in New Zealand to reduce human infection [START_REF] Marshall | Fifty years of leptospirosis research in New Zealand: a perspective[END_REF]).

LEPTOSPIRA BARCODING: TARGETS AND DATABASES

Identification and barcoding of pathogenic Leptospira species is usually performed on bacterial isolates obtained from infected human or animals. Increasingly, these approaches are also applied to DNA extracted directly from clinical or environmental samples following PCR-based pathogen detection. A variety of PCR assays have been described for use in the diagnosis of Leptospira infection in people and animals, and some of these can also be used for DNA-based typing of the infecting Leptospira. Leptospira-specific targets used for molecular diagnosis and typing target either conserved housekeeping genes where sequence-specific primers are used to differentiate between pathogenic and non-pathogenic species, or genes that are found only in the pathogenic species. One advantage of PCR assays designed for medical diagnosis is that they have usually been optimized for both sensitivity and specificity, assets that are useful when attempting to detect and characterize Leptospira in low numbers or in samples that contain high concentrations of non-Leptospira DNA. However, a drawback of these approaches is that diagnostic assays typically target highly conserved gene regions to ensure their sensitivity in detecting a variety of pathogenic Leptospira infections. Therefore, some of the gene targets commonly used for the diagnosis of Leptospira (e.g. lipL32 [START_REF] Levett | Detection of pathogenic leptospires by real-time quantitative PCR[END_REF][START_REF] Stoddard | Detection of pathogenic Leptospira spp. through TaqMan polymerase chain reaction targeting the LipL32 gene[END_REF]) show poor discriminatory power in differentiating between Leptospira species when used alone. Some gene targets that have been used in the diagnosis and typing of Leptospira are shown in Table 1.

Table 1: PCR used or of potential use to generate Leptospira "barcodes". The PCR published for diagnostic purpose are usually optimized for sensitivity and specificity.

Amongst the housekeeping genes, the secY gene has been used most widely for both the diagnosis and typing of Leptospira infections. The Leptospira secY gene is a housekeeping gene located on the CI chromosome that encodes a pre-protein translocase important for the export of proteins across the cytoplasmic membrane [START_REF] Durack | A prl mutation in SecY suppresses secretion and virulence defects of Listeria monocytogenes secA2 mutants[END_REF][START_REF] Haake | Leptospirosis in humans[END_REF]. Conserved regions of this gene were the target of one of the earliest diagnostic PCR assays [START_REF] Gravekamp | Detection of seven species of pathogenic leptospires by PCR using two sets of primers[END_REF] and a real-time PCR was designed and validated for use in human clinical diagnosis [START_REF] Ahmed | Development and validation of a real-time PCR for detection of pathogenic Leptospira species in clinical materials[END_REF]. However, other regions of the secY gene demonstrate marked nucleotide polymorphism. A seminal study of 131 wellcharacterised Leptospira serovars by Victoria et al. [START_REF] Victoria | Conservation of the S10-spc- locus within otherwise highly plastic genomes provides phylogenetic insight into the genus Leptospira[END_REF] demonstrated the phylogenetic value of the variable regions of the secY gene. Sequence analysis of these regions can discriminate between known pathogenic Leptospira species and strains, and have been used in many studies to identify the infecting species of Leptospira (examples are listed in Table 2). An assay that is proving promising with regards to diagnosis and typing from a single assay is a SYBR Green I diagnostic qPCR developed to target lfb1, a putative fibronectin-binding protein present in pathogenic leptospires [START_REF] Merien | A rapid and quantitative method for the detection of Leptospira species in human leptospirosis[END_REF]. Interestingly, the PCR product generated has been shown to have a sequence polymorphism of epidemiological interest, and performs well in comparison to multi-locus sequence typing (MLST) for a selection of serovars belonging to the L. interrogans and L. borgpetersenii species [START_REF] Perez | Rapid Leptospira identification by direct sequencing of the diagnostic PCR products in New Caledonia[END_REF]. Originally described for rapid identification of infecting Leptospira species from human clinical cases in New Caledonia, this approach has also revealed novel insights into the epidemiology and diversity of Leptospira infection in rodents in Madagascar (Moseley et al., in preparation) and livestock in Tanzania (K. Allan, unpublished data).

Another target that has been used to discriminate between Leptospira species is the flaB gene. This gene target, which encodes a flagellum protein, has been used successfully to identify other bacterial species including Campylobacter [START_REF] Harrington | Inter-laboratory evaluation of three flagellin PCR/RFLP methods for typing Campylobacter jejuni and C. coli: the CAMPYNET experience[END_REF] and Borrelia [START_REF] Lin | Molecular characterization of Borrelia isolates from ticks and mammals from the southern United States[END_REF]. Restriction Fragment Length Polymorphism of the PCR product (PCR-RFLP) of this gene has been successfully used to discriminate between Leptospira species in the laboratory [START_REF] Kawabata | flaB-polymerase chain reaction (flaB-PCR) and its restriction fragment length polymorphism (RFLP) analysis are an efficient tool for detection and identification of Leptospira spp[END_REF] and was recently used in field settings to study the molecular epidemiology of canine leptospirosis in Japan [START_REF] Koizumi | Molecular and serological investigation of Leptospira and leptospirosis in dogs in Japan[END_REF] as well as to study the phylogenetic diversity in fruit-bat kidney specimens from Congo, revealing unique genotypes [START_REF] Ogawa | Molecular epidemiology of pathogenic Leptospira spp. in the straw-colored fruit bat (Eidolon helvum) migrating to Zambia from the Democratic Republic of Congo[END_REF].

With regards to Leptospira barcoding, it is worth considering the so-called "universal" highly conserved genes used in large population or metagenomics studies of bacteria. In particular, the ribosomal 16S rRNA gene (rrs) has a recognized phylogenetic value for bacterial species classification, and was the first DNA sequence available for most Leptospira species as well as being used as a target for many diagnostic PCR assays [START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF][START_REF] Smythe | A quantitative PCR (TaqMan) assay for pathogenic Leptospira spp[END_REF]. Of note, among the published diagnostic PCRs, these 2 latter ones targeting rrs are currently the only ones which can detect pathogen as well as intermediate species, in spite of a single nucleotide polymorphism in the sequence of intermediates matching the LeptoF primer [START_REF] Smythe | A quantitative PCR (TaqMan) assay for pathogenic Leptospira spp[END_REF] or by using a combination of the Forward primer A and the Reverse primer D [START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF]. The 16S rRNA variable regions 3 & 4 sequence frequently used in metagenomics [START_REF] Klindworth | Evaluation of general 16S ribosomal RNA gene PCR primers for classical and next-generation sequencing-based diversity studies[END_REF] has a good capacity to discriminate between the three Leptospira clusters, i.e. pathogens, intermediates and saprophytes. However, these regions have a low discriminatory power to differentiate between Leptospira species within a given clade. As an example, the 16S rRNA regions V3-V4 cannot be used to differentiate between the pathogenic species L. interrogans, L. noguchii and L. kirschnerii, which are classified within the same mOTU. Similarly, all saprophytic Leptospira species but Leptospira idonii belong to a single mOTU (Figure 1).

More recently, the RNA polymerase β-subunit gene rpoB, widely used in phylogenetic analyses of a number of bacterial genera, was proposed for Leptospira typing to circumvent the limitations of the 16S rRNA discrimination (La [START_REF] Scola | Partial rpoB gene sequencing for identification of Leptospira species[END_REF]. Bioinformatics studies later confirmed its high value for discrimination [START_REF] Cerqueira | Bioinformatics describes novel Loci for high resolution discrimination of leptospira isolates[END_REF] and its utility in epidemiological studies was demonstrated by work in Brazil and India that used this scheme to type Leptospira isolates from people and animals [START_REF] Balamurugan | Characterization of leptospira isolates from animals and humans: phylogenetic analysis identifies the prevalence of intermediate species in India[END_REF][START_REF] Jorge | Leptospira borgpetersenii from free-living white-eared opossum (Didelphis albiventris): First isolation in Brazil[END_REF].

Another bacterial gene that is widely used in phylogenetic studies is the gyrB gene, which is reported to have a higher nucleotide divergence in Leptospira species than the 16S RNA rrs gene [START_REF] Huang | Bacterial diversity based on type II DNA topoisomerase genes[END_REF][START_REF] Slack | Identification of pathogenic Leptospira species by conventional or real-time PCR and sequencing of the DNA gyrase subunit B encoding gene[END_REF]. This gene target has also been used for Leptospira diagnostic assays [START_REF] Slack | Identification of pathogenic Leptospira species by conventional or real-time PCR and sequencing of the DNA gyrase subunit B encoding gene[END_REF] and typing of isolates carried by rodents in Japan and the Philippines [START_REF] Kawabata | First record of Leptospira borgpetersenii isolation in the Amami Islands, Japan[END_REF][START_REF] Saito | The usefulness of semi-solid medium in the isolation of highly virulent Leptospira strains from wild rats in an urban area of Fukuoka, Japan[END_REF][START_REF] Villanueva | Leptospira-rat-human relationship in Luzon, Philippines[END_REF].

