Andrés E Ibañez William F Mills

Paco Bustamante

Ana P B Carneiro

Stuart Bearhop

Yves Cherel

Rocío Mariano-Jelicich

Rona A R Mcgill

Diego Montalti

Stephen C Votier

Andrés E Ibañez

Richard A Phillips

F William

Mills

Spatial and sex differences in mercury contamination of skuas in the Southern Ocean

Keywords: seabird, pollutants, metals, stable isotopes, Antarctica, Southern Hemisphere

établissements d'enseignement et de recherche

Introduction

Mercury (Hg) is a pervasive environmental contaminant of major concern for both humans and wildlife. Hg derives from both natural and anthropogenic sources; however, human activities (e.g., coal burning, artisanal and small-scale gold mining) have increased the global Hg pool [START_REF] Eagles-Smith | Modulators of mercury risk to wildlife and humans in the context of rapid global change[END_REF]UN Environment, 2019). The gaseous, elemental form of Hg (Hg 0 ) can travel long distances via atmospheric transport to remote locations that are isolated from major emission sources, including the Antarctic [START_REF] Fitzgerald | The case for atmospheric mercury contamination in remote areas[END_REF][START_REF] Driscoll | Mercury as a global pollutant: sources, pathways, and effects[END_REF].

Once deposited in the marine environment, inorganic Hg (Hg II ) is converted via biotic in situ methylation to the more toxic form, methyl-Hg (MeHg, [CH3Hg] + ), which, once assimilated, bioaccumulates within marine organisms (i.e., concentrations increase within the body over time) and biomagnifies through marine food webs from lower to higher trophic levels [START_REF] Bargagli | Biomagnification of mercury in an Antarctic marine coastal food web[END_REF][START_REF] Blum | Methyl-mercury production below the mixed layer in the North Pacific Ocean[END_REF][START_REF] Seco | Mercury biomagnification in a Southern Ocean food web[END_REF]. Long-lived, upper trophic level predators, such as many seabirds, are potentially exposed to high levels of Hg through their diets [START_REF] Cherel | Accumulate or eliminate? Seasonal mercury dynamics in albatrosses, the most contaminated family of birds[END_REF].

Seabirds are effective bioindicators of Hg contamination in marine ecosystems [START_REF] Monteiro | Seabirds as monitors of mercury in the marine environment[END_REF][START_REF] Monteiro | Mercury concentrations in prey fish indicate enhanced bioaccumulation in mesopelagic environments[END_REF][START_REF] Carravieri | Penguins as bioindicators of mercury contamination in the southern Indian Ocean: geographical and temporal trends[END_REF]. Hg contamination may also negatively impact aspects of seabird behaviour, physiology and development, and can have short-or long-term fitness consequences [START_REF] Goutte | Demographic responses to mercury exposure in two closely-related Antarctic top predators[END_REF][START_REF] Ackerman | Avian mercury exposure and toxicological risk across western North America: a synthesis[END_REF][START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF]. Studies of seabird communities in the Southern Ocean, from the Antarctic continent to the subtropics, have demonstrated extensive interspecific variation in Hg contamination (Anderson et al., 2009a;Carravieri et al., 2014a;[START_REF] Becker | Feather mercury concentrations in Southern Ocean seabirds: variation by species, site and time[END_REF][START_REF] Polito | Differing foraging strategies influence mercury (Hg) exposure in an Antarctic penguin community[END_REF]. Hg contamination of seabirds also often differs among conspecifics, and this variation may be driven by factors such as age, sex, breeding status and trophic ecology (Bearhop et al., 2000a;[START_REF] Polito | Differing foraging strategies influence mercury (Hg) exposure in an Antarctic penguin community[END_REF][START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF]. Moreover, several studies, mostly undertaken in the Indian Ocean sector of the Southern Ocean, have demonstrated that Hg contamination is lower for seabirds feeding in Antarctic compared to sub-Antarctic and subtropical waters (Carravieri et al., 2014b[START_REF] Carravieri | Penguins as bioindicators of mercury contamination in the southern Indian Ocean: geographical and temporal trends[END_REF][START_REF] Carravieri | From Antarctica to the subtropics: contrasted geographical concentrations of selenium, mercury, and persistent organic pollutants in skua chicks (Catharacta spp.)[END_REF][START_REF] Carravieri | Trace elements and persistent organic pollutants in chicks of 13 seabird species from Antarctica to the subtropics[END_REF][START_REF] Cherel | Accumulate or eliminate? Seasonal mercury dynamics in albatrosses, the most contaminated family of birds[END_REF][START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF][START_REF] Renedo | A "seabird-eye" on mercury stable isotopes and cycling in the Southern Ocean[END_REF].

Stable isotope analysis is a well-established method for studying the trophic ecology of seabirds [START_REF] Cherel | Using stable-isotope analysis of feathers to distinguish moulting and breeding origins of seabirds[END_REF][START_REF] Phillips | Stable isotopes reveal individual variation in migration strategies and habitat preferences in a suite of seabirds during the nonbreeding period[END_REF][START_REF] Phillips | Sexual segregation in distribution, diet and trophic level of seabirds: insights from stable isotope analysis[END_REF]. Stable isotope ratios of carbon ( 13 C/ 12 C, expressed as δ 13 C) and nitrogen ( 15 N/ 14 N, δ 15 N) offer powerful alternatives to conventional diet studies (e.g., analyses of regurgitates or pellets), as stable isotope ratios of seabird tissues (e.g., blood) reflect those of their prey in a predictable way [START_REF] Peterson | Stable isotopes in ecosystem studies[END_REF][START_REF] Hobson | Assessing avian diets using stable isotopes I: turnover of 13 C in tissues[END_REF][START_REF] Bearhop | Factors that influence assimilation rates and fractionation of nitrogen and carbon stable isotopes in avian blood and feathers[END_REF][START_REF] Inger | Applications of stable isotope analyses to avian ecology[END_REF]. δ 15 N values increase in a stepwise manner by ~3-5 ‰ at each trophic level, whereas δ 13 C values increase less with trophic level (~0.5-1 ‰) but can be used to infer foraging habitat [START_REF] Peterson | Stable isotopes in ecosystem studies[END_REF][START_REF] Hobson | Assessing avian diets using stable isotopes I: turnover of 13 C in tissues[END_REF][START_REF] Bearhop | Factors that influence assimilation rates and fractionation of nitrogen and carbon stable isotopes in avian blood and feathers[END_REF][START_REF] Cherel | Geographical variation in carbon stable isotope signatures of marine predators: a tool to investigate their foraging areas in the Southern Ocean[END_REF][START_REF] Phillips | Sexual segregation in distribution, diet and trophic level of seabirds: insights from stable isotope analysis[END_REF]. In the marine environment, this includes the relative reliance on an inshore vs. offshore, benthic vs. pelagic diet, and latitude or water mass where a gradient exists, such as in the Southern Ocean [START_REF] Cherel | Geographical variation in carbon stable isotope signatures of marine predators: a tool to investigate their foraging areas in the Southern Ocean[END_REF][START_REF] Jaeger | Seabird satellite tracking validates the use of latitudinal isoscapes to depict predators' foraging areas in the Southern Ocean[END_REF][START_REF] Phillips | Stable isotopes reveal individual variation in migration strategies and habitat preferences in a suite of seabirds during the nonbreeding period[END_REF][START_REF] Quillfeldt | Diet and foraging areas of Southern Ocean seabirds and their prey inferred from stable isotopes: review and case study of Wilson's storm-petrel[END_REF][START_REF] Quillfeldt | Moving polewards in winter: a recent change in the migratory strategy of a pelagic seabird?[END_REF][START_REF] St John Glew | Isoscape models of the Southern Ocean: predicting spatial and temporal variability in carbon and nitrogen isotope compositions of particulate organic matter[END_REF]. δ 15 N values in seabird tissues may also reflect spatial variation in baselines [START_REF] Elliott | Beyond bulk δ 15 N: combining a suite of stable isotopic measures improves the resolution of the food webs mediating contaminant signals across space, time and communities[END_REF]. Stable isotope ratios measured in seabird blood samples are appropriate for examining the relationships between Hg contamination and trophic ecology, owing to the broadly similar timeframe for integration into the blood system [START_REF] Bond | Relationships between stable isotopes and metal contaminants in feathers are spurious and biologically uninformative[END_REF][START_REF] Albert | Using blood and feathers to investigate large-scale Hg contamination in Arctic seabirds: a review[END_REF].

