Philippe Borsa
email: philippe.borsa@noumea.ird.nc

Sarah Lemer

Didier Aurelle

Patterns of lineage diversification in rabbitfishes

Fishes of the tropical Indo-Pacific family Siganidae comprise 28 species, characterized by their body proportions and their colour patterns. A mitochondrial phylogeny of 20 Siganidae species was produced to infer their evolutionary history. Three distinct, major clades were found, that also correspond to the early radiation of the family into three major ecological types: fusiform species that also live in schools on the inshore reef flats (S. canaliculatus, S. fuscescens, S. luridus, S. rivulatus, S. spinus, S. sutor); deep-bodied species including brightly coloured ones whose adults live in pairs on the reef front (S. corallinus, S. doliatus, S. puellus, S. punctatus, S. unimaculatus, S. virgatus, S. vulpinus), and species that live in small schools in mangroves, estuaries and estuarine lakes (S. guttatus, S. javus, S. lineatus, S. randalli, S. vermiculatus); and a third clade including a cosmopolitan species, S. argenteus, the only species of the family known to possess a pelagic, prejuvenile stage and S. woodlandi, a recently described species from New Caledonia and morphologically close to S. argenteus. The partition of the genus into two sub-genera, Lo (erected for S. unimaculatus, S. vulpinus and three related species possessing a tubular snout) and Siganus (all the other species), had no phylogenetic rationale. The present results indicate that the tubular snout, which apparently results from ecological specialization, is a recent acquisition within the deep-body clade. The Western Indian Ocean endemic S. sutor appeared as the sister-species of the Red Sea endemic S. rivulatus within a well-supported subclade that also included S. canaliculatus and S. fuscescens. S. spinus did not appear as sister-species to S. luridus. S. lineatus haplotypes formed a paraphyletic group with S. guttatus, and an early isolation of Maldives S. lineatus was suggested. Unexpectedly, S. randalli did not appear as the sister-species of S. vermiculatus, but its haplotypes instead were embedded within the West Pacific S. lineatus haplogroup, suggesting recent introgression. Among currently-recognized sister-species with parapatric distribution, S. doliatus and S. virgatus haplotypes formed a single, unresolved haplogroup, as did S. unimaculatus and S. vulpinus. The occurrence of two distinct clades within S. fuscescens was confirmed.

Introduction

Increasingly complex theories are being developed regarding the origin and evolution of marine species in the central Indo-West Pacific region, whose coral reef and lagoon habitats harbour the highest biological diversity of all seas [START_REF] Woodland | Zoogeography of the Siganidae : an interpretation of distribution and richness patterns[END_REF][START_REF] Palumbi | What can molecular genetics contribute to marine biogeography? An urchin's tale[END_REF][START_REF] Hughes | Biodiversity hotspots, centres of endemicity, and the conservation of coral reefs[END_REF][START_REF] Barber | Biodiversity hotspots: evolutionary origins of biodiversity in wrasses (Halichoeres: Labridae) in the Indo-Pacific and new world tropics[END_REF][START_REF] Briggs | Proximate sources of marine biodiversity[END_REF]. Molecular phylogenies provide the information against which hypotheses on the biogeography of species and scenarios of ecological specialization can be tested.

Rabbitfishes (Siganidae) are typical Indo-Pacific coral-reef fishes, that occupy all types of coastal habitats, from estuaries and mangroves to the reef front, the reef flat, and seaweed mats in the lagoon. Twenty eight nominal species are currently recognized in that family, based on morphology and colour patterns [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Randall | Siganus woodlandi, new species of rabbitfish (Siganidae) from New Caledonia[END_REF]. Fishes of the family Siganidae exhibit uniformity in those characters (i.e. numbers of fin spines and rays, tooth shape, tooth count) which the systematics of fishes usually rely on. The fact that a majority of fishes of the family have bright and unique colour patterns has been exploited for defining species boundaries, but higher-level classification essentially relies on gross body proportions, shape of tail, and length of snout [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]. The family Siganidae in its present description consists of a single genus, Siganus, which has been subdivided into sub-genera Siganus and Lo, the latter to distinguish those five species that possess a prominent, tubular snout [START_REF] De Beaufort | The fishes of the Indo-Australian archipelago[END_REF][START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Randall | Reef and shore fishes of the South Pacific[END_REF]. The other species have "pointed, blunt, or tumid snouts" [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]. Lo was originally erected as a genus by [START_REF] Seale | Fishes of the south Pacific[END_REF], but [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF] considered that the differences in snout shape between Lo and Siganus were not sufficiently clear-cut for being recognized as different genera, arguing that the pointed shape of the snout of S. corallinus approaches the condition of S. (Lo) uspi, whose snout is the shortest of all 5 Lo species. Presumed, closely related (sibling) species of Siganidae have essentially parapatric distributions. Nine such groups of sibling taxa have been recognized [START_REF] Woodland | An examination of the effect of ecological factors, especially competitive exclusion, on the distributions of species of an inshore, tropical, marine family of Indo-Pacific fishes (Siganidae)[END_REF], most of which share their common boundaries in the central Indo-West Pacific region. It has been argued that this phenomenon may result from habitat specialization together with competitive exclusion, and be a cause of higher species richness in an area where the diversity of habitats is greater than in other regions of the Indo-Pacific [START_REF] Woodland | Zoogeography of the Siganidae : an interpretation of distribution and richness patterns[END_REF]1999;[START_REF] Barber | Biodiversity hotspots: evolutionary origins of biodiversity in wrasses (Halichoeres: Labridae) in the Indo-Pacific and new world tropics[END_REF].

Only scarce genetic data are available concerning fishes of the family Siganidae. An allozyme study conducted on ten Siganus spp. species allowed phylogenetic inference based on allozyme distances [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF]. The authors provisionally concluded that a major dichotomy separated deep-bodied and shallow-bodied Siganus spp. They observed that the genetic distance between two sibling species with virtually parapatric distribution (S. randalli and S. vermiculatus) was of the same order as those estimated between geographic populations within a species (Fig. 1). Also, the subgenus Lo, represented by S. vulpinus, did not appear as a clade distinct from the other species. Instead, S. vulpinus paired with S. punctatus (Fig. 1), a result that was deemed "unpredicted" by [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF]. No test of robustness of the allozyme tree was, nor can be performed from the data that were then published, hence it is not clear how much reliable its topology was. These authors noticed that S. argenteus was the least divergent genetically from outgroup Naso lituratus (Acanthuridae), but the topology of the allozyme tree (Fig. 1) apparently contradicted this statement. Other, recent genetic surveys focused on the loss of genetic variation in S. luridus and S. rivulatus populations subsequent to their crossing of the Suez Canal [START_REF] Bonhomme | Lack of mitochondrial differentiation between Red Sea and Mediterranean populations of the Lessepsian rabbitfish, Siganus rivulatus (Perciformes: Siganidae)[END_REF][START_REF] Hassan | Lessepsian invasion without bottleneck: example of two rabbitfish species (Siganus rivulatus and Siganus luridus)[END_REF][START_REF] Azzurro | Genetics of the early stages of invasion of the Lessepsian rabbitfish Siganus luridus[END_REF], and on examining the barcoding potential of a short fragment of the cytochrome b gene, that was also used to estimate the degree of genetic differentiation between populations of eight Siganidae species at the scale of the West Pacific [START_REF] Lemer | Cytochrome b barcoding, molecular systematics, and geographic differentiation in rabbitfishes (Siganidae)[END_REF]. Further phylogenetic analysis is necessary to understand the evolution of morphology (i.e. body proportions and snout shape) and life-history (i.e. duration of the pelagic stage) in Siganidae. As these characters are of obvious ecological relevance, they may have been involved in speciation in Siganidae.

Here, we inferred the phylogeny of twenty Siganus species from the nucleotide sequences of a 825-bp composite fragment of the mitochondrial DNA, with the following objectives: to test the validity of the current taxonomy of Siganidae, based on [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF] extensive revision; to explore the patterns of lineage diversification in that family and eventually relate them to scenarios of ecological specialization; to address the genetic relationships between parapatrically distributed sibling species and to tentatively infer speciation processes.

Materials and methods

Siganidae species were separated by [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF] into "deep-bodied" and "fusiform" species. For the 20 species examined here, the range of variation of the ratio of standard length to body depth was the following: S. argenteus, 2.4-3.0; S. canaliculatus, 2.4-2.8; S. corallinus, 1.7-2.4; S. doliatus, 1.8-2.2; S. fuscescens, 2.3-2.9; S. gutattus, 1.8-2.3; S. javus, 2.0-2.3; S. lineatus, 1.9-2.2; S. luridus, 2.1-2.8; S. puellus, 2.3-2.6; S. punctatus, 1.9-2.3; S. randalli, 2.0-2.2; S. rivulatus, 2.6-3.2; S. spinus, 2.3-2.8; S. sutor, 2.2-2.6; S. unimaculatus, 2.1-2.4; S. vermiculatus, 1.9-2.2; S. virgatus, 1.8-2.3;S. vulpinus, 1.9-2.4;S. woodlandi, 2.1-2.4 [after Woodland (1990) except S. woodlandi: [START_REF] Randall | Siganus woodlandi, new species of rabbitfish (Siganidae) from New Caledonia[END_REF]]. S. puellus tends to show a ratio of standard length to body depth higher than the other deep-bodied species, but nevertheless cannot be considered fusiform, owing to its rather flat, rectangular shape. Some of these species (S. fuscescens, S. luridus, S. rivulatus, S. spinus, S. sutor), all fusiform, have a drab colour while the other species exhibit bright colours and/or contrasted colour patterns [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]. Most species of the reef front, all brightly coloured, are encountered as pairs (S. corallinus, S. doliatus, S. puellus, S. punctatus, S. vulpinus) while the other species usually occur as small schools [START_REF] Randall | Fishes of the Great Barrier Reef and Coral Sea[END_REF][START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Woodland | Siganidae, Rabbitfishes (spinefoots)[END_REF]. [START_REF] Randall | Siganus woodlandi, new species of rabbitfish (Siganidae) from New Caledonia[END_REF] report that S. woodlandi occurs in schools as does S. argenteus, partly based on a picture of a school of S. woodlandi by [START_REF] Fourmanoir | Poissons de Nouvelle-Calédonie et des Nouvelles-Hébrides[END_REF]. However, one of us (P. B.) has regularly observed pairs of adult S. woodlandi on various parts of the reef front around southern New Caledonia at 6-15 m depth. In only one instance did three pairs of S. woodlandi appear to forage together, forming an ephemeral, loose school of 6 individuals. S. argenteus is the only Siganidae known to spawn pelagic eggs and to possess an extended pelagic, prejuvenile stage that is analogous to the acronurus stage of Acanthuridae (which also have pelagic eggs) [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Leis | The larvae of Indo-Pacific coastal fishes: an identification guide to marine fish larvae[END_REF]. All other Siganidae species except, perhaps, S. woodlandi for which no life-history data are available, spawn benthic eggs [START_REF] Popper | Experiments on the propagation of Red Sea siganids and some notes on their reproduction in nature[END_REF][START_REF] Leis | Acanthuroidei : development and relationships[END_REF] or are believed to [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF], and lack a transitional pelagic stage [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Leis | The larvae of Indo-Pacific coastal fishes: an identification guide to marine fish larvae[END_REF]. Four pairs of sibling, parapatric species sensu [START_REF] Woodland | An examination of the effect of ecological factors, especially competitive exclusion, on the distributions of species of an inshore, tropical, marine family of Indo-Pacific fishes (Siganidae)[END_REF] were sampled for the present survey. These were S. doliatus / S. virgatus, S. guttatus / S. lineatus, S. luridus / S. spinus and S. unimaculatus / S. vulpinus.