Other highly conserved genes have been proposed as targets to discriminate bacterial species by sequencing, but have rarely, if ever, been used in Leptospira studies. This includes cpn60, a chaperonin gene (also known as HSP60 in many bacteria or GroEL in Leptospira) proposed as a preferred universal barcode for bacteria compared to the 16S rRNA gene [START_REF] Links | The chaperonin-60 universal target is a barcode for bacteria that enables de novo assembly of metagenomic sequence data[END_REF]. Such highly conserved genes might be of interest for improved discrimination between Leptospira species in microbial communities.

MULTI LOCUS SEQUENCE TYPING OF LEPTOSPIRA

Multilocus sequence typing (MLST) is an unambiguous procedure for characterising isolates of bacterial species using the sequences of internal fragments of several genes, including housekeeping genes [START_REF] Maiden | Multilocus sequence typing: a portable approach to the identification of clones within populations of pathogenic microorganisms[END_REF][START_REF] Urwin | Multi-locus sequence typing: a tool for global epidemiology[END_REF]. For each gene/locus within a particular MLST scheme, a ~500 bp fragment is sequenced and analysed. The sequences present at each locus are assigned a distinct allele code and the combination of those alleles defines an allelic profile or sequence type (ST) for each isolate. Whilst MLST is not a barcoding method per se as it does not focus on a single marker, each locus considered separately can be considered as a barcode and the combination of multiple barcodes is considered one of the most robust genetic methods to identify the infecting Leptospira strain currently available. Three major MLST schemes exist for Leptospira spp.

typing and Leptospira sequence types for all schemes are publically available at the PubMLST website (http://pubmlst.org/leptospira/), which also hosts molecular typing databases for a variety of bacterial pathogens. Through this online portal, allelic profiles of Leptospira isolates can be easily compared to those from reference serovars compiled in the database. Presently, 13 Leptospira genes (including the highly discriminatory secY gene discussed above) from the three different MLST schemes have been included in the online database. MLST scheme #1, referred to as the 7L scheme, uses seven genes (glmU, pntA, sucA, tpiA, pfkB, mreA, caiB) to discriminate between the seven major Leptospira pathogenic species [START_REF] Boonsilp | A Single Multilocus Sequence Typing (MLST) Scheme for Seven Pathogenic Leptospira Species[END_REF]. MLST scheme #3, denoted as the 6L scheme, includes three housekeeping genes (adk, icdA, secY), two genes encoding outer membrane proteins (lipL32, lipL42) and the 16S rRNA gene (rrs) that can be used for typing pathogenic and intermediate species [START_REF] Ahmed | Multilocus sequence typing method for identification and genotypic classification of pathogenic Leptospira species[END_REF]. MLST scheme #2 combines the "best" loci (adk, glmU, icdA, lipL32, lipL41, mreA and pntA) from schemes #1 and #3 [START_REF] Varni | Reassessment of MLST schemes for Leptospira spp. typing worldwide[END_REF] but to date, has been used less commonly in the literature.

Other MLST schemes have been suggested for leptospirosis research, but they are not yet supported by a website with referenced alleles or sequence types. As an example, in silico studies have proposed a reduced 4-loci scheme with high discriminatory power [START_REF] Cerqueira | Bioinformatics describes novel Loci for high resolution discrimination of leptospira isolates[END_REF]. This scheme would be usable in L. interrogans and L. kirschneri with currently validated PCRs, but would need to be further adapted for application with a wider range of pathogenic species. In the future, it is anticipated that the MLST technique will significantly contribute to gaining insights into the evolution and phylogeographic affinities of leptospires.

However, the current multiplicity of available schemes leads to some confusion in the field of leptospirosis research that has limited the comparison between isolates obtained from different studies and geographic areas.

BARCODING SUCCESSES / LIMITATIONS

A major feature of leptospirosis is the great diversity of etiological agents leading to the "leptospirosis" disease. As many as 15 different pathogenic and intermediate Leptospira species are infectious and have been implicated in human or animal infections [START_REF] Balamurugan | Characterization of leptospira isolates from animals and humans: phylogenetic analysis identifies the prevalence of intermediate species in India[END_REF][START_REF] Levett | Leptospira broomii sp. nov., isolated from humans with leptospirosis[END_REF][START_REF] Matthias | Human leptospirosis caused by a new, antigenically unique leptospira associated with a rattus species reservoir in the peruvian Amazon[END_REF][START_REF] Petersen | First isolation of Leptospira fainei serovar Hurstbridge from two human patients with Weil's syndrome[END_REF][START_REF] Schmid | Newly recognized Leptospira species ("Leptospira inadai" serovar lyme) isolated from human skin[END_REF][START_REF] Slack | Leptospira wolffii sp. nov., isolated from a human with suspected leptospirosis in Thailand[END_REF][START_REF] Tsuboi | Imported Leptospira licerasiae Infection in Traveler Returning to Japan from Brazil[END_REF]. However, as mentioned before, most diagnostic PCR only detect Leptospira from the pathogenic cluster and fail to detect intermediate species [START_REF] Bourhy | Comparison of real-time PCR assays for the detection of pathogenic Leptospira spp. in blood and identification of variations in target sequences[END_REF]. Therefore, there is currently a strong bias toward the pathogenic cluster of Leptospira spp, and most frequently, only the pathogenic species might be considered with the current techniques.

A major advantage of using sequence-based genotyping of Leptospira is the ability for the technique to be standardised and compared between different laboratories and geographic sites. In comparison to serotyping, which is only performed at reference laboratories and requires considerable specialist expertise [START_REF] Hartskeerl | The role of leptospirosis reference laboratories[END_REF], Leptospira barcoding techniques can be performed relatively quickly and cheaply, without the need for specialist equipment and extensive panels of reference antisera or monoclonal antibodies.

The increasing availability of molecular diagnostic and sequencing facilities around the world also means that the technique can be performed in a wide variety of settings. Even where facilities are not available in-country, the fact that DNA-based typing does not require propagation or maintenance of live Leptospira cultures makes typing of Leptospira infecting animals and people in resource-limited settings more feasible (e.g. in Kenya and Zambia [START_REF] Halliday | Urban Leptospirosis in Africa: A Cross-Sectional Survey of Leptospira Infection in Rodents in the Kibera Urban Settlement, Nairobi, Kenya[END_REF][START_REF] Ogawa | Molecular epidemiology of pathogenic Leptospira spp. in the straw-colored fruit bat (Eidolon helvum) migrating to Zambia from the Democratic Republic of Congo[END_REF]).

The ability to directly compare Leptospira sequences from different parts of the world has the potential to reveal new insights into the epidemiology of the infection. The application of genotyping techniques has demonstrated outbreaks of human disease caused by a single clonal complex of L. interrogans in Thailand [START_REF] Thaipadungpanit | A Dominant Clone of Leptospira interrogans Associated with an Outbreak of Human Leptospirosis in Thailand[END_REF] and revealed intriguing patterns of animal host-specificity in Madagascar [START_REF] Dietrich | Diversification of an emerging pathogen in a biodiversity hotspot: Leptospira in endemic small mammals of Madagascar[END_REF]Gomard et al., 2016). As yet, comparison of sequences from different geographic regions on a global scale has not been explored. However, the increasing application of standard barcoding or typing approaches has the potential for large-scale patterns of infection to be investigated.

One of the major criticisms about the use of barcoding in diversity analyses is that it relies on a single marker and hence is often unable to discriminate between strains of a single Leptospira species [START_REF] Dupuis | Multi-locus species delimitation in closely related animals and fungi: one marker is not enough[END_REF][START_REF] Mallo | Multilocus inference of species trees and DNA barcoding[END_REF]. The use of multiple barcoding loci to type Leptospira is a way to avoid misinterpretations because of large scale sequence changes such as horizontal gene transfer, which may occur between different Leptospira strains [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF][START_REF] Haake | Molecular evolution and mosaicism of leptospiral outer membrane proteins involves horizontal DNA transfer[END_REF][START_REF] Llanes | Whole Genome Sequencing Allows Better Understanding of the Evolutionary History of Leptospira interrogans Serovar Hardjo[END_REF][START_REF] Picardeau | Genome Sequence of the Saprophyte Leptospira biflexa Provides Insights into the Evolution of Leptospira and the Pathogenesis of Leptospirosis[END_REF][START_REF] Victoria | Conservation of the S10-spc- locus within otherwise highly plastic genomes provides phylogenetic insight into the genus Leptospira[END_REF]. MLST (see above) is based on genotyping and establishing phylogenetic relationships between bacterial isolates using concatenated sequences derived from several loci, thus minimizing the possible biases originating from horizontally acquired DNA. MLST is considered one of the most robust and efficient methods in identifying ancestral relationships between Leptospira and segregating strains isolated from an outbreak, and in identifying the source(s) of human contamination [START_REF] Nalam | Genetic Affinities within a Large Global Collection of Pathogenic Leptospira: Implications for Strain Identification and Molecular Epidemiology[END_REF].