This study focuses on Hg contamination of brown skuas Stercorarius antarcticus lonnbergi from three breeding colonies spanning a large latitudinal gradient in the Southern Ocean (southwest Atlantic region), from the Antarctic Peninsula to South Georgia. Brown skuas are opportunistic predators and scavengers in both marine and terrestrial environments, and use a wide variety of feeding methods including aerial and terrestrial hunting, fishing and kleptoparasitism [START_REF] Furness | The skuas[END_REF][START_REF] Phillips | Diet and long-term changes in population size and productivity of brown skuas Catharacta antarctica lonnbergi at Bird Island, South Georgia[END_REF]Anderson et al., 2009b;[START_REF] Carneiro | Foraging behaviour and habitat use by brown skuas Stercorarius lonnbergi breeding at South Georgia[END_REF]. Brown skua diets are variable among populations, for instance, in our study region, the reliance on penguin prey decreases from the Antarctic continent towards South Georgia [START_REF] Burton | Breeding biology of the brown skua, Catharacta skua lonnbergi (Mathews), at Signy Island, South Orkney Island[END_REF][START_REF] Reinhardt | A review of the diets of Southern Hemisphere skuas[END_REF][START_REF] Phillips | Diet and long-term changes in population size and productivity of brown skuas Catharacta antarctica lonnbergi at Bird Island, South Georgia[END_REF]Anderson et al., 2009b;[START_REF] Graña Grilli | Variation in diet composition during the breeding cycle of an Antarctic seabird in relation to its breeding chronology and that of its main food resource[END_REF][START_REF] Borghello | Diet of the brown skua (Stercorarius antarcticus lonnbergi) at Hope Bay, Antarctic Peninsula: differences between breeders and non-breeders[END_REF]. Brown skuas also show reversed sexual size dimorphism, with females being significantly larger and heavier than males [START_REF] Phillips | Mating patterns and reversed size dimorphism in Southern skuas (Stercorarius skualonnbergi)[END_REF], and Hg burdens are often high in this species owing to their high trophic position [START_REF] Goutte | Demographic responses to mercury exposure in two closely-related Antarctic top predators[END_REF][START_REF] Carravieri | From Antarctica to the subtropics: contrasted geographical concentrations of selenium, mercury, and persistent organic pollutants in skua chicks (Catharacta spp.)[END_REF][START_REF] Seco | Mercury biomagnification in a Southern Ocean food web[END_REF]. Here, our aim was to analyse how Hg contamination of brown skuas varies among breeding colonies located at different latitudes, between sexes and, using bulk stable isotope ratios as proxies, in relation to trophic ecology.

We make the following a priori predictions: (i) Hg contamination will increase from the Antarctic Peninsula to lower-latitude breeding colonies; (ii) Hg contamination will be positively correlated with blood δ 15 N values, reflecting the biomagnification process; and (iii) females will show lower levels of Hg contamination than males, potentially reflecting deposition of Hg into eggs [START_REF] Robinson | Sex differences in mercury contamination of birds: testing multiple hypotheses with meta-analysis[END_REF]. Baseline data on Hg contamination is especially important for this species, given the detrimental consequences of high Hg burdens for breeding success elsewhere in the Southern Ocean [START_REF] Goutte | Demographic responses to mercury exposure in two closely-related Antarctic top predators[END_REF].

Materials and methods

Study area and sample collection

Fielwork was undertaken at three brown skua breeding colonies spanning a latitudinal gradient south of the Antarctic Polar Front (APF) in the Southern Ocean (southwest Atlantic region):

(i) Bahía Esperanza/Hope Bay, Antarctic Peninsula (63°24′S, 57°01′W) in November/December 2019; (ii) Signy Island, South Orkney Islands (60°43'S, 45°36'W) in January 2014; and, (iii) Bird Island, South Georgia (54°00'S, 38°03 'W) in December 2014 (Fig. 1). At each breeding colony, blood samples were obtained during the mid to late incubation periods from either the tarsal or brachial vein of adult birds using a 25-G needle.

Birds return to the breeding colonies a couple of months prior to egg-laying (e.g., most birds return in early to mid-October at Bahía Esperanza/Hope Bay and Bird Island) [START_REF] Burton | Breeding biology of the brown skua, Catharacta skua lonnbergi (Mathews), at Signy Island, South Orkney Island[END_REF]Carneiro et al., 2016;Ibañez, unpublished data). Blood samples were returned to the laboratory within 2-6 hours. Red blood cells were then isolated via centrifugation and removal of the supernatant, and stored frozen prior to laboratory analyses. Birds were sexed by the analysis of DNA extracted from blood samples at Bird Island, and by weight and tarsus lengths at Bahía Esperanza/Hope Bay and Signy Island [START_REF] Fridolfsson | A simple and universal method for molecular sexing of non-ratite birds[END_REF][START_REF] Phillips | Mating patterns and reversed size dimorphism in Southern skuas (Stercorarius skualonnbergi)[END_REF].

The sexes of all birds assigned morphologically at Bahía Esperanza/Hope Bay were later confirmed by DNA analysis.

Total mercury analysis

The vast majority (>90%) of total Hg (THg) in skua blood is MeHg [START_REF] Renedo | Seabird tissues as efficient biomonitoring tools for Hg isotopic investigations: Implications of using blood and feathers from chicks and adults[END_REF], and the estimated half-life of Hg in the blood of great skuas Stercorarius skua is 30-60 days (Bearhop et al., 2000b). Blood samples were freeze-dried and homogenised prior to analysis.

THg concentrations of red blood cells (hereafter "blood THg") were measured using an Advanced Mercury Analyser spectrophotometer (Altec AMA 254) at the laboratory Littoral Environnement et Sociétés (LIENSs, France). For each sample, a minimum of two aliquots (range: 0.29-1.86 mg dry weight [dw]) were analysed, and the means and relative standard deviations between measurements were calculated (all samples relative standard deviation <10%). THg concentrations are presented in µg g -1 dw. Accuracy was tested using a certified reference material (dogfish liver DOLT-5, NRC, Canada; certified Hg concentration: 0.44 ± 0.18 µg g -1 dw) every 10 samples. The measured values were 0.43 ± 0.01 µg g -1 dw (n = 15), and hence the recovery was 97.8 ± 1.7%. Blanks were analysed at the beginning of each set of samples and the detection limit of the method was 0.005 µg g -1 dw.

