Urs ˇa Koce

Damijan Denac

Social foraging and habitat use by a long-distance passerine migrant, Whinchat Saxicola rubetra, at a spring stopover site on the SE Adriatic coast

Keywords: Whinchat (Saxicola rubetra), Spring migration, Social foraging, Habitat use, Effect of physiognomic habitat factors

The preference for foraging in groups and the effect of physiognomic factors of a habitat on its use by foraging Whinchats (Saxicola rubetra) was studied during spring migration stopover in a mosaic cultural landscape at the SE Adriatic coast. Every record of spatially distinct Whinchats, either a solitary individual or a group, was referred to as a Whinchat unit. The units were classified as intensively foraging, less intensively foraging or non-foraging and divided into four size classes. The effect of physiognomic habitat factors on use of habitat by foraging Whinchat units was modelled. All possible additive models using logit link function were constructed from five independent physiognomic variables: (1) natural perches (NP), (2) artificial perches (AP), (3) high herbal vegetation (HHV), (4) open bushes (OB) and (5) heterogeneity of vegetation types (HVT). Variables HHV and OB were included simultaneously in the models. Models that were substantially supported by the data were selected according to second order Akaike's information criterion AIC c . Two such models contained variable(s) (1) NP and (2) NP ? AP. The relative importance weights of physiognomic variables NP, AP, HVT, HHV and OB were 1, 0.38, 0.24, 0.13 and 0.13, respectively. Perches were thus the most important physiognomic habitat factor affecting habitat use by Whinchats in a mosaic cultural landscape. The great majority of Whinchats foraged in groups and the proportion of intensively foraging Whinchat units increased with unit size, leading to the conclusion that Whinchats preferred social to solitary foraging on the spring stopover at the SE Adriatic coast.

Introduction

Birds adapt their migration strategies mainly to minimise overall journey time, energy consumption or predation risk, or combinations of these [START_REF] Alerstam | Optimal bird migration: the relative importance of time, energy, and safety[END_REF].

Stopovers between migratory flights are essential for birds to refuel, take up water and rest [START_REF] Irwin | The migration ecology of birds[END_REF], but also account for the majority of time and energy spent on the entire migration (Hedenstro ¨m [START_REF] Hedenstro ¨m | Optimum fuel loads in migratory birds: distinguishing between time and energy minimization[END_REF][START_REF] Alerstam | The development of bird migration theory[END_REF][START_REF] Wikelski | Avian metabolism: costs of migration in free-flying songbirds[END_REF]. Stopover strategies that minimise these expenditures are therefore favoured in evolution. Behavioural responses such as social foraging [START_REF] Ekman | Avian flocking reduces starvation risk: an experimental demonstration[END_REF][START_REF] Szekely | Flocking behaviour of passerines: a dynamic model for the non-reproductive season[END_REF] and selection of high quality habitats [START_REF] Schaub | Fuel deposition of three passerine bird species along the migration route[END_REF] are involved in successful accomplishment of a stopover.

Presence of competitors limits the amount of food available to an individual but it can still be favourable for birds to forage in flocks. Potential payoffs of social foraging for a bird on migration are improved searching for food, enhanced capture and consumption of food, reduced time and energy costs of foraging or increased protection from predators [START_REF] Ekman | Avian flocking reduces starvation risk: an experimental demonstration[END_REF][START_REF] Giraldeau | Social foraging theory[END_REF]. Whinchats (Saxicola rubetra) are territorial in the breeding season and on the wintering grounds, but in the post-breeding season they form mixed flocks of adults and juveniles [START_REF] Bastian | Das Braunkehlchen: Opfer der ausgera ¨umten Kulturlandschaft[END_REF] and often forage in flocks during migration [START_REF] Glutz Von Blotzheim | Saxicola rubetra (Linnaeus 1758) -Braunkehlchen[END_REF]. There is some evidence that the foraging efficiency of Whinchats on autumn migration stopovers is higher in larger groups [START_REF] Draulans | Flock size and feeding behaviour of migrating whinchats Saxicola rubetra[END_REF], but it is unknown whether social foraging is advantageous and preferred to solitary foraging during spring migration, which is quicker than autumn migration [START_REF] Bastian | Das Braunkehlchen: Opfer der ausgera ¨umten Kulturlandschaft[END_REF], and where an effective time and energy use is expected.

Selection of habitat by birds at migration stopover sites is a complex decision-making process affected by several factors (Hutto 1985a;[START_REF] Maccarone | Foraging microhabitat selection by wading birds in a tidal estuary, with implications for conservation[END_REF][START_REF] Chernetsov | Habitat selection by nocturnal passerine migrants en route: mechanisms and results[END_REF]). Food abundance is of crucial importance (Bibby and Green 1981; [START_REF] Martin | Patch utilization by migrating birds: resource oriented?[END_REF][START_REF] Crawley | Habitat utilization by northern wheatears (Oenanthe oenanthe) stopping over on an offshore island during migration[END_REF], but the physiognomy of a microhabitat may be equally important for species with specific morphological or behavioural constraints [START_REF] Bairlein | Morphology -habitat relationships in migrating songbirds[END_REF][START_REF] Block | The habitat concept in ornithology: theory and applications[END_REF][START_REF] Chernetsov | Habitat selection by nocturnal passerine migrants en route: mechanisms and results[END_REF]. Intra-and interspecific interactions, particularly predation risk [START_REF] Suhonen | Predation risk influences the use of foraging sites by tits[END_REF][START_REF] Walther | The effects of food availability and distance to protective cover on the winter foraging behaviour of tits (Aves: Parus)[END_REF] and competition (Hutto 1985b;[START_REF] Martin | Patch utilization by migrating birds: resource oriented?[END_REF][START_REF] Yong | Stopover ecology and habitat use of migratory Wilson's warblers[END_REF], often influence selection of foraging habitat. Whinchats select specific habitats at migration stopover sites in European cultural landscapes [START_REF] Draulans | Flock size and feeding behaviour of migrating whinchats Saxicola rubetra[END_REF][START_REF] Bairlein | Habitat selection and associations of species in European passerine birds during southward, post-breeding migrations[END_REF][START_REF] Duckworth | Habitat selection by migrants redstarts Phoenicurus phoenicurus and whinchat Saxicola rubetra in lowland English farmland[END_REF]), but the specific environmental factors bearing on this selection are unknown.

The Whinchat breeds in the major part of Europe and northwest Asia and it winters in sub-Saharan Africa [START_REF] Bastian | Das Braunkehlchen: Opfer der ausgera ¨umten Kulturlandschaft[END_REF]. Migration through southeast Europe is largely unknown. Birds passing this region in spring are most probably travelling directly from northern Africa to the eastern part of the species' breeding range [START_REF] Glutz Von Blotzheim | Saxicola rubetra (Linnaeus 1758) -Braunkehlchen[END_REF]. West, central and some east European populations of Whinchats have declined substantially in the past decades (BirdLife International 2004). Loss of breeding habitats is recognised as the main cause for the decline, and attempts have been made to mitigate this process (Mu ¨ller et al. 2005;[START_REF] Britschgi | Impact of grassland farming intensification on the breeding ecology of an indicator insectivorous passerine, the whinchat Saxicola rubetra: lessons for overall Alpine meadowland management[END_REF][START_REF] Horch | Bestandsru ¨ckgang des Braunkehlchens Saxicola rubetra in der Schweiz, mo ¨gliche Ursachen und Evaluation von Fo ¨rdermassnahmen[END_REF]. Loss of high quality habitats at important stopover sites can substantially reduce the success of migration [START_REF] Moore | Habitat requirements during migration: important link in conservation[END_REF] and therefore add to the decline of populations. Basic information on habitat selection and life-history characteristics throughout the Whinchat's range is therefore needed for long-term conservation of the species [START_REF] Moore | Habitat requirements during migration: important link in conservation[END_REF][START_REF] Donovan | Modeling the ecological trap hypothesis: a habitat and demographic analysis for migrant songbirds[END_REF].

The aim of our study was (1) to test whether Whinchats favour social foraging during the spring migration stopover and how flocking affects their foraging activity in heterogeneous environment, and (2) to assess the importance of physiognomic habitat factors in Whinchats' foraging habitat selection in the mosaic cultural landscape on the SE Adriatic coast.

Methods

Study area

The study area was located in the mosaic cultural landscape of the Montenegrin coast in the hinterland of Velika plaz ˇa, a sandy beach extending 10 km south-eastwards from the city of Ulcinj (41.89°N, 19.30°E) (Fig. 1). The area is a part of the delta of the Bojana-Buna river, recently recognised as an area of great ecological value with an extraordinarily rich bird community (Schneider-Jacoby et al. 2006). Among 237 bird species recorded, 52 are regular passage migrants, including the Whinchat. The weather during the study period was rather constant, the majority of days being sunny with moderate winds and midday temperatures between 22 and 27°C.

Foraging and use of habitat by migrating Whinchats were studied at four plots, sized 14, 24, 31 and 31 ha (Fig. 1). Aerial distances between adjacent plots were 1.3, 0.7 and 0.8 km.

Whinchat censuses

The censuses of Whinchats were carried out between 5 and 24 April 2007, during the first half of the passage of the species through the region (S ˇtumberger, personal communication). A total of 54 complete plot censuses were carried out, starting between 0600 and 1800 hours and lasting 30-160 min at a single plot. The starting time of the censuses at each plot was varied in order to avoid time bias. The birds were counted and their sex determined from distances of at least 100 m, to avoid disturbance. Observations were made with 8 9 50 binoculars and a 20-609 spotting scope. We refer to every record of spatially distinct Whinchats, either a solitary individual or a group, as a Whinchat unit. The Whinchat units were classified according to the number of individuals in the unit as (1) solitary birds, (2) small groups (2-3 individuals), (3) medium groups (4-10 individuals) and (4) large groups (C11 individuals). Every Whinchat unit was observed for 5 min. Its activity during this interval was recorded and the exact area that it used was mapped (scale 1:3,000). The unit was classified as foraging if all individuals in the unit foraged within this interval or as non-foraging if none of the individuals foraged during this interval. No groups were encountered in which only some individuals foraged within the observation interval, although the intensity of foraging in some groups differed between individuals. We estimated overall foraging intensity of foraging units on ordinal scale: 1: less intensively foraging; 2: intensively foraging. The areas used by Whinchat units were digitised using GIS software ESRI ArcView 3.1. Three zones were defined within the study area, pooled for all observations:

(1) the foraging zone, used by Whinchat units for foraging, (2) the non-used zone where no Whinchat units were registered at any time of the censuses (forest fragments within the study plots were excluded) and (3) the non-foraging zone, used by non-foraging Whinchat units. During the observation interval some foraging Whinchat units moved across the habitat from one foraging patch to another, during which time their foraging activity ceased (see ''Discussion''). These transient areas were included in the non-foraging zone. The non-foraging zone comprised only 1% of total study area and was not included in further analysis.