Details on the individuals sampled (sampling location and date, voucher specimens) are in Table 1. DNA was extracted from ethanol-preserved fin clips or muscle fragments using either the standard phenol-chloroform extractions with Phase-Lock Gel TM tubes (Eppendorf, Le Pecq, France), or the DNeasy® kit (Qiagen GmbH, Hilden, Germany). Individual DNA extracts were subjected to PCR amplification of two partial mitochondrial genes: a 326-bp fragment of the cytochrome b gene, using a pair of degenerate primers (forward: 5'-TCMGAYATCGCCACAGCCTTCTC-3'; reverse: 5'-AGGAAGTGGAAKGCGAAGAA-3') designed from the alignment of the cytochrome b gene sequences of Siganidae available in GENBANK (accession nos. AY190542-AY190555), and an expected 575-bp fragment of the 16s rRNA gene, using the forward and reverse primers (respectively, 5'-CGCCTGTTTATCAAAAACAT-3' and 5'-CCGGTCTGAACTCAGATCACGT-3') of [START_REF] Clements | Rapid evolutionary divergences in reef fishes of the family Acanthuridae (Perciformes: Teleostei)[END_REF]. The amplification reactions were done in 96-well plates with each well containing 20 µL reaction mixture [2 µL template DNA, 2.5 mM MgCl 2 , 0.48 mM dNTP mix, 0.5 µM of each primer and 0.5 U Taq polymerase (Promega, Madison WI, U.S.A.)] in a Robocycler TM thermocycler (Stratagene, La Jolla CA, U.S.A.). The PCR program consisted of 3 min DNA-denaturation (at 94°C) followed by 35 cycles of 1 min denaturation (94°C) / 1 min annealing (60°C) / 1 min elongation (72°C). The PCR products were shipped to GATC Biotech (Konstanz, Germany), or Macrogen (Seoul, South Korea) for nucleotide sequencing and the sequences were subsequently retrieved from the company's Internet website. Nucleotide sequences were deposited in GENBANK (list in Table 1).

All nucleotide sequences were aligned using BIOEDIT [START_REF] Hall | BIOEDIT: a user friendly biological sequence alignment editor and analysis program for windows 95/98/NT[END_REF]. The phylogenetic relationships among species in the genus Siganus were inferred from the matrix combining cytochrome b and 16S rDNA sequence data using three different algorithms: neighbourjoining (NJ) [START_REF] Saitou | The neighbor-joining method: a new method for reconstructing phylogenetic trees[END_REF], maximum parsimony (MP) [START_REF] Fitch | Towards defining the course of evolution: minimum change for a specific tree topology[END_REF], and maximum likelihood (ML) [START_REF] Felsenstein | Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters[END_REF]. NJ and MP analyses were done using MEGA 3.1 [START_REF] Kumar | MEGA3: Integrated software for molecular evolutionary genetics analysis and sequence alignment[END_REF]. Gaps were treated as deletions in pairwise comparisons of sequences (option "Pairwise-Deletion" in MEGA 3.1). ML analysis was done using PHYML [START_REF] Guindon | A simple, fast and accurate algorithm to estimate large phylogenies by maximum likelihood[END_REF]. Three substitution models were considered for analysing the nucleotide differences between haplotypes: Jukes-Cantor [START_REF] Jukes | Evolution of protein molecules[END_REF], Kimura-2 parameter [START_REF] Kimura | A simple method for estimating evolutionary rate of base substitutions through comparative studies of nucleotide sequences[END_REF], and Tamura-Nei [START_REF] Tamura | Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees[END_REF]. The substitution model for NJ and ML analyses was chosen according to the likelihood approach implemented in MODELTEST [START_REF] Posada | MODELTEST: testing the model of DNA substitution[END_REF]Crandall, 1998), version 3.7 (2006); the best fit was provided by a Tamura-Nei model with Γ-distributed rates of substitution per site (α=0.5).

Results

Mitochondrial-DNA sequence data were obtained on a total of 825 base pairs (bp) contributed by a fragment of the cytochrome b gene (300 bp) and a fragment of the 16S rRNA gene (521-522 bp before alignment), for 164 individuals of 20 Siganidae and three Acanthuridae species (GENBANK accession nos. listed in Table 1). For the cytochrome b gene fragment, 115 nucleotide sites were variable across the whole dataset (19 first positions, 3 second positions, 93 third positions) resulting in 12 amino-acid substitutions. All 16S rDNA data were easily aligned with 6 single-nucleotide gaps, yielding 87 variable nucleotide sites. The NJ tree obtained from the matrix of pairwise nucleotide distances is presented in Fig. 2. MP analysis of the combined dataset yielded a set of 64 most parsimonious trees of 550 steps, whose topology at the supra-specific level was nearly identical to that of the NJ tree, as was that of the tree produced by ML analysis. The only differences concerned the position of the branch leading to S. javus relative to that leading to S. puellus, which was poorly resolved in NJ and unresolved with MP and ML analysis, and the position of the node separating S. vermiculatus from the S. guttatus / S. lineatus haplogroup. Percentages of occurrence of a node after bootstrap resampling are given for each NJ, MP, and ML analysis (Fig. 2).

The inner tree topology was characterized by three well-supported and deeply separated ingroup clades of similar lengths (I-III on Fig. 2). Clade I grouped all deep-bodied species, while Clade III grouped all species with fusiform body except S. argenteus. S. argenteus and S. woodlandi (whose ratio of standard length to body depth is intermediate between those of deep-bodied and fusiform species) formed Clade II. All species that live in pairs on the reef front, except S. woodlandi, were grouped in Clade I, but the latter also included species that live in small schools or pairs in turbid habitats such as mangroves, estuarine lakes and estuaries (S. guttatus, S. javus, S. lineatus, S. vermiculatus). All drab-coloured species, which also have tumid snout and form large schools, were grouped into Clade III.

S. luridus and S. spinus appeared to have diverged relatively early from each other (average nucleotide divergence estimate between haplotypes of the two species, ^d = 0.068) and did not appear as sister-clades (Fig. 2). S. rivulatus and S. sutor appeared to be sister-clades (with ^d = 0.020). S. lineatus haplotypes formed a paraphyletic cluster with S. guttatus. The paraphyly of S. lineatus haplotypes was caused by the external placement of the Maldives S. lineatus haplotype relative to the group formed by S. guttatus and those S. lineatus haplotypes that were sampled in Sulawesi and New Caledonia (i.e., across the West Pacific) (Fig. 2). S. guttatus and West Pacific S. lineatus appeared as very recently differentiated sister-clades (^d = 0.005). S. randalli haplotypes were embedded within the West Pacific S. lineatus haplogroup. S. doliatus haplotypes similarly formed a single, common haplogroup with S. virgatus, and so did S. unimaculatus with S. vulpinus. S. fuscescens haplotypes clustered into two distinct, although closely related haplogroups (^d = 0.009).

Discussion

The present results distinguished three major clades in Siganidae, which had not been identified earlier [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF][START_REF] Lemer | Cytochrome b barcoding, molecular systematics, and geographic differentiation in rabbitfishes (Siganidae)[END_REF]. The early separation between deep-bodied and fusiform species indicates that general body shape has a strong phylogenetic component in Siganidae. This separation however was not complete, as Clade II grouped both a fusiform species (S. argenteus) and a species with intermediate body depth (S. woodlandi). Nevertheless, the caudal fin in the two latter species is strongly forked, unlike in all the other Siganidae species. General body shape thus underwent early diversification in Siganidae and has since then been relatively stable. A similar situation has been described in emperor fishes, Lethrinus spp. (Lethrinidae) (Lo Galbo et al., 2003). This situation is not systematic among Teleosteans, where body proportions may also change rapidly, like in e.g. Naso spp. (Acanthuridae) [START_REF] Klanten | Patterns of lineage diversification in the genus Naso (Acanthuridae)[END_REF] and Cichlidae [START_REF] Kassam | Nuclear markers reveal that inter-lake cichlids' similar morphologies do not reflect similar genealogy[END_REF]. The distinction of two basic morphological types in Siganidae is clearly correlated with distinct life-styles. A proportion of the deep-bodied species occur in pairs close to the hard-coral substratum on the reef front, where they can sneak into crevices for feeding and for seeking protection from predators. This in turn favours territoriality and, perhaps, pairing behaviour. Fusiform species conversely occur on reef flats and algal flats and rely on schooling behaviour and swimming speed for escaping predators. Correlatively, the colour of the fusiform species is drab (an advantage in open habitats also frequented by predators), while that of the species of the reef front is usually bright and contrasted (e.g. [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Randall | Reef and shore fishes of the South Pacific[END_REF].

S. argenteus [also a schooling, fusiform species; [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]] was placed together with S. woodlandi in a distinct clade that appeared to coalesce simultaneously with the two others. This early trichotomy may reflect the true phylogeny, or conceal two successive dichotomies that the present sequence data were not sufficient to resolve. Given that S. argenteus possesses the prejuvenile, pelagic stage that is also present in Acanthuridae, parsimonious reasoning leads to considering the prejuvenile stage as ancestral in Siganidae, in which case the prejuvenile stage would have been lost once, or twice (depending on whether the actual basic divergence was a succession of two dichotomies, or a trichotomy), early in the history of the family. Life-history data for S. woodlandi, which are presently lacking, are desirable for a better understanding of the evolution of the prejuvenile stage in Siganidae.