Though not new, this method is not widely used yet for leptospirosis epidemiologic studies, mostly because it still requires bacterial isolates, in spite of ongoing efforts to type directly from non-cultured material.

DIRECT TYPING WITHOUT ISOLATION

The first objective of barcoding is to identify leptospires at the species level in patients with clinical leptospirosis.

Among the genes and barcoding schemes described in this paper, the 16S rRNA rrs gene and the translocase preprotein secY have been most frequently used for typing of Leptospira species from patient samples. Increasingly, these typing schemes are being directly applied to biological specimens without strain isolation. In acute cases of human leptospirosis, Leptospira DNA can be detected and typed in whole blood, serum or urine samples. In animal carriers of infection, the kidneys or urine have been most frequently used. Similar approaches have been applied to type Leptospira detected in environmental surface water samples [START_REF] Ganoza | Determining risk for severe leptospirosis by molecular analysis of environmental surface waters for pathogenic Leptospira[END_REF], a field of research that has recently gained renewed interest [START_REF] Mason | Distribution and Diversity of Pathogenic Leptospira Species in Peri-domestic Surface Waters from South Central Chile[END_REF][START_REF] Muñoz-Zanzi | Leptospira Contamination in Household and Environmental Water in Rural Communities in Southern Chile[END_REF][START_REF] Thibeaux | Seeking the environmental source of Leptospirosis reveals durable bacterial viability in river soils[END_REF].

Examples of successful genotyping from non-cultured clinical or environmental material are listed in Table 2.

Direct MLST typing of Leptospira from non-isolate clinical specimens has had limited success [START_REF] Agampodi | Utility and Limitations of Direct Multi-Locus Sequence Typing on qPCR-Positive Blood to Determine Infecting Leptospira Strain[END_REF][START_REF] Perez | Rapid Leptospira identification by direct sequencing of the diagnostic PCR products in New Caledonia[END_REF], whatever the primers used. A revision of the MLST scheme #3 has recently been proposed, using newly designed nested primers to improve the sensitivity to make it usable directly from clinical specimens [START_REF] Weiss | An Extended Multilocus Sequence Typing (MLST) Scheme for Rapid Direct Typing of Leptospira from Clinical Samples[END_REF]. However, even this optimized procedure also only proved successful in a subset of clinical specimens. The success of MLST when performed directly on human or animal clinical samples has been shown to be correlated with the bacterial load in the specimen. In one study performed during an outbreak of acute human leptospirosis in Sri Lanka, Agampodi and colleagues demonstrated a substantial difference in the mean bacterial load between specimens with complete MLST (2.2 x 10 5 Leptospira/ml) compared to specimens where the full MLST scheme could not be completed (1.3 x 10 4 Leptospira/mL), as measured by real-time PCR [START_REF] Agampodi | Utility and Limitations of Direct Multi-Locus Sequence Typing on qPCR-Positive Blood to Determine Infecting Leptospira Strain[END_REF]. A relatively high threshold of 4.9 x 10 4 Leptospira/mL was observed for specimens with complete MLST profiles.

In addition to bacterial load, failure of sequence-based typing has also been reported in association with divergent or novel Leptospira types, particularly in areas that have been relatively poorly characterised for circulating Leptospira diversity. Standard typing approaches may fail to amplify target gene sequences due to sequence polymorphism of local serovars at primer binding sites. In a study of Leptospira infection in small mammals in Madagascar [START_REF] Dietrich | Diversification of an emerging pathogen in a biodiversity hotspot: Leptospira in endemic small mammals of Madagascar[END_REF], modification of standard secY primer sequences with inclusion of degenerate bases to account for sequence polymorphisms greatly improved the efficiency of single locus secY typing on Leptospira in non-isolate samples. Similarly, modified primers also facilitated direct typing of Leptospira in clinical samples from livestock in Tanzania [START_REF] Allan | Leptospirosis in northern Tanzania: investigating the role of rodents and ruminant livestock in a neglected public health problem[END_REF] or from rodents in New Caledonia [START_REF] Perez | Rodent abundance dynamics and leptospirosis carriage in an area of hyper-endemicity in New Caledonia[END_REF] where standard-typing assays had failed.

The ability to perform sequence-based typing of Leptospira spp. in the absence of bacterial isolation has helped to improve the utility of these techniques in a clinical setting, but risks neglecting the role of some strains or indeed species in the local epidemiology of leptospirosis. This is especially true in relatively unexplored geographic regions. For example, the most recently described Leptospira species, L. mayottensis [START_REF] Bourhy | Leptospira mayottensis sp. nov., a pathogenic Leptospira species isolated from humans[END_REF] was first detected in human clinical cases on the tropical island of Mayotte, Indian ocean [START_REF] Bourhy | Human Leptospira isolates circulating in Mayotte (Indian Ocean) have unique serological and molecular features[END_REF]. However, qPCR detection of this species was challenging with low diagnostic sensitivity for standard qPCR diagnostic assays [START_REF] Bourhy | Comparison of real-time PCR assays for the detection of pathogenic Leptospira spp. in blood and identification of variations in target sequences[END_REF][START_REF] Bourhy | Human Leptospira isolates circulating in Mayotte (Indian Ocean) have unique serological and molecular features[END_REF]. Following culture and isolation of the infecting Leptospira, more extensive phenotypic and genotypic characterisation was performed leading to the description of a new species, which would have been impossible without a bacterial isolation. Similarly, a major limitation mentioned above is the failure of most current PCR designs to detect Leptospira belonging to the intermediate cluster [START_REF] Bourhy | Comparison of real-time PCR assays for the detection of pathogenic Leptospira spp. in blood and identification of variations in target sequences[END_REF]. Because all species in this cluster have already proven pathogenic and been isolated from clinical specimens, there is growing recognition that these species will need to be considered and new PCR designs will be needed to more extensively address the contribution of these species to animal and human leptospirosis [START_REF] Tsuboi | Imported Leptospira licerasiae Infection in Traveler Returning to Japan from Brazil[END_REF]. These two cases point to the current limitations of approaches only based on PCR with specific primers. Considering that the biodiversity of Leptospira is insufficiently recognized, they show the need for continued efforts of Leptospira isolation.

WHAT'S NEXT?

The rapid rise and development of next generation sequencing (NGS) has exciting applications to the Leptospira field. The first Leptospira genome was fully reported 15 years ago [START_REF] Ren | Unique physiological and pathogenic features of Leptospira interrogans revealed by whole-genome sequencing[END_REF], and since then, whole genome sequencing has been made increasingly easier by the rise of NGS technologies. These massively parallel DNA sequencing methods provide high throughput genomic data faster and cheaper than first generation sequencing.

A large-scale sequencing project entitled "Leptospira Genomics and Human Health" (http://gsc.jcvi.org/projects/gsc/leptospira/) led by the Craig Venter Institute and initiated in 2011 has generated whole genome sequences for numerous strains belonging to 20 Leptospira species from diverse origins and geographical areas [START_REF] Lehmann | Leptospiral Pathogenomics[END_REF]. The global analysis of these genomes has identified a core genome of more than 1760 genes, of which 737 are specific to Leptospira, 369 are specific to species with some degree of pathogenicity (Pathogens and Intermediates), and 416 are specific to pathogenic species [START_REF] Fouts | What Makes a Bacterial Species Pathogenic?:Comparative Genomic Analysis of the Genus Leptospira[END_REF]. Beside all basic knowledge that is (and will still be) gained from these wide comparative genomics studies [START_REF] Xu | Whole genome sequencing revealed host adaptation-focused genomic plasticity of pathogenic Leptospira[END_REF], the identification of these genes offers opportunities to identify highly specific targets for Leptospira barcoding but also improve the feasibility of a universal, multilocus molecular typing system [START_REF] Gerth | A multilocus sequence typing (MLST) approach to diminish the problems that are associated with DNA barcoding: A reply to Stahlhut etal[END_REF].

The availability of new 'single-molecule' sequencing technologies (generally referred to as third-generation sequencing) that can produce longer reads and highly accurate de novo assemblies of hundreds of microbial genomes has enabled greatly improved analysis of genome structure [START_REF] Koren | Reducing assembly complexity of microbial genomes with single-molecule sequencing[END_REF][START_REF] Loman | A complete bacterial genome assembled de novo using only nanopore sequencing data[END_REF]. When the price and computational challenges are overcome, these new technologies, with the prospect of readily available full genomic sequences data, may make core genome MLST (cgMLST) a new gold standard and trigger the downfall of DNA barcoding, especially for bacteria [START_REF] Taylor | An emergent science on the brink of irrelevance: a review of the past 8 years of DNA barcoding[END_REF].

The combination of DNA barcoding with NGS technologies has also facilitated the taxonomic profiling of complex communities through the simultaneous sequencing of many thousands of DNA barcodes from each sample. "Metabarcoding' is distinguished from conventional barcoding by operating on the collective DNA rather than the isolated DNA of individual organisms [START_REF] Baker | Dissecting hostassociated communities with DNA barcodes[END_REF]. This broader community approach has been used by health scientists to investigate animals for zoonotic pathogens, allowing the taxonomic classification of all infecting ones [START_REF] Razzauti | A Comparison between Transcriptome Sequencing and 16S Metagenomics for Detection of Bacterial Pathogens in Wildlife[END_REF], or by microbial ecologists to investigate genetic materials from environmental samples on a tremendous scale and without cloning. Because of this 'inventory' approach, the leptospirosis scientific community may gain unexpected information about Leptospira spp. through the active data mining of the sequence databases fed by metabarcoding studies with no specific focus on leptospirosis.