Habitat data

Eight habitat types were defined and mapped at the study plots. Their areas were obtained in GIS (Table 1). Fortythree non-overlapping sampling squares with 30-m sides were placed at random in the study area using GIS. According to the case-control design [START_REF] Hosmer | Applied logistic regression analysis[END_REF][START_REF] Keating | Use and interpretation of logistic regression in habitat-selection studies[END_REF], 16 sampling squares were placed within the foraging zone and 27 within the non-used zone. The following physiognomic variables of habitat were mapped within the sampling squares between 25 and 28 April: (1) natural perches (NP), (2) artificial perches (wire fence) (AP) and (3) vegetation types. Three distinct vegetation types were recognised: high herbal vegetation (HHV), low herbal vegetation (LHV) and open bushes (OB). Maps were digitised in GIS, and surface areas of vegetation types and lengths of wire fence were obtained.

The physiognomic variables were used in microhabitat analysis as independent (predictor) variables. The variable NP was quantified as the abundance of outstanding plant stems and small individual isolated bushes (at least 30% above the rest of vegetation). The abundance was estimated in the field according to the following ordinal scale: 0: no natural perches; 1: some natural perches; 2: considerable amount of natural perches; 3: many natural perches. The variable AP was quantified as the length of wire fence inside a sampling square. The lengths were classified to six length classes: 0: 0 m; 1: 1-10 m; 2: 11-20 m; 3: 21-30 m; 4: 31-40 m; 5: 41-50 m. The vegetation types (HHV, LHV, OB) were quantified as surface areas in square metres. HHV was defined as herbal vegetation which was generally higher than 20 cm, LHV as herbal vegetation which was generally lower than 20 cm and OB as herbal vegetation overgrown with bushes which covered at least 25% of the patch surface. When the bushes were isolated and covered less than 25% of the patch surface, they were classified as natural perches (NP) within HHV or LHV.

Data analysis

Using v 2 test, we tested whether time of the day, date, habitat type or unit size affected a Whinchat unit's foraging activity (no foraging/less intensive foraging/intensive foraging). Furthermore, using the Cochran-Mantel-Haenszel test, we tested whether there was a difference in the proportion of foraging units between solitaries and groups, after controlling for habitat type. The data used in the test were: foraging (yes/no) and habitat type as control factors, and unit size (solitary/group) as an additional control factor. Three habitat types where 85% of the Whinchat units foraged (OPED, EXPA and INPA), and two classes of units: (1) solitary and (2) group (joint size classes 2-3, 4-10 and 11-29) were used in the analysis. Following [START_REF] Block | The habitat concept in ornithology: theory and applications[END_REF], our study was carried out at macrohabitat and microhabitat spatial levels. At the macrohabitat level, we tested whether Whinchat units used habitat types according to their availability, using v 2 test. Furthermore, we did all possible pairwise comparisons of habitat types according to use by Whinchat units, using v 2 tests with Bonferonni correction. Only those habitat types which exceeded 10% of the total study area (OPED, FOED, EXPA and INPA) were included in this analysis.

At the microhabitat level, we modelled the use of a patch (represented by a sampling square) by foraging Whinchats in relation to physiognomic variables. Modelling was carried out in R software using the informationtheoretic approach [START_REF] Burnham | Model selection and multimodel inference. A practical information-theoretic approach[END_REF] and was considered exploratory. Information in the data was modelled with logistic regression (logit link function) since the dependent variable (Ufor-use of a patch by foraging Whinchats) was binary (used/not used) and independent variables (physiognomic variables) were continuous and discrete [START_REF] Tabachnick | Using multivariate statistics[END_REF]. Besides the five physiognomic variables obtained in the field (NP, AP, HHV, LHV and OB), an additional independent variable Shannon-Wiener index was calculated from the proportions of vegetation types in a sampling square [START_REF] Krebs | Ecological Methodology[END_REF] and was used as index of heterogeneity of vegetation types (HVT). We calculated variance inflation factors (VIF)scaled versions of the multiple correlation coefficients between each of the six variables and the rest of the independent variables-to detect potential multicolinearity between the independent variables. Where VIF was larger than 10 or the tolerance value was less than 0.1, the variable was excluded [START_REF] Montgomery | Introduction to regression analysis[END_REF][START_REF] Neter | Applied linear statistical models[END_REF][START_REF] Lo ´pez-Lo ´pez | Modelling breeding habitat preferences of Bonelli's eagle (Hieraaetus fasciatus) in relation to topography, disturbance, climate and land use at different spatial scales[END_REF]). According to these criteria, the variable LHV was excluded from further analysis.

Using the five remaining independent variables (Fig. 2), all possible additive models and the null model (intercept only) were constructed. Both vegetation types (HHV ? OB) were included simultaneously in models, thus 16 models were constructed (Table 2). All models were ranked according to the second-order information criterion AIC c , since the ratio n/K was 8.6. Likelihoods and probabilities (w i ) were calculated for all models, and relative variable importance (w ? (j)) was calculated for each variable in the set of models. AIC c differences (D i ), relative to the smallest AIC c value in the set of models, were used as criteria for model selection and inference [START_REF] Burnham | Model selection and multimodel inference. A practical information-theoretic approach[END_REF][START_REF] Johnson | Model selection in ecology and evolution[END_REF].

Goodness-of-fit of the global model (Ufor * HHV ? OB ? NP ? AP ? HVT) was calculated using nonparametric bootstrap [START_REF] Crawley | Habitat utilization by northern wheatears (Oenanthe oenanthe) stopping over on an offshore island during migration[END_REF]. The rank of deviance of the global model was determined in sorted deviances of simulated models (100 bootstraps) and proved a good model fit (P = 0.22) and justified inference from reduced models. Since we used a random case-control sampling Fig. 2 Differences in physiognomic variables between the area used by Whinchats (Saxicola rubetra) for foraging (black boxes) and unused area (empty boxes). The boxes are quartiles, are whiskers minima and maxima, and the squares inside the boxes are medians. Units for LHV, HHV and OB are m 2 9 0.01 design, we interpret parameter estimates of selected models in terms of odds ratios [START_REF] Keating | Use and interpretation of logistic regression in habitat-selection studies[END_REF].

Results

We recorded 71 Whinchat units (47 foraging, 24 non-foraging). Percentages of solitary birds, small, medium and large Whinchat groups were 22, 30, 37 and 11%, respectively. The total number of observed Whinchats was 365 (261 males, 104 females). Minimum, maximum and average numbers of Whinchats in a unit were 1, 29 and 5.1 ± 0.6 (SD), respectively. A total of 96% of all observed Whinchats were members of groups of different sizes and 4% were solitaries, while 87% of all observed Whinchats belonged to foraging groups (7% to small groups, 46% to medium groups, 34% to large groups) and 1% were foraging solitaries, with 12% being non-foraging Whinchats, mainly solitaries and members of small groups.

There was a strong association between foraging activity of units and their size (v 2 = 32.16, df = 6, P \ 0.001; Fig. 3). There was no association between foraging activity of units and hours (v 2 = 15.40, df = 22, P = 0.844) nor between foraging activity of units and days during the study (v 2 = 33.5, df = 30, P = 0.300). The selected habitat types did not differ significantly between intensively foraging, less intensively foraging and non-foraging Whinchat units (v 2 = 8.66, df = 8, P = 0.371). There was a significant difference in the proportion of foraging units between the solitaries and groups, after controlling for habitat type (v 2 MH = 15.210, df = 1, P \ 0.001). In each of the three habitat types (OPED, EXPA and INPA), the proportions of foraging to non-foraging solitaries were smaller than proportions of foraging to non-foraging groups. Whinchats significantly selected particular habitats and avoided others (v 2 = 42.06, df = 3, P \ 0.001; Fig. 4). The most preferred habitat type was open edge. Surface areas of the foraging, non-foraging and non-used zones were 6, 1 and 89 ha, respectively. The remaining 4 ha within the study area (100 ha) were forest islands.

Of the physiognomic variables, the natural and artificial perches best predicted the use of a patch by foraging Whinchats. In the set of models, two were supported substantially by the data (D i B 2), five considerably less well supported (2 \ D i B 7), and nine essentially not supported by the data (D i [ 7) (Table 2). The predictor variables for the presence of foraging Whinchat units were, in order of importance, NP, AP, HVT, HV and OB, with relative importance weights 1, 0.38, 0.24, 0.13 and 0.13, respectively. Increase of the parameter value of the most important variable NP by one level means four times the odds that the habitat is selected by a Whinchat unit for foraging (Table 3).

Discussion

The great majority of Whinchats foraged in groups, indicating the preference for social foraging on spring migration. Small passerine birds travel at night solitarily or in very loose associations [START_REF] Bruderer | The study of bird migration by radar. Part 2: major achievements[END_REF]). The groups of Whinchats observed on the Montenegrin coast had therefore most probably formed at the stopover site in order to forage socially. Most of the medium and large groups foraged intensively, while high proportions of solitaries and small groups foraged less intensively or did not forage at all. These individuals were either less successful in finding a food-rich patch or were momentarily not motivated for foraging. Although the primary goal of birds on migration stopover is refuelling, they also spend time on other activities (e.g. resting, being cautious, defending temporary territories) [START_REF] Dierschke | Time allocation in migrating northern wheatears (Oenanthe oenanthe) during stopover: is refuelling limited by food availability or metabolically?[END_REF]. It is possible that the non-foraging solitaries and small groups in our study were the newcomers having a rest after a long non-stop flight [START_REF] Euronatur | Do migratory birds need a nap after long non-stop flight?[END_REF]) and which had not yet encountered their congeners to join for active foraging. [START_REF] Draulans | Flock size and feeding behaviour of migrating whinchats Saxicola rubetra[END_REF] reported that foraging intensity of individual Whinchats was higher in larger groups in homogenous environment. They suggested that foraging Whinchats flush the insects which become available to other group members and this enhances their foraging intensity. Whinchats at the Montenegrin stopover tended to maximise foraging intensity through social foraging since most of medium and large groups foraged intensively. However, medium groups were much more common than large groups and more individuals were members of medium groups. If foraging intensity of the Whinchat groups in our study was dependent only on group size, like in the study of [START_REF] Draulans | Flock size and feeding behaviour of migrating whinchats Saxicola rubetra[END_REF], then Whinchats would tend to forage in large groups. Unlike the study of Draulans and van Vessem, our study was done in a heterogeneous environment. We suggest that, regarding the intensity of foraging, the optimal Whinchat foraging group size also depends on abundance and distribution of food in the environment. However, we do not have any data on insect abundance in our study sites to support this hypothesis. The groups can change in size during the stopover, since there are no tight bonds between individuals [START_REF] Bastian | Das Braunkehlchen: Opfer der ausgera ¨umten Kulturlandschaft[END_REF].