The present results do not support the phylogenetic separation of Siganidae species with tubular snout, heretofore grouped under subgenus Lo [START_REF] Seale | Fishes of the south Pacific[END_REF], versus the other species (subgenus Siganus), thus confirming [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF] preliminary conclusions from allozymes. S. (Lo) unimaculatus and S. (Lo) vulpinus branched within a subclade of Clade I, as sister-species to S. puellus and S. punctatus, both with slightly elongate snout and placed under subgenus Siganus. We hypothesize that the mechanism for the apparition of the tubular snout of S. unimaculatus, S. vulpinus and related species (namely, S. magnificus, S. niger and S. uspi) is ecological specialization, as a longer snout allows easier access to pockets of algae growing at the dead basis of hard-coral colonies [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]. Albeit moderate compared to S. unimaculatus and S. vulpinus, an elongate snout independently evolved in S. corallinus (Fig. 2), which is another deep-bodied species typical of the coral-reef front habitat. Therefore, the elongate / tubular snout appears to be a specialized state that arose in deepbodied species dwelling on the coral reef.

Quoting [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF], "S. sutor is very similar in proportions to S. canaliculatus and S. fuscescens", but only "field observations of the colours of live fish indicate that it is distinct". According to the present results, S. sutor actually appears as the sister-species of S. rivulatus. Those two species form a subclade within a strongly supported monophyletic group that also comprises S. canaliculatus and S. fuscescens. Both S. canaliculatus and S. fuscescens have an Indo-Pacific distribution, but both are geographically isolated from S. sutor and S. rivulatus [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]. S. sutor is endemic to the western Indian Ocean while until recently the distribution of S. rivulatus was confined to the Red Sea [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]. Therefore, it is sensible to assume that the two latter species arose by allopatric speciation, and that they are an offshoot of an ancestral S. canaliculatus / S. fuscescens form from which their ancestor was geographically isolated.

We examined another pair of presumed sibling species within Clade III, namely S. luridus / S. spinus. [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]1999) rationale for placing S. luridus and S. spinus as sibling species was their similar ratio of total length to body depth, the similar size and stoutness of their fin spines, and their parapatric distribution. The topology of the mitochondrial tree (present results) however does not support the sibling-species hypothesis. The genetic divergence patterns reported here and above thus highlighted the limitations of general morphology for accurately assessing evolutionary relationships at the immediate supraspecific level, at least in fusiform, drab species.

Among the other currently-recognized sister-species with parapatric distribution, S. doliatus and S. virgatus haplotypes formed a single, unresolved haplogroup, as did S. unimaculatus and S. vulpinus. Since S. doliatus and S. virgatus are believed to hybridize in their zone of contact in the Indo-Malay region [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF][START_REF] Randall | Reef and shore fishes of the South Pacific[END_REF], it is possible that the latter harbours S. doliatus mitochondria as a result of introgression. In that case, further sampling of S. virgatus would be necessary, ideally outside the zone of overlap to sample 'true' S. virgatus mitochondria. Alternatively, the divergence between the two species may be recent, to the point that the sorting of their mitochondrial lineages is still not perceptible. The same rationale applies to the pair S. unimaculatus / S. vulpinus.

In cases where several haplotypes were sampled in a species, they clustered as distinct haplogroups and intraspecific nucleotide distances were at least about one order of magnitude lower than the distances separating two nominal species, thus validating [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF] taxonomy at the species level. Apart from the two pairs of sibling species discussed in the above paragraph, there was one noticeable exception to this general pattern, which concerned the ensemble formed by S. lineatus, S. guttatus and S. randalli haplotypes. Although restricted to a single haplotype, the Maldives sample of S. lineatus appears as clearly distinct from all five other S. lineatus haplotypes, sampled across the West Pacific. Moreover, the Maldives S. lineatus haplotype branches externally to the clade formed by S. guttatus and West-Pacific S. lineatus. Considering both the geographic distribution and the patterns of genetic differentiation observed in the S. guttatus / S. lineatus species complex, a two-step scenario of genetic differentiation may be proposed, with a first event of allopatric differentiation separating a Maldives population from a stock ancestral to both S. guttatus and West-Pacific S. lineatus and a subsequent, second event of allopatric differentiation between the two latter. S. guttatus and West Pacific S. lineatus subsequently underwent secondary contact in the Indo-Malay region. Both the pattern of reciprocal monophyly here observed between the two latter entities and the maintaining of two distinct ornamentation types (spotted: S. guttatus; lineate: S. lineatus) on either side of a narrow zone of contact in the Indo-Malay archipelago [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF]) despite possible hybridization [START_REF] Lemer | Cytochrome b barcoding, molecular systematics, and geographic differentiation in rabbitfishes (Siganidae)[END_REF] confirm they have reached the status of biological species. The present results, if confirmed by a larger sample of haplotypes, therefore may challenge the current placement of Maldives S. lineatus as conspecific with West Pacific S. lineatus. Alternatively, the paraphyly of S. lineatus may be only apparent, with West-Pacific S. lineatus having been recently introgressed by S. guttatus mitochondria while the genomic integrity of Maldives S. lineatus was preserved because of its geographical isolation. An indirect way of addressing that question is now to study the population genetics of the S. guttatus / S. lineatus contact zone, using nuclear-DNA markers.

Both morphology and colour patterns [START_REF] Woodland | Revision of the fish family Siganidae with description of two new species and comments on distribution and biology[END_REF], and allozymes [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF]; Fig. 1) indicate a close relationship of S. randalli with S. vermiculatus. Unexpectedly, S. randalli haplotypes did not form a sister-clade to those of S. vermiculatus, but instead were embedded within the West-Pacific S. lineatus haplogroup, suggesting recent introgression of S. randalli by S. lineatus mitochondria. Although the allozyme study of [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF] unfortunately did not include S. lineatus samples, the genetic distance between its close relative S. gutattus and S. vermiculatus was nearly one order of magnitude larger than the distance between S. randalli and S. vermiculatus.

Another point deserving further attention is the confirmation of two distinct subclades within S. fuscescens. This was earlier hinted by [START_REF] Lemer | Cytochrome b barcoding, molecular systematics, and geographic differentiation in rabbitfishes (Siganidae)[END_REF], based on a much shorter mtDNA fragment and on smaller sample sizes. Here, one subclade appeared to be geographically widely distributed, from the Riau archipelago to New Caledonia, while despite substantial sampling effort the other subclade seemed to be restricted to the South-West Pacific, with haplotypes sampled exclusively in the Solomon Islands and New Caledonia. This phylogeographic pattern may correspond to a former history of allopatric differentiation followed by secondary contact, or, perhaps, to introgression from a yet undescribed, cryptic species within the current taxon S. fuscescens. Our suspicion that S. fuscescens might consist of two reproductively isolated forms is reinforced by [START_REF] Woodland | An examination of the effect of ecological factors, especially competitive exclusion, on the distributions of species of an inshore, tropical, marine family of Indo-Pacific fishes (Siganidae)[END_REF] sibylline notice that "further study since the publication of [his 1990] revision suggests that cryptic species may need to be dissected out of Siganus fuscescens". The use of nuclear markers [e.g. lengthpolymorphic introns; [START_REF] Hassan | Seventeen new exon-primed intron-crossing polymerase chain reaction amplifiable introns in fish[END_REF]] to test the null hypothesis of panmixia in populations harbouring the two mitochondrial types is warranted. 1: Kumar et al. (2004)] built from pairwise Rogers' genetic distances estimated from allelomorph frequencies at 14 enzyme loci [Table 2 of [START_REF] Lacson | Genetic distances among fishes of the genus Siganus (Siganidae) from the western Pacific ocean[END_REF]]. Naso lituratus (Acanthuridae) chosen as outgroup [see [START_REF] Tang | The phylogenetic relationships of the suborder Acanthuroidei (Teleostei: Perciformes) based on molecular and morphological evidence[END_REF] for a justification]. Scale bar: 10% Rogers' genetic distance.

Fig. 2 .

 2 Fig. 2. Siganus spp haplotypes (Acanthurus blochii , A. triostegus and Naso unicornis haplotypes as outgroup). Neighbour-joining (NJ) phylogeny obtained from the combined nucleotide sequence data set of cytochrome b (300 bp) and 16s rRNA (525 bp) gene fragments. Nucleotide distances estimated according to a Tamura-Nei model with Γ-distributed rates of substitution [MEGA 3.1: Kumar et al. (2004)]. Bootstrap resampling scores >50% given as % left to a node [bold: NJ, 1000 resamplings; italics: maximum parsimony (MEGA 3.1), 1000 resamplings; regular: maximum likelihood (PHYML: Guindon and Gascuel [2003]), 100 resamplings]. Geographic origin of samples: Syria (x); Mascarene archipelago (+); Addu atoll, Maldives (□); Riau archipelago (Δ); Sulu Sea ( ); Makassar strait, Sulawesi (▲); Truk, Caroline Islands (■); Bismarck and Louisiades archipelagoes ( ); Solomon Islands ( ); New Caledonia (•); Ouvéa, Loyalty Islands (○); Moorea, Society Islands ( ). Behaviour: S, schooling; P, pairing; (references in section 2.). Scale bar: 2% nucleotide distance.

Table 1

 1 Samples of Acanthuridae and Siganidae analysed for the present survey. IRDN : Institut de recherche pour le développement, Nouméa; MNHN: Museum national d'histoire naturelle, Paris; BPBM: Bernice Pauahi Bishop museum, Honolulu. Siganus spp. Neighbour-joining tree [MEGA 3.