Stable isotope analysis

Stable isotope ratios were measured in the same blood samples as above. In great skuas, δ 13 C and δ 15 N in blood have half-lives of 15.7 and 14.4 days, respectively (i.e., of similar magnitude to the integration period to Hg, see above) [START_REF] Bearhop | Factors that influence assimilation rates and fractionation of nitrogen and carbon stable isotopes in avian blood and feathers[END_REF]. Stable isotope analyses were conducted at the Natural Environment Isotope Facility (NEIF) Stable Isotope Ecology Lab, SUERC. Stable isotope ratios of carbon and nitrogen were determined by a continuous-flow mass spectrometer (Delta Plus XP; Thermo Scientific, Bremen, Germany) coupled to an elemental analyser (vario PYRO cube; Elementar, Langenselbold, Germany). To correct for instrument drift, three internal laboratory standards were analysed for every 10 samples. Stable isotope ratios are reported as δ-values and expressed as ‰ according to the equation: δX = [(Rsample/Rstandard) -1] x 10 3 , where X is 13 C or 15 N, R is the corresponding ratio 13 C/ 12 C or 15 N/ 14 N, and Rstandard is the ratio of international references Vienna PeeDee Belemnite for carbon and atmospheric N2 (AIR) for nitrogen. Measurement precision (standard deviation associated with replicate runs of USGS40) was <0.2 ‰ for both δ 13 C and δ 15 N.

Data analysis

General linear models (GLMs; Gaussian distribution and identity link function) were used to assess variation in log-transformed blood THg concentrations. Predictor variables included sex, breeding colony (three-level factor), blood δ 15 N and blood δ 13 C values. Blood δ 15 N values were included as a predictor variable despite the baseline 15 N enrichment with latitude in the Southern Ocean, as this is more pronounced at the Subtropical Front than south of the APF, where our study populations are located [START_REF] Cherel | Geographical variation in carbon stable isotope signatures of marine predators: a tool to investigate their foraging areas in the Southern Ocean[END_REF][START_REF] Jaeger | Seabird satellite tracking validates the use of latitudinal isoscapes to depict predators' foraging areas in the Southern Ocean[END_REF]. Blood δ 13 C values of brown skuas differed significantly among breeding colonies (Kruskal-Wallis test, H = 67.2, p < 0.001), and so separate models were parameterised with either the breeding colony or δ 13 C as an explanatory variable. Blood δ 15 N and δ 13 C values were not highly correlated and were included in the same models (Spearman's correlation, rS = 0.34, p < 0.01).

Models included relevant two-way interactions among predictor variables and were ranked using the Akaike Information Criteria adjusted for small sample sizes (AICC) and models within two AICC units of the top model (≤2 AICC) were considered equally plausible [START_REF] Burnham | Model Selection and Inference: A Practical Information-theoretic Approach[END_REF]. Akaike weights (ωi) were used to assess the weight of evidence in favour of a given model among the candidate set [START_REF] Burnham | Model Selection and Inference: A Practical Information-theoretic Approach[END_REF]. All analyses were conducted using R version 3.4.4 (R Core Team, 2019).

Results

Blood THg concentrations were measured in 82 individual brown skuas. Mean (± SD) blood THg concentrations were 3.13 ± 2.08 µg g -1 dw (range: 0.49-8.67 µg g -1 dw) (Table 1). The most parsimonious GLM (i.e., ΔAICC = 0.00) explaining variation in log-transformed blood THg concentrations included breeding colony, which reflects an increase in mean blood THg concentrations from Bahía Esperanza/Hope Bay (0.95 ± 0.45 µg g -1 dw, range: 0.49-2.33 µg g -1 dw, n = 23) to Signy Island (3.42 ± 2.29 µg g -1 dw, range: 1.10-8.67 µg g -1 dw, n = 28) and then Bird Island (4.47 ± 1.10 µg g -1 dw, range: 3.02-7.46 µg g -1 dw, n = 31) (Table 1 and Fig. 2). The most parsimonious GLM also contained δ 15 N values, sex and their interaction (Table 2 and Fig. 3A). This reflects a weak positive relationship between blood THg concentrations and blood δ 15 N values, and that although the slopes differed between sexes, mean blood THg concentrations were higher in males than females in all populations (Table 1 and Fig. 3A). GLMs replacing the breeding colony variable with blood δ 13 C values produced similar results (Table 1), and indicated a strong positive relationship between blood THg concentrations and blood δ 13 C values (Fig. 3B).

Discussion

Antarctic marine ecosystems are often considered to be pristine environments, yet wildlife in the polar regions may still be exposed to high levels of environmental contaminants [START_REF] Ibañez | Plastic ingestion risk is related to the anthropogenic activity and breeding stage in an Antarctic top predator seabird species[END_REF][START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF]. This study provides a detailed evaluation of the underlying drivers of blood THg contamination of brown skuas from three breeding colonies located south of the APF in the Antarctic Zone of the Southern Ocean. Blood samples provide a non-lethal means of obtaining information about Hg contamination of seabirds, and measuring THg in skua blood samples provides information about contamination of prey and hence exposure to MeHg in food webs [START_REF] Albert | Using blood and feathers to investigate large-scale Hg contamination in Arctic seabirds: a review[END_REF].

Latitudinal differences: from the Antarctic Peninsula to South Georgia

Our analysis demonstrates clear differences in Hg contamination of brown skuas among the three breeding colonies located at different latitudes south of the APF. Blood THg concentrations were lowest at the Antarctic Peninsula, intermediate at the South Orkney Islands and highest at South Georgia. Indeed, mean blood THg concentrations were 4.7x higher at Bird Island compared to Bahía Esperanza/Hope Bay. This pattern is corroborated by the strong positive correlation between THg and δ 13 C values (Fig. 3B), as δ 13 C increases from the Antarctic continent towards the subtropics in the Southern Ocean [START_REF] Cherel | Geographical variation in carbon stable isotope signatures of marine predators: a tool to investigate their foraging areas in the Southern Ocean[END_REF][START_REF] Jaeger | Seabird satellite tracking validates the use of latitudinal isoscapes to depict predators' foraging areas in the Southern Ocean[END_REF][START_REF] Quillfeldt | Diet and foraging areas of Southern Ocean seabirds and their prey inferred from stable isotopes: review and case study of Wilson's storm-petrel[END_REF][START_REF] Quillfeldt | Moving polewards in winter: a recent change in the migratory strategy of a pelagic seabird?[END_REF][START_REF] Phillips | Stable isotopes reveal individual variation in migration strategies and habitat preferences in a suite of seabirds during the nonbreeding period[END_REF][START_REF] St John Glew | Isoscape models of the Southern Ocean: predicting spatial and temporal variability in carbon and nitrogen isotope compositions of particulate organic matter[END_REF].