Perches are used by Whinchats for singing and foraging and have been shown to be a limiting factor in the settlement of Whinchats on the breeding grounds [START_REF] Labhardt | Siedlungsstruktur von Braunkelchen-Populationen auf zwei Ho ¨henstufen der Westschweizer Voralpen[END_REF][START_REF] Oppermann | Suitability of different vegetation structure types as habitat for the whinchat (Saxicola rubetra)[END_REF][START_REF] Bastian | Das Braunkehlchen: Opfer der ausgera ¨umten Kulturlandschaft[END_REF]. Whether they also influence the distribution of Whinchats at migration stopover sites has, however, not been Fig. 4 Expected and observed use of habitat types by Whinchat units. Expected frequencies were calculated from proportions of available habitat types (see Table 1 for habitat type codes) determined. We argue that the intensive pastures at the Montenegrin coast were avoided due to lack of perches and not because of poor insect availability. Regular observation in this habitat type of other foraging migrating insectivore passerines (Northern Wheatears Oenanthe oenanthe, Yellow Wagtails Motacilla flava), which normally forage by pecking, suggests that the invertebrate food was also present on intensive pastures. Open edge and extensive pastures, both characterised by abundant perches, were selected preferentially by Whinchat units. We propose that the perches are an important cue for habitat selection and an important feature for habitat exploration by Whinchats within the stopover site. When the Whinchat groups moved across the habitat they consistently used perches. Some groups were observed moving across habitat in such a manner that individuals alternated in making short flights between natural perches or along the wire fence. From time to time some of them performed foraging flights which indicated scanning of the microhabitat for food. When the group encountered a suitable patch (probably assessed as high frequency of food items encountered), it stopped, started to forage intensively and stayed there for some time (even an hour or more). Specific vegetation types (HHV, OB) did not affect foraging patch selection. The type of herbal vegetation cover is important in Whinchats' choice of habitat during the breeding season, because it provides proper cover for the nest [START_REF] Oppermann | Suitability of different vegetation structure types as habitat for the whinchat (Saxicola rubetra)[END_REF][START_REF] Denac | Populacijska dinamika repaljs ˇc ˇice (Saxicola rubetra) v mozaiku niz ˇinskih habitatnih tipov[END_REF]. We expected that the heterogeneity of vegetation types (HVT) would positively affect the selection of a foraging patch, because the abundance of grassland invertebrates is usually higher in heterogeneous than in homogenous herbal layers [START_REF] Dennis | Distribution and abundance of small insects and arachnids in relation to structural heterogeneity of grazed, indigenous grasslands[END_REF][START_REF] Britschgi | Impact of grassland farming intensification on the breeding ecology of an indicator insectivorous passerine, the whinchat Saxicola rubetra: lessons for overall Alpine meadowland management[END_REF]). However, the models that contained this variable were less supported by the data and the importance of HVT relative to the most important variable (NP) was fairly low.

We conclude that Whinchats at the spring migration stopover site on the Montenegrin coast prefer social to solitary foraging. When they remain solitary or in very small groups, it is most probably because they have not encountered congeners. We also propose that perches are an essential habitat feature, substantially affecting habitat use and foraging patch selection by Whinchats in mosaic cultural landscapes on migration stopovers. Other physiognomic factors of open grasslands are likely to be important only to the extent to which they affect invertebrate abundance. The conservation efforts at Whinchat stopover sites should aim at preserving invertebrate rich habitat types with abundant perches and the presence of open edge. This can be achieved through extensive pasture characterised by low grazing density and small pastures lined off with wire fence and hedgerows. NP ? AP. Die relativen Gewichtungen der physiognomischen Variablen NP, AP, HVT, HHV und OB betrugen 1, 0,38, 0,24, 0,13 und 0,13. Sitzpla ¨tze waren daher die wichtigsten physiognomischen Habitatfaktoren, welche die Habitatnutzung durch Braunkehlchen in einer Mosaik-Kulturlandschaft beeinflussten. Die große Mehrheit der Braunkehlchen suchte in Gruppen nach Futter, und der Anteil intensiv nach Futter suchender Braunkehlchen-Einheiten nahm mit der Gro ¨ße der Einheit zu. Dies fu ¨hrte zu der Schlussfolgerung, dass Braunkehlchen am Fru ¨hjahrs-Rastplatz an der su ¨dostadriatischen Ku ¨ste die soziale der individuellen Futtersuche vorzogen.

Fig. 1

 1 Fig. 1 Left Adriatic region and location of the study area (circle). Right Part of the delta of Bojana-Buna river and positions of study plots (A-D)

Fig. 3

 3 Fig. 3 Proportions of intensively foraging, less intensively foraging and non-foraging Whinchat units in relation to unit size. The numbers in the bars are the frequencies of observed Whinchat units

Zusammenfassung

  Soziale Futtersuche und Habitatnutzung bei einem langstreckenziehenden Sperlingsvogel, dem Braunkehlchen Saxicola rubetra, an einem Fru ¨hjahrs-Rastplatz an der su ¨dostadriatischen Ku ¨ste Die Vorliebe fu ¨r die Futtersuche in Gruppen und der Einfluss physiognomischer Faktoren eines Habitats auf seine Nutzung durch futtersuchende Braunkehlchen (Saxicola rubetra) wurde wa ¨hrend einer Rast auf dem Fru ¨hjahrszug in einer Mosaik-Kulturlandschaft an der su ¨dostadriatischen Ku ¨ste untersucht. Jede Erfassung einzelner Braunkehlchen oder ra ¨umlich abgegrenzter Braunkehlchen-Gruppen wurde als eine Braunkehlchen-Einheit betrachtet. Die Einheiten wurden als intensiv nach Futter suchend, weniger intensiv nach Futter suchend oder nicht nach Futter suchend klassifiziert und in vier Gro ¨ßenklassen aufgeteilt. Der Einfluss physiognomischer Habitatfaktoren auf die Habitatnutzung durch futtersuchende Braunkehlchen-Einheiten wurde modelliert. Alle mo ¨glichen additiven Modelle, die eine Logit-Link-Funktion benutzen, wurden aus fu ¨nf unabha ¨ngigen physiognomischen Variablen erstellt: (a) natu ¨rliche Sitzpla ¨tze (NP), (b) ku ¨nstliche Sitzpla ¨tze (AP), (c) hochwu ¨chsige krautige Vegetation (HHV), (d) offenes Gestra ¨uch (OB) und (e) Heterogenita ¨t der Vegetationstypen (HVT). Die Variablen HHV und OB wurden gleichzeitig in die Modelle aufgenommen. Anhand von Akaikes Informationskriterium zweiter Ordnung AICc. wurden die Modelle ausgewa ¨hlt, die von den Daten am besten gestu ¨tzt wurden. Zwei dieser Modelle enthielten die Variable(n) (a) NP und (b)

Table 1

 1 Definitions, general characteristics, areas and proportions of the habitat types at the study plots

	Habitat type code	Habitat type	Definition	General characteristics	ha	%
	EXME	Extensive meadow	Mown once a year, no mineral	Abundant natural perches, high	8.3	8
			fertilisers	diversity of plant species
	INME	Intensive meadow	Mown more than once a year,	No or very few perches, low	4.2	4
			mineral fertilisers	diversity of plant species
	EXPA	Extensive pasture	Pasture with low grazing density	High physiognomic heterogeneity,	12.8	13
			(cattle, sheep or both)	natural perches present in low to
				high abundance
	INPA	Intensive pasture	Pasture with high grazing density	Very low vegetation (grazed),	29.8	30
			(cattle, sheep or both)	physiognomic homogeneity, no
				or very few perches
	ARLA	Arable land	Ploughed field	No plants, bare ground-soil	1.2	1
	OPED	Open edge	30-m-wide band on the borders	Wire fences or hedgerows, high	21.3	21
			between pastures and/or	physiognomic heterogeneity
			meadows
	FOED	Forest edge	30-m-wide band along forest	Immediate proximity of forest	17.5	18
			patches
	FOFR	Forest fragment	Patch of forest inside cultivated	Deciduous tree species	4.0	4
			area

Table 2

 2 Logistic regression models with physiognomic variables as independent variables predicting use of a patch by foraging Whinchats (Saxicola rubetra)

		Model	K	AIC c	D i	Model likelihood	w i
	1	NP	2	46.255	0.00	1.000	0.41
	2	N P1 AP	3	47.180	0.93	0.630	0.26
	3	HVT ? NP	3	48.553	2.30	0.317	0.13
	4	HVT ? NP ? AP	4	49.612	3.36	0.187	0.08
	5	HHV ? OB ? NP	4	49.888	3.63	0.163	0.07
	6	N P? AP ? HHV ? OB	5	51.273	5.02	0.081	0.03
	7	HHV ? OB ? HVT ? NP	5	52.355	6.10	0.047	0.02
	8	HHV ? OB ? NP ? AP ? HVT	6	53.763	7.51	0.023	0.01
	9	AP	2	58.375	12.12	0.002	0.00
	10	Null	1	58.863	12.61	0.002	0.00
	11	HVT	2	59.928	13.67	0.001	0.00
	12	HVT ? AP	3	60.165	13.91	0.001	0.00
	13	HHV ? OB	3	62.676	16.42	0.000	0.00
	14	HHV ? OB ? AP	4	62.750	16.50	0.000	0.00
	15	HHV ? OB ? HVT	4	64.644	18.39	0.000	0.00
	16	HHV ? OB ? HVT ? AP	5	65.133	18.88	0.000	0.00

The models with substantial support from the data are in bold K Number of estimable parameters in model, AIC c a second-order Akaike's information criterion, D i AIC c differences, relative to the smallest AIC c value in the set of models, w i Akaike weights NP natural perches, AP artificial perches, HHV high herbal vegetation, LHV low herbal vegetation, OB open bushes, HVT heterogeneity of vegetation types

Table 3

 3 Coefficients and odds ratios for models with substantial support from the data

	Model	Variable in the model
		NP		AP		Intercept
		b	exp (b)	b	exp (b)
	NP	1.471	4.35			-3.321
	NP ? AP	1.437	4.21	0.278	1.32	-3.523

J Ornithol (2010) 151:655-663

Acknowledgments

The study was supported by the Slovenian Research Agency, through the programme of financing the postgraduate education of junior researchers, and by Euronatur foundation. We thank the Montenegrin National Institute for Protection of Nature for enabling us to carry out the fieldwork. We thank Borut S ˇtumberger and Tomaz ˇSkrbins ˇek for advice during the research and to dr. Reto Spaar, dr. Davorin Tome and an anonymous reviewer for their valuable comments on the manuscript.