	Species, Sampling location	Sampling date	Voucher specimens	GENBANK accession nos. Cytochrome b 16S rRNA
	ACANTHURIDAE
	Acanthurus blochii
	Southern lagoon, New Caledonia Apr. 2006	IRDN Ablo1, 2 a	DQ898027	DQ898095, 096
	A. triostegus
	Moruroa, Gambier archipelago	Jul. 2006	MNHN 2007-0003	EF210172	EF210160
	Naso unicornis
	Southern lagoon, New Caledonia Nov. 2006	-	EF210173	EF210162
	SIGANIDAE
	Siganus argenteus
	Rodrigues I.	Aug. 2006	-	DQ898028; EF210174	DQ898097; EF210163
	Truk, Caroline Is.	Apr. 2006	-	DQ898035	DQ898097
	Honiara, Solomon Is.	Aug. 2006	-	DQ898030, 031	DQ898097
	Southern lagoon, New Caledonia Feb. 2005-Mar. 2006 IRDN Sarg 5-8 a ; MNHN 2006-1525	DQ898028, 030, 035, 036	DQ898097
	Ouvea lagoon, Loyalty Is.	Feb. 2006	-	DQ898036	DQ898098
	S. canaliculatus
	Riau archipelago	Nov. 2006	MNHN 2007-0005	EF210175	EF210164
	Honiara, Solomon Is.	Aug. 2006	-	EF210176	EF210165
	S. corallinus
	Manus I., Bismarck archipelago	Aug. 2006	-	DQ898037	DQ898105
	Honiara, Solomon Is.	Aug. 2006	-	DQ898037, EF210177	DQ898105
	Southern lagoon, New Caledonia Feb.-July 2005	MNHN 2006-1526; MNHN 2007-0006 DQ898037	DQ898105
	S. doliatus
	Truk, Caroline Is.	Apr. 2006	-	DQ898038	DQ898106
	Southern lagoon, New Caledonia Feb. 2005-Apr. 2006 IRDN Sdol 2-4 a ; MNHN 2006-1527; MNHN 2007-0007, 0008	DQ898038, 039	DQ898106, 107
	S. fuscescens
	Riau archipelago Misima I., Louisiades archipelago Nov. 2006 Nov. 2006 Honiara, Solomon Is. Aug. 2006	IRDN Scff 2-5 a ; MNHN 2007-0009 --	EF210179-181 EF210182-184 DQ898040-042, EF210178	DQ898099; EF210166 DQ898100; EF210167, 168 DQ898099, 100
	Southern lagoon, New Caledonia June 2005-Feb. 2006 MNHN 2006-1528, 1529, 1530	DQ898040-045	DQ898099-104
	S. guttatus
	Makassar, Sulawesi I.	Sep. 2005	-	DQ898047, 049, 050 DQ898108
	S. javus
	Makassar, Sulawesi I.	Sep. 2005	-	DQ898052-054	DQ898109
	S. lineatus
	Addu atoll, Maldives archipelago	Aug. 2005	BPBM 40390	DQ898062	DQ898108
	Makassar, Sulawesi I.	Sep. 2005	-	DQ898055, 059-061 DQ898108
	Honiara, Solomon Is.	Aug. 2006	-	DQ898059	DQ898108
	New Caledonia	Apr. 2002-Mar. 2006 IRDN Slin 0, 2 a ; MNHN 2006-1531	DQ898055, 059-061 DQ898108
	S. luridus
	Lattaqiah, Syria	2002	-	DQ898056-058	DQ898110, 111
	Reunion I.	May. 2006	-	EF210185, 186	DQ898110
	S. puellus
	Southern lagoon, New Caledonia Feb.-July 2005	IRDN Spue 2-4 a ; MNHN 2006-1532 DQ898063	DQ898112
	Truk, Caroline Is.	Apr. 2006	-	DQ898063	DQ898112

Acknowledgements

Funded by IRD-UR 128, Dimar, ZoNéCo, and Fonds Pacifique pour le développement (French Government). The following people contributed fish specimens or tissue samples: R.C. Anderson, P. Boblin, L. Carassou, A. Collet, E. Hardman, M. Hassan, J.-L. Justine, J. Kwik, D. Lecchini, M. Leopold, the Li-Khau family, M. Low, C. Mellin, G. Mou Tham, D. Neo, J.E. Randall, E. Tardy, E. Tessier, L. Vigliola, and P. Villard. C. Rocher offered technical assistance at the early stages of this work. Helpful comments on earlier versions of this manuscript were made by J.-D. Durand, J.E. Randall, and two anonymous reviewers. The hypothesis of a distinct Maldives S. lineatus population was first pointed out by R.C. Anderson and J.E. Randall in e-mails to P.B.

0.02


Abhijit Sarkar

Laurent Blondé

Patrick Le Callet

Florent Autrusseau

Jürgen Stauder

Patrick Morvan

How

How Modern Displays Push Conventional Colorimetry to its Limit

come

x-lambda-bar, y-lambda-bar etc) are integrated over a range of wavelengths (λ). Mathematically, the integration is done by multiplication followed by summation, as shown in Eq. (1) The result is then normalized by a factor k, so as to assign the luminance (given by Y) of white an arbitrary value of 100. More details on the fundamentals of colorimetry are available in [START_REF] Berns | Billmeyer and Saltzman's principles of color technology[END_REF].

(

) 1
The above equation is the basis of all colorimetric computations in basic and applied colorimetry.

Practically, all mathematical representations of color in applied colorimetry originate from this equation. The Very recently, studios have started offering remote color grading services, which means multiple devices being used by various professionals at multiple locations for color grading, a trend that is sure to make the issue of observer variability even more pertinent in the media and entertainment industry. Thus, it is of interest to study the effect of observer variability in color matching across conventional and modern displays, and to acquire experimental data in such a context, which can be subsequently used to better model the observer variability, and to find solutions to the associated problems.

                               y S k z R S k Z y R S k Y x R S k

A COLOR MATCHING EXPERIMENT:

A preliminary set of color matching experiments [START_REF] Sarkar | A color matching experiment using two displays: design considerations and pilot test results[END_REF] were performed on a modern, wide-gamut LCD (Liquid Crystal Display) with narrow-band primaries, and a conventional studio CRT with broadband primaries. Because of the significant difference in the spectral characteristics of the CRT and the LCD, color matches were expected to vary significantly from one observer to the other.

1 1 1

 1 How Modern Displays Push Conventional Colorimetry to its LimitAbhijitSarkar 1,2 , Laurent Blondé 1 , Patrick Le Callet 2 , Florent Autrusseau 2 , Jürgen Stauder 1 , Patrick Morvan Technicolor Research, Rennes, France, 2 IRCCyN-IVC, Polytech' Nantes, University of Nantes, France ABSTRACT: Various recent studies have shown that variations in observers' color vision characteristics can be a significant issue in modern display colorimetry, since peaky color primaries (commonly red, green and blue) are often used to achieve more vivid and saturated colors. This paper presents an overview of this problem in the context of media and entertainment industry applications. The significance of the effect of observer variability is demonstrated through recent experimental results. 1. INTRODUCTION: Color is defined as the perception that depends on the response of the human visual system to light and the interaction of light with objects. Thus, the perception of color requires three components, a light source, an object and an observer. The most commonly used mathematical way of describing color is through the CIE tristimulus values, X, Y and Z. To compute these values, contributions of relative spectral power of a CIE standard light source (Sλ), the reflectance factor of the object (Rλ), and the spectral sensitivities of color sensors (called color matching functions) of an average, standard observer (  x ,  y and  z , read as

  matching functions (CMFs) represent average color matching functions of a given group of observers, measured through visual experiments. Two sets of standard observer CMFs are commonly used in conventional colorimetry, CIE 1931 standard observer functions for 2° visual field, and CIE 1964 standard observer functions for 10° visual field. It is assumed that the standard observer represents the average of the whole population of color normal observers. However, for various physiological reasons [2], color vision characteristics of any real observer can be significantly different from the standard observer functions, which can result in misrepresentation of the color perception of a real observer. The difference between the CMFs of a standard observer and those of a real observer gives rise to another important and fundamental issue, as described next. 2. OBSERVER VARIABILITY AND OBSERVER METAMERISM: When two color stimuli produce the same visual response, a visual match is obtained, where XYZ values corresponding to two stimuli are identical. Since XYZ values are computed by wavelength-wise integration, two stimuli with very different spectral power distribution can give rise to identical cone response for a given observer, leading to a "metameric" color match that is obtained by using a combination of a specific illuminant and a specific standard observer. Such a match established by one observer can, and quite often does, lead to a mismatch for a different observer, as the second observer has a different set of CMFs than the former.This phenomenon is commonly termed as observer metamerism.The relevance of this issue is obviously quite dependent on the application context. When a display color is compared with its printed version on paper, the significance of observer variability is questionable [3]. However, the topic of observer metamerism has sparked renewed interest in the recent years with the proliferation of wide color-gamut displays. Whether based on LED (Light Emitting Diode) or employing laser primaries, all these displays compete with each other in achieving more vivid, more saturated and brighter colors. On the flipside, these displays are particularly susceptible to observer variability [4][5], since their narrow-band (i.e. peaky spectral characteristics) primaries cause noticeable shift in chromaticities of perceived colors with relatively minor change in the visual characteristics of the observer. In a theoretical analysis by the present authors [6], it was found that the CIE 10° standard observer functions, as well as the average observer functions from a recent physiological model (proposed by CIE in 2006 [2]), do not accurately predict real observers' CMFs averaged within various age-groups. Because of this prediction error, colors on a narrow-band, widegamut display and a broad-band (smooth spectral characteristics) CRT display (Cathode Ray Tube), which are supposed to be matches based on real observer data and actual display spectral characteristics, were predicted to have significant colorimetric differences. The experimental data used in the study came from the most comprehensive color matching experiments till date, performed by Stilesand Burch in 1959[START_REF] Stiles | colourmatching investigation: final report[END_REF], on which the CIE 10° standard observer is based. This analysis showed that when it comes to modern displays, the issue of observer variability can cause conventional colorimetry to fail.The extent of this failure will depend on the spectral characteristics of the display, the specific colors that are being reproduced on the display, as well as on the CMFs of the observer viewing the display. Similar failure of CIE colorimetry has been observed when narrow band RGB-LEDs were matched with broadband lights[START_REF] Csuti | Colour matching experiments with RGB-LEDs[END_REF]. Now, the question is: when is this failure inconsequential, and when it is serious enough to necessitate a solution? 3. ENTERTAINMENT INDUSTRY APPLICATIONS WHERE OBSERVER VARIABILITY CAN BE A SERIOUS PROBLEM: Observer variability and metamerism can be a nontrivial issue in critical color matching tasks, for example in post-production applications. Suppose, for example, the color adjustment process (called color grading) of the raw movie content at the post-shooting stage. The Colorist has to work with the Director of Photography (DP) to adjust the colors in the original content so as to achieve color coherence and homogeneity throughout various scenes, while maintaining the artistic expressions originally envisioned by the Film Director and the DP. Further, the film may have to be converted to a version suitable for television or DVD (a process known as digital mastering). Processes like color grading and digital mastering are color critical, requiring high-fidelity color reproduction, often involving displays. Even though film studios have principally relied upon reference CRTs with broadband primaries, a rapid market adoption of widegamut, high-definition displays and projectors and gradual discontinuation of manufacturer support on CRTs may soon require the studios to employ these modern displays for post-production operations. However, if the Colorist and the DP have different color vision characteristics, they will perceive colors differently, and the colors that look similar to one will look perceptibly different to the other. Conventional colorimetry will fail to account for this difference.

Figure 1 .