Hence, our study suggests geographic differences in the transfer of Hg to skuas in the southwest Atlantic sector of the Southern Ocean, and our first a priori prediction is supported. This result contrasts with other studies concluding that breeding latitude has a limited effect on Hg contamination of seabirds in waters south of the APF [START_REF] Cherel | Accumulate or eliminate? Seasonal mercury dynamics in albatrosses, the most contaminated family of birds[END_REF][START_REF] Carravieri | Trace elements and persistent organic pollutants in chicks of 13 seabird species from Antarctica to the subtropics[END_REF]. Nonetheless, a pattern of increasing Hg contamination of seabirds from Antarctic waters towards the sub-Antarctic and subtropics is commonly observed in the Southern Hemisphere (Carravieri et al., 2014b[START_REF] Carravieri | Penguins as bioindicators of mercury contamination in the southern Indian Ocean: geographical and temporal trends[END_REF][START_REF] Carravieri | From Antarctica to the subtropics: contrasted geographical concentrations of selenium, mercury, and persistent organic pollutants in skua chicks (Catharacta spp.)[END_REF][START_REF] Carravieri | Trace elements and persistent organic pollutants in chicks of 13 seabird species from Antarctica to the subtropics[END_REF][START_REF] Cherel | Accumulate or eliminate? Seasonal mercury dynamics in albatrosses, the most contaminated family of birds[END_REF][START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF][START_REF] Renedo | A "seabird-eye" on mercury stable isotopes and cycling in the Southern Ocean[END_REF]. For instance, blood THg concentrations of skua chicks in the southern Indian Ocean increase from breeding sites in the Antarctic to those in the sub-Antarctic and subtropics, with skuas at Amsterdam Island showing the highest recorded concentrations for seabird chicks globally (3.98 ± 0.77 µg g -1 dw) [START_REF] Carravieri | From Antarctica to the subtropics: contrasted geographical concentrations of selenium, mercury, and persistent organic pollutants in skua chicks (Catharacta spp.)[END_REF]; Table 3). The majority of MeHg accumulated by seabirds has a mesopelagic origin, and it has been suggested that more efficient methylation of Hg at depth at lower compared to higher latitudes (i.e., subtropical compared to Antarctic waters), combined with higher vertical mixing, could deliver newly formed MeHg to the surface and therefore determine the regional differences in the bioavailability to seabirds [START_REF] Renedo | A "seabird-eye" on mercury stable isotopes and cycling in the Southern Ocean[END_REF]. To our knowledge, birds from Bahía Esperanza/Hope Bay show the lowest mean blood THg concentrations among adults of all large skua species for which data are available (Table 3); whereas blood THg concentrations at Bird Island were only lower than adults from Kerguelen, and great skuas from St Kilda (Table 3).

Differences in Hg contamination among the three breeding colonies may also be exacerbated by dietary differences. Blood δ 13 C values suggest that not all brown skuas from our study populations feed exclusively on Antarctic prey during the incubation and pre-laying periods (i.e., the timeframe reflected by blood δ 13 C values), and feed to some degree on prey from warmer waters north of the APF (Fig. 3B). At Bird Island, brown skuas mainly undertake coastal foraging trips during incubation and feed on the placentae from Antarctic fur seals Arctocephalus gazella, supplemented by carrion, particularly male seals killed during territorial conflicts [START_REF] Phillips | Diet and long-term changes in population size and productivity of brown skuas Catharacta antarctica lonnbergi at Bird Island, South Georgia[END_REF]Anderson et al., 2009b;[START_REF] Carneiro | Foraging behaviour and habitat use by brown skuas Stercorarius lonnbergi breeding at South Georgia[END_REF]. Many of the female fur seals would have spent the winter foraging north of the APF, and potentially over the Patagonian Shelf [START_REF] Staniland | Winter distribution and haul-out behaviour of female Antarctic fur seals from South Georgia[END_REF]. Conversely, pellet analyses indicate that penguins are the dominant prey consumed at the higher latitude colonies (Signy Island and Bahía Esperanza/Hope Bay) [START_REF] Burton | Breeding biology of the brown skua, Catharacta skua lonnbergi (Mathews), at Signy Island, South Orkney Island[END_REF][START_REF] Graña Grilli | Variation in diet composition during the breeding cycle of an Antarctic seabird in relation to its breeding chronology and that of its main food resource[END_REF][START_REF] Borghello | Diet of the brown skua (Stercorarius antarcticus lonnbergi) at Hope Bay, Antarctic Peninsula: differences between breeders and non-breeders[END_REF]Ibañez et al., unpublished data), which forage in Antarctic waters [START_REF] Lynnes | Conflict or co-existence? Foraging distribution and competition for prey between Adélie and chinstrap penguins[END_REF]. Indeed, the brown skuas at Bahía Esperanza/Hope Bay breed in close proximity to a large Adélie penguin Pygoscelis adeliae colony (approximately 100,000 breeding pairs), and two smaller gentoo penguin P. papua colonies [START_REF] Santos | Abundance estimation of Adélie penguins at the Esperanza/Hope Bay mega colony[END_REF][START_REF] Borghello | Diet of the brown skua (Stercorarius antarcticus lonnbergi) at Hope Bay, Antarctic Peninsula: differences between breeders and non-breeders[END_REF]. Another contributing factor is that birds may undertake a pre-laying exodus after returning to the colony.

A considerable proportion of brown skuas from Bird Island perform a pre-laying exodus north to sub-Antarctic and mixed sub-Antarctic-subtropical waters where the bioavailability of Hg is relatively high [START_REF] Phillips | Movements, winter distribution and activity patterns of Falkland and brown skuas: insights from loggers and isotopes[END_REF]Carneiro et al., 2016a). Unfortunately, the pre-laying exodus is not well described at other colonies, including at the higher latitude breeding colonies studied here. Prey ingested around the colony during breeding will therefore represent the primary influence on blood THg in skuas; however, there may be a weak carry-over effect of Hg exposure during winter, and hence differing migration strategies may also have contributed to the patterns observed here.

Relationships with blood δ 15 N values

The most parsimonious GLMs explaining blood THg concentrations included blood δ 15 N values as a predictor variable, which provide a proxy for trophic position, and supports our second a priori prediction. Although the slopes differed between sexes, the weak positive correlation between blood THg and δ 15 N values is likely to reflect, at least in part, the biomagnification of MeHg within marine food webs, such that individuals foraging at higher trophic levels were exposed to greater levels of Hg. However, the positive relationships between blood THg and δ 13 C values were stronger than with δ 15 N values (Fig. 3A and Fig. 3B).

Biomagnification of Hg has been demonstrated in the Scotia Sea ecosystem, from particulate organic matter through to higher trophic levels (Anderson et al., 2009a;[START_REF] Seco | Mercury biomagnification in a Southern Ocean food web[END_REF]. Indeed, mean blood THg concentrations of several large seabird species in our study region are higher than those of brown skuas in this study; however, it is notable that those of southern giant petrels Macronectes giganteus (2.74 ± 1.05 µg g -1 dw, range: 1.52-4.74 µg g -1 dw), and northern giant petrels M. halli (3.93 ± 1.37 µg g -1 dw, range: 2.18-6.38 µg g -1 dw) from Bird Island in 2001/02 were lower than in brown skuas from Bird Island in 2014/15 (Anderson et al., 2009a;this study). The relationship between δ 15 N and Hg contamination is often apparent when comparing values among different species within seabird communities (e.g., [START_REF] Blévin | Wide range of contamination in chicks of Southern Ocean seabirds[END_REF]Anderson et al., 2009a), but is observed less frequently within a single species, and was apparent across our study populations despite relatively little variation in δ 15 N values (range: 10.2 to 12.8 ‰). Alternatively, because there is a baseline 15 N enrichment from the Antarctic towards the subtropics in the Southern Ocean [START_REF] Cherel | Geographical variation in carbon stable isotope signatures of marine predators: a tool to investigate their foraging areas in the Southern Ocean[END_REF][START_REF] Jaeger | Seabird satellite tracking validates the use of latitudinal isoscapes to depict predators' foraging areas in the Southern Ocean[END_REF], the relationship between Hg and δ 15 N may simply reflect the increasing contamination with latitude (i.e., trophic variation may be obscured by spatial variation). However, changes in baseline δ 15 N are less pronounced south of the APF [START_REF] Cherel | Geographical variation in carbon stable isotope signatures of marine predators: a tool to investigate their foraging areas in the Southern Ocean[END_REF][START_REF] Jaeger | Seabird satellite tracking validates the use of latitudinal isoscapes to depict predators' foraging areas in the Southern Ocean[END_REF]. Moreover, differences in mean blood δ 15 N values among populations were small (means at Bird Island are ~0.2 ‰ higher than at Bahía Esperanza/Hope Bay; Table 1), and mean δ 15 N values were slightly lower at Signy Island than at Bahía Esperanza/Hope Bay (Table 1).