A Dawiec

B Dinkespiler

P Breugnon

K Arnaud

P.-Y Duval

S Godiot

S Hustache

K Medjoubi

Jean-François Bérar

Nathalie Boudet

Development of a PCI Express Based Readout Electronics for the XPAD3 X-Ray Photon Counting Image

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

HE XPAD3 camera is a large surface silicon photon counting detector (12 x 7.5 cm 2 ) developed at CPPM to meet the requirement of experiments on high flux [START_REF] Pangaud | XPAD3-S: A fast hybrid pixel readout chip for X-ray synchrotron facilities[END_REF] and high brilliance 3 rd generation synchrotron sources and on low dose photon counting cone beam (CB) CT [START_REF] Pangaud | XPAD3: a new photon counting chip for X-ray CT-scanner[END_REF][START_REF] Brunner | Imaging performance of the hybrid pixel detector XPAD3-S[END_REF]. The detector is composed of eight tiled modules operating in parallel in order to obtain a large detection surface with minimal dead areas. Essential features of the detector are its energy thresholds that can be set individually for every pixel and its fast data acquisition system that can read out the complete detector every 2 ms without dead-time. Three complete detectors were assembled at CPPM.

In this paper, we describe the readout architecture of the XPAD3 camera based on a PCI Express interface and present preliminary scans obtained with a monochromatic beam at ESRF and a polychromatic beam from a X-ray tube manufactured by RTW.

II. XPAD3 HYBRID PIXEL DETECTOR

The XPAD3 detector is a hybrid pixel detector built of eight modules, each composed of seven XPAD3 photon counting circuits [START_REF] Pangaud | First results of XPAD3, a new photon counting chip for X-ray CT-scanner with energy discrimination[END_REF] connected to a 500 µm thick silicon sensor (Fig. 2). The concept of the XPAD3 detector is shown in Fig. 1. The sensor is connected to its electronic readout circuit using flipchip and bump bonding technologies. Both the sensor and its readout chips are pixelized with the same pitch and each one of the sensor pixels is connected to a pixel of the electronic readout circuit. I. Every pixel has a 12 bits counter with overflow. Reading the overflow at a higher rate than the counter actually fills up allow to increase the dynamics of the counter almost without limitations, but the depth of the software encoding.

III. READOUT ARCHITECTURE OF THE IMAGER

The readout architecture of the imager can be divided into three main blocks: the XPAD3 detector, a HUB board and a PCI Express interface, which is connected to a PC running the data acquisition (DAQ) software. A detector simplified architecture is presented in Fig. 3. Fig. 4 shows a picture of the detector mounted on a goniometer at the synchrotron SOLEIL.

A. The XPAD3 Detector Eight independent modules, each of them being connected to its own readout electronics, form the XPAD3 camera. The electronic boards of the modules can configure the XPAD3 circuits with calibration data, process on the fly the overflow bit during exposition, read the counters of the pixels and organize the image data in a format preselected by the user (counts per pixel stored on 2 or 4 bytes). Furthermore, a gate signal may be generated locally in the board or can be provided by an external source. The detector bias voltage and the analog calibration pulses are distributed individually to every electronic board.

B. The HUB Board

The HUB board stays midway within the detector readout chain. All messages between the DAQ software and the detector modules pass trough the HUB board.

C. PC with PCI Express Board

In order to read out the detector as fast as possible, a PCI Express interface is used to transfer the data arriving from the HUB board directly to the computer embedded memory. A PCI Express x8 (8 lanes) in 1.1 standard is used. It has a theoretical bandwidth of 32 Gbits/s of un-encoded data (before 8b/10b encoding). In order to fully benefit from the high bandwidth of the PCI Express link, we use direct memory access (DMA) to transfer data from the PCI Express interface to the PC's memory. Table II The PCI-E board includes a FPGA chip connected to several SFP optical transceivers. The FPGA embedded system comprises a PCI Express controller, a DMA engines (reading and writing) and a data management unit. The DMA transfer configurations (address and size) are stored in a set of local registers that can be dynamically changed by the software application. The data from the optical fibers are first deserialized and stored in the reception buffer. Then the DMA transfer is stored to the address specified in the register as soon as the buffer has received the data size set by the user. The implemented setup allows to send data from the complete detector to the PC in 2 ms. Today the size of the RAM embedded in the PC limits the size of the image sequence that can be acquired. In the future, compression, fast disk storage or network distribution could release this limitation.

IV. PRELIMINARY SCANS

The specification of the XPAD3 camera, its programmable thresholds, its high count rate dynamics and fast data readout makes it a suitable device for experiments in the fields of crystallography and small animal imaging capable of capturing dynamic processes.

In Fig. 5, the result of powder diffraction is presented. The thresholds of the detector were set at 8 keV and the detector was exposed to a 16 keV beam over 100 s. Debye rings resulting from the diffraction of the X-rays on a silver behenate (AgBe) powder are clearly visible.

As an illustration, Fig. 6 shows the result of a CB CT scan of a gecko acquired with the XPAD3 camera using a RTW Mo target X-ray tube operated at 40 kV [START_REF] Nicol | Design and condtructon of the ClearPET/XPAD small animal PET/CT scanner[END_REF]. In order to obtain a pseudo-monochromatic beam strongly peaked around 17 keV, a Nb/Mo filter was inserted in between the X-ray tube and the object under study.

V. CONCLUSION

The architecture of the XPAD3 detector and the results obtained so far with this device open the possibility to make series of experiments which were hardly feasible up to now. Moreover parallel readout of the detection modules makes it possible to scale it up to larger detectors without loss in image acquisition speed.

  Development of a PCI Express based Readout Electronics for the XPAD3 X-Ray Photon Counting Imager A. Dawiec, B. Dinkespiler, P. Breugnon, F. Bompard, K. Arnaud, P.-Y. Duval, S. Godiot, S. Hustache, K. Medjoubi, J.-F. Berar, N. Boudet, C. Morel Abstract-XPAD3 is a large surface X-ray photon counting imager with high count rates, large counter dynamics and very fast data readout. Data are readout in parallel by a PCI Express interface using DMA transfer. The readout frame rate of the complete detector comprising 0.5 MPixels amounts to 500 images per second without dead-time.

Fig. 1 .

 1 Fig. 1. Scheme of the XPAD3 hybrid pixel detector: a silicon sensor is connected to the electronic readout circuit using flip-chip and bump bonding technologies

Fig. 2 .

 2 Fig. 2. Picture of a module of the XPAD3 camera made of a pixelized silicon sensor comprising 67'200 pixels connected to seven XPAD3 chips The XPAD3 chip has been designed in IBM 0.25 µm technology. It is composed of 9'600 pixels organized in 80 columns of 120 rows. The detector specifications are summarized in TableI. Every pixel has a 12 bits counter with overflow. Reading the overflow at a higher rate than the counter actually fills up allow to increase the dynamics of the counter almost without limitations, but the depth of the software encoding.

TFig. 3 .

 3 Fig. 3. Architecture of the XPAD3 detector

  Eight modules are connected to this board via a set of flat copper cables. Communication with the PC is done trough a pair of optical fibers. The data from the DAQ are first decoded according to the addresses encoded in the data frames. Each one of the detector modules writes its data to dedicated buffers implemented on the HUB board. The HUB selector then sequentially extracts and sends them to the PCI Express interface via two optical fibers. Besides detector data management functions, the HUB board can operate communication diagnostic tests and distribute external gate signals to every module in order to perform time resolved experiments.

Fig. 4 .

 4 Fig. 4. Picture of the XPAD3 camera mounted on a goniometer at the synchrotron SOLEIL.

Fig. 5 .

 5 Fig. 5. Diffraction rings on a powder of silver behenate (AgBe) recorded at ESRF using a monochromatic beam of 16 keV X-rays

Fig. 6

 6 Fig. 6 Volume renderings of a CB CT scan of a gecko.

TABLE I .

 I SPECIFICATIONS OF THE XPAD3 CAMERA

	Number of pixels	537'000
	Pixel size	130 x 130 µm 2
	Counter depth	12 bits + overflow
	Readout time	2 ms
	Maximum count rate	10 6 photons/pixel/s
	On the fly readout	Yes
	Discrimination mode	Single leading edge threshold
	Minimum threshold	~ 4 keV

  summarizes measured data rates over PCI Express 1.1 x8 during DMA data transfer.

TABLE II .

 II PCI-E MEASURED DATA RATES

	Writing (DAQ to PCI-E):	500 MBytes/s
		500 images/s
	Reading (PCI-E to DAQ):	1000 MBytes/s
		1000 images/s


M Piraud

P Lugan

P Bouyer

A Aspect

L Sanchez-Palencia

Localization of a matter wave packet in a disordered potential

Keywords: numbers: 05.60.Gg, 72.15.Rn, 67.85.-d, 03.75.-b

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.

The field of Anderson localization (AL) is attracting considerable attention and produced landmark results in the recent years [1]. In this respect, quantum gases stimulate intensive experimental and theoretical research. On one hand, they offer unprecedented control of their parameters, and novel measurement tools [2], which, for instance, paved the way to the direct observation of onedimensional (1D) AL of matter waves [3,4]. On the other hand, they sustain original effects, which require special analysis in its own right [5][6][7].

In weak disorder, AL is due to the interference of waves multiply scattered from random defects, which results in absence of diffusion and spatially localized wavefunctions [8]. The paradigmatic signature of AL is obtained from the average logarithm of the transmission of a wave of energy E through a disordered region. In 1D, it is a self-averaging quantity characterized by the exponential decay ln |ψ E (z)| 2 ≃ -2γ(E)|z|, with γ(E) the Lyapunov exponent (inverse localization length) [START_REF] Lifshits | Introduction to the Theory of Disordered Systems[END_REF]. The localization of a wave packet is a more complicated issue as it is determined by the superposition of many energy components. Since the latter cannot be separated from each other, the relevant quantity is rather the average of the localized density profile, n(z) = |ψ(z)| 2 , which is not selfaveraging [START_REF] Lifshits | Introduction to the Theory of Disordered Systems[END_REF]. Moreover, each energy component localizes exponentially with its own localization length, and the superposition of all their contributions can lead to nonexponentially decaying density profiles [5,[START_REF] Skipetrov | [END_REF].

Localization of wave packets is for instance relevant to experiments where a Bose-Einstein condensate (BEC) propagates in a disordered potential [3]. The situation is modeled by the following scenario [5,11]: A nondisordered, interacting BEC (with initial healing length ξ in ) is first released from a trap. It expands in free space and its initial interaction energy is converted into kinetic energy. At a given time t i , a speckle potential (with correlation length σ R ) is switched on and the interactions off. This creates a wave packet with a broad energy distribution. The energy components are then independent and eventually localize exponentially in the disordered potential, which results in the localization of the matter wave. For ξ in > σ R , recent experiments report an exponential decay of the density profile, in fair agreement with the prediction of the above scenario [3,12]. The data however suggest deviations from exponential decay in the wings, the origin of which remains to be elucidated.

