Samir Ait Said

Catherine Fernandez

Stéphane Greff

Arezki Derridj

Thierry Gauquelin

Jean-Philippe Mevy
email: jean-philippe.mevy@univ-provence.fr

Inter-population variability of leaf morpho-anatomical and terpenoid patterns of Pistacia atlantica Desf. ssp. atlantica growing along an aridity gradient in Algeria

Keywords:

Three Algerian populations of female Pistacia atlantica shrubs were investigated in order to check whether their terpenoid contents and morpho-anatomical parameters may characterize the infraspecific variability. The populations were sampled along a gradient of increasing aridity from the Atlas mountains into the northwestern Central Sahara.

As evidenced by Scanning Electron Microscopy, tufted hairs could be found only on seedling leaves from the low aridity site as a population-specific trait preserved also in culture. Under common garden cultivation seedlings of the high aridity site showed a three times higher density of glandular trichomes compared to the low aridity site. Increased aridity resulted also in reduction of leaf sizes while their thickness increased. Palisade parenchyma thickness also increases with aridity, being the best variable that discriminates the three populations of P. atlantica.

Analysis of terpenoids from the leaves carried out by GC-MS reveals the presence of 65 compounds. The major compounds identified were spathulenol (23 g g -1 dw), ␣-pinene (10 g g -1 dw), verbenone (7 g g -1 dw) and ␤-pinene (6 g g -1 dw) in leaves from the low aridity site; spathulenol (73 g g -1 dw), ␣-pinene (25 g g -1 dw), ␤-pinene (18 g g -1 dw) and ␥-amorphene (16 g g -1 dw) in those from medium aridity and spathulenol (114 g g -1 dw), ␣-pinene (49 g g -1 dw), germacrene D (29 g g -1 dw) and camphene (23 g g -1 dw) in leaves from the high aridity site. Terpene concentrations increased with the degree of aridity: the highest mean concentration of monoterpenes (136 g g -1 dw), sesquiterpenes (290 g g -1 dw) and total terpenes (427 g g -1 dw) were observed in the highest arid site and are, respectively, 3-, 5-and 4-fold higher compared to the lower arid site. Spathulenol and ␣-pinene can be taken as chemical markers of aridity. Drought discriminating compounds in low, but detectable concentrations are ␦-cadinene and ␤-copaene. The functional roles of the terpenoids found in P. atlantica leaves and principles of their biosynthesis are discussed with emphasis on the mechanisms of plant resistance to drought conditions.

Introduction

Plants respond to environmental variations, particularly to water availability through morphological, anatomical and biochemical adjustments that help them cope with such variations [START_REF] Lukovic | Histological characteristics of sugar beet leaves potentially linked to drought tolerance[END_REF]. Plants are adapted to drought stress by developing xeromorphic characters based mainly on reduction of leaf size [START_REF] Trubat | Plant morphology and root hydraulics are altered by nutrient deficiency in Pistacia lentiscus L[END_REF] and increase in thickness of cell walls, a more dense vascular system, greater density of stomata and an increased development of palisade tissue at the expense of the spongy tissue [START_REF] Bussotti | Structural and functional traits of Quercus ilex in response to water availability[END_REF][START_REF] Bacelar | Immediate responses and adaptative strategies of three olive cultivars under contrasting water availability regimes: changes on structure and chemical composition of foliage and oxidative damage[END_REF][START_REF] Syros | Leaf structural dynamics associated with adaptation of two Ebenus cretica ecotypes[END_REF].

Terpenes are one of the most diverse family of chemical compounds found in plant kingdom and they exhibit several roles in plant defense and communication [START_REF] Kirby | Biosynthesis of plant isoprenoids: perspectives for microbial engineering[END_REF]. In response to drought conditions, significant changes of terpene emissions were shown in many Mediterranean species (Orme ño et al., 2007a;[START_REF] Lavoir | Drought reduced monoterpene emissions from the evergreen Mediterranean oak Quercus ilex: results from a throughfall displacement experiment[END_REF]. Similar results were reported regarding the occurrence of terpenic components from Erica multiflora and Globularia alypum [START_REF] Llusià | Net ecosystem exchange and whole plant isoprenoid emissions by a Mediterranean shrubland exposed to experimental climate change[END_REF]. It has been shown also that monoterpenes and sesquiterpenes have a role in protecting plants from thermal damage (Pe ñuelas [START_REF] Pe Ñuelas | Linking photorespiration, monoterpenes and thermotolerance in Quercus[END_REF][START_REF] Loreto | Impact of ozone on monoterpene emissions and evidence for an isoprene-like antioxidant action of monoterpenes emitted by Quercus ilex leaves[END_REF][START_REF] Llusià | Airborne limonene confers limited thermotolerance to Quercus ilex[END_REF][START_REF] Pe Ñuelas | Linking isoprene with plant thermotolerance, antioxidants and monoterpene emissions[END_REF]. Terpenes are recognized as being relatively stable and also as precursors of numerous potential physiological components including growth regulators [START_REF] Byrd | Narrow hybrid zone between two subspecies of big sagebrush, Artemisia tridentata (Asteraceae). VIII. Spatial and temporal pattern of terpenes[END_REF]. Another property of these compounds is their great variability in time and depending on the geographic distribution of species as shown by many studies in literature [START_REF] Lang | Abies alba Mill -differentiation of provenances and provenance groups by the monoterpene patterns in the cortex resin of twigs[END_REF][START_REF] Staudt | Seasonal variation in amount and composition of monoterpenes emitted by young Pinus pinea trees -implications for emission modeling[END_REF][START_REF] Hillig | A chemotaxonomic analysis of terpenoid variation in Cannabis[END_REF][START_REF] Smelcerovic | Essential oil composition of Hypericum L. species from Southeastern Serbia and their chemotaxonomy[END_REF]. As a result, many studies relate terpenic constituents with plant systematic and population issues [START_REF] Adams | Systematics of multi-seeded eastern hemisphere Juniperus based on leaf essential oils and RAPD DNA fingerprinting[END_REF][START_REF] Naydenov | Structure of Pinus nigra Arn. populations in Bulgaria revealed by chloroplast microsatellites and terpenes analysis: provenance tests[END_REF].

The genus Pistacia (Anacardiaceae) consists of at least eleven dioecious species [START_REF] Zohary | A monographic study of the genus Pistacia[END_REF][START_REF] Kokwaro | Notes on the Anacardiaceae of Eastern Africa[END_REF]) that all intensely produce terpenes. There are three wild Pistacia species in Algeria: P. atlantica Desf. ssp. atlantica which exhibits high morphological variability [START_REF] Belhadj | Analyse de la variabilité morphologique chez huit populations spontanées de Pistacia atlantica en Algérie[END_REF], P lentiscus L. and less frequently P. terebinthus L. Pistacia atlantica is considered to be an Irano-Turanian species which is distributed from south-west Asia to north-west Africa [START_REF] Zohary | A monographic study of the genus Pistacia[END_REF]. In Algeria, it occurs in the wild from sub-humid environments to extreme Sahara sites [START_REF] Monjauze | Note sur la régénération du Bétoum par semis naturels dans la place d'éssais de Kef Lefaa[END_REF][START_REF] Quézel | Ecologie et biogéographie des forêts du bassin méditerranéen[END_REF][START_REF] Benhassaini | The chemical composition of fruits of Pistacia atlantica Desf. subsp. atlantica from Algeria[END_REF]. As a thermophilous xerophyte P. atlantica grows in dry stony or rocky hill sides, edges of field, roadsides, near the base of dry stone walls and other similar habitats [START_REF] Tzakou | Volatile metabolites of Pistacia atlantica Desf. from Greece[END_REF]. The species grows well on clay or silty soils, although it can thrive also on calcareous rocks where roots develop inside cracks. Hence, P. atlantica has a wide ecological plasticity as also shown by [START_REF] Belhadj | Comparative morphology of leaf epidermis in eight populations of atlas pistachio (Pistacia atlantica Desf., Anacardiaceae)[END_REF] through leaf epidermis analysis. For all these reasons, P. atlantica is used in re-planting projects in Algeria but only few studies are carried out on the infraspecific variability of this plant.