Sex differences in Hg contamination

Sex was also included as a predictor variable in the most parsimonious GLM, and blood THg was lower in females than males at each breeding colony (Table 1). Hence, our third a priori prediction is supported. As the blood samples were taken in mid to late incubation, two nonmutually exclusive hypotheses may explain the sex differences. First, egg production offers a route by which females are able to eliminate Hg [START_REF] Bond | Total and methyl mercury concentrations in seabird feathers and eggs[END_REF][START_REF] Robinson | Sex differences in mercury contamination of birds: testing multiple hypotheses with meta-analysis[END_REF][START_REF] Ackerman | Synthesis of maternal transfer of mercury in birds: implications for altered toxicity risk[END_REF], and Hg in eggs is thought to reflect dietary intake by females in the period before laying [START_REF] Lewis | Mercury levels in eggs, tissues, and feathers of herring gulls Larus argentatus from the German Wadden Sea Coast[END_REF][START_REF] Monteiro | Seabirds as monitors of mercury in the marine environment[END_REF]. Second, our data show slight sex differences in blood δ 15 N and δ 13 C values for all three populations (Table 1); hence, there may also be trophic differences between sexes. At Bird Island at least, females are more likely than males to undertake a pre-laying exodus [START_REF] Phillips | Movements, winter distribution and activity patterns of Falkland and brown skuas: insights from loggers and isotopes[END_REF]Carneiro et al., 2016a). However, during late incubation and early chick-rearing at Bird Island, the sexes show similar territorial attendance, foraging time and habitat use, and a previous stable isotope study at South Georgia found no evidence for sex-specific foraging preferences during the breeding period (Anderson et al., 2009b;[START_REF] Carneiro | Foraging behaviour and habitat use by brown skuas Stercorarius lonnbergi breeding at South Georgia[END_REF]. This is despite pronounced reverse sexual size dimorphism in this species [START_REF] Catry | Evolution of reversed sexual size dimorphism in skuas and jaegers[END_REF][START_REF] Phillips | Mating patterns and reversed size dimorphism in Southern skuas (Stercorarius skualonnbergi)[END_REF].

Could Hg contamination have fitness implications?

Hg is a neurotoxin and endocrine disruptor [START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF], and contamination may impact various aspects of development, physiology and breeding behaviour in seabirds [START_REF] Burger | Risk, mercury levels, and birds: Relating adverse laboratory effects to field biomonitoring[END_REF][START_REF] Evers | Adverse effects from environmental mercury loads on breeding common loons[END_REF][START_REF] Tartu | To breed or not to breed: endocrine response to mercury contamination by an Arctic seabird[END_REF][START_REF] Goutte | Survival rate and breeding outputs in a high Arctic seabird exposed to legacy persistent organic pollutants and mercury[END_REF]. Hg contamination has also been associated with reduced breeding success [START_REF] Goutte | Demographic responses to mercury exposure in two closely-related Antarctic top predators[END_REF][START_REF] Ackerman | Avian mercury exposure and toxicological risk across western North America: a synthesis[END_REF][START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF]. The mean blood THg (dw) concentrations reported here are equivalent to 0.94 µg g -1 wet weight (ww), 0.72 µg g -1 ww and 0.20 µg g -1 ww at Bird Island, Signy Island and Bahía Esperanza/Hope Bay, respectively (assuming a 79% moisture content) [START_REF] Eagles-Smith | Mercury correlations among six tissues for four waterbird species breeding in San Francisco Bay, California, USA[END_REF][START_REF] Ackerman | Avian mercury exposure and toxicological risk across western North America: a synthesis[END_REF]. These values suggest a low risk of MeHg toxicity [START_REF] Ackerman | Avian mercury exposure and toxicological risk across western North America: a synthesis[END_REF]. Indeed, mean blood THg concentrations in our study were far lower than those of brown skuas at Kerguelen; however, blood THg concentrations at Bird Island and Signy Island exceeded those of south polar skuas Stercorarius maccormicki at Adélie Land [START_REF] Goutte | Demographic responses to mercury exposure in two closely-related Antarctic top predators[END_REF]; Table 3). [START_REF] Goutte | Demographic responses to mercury exposure in two closely-related Antarctic top predators[END_REF] found short-term associations between Hg contamination and breeding success in both skua species, yet long-term reproductive impacts were more severe in south polar skuas than brown skuas, despite their lower blood THg concentrations. Selenium (Se) offers a well-known protective effect against Hg toxicity when in molar excess (i.e., when Se:Hg > 1), and blood Se:Hg molar ratios of south polar skuas were three times lower than the brown skuas [START_REF] Carravieri | From Antarctica to the subtropics: contrasted geographical concentrations of selenium, mercury, and persistent organic pollutants in skua chicks (Catharacta spp.)[END_REF][START_REF] Manceau | In vivo formation of HgSe nanoparticles and Hg-tetraselenolate complex from methylmercury in seabirds implications for the Hg-Se antagonism[END_REF]. Hence, although it currently appears unlikely that there are fitness consequences of Hg contamination for brown skuas in our study region (though we did not test this directly), the role of Se requires evaluation. Populations of brown skuas at Signy Island and Bird Island increased rapidly from the late-1950s to early-1980s (by 3.3% and 3.6% pa, respectively), but then rates slowed until the 2010s (0.4% pa) and 2000s (0.9% pa), respectively [START_REF] Phillips | Diet and long-term changes in population size and productivity of brown skuas Catharacta antarctica lonnbergi at Bird Island, South Georgia[END_REF]Carneiro et al., 2016b). Rather than a consequence of Hg contamination, the slower population growth rates seem more likely to be related to changes in prey availability and increased density-dependent competition [START_REF] Phillips | Diet and long-term changes in population size and productivity of brown skuas Catharacta antarctica lonnbergi at Bird Island, South Georgia[END_REF]Carneiro et al., 2016b).

Conclusion

Our study provides important baseline data on Hg contamination of brown skuas in the Southern Ocean, and analyses the underlying drivers of variation in contamination. Given the relatively high levels of Hg contamination of brown skuas at Bird Island, which in the early 2000s was likely the most densely-populated colony in the world (132 nesting pairs per km 2 of suitable habitat) [START_REF] Phillips | Diet and long-term changes in population size and productivity of brown skuas Catharacta antarctica lonnbergi at Bird Island, South Georgia[END_REF], further monitoring is required, particularly as there is some evidence for increasing Hg contamination of other seabirds at South Georgia [START_REF] Mills | Mercury exposure in an endangered seabird: longterm changes and relationships with trophic ecology and breeding success[END_REF]. Moreover, MeHg concentrations peak in low-oxygen subsurface waters, and in a warming world, oxygen minimum zones are expected to increase, hence potentially enhancing methylation of Hg and its bioavailability to marine predators [START_REF] Blum | Methyl-mercury production below the mixed layer in the North Pacific Ocean[END_REF]. Further work should also examine the potential protective effects of Se on Hg toxicity in brown skuas, and the risks posed by other contaminants to these skua populations, especially given the incidence of plastic ingestion by this species at the Antarctic Peninsula and the potential role of plastics in contaminant transmission [START_REF] Lavers | Ingested plastic as a route for trace metals in Laysan Albatross (Phoebastria immutabilis) and Bonin Petrel (Pterodroma hypoleuca) from Midway Atoll[END_REF][START_REF] Ibañez | Plastic ingestion risk is related to the anthropogenic activity and breeding stage in an Antarctic top predator seabird species[END_REF].