Here, we revisit the theoretical model for AL of matter wave packets in 1D disorder. Beyond previous models, our approach allows us to include (i) the phase-space density of the matter wave at time t i , and (ii) the spectral broadening induced by the disorder. We show that these ingredients significantly affect the predicted density profile of the localized matter wave at both short and long distances. It predicts a complex behavior of the density profile, which significantly deviate from pure exponential decay. Our results are confirmed by large-scale and long-time numerical calculations. They shed new light on the AL of matter wave packets, in particular on the experiments of Refs. [3,12].

We consider a 1D matter wave subjected to a harmonic trap and a disordered potential, with repulsive shortrange interactions. In the weakly interacting regime (i.e. for large enough 1D density, n ≫ mg/ 2 , where m is the atomic mass and g is the coupling parameter), its dynamics is governed by the Gross-Pitaevskii equation,

i ∂ t ψ = -( 2 /2m)∂ 2 z + V ho (z) + V (z) + g|ψ| 2 -µ ψ, ( 1
)
where µ is the chemical potential, the wavefunction is normalized to the total number of atoms ( dz|ψ| 2 = N ), V ho (z) = mω 2 z 2 /2 is the trapping potential, and V (z) is the disordered potential. The latter is assumed to be stationary with a null ensemble average, V = 0. It is characterized by the correlation function C(z) = V (z ′ )V (z ′ + z). Hereafter, the quantities V R and σ R denote the amplitude and correlation length of the disorder (see below for precise definitions). We define the healing length of the trapped BEC by ξ in ≡ / √ 4mµ. In the following, we study the average density profile: n(z, t) = Tr[ρ(t)n(z)], with ρ, the one-body density matrix and n(z) = δ(zẑ), the spatial density operator.

Following the scenario of Refs. [5,11], an interact-ing BEC is first produced in the harmonic trap and in the absence of disorder. For interactions strong enough that n ≫ ω/g [Thomas-Fermi regime (TF)], the phase is uniform and the density profile is a truncated inverted parabola, n 0 (z) = (µ/g)[1 -(z/L TF ) 2 ] ⊕ , where L TF = 2µ/mω 2 and [f (z)] ⊕ = f (z) for f (z) > 0 and 0 otherwise. Then, an expanding matter wave is produced by switching off the trap (V ho → 0) at time t = 0. We assume that, in the first expansion stage (0 ≤ t ≤ t i ), the disordered potential is still off, so that the density matrix at time t i is pure state: ρ(t i ) = |ψ i ψ i |, where ψ i (z) = e iθi(z) n i (z) is determined by the integration of Eq. ( 1) with V ≡ 0. The solution reads [13]

n i (z) = n 0 z/b(t i ) /b(t i ) and θ i (z) = mz 2 ḃ(t i )/2 b(t i ), (2)
where the scaling parameter is the unique solution of b

(t)[b(t) -1] + ln[ b(t) + b(t) -1] = √ 2ωt [14]. For t ≫ 1/ω, we have b(t) ≃ √ 2ωt + (1/2)[1 -ln(4 √ 2ωt)
]. The second expansion stage (t > t i ) starts when the disorder is suddenly switched on and the interactions off (V ≡ 0 and g → 0). Then, Eq. ( 1) reduces to the linear Schrödinger equation of Hamiltonian Ĥ = -2 ∂ 2 z /2m + V (z) with the initial state given by Eq. ( 2) at time t i . Turning to the Heisenberg picture, we get:

n(z, t) = Tr[ρ(t i )n(z, t -t i )]. (3)
We now treat the initial state of the second expansion stage semiclassically and apply the substitution ρ

(t i ) → dzdE δ(z -ẑ)N (E) -1 f i (z, E)δ(E -Ĥ)
, where N (E) is the density of states per unit length associated to the Hamiltonian Ĥ above and f i (z, E) represents the probability density to find an atom at position z with energy E [START_REF]We may use alternative semi-classical approaches. For instance, the Wigner distribution provides similar results[END_REF]. Inspection of Eq. ( 2) legitimizes the semi-classical approximation: The initial state is characterized by the velocity field v i (z) ≡ ( /m)∂ z θ i = z ḃ(t i )/b(t i ), associated to the local de Broglie wavelength λ dB (z) ≡ /mv i (z) ∼ t i /mz for t i ≫ 1/ω, and we find λ dB (z) ≪ n i /|∂ z n i |, except in a small region of width ∆z ∼ ξ in near the edges of the BEC. For t i ≫ 1/ω, we can then use the phase-space distribution

W i (z, p) ≃ n i (z) × δ p -mv i (z) , i.e. W i (z, p) ≃ D i (p) × δ z -b(t i )/m ḃ(t i ) p (4)
where

D i (p) = 3N /4p m (t i ) [1-(p/p m (t i )) 2 ] ⊕ is the mo- mentum distribution, with p m (t i ) ≡ ( /ξ in )( ḃ(t i )/ √ 2ω) [16]
. Averaging over the disorder, we can then write

f i (z, E) ≃ dp W i (z, p)A(p, E)
, where A(p, E) = -Im p G(E) p /π is the spectral function, which represents the probability density that a particle in the state of momentum p, |p , has energy E in the disorder. Here, G(E) = [E -Ĥ + i0 + ] -1 is the retarded Green operator associated to Hamiltonian Ĥ at energy E [START_REF] Skipetrov | [END_REF]. In order to evaluate the BEC density, we finally insert these formulas into the rhs term of Eq. (3) [17], which yields

n(z, t) = dz i dE dp W i (z i , p)A(p, E)P (z -z i , t -t i |E) (5) with P (z-z i , τ |E) ≡ N (E) -1 Tr[δ(E -Ĥ)n(z, τ )δ(z i -ẑ)].
The quantity P (z -z i , t-t i |E) is interpreted as the probability of quantum diffusion, that is the probability density to find in z at time t, a particle of energy E that was located in z i at time t i [START_REF] Berezinskii | [END_REF]. Equation ( 5) allows us to determine the density profile of the matter wave packet. Our approach goes beyond that of Ref. [5]. It allows us to take into account (i) the initial position distribution and (ii) the spectral broadening A(p, E) of a particle of momentum p in the disordered potential [19]. We will show below that both play a significant role in the localization process.

In order to calculate the average spectral function, we solve the Dyson equation,

G = G 0 + G 0 ΣG, where G 0 (E) = [E -p2 /2m + i0 + ] -1 is the free Green op- erator and Σ(E) = Σ ′ (E) + iΣ ′′ (E) is the self-energy, both in the retarded form. For V 2 R ≪ E 3/2 E 1/2 c
where

E c ≡ 2 /2mσ 2 R [i.e. γ(E) ≪ p E / ], we find [20] A(p, E) = (-1/π) Σ ′′ (E, p) E -p 2 /2m -Σ ′ (E, p) 2 + Σ ′′ (E, p) 2 (6)
with Σ(E, p) ≃ p V G 0 (E)V p Performing the integration, we get the explicit formula

Σ ′′ (E, p) ≃ -(m/2 p E ) C(p E -p) + C(p E + p) (7)
where C(p) ≡ dz C(z) exp(-ipz/ ) is the Fourier transform of the correlation function, and p E ≡ √ 2mE is the momentum associated to energy E in free space. The real-part of the self-energy, Σ ′ (E, p) = dq 2π C(qp) × PV 1 E-q 2 /2m with PV the Cauchy principal value, turns out to be negligible and we disregard it in the remainder of this work.

In order to calculate the probability of quantum diffusion, we rely on the diagrammatic method developed in Refs. [START_REF] Berezinskii | [END_REF][START_REF] Gogolin | [END_REF]. In the weak disorder limit (γ(E) ≪ σ -1 R , p E / ), it provides the infinite-time limit [22]

P ∞ (z|E) = π 2 γ(E) 8 ∞ 0 du u sinh(πu) 1 + u 2 1 + cosh(πu) 2 ×exp -(1 + u 2 )γ(E)|z|/2 (8)
with the Lyapunov exponent

γ(E) ≃ (m 2 /2 2 p 2 E ) C(2p E ). ( 9
)
We now compare the predictions of our analytical model to the results of numerical calculations. In order to integrate Eq. ( 1), we use a Crank-Nicolson algorithm, with space step ∆z = 0.1σ R and time step ∆t = 0.05 /E c , in a box with Dirichlet boundary conditions [23]. The disorder is a 1D speckle potential, which can be written in the form V (z) = V R × {v(z) -v}, where v(z) ≥ 0 represents the speckle intensity pattern and the sign of V R depends on the detuning of the laser light with respect to the atomic resonance: V R > 0 for blue detuning, and V R < 0 for red detuning [START_REF] Goodman | Speckle Phenomena in Optics: Theory and Applications[END_REF][START_REF] Clément | [END_REF]. We use parameters close to those of Ref. [3] and both blue and red detunings (V R = ±0.0325E c ). In both cases, the correlation function reads

C(p) = πV 2 R σ R [1 -|p|σ R /2 ] ⊕ , (10)
in Fourier space. Our numerical calculations differ from those of Ref. [5] in that we use significantly larger boxes and longer times. Moreover, we consider here exactly the above scenario where the disorder is switched on and the interactions off at a time t i ≫ 1/ω, while in the numerics of Ref. [5], both disorder and interactions were on during the whole expansion. Due to the cutoffs of C(p) at p = ±2 /σ R , the quantities γ(E) and P ∞ (z|E) vanish for E > E c and it is useful to distinguish two cases for the analysis of the density profiles. Case 2µ < E c (i.e. ξ in > σ R ) -The left panel of Fig. 1 shows the time evolution of the density profile in semi-logarithmic scale for ξ in > σ R . For t < t i ≡ 10/ω [Fig. 1(a1)], the matter wave expands in free space, with the shape of a truncated inverted parabola of increasing size, according to Eq. ( 2). When the disorder is switched on and the interactions off, the matter wave continues expanding and develops long wings [Fig. 1(a2)]. In the long-time limit [Fig. 1(a3)], the density profile converges to a stationary shape, hence demonstrating AL. The localized density profile is in fair agreement with the theoretical prediction based on Eq. ( 5), using Eqs. ( 4), ( 6) and ( 8) for the correlation function [START_REF] Skipetrov | [END_REF], with a global multiplying factor as the only fitting parameter [see the solid black line in Fig. 1(a3)]. This holds over the full space, except very close to the center. There, for the chosen parameters, Eq. ( 5) predicts a nonphysical dip due to the overestimation of the Lyapunov exponents and the spectral broadenings at low energies in the lowest-order perturbation theory used to derive Eqs. ( 6) and ( 8). This dip affects the balance between the center and the wings in the normalization of the wavefunction, which justifies the multiplying factor to correctly fit the wings. These results validate the localization model of the matter wave.