Regarding the phytochemistry of P. atlantica, essential oils from samples harvested in Greece [START_REF] Tzakou | Volatile metabolites of Pistacia atlantica Desf. from Greece[END_REF] and Morocco [START_REF] Barrero | Chemical composition of the essential oils of Pistacia atlantica Desf[END_REF] were described. Recently also a study was published describing essential oils and their biological properties from P. atlantica harvested in Algeria [START_REF] Gourine | Chemical composition and antioxidant activity of essential oil of leaves of Pistacia atlantica Desf. from Algeria[END_REF]. However, to the best of our knowledge, there is no detailed study on the relationship between the phytochemistry of P. atlantica and its ecological conditions of growth.

The aim of this work is to investigate the intraspecific diversity of three populations of P. atlantica growing wild in arid zones of Algeria through terpenoid analysis and leaf morpho-anatomical traits. We also examined the possible links that may exist between plant chemical composition and aridity conditions of these three locations.

Material and methods

Sampling sites

Pistacia atlantica Desf. ssp. atlantica was harvested in June 2008 from three Algerian sites chosen along a Northeast-Southwest transect of increasing aridity: Oued-Besbes (Medea)-Low aridity, Tilghemt (Laghouat)-Medium aridity and Beni-Ouniff (Bechar)-High aridity (Fig. 1). Specimens were deposited at the herbarium of the University of Provence Marseille and referred as Mar-PA1-2008;Mar-PA2-2008;Mar-PA3-2008 for the locations of Medea, Laghouat and Bechar, respectively. Ecological factors of samplings sites are described in Table 1.

For all the sites, sampling was carried out during fructification stage in order to take into account the phenological shift due to local climatic conditions. Ten healthy female individuals with the same age were chosen per site. Plants density and soil conditions were similar for the different sites.

Leaf morphology and anatomy

From each of the three locations, ten female trees were selected and thirty leaves fully sun exposed were harvested per tree. Once harvested, these leaves were carefully dried and kept in herbarium prior to biometric measurements: leaf length and width, petiole length, rachis length and the terminal leaflet length and width.

For anatomical parameters, cross sections were prepared across the middle part of three fresh leaflets per leaf, stained with carmino-green, and thickness measured using light microscopy of abaxial and adaxial epidermis, cuticle, palisade and spongy parenchyma and total leaflet.

Scanning Electron Microscopy (SEM) of seedling leaves

Seeds were collected in August 2008 at Medea and Bechar sites. After germination the seedlings were transplanted in pots filled with peat and sand, then kept in a growth chamber at constant temperature of 25 • C. The photoperiod was set at 11/13 h and the light irradiance was 500 mol photons m -2 s -1 . After 11 months of culture eight plants from each location were randomly selected, then three leaves per plant were harvested and carefully dried prior to SEM observations. Micromorphological observations were carried out on three leaflet samples (adaxial and abaxial surfaces) per leaf. These were gold coated before scanning through an electronic microscope: FEI XL30 ESEM (USA).

Terpenoids extraction

Mature and sun exposed leaves were harvested in the field, dried in dark at ambient air temperature conditions until constant weight, then, 100 g per tree were grounded and stored until use. Shade-drying method has no significant effect on the qualitative composition of volatile oils compared to fresh, sun-drying and oven-drying at 40 or 45 • C [START_REF] Omidbaigi | Influence of drying methods on the essential oil content and composition of Roman chamomile[END_REF][START_REF] Sefidkon | Influence of drying and extraction methods on yield and chemical composition of the essential oil of Satureja hortensis[END_REF][START_REF] Ashafa | Effect of drying methods on the chemical composition of essential oil from Felicia muricata leaves[END_REF]. The extraction method used consisted of suspending leaf dry matter in dichloromethane according to a ratio of 1:2 (w/v), for 30 min, under constant shaking at room temperature. 50 l of dodecane (5 mg ml -1 ) were added as internal standard for quantification.

Quantitative and qualitative analysis of terpenoids

Extracts were filtered on RC syringe filter (regenerated Cellulose, 0.45 m, 25 mm; Phenomenex, Le Pecq, France) then analyzed with a gas chromatograph Hewlett Packard ® GC 6890 coupled to a mass selective detector 5973 Network. The system was fitted with an HP-5MS capillary column 30 m, 0.25 mm, 0.25 m. 2 l of extracts was injected through an automatic injector ALS 7683 in splitless mode. Purge was set at 50 min ml -1 after 1 min. Injection temperature was maintained at 250 • C. Helium was used as carrier gas. A constant flow rate of 1 ml min -1 was set throughout the run. The oven temperature initially set at 40 • C was increased to 270 • C at a rate of 4 • C min -1 and remained constant for 5 min. The MSD transfer line heater was maintained at 280 • C.

Terpenes were identified by comparison of their arithmetic index (AI) and mass spectra with those obtained from authentic samples and literature [START_REF] Adams | Identification of Essential Oil Components by Gas Chromatography/Mass Spectrometry[END_REF].

Statistical analysis

The data were analyzed by a one-way ANOVA model. Newman-Keuls test was used to test for significant differences in monoterpene, sesquiterpene, total terpene concentrations and morpho-anatomical measurement data between the three populations. In order to evaluate the information contained in the collected chemical data, Principal Component Analysis was carried out. The statistical analyses were performed using R statistical software and packages "ade4".

Results

Morpho-anatomical measurements

Among the biometric parameters studied it appears that leaf length and width as well as terminal leaflet length and width highly discriminate statistically the three populations of P. atlantica (Table 2). The population from the most arid site shows the lowest leaf and terminal leaflet sizes. However the number of leaflet pairs increases with aridity. Regarding the anatomical data, the thickness of palisade parenchyma is the major discriminating variable and it increases with aridity (Table 3).

SEM observations

The epidermis of seedling leaves has markedly sinuous walls in both Medea and Bechar populations. Abaxial and adaxial leaf surfaces of each population are covered with two types of trichomes, elongated hairs and glandular trichomes. The former are essen- tially located at midrib of the adaxial leaf surface (Fig. 2A) and at the rachis forming parallel rows (Fig. 2B). The latter (Fig. 2C) are distributed over the entire leaf surface (essentially at the abaxial surface) with high density (18.31 ± 0.29 mm -2 ) in plants that seeds were sampled from the population of the most arid site (Bechar).

Trichome density of the plants raised from seeds sampled from the population that grows under less arid conditions (Medea) was 6.15 ± 0.21 mm -2 when both seedling lots were cultivated in the same environment (Fig. 2D andE). The Medea population could further be discriminated by the presence of tufted hairs which never were observed in the Bechar population on P. atlantica, neither in seedlings nor in adult plants (Fig. 2F).

Terpenoid analysis

P. atlantica leaves contain forty nine compounds identified (Table 4). Among these, twenty two were monoterpenes (8 hydrocarbons and 14 oxygenated) and twenty five were sesquiterpenes (16 hydrocarbons and 9 oxygenated). In the high aridity site, the major compounds identified were spathulenol (114 g g -1 dw), ␣-pinene (49 g g -1 dw), germacrene D (29 g g -1 dw) and camphene (23 g g -1 dw) while from the low aridity site spathulenol (23 g g -1 dw), ␣-pinene (10 g g -1 dw), verbenone (7 g g -1 dw) and ␤-pinene (6 g g -1 dw) were the dominant constituents. For the medium aridity site situated between these two extreme con-ditions of aridity, spathulenol (73 g g -1 dw), ␣-pinene (25 g g -1 dw), ␤-pinene (18 g g -1 dw) and ␥-amorphene (16 g g -1 dw) were the main terpenes found.

The quantitative analysis showed significant differences in both monoterpene, sesquiterpene and total terpene concentrations of the P. atlantica leaves according to the sites investigated (Fig. 3). Three distinct groups were obtained (Newman-Keuls test, 5% level). Terpene concentrations increase with the degree of aridity. The highest mean concentrations of monoterpenes (136 g g -1 dw), sesquiterpenes (290 g g -1 dw) and total terpenes (427 g g -1 dw) were observed in the high aridity site, whereas these figures were: 57 g g -1 dw, 57 g g -1 dw and 113 g g -1 dw, respectively, at the low aridity site.