As an emerging and re-emerging infectious disease, a future challenge of Leptospira typing will be to continue to develop and adapt barcoding, typing and Leptospira classification schemes to deal with the increasing array of pathogen diversity described in the literature.

New Leptospira species are still being discovered, more than a century after the first isolation of pathogenic Leptospira [START_REF] Bourhy | Leptospira mayottensis sp. nov., a pathogenic Leptospira species isolated from humans[END_REF][START_REF] Ido | The rat as a carrier of Spirochaeta Icterohaemorrhaguae, the causative agent of Weil's disease (Spirochaetosis Icterohaemorrhagica)[END_REF], and additional species may still be waiting to be discovered. In relatively poorly characterised regions of the world such as Africa, studies that are performed often detect new or divergent Leptospira strains [START_REF] Allan | Leptospirosis in northern Tanzania: investigating the role of rodents and ruminant livestock in a neglected public health problem[END_REF][START_REF] Allan | Epidemiology of Leptospirosis in Africa: A Systematic Review of a Neglected Zoonosis and a Paradigm for 'One Health' in Africa[END_REF][START_REF] Mgode | Leptospira Serovars for Diagnosis of Leptospirosis in Humans and Animals in Africa: Common Leptospira Isolates and Reservoir Hosts[END_REF]. The challenge remains to identify the best DNA targets and amplification techniques for this purpose. These should fulfil two hardly compatible needs: (i) a need to be highly sensitive to account for the frequently very low bacterial burden of clinical specimens and (ii) a need to generate DNA products with a sequence polymorphism of epidemiological relevance. Additionally, these should still take into account the wide diversity of the genus Leptospira.

Estimating the true diversity of Leptospira is tied to how well the genomic diversity of the community is represented by the genomes available in sequence databases.

Whilst barcoding and multi-locus typing of infectious Leptospira allow genetic classification of the infecting leptospires, diagnosis and surveillance of infection as well as vaccination are still heavily dependent upon serology and the serological classification schemes. As yet, a major challenge for the leptospirosis community is to reconcile the serological and molecular Leptospira classification schemes. The different molecular typing methods described in this review do not identify serovars but at best point to "putative serovars" based on correlations determined previously. The effective marriage of serovars and genotypes might be achieved through a molecular-based serovar typing system. The nucleotide sequence of the LPS biosynthetic operon rfb has therefore been pointed as a potential target for genotyping leptospires at the serovar level [START_REF] Ahmed | Molecular Approaches in the Detection and Characterization of Leptospira[END_REF][START_REF] Bezerra Da Silva | Evaluation of the Use of Selective PCR Amplification of LPS Biosynthesis Genes for Molecular Typing of Leptospira at the Serovar Level[END_REF]. Although the performance of the method did not provide optimal results yet, the approach in itself proved very useful and promising (Bezerra da [START_REF] Bezerra Da Silva | Evaluation of the Use of Selective PCR Amplification of LPS Biosynthesis Genes for Molecular Typing of Leptospira at the Serovar Level[END_REF], and whole genome sequences might be used in the future to infer serological features. For now, the ongoing challenge of a double non-convergent taxonomy -serovar vs genotype -looks set to continue. However, the exciting developments in the field of WGS may yet offer new insights into understanding the epidemiology, pathogenesis and taxonomy of this complex but important zoonotic pathogen.

FINANCIAL SUPPORT

This review work was supported by the author's institutions and was not funded by any external grant. [START_REF] Goarant | An exotic case of leptospirosis imported into an endemic area[END_REF] lfb1 [START_REF] Merien | A rapid and quantitative method for the detection of Leptospira species in human leptospirosis[END_REF], secY [START_REF] Ahmed | Development and validation of a real-time PCR for detection of pathogenic Leptospira species in clinical materials[END_REF], lipL32 [START_REF] Levett | Detection of pathogenic leptospires by real-time quantitative PCR[END_REF], 16SrRNA [START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF] Human blood Identification of an exotic Leptospira species (L. borgpetersenii, L. interrogans, L. kirschneri and L. weilii) and subspecific genotypes [START_REF] Ogawa | Molecular epidemiology of pathogenic Leptospira spp. in the straw-colored fruit bat (Eidolon helvum) migrating to Zambia from the Democratic Republic of Congo[END_REF] flaB [START_REF] Koizumi | Investigation of reservoir animals of Leptospira in the northern part of miyazaki prefecture[END_REF], secY [START_REF] Gravekamp | Detection of seven species of pathogenic leptospires by PCR using two sets of primers[END_REF], 16SrRNA [START_REF] Ogawa | Molecular epidemiology of pathogenic Leptospira spp. in the straw-colored fruit bat (Eidolon helvum) migrating to Zambia from the Democratic Republic of Congo[END_REF] Kidneys from bats Identification of Leptospira species (L. kirschneri and L. borgpetersenii) as well as novel genotypes (probable novel pathogenic species) [START_REF] Pagès | Leptospirosis after a stay in Madagascar[END_REF] lfb1 [START_REF] Merien | A rapid and quantitative method for the detection of Leptospira species in human leptospirosis[END_REF] ( [START_REF] Guernier | Human Leptospirosis on Reunion Island, Indian Ocean: Are Rodents the (Only) Ones to Blame?[END_REF] MLST [START_REF] Ahmed | Multilocus sequence typing method for identification and genotypic classification of pathogenic Leptospira species[END_REF], 16SrRNA [START_REF] Fenner | Analysis of 16S rDNA sequences from pathogenic Leptospira serovars and use of single nucleotide polymorphisms for rapid speciation by D-HPLC[END_REF][START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF], secY [START_REF] Gravekamp | Detection of seven species of pathogenic leptospires by PCR using two sets of primers[END_REF] Human sera, santarosai) and genotype diversity [START_REF] Obiegala | Prevalence and Genotype Allocation of Pathogenic Leptospira Species in Small Mammals from Various Habitat Types in Germany[END_REF] gyrB [START_REF] Slack | Identification of pathogenic Leptospira species by conventional or real-time PCR and sequencing of the DNA gyrase subunit B encoding gene[END_REF], MLST [START_REF] Thaipadungpanit | A Dominant Clone of Leptospira interrogans Associated with an Outbreak of Human Leptospirosis in Thailand[END_REF] Kidneys from small Mammals Identification of Leptospira species (L.

interrogans, L. borgpetersenii and L. kirschneri).

ST for some samples.

  Leptospira species (L. borgpetersenii, L. kirschneri and L. mayottensis)[START_REF] Cosson | Epidemiology of leptospira transmitted by rodents in southeast Asia[END_REF] secY, adk, 16SrRNA[START_REF] Ahmed | Multilocus sequence typing method for identification and genotypic classification of pathogenic Leptospira species[END_REF] Kidneys from rodents Identification of Leptospira species (L.

  Leptospira species (L. interrogans, L. kirschneri, L. borgpetersenii and L. mayottensis) Identification of complete or partial ST from MLST (Hamond et al., 2016) secY (Ahmed et al., 2006) Urine from cattle Identification of Leptospira species (L. interrogans, L. borgpetersenii, L. noguchii and L.

(

  [START_REF] Weiss | An Extended Multilocus Sequence Typing (MLST) Scheme for Rapid Direct Typing of Leptospira from Clinical Samples[END_REF] MLST adapted from(Boonsilp et al., Leptospira species (L. borgpetersenii, L. kirschneri, L. santarosai and L. weilii). Partial or complete ST.

Figure 1 :

 1 Figure 1: Phylogeny deduced from (A) 1262 bp or (B) the variable regions V3 & V4 (440 bp) of the 16S rRNA rrs gene. The phylogenetic topology of the genus Leptospira is shown in the upper panel A. Unique sequences of the V3 & V4 regions of the rrs gene, frequently used in metagenomics studies, discriminate only 12 mOTUs from the 22 Leptospira species currently described. The corresponding resolution losses are highlighted in red in lower panel B. Reference sequences were retrieved from GenBank and used to establish phylogeny (Neighbour Joining). Scale bars are substitution rates.

Table 2 : Examples of successful typing of Leptospira from single short DNA sequences and corresponding discriminatory capacity.

 2

Table 1 :

 1 PCR used or of potential use to generate Leptospira "barcodes". The PCR published for diagnostic purpose are usually optimized for sensitivity and specificity.