Table 2. Model selection for factors explaining variation in log-transformed total mercury (THg) concentrations (μg g -1 dw) of red blood cells from adult brown skuas Stercorarius antarcticus lonnbergi. The top 4 models are shown, and all are GLMs (Gaussian distribution and identity link function). k is the number of parameters; ΔAICC is the change in the Akaike information criterion corrected for small sample sizes (AICC) from the best-supported model; ωi is the Akaike weight; Exp. Dev. is the percentage explained deviance of the top model.

a Weights across all models sum to 1.00 (not all shown). b We did not consider an interaction between blood δ 13 C and δ 15

Figure 1 .

 1 Figure 1. Location of the three study sites in relation to the Sub-Antarctic Front (SAF), the Antarctic Polar Front (APF) and the southern Antarctic Circumpolar Current Front (sACCF).The study sites are: (i) Bahía Esperanza/Hope Bay, Antarctic Peninsula (63°24'S, 57°01'W);(ii) Signy Island, South Orkney Islands (60°43'S, 45°36'W); and (iii) Bird Island, South Georgia (54°00'S, 38°03'W).

Figure 2 .

 2 Figure 2. Box plots showing significant differences in the total mercury (THg) concentrations (µg g -1 dw) of red blood cells sampled from adult brown skuas Stercorarius antarcticus lonnbergi at: Bahía Esperanza/Hope Bay, Antarctic Peninsula (63°24′S, 57°01′W); Signy Island, South Orkney Islands (60°43'S, 45°36'W); and, Bird Island, South Georgia (54°00'S2, 38°03'W). Red crosses are mean values.

Figure 3 .

 3 Figure 3. Relationships between total mercury (THg) concentrations (µg g -1 dw) and bulk stable isotope ratios of (A) nitrogen (δ 15 N), and (B) carbon (δ 13 C) in red blood cells sampled from adult brown skuas Stercorarius antarcticus lonnbergi from three breeding colonies: Bahía Esperanza/Hope Bay, Antarctic Peninsula (63°24′S, 57°01′W); Signy Island, South Orkney Islands (60°43'S, 45°36'W); and, Bird Island, South Georgia (54°00'S2, 38°03'W).

Table 3 .

 3 N values. Review of published blood total mercury (THg) concentrations (μg g -1 dw) in adults and chicks of large skua species in the Northern and Southern Hemispheres. Values are means ± SDs.

	Models

Acknowledgements

William Mills is supported by a NERC GW4+ Doctoral Training Partnership studentship from the Natural Environment Research Council (NERC; grant no. NE/L002434/1). The Institut Universitaire de France (IUF) is acknowledged for its support to Paco Bustamante as a Senior Member. Stable isotope analyses were funded by the Natural Environment Isotope Facility (grant no. 2325.0920). The authors are grateful to Maud Brault-Favrou for her assistance with Hg analyses. Thanks are also due to the CPER (Contrat de Projet Etat-Région) and the FEDER (Fonds Européen de Développement Régional) for funding the AMA of LIENSs laboratory. The authors are also grateful to the Dirección Nacional del Antártico (DNA) and Instituto Antártico Argentino (IAA) for the support of the field-work activities and logistics in the Antarctic. Thanks to CONICET and Agencia Nacional de Promoción Cientifica y Tecnológica (ANPCyT) for the financial support. Comments from two anonymous reviewers greatly improved the manuscript. This work represents a contribution to the Ecosystems component of the British Antarctic Survey Polar Science for Planet Earth Programme, funded by the Natural Environment Research Council.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

CRediT


Gael Bougaran

Olivier Bernard
email: olivier.bernard@inria.fr

Antoine Sciandra

MODELLING CONTINUOUS CULTURES OF MICROALGAE COLIMITED WITH NITROGEN AND PHOSPHORUS

The culture of microalgae is currently more and more developed at the industrial scale. In many applications, a substrate limitation is necessary to induce the production of a specific metabolite. The question of a better yield when inducing a stress by two nutrients simultaneously motivates a better modelling of microalgae colimited by two nutrients.

We present a new model that represents growth of microalgae colimited both by nitrogen and phosphorus. We show that the key point in modeling this complex biological system is the expression for the absorption rate. Phosphorus uptake must be a decreasing function of the phosphorus internal quota. The situation for the nitrogen uptake is different and we show that it must be an increasing function of the phosphorus quota to be able to represent experimental observations. Finally we end up with a model that explains the a priori paradoxical opposite response of nitrogen and phosphorus to dilution rate. The proposed model is compared with data of Selenastrum minutum and is validated both qualitatively and quantitatively.

Introduction

The culture of microalgae is currently in a strong growing phase with many new fields of application, like fine chemical production, hatcheries feeding or bioenergy [START_REF] Pulz | Photobioreactors: production systems for phototrophic microorganisms[END_REF][START_REF] Chisti | Biodiesel from microalgae[END_REF]. In many applications, like e.g. astaxanthin production [START_REF] Aflalo | On the relative efficiency of two-vs. one-stage production of astaxanthin by the green alga haematococcus pluvialis[END_REF], a substrate limitation is necessary to induce the production of a specific metabolite. These metabolic inductions can often be obtained by a nutrient stress, so that the question of a better yield when inducing a stress by two nutrients simultaneously arises. The most popular model to reproduce growth of microalgae under substrate limitation is the Droop model [START_REF] Droop | Vitamin B12 and marine ecology. IV. the kinetics of uptake growth and inhibition in Monochrysis lutheri[END_REF][START_REF] Burmaster | The unsteady continuous culture of phosphate-limited monochrisis lutheri droop : Experimental and theoretical analysis[END_REF][START_REF] Droop | 25 years of algal growth kinetics, a personal view[END_REF]. It is widely used since it reproduces the ability of microalgae to uncouple substrate absorption and growth. This model has been deeply studied (see [START_REF] Lange | The attractiveness of the Droop equations[END_REF][START_REF] Bernard | Transient Behavior of Biological Loop Models, with Application to the Droop Model[END_REF][START_REF] Vatcheva | Experiment selection for the discrimination of semi-quantitative models of dynamical systems[END_REF]), validated and proved to be relevant [START_REF] Droop | 25 years of algal growth kinetics, a personal view[END_REF][START_REF] Sciandra | The limitations of continuous cultures with low rates of medium renewal per cell[END_REF][START_REF] Bernard | Nonlinear qualitative signal processing for biological systems: application to the algal growth in bioreactors[END_REF] to represent conditions of nitrogen or phosphorus limitations even in dynamical influent conditions [START_REF] Bernard | Nonlinear observers for a class of biological systems. Application to validation of a phytoplanktonic growth model[END_REF]. However, when both nitrogen and phosphorus are suboptimal at the same time, as it can be the case for some biotechnological applications, a new model must be designed. Nitrogen and phosphorus play a major role in the cell metabolism as they are part of many biochemical compartments of the cell. Cell nitrogen is mainly involved in proteins, amino acids and nucleic acids while phosphorus is mostly constitutive of the nucleic acids and phospholipids [START_REF] Geider | Redfield revisited : variability of c:n:p in marine microalgae and its biochemical basis[END_REF]. The possible existence of a physiological state where both nitrogen and phosphorus are suboptimal (called colimitation) is not clear and it is still a matter of debate. Because nitrogen and phosphorus interact at many biochemical levels and no clear biochemical process of interaction could be identified, both [START_REF] Arrigo | Marine microorganisms and global nutrient cycles[END_REF] and [START_REF] Saito | Some thoughts on the concept of colimitation: Three definitions and the importance of bioavailability[END_REF] suggested to consider these two nutrients as operationally independent nutrients. On the other hand N-P colimitation has frequently been invoked in natural environment by several workers that demonstrated that N and P had to be supplied together in order to promote the community phytoplankton growth [START_REF] Seppala | Experimental evaluation of nutrient limitation of phytoplankton communities in the gulf of riga[END_REF][START_REF] Maberly | Nutrient limitation of phytoplankton and periphyton growth in upland lakes[END_REF][START_REF] Zohary | Deep Sea Research Part II: Topical Studies in Oceanography On the Nature of Phosphorus Cycling and Limitation in the Eastern[END_REF]. Some laboratory experiments on monospecific cultures also gave evidence of more complex N-P interactions. This is the case of the work of [START_REF] Davies | The photosynthetic response of nutrient-depleted dilute cultures of skeletonema costatum to pulses of ammonium and nitrate; the importance of phosphate[END_REF] that demonstrated that carbon fixation of N and P starved Skeletonema costatum could be significantly increased only when both N and P were simultaneously added. [START_REF] Terry | Nitrogen and phosphorus requirements of pavlova lutheri in continuous culture[END_REF] also pointed out that while the minimum law prevailed for most of the N:P ratio a synergetic effect on Pavlova lutheri could occur between the two nutrients in a narrow range of N:P ratio.