Multivariate analysis was applied to the terpenoid contents of 30 solvent extracts. Fig. 4 shows the two-dimensional mapping of the Principal Component Analysis which comprises 77% of the total inertia. Axis 1 represents 62% of the information and is characterized on the positive side by thuja-2,4(10)-diene and on the negative side by a couple of compounds, essentially tricyclene, ␣-pinene, camphene, isoborneol acetate, ␤-cubebene, ␤-copaene, germacrene D, ␦-cadinene and spathulenol. Axis 2 representing 15% of the information is characterized on the negative side by ␤-pinene and terpinen-4-ol.

Positions of the individual samples from leaf extractions in the two-axes space show an overall homogeneity between leaf extracts belonging to the same study site (Fig. 5). Three main groups which are characterized by the geographical provenances can be distinguished. The first group is situated on the positive side of Axis 1 and includes samples from individuals of the low aridity site. The second group is located on the negative side of Axis 1 and includes all individuals of the high aridity site. The third group situated on the negative side of Axis 2, between the points related to samples from the two extreme sites, includes in the majority samples from individuals of the medium aridity site. These three groups are clearly separated along Axis 1 which can be interpreted as indicating the aridity gradient. The most discriminating variables encompass ␣-pinene, spathulenol, ␦-cadinene and ␤copaene.

Discussion

Increase of epidermis, cuticle, palisade parenchyma and total leaf thickness with the degree of aridity may enhance survival and growth of P. atlantica by improving water relations and providing higher protection for the inner tissues in the high aridity site. Such patterns were observed in many species submitted to water stress (e.g., [START_REF] Bussotti | Structural and functional traits of Quercus ilex in response to water availability[END_REF][START_REF] Bacelar | Immediate responses and adaptative strategies of three olive cultivars under contrasting water availability regimes: changes on structure and chemical composition of foliage and oxidative damage[END_REF][START_REF] Guerfel | Impacts of water stress on gas exchange, water relations, chlorophyll content and leaf structure in the two main Tunisian olive (Olea europaea L.) cultivars[END_REF]. Also, a pronounced decrease of leaf size reduces transpiration in sites where water is scarce, as also reported for other plants [START_REF] Huang | Leaf morphological and physiological responses to drought and shade in two Populus cathayana populations[END_REF][START_REF] Macek | Morphological and ecophysiological traits shaping altitudinal distribution of three Polylepis treeline species in the dry tropical Andes[END_REF]. The high morpho-anatomical plasticity of Pistacia atlantica in response to aridity may explain its wide ecological distribution in northern Africa. Trichomes are considered as important taxonomic characters [START_REF] Krak | Trichomes in the tribe Lactuceae (Asteraceae) -taxonomic implications[END_REF][START_REF] Salmaki | Trichome micromorphology of Iranian Stachys (Lamiaceae) with emphasis on its systematic implication[END_REF][START_REF] Shaheen | Diversity of foliar trichomes and their systematic relevance in the genus Hibiscus (Malvaceae)[END_REF]. The absence of tufted hairs in Bechar population suggests the existence of genetic differences between the populations studied.

Regarding the phytochemistry of P. atlantica, no data were reported before on extractable terpenoids composition of the pistacia leaves. However, qualitative and quantitative analyses of essential oils from leaves of P. atlantica were reported by several authors. Oils from female plants originating from Greece contained myrcene (17.8-24.8%), sabinene (7.8-5.2%) and terpinene (6-11.6%) as major components [START_REF] Tzakou | Volatile metabolites of Pistacia atlantica Desf. from Greece[END_REF]. Some compounds found in our samples like ␥-amorphene, p-mentha-1,3,5-triene, cis-and trans-sabinene hydrate, ␣-campholenic aldehyde, trans-verbenol, myrtenal, myrtenol, verbenone, ␣muurolene and spathulenol were not found in leaves of P. atlantica from Greece. A provenance from Morocco whose sex was not specified was rich in terpinen-4-ol (21.7%) and elemol (20.0%) [START_REF] Barrero | Chemical composition of the essential oils of Pistacia atlantica Desf[END_REF]. These compounds were found in small amounts (less than 1.1%) also in our samples. Recently, [START_REF] Gourine | Chemical composition and antioxidant activity of essential oil of leaves of Pistacia atlantica Desf. from Algeria[END_REF] have identified 31 compounds from samples harvested at Laghouat with ␤-pinene (19.1%), ␣-terpineol (12.8%), bicyclogermacrene (8.2%) and spathulenol (9.5%) as the principal molecules. Qualitative and quantitative differences between literature data and our results may be explained by such factors as sex of the plants [START_REF] Tzakou | Volatile metabolites of Pistacia atlantica Desf. from Greece[END_REF], period of plant collection [START_REF] Barra | Characterization of the volatile constituents in the essential oil of Pistacia lentiscus L. from different origins and its antifungal and antioxidant activity[END_REF][START_REF] Gardeli | Essential oil composition of Pistacia lentiscus L. and Myrtus communis L.: evaluation of antioxidant capacity of methanolic extracts[END_REF][START_REF] Hussain | Chemical composition, antioxidant and antimicrobial activities of basil (Ocimum basilicum) essential oils depends on seasonal variations[END_REF]), plant competition (Orme ño et al., 2007b), position of leaves in the trees [START_REF] Gambliel | Terpene changes due to maturation and canopy level in douglas-fir (Pseudotsuga-menziesii) flush needle oil[END_REF][START_REF] Barnola | Intraindividual variations of volatile terpene contents in Pinus caribaea needles and its possible relationship to Atta laevigata herbivory[END_REF], soil nutrient availability [START_REF] Yang | Effects of ammonium concentration on the yield, mineral content and active terpene components of Chrysanthemum coronarium L. in a hydroponic system[END_REF][START_REF] Orme Ño | Production and diversity of volatile terpenes from plants on calcareous and siliceous soils: effect of soil nutrients[END_REF][START_REF] Blanch | Drought, warming and soil fertilization effects on leaf volatile terpene concentrations in Pinus halepensis and Quercus ilex[END_REF] and water availability [START_REF] Turtola | Drought stress alters the concentration of wood terpenoids in Scots pine and Norway spruce seedlings[END_REF][START_REF] Blanch | Drought, warming and soil fertilization effects on leaf volatile terpene concentrations in Pinus halepensis and Quercus ilex[END_REF]. Moreover, according to the method of extraction used, recovering the true components of the plant in vivo still remains a matter of debate. Indeed through hydrodistillation, thermal hydrolysis in acid medium may be a source of artifacts in terms of the essential oil composition [START_REF] Adams | Cedar wood oil -analysis and properties[END_REF].

However, the chemical analysis indicated that there are significant differences between the three populations which were analyzed by the same method. These differences comprise both the quantitative and the qualitative composition of the terpenoids. Spathulenol and ␣-pinene are the dominant compounds that clearly discriminate quantitatively the three stations. Although being identified in minor contents from samples of low and medium aridity stations, thuja-2,4(10)-diene, p-mentha-1,3,5triene, nopinone and trans-3-pinocarvone were not registered from high arid station samples. This raises the question of the role of indi-vidual terpenoid components in plant responses to aridity and the central issue of phenotypic/genotypic diversity of the investigated populations.

Allelopathic properties of ␣-pinene are reported in literature. This hydrocarbon monoterpene inhibits radicula growth of several species, enhances root solute leakage and increases level of malondialdehyde, proline and hydrogen peroxide indicating lipid peroxidation and induction of oxidative stress [START_REF] Singh | alpha-Pinene inhibits growth and induces oxidative stress in roots[END_REF]. It is likely that, the high content of ␣-pinene found in the leaves from the driest site may influence interspecific competition for water resources. For all sites investigated, the understory diversity was low, composed mainly of Ziziphus lotus. Hence, ␣-pinene might play direct and indirect roles in P. atlantica responses to drought situations.