	Initial purpose	Gene target	Technology	Product size	Reference
	Diagnostic	16S rRNA rrs	Conventional nested PCR	331 bp	(Merien et al., 1992)
				290 bp	Primers A & D detect all Leptospira
					species
	Diagnostic	lipL32	SYBR Green I qPCR	423 bp	(Levett et al., 2005)
	Diagnostic	lipL32	TaqMan qPCR	242 bp	(Stoddard et al., 2009)
	Diagnostic	secY	SYBR Green I qPCR	202 bp	(Ahmed et al., 2009)
	Diagnostic	lfb1	SYBR Green I qPCR	331 bp	(Merien et al., 2005)
	Diagnostic	flaB	Conventional PCR	793 bp	(Kawabata et al., 2001)
	Diagnostic	secY	Conventional PCR	285 bp	(Gravekamp et al., 1993)
	Typing	gyrB	Conventional PCR or SYBR Green I qPCR	504 bp	(Slack et al., 2006)
	Typing	rpoB	Conventional PCR	600 bp	(La Scola et al., 2006)
	Typing (MLST)	16SrRNA rrs	Conventional PCR	541 bp	(Ahmed et al., 2006)
	Typing (MLST)	secY	Conventional PCR	549 bp	(Ahmed et al., 2006)
	Typing (MLST)	lipL32	Conventional PCR	474 bp	(Ahmed et al., 2006)
	Metagenomics	16SrRNA rrs regions V3-V4	Conventional PCR	~450 bp	(Klindworth et al., 2013)
	Metagenomics	cpn60 (hsp60) Conventional PCR	~550-600 bp	(Goh et al., 1996; Klindworth et al., 2013)
	Barcoding	COI-1	Conventional PCR	~550 bp	(Smith et al., 2012)

Table 2 :

 2 Examples of successful typing of Leptospira from single short DNA sequences and corresponding discriminatory capacity

	Article	Molecular target(s)	Starting material	Finding(s)
	(Ganoza et al., 2006)	Nested 16SrRNA (Ganoza et al., 2006) (product cloned in E. coli)	Surface waters	Presumptive Leptospira species and comparison with human isolates, unknown Leptospira clade
	(Perez & Goarant, 2010)	lfb1 (Merien et al., 2005), secY (Ahmed et al., 2009), MLST (Thaipadungpanit et al., 2007)	Human serum, deer kidneys	Identification of putative serovar (as a correlate in a specific island epidemiology)
	(Agampodi et al., 2011)	16SrRNA (Agampodi et al., 2011)	Human blood	Identification of Leptospira species (L. interrogans and L. weilii) in 6/8 samples
			Rodent kidneys	Identification of putative serovar Identification of an unknown pathogenic Leptospira
	(Agampodi et al., 2013)	MLST (Thaipadungpanit et al., 2007)	Human serum or whole blood	Determination of partial to complete ST in 12/58 samples
	(Koizumi et al., 2013)	flaB (Koizumi et al., 2008)	Blood or urine from dogs	Identification of Leptospira species (L. interrogans)
	(Halliday et al., 2013)	secY (Ahmed et al., 2009)	Kidneys from rodents	Identification of Leptospira species (L. interrogans and L. kirschneri)
	(Agampodi et al., 2014)	Nested 16SrRNA (Agampodi et al., 2011; Ganoza et al., 2006)	Human serum or whole blood	Identification of Leptospira species (L. kirschneri, L. interrogans and L. borgpetersenii) in 28/32 samples

[START_REF] Perez | Rodent abundance dynamics and leptospirosis carriage in an area of hyper-endemicity in New Caledonia[END_REF]

lfb1

[START_REF] Merien | A rapid and quantitative method for the detection of Leptospira species in human leptospirosis[END_REF]

, lipL32

[START_REF] Levett | Detection of pathogenic leptospires by real-time quantitative PCR[END_REF]

, 16SrRNA

[START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF]

  , secY (Ahmed et Human urine Identification of Leptospira species (L.

		al., 2009)		interrogans) from lfb1 sequence only
	(Verma et al., 2015)	MLST (Ahmed et al., 2006)	Kidneys from pigs	Identification of Leptospira species (L. interrogans). All genes but adk amplified and sequenced.
	(Gomard et al., 2016)	secY, adk, 16SrRNA (Ahmed et al., 2006)	Pool of kidney, spleen and lung from bats	Identification of Leptospira species (L. kirschneri and L. borgpetersenii) as well as novel genotypes (probable novel pathogenic species).

coat, urine) [START_REF] Ayral | Hedgehogs and Mustelid Species: Major Carriers of Pathogenic Leptospira, a Survey in 28 Animal Species in France (20122015)[END_REF] 16SrRNA [START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF], Multispacer

Sequence Typing [START_REF] Zilber | High-resolution typing of Leptospira interrogans by Multispacer Sequence Typing[END_REF] Kidneys from small Mammals Identification of Leptospira species (L.

interrogans, L. borgpetersenii and L. kirschneri).

Putative serogroup or serovar from Multispacer ST. [START_REF] Lagadec | Identification of Tenrec ecaudatus, a Wild Mammal Introduced to Mayotte Island, as a Reservoir of the Newly Identified Human Pathogenic Leptospira mayottensis[END_REF] 16SrRNA [START_REF] Merien | Polymerase chain reaction for detection of Leptospira spp. in clinical samples[END_REF]


Angela Minzoni
email: angela.minzoni@ecp.fr

Eléonore Mounoud
email: eléonore.mounoud@ecp.fr

Vesa A Niskanen
email: vesa.a.niskanen@helsinki.fi

A Case Study on Time-Interval Fuzzy Cognitive Maps in a Complex Organization

Keywords: temporality, organizational design, coordination, fuzzy cognitive maps

Temporal issues within modeling organizational systems are examined generally and with fuzzy cognitive maps. These maps give the opportunity to consider temporal factors when studying organizational models. The knowledge we gain about the system is useful when the aim is not to optimize time intervals in well-known and instrumented contexts, but also to discover the behavior of the system while different temporal factors are implemented by the management. We will present an adapted resolution for including these factors as key elements in organizational models with fuzzy cognitive map examples for middle and back office application.

I. INTRODUCTION

When modelling organizational and social systems, it is important to acknowledge the importance of temporal aspects, both in duration and pace, because some relationships not only base on the immediate causal interconnections but there may be a certain time interval between the causes and their effects. The identification of temporality in interrelationships are particularly challenging in model constructions.

Minzoni and Mounoud provide in [START_REF] Minzoni | Rethinking operating models for intangible services : from a mechanistic structure to a sustainable model[END_REF] an overview of the general methodological approach adopted for the system under study, viz., the middle and back office operations for banking services. It should to be recalled here that the operations are considered as embedded in their organizational context, i.e., including strategy, governance, procedures, etc. It is thus the behavior of the entire system which is considered, knowing that the available data are almost exclusively qualitative and that there are no tools giving a global picture of the necessary interconnections to carry out the operations. In our study fuzzy cognitive maps (FCM) have provided a method for experts to elicit and identify interrelationships between the given concepts for understanding the features of the system when temporal factors are introduced in the model. Thus, this is one approach to the complex mixture of human and artificial cognitive capabilities in human computer interaction processes as well as to socio-cognitive ICT which utilizes or influences on collective knowledge [START_REF] Baranyi | Cognitive Infocommunications (CogInfoCom)[END_REF]. The data and expertise presented below are thus originating from real back office operations.

Our interrelationships are only approximately stated, weak (0.5) or strong [START_REF] Axelrod | Structure of Decision, The Cognitive Maps of Political Elites[END_REF], positive or negative, because our principal aim is not to support decision making but rather to provide more knowledge about the organizational system and the global view by uncovering previously unknown patterns to the management team. FCMs enable us to simulate temporal scenarios and to understand system's global operational states by providing holistic information rather than to optimize its parts to the detriment of the whole.

The FCMs thus seem to be viable models for examining the foregoing systems because they enable us to study the complex phenomena of the real world [START_REF] Axelrod | Structure of Decision, The Cognitive Maps of Political Elites[END_REF][START_REF] Kosko | Fuzzy Engineering[END_REF][START_REF] Niskanen | Concept map approach to approximate reasoning with fuzzy extended logic[END_REF][START_REF] Pedrycz | Design of Fuzzy Cognitive Maps for Modeling Time Series[END_REF][START_REF] Stylios | Modeling Complex Systems Using Fuzzy Cognitive Maps[END_REF]. Their constructions usually base on human expertise or empirical (historic) data. Both numeric and linguistic models may be applied in this context [START_REF] Carvalho | Rule Based Fuzzy Cognitive Maps in Socio-Economic Systems[END_REF][START_REF] Kosko | Fuzzy Engineering[END_REF]. However, the extended time inclusive approach is still quite rarely adopted within the FCMs even though it plays an important role particularly when organizational design aspects are involved in these systems [START_REF] Carvalho | Rule Based Fuzzy Cognitive Maps in Socio-Economic Systems[END_REF][START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF][START_REF] Stach | Higher-order Fuzzy Cognitive Maps[END_REF].