Here we propose a Droop-based model designed on the idea that colimitation between nitrogen and phosphorus could arise from the uptake of nutrients rather than from the strict growth function and we demonstrate the ability of the model to properly represent both qualitative and quantitative behaviour of the experimental data that [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] obtained on Selenastrum minutum.

Model development 2.1 Presentation of the Droop model

The Droop model is widely used since its reproduces the ability of microalgae to uncouple substrate uptake ρ and growth rate μ [START_REF] Droop | Vitamin B12 and marine ecology. IV. the kinetics of uptake growth and inhibition in Monochrysis lutheri[END_REF][START_REF] Droop | 25 years of algal growth kinetics, a personal view[END_REF]. When considering nitrogen the Droop model can be writen as follows :

⎧ ⎨ ⎩ ṅ = Dn in -ρ N (n)x -Dn qN = ρ N (n) -μ(q N )q N ẋ = μ(q N )x -Dx (1)
where q N is the internal carbon-based quota of nitrogen, D is the dilution rate of the chemostat, n is the ambient concentration of nitrogen and x the carbon-biomass.

Or with phosphorus :

⎧ ⎨ ⎩ ṗ = Dp in -ρ P (p)x -Dp qP = ρ P (p) -μ(q P )q P ẋ = μ(q P )x -Dx (2)
In this model the uptake function ρ and growth rate function μ are generally taken as Michaelis-Menten and Droop functions respectively :

ρ(s) = ρ m s s+K s μ(q) = μ(1 -q 0 q ) (3)
Where K s is the half saturation constant for uptake, ρ m is the maximum uptake rate, q 0 the minimal quota that the algae can reach and μ the growth rate when the quota q of the limiting nutrient tends toward infinity.

It can be proved [START_REF] Bernard | Transient Behavior of Biological Loop Models, with Application to the Droop Model[END_REF])that the internal quota will stay between two bounds:

q 0 ≤ q ≤ q max (4)
Where it can be mathematically shown that q max = q 0 + ρ m μ represents the maximum quota obtained in conditions of non limiting nutrients, associated to μ max = μ(q max ).

Extension of Droop's model to deal with colimitation

Now the problem consists in modifying the Droop's model to deal with colimitation by nitrogen and phosphorus. [START_REF] Klausmeier | Optimal nitrogen-to-phosphorus stoichiometry of phytoplankton[END_REF] proposed to allocate ressouces to two broad classes of cellular functional machinery : the acquisition and assembly machineries. The acquisition machinery that combines pigments and membrane porters is quantitatively N-rich but P-poor ; nevertheless phosporus is qualitatively involved into the active uptake of both nitrogen (NO 3 ) and inorganic phosphorus. Conversely, the assembly machinery that builds the growth rate can be represented by the nucleic acids and is N and P-rich. Consequently, we now assume that uptake of a nutrient is function of the ambient nutrient under consideration and the internal quota of both nutrients as well. We also assume that growth rate can be driven by either the nitrogen and the phosphorus quota. The generic model wich results is the following:

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ ṅ = Dn in -ρ N (n, q N , q P )x -Dn ṗ = Dp in -ρ P (p, q N , q P )x -Dp qN = ρ N (n, q N , q P ) -μ(q N , q P )q N qP = ρ P (p, q N , q P ) -μ(q N , q P )q P ẋ = μ(q N , q P )x -Dx (5)
The question consists now in finding appropriate expressions for ρ N , ρ P and μ.

Modelling of the growth rate

We based our growth rate modelling approach on the assumption that N and P are both involved in a constant ratio in nucleic acids and particularly in RNA. We therefore assume that N or P can either limit growth rate depending on which of the two quota is the most limiting. Actually this assumption is supported by the findings of [START_REF] Droop | Some thoughts on nutrient limitation in algae[END_REF][START_REF] Droop | The nutrient status of algal cells in continuous culture[END_REF] and [START_REF] Rhee | Effects of n:p atomic ratios and nitrate limitation on algal growth, cell composition, and nitrate uptake[END_REF]. This is also supported by the results of [START_REF] Berdalet | Effects of nitrogen and phosphorus starvation on nucleic acid and protein content of heterocapsa sp. 10.1093/plankt/16.4.303[END_REF] on Heterocapsa sp. who found that both N and P starvation affected the RNA content while the DNA content remained approximately constant.

Since the 70's, several studies focused on how interaction between nutrients can affect the growth of phytoplankton. [START_REF] Droop | Some thoughts on nutrient limitation in algae[END_REF][START_REF] Droop | The nutrient status of algal cells in continuous culture[END_REF] that worked on the interaction between vitamin B12 and phosphorus on Monochrysis lutheri first demonstrated that growth rate was limited by the most limiting nutrient in a strict Liebig fashion, where the ambient nutrient in least supply is that which limits growth. [START_REF] Rhee | Effects of n:p atomic ratios and nitrate limitation on algal growth, cell composition, and nitrate uptake[END_REF] achieved the same conclusion on Scenedesmus sp. with nitrogen and phosphorus. [START_REF] Terry | Nitrogen and phosphorus requirements of pavlova lutheri in continuous culture[END_REF], [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] and [START_REF] Leonardos | Elemental and biochemical composition of rhodomonas reticulata (cryptophyta) in relation to light and nitrate-to-phosphate supply ratios[END_REF] also argued in favour of a growth rate modelling based on the so-called minimum law, where growth rate depends on the most limiting extracellular nutrient. These works were extended to the concept of the critical ratio (Rc) corresponding to a threshold model of nutrient limitation computed from the intracellular quota [START_REF] Agren | The c:n:p stoichiometry of autotrophs -theory and observations[END_REF]. We therefore assume that the most limiting nutrient will drive the growth rate. Thus the growth rate results from a min function:

μ = min(μ N (q N ), μ P (q P )) (6)
For sake of simplicity, we choose an expression:

μ = μ max min 1 -q N0 q N 1 -q N0 q NL , 1 -q P0 q P 1 -q P0
q PL [START_REF] Bernard | Nonlinear observers for a class of biological systems. Application to validation of a phytoplanktonic growth model[END_REF] Where parameters q NL and q PL represent maximal values of nitrogen and phosphorus quota.