Spathulenol is an azulenic sesquiterpene alcohol that occurs in several plant essential oils [START_REF] Mévy | Composition of the volatile constituents of the aerial parts of an endemic plant of Ivory Coast, Monanthotaxis capea (E. G. & A. Camus) Verdc[END_REF][START_REF] Cavar | Chemical composition and antioxidant and antimicrobial activity of two Satureja essential oils[END_REF]. Azulenes are also known as allelochemicals [START_REF] Inderjit | Principles and Practices in Plant Ecology: Allelochemical Interactions[END_REF]. Especially their bactericidal activity has been proven as well as their function as plant growth regulator precursors [START_REF] Muir | Azulene derivatives as plant growth regulators[END_REF][START_REF] Konovalov | Natural azulenes in plants[END_REF]. Azulene is a polycyclic hydrocarbon, consisting of an unsaturated five member ring linked to an unsaturated seven member ring. This molecule absorbs red light 600 nm for the first excited state transition and UVA 330 nm light for the second excited state transition producing a dark blue color in aqueous medium [START_REF] Tetreault | Control of the photophysical properties of polyatomic molecules by substitution and solvation: the second excited singlet state of azulene[END_REF]. The high content of spathulenol found from leaves collected in the high arid station may be interpreted as a defense mechanism against deleterious effects of biotic interactions and UV-light during summer.

Our results are in accordance with several authors who reported increased terpene concentrations in plants under high temperature and water stress conditions [START_REF] Llusià | Changes in terpene content and emission in potted Mediterranean woody plants under severe drought[END_REF][START_REF] Loreto | Impact of ozone on monoterpene emissions and evidence for an isoprene-like antioxidant action of monoterpenes emitted by Quercus ilex leaves[END_REF][START_REF] Pe Ñuelas | Linking isoprene with plant thermotolerance, antioxidants and monoterpene emissions[END_REF][START_REF] Llusià | Net ecosystem exchange and whole plant isoprenoid emissions by a Mediterranean shrubland exposed to experimental climate change[END_REF]. For instance, 54 and 119% increases of total terpene contents under drought treatment were recorded from Pinus halepensis and Quercus ilex, respectively [START_REF] Blanch | Drought, warming and soil fertilization effects on leaf volatile terpene concentrations in Pinus halepensis and Quercus ilex[END_REF]. Because monoterpene biosynthesis is strictly dependent on photosynthesis [START_REF] López | Allelopathic potential of Tagetes minuta terpenes by a chemical, anatomical and phytotoxic approach[END_REF] the increase of their content along with aridity suggests an involvement of specific metabolic pathways that sustain photosynthesis in harsh environmental conditions. In our study, the high thickness of palisade parenchyma can be mentioned in favor of this assumption. On the other hand, monoterpenes act as plant chloroplast membrane stabilizers and protectors against free radicals due to their lipophily and the presence of double bonds in their molecules (Pe ñuelas [START_REF] Pe Ñuelas | Linking photorespiration, monoterpenes and thermotolerance in Quercus[END_REF][START_REF] Chen | Inhibition of monoterpene biosynthesis accelerates oxidative stress and leads to enhancement of antioxidant defenses in leaves of rubber tree (Hevea brasiliensis)[END_REF]. Hence, the increase of monoterpenes may be considered as a regulatory feedback loop that protects photosynthesis machinery from oxidative and thermal damages.

Glandular trichomes are one of the most common secretory structures that produce and store essential oil in plants [START_REF] Covello | Functional genomics and the biosynthesis of artemisinin[END_REF][START_REF] Giuliani | Insight into the structure and chemistry of glandular trichomes of Labiatae, with emphasis on subfamily Lamioideae[END_REF][START_REF] Biswas | Essential oil production: relationship with abundance of glandular trichomes in aerial surface of plants[END_REF]. The high terpenoid contents in Bechar population could be related to the high density of glandular trichomes in this population, which would be also in accordance with other results found by several authors [START_REF] Mahmoud | Cosuppression of limonene-3hydroxylase in peppermint promotes accumulation of limonene in the essential oil[END_REF][START_REF] Fridman | Metabolic, genomic, and biochemical analyses of glandular trichomes from the wild tomato species Lycopersicon hirsutum identify a key enzyme in the biosynthesis of methylketones[END_REF][START_REF] Ringer | Monoterpene metabolism. Cloning, expression, and characterization of (-)-isopiperitenol/(-)-carveol dehydrogenase of peppermint and spearmint[END_REF].

␦-cadinene and ␤-copaene are two compounds found in low contents (0.5-3.8 and 1-4.9 g g -1 dw, respectively) and are similarly as spathulenol and ␣-pinene correlated with the increased aridity the populations are experiencing. Except for antibacterial effects [START_REF] Townsend | Antisense suppression of a (+)-delta-cadinene synthase gene in cotton prevents the induction of this defense response gene during bacterial blight infection but not its constitutive expression[END_REF][START_REF] Bakkali | Biological effects of essential oils -a review[END_REF], no information is available about specific ecological roles of ␤-copaene and ␦-cadinene. It should be noted that they are germacrene D derivatives [START_REF] Bülow | The role of germacrene D as a precursor in sesquiterpene biosynthesis: investigations of acid catalyzed, photochemically and thermally induced rearrangements[END_REF] which is found in high concentration in Cupressus sempervirens after long-term water stress [START_REF] Yani | The effect of a long-term waterstress on the metabolism and emission of terpenes of the foliage of Cupressus sempervirens[END_REF]. Also, the content of germacrene D from Pistacia lentiscus was shown to increase four time during the summer season compared to spring [START_REF] Gardeli | Essential oil composition of Pistacia lentiscus L. and Myrtus communis L.: evaluation of antioxidant capacity of methanolic extracts[END_REF].

The different terpenoids can be appreciated as aridity markers characterizing the three P. atlantica populations. It is not clear whether they are constitutively synthesized or induced by the environmental conditions. Morphological data of leaves indicate that the three populations significantly differ. Scanning electronic microscopy of leaves of seedlings from the high aridity and low aridity provenances grown under controlled conditions reveals that the two populations keep their morphological differences with respect to trichome typology and density. Hence it is likely that the three populations investigated indeed are genetically different. Therefore the chemical variability observed might be as well genetically based. This should be tested in the future by submitting clones selected from the three populations to the same conditions of drought.

Fig. 1 .

 1 Fig. 1. Geographical location of the investigated P. atlantica populations. Sites: ᭹.

Fig. 2 .

 2 Fig. 2. Scanning electron micrographs showing epidermis and trichomes of P. atlantica seedling leaves. (A) Midrib of adaxial leaf surface, covered by elongated trichomes. Bar = 200 m. (B) Elongated trichomes in parallel rows. Bar = 10 m. (C) Glandular trichome. Bar = 20 m. (D and E) Low density of glandular trichomes in Medea population (D) compared to Bechar population (E). Bar = 500 m. (F) Tufted hairs at the adaxial leaf surface in Medea population. Bar = 50 m.

Fig. 3 .

 3 Fig. 3. Variance analysis of monoterpene, sesquiterpene and total terpene contents found in female Pistacia atlantica ssp. atlantica leaves from low, medium and high aridity sites in Algeria. Means of n = 10 with standard errors, p < 0.05.

Fig. 4 .

 4 Fig.4. Correlation of occurrences of terpenoid compounds (g g -1 dw) from female Pistacia atlantica ssp. atlantica leaves from low, medium and high aridity sites in Algeria; shown are only those terpenoids among which high correlation could be found.

Fig. 5 .

 5 Fig.5. Two dimensional PCA of Pistacia atlantica ssp. atlantica individual samples originating from low (la), medium (ma) and high (ha) aridity sites in Algeria.

Table 1

 1 Ecological factors of the Pistacia atlantica collection sites, selected to define the aridity gradient.

	Site	Mean annual	Maximal	Drought duration in	Emberger, Q2 a	Latitude	Elevation (m)
		precipitation (mm)	temperature M ( • C)	months (Bagnouls and
			of the driest month	Gaussen, 1953)
	Medea low aridity	393.10	31.00	4	15.40	36 • 11 -36 • 22 north	720
						3 • 00 -3 • 10 east
	Laghouat medium aridity	116.60	39.40	10	04.34	28 • 00 north	780
						3 • 00 east
	Bechar high aridity	57.70	40.70	12	02.36	31 • 38 -32 • 03 north	790
						1 • 13 -2 • 13 west

a Emberger's pluviothermic quotient.