 1 Fig 2 plots the perceptual color differences between the two displays after each of the ten observers obtained a color match. There are nine colors shown along the x-axis. The color differences along the yaxis are represented in the form of bars, grouped by the ten observers. The color differences are calculated using 10° standard observer and an advanced color difference formula denoted by ∆E*00 (read as delta E 2000). In other words, if colorimetry worked perfectly in spite of observer variability, all these color differences would have been zero. In a carefully controlled experimental setup where uniform color stimuli are matched, more than 1 unit of ∆E*00 color difference can be visually perceived by majority of experienced observers. In our experiments, the mean and maximum values of the standard observerpredicted color difference of individual observer color matches were 1.4 and 3.3 ∆E*00 respectively. Thus, on an average, colorimetry predicted that the colors


TRANSPORTATION'ROLE IN THE SUPPLIER SELETION DECISION

A AGUEZZOUL, P. LADET Automatic Laboratory of Grenoble ENSIEG -INPG, Rue de la Houille Blanche, BP 46 38402, Saint Martin d'Heres Cedex-France Phone : (+33) 04.76.82.73.13,Fax : (+33) 04.76.82.63.88,Email : (Aicha.Aguezzoul, Pierre.Ladet@inpg.fr) Abstract -A review of literature on the supplier selection problem show that very few studies highlight explicitly, the weight of the transportation policy in this selection. In this paper, we propose a mixed nonlinear programming model which determine, for a product, the number of suppliers to choose, the quantity to be ordered to each one and the impact of transportation in suppliers, transit and buyer inventories. An evaluation of the model is presented under various scenarios.

I. INTRODUCTION

In the current competitive environment, it is extremely difficult to successfully produce high quality, low cost product without collaborating and narrowly with a network of effective and reliable suppliers. The supplier selection process becomes strategic because, on the one hand, the costs of raw materials and finished components are very significant and can go from 50% to 80% of total product cost [WEB,91] and on the other hand, because this process imp lies decisions which directly affect the total performance of an organization.

A review of literature on the supplier selection problem shows that many studies are focused in the determination of supplier selection criteria and methods to evaluate their performance. However, very few contributions highlight, in an explicit way, the role that the transportation policy can play in this selection. This is a great limitation because transportation cost represent up to 50% of total logistic cost [THO, 96], [STA, 00], which is extremely heavy for the buyer. Additionally, transportation and inventory elements (of the supplier, in transit, of the buyer) are highly interrelated and contribute most to the total cost of logistics : costs incurred in the suppliers while the products await to be shipped, costs represented by the products in transit, storage costs at the recipient. In this article, we propose a supplier selection model which taking account of transportation. We expose our approach while presenting in a f irst part, a review of literature on the supplier selection problem. In the second part, we present our model before drawing some conclusions and prospects.

II. REVIEW OF LITERATURE

The first writings on supplier selection problem are those of Dickson [DIC,66] which, starting from an investigation carried out near 274 reponsables of the purchasing department in Canada and USA, could identify 23 criteria used by the companies in the Sixties to select their suppliers. This study also indicates that the supplier selection process is multi-criterion. [START_REF] Weber | Vendor selection criteria and methods[END_REF] confirm this result by showing, starting from an analysis of 74 articles on the supplier selection problem, that the work of Dickson is in reference in the majority of them. On the other hand, the change of the industrial context and the introduction of the Just-In-Time concept modified relative importance of each criterion. The same authors also showed that the quantitative approaches of supplier evaluation may be grouped into three categories which are : linear weighting models, mathematical programming models and the statistical/probabilistic approaches. Ten years later, other techniques appeared in the literature. We can mention : data envelopment analysis [WEB, 96], [LIU, 00], goal programming [WEB, 00], interpretive structural modeling [MON, 94], expert system [VOK, 96], etc. In these various approaches, transportation cost is only considered implicitly in total product cost. To evaluate this cost, a review of literature indicates that there are several modeling [BUR,85], [GAN,99], [MAR,01]; each allows to reflect the economies of scale that the company can carry out while transporting of larger loads.

In the continuation of this article, we propose a model which treat, in an explicit way, the transportation's role in the supplier selection decision.

III. PROPOSED MODEL

We are interested in transportation between the suppliers and the buyer central warehouse. Transportation between buyer central warehouse and its warehouses/workshops does not return within the framework of our problem.. The buyer company must make a choice among several suppliers, on the basis of criterion which takes into account transportation, namely : total product cost and lead time. The objective is t o minimize the total cost including purchasing, ordering, transportation and storage costs. The lead time is formulated as a constraint.

To evaluate the transportation cost, we retain the modeling suggested by Martel [MAR,01], which consists in finding a linear approximation of this cost by regression between an origin and a given destination.

As for the storage cost, we consider that it is composed of three costs:

the cost incurred in each supplier while the product await de be sipped, -the cost incurred during the transit, -the cost incurred in the buyer central warehouse.

The most important constraints of the problem are : -for each supplier : lead time required and production capacity, -for the buyer : lead time imposed and period demand, -for transportation : capacity and means of transport.

Moreover, the following assumptions are considered : -each vehicle is affected to each supplier, -a vehicle has the same mean transit time between a supplier and buyer, -the periodic demand is known and constant.

Our model takes the form of a mixed non-linear program. Two types of decision variables are employed : the binary variables which correspond to the supplier selection and the variables which correspond to the percentages of total lot size to be shipped to each supplier by a means of transport given. An evaluation of this model is presented under various scenarios.

IV. CONCLUSIONS

A review of the literature on the supplier selection problem allows us to note that very little studies was interested in the transportation' role in this selection. We proposed a model which contributes to a step of assistance to the suppliers choice and for a product, to determiner the number of suppliers to be retained, the quantity to be ordered to each one and the impact of transportation in suppliers, transit and buyer storage.

Work remaining to be made relates to the model validation and its application on real cases.


Aicha Aguezzoul
email: aicha.aguezzoul@inpg.fr

Pierre Ladet
email: pierre.ladet@inpg.fr

A multiobjective approach to vendor selection taking into account transportation

Keywords: Multiobjective programming, Supplier selection, Transportation, Inventory

The analysis of the most researches related to the supplier selection shows that very little attention is given to transportation although its cost may be significant important to this selection. In this paper, we present a multiobjective approach of selecting suppliers and allocating the order quantity among them, taking into account transportation. The objectives to minimize in the model are the total cost and the lead-time. The total cost is the sum of transportation, inventory and ordering costs. The constraints related to suppliers, buyer and transportation are also considered in the model. The model is implemented in Matlab, software specialized in optimization. An evaluation of the model is presented under various scenarios.

INTRODUCTION

In today's increasing competitive business world, the suppliers selection and evaluation is one of the most critical activities of a company and a strategic purchasing decision that commit signifiant ressources (40% to 80% of total product cost) and impact the total performance of the firm. The studies in that field show that this decision is a complex process involving various criteria such as procurement cost, product quality, delivery performance, etc. These criteria may vary depending on the type of product considered and are often in conflict with one another. For example, low prices can be offset by poor quality or delivery reliability. Therefore, the supplier selection is an inherently multiobjective decision. In 1966, Dickson has identified at least 23 criteria in his empirical study in various vendor selection problems. Moreover, a review of 74 articles by [START_REF] Weber | Vendor selection criteria and methods[END_REF] obtained similar results and also showed that several approaches have been suggested to take into account the multiobjective nature of the decision problem. These approaches may be grouped into three categories, which are: linear weighting models, mathematical programming models and statistical/probabilistic approaches. However, that study identified very few articles that have proposed mathematical programming techniques to analyze supplier selection decision. Over the past few years, other techniques are suggested in the literature. We can mention: interpretive structural modeling [START_REF] Mondal | Vendor selection using Interpretive Structural modeling (ISM)[END_REF], expert system [START_REF] Vokurka | A prototype expert system for the evaluation and selection of potential suppliers[END_REF], data envelopment analysis [START_REF] Weber | A data envelopment analysis approach to measuring vendor performance[END_REF][START_REF] Liu | Using data envelopment analysis to compare suppliers for supplier selection and performance improvement[END_REF], multiobjective programming [START_REF] Weber | An optimization approach to determining the number of vendors to employ[END_REF], etc. Other models have been examined by [START_REF] Youssef | Supplier selection in an advanced manufacturing technology environment: an optimization model[END_REF]. However, the transportation aspect is not considered explicitly in these techniques. This is a great limitation because splitting orders across multiple suppliers will lead to smaller transportation quantities which will likely imply larger transportation cost. Moreover, transportation and inventory elements are highly interrelated and contribute most to the total logistics costs: costs incurred in the suppliers while the products wait to be shipped, costs represented by the products in transit and costs incurred in the buyer while the products wait to be used. Finally, transportation has a direct impact on the lead-time, which affects the firm's total cycle time.

The most important articles that have addressed the problem of multi-sourcing, in particular dual sourcing and transportation are described bellow: [START_REF] Hong | Just-In-Time purchasing: Single or multiple sourcing[END_REF] have discussed reducing lot size in the JIT purchasing environment with multiple vendors. A nonlinear programming problem is formulated and the objective function is to minimize the aggregate ordering and holding costs under delivered cost and quality constraints. Transportation cost is not formulated explicitly in the model. For multiple sourcing, the model gives the optimal selection of suppliers and the size of the split orders whereas, for the single sourcing, it determines the optimal number of deliveries. [START_REF] Ganeshan | Dual sourced supply chains the discount supplier option[END_REF] examine the dynamics of a supply chain that has the option of using two suppliers: one reliable and other unreliable. The unreliable supplier is characterized with long lead-time. Although the use of that supplier might warrant higher inventory and transportation costs, it's attractive to the firm because he is willing to provide a discount on the purchase price.

In that study, the authors present a model, which minimize the sum of purchasing, ordering, holding and transportation costs. Holding cost includes cycle-stock, in-transit stock and safety stock carrying costs. The expected shortage per replenishment cycle is the only constraint of the model. A simple heuristic in used to determine the level of discount that needs to be offered and the portion of the order that should be placed with secondary supplier More recently, [START_REF] Tyworth | Transportation' role in the sole-versus dual sourcing decision[END_REF] investigate the role of transportation in the sole versus dual sourcing decision. They present a model, which minimize the sum of purchasing, ordering, storage and transportation costs. No constraints are defined in the model. They demonstrated that dual supplier sourcing could yield savings under some conditions on supplier price, annual demand, lead-time performance and line-haul distance.

In these various researchs, stocks in all the transportation network (suppliers, transit, buyer) are not clarified and the constraints related to transportation policy are not considered. The contribution of our paper is the integration of all these elements in the multi-objective programming (MOP) approach that we propose. The MOP model was first introduced by weber and Ellram (1993) as a technique for selecting vendors in procurement environment characterised by multiple conflicting criteria. In our case, the objectives to minimize in the model are total cost and lead-time criteria under suppliers, buyer and transportation constraints. Total cost includes transportation, ordering and inventory costs. Total purchasing cost is not considered here and we suppose that the product, which is purchased over a given horizon of time, has the same unit price from all the suppliers. The model simultaneously determines the optimal number of suppliers to employ and the order quantities to allocate to them, taking into account the transportation. The model is validated using a numerical example. This paper is structured as follows. In the next section, we present the mathematical form of our model. In section 3, we give a solution methodology of the multiobjective model. Section 4 reports the results of computational experiments made using MATLAB, software specialized in optimization, to solve the model. The final section contains concluding remarks.