Let us now discuss the density profile in more detail, and accordingly examine the impact of the various terms in Eq. ( 5). For |z| b(t i )L TF , the stationary density profile is mainly determined by particles originating from the BEC at time t i that propagate over very short distances in the disordered potential. Using the full phase-space distribution W i (z, p) is then necessary to account for the central feature of the density profile. For |z| b(t i )L TF only, we can neglect the initial density distribution and rely on the approximation W i (z, p) → D(p) × δ(z) in Eq. ( 5). For b(t i )L TF |z| 1/2γ(2µ), we find that the density profile shows an essentially exponential decay of rate approximately equal to 2γ(2µ) [see the dashed green line in Fig. 1(a3)]. This is consistent with experimental observations [3]. For longer distances however, the logarithmic derivative of the density continuously decreases in modulus. Neglecting the spectral broadening induced by the disorder [5,11], A(p, E) → δ(E -p 2 /2m), we are able to reproduce the numerical results over about five decades [see the dotted black line in Fig. 1(a3)]. This approximation cuts all components with E > 2µ and predicts a long-distance exponential decay of rate γ(2µ)/2 [5,22]. This behavior can be understood on the basis of the probability of quantum diffusion (8), which continuously interpolates from d ln P ∞ (z|E)/dz ≃ -2γ(E) for |z| ≪ 1/2γ(E) to d ln P ∞ (z|E)/dz ≃ -γ(E)/2 for |z| ≫ 2/γ(E) [START_REF] Gogolin | [END_REF]. For |z| ≫ 2/γ(2µ), the numerics show significant deviation from exponential decay, owing to the Lorentzian-like form of the spectral function ( 6) which populates components with E > 2µ. Then, taking into account the full spectral function, Eq. ( 5) fits the numerics well [see the solid black line in Fig. 1(a3)]. Finally, note that our model relies on the Born approximation which is not sufficient to account for components with E > E c [6]. To do so, it would be necessary to include arbitrary high-order terms at arbitrary large distances. It however appears irrelevant in the space window used for the numerics.

Case 2µ > E c (i.e. ξ in < σ R ) -The right panel of Fig. 1 shows the counterpart of the left panel for ξ in < σ R and in log-log scale. In this regime too, the complete model of Eq. (5) reproduces well the numerical results over the full space (except very close to the center), with a multiplying factor as the only fitting parameter [see the solid black line in Fig. 1(b3)]. In 1D speckle potentials, the correlation function provides a high-momentum cutoff which strongly suppresses backscattering of matter waves with momentum p > /σ R [5,6]. For E > E c , the Lyapunov exponent, calculated in the Born approximation then vanishes [see Eq. ( 9)], and the determination of P ∞ (z|E) would require an extension of the formalism of Refs. [START_REF] Berezinskii | [END_REF][START_REF] Gogolin | [END_REF] by at least two orders in perturbation theory. Using the results of Refs. [6] based on the phaseformalism approach, we estimate that, for our parameters, the Lyapunov exponent drops by about two orders of magnitude around E ≃ E c and we neglect localization of waves with E > E c . Since E c < 2µ, the spectral broadening has little importance here and we can safely rely on the approximation A(p, E) → δ(E-p 2 /2m). The above model then predicts algebraic localization, n(z) ∝ 1/|z| 2 [5]. Fitting an algebraic function, A/|z| β with A and β as fitting parameters, to the numerical data of three different realizations of blue-and reddetuned speckle potentials in the intervals [-30, -10] and [+10, +30] independently, we find β ≃ 1.91 ± 0.22. This is in fair agreement with the analytical prediction (within the error bars) and was observed in Ref. [3].

In summary, we have developed a theoretical model for the AL of a matter wave packet with initial healing length ξ in in a 1D speckle potential with correlation length σ R . It extends previous approaches by including (i) the initial phase-space density of the matter wave, and (ii) the spectral broadening induced by the disorder. We have shown that these ingredients affect the localized density profiles, which significantly deviate from a pure exponential decay. For 2µ < E c , we found that n(z) essentially shows an exponential decay of rate 2γ(2µ) at short distance, in accordance with experimental observations [3]. For larger distance, n(z) crosses over to an exponential decay of rate γ(2µ)/2 and then deviates from exponential decay due to the disorder-induced spectral broadening. This may explain the very large distance behavior of experimental data [3,12]. For 2µ > E c , we found algebraic localization, n(z) ∝ 1/|z| 2 , as observed in Ref. [3].

In the future, it would be interesting to extend the present approach toward two directions. First, our analysis relies on the calculation of the probability of quantum diffusion, P ∞ (z|E), to lowest order, which is valid only below the effective mobility edge at E = E c [6]. Extending the diagrammatic method of Refs. [START_REF] Berezinskii | [END_REF][START_REF] Gogolin | [END_REF] to higher orders would allow one to incorporate the components of energy E > E c . In addition, it may explain the slight difference in the localized density profiles found for blue-and red-detuned speckle potentials [see Fig. 1(a3)]. Second, although ultracold atoms allow for an exact realization of the above scenario using time-dependent control of optical disorder and of interactions via Feshbach resonance techniques, recent experiments have followed a slightly different scheme where the BEC is created already in the presence of the disorder and the interactions are not switched off [3,12]. Extending our model to this case would require one to include (i) the effect of the disorder at t 1/ω, which can significantly modify the relevant phase-space density W i (z, p) and (ii) the effect of interactions in the probability of quantum diffusion P ∞ (z|E). Whether and how interactions destroy localization in this scheme is still a very debated subject [26].

Figure 1 .

 1 Figure 1. (color online) Time evolution of the density profile of a matter wave expanding in 1D speckle potentials for 2µ < Ec (left panel) and 2µ > Ec (right panel). Shown are the running averages, ñ(z) = +l/2 -l/2

We thank Peter Schlagheck, Luca Pezzé, Dominique Delande, Georgy Shlyapnikov and Randy Hulet for stimulating discussions.

This research was supported by the European Research Council (FP7/2007-2013 Grant Agreement No. 256294), Agence Nationale de la Recherche (ANR-08-blan-0016-01), Ministère de l'Enseignement Supérieur et de la Recherche, Triangle de la Physique and Institut Francilien de Recherche sur les Atomes Froids (IFRAF). We acknowledge GMPCS high performance computing facilities of the LUMAT federation.


Companyo Beltran

V Jiménez

R Companyó

Jacinto Guiteras
email: jacinto.guiteras@ub.edu

Preparation of quality control materials for the determination of sulfonamides in animal feed

Keywords: Chromatographic analysis, HPLC Additives/Contaminants: Veterinary drug residues -antibiotics, Veterinary drugs Sulfonamides, animal feed, reference material, quality control material, liquid chromatography

Preparation of quality control materials for the determination of sulfonamides in animal feed

Jacinto Guiteras, Vanesa Jimenez, R.

Introduction

Food safety includes all steps in the food production chain. In the case of food from animal origin, it covers from the feed the cattle are given through to the final products reaching the consumers. In the European Union, the use of antimicrobial agents in animal feeds is regulated by law. At present, the use of antibiotics as growth promoters is forbidden (EC No 1831/2003), as they can be directly related with a detected increase in cases of resistance to antimicrobial drugs employed in medicine [START_REF] Turnidge | Antibiotic use in animals-prejudices, perceptions and realities[END_REF][START_REF] Phillips | Antibiotic use in animals[END_REF][START_REF] Emborg | Use of antimicrobial agents and occurrence of antimicrobial resistance in bacteria from food animals, foods and humans in Denmark[END_REF]. This is why animal feeds can only contain antibiotics for therapeutic or prophylactic reasons. Medicated feeds, which contain active principles at therapeutic levels, are prepared under veterinary prescription from authorised medical pre-mixtures that comply to the requirements of European Directive 90/167 (EC No 90/167 1990).

Medicated feeds are prepared in the same production lines as regular feeds, and this leads to a high risk of carry-over, as antibiotic concentrations in medicated feed are quite high (100-1000 µg g -1 ) and full elimination of their residues before switching back to a normal production is very difficult. This kind of contamination may affect cattle producers, as the consumption of feed that has become contaminated with antibiotic residues by animals about to be slaughtered may lead to food products containing concentrations exceeding the corresponding Maximum Residue Limits (MRLs). Moreover, the presence of antimicrobial residues in food of animal origin can also come from fraudulent uses of medicated feeds, and in order to detect these illegal practices, sanitary authorities carry out compulsory inspections in farms, in which samples of feeds are taken.

Ensuring safety in this first stage of the food chain requires reliable and rugged analytical methodology, suitable for an efficient control of the presence of antibiotics in animal feed. In order to validate analytical methods, or to control the quality of the analytical results, the availability of reference materials (RM) is a key point. These materials can also be used in intercomparison exercises for the external assessment of laboratory quality. Due to the variety and complexity of the matrices found in feeds, RMs must be as similar as possible to the samples analysed, both in matrix composition and analyte concentration. Additionally, analytes should have been incorporated in the same way as at industrial level.

Because of the variety in the characteristics and in the applications of RM, there is some confusion in the terminology used to designate them (Quevauviller 1999; [START_REF] Walker | Pitfalls in terminology and use of reference materials[END_REF]Zschunke 2000;Barwick 2001;[START_REF] Emons | Reference materials: terminology and use. Can't one see the forest for the trees?[END_REF]). In the present paper, the terms proposed by Emons et al. [START_REF] Emons | Reference materials: terminology and use. Can't one see the forest for the trees?[END_REF]) are used. According to this terminology, quality control materials (QCMs) intended for the statistical control of the quality of the analytical results were prepared. These materials can also be used for method development and validation and as samples for interlaboratory comparisons. Although certified reference materials (CRMs) are at the top of the metrological hierarchy, their scarcity in most areas of food analysis means that QCM must frequently be used. Moreover, QCMs can be prepared in such a way that they match the samples analysed by a laboratory, or a group of laboratories, better than the commercially available CRMs. Additionally, they are a lower cost alternative when frequent use is required.

The objective of the research work described in this paper has been to study the feasibility of the preparation of two QCMs, consisting of an animal feed used for pig rearing spiked with two sulfonamides: sulfadiazine (SDZ) and sulfadimidine (SDD). The drugs have been spiked at several concentration levels, representing what can be found in a medicated feed (500 µg g -1 ) and in a drug-free feed that has been contaminated during the fabrication process (2 and 5 µg g -1 ).