Table 2

 2 Morphological data (cm) of female P. atlantica ssp. atlantica leaves from low, medium and high aridity sites in Algeria. Mean of 30 measurements per tree with standard errors.

	Leaf biometry (cm)	Low aridity site (Medea)	Medium aridity site (Laghouat)	High aridity site (Bechar)	p
	Leaf length	9.63 ± 0.19 a	9.17 ± 0.17 b	8.92 ± 0.18 c	<0.001
	Leaf width	7.61 ± 0.16 a	7.16 ± 0.14 b	6.65 ± 0.17 c	<0.001
	Rachis length	4.09 ± 0.10 a	3.78 ± 0.07 b	3.72 ± 0.08 b	<0.001
	Petiole length	2.13 ± 0.04	2.11 ± 0.05	2.05 ± 0.06	>0.05
	Terminal leaflet length	3.41 ± 0.03 a	3.29 ± 0.03 b	3.14 ± 0.02 c	<0.001
	Terminal leaflet width	1.58 ± 0.03 a	1.49 ± 0.01 b	1.45 ± 0.02 c	<0.001
	Number of leaflet pairs	3.09 ± 0.07 b	3.12 ± 0.08 b	3.26 ± 0.10 a	<0.05

Table 3

 3 Anatomical data (m) of female P. atlantica ssp. atlantica leaves from low, medium and high aridity sites in Algeria. Mean of 30 measurements per plant (3 replicates per leaf) with standard errors.

	Leaf anatomy (m)	Low aridity site (Medea)	Medium aridity site (Laghouat)	High aridity site (Bechar)	p
	Abaxial cuticle	4.98 ± 0.08 b	5.99 ± 0.12 a	6.08 ± 0.13 a	<0.001
	Adaxial cuticle	4.32 ± 0.06 b	4.88 ± 0.16 a	4.91 ± 0.12 a	<0.01
	Abaxial epidermis	12.70 ± 0.18 b	12.69 ± 0.18 b	14.07 ± 0.20 a	<0.001
	Adaxial epidermis	13.26 ± 0.16 b	13.30 ± 0.14 b	13.45 ± 0.18 a	<0.05
	Palisade parenchyma	64.66 ± 1.5 c	72.77 ± 1.38 b	95.76 ± 1.42 a	<0.001
	Spongy parenchyma	98.67 ± 1.64	102.45 ± 1.81	106.34 ± 1.86	>0.05
	Leaf thickness	198.53 ± 2.78 c	212.08 ± 2.97 b	240.61 ± 3.51 a	<0.001

Table 4

 4 Concentrations of terpenoids (g g -1 dw) found in female Pistacia atlantica ssp. atlantica leaves from low, medium and high aridity sites in Algeria. Mean of 10 extractions per site with standard errors.

	Group		Compounds	AI	Compound content in leaves (g g -1 dw) and location
					Low aridity	Medium aridity	High aridity	p
	Hydrocarbon	1	Tricyclene	914	1.2 ± 0.2 b	2.4 ± 0.4 b	8.7 ± 0.5 a	<0.001
	monoterpenes	2	␣-Pinene	926	10.0 ± 0.4 c	24.5 ± 0.8 b	49.4 ± 1.0 a	<0.001
		3	Camphene	941	3.1 ± 0.5 b	5.5 ± 0.9 b	23.2 ± 1.1 a	<0.001
		4	Thuja-2,4(10)-diene	948	1.0 ± 0.1 a	0.6 ± 0.0 b	-	<0.001
		5	␤-Pinene	971	6.5 ± 2.3 b	18.1 ± 0.9 a	12.6 ± 0.7 ab	<0.001
		6	Mentha-1,3,5-triene, p-	1007	0.7 ± 0.1 a	0.1 ± 0.0 b	-	<0.001
		7	Cymene, p-	1023	0.7 ± 0.1 b	1.9 ± 0.2 a	0.2 ± 0.0 b	<0.001
		8	␥-Terpinene	1058	0.6 ± 0.3 ab	1.6 ± 0.3 a	0.3 ± 0.0 b	<0.001
	Oxygenated	9	Sabinene hydrate, cis-(IPP vs OH)	1067	0.4 ± 0.2 b	1.6 ± 0.3 a	0.2 ± 0.0 b	<0.001
	monoterpenes	10	NI	1088	0.6 ± 0.1 a	0.5 ± 0.0 a	0.2 ± 0.0 b	<0.001
		11	Sabinene hydrate, trans-(IPP vs OH)	1098	0.6 ± 0.2 b	1.5 ± 0.2 a	0.1 ± 0.0 b	<0.001
		12	NI	1101	5.8 ± 1.5	3.9 ± 0.5	4.9 ± 0.4	>0.05
		13	␣-Campholenic aldehyde	1125	1.9 ± 0.4	2.1 ± 0.3	1.9 ± 0.3	>0.05
		14	Nopinone	1133	0.3 ± 0.1	-	-	<0.05
		15	Pinocarveol, trans-	1138	1.8 ± 0.4 ab	1.5 ± 0.1 b	3.2 ± 0.4 a	<0.01
		16	Verbenol, trans-	1146	6.0 ± 1.6	3.9 ± 0.6	6.1 ± 0.8	>0.05
		17	3-Pinocarvone, trans-	1157	1.2 ± 0.4 ab	1.9 ± 0.4 a	-	<0.001
		18	Pinocarvone	1161	0.8 ± 0.1 b	0.7 ± 0.1 ab	1.2 ± 0.2 a	<0.05
		19	Terpinen-4-ol	1177	1.3 ± 0.3 b	3.8 ± 0.4 a	1.3 ± 0.2 b	<0.001
		20	Myrtenal	1194	0.4 ± 0.2 b	0.6 ± 0.2 b	1.4 ± 0.2 a	<0.001
		21	Myrtenol	1197	1.4 ± 0.3	1.9 ± 0.4	1.5 ± 0.2	>0.05
		22	Verbenone	1208	7.0 ± 1.7	3.9 ± 0.7	5.1 ± 0.9	>0.05
		23	Carveol, trans	1221	0.8 ± 0.2 b	0.4 ± 0.1 ab	0.9 ± 0.1 a	<0.05
		24	Borneol, iso-, acetate	1285	2.6 ± 0.5 b	3.9 ± 0.4 b	13.9 ± 0.7 a	<0.001
	Hydrocarbon	25	␦-Elemene	1337	1.4 ± 0.6 b	14.0 ± 3.7 a	22.0 ± 1.8 a	<0.001
	sesquiterpenes	26	␣-Cubebene	1349	0.3 ± 0.0 b	0.7 ± 0.2 b	1.5 ± 0.2 a	<0.001
		27	␣-Copaene	1375	0.2 ± 0.0 b	0.5 ± 0.1 ab	1.0 ± 0.1 a	<0.001
		28	␤-Bourbonene	1383	0.9 ± 0.2	1.2 ± 0.2	0.8 ± 0.2	>0.05
		29	␤-Cubebene	1389	0.2 ± 0.0 b	0.5 ± 0.1 ab	0.8 ± 0.1 a	<0.001
		30	␤-Elemene	1392	0.1 ± 0.0 b	0.5 ± 0.1 ab	0.8 ± 0.2 a	<0.001
		31	␤-Ylangene	1418	1.6 ± 0.2 b	9.0 ± 1.3 a	7.2 ± 0.9 a	<0.001
		32	␤-Copaene	1429	0.5 ± 0.1 b	1.2 ± 0.1 b	3.8 ± 0.6 a	<0.001
		33	␥-Elemene	1433	0.5 ± 0.0 b	2.6 ± 0.8 b	7.4 ± 0.9 a	<0.001
		34	Guaia-6,9-diene	1438	0.3 ± 0.1 b	2.0 ± 0.2 a	1.9 ± 0.4 a	<0.001
		35	NI	1444	0.1 ± 0.0 b	0.6 ± 0.1 b	1.3 ± 0.2 a	<0.001
		36	NI	1453	0.2 ± 0.1 b	1.4 ± 0.3 a	2.2 ± 0.3 a	<0.001
		37	Caryophyllene, 9-epi-	1461	0.8 ± 0.2 b	4.0 ± 0.6 a	3.8 ± 0.3 a	<0.001
		38	NI	1470	0.8 ± 0.4	0.4 ± 0.0	1.1 ± 0.1	>0.05
		39	Germacrene D	1482	3.0 ± 0.4 b	5.2 ± 1.0 b	29.0 ± 2.9 a	<0.001
		40	␥-Amorphene	1496	1.8 ± 0.6 b	15.5 ± 2.8 a	20.5 ± 2.2 a	<0.001
		41	␣-Muurolene	1501	0.3 ± 0.0 b	3.7 ± 0.4 a	0.9 ± 0.1 b	<0.001
		42	␥-Cadinene	1515	0.3 ± 0.0 b	0.7 ± 0.1 b	2.0 ± 0.3 a	<0.001
		43	␦-Cadinene	1524	1.0 ± 0.1 b	2.0 ± 0.2 b	4.9 ± 0.6 a	<0.001
	Oxygenated	44	Cubebol	1518	1.1 ± 0.1 b	1.2 ± 0.1 ab	1.7 ± 0.1 a	<0.01
	sesquiterpenes	45	NI	1527	0.7 ± 0.4	1.4 ± 0.2	1.6 ± 0.3	>0.05
		46	Elemol	1552	0.7 ± 0.1 b	2.1 ± 0.6 b	5.8 ± 0.9 a	<0.001
		47	NI	1557	1.0 ± 0.2 b	2.0 ± 0.6 ab	3.1 ± 0.7 a	<0.05
		48	NI	1568	0.4 ± 0.0	0.5 ± 0.2	0.8 ± 0.2	>0.05
		49	Spathulenol	1581	23.2 ± 1.1c	72.9 ± 1.9 b	114.4 ± 2.2 a	<0.001
		50	NI	1586	3.5 ± 0.8 b	10.1 ± 0.6 a	3.4 ± 0.3 b	<0.001
		51	NI	1590	0.4 ± 0.1 b	1.2 ± 0.3 ab	2.4 ± 0.5 a	<0.01
		52	Salvial-4(14)-en-1-one	1595	0.8 ± 0.1 b	1.5 ± 0.2 ab	2.4 ± 0.3 a	<0.001
		53	NI	1609	0.6 ± 0.2 b	1.1 ± 0.2 ab	1.9 ± 0.5 a	<0.05
		54	NI	1615	1.4 ± 0.2 b	2.8 ± 0.3 b	5.1 ± 0.8 a	<0.001
		55	NI	1620	0.7 ± 0.2	1.0 ± 0.5	0.8 ± 0.1	>0.05
		56	Germacrene D-4-ol	1623	0.3 ± 0.0 b	0.8 ± 0.2 b	2.1 ± 0.3 a	<0.001
		57	␥-Eudesmol	1634	0.2 ± 0.0 b	0.7 ± 0.1 b	1.3 ± 0.2 a	<0.001
		58	NI	1641	1.4 ± 0.3 b	9.5 ± 1.2 a	12.8 ± 1.3 a	<0.001
		59	␣-Muurolol	1645	0.3 ± 0.1 b	1.1 ± 0.1 ab	1.6 ± 0.3 a	<0.001
		60	Cedr-8(15)-en-10-ol	1650	0.5 ± 0.1 b	1.3 ± 0.3 ab	2.7 ± 0.4 a	<0.001
		61	␤-Eudesmol	1653	0.4 ± 0.0 b	2.0 ± 0.3 b	4.7 ± 0.5 a	<0.001
		62	NI	1657	2.0 ± 0.2 b	3.7 ± 0.8 b	10.2 ± 1.3 a	<0.001
		63	NI	1677	0.7 ± 0.3 b	2.3 ± 0.3 a	0.7 ± 0.1 a	<0.001
	Others	64	Hex-3-en-1-ol benzoate, (Z)-	1572	tr	0.5 ± 0.1	1.0 ± 0.1
		65	Actinolide, dihydro-	1530	2.0 ± 0.3	2.8 ± 0.3	2.3 ± 0.1