MODEL FORMULATION

The buyer must make a choice of a set of n potential suppliers, on the basis of criterion, which take into account transportation, namely total product cost and lead-time. The objectives to minimize simultaneously in the model are these two criteria. Total cost includes ordering, transportation and storage costs subject to lead-time and capacity of each supplier; lead-time imposed by the buyer and transportation mode used constraints. Moreover, we assume that the demand of the buyer is known and constant and that the transportation capacity is unlimited.

Let's define the following variables and formulas: n = number of suppliers D = unit time demand of buyer Q = ordered quantity to all suppliers in each period Q i : ordered quantity to i th supplier in each period A i =ordering cost per order, of i th supplier P i = purchase price of i th supplier C i = production capacity of i th supplier l i =lead-time required by i th supplier T i = average transit time from i th supplier to buyer L = lead-time imposed by the buyer r = holding rate of the buyer r i = holding rate of i th supplier rt i = in-transit holding rate of i th supplier Cf i = fixed shipping cost of i th supplier Cv i = variable shipping cost of i th supplier Decision variables:

X i = fraction of Q allocated to i th supplier Y i = 1 if X i >1 (i th supplier is selected) 0 if X i =0
In addition, D/Q is the number of periods during the time considered.

The total cost (TC) can be written as:

] ) )( 2 / ( ( ) / ( ) )( 1 / [( i i i i i i i i i i i i X r r D Q rt T P DX Y A Q D Cv QX Y Cf n i Q D TC + + + + + ∑ = =
The first term in this expression is the total transportation cost. We use the modeling (Cf/Q + Cv) suggested by [START_REF] Hall | Dependence between shipment size and mode in freight transportation[END_REF]. The fixed shipping cost Cf is independent of a load and includes cost of stop and cost per unit distance. The variable shipping cost Cv is a cost per load and it's independent of the distance covered. The second term represents the total ordering cost. A i is restricted to traditional (non-transportation) ordering and inspection cost elements. The last term is the total inventory cost. In a transportation network, inventory includes items waiting to be shipped from each supplier, items in transit to buyer and items waiting to be used by buyer. That supposes that each supplier produces items at a constant rate and the production planning is synchronized with that of transport. The average time required to i th supplier to produce a shipment of size Q i is Q i /D. Each item in the load waits on average half of this time before being shipped Q i /2D. After arriving, each item waits on average Q i /2D before being used. The average time spend by an item from i th supplier to buyer is Q i /D + T i .

As Q is the optimum order quantity, it can be calculated by using the derivative of TC:

∑ ∑ + + = ⇒ = ∂ ∂ = = n i n i i i i i i i r r X P Y Cf A D Q Q TC 1 1 2 ) ( / ) ) ( ( 2 0 By substituting for Q in TC, it becomes: ) 1 ( ) ( )) ( )( ) ( ( 2 1 1 1 2 a Cv P T rt DX r r X P Y Cf A D TC i i n i i i i n i n i i i i i i i + ∑ + ∑ ∑ + + = = = =
An appropriate aggregate performance measure for delivery to the buyer is given in [START_REF] Pan | Allocation of order quantity among suppliers[END_REF] in the expression (1b) bellow:

) b 1 ( X l LD i n 1 i i ∑ = =
This expression must by less than the lead-time imposed by the buyer. This implies that the long lead-time of one supplier is compensated by the sort lead-time of other suppliers.

The mathematical formulation of the nonlinear multi-objective program model (NMOP) is given as follow:

(1)

(2) (3) (4) (5) (6) (7) Min Z = (TC, LD) S. T. n i Y n i X n i Y X Y X L X l n i C D X i i i i i n i i i n i i i i , 1 1 , 0 , 1 0 , 1 1 , 1 1 1 = = = ≥ = ≤ ≤ ε = ≤ = ≤ ∑ ∑ = =
Equation (1) specifies the multiobjective function whose components expressions are given by equations ( 1a) and (1b).

Constraints (2) represent the supplier production capacity restriction. Constraint (3) is an aggregate performance measure for delivery for all suppliers. Constraint (4) indicates that demand is placed with the set of n suppliers. Constraints (5) require that an order is placed with a supplier if only he is selected; ε is a positive number, slightly greater than zero. Constraints (6) enforce the non-negativity restriction on the decision variables X i. Constraints (7) impose binary requirements on the Y i variables.

SOLUTION METHODOLOGY

The multiobjective programming is often used to find a compromised solution, which simultaneously satisfy a number of design criteria. In solving the multiobjective programming problems, classical methods reduce them into a single objective of minimizing a weighted sum of deviations from goals. In our case and since the cost and time-time criteria have different orders in magnitude; we have normalized the objectives by using the absolute values of the relative variations of each objective compared to its goal. Thus, the multiobjective function (1) can be rewritten as:

] 2 / 2 )[ 1 ( ] 1 / 1 )) ( )) ( )( ( ( 2 ( [ 1 1 1 1 2 G G X l w G G Cv P T rt DX r r X P Cf A D w Z Min n i i i n i i i i i i n i n i i i i i i - - + ∑ - + + ∑ ∑ + + = ∑ = = = =
This equation is a single objective function and our NMOP can be solved as a single objective optimization problem subject to constraints (2)-( 7).

G1, G2, w and (1-w) respectively are the cost, lead-time goals and the weighting factors for the absolute values of the relative variations of each criterion.

To find G1, we solve the model in section 2 by considering the cost as the only objective function (Z= TC), even thing for G2 (Z=DL).

The next section presents a numerical example to evaluate the model. All results presented are generated on a personal computer (Intel Pentium IV, 2,40 GHz) using Matlab version 6.5, a highperformance language that offers the optimization Toolbox which consists of functions that perform minimization (or maximization) on general nonlinear functions. One of these functions is fmincon which allows to find a constrained minimum of a scalar function of several variables starting at an initial estimate. This is generally referred to as constrained nonlinear optimization.

Fmincon uses a Sequential Quadratic Programming (SQP) method. In this method and at each iteration, a Quadratic Programming (QP) subproblem is solved and an estimate of the Hessian of the Lagrangian is updated.

The model is solved several times, evaluating various scenarios. Each scenario depends on the type of shipment used to move the products from suppliers to buyer.

MODEL VALIDATION

In this section, we first study the performance of the model by representing the CPU time in function of the number of suppliers and then, present a case study of three suppliers who have capacities limited and according to five scenarios, each one depends on the type of shipment employed by each supplier, as follows:

-scenario 1 : each supplier uses a LTL, -scenario 2 : each supplier uses a TL, -scenario 3 : supplier 1 uses a TL while suppliers 2 and 3 use LTL each one, -scenario 4 : supplier 2 uses a TL while suppliers 1 and 3 use LTL each one, -scenario 5 : supplier 3 uses a TL while suppliers 1 and 2 use LTL each one LTL and TL are respectively a truckload (TL) and a less than truckload (LTL) characterized respectively by the in-transit holding rate 10% and 12%. The demand of the buyer is 1000 per week, r=20%, the maximum accepted lead-time is 3 days, the ordering, the purchasing costs and the holding rate of each supplier are respectively 10$, 5$ and 20%. This time appears to grow exponentially in the number of suppliers, especially for value 7 of n. In this case, CPU time varies from 1 minute for n=7 to 30 minutes for n=10. This increase is attributed to the combinations of binary variables Y i (2 n ). But we can conclude that our model can be solved in a rather reasonable amount of time.

For each of the five scenarios referred to above, table 3 bellow respectively gives the values of G1, G2 and other computational results corresponding to each goal. LT* and TC* respectively represents lead-time and total cost for G1 and G2. of the NMOP. In our experiment, we vary the values of w from 0 to 1 with a step of 0.1. Usually, this factor is fixed by the decision maker, which makes the method subjective to the user.

Let us note that we did not represent the correspondents' results with scenarios 1 and 2 (when suppliers use all the same type of shipment) because the suppliers to be selected in this case remain 1 and 2. 4 illustrates that varying the weights of the criteria will result in different suppliers being selected with varying order quantities. Indeed, for scenario 3, the buyer will choose suppliers 2 and 3 if w takes valeus 1 or 0.9 and suppliers 1 and 2 if w takes other values.

For scenario 4, the choice will relate to suppliers 1 and 3 if w varies from 0.6 to 1 and suppliers 1 and 2 if w varies from 0 to 5. Finally, for scenario 5, the buyer will select suppliers 1 and 2 if w varies from 0.3 to 1 and suppliers 1 and 3 if w varies from 0 to 0.2.

Thus, supplier selection depends well on transport.

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-For a given value of w, example w=0.5, the minimum of all the Z is reached for scenarios 1 and 5. The buyer will choose suppliers 1 and 2. In both scenarios, suppliers use a LTL transportation type, which gives a minimum transportation cost (253.03) with a percentage of 35.32% of the total cost. The optimum order allocations assigned to each supplier are respectively, in proportion 0.80 and 0.20. The optimum order quantity is 188 and the order quantities, which should be purchased from suppliers, respectively are 150 and 38 for each of the five periods because there are D/Q (=5.32) periods. At the 6th period, the buyer may order the rest of quantities to buyer 1 (60) to satisfy the demand (see fig. 1)

-Always for w=0.5, the in-transit inventory cost is maximum for selected suppliers (case 2 of scenarios 1 and 5) whereas it's minimum for the same case, for the other scenarios and especially for scenario 2. Indeed, a TL is faster and thus the products remain less longer in the road. This cost is also less significant if one of the two suppliers uses a TL (scenarios 4 and 3). Conversely, the inventory cost of buyer is minimum for scenarios 1 and 5 whereas it's significant for scenario 3, then for scenario 4 and more significant for scenario 2. The use of a TL implies that the products arrive quickly to the buyer and its stock is maximum. In this research, we have developed and demonstrated the use of a multiobjective programming approach for improving the impact of transportation in supplier selection problem. Our model can assist the buyer in selecting the appropriate suppliers and determining the size of the split orders.

The proposed approach is likely to find multiple solutions to the problem, each corresponding to a different setting of the weight factors. This makes this approach independent from the user.

Solving five test scenarios has showed the efficacy of this approach.

Usually, this factor is fixed by the decision maker, which makes the method subjective to the user. Moreover, the solution of the problem largely depends on the value chosen for this factor.

The results of the numerical example demonstrated that transportation is likely to play a pivotal role in the supplier selection decision but also in the inventory system of the suppliers, in transit and of the buyer.