This study introduces temporal approach to FCM by representing relations that are not always active in a simulation. This method allows a direct modeling of real world situations that are not much currently addressed in FCM. Chapter 2 considers how temporal aspects have been considered within organization studies. Chapter 3 considers the challenges of FCM construction especially when time intervals are involved in these models, and detailed examples are provided. These considerations are based on the FCM models and their computer simulations carried out by Niskanen, following the initiatives and monitoring of Minzoni, and at the first stage, also by the work of the Hungarian research group under the supervision of Koczy [START_REF] Buruzs | Expert-Based Method of Integrated Waste Management Systems for Developing Fuzzy Cognitive Map[END_REF][START_REF] Hatwagner | Behavioral Analysis of Fuzzy Cognitive Map Models by Simulation[END_REF]. Chapter 4 concludes our considerations.

II. CONSIDERING TEMPORAL FACTORS IN ORGANIZATIONS

Our study pivots on the problems of causality and temporality. In causality we may apply causa efficiens and causa finalis if Aristotle's terms are used. The former is used in the Natural Sciences, whereas both of these are applied to the Human Sciences (this also including Economics).

The final causes seem more challenging to dynamical systems because they represent teleological relationships which are typical of the human goal-oriented behavior, i.e., their present acts are the effects caused by their goals located in the future. Also, unlike in the control applications based upon the deterministic efficient causes, the socio-economic systems often deal with relationships which are only probabilistic by nature. Various causal chains are also more usual and thus our systems may include delays and other temporal factors.

When trying to understand the large corporations' dynamic organization, the temporal issue is a key concept. This issue is mostly considered by introducing "delay" that means time spans considered too long comparatively to the expected time. In order to estimate delays, the system needs to be understood well enough for knowing what normal and delayed time intervals and durations are. Not all systems have already such a refined quantitative knowledge to estimate whether their cause-effect relations are delayed or immediate. When the behavioral pattern of the system is unknown, application of temporal factors in FCM calculations allows experts to discover this pattern, throwing new light on their system's understanding and time span calibration [START_REF] Park | Fuzzy cognitive maps considering time relationships[END_REF][START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF][START_REF] Lee | Learning Rule for Time Delay in Fuzzy Cognitive Maps[END_REF][START_REF] Stach | Higher-order Fuzzy Cognitive Maps[END_REF][START_REF] Zhong | Temporal fuzzy cognitive maps[END_REF].

We can picture time in different ways according to cultures and organizations, drawing on different sets of imagery, or using different metaphors [START_REF] Hassard | Commodification, construction and compression: a review of time metaphors in organizational analysis[END_REF]. Anthropologists have often described cultures as having either cyclical or linear notions of time. Cyclical time, naturally enough, emphasizes repetition and is very much influenced by the cycles of the natural world. The line and the cycle are the similar two key time metaphors by which time is thought in organization theory. In the history of organization, the focus has initially been upon linear time images that stem from the progressive commodification of the labor process. An example is the homogeneous time-reckoning systems of Taylorism [START_REF] Weick | Managing the unexpected: Resilient performance in an age of uncertainty[END_REF]. Taylor maintained time as a commodity to be factored into job design, organization processes and control mechanisms.

Hassard [START_REF] Hassard | Commodification, construction and compression: a review of time metaphors in organizational analysis[END_REF] has pointed out beyond the issues of clocktime, the importance of what has been referred to as "instantaneous-time", whereby organizational practices are based on time-frames that lie beyond conscious human experience. He associates this concept with the complex shifts from Fordism to the flexible accumulation of "post-Fordism". Management and organization theory have viewed time as a significant resource and put forward multiple views as to how time is both managed and experienced [START_REF] Carr | Space and time in organizational change management[END_REF]. The way we experience time is open to manipulation and specifically time compression that displaces critical reflection and may make individuals "managed by (others') time". In [START_REF] Perlow | THE SPEED TRAP: Exploring the Relationship Between Decision Making and Temporal Context[END_REF] was developed the idea of the speed trap and showed how the need for fast action, traditionally conceptualized as an exogenous feature of the surrounding context, is a product of an organization's own past emphasis on speed.

More recently in [START_REF] Reinecke | When Times Collide: Temporal Brokerage at the Intersection of Markets and Developments[END_REF] was studied the influence of clocktime orientation market-based models for human development. While a linear, clock-time orientation optimized for markets is meant to enhance efficiency, coordination, and control, it may be unsuitable for managing emergent, complex, and indeterminate processes such as development. This work develops an agentic view of time, where time is used as a cultural resource to regulate attention and render social phenomena amenable to managerial action and how organizations accommodate seemingly contradictory temporal orientations.

In this study, we used FCM modeling to establish a collective (and thus possible to share and discuss between organizational members) overview on the interrelationships and other temporal issues, such as effects of speed, fire-fighting, escalation and fast pace course of action [START_REF] Perlow | THE SPEED TRAP: Exploring the Relationship Between Decision Making and Temporal Context[END_REF]. FCMs were used to support the discovery of organizational hidden patterns. In our case this means the temporal patterns for providing ways of integrating each person's personal schema as well as the backdrop of the organization's objectives. It helps both to interpret the information and to coordinate that information to make it meaningful for the members of the organization and its goals. It enables the sense-making process by which organizational members incessantly create and re-create conceptions of themselves and of the world all around them. As described in [START_REF] Zaheer | Time Scales and Organizational Theory[END_REF], sense-making is an action which involves turning circumstances into a situation that is comprehended explicitly in words or speech and that serves as a springboard to action. In [START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF], in turn, was noticed that research and theory on organizations are lacking a critical specification on time scale. Specification of the relevant time scale is as critical as the specification of the appropriate level or unit of analysis, a concept to which it is related. They showed how the choice of time scale has important implications for the development of organization theory.

After unfolding the simulation details by applying temporal factors in FCM, we will present a short reflection from the organizational science perspective. Within this context organizational patterns are understood as those internal relationships which provide the system with its coherence and keep it from being an accumulation of fragmented activities.

III. MODEL CONSTRUCTION EXAMPLES ON TEMPORAL FUZZY COGNITIVE MAPS

In our project, Niskanen, Koczy and Hatwagner carried out thorough analysis of expert-based FCM models which represented the middle and back office operations for banking services in a private French bank (and thus certain confidentiality should be maintained below) [START_REF] Hatwagner | Behavioral Analysis of Fuzzy Cognitive Map Models by Simulation[END_REF].

Standard methods were used in basic simulations, and thus the concept (node) values ranged from zero to unity and the weights or intensities of the interrelationships in the connection matrices belonged to the closed intervals from -1 to 1 [START_REF] Kosko | Fuzzy Engineering[END_REF][START_REF] Pedrycz | Design of Fuzzy Cognitive Maps for Modeling Time Series[END_REF][START_REF] Stylios | Modeling Complex Systems Using Fuzzy Cognitive Maps[END_REF]. Our FCM models contained 12 to 35 concepts, each of these being possible inputs and ouputs, and expectedly, especially the large connection matrices were particularly challenging in computations due to their many parameters.

Hence, in the basic FCM computer simulations we applied the matrix product, *,

V t+1 = f(V t *M), (1)
in which state vector, V t , contains m concept values at time t, M is an m×m connection matrix, f is the transformation function and vector V t+1 contains the new concept values at time t+1 [START_REF] Pedrycz | Design of Fuzzy Cognitive Maps for Modeling Time Series[END_REF]. One time unit of t denoted in our models one month. For function f we applied the usual sigmoid function,

f(x) = 1 / (1+exp(-𝛌x)), (2)
in which exp is the exponential function and parameter 𝛌>0 [START_REF] Pedrycz | Design of Fuzzy Cognitive Maps for Modeling Time Series[END_REF].

Numerous simulations were performed when our models were studied [START_REF] Hatwagner | Behavioral Analysis of Fuzzy Cognitive Map Models by Simulation[END_REF]. First 1000 to 10 000 random initial concept vectors were used for each FCM model for examining their general variation in iterations. In this context, various lambda values were also tested for obtaining their optimal values, i.e., the values which caused large standard deviations to the output values [START_REF] Hatwagner | Behavioral Analysis of Fuzzy Cognitive Map Models by Simulation[END_REF]. In this manner, we also observed such variation as possible fixed-point attractors and examined statistical distributions of concept outcomes in our models.

Various alternative initial state vectors and connection matrices were also tested by using genetic and bacterial evolutionary algorithms in optimization. By assigning appropriate goal vectors, this method revealed us how fixed-point attractors or chaotic variation can be created, inter alia. We also examined how to reduce the converging speed of the state vectors to their fixed points.

Below we focus on the above-mentioned temporal issues. We aimed to also apply such external temporal factors which could take into account the distinct time intervals between the causes and their effects in our FCM modeling. This approach is thus a more challenging task than with those prevailing models which are based on historic data or do not deal with the extended temporal aspects [START_REF] Carvalho | Rule Based Fuzzy Cognitive Maps in Socio-Economic Systems[END_REF][START_REF] Pedrycz | Design of Fuzzy Cognitive Maps for Modeling Time Series[END_REF][START_REF] Stach | Higher-order Fuzzy Cognitive Maps[END_REF].