NI: non-identified; AI: arithmetic index of

[START_REF] Adams | Identification of Essential Oil Components by Gas Chromatography/Mass Spectrometry[END_REF]

calculated with the formula of

[START_REF] Van Den Dool | A generalization of the retention index system including linear temperature programmed gas-liquid partition chromatography[END_REF]

; tr: trace.

Acknowledgments

The authors gratefully acknowledge F. Torre for statistical analysis, R. Zergane of Beni Slimane and people of Laghouat and Bechar forestry conservation for their help in plant collection, and A. Tonetto for Scanning Electron Micrographs. The French and Algerian Inter-university Cooperation is also gratefully acknowledged for funding this work.


Andrea Costa
email: andrea.costa@pusan.ac.kr

Anne A Petrenko

Katell Guizien

Andrea M Doglioli

On the Calculation of Betweenness Centrality in Marine Connectivity Studies Using Transfer Probabilities

Betweenness has been used in a number of marine studies to identify portions of sea that sustain the connectivity of whole marine networks. Herein we highlight the need of methodological exactness in the calculation of betweenness when graph theory is applied to marine connectivity studies based on transfer probabilities. We show the inconsistency in calculating betweeness directly from transfer probabilities and propose a new metric for the node-to-node distance that solves it. Our argumentation is illustrated by both simple theoretical examples and the analysis of a literature data set.

Introduction

In the last decade, graph theory has increasingly been used in ecology and conservation studies [START_REF] Moilanen | On the limitations of graph-theoretic connectivity in spatial ecology and conservation[END_REF] and particularly in marine connectivity studies (e.g., [START_REF] Treml | Modeling population connectivity by ocean currents, a graph theoretic approach for marine conservation[END_REF] [3] [4] [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF] [START_REF] Rossi | Hydrodynamic provinces and oceanic connectivity from a transport network help desining marine reserves[END_REF]).

Graphs are a mathematical representation of a network of entities (called nodes) linked by pairwise relationships (called edges). Graph theory is a set of mathematical results that permit to calculate different measures to identify nodes, or set of nodes, that play specific roles in a graph (e.g., [START_REF] Bondy | Graph theory with applications[END_REF]). Graph theory application to the study of marine connectivity typically consists in the representation of portions of sea as nodes. Then, the edges between these nodes represent transfer probabilities between these portions of sea.

Transfer probabilities estimate the physical dispersion of propagula [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF] [START_REF] Berline | A connectivity-based ecoregionalization of the Mediterranean Sea[END_REF] [10] [START_REF] Jonsson | How to select networks of marine protected areas for multiple species with different dispersal strategies[END_REF], nutrients or pollutants [START_REF] Doglioli | Development of a numerical model to study the dispersion of wastes coming from a marine fish farm in the Ligurian Sea (Western Mediterranean)[END_REF], particulate matter [START_REF] Mansui | Modelling the transport and accumulation of floating marine debris in the Mediterranean basin[END_REF], or other particles either passive or interacting with the environment (see [START_REF] Ghezzo | Connectivity in three European coastal lagoons[END_REF] [START_REF] Bacher | Probabilistic approach of water residence time and connectivity using Markov chains with application to tidal embayments[END_REF] and references therein). As a result, graph theory already proved valuable in the identification of hydrodynamical provinces [START_REF] Rossi | Hydrodynamic provinces and oceanic connectivity from a transport network help desining marine reserves[END_REF], genetic stepping stones [START_REF] Rozenfeld | Network analysis identifies weak and strong links in a metapopulation system[END_REF], genetic communities [START_REF] Kininmonth | Determining the community structure of the coral Seriatopora hystrix from hydrodynamic and genetic networks[END_REF], sub-populations [START_REF] Jacobi | Identification of subpopulations from connectivity matrices[END_REF], and in assessing Marine Protected Areas connectivity [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF].