The perspective of this research is to study the combined transport, which is generally regarded as the most promising market for external logistics suppliers.

  Fig. 1. Inventory level of the buyer

Table 1

 1 below contains information on the suppliers, according to whether they use one or the other type of shipment.

		Table 1: Supplier information
			Supplier 1	Supplier 2	Supplier 3
	Capacity		900	800	700
	Distance to buyer (miles)		100	150	200
	Lead time (days)	LTL	1.43	2.14	2.86
		TL	0.57	0.86	1.14
	Transit time (week)	LTL	0.14	0.21	0.29
		TL	0.06	0.09	0.11
	Fixed shipment cost	LTL	15.28	22.92	30.56
		TL	132	198	264
	Variable shipment cost	LTL	0.05	0.05	0.05
		TL	0	0	0

Table 2

 2

gives the CPU time which includes the generation, compilation and execution times in seconds, to provide an optimal solution for each value of n.

Table 2 :

 2 Computational time in CPU seconds

	n	CPU (seconds)
	2	0.97
	3	1.58
	4	1.70
	5	4.48
	6	22.19
	7	63.92
	8	196.26
	9	538.66
	10	1827.61

Table 3 :

 3 Computational results

		Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
	X1 0.54	0.90	0.51	0.90	0	0.90	0.58	0.20	0.54	0.30
	X2 0.46	0.10	0.49	0.10	0.54	0.10	0	0.80	0.46	0
	X3 0	0	0	0	0.46	0	0.42	0	0	0.70
	Q	219	170	583	453	251	315	233	402	219	499
	G1 662.69		1256.05		802.31		731.62		662.69
	LT* 1.76		0.71		2.47		2.03		1.76
	G2		1.50		0.60		0.73		0.97		1.23
	TC*		796.73		1591.33		1171.25		1268.58		1307.96
	By considering the values of G1 and G2 for each scenario, table 4 below summarizes the results

Table 4 :

 4 Computational results of the NMOP

	Weight (w1)	X1	X2	X3	Q	Transportatio	n cost	In transit	inventory cost	Inventory cost	of supplier 1	Inventory cost	of supplier 2	Inventory cost	of supplier 3	Inventory cost	of buyer	Optimum total	cost	Optimum total	lead-time	Z*
	Scenario 1
	1	0.54 0.46 0		219 224.55 172.20 63.81	46.31 0		110.12 662.69	1.757 0
	0.9 0.56 0.44 0		218 225.25 170.79 68.39	42.17 0		110.56 663.04	1.742 0.016
	0.8 0.59 0.41 0		216 226.54 169	74.24	37.13 0		111.37 664.49	1.724 0.032
	0.7 0.62 0.38 0		214 228.91 166.62 81.99	30.88 0		112.87 668.12	1.700 0.046
	0.6 0.67 0.33 0		208 233.51 163.27 92.78	23		0		115.78 676.37	1.666 0.057
	0.5 0.74 0.26 0		197 243.43 158	108.97 13.06 0		122.03 696.14	1.613 0.063
	0.4 0.89 0.11 0		173 270.77 147.67 137.20 2.08	0		139.28 754.78	1.508 0.059
	0.3 0.90 0.10 0		171 272.82 147	138.86 1.72	0		140.58 759.31	1.501 0.044
	0.2 0.90 0.10 0		171 272.82 147	138.86 1.72	0		140.58 759.31	1.501 0.030
	0.1 0.90 0.10 0		171 272.82 147	138.86 1.72	0		140.58 759.31	1.501 0.015
	0	0.90 0.10 0		226 354.26 147	183.05 2.26	0		185.31 938.26	1.501 0
	Scenario 2
	1	0.51 0.49 0		583 566.01 89.72 150.29 141.29 0		291.58 1256.05	0.713 0
	0.9 0.52 0.48 0		583 566.50 89.20 158.84 132.98 0		291.83 1256.54	0.709 0.018
	0.8 0.54 0.46 0		581 567.79 88.55 169.71 122.78 0		292.49 1258.53	0.703 0.036
	0.7 0.56 0.44 0		578 570.56 87.70 183.99 109.94 0		293.93 1263.40	0.696 0.052
	0.6 0.60 0.40 0		573 576.33 86.54 203.54 93.36 0		296.90 1274.12	0.687 0.067
	0.5 0.64 0.36 0		561 588.77 84.84 232.04 71.26 0		303.30 1298.05	0.673 0.078
	0.4 0.72 0.28 0		533 619.23 82.01 277.82 41.18 0		319		1358.01	0.651 0.083
	0.3 0.90 0.10 0		457 721.56 75.76 366.72 4.99	0		371.71 1562.62	0.600 0.074
	0.2 0.90 0.10 0		457 722.33 75.72 367.22 4.89	0		372.11 1564.17	0.599 0.049
	0.1 0.90 0.10 0		457 722.33 75.72 367.22 4.89	0		372.11 1564.165 0.599 0.025
	0	0.898 0.100 0.002 611 972.73 75.71 492.488 6.155 0.001 498.645 2070.288 0.60 0
	Scenario 3
	1	0	0.54 0.46 251 262.93 246.81 0			73.19 53.19 126.38 802.31	2.471 0
	0.9 0	0.58 0.42 248 265.27 243.24 0			84.87 42.89 127.76 804.29	2.44 0.236
	0.8 0.71 0.29 0		375 427.34 112.54 187.24 32.40 0		219.64 1005.80	1.03 0.285
	0.7 0.85 0.15 0		333 472.28 93.01 239.60 7.73	0		247.33 1089.95	0.81 0.283
	0.6 0.90 0.10 0		318 492.71 86.07 256.25 3.30	0		259.55 1129.3449 0.73 0.245
	0.5 0.90 0.10 0		318 492.72 86.06 256.25 3.30	0		259.55 1129.351 0.73 0.204
	0.4 0.90 0.10 0		318 492.72 86.06 256.25 3.30	0		259.55 1129.3548 0.73 0.163
	0.3 0.90 0.10 0		318 492.72 86.06 256.25 3.30	0		259.55 1129.3547 0.73 0.122


Andrew Wildes

Nikos Theodorakopoulos

Jessica Valle-Orero

Santiago Cuesta-López

Jean-Luc Garden

Michel Peyrard

The thermal denaturation of DNA studied with neutron scattering

Keywords: numbers: 87.14.gk, 87.15.Zg, 87.64.Bx

The melting transition of deoxyribonucleic acid (DNA), whereby the strands of the double helix structure completely separate at a certain temperature, has been characterized using neutron scattering. A Bragg peak from B-form fibre DNA has been measured as a function of temperature, and its widths and integrated intensities have been interpreted using the Peyrard-Bishop-Dauxois (PBD) model with only one free parameter. The experiment is unique, as it gives spatial correlation along the molecule through the melting transition where other techniques cannot.

Deoxyribonucleic acid (DNA) is a highly dynamic molecule in which the base pairs, which carry the genetic information, fluctuate widely. This can lead to a temporary breaking of a "closed" pair and a local separation of the two strands. Local openings may be activated by heating. At a certain temperature, local openings of the double helix extend over the full molecule, resulting in a complete separation of the two strands. This is called the "melting" of DNA, and may be considered a very rare example of a one-dimensional (1D) structural phase transition 1,2 . DNA melting attracted attention soon after the discovery of the double helix structure 3,4 and was widely studied because it shows some similarity with DNA unwinding in the cell. There is recent renewed interest in biology due to high resolution melting methods 5 .

Despite numerous attempts, the understanding of this transition is still a challenge. One difficulty in making progress is the absence of structural information at the transition. This is because experimental studies of DNA melting, made using techniques such as UV absorbance, circular dichroism and calorimetric studies, do not provide spatial information.

Diffraction techniques can provide this information. Indeed, the double-helix structure of DNA was solved by modeling the x-ray diffraction patterns from semicrystalline fibre samples, measured by Franklin et al. 6 . The data were analyzed for peak positions which revealed the double helix structure, and also that the molecules could have different configurational structures 6 . Many configurations are known to exist 7 , however the majority of the work to date has been on so-called 'B-form' DNA.

A Bragg peak contains more information than simply its position. Analysis of the shape and width can determine a correlation function and its characteristic length. The integrated intensity gives a measure of the quantity of the sample that scatters coherently. These quantities change dramatically close to a phase transition, and scattering techniques have proved to be excellent probes 8 .

We have used neutron scattering to measure the tem-perature dependence of a strong Bragg peak from a fibre sample of B-form DNA. The data have been analyzed to extract the widths and the integrated intensities as the sample was heated through the melting transition.

The structural information was compared with calculations using an adapted form of a mesoscopic statistical mechanics model for DNA, known as the Peyrard-Bishop-Dauxois (PBD) model 9 .

While the DNA molecules in a fibre are confined, large scale configurational changes are possible and are driven by a simple change in relative humidity 6,7 . DNA melting is observable in a fibre and, given the favourable agreement between the theory and experiment, much of the physics of the transition can be understood from the application of the PBD model.

The fibre sample was created using the "wet spinning" method 10 with DNA extracted from salmon testes (Fluka), precipitated from a 0.4 M Li-salt solution. Samples produced in this method are semicrystalline 7 with the DNA molecules aligned to within 5 • of the fibre axis 11 . The water content was set by keeping the sample in an atmosphere humidified to 75 % with deuterated water. This ensured a B-form configurational structure, proven with X-ray fibre diffraction, and significantly reduced incoherent neutron scattering from protonated hydrogen in the sample.

The thermodynamic behaviour of B-form fibre DNA was characterized by measuring the heat capacity using differential scanning calorimetry (DSC) at the Institut Néel, Grenoble, France. The samples were hermetically sealed in a hastalloy sample tube. The specific heat was measured in a Seratam Micro DSC III calorimeter relative to an empty reference tube. The differential heat flux was measured as the samples were heated from 278 K to the maximum temperature (∼ 380 K) at a rate of 0.6 K / min. Typical data are shown in Fig. 1. The data are sharply peaked at 360 K for this sample, which represents its thermal denaturation temperature. The transition is not reversible. After humidification, the sample for the neutron scattering measurements was placed in a Nb envelope and then sealed in an Al cassette using Pb wire for the seal. The cassette assisted in the thermalization of the sample and ensured that the water content for the sample environment stayed constant throughout the measurement. The scattering was first characterized using the IN3 spectrometer at the Institut Laue-Langevin (ILL), France. The main Bragg peak, found at a momentum transfer along the fibre axis, Q , is seen in the reciprocal space map in Fig. 2a. Its lattice spacing corresponds to the average distance between the base pairs, a ≈ 3.4 Å. The peak is very broad in the momentum transfer perpendicular to the fibre axis, Q ⊥ . The sample can largely be regarded as a quasi-1D crystal, and is treated as such. Some DNA features are seen off the fibre axis due to its double helix structure, as is a weak powder ring from Pb at |Q| = 2.2 Å-1 . Stronger rings from Al, seen at |Q| = 2.68 Å-1 , were monitored throughout the experiment as a check on instrument and sample alignment.