Our methods for temporal factors seem somewhat analogous to those of in [START_REF] Lee | Learning Rule for Time Delay in Fuzzy Cognitive Maps[END_REF][START_REF] Zhong | Temporal fuzzy cognitive maps[END_REF] from the theoretical standpoint, but in practice we used different calculations in the models. Hence, this paper provides a case study based on a real-world application.

According to the foregoing simulations, we used lambda value of 1 because then the outputs have larger dispersions in their transformed values even though value of 5 seems more frequent within the FCMs. The value of 1 is also used below.

Since lack of space precludes wider analyses, we only focus below on a concrete example concerning our bank's organizational FCM with its thirteen concepts, viz., In the real-world FCM applications the preceding values of concepts are usually relevant in the succeeding iteration. Thus, in our computations the diagonals of our connection matrices also contained nonzero values, and we mainly used the values of 1. Table 1 provides an example on a connection matrix which was specified according to bank's experts (Fig. 1). One challenge in simulations was that the matrices only contained a quite small number of rounded weights which is a typical feature, and disadvantage, in expert-based models. Thus, with this matrix, our concept values may vary as presented in Tables 2 and 3 when 1000 random initial concept vectors are used. These statistics are only approximate by nature because, due to the combinatorial explosion, we were unable to use all combinations of values as initial vectors.

We notice in Table 2 that the ranges of some concepts values are so wide that it is justified to use small values of 𝛌 in (2) because then the corresponding transformation function is not too steep. However, Table 3 presents, for example, that still small concept values are not obtained. In addition, our basic FCM models often yielded quite fast fixed-point attractors to our concept values (Fig. 2). In this case the fixed-point attractors were virtually attained in less than ten iterations. Most of the concepts also have values very close to the maximum of 1. However, these results still seemed to allow the managers to acknowledge the non-chaotic variation of their organization.

Since we were unable to influence on the values of weights in computation, we do not consider below much the meaningfulness of our concepts or their interrelationships but rather we focus on their mere technical and computational aspects in order to acquire information by examining their patterns of behavior and variation. Matlab TM and R with their Toolboxes were used in computations. 1 1 0 0.5 0 0 0.5 1 0.5 0 0.5 1 0.5 0 2 1 1 0.5 1 0 0 1 1 0.5 0 1 1 0 3 1 0.5 1 0 0 -1 0 -1 1 0 1 1 1 4 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 1 -0.5 1 0 0 -1 0 0 0 1 0 6 0 0 0 0 -0.5 1 0 0 0 0 0 0 0 7 0.5 0 0.5 1 0 0.5 1 0 0 -0.5 0 0 0 8 0 0 0 0 0 -0.5 0 1 0 0.5 0 0 -0.5 9 0 0 0 1 0 0.5 0.5 0.5 1 -0.5 0 0.5 0 10 0.5 0 0 0 0 0 0.5 0.5 0.5 1 1 0 0 11 0 0 0.5 0.5 0 0 0 0 0.5 0.5 1 0 1 12 0 0 0.5 0.5 0 0 1 0 0.5 0 0.5 1 -0.5 13 0 0 1 0 0 0.5 0 0 0 0 1 0 1 Fig. 1. Fuzzy cognitive map based on Table 1 (self-loops are not presented).

Moreover, generally in the human-scientific models, we should have both causal and teleological temporal interconnections. The latter factors, which comprise peoples' intentions, motives and their other underlying causes, are more challenging than the causal effects. Thus, often in these real-world ap-plications, the FCM models should also take into account the time spans, delayed effects and even the present goals of the decision makers, and these aspects have not been studied much thus far [START_REF] Carvalho | Rule Based Fuzzy Cognitive Maps in Socio-Economic Systems[END_REF][START_REF] Park | Fuzzy cognitive maps considering time relationships[END_REF][START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF][START_REF] Lee | Learning Rule for Time Delay in Fuzzy Cognitive Maps[END_REF][START_REF] Stach | Higher-order Fuzzy Cognitive Maps[END_REF][START_REF] Zhong | Temporal fuzzy cognitive maps[END_REF][START_REF] Zhuge | Knowledge map: mathematical model and dynamic behaviors[END_REF]. For example, political decisions often have impacts in the long term, whereas in control applications immediate responses are usual. One well-known resolution to temporal factors is suggested in [START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF] who, all in all, applied nonlinear, conditional and fixed time-delayed relationships. In [START_REF] Park | Fuzzy cognitive maps considering time relationships[END_REF] fixed time delays were also used. In [START_REF] Zhuge | Knowledge map: mathematical model and dynamic behaviors[END_REF] simple cause-effect, time-delay causal and conditional probabilistic relations, as well as sequential, special time-delayed, relations were suggested. These extended FCM models based on their manual developments, and thus more or less subjective values to the delays were also assigned. In [START_REF] Stach | Higher-order Fuzzy Cognitive Maps[END_REF] a genetic learning algorithm method with data, referred to as the higher order FCM, was introduced which was able to take into account the given number of the previous concept values when their current values were computed.

As stated above, we also considered temporal factors in our framework. In [START_REF] Lee | Learning Rule for Time Delay in Fuzzy Cognitive Maps[END_REF][START_REF] Zhong | Temporal fuzzy cognitive maps[END_REF] three types of meanings for delay were presented, time delay between the cause and effect, the period of time when the cause is actualizing in the effect, and the combination of these two. This approach to temporal aspects was somewhat analogous to our objectives below. Hence, we assumed in the simulations first that different time intervals may prevail between the causes and their effects, and second, that there are even different time intervals or periods of time for the process how certain causes will emerge. In practice, in our extended temporal models certain nonzero links were always active, whereas others were inactive except in the given iterations. A simple real-world example would be the quarterly changes of Central Bank's interest rates to the markets because they stay fixed or inactive in certain iterations.

The use of time intervals and other additional temporal factors opens new prospects for examining the FCM models. For example, then the concept values may start oscillating, and this type of variation often corresponds better to the daily variation between busy and more relaxed time periods in the company or organization.

We used our own matrix-based calculation methods in computing because this approach may be more user-friendly when time intervals are specified and simpler in computations. Thus, we designed first an additional m×m matrix, D, which controlled the actions of the concepts (Table 4). This matrix represented the time intervals within the impacts of the concepts. Hence, if the link from concept C i to C j is only active in every k th iteration, then D(i,j) = k. If link C i to C j is always active, D(i,j) = 1. Otherwise D(i,j) = 0 when i and j = 1, 2, 3, …, m. In computations, in each iteration, k, we created with D such m×m indicator matrix, IM k , in which IM k (i,j) = 1 when D(i,j) = k or 1, otherwise IM k (i,j) = 0. We now replaced in (1) the operation V t *M by V t *(M•IM k ) in which M•IM k means the cell-by-cell multiplication of M and IM k . Hence, in iterations k ≥ 1,

V t+1 = f(V t *(M•IM k )) (3)
TABLE 4. EXAMPLE OF OUR MATRIX, D.

1 2 3 4 5 6 7 8 9 10 11 12 13 1 1 0 1 0 0 36 1 18 0 36 36 1 0 2 1 1 1 1 0 0 1 1 1 0 1 1 0 3 1 1 1 0 0 1 0 1 1 0 1 1 1 4 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0 0 1 1 1 0 0 18 0 0 0 18 0 6 0 0 0 0 1 1 0 0 0 0 0 0 0 7 36 0 1 1 0 36 1 0 0 18 0 0 0 8 0 0 0 0 0 1 0 1 0 36 0 0 18 9 0 0 0 1 0 36 1 1 1 36 0 6 0 10 36 0 0 0 0 0 18 36 36 1 36 0 0 11 0 0 1 1 0 0 0 0 36 60 1 0 18 12 0 0 1 1 0 0 1 0 36 0 1 1 36 13 0 0 1 0 0 36 0 0 0 0 3 0 1

We also applied the m×m frequency matrix, F, which controlled the frequencies of taking action in the occasional links in matrix D (Table 5). Hence, F(i,j) > 1 when D(i,j) > 1, otherwise F(i,j) = 0. Now the actual initial values for the time intervals were D = D + F. In each iteration, k > 1, we applied method (3) and then updated those cell values of D in which D(i,j) = k, D(i,j) = D(i,j) + F(i,j); i, j = 1, 2, …, m.