In many marine connectivity studies, it is of interest to identify specific portions of sea where a relevant amount of the transfer across a graph passes through. A well-known graph theory measure is frequently used for this purpose: betweenness centrality. In the literature, high values of this measure are commonly assumed to identify nodes sustaining the connectivity of the whole network. For this reason a high value of betweenness has been used in the framework of marine connectivity to identify PLOS 1/10 migration stepping stones [START_REF] Treml | Modeling population connectivity by ocean currents, a graph theoretic approach for marine conservation[END_REF], genetic gateways [START_REF] Rozenfeld | Network analysis identifies weak and strong links in a metapopulation system[END_REF], and marine protected areas ensuring a good connectivity between them [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF].

Our scope in the present letter is to highlight some errors that can occur in implementing graph theory analysis. Especially we focus on the definition of edges when one is interested in calculating the betweenness centrality and other related measures.

We also point out two papers in the literature in which this methodological inconsistency can be found: [START_REF] Kininmonth | Graph theoretic topology of the Great but small Barrier Reef world[END_REF] and [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF].

In Materials and Methods we introduce the essential graph theory concepts for our scope. In Results we present our argument on the base of the analysis of a literature data set. In the last Section we draw our conclusions.

Materials and Methods

A simple graph G is a couple of sets (V, E), where V is the set of nodes and E is the set of edges. The set V represents the collection of objects under study that are pair-wise linked by an edge a ij , with (i,j) ∈ V , representing a relation of interest between two of these objects. If a ij = a ji , ∀(i,j) ∈ V , the graph is said to be 'undirected', otherwise it is 'directed'. The second case is the one we deal with when studying marine connectivity, where the edges' weights represent the transfer probabilities between two zones of sea (e.g., [3] [4] [5] [START_REF] Rossi | Hydrodynamic provinces and oceanic connectivity from a transport network help desining marine reserves[END_REF]).

If more than one edge in each direction between two nodes is allowed, the graph is called multigraph. The number of edges between each pair of nodes (i,j) is then called multiplicity of the edge linking i and j.

The in-degree of a node k, deg + (k), is the sum of all the edges that arrive in k:

deg + (k) = i a ik . The out-degree of a node k, deg -(k)
, is the sum of all the edges that start from k: deg -(k) = j a kj . The total degree of a node k, deg(k), is the sum of the in-degree and out-degree of k: deg(k

) = deg + (k) + deg -(k).
In a graph, there can be multiple ways (called paths) to go from a node i to a node j passing by other nodes. The weight of a path is the sum of the weights of the edges composing the path itself. In general, it is of interest to know the shortest or fastest path σ ij between two nodes, i.e. the one with the lowest weight. But it is even more instructive to know which nodes participate to the greater numbers of shortest paths. In fact, this permits to measure the influence of a given node over the spread of information through a network. This measure is called betweenness value of a node in the graph. The betweenness value of a node k, BC(k), is defined as the fraction of shortest paths existing in the graph, σ ij , with i = j, that effectively pass through k,

σ ij (k), with i = j = k: BC(k) = i =k =j σ ij (k) σ ij (1)
with (i,j,k) ∈ V . Note that the subscript i = k = j means that betweenness is not influenced by direct connections between the nodes. Betweenness is then normalized by the total number of possible connections in the graph once excluded node k:

(N -1)(N -2)
, where N is the number of nodes in the graph, so that 0 ≤ BC ≤ 1.

Although betweenness interpretation is seemingly straightforward, one must be careful in its calculation. In fact betweenness interpretation is sensitive to the node-to-node metric one chooses to use as edge weight. If, as frequently the case of the marine connectivity studies, one uses transfer probabilities as edge weight, betweenness loses its original meaning. Based on additional details -personally given by the authors PLOS 2/10 of [START_REF] Kininmonth | Graph theoretic topology of the Great but small Barrier Reef world[END_REF] and [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF]-on their methods, this was the case in those studies. In those cases, edge weight would decrease when probability decreases and the shortest paths would be the sum of edges with lowest value of transfer probability. As a consequence, high betweenness would be associated to the nodes through which a high number of improbable paths pass through. Exactly the opposite of betweenness original purpose.

Hence, defining betweenness using Equation 1(the case of [START_REF] Kininmonth | Graph theoretic topology of the Great but small Barrier Reef world[END_REF] and [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF]) leads to an inconsistency that affects the interpretation of betweenness values.

Alternative definitions of betweenness accounting for all the paths between two nodes and not just the most probable one have been proposed to analyze graphs in which the edge weight is a probability [START_REF] Newman | A measure of betweenness centrality based on random walks[END_REF] and avoid the above inconsistency.

Herein, we propose to solve the inconsistency when using the original betweenness definition of transfer probabilities by using a new metric for the edge weights instead of modifying the betweenness definition. The new metric transforms transfer probabilities a ij into a distance in order to conserve the original meaning of betweenness, by ensuring that a larger transfer probability between two nodes corresponds to a smaller node-to-node distance. Hence, the shortest path between two nodes effectively is the most probable one. Therefore, high betweenness is associated to the nodes through which a high number of probable paths pass through.

In the first place, in defining the new metric, we need to reverse the order of the probabilities in order to have higher values of the old metric a ij correspond to lower values of the new one. In the second place we also consider three other facts: (i) transfer probabilities a ij are commonly calculated with regards to the position of the particles only at the beginning and at the end of the advection period; (ii) the probability to go from i to j does not depend on the node the particle is coming from before arriving in i; and (iii) the calculation of the shortest paths implies the summation of a variable number of transfer probability values. Note that, as the a ij values are typically calculated on the base of the particles' positions at the beginning and at the end of a spawning period, we are dealing with paths whose values are calculated taking into account different numbers of generations. Therefore, the transfer probabilities between sites are independent from each other and should be multiplied by each other when calculating the value of a path. Nevertheless, the classical algorithms commonly used in graph theory analysis calculate the shortest paths as the summation of the edges composing them (e.g., the Dijkstra algorithm, [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] or the Brandes algorithm [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF]).

Therefore, these algorithms, if directly applied to the probabilities at play here, are incompatible with their independence.

A possible workaround could be to not use the algorithms in [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] and [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF] and use instead the 10 th algorithm proposed in [START_REF] Brandes | On variants of shortest-path betweenness centrality and their generic computation[END_REF]. Therein, the author suggests to define the betweenness of a simple graph via its interpretation as a multigraph. He then shows that the value of a path can be calculated as the product of the multiplicities of its edges. When the multiplicity of an edge is set equal to the weight of the corresponding edge in the simple graph, one can calculate the value of a path as the product of its edges' weights a ij . However, this algorithm selects the shortest path on the basis of the number of steps (or hop count) between a pair of nodes (Breadth-First Search algorithm [START_REF] Moore | The shortest path through a maze[END_REF]). This causes the algorithm to fail in identifying the shortest path in some cases. For example, in Fig 1 it would identify the path ACB (2 steps with total probability 1 × 10 -8 ) when, instead, the most probable path is ADEB (3 steps with total probability 1 × 10 -6 ). See Table 1 for more details.

However, by changing the metric used in the algorithms, it is possible to calculate the shortest path in a meaningful way with the algorithms in [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] and [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF]. In particular, we propose to define the weight of an edge between two nodes i and j as:

Fig 1.
Example of graph in which the 10 th algorithm in [START_REF] Brandes | On variants of shortest-path betweenness centrality and their generic computation[END_REF] would fail to identify the shortest path between A and B (ADEB) when using a ij as metric.

d ij = log 1 a ij ( 2
)
This definition is the composition of two functions: h(x) = 1/x and f (x) = log(x).

The use of h(x) allows one to reverse the ordering of the metric in order to make the most probable path the shortest. The use of f (x), thanks to the basic properties of logarithms, allows the use of classical shortest-path finding algorithms while dealing correctly with the independence of the connectivity values. In fact, we are de facto calculating the value of a path as the product of the values of its edges.