The neutron three axis spectrometer IN8, also at ILL, was used to measure the main Bragg peak as a function of temperature. This instrument was configured with an incident wavelength of 1.53 Å ( ≡ 35 meV). The Qresolution was defined with 40 ′ collimation before and after the sample, and was measured by making a reciprocal space map of a Bragg peak from a Si single crystal. No energy analysis was used, thus the static approximation was assumed to hold for the measurements. Temperature control was achieved using a liquid helium cryofurnace.

Two scans were repeated at all temperatures. Examples are shown in Fig. 2b. Their trajectories were calculated for nominally elastic scattering and are shown in Fig. 2a. Scan 1 was along the fibre axis, through the centre of the Bragg peak. The Q ⊥ for scan 2 was chosen such that, when Q = 2π/a, the direction of the scattered beam would be perpendicular to the fibre axis. This type of scan has been used to measure critical phase transitions in low dimensional magnets 8 . The temperature steps close to the melting transition were very small (0.1 K) and measurements at a given temperature were repeated numerous times to ensure thermal equilibrium and reproducibility.

The data were fitted with a Lorentzian lineshape:

S Q = ∞ -∞ S Q , ω dω = I 0 π Γ/2 (Γ/2) 2 + Q -Q 0 2 , (1)
where I 0 is the integrated intensity, Q 0 is the peak centre, and Γ is the width which is inversely proportional to the correlation length along the molecule. The function was convoluted with the instrument resolution. A second Lorentzian centered at Q ≈ 1.5 Å-1 was needed to fit the scan 2 data. The amplitudes for these two peaks were free parameters, however their widths were set to be equal in the fits. Fig. 2b shows examples of the fits. The fit results are shown in Fig. 3. The normalized intensities for both scans followed exactly the same curve. A small deviation in the data at T ≈ 345 K was due to the discovery of an alignment issue that was found and rectified. The widths were qualitatively different and are shown for both scans.

The samples used for the neutron and DSC measurements were produced by the same methods and apparatus with nominally the same ion concentration and humidity. While melting transitions are qualitatively the same, the precise temperatures involved depend strongly on external conditions 12 . Hence, it is no surprise that the transition temperatures differ between neutrons and DSC. Subsequent analysis will discuss the transition in terms of a reduced temperature, θ = T /T c , where T c is defined as where half of the base pairs are open.

The theoretical modeling of the data required the derivation of the scattering profile from a finite length of DNA, accounting for disorder due to variations in the base pair sequence and to thermal fluctuations. A generalization of the profile for a 1D paracrystal of finite size 15 results in an expression for m closed base pairs:

S m (Q) = m + 2 m-1 n=1 (m -n) cos Q na e -n∆ , lim m→∞ (S m (Q) /m) ≈ S ′ (Q) = sinh ∆ cosh ∆-cos(Q a) , (2) where 2∆ = Q 2 σ 2 + ξ 2 + Q 2 ⊥ σ 2 ⊥ + ξ 2 ⊥ + 2Q ⊥ Q χ σ 2 ⊥ σ 2 1/2
. The Gaussian displacements, σ ⊥, , characterize the structural disorder perpendicular and parallel to the molecule, and may be obtained from conformational analysis 13 to be σ 2 1/2 = 0.18 Å and σ 2 ⊥ 1/2 = 0.55 Å. The terms, ξ ⊥, account for thermal fluctuations. Along the molecule, ξ amounts to a Debye-Waller correction that can be calculated from the total DNA mass per base pair and from the measured sound speed 11,14 , while ξ ⊥ approximates displacements perpendicular to the molecule axis. The parameter χ characterizes the correlation between longitudinal and transverse structural disorder, with χ = 0 for no correlation.

The PBD model 9 was developed to describe the melting behaviour of DNA. It may be used to calculate the probability, P (m), of having a closed cluster of m consecutive base pairs at a given temperature. It has been recently extended to model genomic DNA with no free parameters 16 , and appropriate parameters from that work were used in the calculations here. The parameters were derived using sequence information from pyrococcus abyssi DNA and were used to model the DSC data in Fig. 1 with satisfactory agreement. Natural DNA has ∼ 10 6 base pairs. While P (m) may be calculated up to ∼ 10 2 base pairs, it will scale 17 exponentially with m and may be replaced by P (m > M ) = P 0 ζ m . The expected neutron scattering can then be calculated in three regimes using the equation:

S C (Q) = M m=1 P (m)S m (Q) + M0 m=M+1 P 0 ζ m S m (Q) +S ′ (Q)P 0 ζ M0+1 M0 1-ζ + 1 (1-ζ) 2 .
(3) The first term was calculated for M = 150 and the others for M 0 = 1000. The calculated structure factors were then fitted with eq. 1. Fig. 3 shows the results, and the experimental data, as a function of θ.

Theory and experiment are very well matched until θ ≈ 1, in particular for the integrated intensities where the agreement is almost perfect. As shown by eq. 3, the intensity scales with the number of closed pairs. The intensities are almost constant with increasing temperature until θ ≈ 0.97, due to there being a very low fraction of open base pairs in this temperature range. They then begin to fall in a smooth manner as the number of closed pairs decreases. This rounded, continuous behavior of the transition over a finite temperature range represents the "genomic" limit of multistep melting proposed in model calculations of heterogeneous DNA 18 .

The comparison of the widths provide spatial information that standard observations of DNA denaturation cannot. Globally, the comparison between theory and experiment is reasonable. For θ < 0.97 there is a qualitative difference, with the calculated widths slowly increasing with temperature while the experimental data show a decrease. Subsequent experiments show that this is a form of annealing in the sample, with the widths staying constant when the temperature is decreased, and hence is due to the fibre structure rather than DNA denaturing.

There are no free parameters in the calculation of the widths for scan 1, where Q ⊥ = 0. Theory and data match quantitatively with a discrepancy of < 15%, validating the conformational analysis 13 . The widths hardly vary with temperature until θ = 1, showing that the base pair openings, which start to be significant at θ = 0.98, do not cause a sharp decrease in the size of the diffracting clusters until denaturation has occurred. Clusters of ∼ 100 base pairs remain intact well in to the denaturation region and then denature as a whole.

Scans 2, with Q ⊥ = 0, require the introduction of χ. Two calculations are shown in Fig. 3. The first assumes no correlation (χ = 0) and is unacceptably lower than the experimental data. A moderate value (χ = 0.35) gives a width that matches the data for θ ≈ 0.97, judged to be representative for an "annealed" sample. It would be interesting to test the value of χ with conformational analysis.

The experimental widths of scans 2 show an upturn in the vicinity of the phase transition (0.99 ≤ θ < 1) which is not accurately modeled. The theory does account for transverse thermal fluctuations through ξ 2 ⊥ , however this effect is small as only fluctuations from closed clusters can contribute. More likely, the upturn is due to thermally induced misalignment of the molecules with respect to the fibre axis. A misalignment of 10% would change the width along the fibre axis by δQ /Q = 2%, but the projection at non-zero Q ⊥ would create a change of 17%. The assumption of a 1D structure begins to break down at these temperatures and the theory would have to be extended to account for that.

The theory and experiment cease to match at θ ≈ 1 when the experimental intensities fall precipitously while the theory continue to show a narrow but smooth decay. The data in Fig. 2b show examples of the scattering below and above this temperature. The fall is due to the collapse of the fibre structure, as verified by optical microscopy on similar samples and by visual inspection of this sample after the experiment. The structural change in the fibre is distinct from DNA melting, which refers to the denaturing of the double helix, and is not explicitly described by the theory. Nevertheless, the theory gives some insight to the phenomenon. As T c is approached the open regions will quickly grow in size. Single strands are very flexible and can gain entropy by losing their initial orientation. The resulting structure would have the remaining closed, relatively rigid regions embedded in a liquid-like medium. Once the open regions reach a certain average size, the closed regions will have flexibility to move. The highly oriented fibre structure will break down, heralded by the upturn in the scan 2 widths and the disappearance of the Bragg peak seen in Fig. 2b.

Despite the loss of the Bragg peak, it is interesting to note that the theory predicts that the size of the closed segments is still large (∼ 80 -90 base pairs) slightly above θ = 1. This is indirectly confirmed by agarose gel electrophoresis analysis before and after the experiment. Before heating, the DNA had > 20000 base pairs, while after it had broken in to fragments of ∼ 100 base pairs. The breaking can be due to the high stress concentration that occurs at the end of the rigid closed segments, linked to each other by flexible single strands, as they rotate in the breakdown of the fibre structure.

In conclusion, neutron scattering has been used to give spatial information on the melting of B-form DNA in fibre form. The data could be understood using simple non-linear lattice dynamics theory with minimal free parameters, showing the transition to be smooth and continuous. The comparison was excellent to a point midway through the melting transition where the analysis was complicated by the collapse of the fibre structure. Results showed that large clusters of closed base pairs continue to exist well in to the denaturation regime, and showed correlations between thermal fluctuations along and perpendicular to the molecule.

The authors would like to thank Prof. M. Johnson, Dr. L. van Eijck, and Prof. V. T. Forsyth for valuable discussions. The allocation of beam time by the ILL and the aid of the IN8 and IN3 instrument teams are gratefully acknowledged.

FIG. 1 .

 1 FIG. 1. Differential calorimetry signal, Cp, from a Li-DNA sample similar to that used in the neutron experiments, and the theoretical denaturation profile calculated from Pyrococcus abyssi DNA used for the analysis where κ is the fraction of open base pairs

FIG. 2

 2 FIG. 2. a) Reciprocal space map of B-form Li-DNA. The axes are the momentum transfer parallel (Q ) and perpendicular (Q ⊥ ) to the fibre axis. The strong Bragg peak is observed at Q = 2π/a, where a ≈ 3.4 Å is the distance between the base pairs along the fibre axis. b) Examples of scans, fitted using eq. 1. The data at 299 K represent the starting point for the experiment. The sample is in the melting transition at 348.8 K. The fibre structure has collapsed at 349.1 K.

FIG. 3 .

 3 FIG.3. The integrated intensities and widths of the Bragg peaks as a function of temperature. The points show the experimental results, while the lines plot the theory. For the widths: the solid line shows the calculation for scans 1; the dotted line for scans 2 assuming uncorrelated components of structural disorder (χ = 0); the dashed line for scans 2 and correlated disorder with χ = 0.35.