Sulfonamides are among the most widely used veterinary drugs in the European Union. In Spain, only two of them, sulfadiazine (SDZ) and sulfadimidine (SDD), can be added to medicated pre-mixtures, and they are mainly used for pig rearing. This is why they have been selected for the preparation of the QCMs. In recent years, several analytical methods for the determination of antimicrobials in animal feed have been proposed. In the case of sulfonamides, the methods found in the literature for their analysis in feeds are scarce and quite old [START_REF] Stringham | Use of post-column derivatization in liquid chromatographic determination of sulfamethazine and sulfathiazole in feeds and feed premixes[END_REF][START_REF] Torel | Determination of oxytetracycline, sulfamethazine and sulfamethoxypyridazine in feed premixes[END_REF][START_REF] Smallidge | Sulfamethazine and sulfathiazole determination at residue levels in swine feeds by reverse-phase liquid chromatography with post-column derivatization[END_REF]. They are based on HPLC with spectrometric detection at 254 nm or at 450 nm, after derivatization with dimethylaminobenzaldehide, the target compounds being SDD, sulfathiazole and sulfamethoxipyridazine. An ELISA screening assay for SDD in feeds has also been proposed [START_REF] Dixon-Holland | Competitive direct enzyme-linked immunosorbent screening assay for the detection of sulfamethazine contamination of animal feeds[END_REF]. More recently, a collaborative study, launched by AOAC, on the determination of SDD in swine and cattle feed was carried out [START_REF] Albert | Determination of sulfamethazine in swine and cattle feed by reversed-phase liquid chromatography with post-column derivatization: collaborative study[END_REF]. In the present work, the analytical methodology required for the determination of the concentrations of SDZ and SDD for the assessment of the homogeneity and stability of the prepared QCMs has been developed and validated.

Materials and methods

Chemicals and solutions

Sulfadiazine and sulfadimidine , Vetranal grade, supplied by Riedel-de Haën (Buchs, Switzerland), Fluorescamin, ≥99,0%, supplied by Fluka (Buchs, Switzerland), acetonitrile and methanol, LC gradient grade (Merck, Darmstadt, Germany), and doubly de-ionised water (Milli-Q, Millipore, Molsheim, France) of 18.2 mΩ cm -1 resistivity were used. All other reagents were of analytical reagent grade.

Stock solutions (50 mg l -1 ) of each sulfonamide in methanol were prepared monthly from the solid compounds. Standard solutions were freshly prepared by dilution of the stock solutions with the mobile phase (LC-UV method) or acetonitrile (LC-fluorescence method). A 0.2% (w/v) fluorescamine solution in acetonitrile was prepared daily.

Mobile phases of several compositions were prepared by mixing acetonitrile with the appropriate volumes of 0.01 mol l -1 acetic acid/sodium acetate or 0.01 mol l

Animal feed

Pig-rearing feeds were kindly supplied by the Associació Catalana de Fabricants de Pinsos (ASFAC). They were not granulated and were used as received. On arrival, they were stored at 4º C in PVC flasks. Information about their composition is shown in Figure 1a. Particle size distribution was determined by sample sieving, and the obtained curve is shown in Figure 1b. Feed moisture, determined as the weight loss at 103ºC for 4 hours, was about 11%.

Apparatus

Chromatographic analysis was carried out in a Shimadzu system (Kyoto, Japan) consisting of a LC-10AD VP quaternary pump, a SIL-10AD VP automatic injector, a SPD-M10A VP diode array detector with deuterium and tungsten lamps and a RF-10A XL fluorescence detector with a 150 w Xenon lamp. The analytical column was a Supelcosil (Bellefonte, PA, USA) LC-PAH RP-18 column (150 mm × 4.6 mm, 5 µm particle-size), equipped with a Supelcoguard LC-18 2 cm guard column.

For microwave assisted extraction, a Milestone ETHOS E system (Sorisole, Italy) was used. It consists of a microwave unit designed for extraction with organic solvents, a twelve-position segmented rotor (MPR-600/12S), twelve teflon vessels (100 ml) with magnetic stirring, an optical-fibre temperature probe and an ETHOS E 320 touch-screen terminal.

Mechanical shaking was carried out with a Breda 34526 (Breda Scientific, Breda, Netherlands) rotary mixer. A Heraeus Christ Labofuge 400 centrifuge (Osterode am Harz, Germany), with a 600 -6000 rpm speed range, was used. The pH was measured with a Crison GLP21 pH-meter (Alella, Spain) equipped with a Crison 52-02 Ag/AgCl combined glass electrode. For the preparation of the QCM, two cylindrical PVC containers of five and ten litres, respectively, were used. Ceramic balls (3 cm diameter) were mixed with the feed to ease the homogenization process. The containers were placed on a specially designed roller table (Metalitzats Cat, Barcelona, Spain) that makes controlled rotation speed possible.

Procedures

Determination by HPLC with ultraviolet detection

Feed (1 g) and acetonitrile (10 ml) were placed in the reactors of the microwave system and kept at 110º C for 20 min with magnetic stirring. After allowing the system to cool, the resulting mixture was transferred to a centrifuge tube and centrifuged at 3500 r.p.m. for 7 min. Aliquots of the clear extracts thus obtained were diluted ten-fold with acetonitrile/0.01 mol l -1 acetic acid/acetate buffer (13:87) mobile phase. The resulting solutions were filtered through a 0.45 µm nylon membrane and injected into the chromatographic system.

The gradient elution program used was as follows: keep a 13:87 mixture of acetonitrile and 0,01 mol l -1 acetic acid-sodium acetate buffer solution (pH 4.7) for 4 min, switch to a 10:90 ratio and maintain it up to minute 10, return to the initial composition and equilibrate for 5 min.

The mobile phase flow rate was 1 ml min -1 , the injection volume was 20 µl and the diode array detector was set at 268 nm.

Determination by liquid chromatography with fluorimetric detection.

Sulfonamides were extracted from the feed as described in section "Determination by liquid chromatography with ultraviolet detection". Feed extract (1 ml) or 1 ml of a standard solution in acetonitrile were mixed in an amber-coloured vial with 2 ml of formic acid-sodium formiate aqueous buffer solution (pH 3.4) and 1 ml of 0.2% fluorescamine solution in acetonitrile. The mixture was left to stand at least 2 hours at room temperature, filtered through a 0.45 µm nylon membrane and 50 µl were injected into the chromatographic system. An isocratic elution with a 29:71 mixture of acetonitrile and 0.01 mol l -1 formic acid-sodium formiate buffer at pH 3.4 was used. The mobile phase flow rate was 1.2 ml min -1 . The fluorescence detector was set at λ exc : 405 nm and λ em : 485 nm. The fluorescence of the derivatised sulfonamides remained constant for about 8 h.

Preparation of the quality control material

The schema followed is shown in Figure 2. For the preparation of the 500 µg g -1 material, 1.5 g of sulfadiazine (SDZ) and of sulfadimidine (SDD) were mixed with 3 Kg of animal feed. The mixture was placed in a PVC flask containing ceramic balls and made to roll on a rolling table for at least 90 hours. Homogeneity was checked by periodically taking samples from different parts of the material and determining the concentration of the sulfonamides by liquid chromatography with UV detection. After the homogeneity of the material was confirmed, 100 g were taken and diluted with 900 g of animal feed to obtain the 50 µg g -1 material. Homogenization and homogeneity checking of this material were made as previously described.

In the subsequent step, 300 g of the 50 µg g -1 material were mixed with 2.7 Kg of feed to obtain the 5 µg g -1 QCM, while 120 g were mixed with 2.88 Kg of feed to obtain the 2 µg g -1 QCM. Homogenization was as previously explained. After checking their homogeneity, both QCMs were placed in shuttered, screw-stopped, ambercoloured glass-flasks, each containing 10 g of material. After testing the homogeneity of the bottled materials, 10 flasks of each QCM were stored at three different temperatures (room temperature, 4ºC and -20ºC) and their stability was tested for 18 months. Samples of the homogeneity and stability studies of the 2 and 5 µg g -1 materials were analysed by a liquid chromatography with fluorimetric detection method.

Results and discussion

Analytical methodology

The objective of this part of the work was to optimize and validate an as simple as possible methodology for the determination of SDZ and SDD in feed samples coming from the homogeneity and stability studies included in the preparation of QCMs. The concentration levels of sulfonamides present in medicated or contaminated feeds are high enough to make a dilution of the extracts before injection in the chromatographic system possible. This avoids a clean-up step, which would have lengthened the analysis and increased their cost.

Liquid chromatography-UV detection

Mixtures of acetonitrile and aqueous acetic acid-sodium acetate buffers have been frequently used as mobile phases for the analysis of sulfonamides by LC-UV. In the present research work, the composition of the mobile phase has been optimised for the analytes of interest. Acetic acid-sodium acetate buffer solutions at pH 3.5, 4 and 4.7 were tested, using a 20:80 acetonitrile/buffer solution mixture. No influence of pH on sulfonamide retention time was detected. A pH of 4.7 was used for further work, to take advantage of the higher buffer capacity. Acetonitrile percentage was varied between 30% and 10%. A 22:78 acetonitrile /acetic acid-sodium acetate buffer mobile phase was initially selected, as this led to good analyte separation and short analysis times.

However, when blank feed extracts were injected in these experimental conditions, two peaks having virtually the same retention times as the sulfonamides were observed. Different mobile phase compositions were tested again and the problem was solved with a gradient that decreased acetonitrile percentage in the mobile phase from 13% to 10% between minutes 4 and 5. No significant matrix interferences were observed in these conditions. In Figure 3 (a andb) the chromatograms of a standard solution and of extracts of a blank and a spiked feed are shown.

Six standard solutions of SDZ and SDD, with concentrations ranging from 50 to 1000 µg l -1 were injected in these conditions. Plots were linear for both SDZ (r=0.9998) and SDD (r=0.9995). The relative standard deviations of the slopes of calibration lines obtained in four different days were 4% for SDZ and 6% for SDD. From the injection of six standards of 250 µg l -1 , in conditions of repeatability, the precision of retention time (< 1%) and peak areas (2% -3%) was assessed. Limits of detection (LOD) and limits of quantification (LOQ) were calculated on the basis of 3 and 10 times, respectively, the standard deviation of the base line of the chromatographed blank feed extract, using low concentration standard solutions. LOD and LOQ values are shown in Table 1. Therefore, liquid chromatography with UV detection at 268 nm offers the sensitivity and precision required for the analysis of samples of feeds spiked with SDZ and SDD at 50 and 500 µg g -1 .

Liquid chromatography-fluorimetric detection

A method described in a previous paper [START_REF] Raich-Montiu | Analysis of trace levels of sulfonamides in surface water and soil samples by liquid chromatographyfluorescence[END_REF]) was suitably modified for the determination of sulfonamides in feeds. The percentage acetonitrile was varied between 36% and 29%. Results indicated that a 29:71 acetonitrile/formic acid-sodium formiate aqueous buffer solution led to adequate analyte separation and short analysis times. The pH of the aqueous buffer solution was then varied between 3 and 4, while keeping a 29% acetonitrile content in the mobile phase. An increase in pH considerably decreased analyte retention times. A pH of 3.4, a value giving short retention times and suitable separation, was selected for all further work. When blank feed extracts were injected using the above mentioned conditions, no matrix interferences were observed at the retention times of the analytes (Figure 3, c andd).