For example, if originally D(i,j) = 6 months and F(i,j) = 3 months, then first IM k (i,j) = 1 (and the link M(i,j) is thus active) in iteration k = 6+3 = 12. After this, M(i,j) is again active when k = 9+n•3 and n = 2, 3, … TABLE 5. EXAMPLE OF OUR MATRIX, F. 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 0 0 0 0 3 0 3 0 3 3 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 3 0 0 0 3 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 0 0 0 0 3 0 0 0 3 0 0 0 8 0 0 0 0 0 0 0 0 0 3 0 0 3 9 0 0 0 0 0 3 0 0 0 3 0 3 0 10 3 0 0 0 0 0 3 3 3 0 3 0 0 11 0 0 0 0 0 0 3 3 0 0 3 12 0 0 0 0 0 0 0 0 3 0 0 0 3 13 0 0 0 0 0 3 0 0 0 0 3 0 0 Fig. 3 depicts in a simplified form this variation of the profit/loss concept when only the link from investment has the time interval of 6 and frequency of 3 months. Hence, this link is first active in 6+3 = 9 th iteration, and after this in every 3 th iteration. We notice that instead of converging to the fixed point, the profit/loss concept now has more limit-cycling variation. Introducing time through time intervals and frequencies provides a different viewpoint on the system. It enables the system to oscillate. This variation is consistent with the daily experience of ups and downs, the alternation of fast pace and more relaxed periods in the company. Fig. 5 depicts this variation with all our concepts together. We notice limit-cycling, or even chaotic, variation compared to Fig. 2, as was expected in these conditions. Table 6 presents the possible concept values within 60 iterations when 1000 random initial concept vectors were used. We notice somewhat more variation in the concept values than in Table 3, but still small values are not obtained. Also, depending upon the values of frequencies and time intervals, the amplitude of oscillations can change dramatically, and for example Fig. 4 illustrates well an idea on the abovementioned speed trap in [START_REF] Perlow | THE SPEED TRAP: Exploring the Relationship Between Decision Making and Temporal Context[END_REF]. It reveals the impacts of the activating links with higher frequency than desired and the types of their outcomes. We thus may observe how the crests and troughs, traditionally conceptualized as an exogenous feature of the surrounding context, are a consequence of frequently activating links and thus being a result of organizational behavior. In the manner of ECG curve revealing the functioning of the heart, Fig. 4 is revealing in the transactions system the changing values of our concepts. We may thus diagnose if any 'tachycardia' is affecting on the system. The numeric FCM approach which we have adopted thus far is not the only possibility to operate with temporal aspects [START_REF] Carvalho | Rule Based Fuzzy Cognitive Maps in Socio-Economic Systems[END_REF][START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF]. In the numeric case, we will meet additional challenges due to their mathematical properties [START_REF] Hagiwara | Extended fuzzy cognitive maps[END_REF]. One central challenge to us was how we can optimize the connection matrix weights from the mathematical standpoint if historic data is unavailable? The human experts can only assign a more or less limited number of subjective and rounded values, and this may naturally affect on the goodness of the outcomes. This question still arises even though certain resolutions have been suggested already [START_REF] Lee | Learning Rule for Time Delay in Fuzzy Cognitive Maps[END_REF][START_REF] Stach | Higher-order Fuzzy Cognitive Maps[END_REF]. This was one study area in which we also tested with evolutionary computing such alternative connection matrices which yielded lower concept values or attained with reduced speed the fixed-point attractors [START_REF] Hatwagner | Behavioral Analysis of Fuzzy Cognitive Map Models by Simulation[END_REF]. Various values of parameter 𝛌 were also tested in this context. We examined each tentative model with 1000 random initial vectors for finding their essential characteristics [START_REF] Hatwagner | Behavioral Analysis of Fuzzy Cognitive Map Models by Simulation[END_REF].

IV. CONCLUSIONS

In the last decade, management sciences have become increasingly interested in and influenced by operations research, in particular intensive data acquisition and computing capabilities. The organizations nevertheless encounter such situations in which, prior to operationally optimizing their existing practices, they instead of only performing these operations in a faster or cheaper manner, have to consider new ways of organizing operations within broader conceptual frameworks.

When having this type of wide problem area, the available data are highly heterogeneous and we often lack appropriate historic data. In such cases FCMs may still provide a particularly suitable method when elaborating macro models for delivering such provisional assumptions. These models, in turn, help the Managers to keep a prospective attitude while running their daily operations. There may also be various time intervals between the causes and their effects, and these temporal factors in interrelationships are particularly challenging in model construction. This issue was studied in the light of FCM modeling above. Since only a few studies have examined this type of temporal aspects, one new method was suggested and used in our applications. It applied both time intervals and their frequencies, and a concrete example was presented. Thus, we could identify which impulses were sent too frequently, and this enabled us to calibrate managerial actions and objectives in necessariy time rather than disrupting the system by over-sending impulses.

Our temporal effects caused more variation to the model's concept values, as was expected. Another interesting feature was that the systems could oscillate and reveal different oscillation amplitudes for concept value's, while keeping their stability. This oscillatory variation may be compared to the ECGtype results in cardiology.

Our FCM modeling thus seems to shed new light for organizing and monitoring such operations which comprise long time intervals and presuppose the project members to respond in good time and with full understanding of the organization's dynamics. Such time patterns contribute to reflexive practices within the organization, saving energy and preventing stress. More generally, such socio-cognitive ICT and computational intelligence was applied which both utilized and influenced upon collective knowledge in an organization.

Our innovative results address the capital issue of introducing explicit temporalities in the FCM. However, the computerization of time intervals in the complex dynamical systems is still a quite a new frontier, and thus further studies are expected in this area.

  1 = clients, 2 = rules & regulations, 3 = new IT solutions, 4 = funding, 5 = cost reduction, 6 = profit/loss, 7 = investments, 8 = staff, 9 = new services, 10 = quality, 11 = client development, 12 = service development, 13 = productivity.

Fig. 2 .

 2 Fig. 2. Concept values in eight iterations when applying method(1), iteration 0 denotes random initial values.

Fig. 3 .

 3 Fig. 3. Variation of profit/loss concept values with method (3) when investments have time interval of 6 and frequency of 3 months (iteration 0 denotes random initial values).

Fig. 4 .

 4 Fig. 4. Example on the variation of profit/loss concept with method (3) when time intervals and frequencies in Tables 4-5 are used (iteration 0 denotes random initial values).

Fig. 5 Fig. 5 .

 55 Fig.5also provides an overview of the system and shows the multiple oscillations that create crests and troughs in the model. It highlights the importance to coordinate frequencies in relation to time intervals for avoiding (uncomfortable when experienced) huge variations in too many domains in the organization.

TABLE 1 .

 1 EXAMPLE OF OUR CONNECTION MATRIX, M.

TABLE 2 .

 2 POSSIBLE CONCEPT VALUES BY USING OUR CONNECTION MATRIX PRIOR TO TRANSFORMATION OF (2).

		Range	Min	Max Mean Std. Deviation
	Clients	4	0	4	2.01	0.55
	Rules_regulations	1.5	0	1.5	0.77	0.32
	NewITsolutions	5.5	0	5.5	2.76	0.62
	Funding	4.5	0	4.5	2.25	0.67
	Cost_reduction	1.46	-0.46	1	0.26	0.32
	Profit_loss	2.96	-0.86 2.09	0.71	0.52
	Investments	5	0	5	2.48	0.64
	Staff	3.83	-1.26 2.58	0.73	0.64
	New_services	4	0	4	2.00	0.52
	Quality	2.51	-0.53 1.99	0.76	0.43
	Client_development	6.5	0	6.5	3.27	0.74
	Service_development	5	0	5	2.49	0.63
	Productivity	3.32	-0.59 2.72	1.03	0.54
	TABLE 3. POSSIBLE CONCEPT VALUES BY USING OUR CONNECTION MATRIX
	AFTER TRANSFORMATION (2).
		Range	Min	Max	Mean	Std. Devia-
						tion
	Clients	0.48	0.5	0.98	0.87	0.06
	Rules_regulations	0.32	0.5	0.82	0.68	0.07
	NewITsolutions	0.5	0.5	1	0.93	0.04
	Funding	0.49	0.5	0.99	0.89	0.06
	Cost_reduction	0.33	0.39	0.72	0.56	0.08
	Profit_loss	0.59	0.3	0.89	0.66	0.11
	Investments	0.49	0.5	0.99	0.91	0.05
	Staff	0.71	0.22	0.93	0.66	0.13
	New_services	0.48	0.5	0.98	0.87	0.06
	Quality	0.51	0.37	0.88	0.68	0.09
	Client_development	0.5	0.5	1	0.95	0.04
	Service_development	0.49	0.5	0.99	0.91	0.05
	Productivity	0.58	0.36	0.94	0.73	0.10

TABLE 6 .

 6 POSSIBLE CONCEPT VALUES WHEN MATRICES D AND F ARE ALSO USED IN 60 ITERATIONS.

		Range	Min	Max	Mean Std. Deviation
	Client	0.47	0.5	0.97	0.94	0.02
	Rules_regulations	0.32	0.5	0.82	0.78	0.02
	NewITsolution	0.5	0.5	1	0.99	0.01
	Funding	0.49	0.5	0.99	0.99	0.02
	Cost_reduction	0.34	0.39	0.72	0.61	0.02
	Profit_loss	0.51	0.2	0.72	0.32	0.15
	Investments	0.49	0.5	0.99	0.98	0.01
	Staff	0.6	0.29	0.9	0.73	0.03
	New_services	0.47	0.5	0.97	0.91	0.03
	Quality	0.23	0.5	0.73	0.64	0.04
	Client_development	0.5	0.5	1	0.97	0.02
	Service_development	0.49	0.5	0.99	0.97	0.02
	Productivity	0.42	0.5	0.92	0.87	0.03

ACKNOWLEDGEMENTS

We express our thanks to the anonymous referees for their valuable comments.