It is worth mentioning that the values d ij = ∞, coming from the values a ij = 0, do not influence the calculation of betweenness values via the Dijkstra and Brandes algorithms. Note that d ij is additive:

d il + d lj = log 1 a il •a lj = log 1 aij = d ij ,
for any (i,l,j) ∈ V thus being suitable to be used in conjunction with the algorithms proposed by [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] and [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF]. Also, note that both a ij and d ij are dimensionless. Equation 2 is the only metric that allows to consistently apply the algorithms in [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] and [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF] to transfer probabilities. Other metrics would permit to make the weight decrease when probability increases: for example, 1

-a ij , 1/a ij , -a ij , log(1 -a ij ).
However, the first three ones do not permit to account for the independence of the transfer probabilities along a path. Furthermore, log(1 -a ij ) takes negative values as 0 ≤ a ij ≤ 1. Therefore, it cannot be used to calculate shortest paths because the algorithms in [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] and [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF] would either endlessly go through a cycle (see Fig 2a and

Results

The consequences of the use of the raw transfer probability (a ij ) rather than the distance we propose (d ij ) are potentially radical. To show this, we used 20 connectivity matrices calculated for [START_REF] Guizien | Vulnerability of marine benthic metapopulations: implications of spatially structured connectivity for conservation practice[END_REF]. They were calculated from Lagrangian simulations using a Table 1. Paths and respective probabilities, weights and hop count for the graph in In particular matrix #1 was obtained after a period of reversed (eastward) circulation. Indeed, this case of circulation is less frequent than the westward circulation [START_REF] Petrenko | Barotropic eastward currents in the western Gulf of Lion, north-western Mediterranean Sea, during stratified conditions[END_REF]. Matrices #14, #10 and #13 correspond to a circulation pattern with an enhanced recirculation in the center of the gulf. Finally, matrices #2, #3, #5, #6, #8, #9, #14, #16, #18, #19, #20 correspond to a rather mixed circulation with no clear pattern. The proportions of particles coming from an origin node and arriving at a settlement node after 3, 4 and 5 weeks were weight-averaged to compute a connectivity PLOS 5/10

-a ij ) Figure 2a ADEDE. . . DEB → 0 → -∞ ACFB (1 × 10 -3 ) 3 = 1 × 10 -9 -3 × 10 -3 Figure 2b ADEFB (1 × 10 -3 ) 4 = 1 × 10 -12 -4 × 10 -3 ACB (1 × 10 -3 ) 2 = 1 × 10 -6 -2 × 10 -3
matrix for larvae with a competency period extending from 3 to 5 weeks. Furthermore, it is expected to have a positive correlation between the degree of a node and its betweenness (e.g., [START_REF] Valente | How correlated are network centrality measures?[END_REF] and [START_REF] Lee | Correlations among centrality measures in complex networks[END_REF]). However, we find that the betweenness values, calculated on the 20 connectivity matrices containing a ij , have an average correlation coefficient of -0.42 with the total degree, -0.42 with the in-degree, and -0.39 with the out-degree. Instead, betweenness calculated with the metric of Equation 2 has an average correlation coefficient of 0.48 with the total degree, 0.45 with the in-degree, and a not significant correlation with the out-degree (p-value > 0.05). Fig 4, betweenness values of the 32 nodes calculated using the two node-to-node distances a ij and log(1/a ij ) are drastically different between each other. Moreover, in 10 out of 20 connectivity matrices, the correlation between node ranking based on betweenness values with the two metrics were not significant. In the 10 cases it was (p-value < 0.05), the correlation coefficient was lower than 0.6 (data not shown). Such partial correlation is not unexpected as the betweenness of a node with a lot of connections could be similar when calculated with a ij or d ij if among these connections there are both very improbable and highly probable ones, like in node 21 in the present test case. Furthermore, it is noticeable that if one uses the a ij values (Fig 4a ), the betweenness values are much more variable than the ones obtained using d ij (Fig 4b). This is because, in the first case, the results depend on the most improbable connections that, in the ocean, are likely to be numerous and unsteady.

As an example, in

As we show in

Conclusion

We highlighted the need of methodological exactness inconsistency in the betweenness calculation when graph theory to marine transfer probabilities. Indeed, the inconsistency comes from the need to reverse the probability when calculating shortest paths. If this is not done, one considers the most improbable paths as the most probable ones. We showed the drastic consequences of this methodological error on the analysis of a published data set of connectivity matrices for the Gulf of Lion [START_REF] Guizien | Vulnerability of marine benthic metapopulations: implications of spatially structured connectivity for conservation practice[END_REF].

On the basis of our study, it may be possible that results in [START_REF] Kininmonth | Graph theoretic topology of the Great but small Barrier Reef world[END_REF] and [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF] might also be affected. A re-analysis of [START_REF] Kininmonth | Graph theoretic topology of the Great but small Barrier Reef world[END_REF] would not affect the conclusions drawn by the authors about the small-world characteristics of the Great Barrier Reef as that is purely topological characteristics of a network. About [START_REF] Andrello | Low connectivity between Mediterranean Marine Protected Areas: a biophysical modeling approach for the dusky grouper: Epinephelus Marginatus[END_REF], according to Marco Andrello (personal communication), due to the particular topology of the network at study, which forces most of the paths -both probable or improbable-to follow the Mediterranean large-scale steady circulation (e.g., [START_REF] Pinardi | The physical and ecological structure and variability of shelf areas in the Mediterranean Sea[END_REF]). As a consequence, sites along the prevalent circulation pathways have high betweenness when using either a ij or d ij . However, betweenness values of sites influenced by smaller-scale circulation will significantly vary according to the way of calculating betweenness.

To solve the highlighted inconsistency, we proposed the use of a node-to-node metric that provides a meaningful way to calculate shortest paths and -as a consequencebetweenness, when relying on transfer probabilities issued from Lagrangian simulations and the algorithm proposed in [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] and [START_REF] Brandes | A faster algorithm for betweenness centrality[END_REF]. The new metric permits to reverse the probability and to calculate the value of a path as the product of its edges and to account for the independence of the transfer probabilities. Moreover, this metric is not limited to the calculation of betweenness alone but is also valid for the calculation of every graph theory measure related to the concept of shortest paths: for example, shortest cycles, closeness centrality, global and local efficiency, and average path length [START_REF] Costa | Tuning the interpretation of graph theory measures in analyzing marine larval connectivity[END_REF].

1 ADEB ( 1 × 10 - 2 ) 3 = 1 × 10 Fig 2 .

 1110231102 Figure 1

  Fig 3 we show the representation of the graph corresponding to matrix #7. The arrows starting from a node i and ending in a node j represent the direction of the element a ij (in Fig 3a) or d ij (in Fig 3b). The arrows' color code represents the magnitude of the edges' weights. The nodes' color code indicates the betweenness values calculated using the metric a ij (in Fig 3a) or d ij (in Fig 3b). In Fig 3a the edges corresponding to the lower 5% of the weights a ij are represented. These are the larval transfers that, though improbable, are the most influential in determining high betweenness values when using a ij as metric. In Fig 3b the edges corresponding to the lower 5% of the weights d ij are represented. These are the most probable larval transfers that -correctly-are the most influential in determining high betweenness values when using d ij as metric. While in Fig 3a the nodes with highest betweenness are the nodes 31 (0.26), 27 (0.25) and 2 (0.21); in Fig 3b the nodes with highest betweenness are nodes 21 (0.33), 20 (0.03) and 29 (0.03).

Fig 3 .Fig 4 .

 34 Fig 3. Representation of matrix #7 from [21], the right side colorbars indicate the metric values. a) Results obtained by using a ij as edge weight, b) results obtained by using d ij as edge weight. In a) the lowest 5% of edges weights are represented. In b) the lowest 5% of edges weights are represented. Note the change in the colorbars' ranges.

Table 2 )

 2 or choose the path with more edges (see Fig 2b and Table2), hence arbitrarily lowering the value of the paths between two nodes.

Table 2 .

 2 Paths and respective probabilities and weights for the networks in Fig 2.

	Path	Probability	Weight using log(1

Acknowledgments

The authors thank Dr. S.J. Kininmonth and Dr. M. Andrello for kindly providing the code they used for the betweenness calculation in their studies. The first author especially thanks Dr. R. Puzis for helpful conversations. Andrea Costa was financed by a MENRT Ph.D. grant. The research leading to these results has received funding from the European Union's Seventh Framework Programme for research, technological development and demonstration under Grant Agreement No. 287844 for the project 'Towards COast to COast NETworks of marine protected areas (from the shore to the high and deep sea), coupled with sea-based wind energy potential' (COCONET). The project leading to this publication has received funding from European FEDER Fund under project 1166-39417.