No modifications were required for the derivatization process with fluorescamine.

Six standard solutions of SDZ and SDD, with concentrations ranging from 5 to 200 µg l -1 were injected in these conditions. Plots were linear for both SDZ (r=0.9997) and SDD (r=0.9997). The slopes of calibration lines obtained in four different working sessions showed a good reproducibility for both analytes: 2% for SDZ and 7% for SDD.

The injection of six standards of 100 µg l -1 , in conditions of repeatability, led to estimates of the precision of retention time (< 1%) and peak areas (2%). The LOD and LOQ were calculated as described in section "Liquid chromatography-UV detection".

Their values are shown in Table 1. Therefore, liquid chromatography with fluorimetric detection has the sensitivity and precision required for the analysis of samples of feeds spiked with SDZ and SDD at 2 and 5 µg g -1 .

Extraction

First attempts at sulfonamide extraction from animal feed were carried out with mechanical shaking. Three different extracting agents were tested: acetonitrile, 0.1 mol l -1 HCl aqueous solution and 10 -3 mol l -1 NaOH aqueous solution. Acetonitrile was found to be the most suitable, as both HCl and NaOH gave extracts containing many co-extracted matrix components, which prevented their direct injection and would have required a clean-up step. Extraction time was varied between 1.5 and 3 hours, but recoveries after 3 h shaking were only 5% higher than those obtained with just 1.5 h.

For a feed spiked at 50 µg g -1 , recoveries with a 1.5 h extraction time were 62% for SDZ and 36% for SDD.

Microwave-assisted extraction was then tested and found to be more efficient than mechanical shaking, as higher recoveries were obtained. Optimum temperature and irradiation time were determined with a feed spiked at 50 µg g -1 . Triplicate extractions of 1 g of feed with 10 ml acetonitrile were carried out at 80ºC, 90ºC, 100ºC and 110ºC, with 15 minutes irradiation time. The effect of 20 and 30 minutes irradiation times was then checked at 90ºC, 100ºC and 110ºC. As shown by results given in Figure 4, no significant differences in recoveries were observed. Finally, 110º C and 20 minutes irradiation time were selected as working conditions for all further extractions.

Recoveries in these conditions were 104% for SDZ and 89% for SDD.

Precision of the whole method was assessed analysing materials spiked at 50 µg g -1 , 5 µg g -1 and 2 µg g -1 in five different sessions, with the same technician and the same instrument. Three determinations were carried out in each session, so that fifteen results for each analyte were available. A one way (day) ANOVA for a 95% confidence level was applied to obtain intersession variation (s L ), intrasession variation (s r ) and intralaboratory total standard deviation (s R ) (ISO 1994). Results are shown in Table 2 as relative standard deviation. The HorRat values were calculated to confirm that the precision was adequate for the intended purpose [START_REF] Horwitz | The Horwitz Ratio (HorRat): A Useful Index of Method Performance with Respect to Precision[END_REF].

Preparation of the QCMs

Spiking

Several procedures for the addition of the sulfonamides to the feed matrix were tested.

Initially, sulfonamides were added in methanolic solutions and methanol was subsequently evaporated in a vacuum desiccator. Later, sulfonamides dissolved in a 90:10 water/methanol mixture were added to the feed and the solvent was eliminated by lyophilization. However, these spiking procedures were found to be inadequate, because they either induced changes in the matrix of the spiked samples, which difficulted the extraction process (effect of lyophilization) or led to extracts containing co-extracted components that interfered in sulfonamide determination (effect of spiking with sulfonamides in methanolic solution).

Finally, the decision was taken to spike samples by mixing solid sulfonamide standards with the feed; besides making sulfonamide determination easier, this had the added advantage that analytes were incorporated to the feed matrix in a way similar to the industrial preparation of medicated feeds.

As described in section "Preparation of the quality control material", and schematically shown in Figure 2, a feed containing 500 µg g -1 of both SDZ and SDD was first prepared, and then it was diluted with blank feed to obtain materials containing 2 µg g -1 and 5 µg g -1 . Homogeneity of the different bulk materials was tested after each dilution step. For this purpose, 5 sub-samples (1 g each) were taken every 24 hours in different positions of the homogenization container during the homogenization process. The sub-samples were analysed, making use of the suitable methodology, and the average concentration, standard deviation and relative standard deviation for each sulfonamide were calculated. The criterion for homogeneity was that the variation coefficient for the determinations should be lower than, or similar to, the method RSD r for each analyte.

Homogeneity study

Once the homogeneity of the bulk materials was verified, they were stored in bottles, each unit containing 10 g of material. To assess the homogeneity of the bottled materials containing 2 and 5 µg g -1 , ten bottles were randomly selected and analysed in duplicate in a single working session. One way ANOVA for a 95 % confidence level was performed with the results, and the conclusion was that there were no significant differences in the concentrations found in the different units in which both materials were bottled. The results of the ANOVA are shown in Table 3 as the relative standard deviations obtained within and between units. Since the calculated F values are lower than the critical value, it can be concluded that the material is homogeneous.

Stability study

Having confirmed the homogeneity of the 2 and 5 µg g -1 materials, their stability was studied. Among the experimental designs used for stability studies of reference materials, the model in which different portions of the material are stored at several temperatures and samples are periodically taken and analyzed in reproducibility conditions has been chosen (Lamberty et al. 1998). In the present study, room temperature, 4ºC and -20ºC have been assessed as storage temperatures. In order to minimize the influence of the long-term analytical fluctuations on the conclusions of the stability study, results obtained on the materials stored at room temperature and 4ºC have been referred to those corresponding to the material stored at -20ºC. The stability at this temperature has been previously verified by means of a regression model [START_REF] Linsinger | Estimating the uncertainty of stability for matrix CRMs[END_REF]: if the slopes of the regression lines representing analyte concentration vs. storage time do not differ significantly from zero, a dependence between these variables can be discarded and the materials can be considered to be stable. In order to ascertain whether the slope significantly differs from zero, an ANOVA has been applied to the regression model for each sulfonamide and each concentration. The results obtained have confirmed the null hypothesis and thus both QCMs can be considered to be stable at -20ºC along the eighteen-month period studied. As an example, the regression lines corresponding to the 5 µg g -1 material are shown in Figure 5.

For each storage time, the ratios between the sulfonamide content in each material stored at either 4ºC or room temperature (X t(T) ) and the corresponding values for the materials stored at -20ºC (X t(-20ºC) ) are obtained by equation ( 1)

) º 20 ( ) ( C t T t t X X R - = (1)
Estimated uncertainty for R t (U t ) is obtained by means of equation (2) [START_REF] Kramer | Practical manual for the production of laboratory reference materials; prepared for the European Commission in TRAP-LRM[END_REF]

): 100 ) ( 2 / 1 2 ) º 20 ( 2 ) ( C t T t t t CV CV R U - + × = (2)
where CV t is the variation coefficient at each time. Materials stored at 4ºC and room temperature can be considered to be stable if R t values are randomly distributed about 1 and their U t lie within the range around 1 determined by the method intralaboratory reproducibility (average of RSD R values obtained for the 2 and 5 µg g -1 materials).

Results obtained with this criterion along the eighteen-month stability study are shown in Figure 6. Materials stored at 4ºC can be considered to be stable, both at the 5 µg g -1 and 2 µg g -1 levels, over the whole period tested. In the case of materials stored at room temperature, stability is reduced in all cases to just over 6 months. From the middle scale feasibility study carried out in the present work, the conclusion can be reached that spiking animal feeds with solid sulfonamides and successive dilutions with blank feed to the desired level of concentration, including a thorough homogenization on a rolling table in each step, is a suitable and quick method for the preparation of homogeneous materials. In order to guaranty the stability of the QCM for a period of at least eighteen months, a storage temperature of 4˚C, or lower, is mandatory. At room temperature, the contents of SDZ and SDD slowly decrease after six months, and additionally, the risk of biological degradation cannot be discarded in these conditions.

Conclusions

There is a clear lack of reference materials for the analysis of veterinary drugs in feeds, which hinders method validation and quality control activities in the feed industry laboratories and also in those devoted to food quality control. This work could be considered to be a first step for a future development and commercialisation of this kind of materials, which would be useful tools for the analytical laboratories involved in feed analysis.

F

  Compound feed composition (a). Particle size distribution curve of the compound feed (bSchema of the procedure followed for the preparation of the quality control materials. 96x82mm (305 x 305 DPI) chromatograms of a 500 µg l-1 standard and of a blank animal feed extract (a) and an extract of an animal feed containing 50 µg g-1 of SDZ and SDD (b). LC -fluorimetry chromatograms of a 125 µg l-1 standard and of a blank animal feed extract (c) and an extract of an animal feed containing 5 µg g-1 of SDZ and SDD (d). 172x124mm (305 x 305 DPI) Effect of temperature and irradiation time of the microwave-assisted extraction on the recoveries of SDZ (a) and SDD (b). 131x61mm (305 x 305 DPI) Results of the regression analysis of the material of 5 µg g-1 stored at -20şC. SDZ (a) and SDD (b). 171x69mm (300 x 300 DPI) Variation of the Rt values with time for the materials stored at room temperature and at 4şC. SDZ (2 µg g-1) (a), SDD (2 µg g-1) (b), SDZ (5 µg g-1) (c) and SDD (5 µg g-1

Table 1 .

 1 LOD and LOQ determined for SDZ and SDD with each method.

	o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Table 2 .

 2 Precision of the methods in repeatability (RSD r ) and intralaboratory

	reproducibility conditions (RSD R ).
	Material concentration	Method	SDZ	RSD r	SDD	SDZ	RSD R	SDD
	50 µg g -1	LC -UV	3		3	4		5
	5 µg g -1	LC -fluorimetry	6		7	15		13
	2 µg g -1	LC -fluorimetry	7		6	11		15

Table 3 .

 3 Homogeneity results obtained from the ANOVA between the units in which both materials were bottled.

		5 µg g -1 material	2 µg g -1 material
		SDZ	SDD	SDZ	SDD
	RSD within units	5	4	7	6
	RSD between units	6	6	9	8
	*F calculated	1.57	1.96	1.84	1.64

*Critical F value = 3.02 Page 21 of 27 http://mc.manuscriptcentral.com/tfac Email: fac@tandf.co.

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Acknowledgements

Financial support from the Spanish Ministerio de Educación y Ciencia (Project AGL2005-07700-C06-04) is gratefully acknowledged. The authors acknowledge Associació Catalana de Fabricants de Pinsos (ASFAC) for providing feed samples and the MAT CONTROL Laboratory of the Department of Analytical Chemistry of the University of Barcelona for allowing the use of facilities for QCMs preparation. V.

Jiménez also thanks the Spanish Ministerio de Educación y Ciencia for a FPI grant.