As a consequence, in the steady-state analysis we will assume that a N-limited culture has a growth rate of the form μ = μ(1 -q N0 q N ) while a P-limited culture has a growth rate: μ = μ(1 -q P0 q P ).

Modelling of the uptake rate

The classical modelling for uptake of an external nutrient is the Michelis-Menten based modelling of [START_REF] Dugdale | Nutrient limitation in the sea: dynamics, identification and significance[END_REF]. For sake of illustration, let us assume that N is the limiting nutrient at steady state of the chemostat, where μ = D, then the phosphorus quota q P is given by the following equation :

ρ(P) = Dq P (8)
Assuming that P is not limiting (P >> K SP ), we have ρ(P) = ρ P max This leads to a steady state value q P = ρ P max D and shows that if the dilution rate tends toward zero, the phosphorus internal quota will tend toward infinity. This demonstrates that a regulation mechanism must be included in the model in order to guaranty that the quota will stay bounded between reasonable bounds. This mathematical results is supported by biological arguments. Indeed, it is usual to consider that uptake of a nutrient can be down regulated by its own internal quota [START_REF] Morel | Kinetics of nutrient uptake and growth in phytoplankton[END_REF]. This reasoning lead to a slighlty different uptake modelling, as developped by [START_REF] Gotham | Comparative kinetic studies of phosphate-limited growth and phosphate uptake in phytoplankton in continuous culture[END_REF]. They demonstrated that under both N and P-limitations their model gave satisfying fits for several species. This reasoning of course holds for any nutrient.

We have thus, for the phosphorus: ρ(p, q P ) = ρ Pmax p p + K p q PLq P q PLq P0 [START_REF] Chisti | Biodiesel from microalgae[END_REF] As [START_REF] Flynn | The importance of the form of the quota curve and control of non-limiting nutrient transport in phytoplankton models[END_REF] pointed out there is no particular reason for the critical level q PL to equal the Droop-maximum quota Qmax (and this obviously holds for q NL too). Indeed, the data of [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] showed that the maximum achievable quota of a non limiting nutrient could exceed the observed Qmax when the same nutrient was limiting growth. This was particularly true for P that could be stored up to 16 times the actual needs of Selenastrum minutum, while N luxury consumption didn't exceed 4. Therefore q PL is chosen larger than the maximal internal quota.

In conditions of limitations with phosphorus, we have thus qP = ρ Pmax q PLq P q PLq P0 -Dq P [START_REF] Davies | The photosynthetic response of nutrient-depleted dilute cultures of skeletonema costatum to pulses of ammonium and nitrate; the importance of phosphate[END_REF] and when steady-state is achieved, it follows that

q P = ρ Pmax q PL ρ Pmax + D(q PL -q P0 ) (11)
Therefore, q P is a decreasing function of the dilution rate, and is thus a decreasing function of the limiting nutrient N.

Actually this is what has been observed by [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] who showed that the phosphorus quota was decreasing for Nlimited culture. Besides, our model assumes that there is no interaction between the N status and P-uptake and therfore P-uptake is solely governed by the internal P-quota. Indeed, as it will be discuted in the following, the model fitting to the experimental data of [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] showed a satisfying adequation leading to the conclusion that a model with such an interaction is not necessary to support the available experimental data.

However the situation is different for nitrogen. Indeed, [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] showed that the nitrogen quota of phosphorus limited culture is increasing with the dilution rate. This proves that the uptake rate for nitrogen cannot solely be regulated by the internal nitrogen quota. Now we explore another mechanism based on the idea that the transport of nitrate is active and therefore needs energy and cofactors associated to the phosphorus pool. A major feature of the porters involved in NO 3 and PO 4

1.8 day -1 q n0 6 10 -2 molN. molC -1 q p0

1.8 10 transport is that they require energy (i.e. ATP) for their activity that could be related in some extent to the P-pool status of the cell. Thus the modelling of N-uptake must ensure that as cells are getting P-starved, their P-quota lowers and consequently the transport rate of N tends to decrease. Indeed [START_REF] Davies | The photosynthetic response of nutrient-depleted dilute cultures of skeletonema costatum to pulses of ammonium and nitrate; the importance of phosphate[END_REF] demonstrated that when N and P-starved cultures of Skeletonema costatum were resupplied with N the C-fixation was inhibited. They assumed that the addition of N led to an enhanced demand of ATP and NADH and to mobilization of the limited phosphorus quota for N-uptake and this was detrimental to the carbon fixation.

As a consequence we assume that the uptake of nitrogen can be represented as follows:

ρ(n, q N , q P ) = ρ Nmax n n + K n q NLq N q NLq N0 q Pq P0 q PLq P0 [START_REF] Droop | Some thoughts on nutrient limitation in algae[END_REF] From that, we can infer that, in transient situations where P becomes limiting, the P-status of the cells could induce a N-uptake limitation leading to N-P colimitation. Conversely, when q P is high, the P-driven term allow a maximum potential of N-uptake.

Let us compute the non limiting quota q N in conditions of P-limitation. From [START_REF] Bernard | Nonlinear observers for a class of biological systems. Application to validation of a phytoplanktonic growth model[END_REF] the growth rate can be represented by a Droop model:

μ(q P ) = μ(1 - q P0 q P ) (13)
At steady state in the chemostat, the non limiting nitrogen concentration is much greater than K n , such that: qN = ρ Nmax q NLq N q NLq N0 q Pq P0 q PLq P0 -μ(1 -q P0 q P )q N [START_REF] Droop | 25 years of algal growth kinetics, a personal view[END_REF] It follows that the steady state value of the nitrogen quota for P-limited cultures is then given by: q N = ρ Nmax q P μ(q NLq N0 )(q PLq P0 ) + ρ Nmax q P q NL [START_REF] Droop | 25 years of algal growth kinetics. a personnal view[END_REF] Thus q N is an increasing function of q P . Since, from Droop model, q P is itself an increasing function of the dilution rate, it follows that q N is increasing with the dilution rate. It is worth remarking that this conclusion is opposite to the decreasing behaviour of q P in condition of nitrogen limitation.

Discussion

Model prediction at physiological limit boundaries

The results of [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF] on Selenastrum minutum were obtained with extreme N:P ratios (n : p = 200 and n : p = 1) that greatly differed from the critical ratio [START_REF] Agren | The c:n:p stoichiometry of autotrophs -theory and observations[END_REF]. In these extreme conditions we can assume that the non limiting C-quota were saturated in both experiments. Besides, this assumption is supported by the high ambient concentrations of the non-limiting nutrient in the two experiments.

In conditions where N is limiting and P is in large excess (i.e. P-uptake is maximum), the model fits the data with a q P decreasing trend as growth rate increases (figure 2), according to equation 11. When defining the luxury consumption as the ratio between the maximum achievable quota of a non limiting nutrient and the quota of the same but limiting nutrient, it can be seen (figure 2) that the capacity of P-luxury consumption also decreases with growth rate. Opposite to the trend of q P under N-limitation the experimental data of saturated q N under P-limitation turned out to be an increasing function of the growth rate for Selenastrum minutum. Under the assumption of [START_REF] Droop | 25 years of algal growth kinetics. a personnal view[END_REF] that a non-limiting quota follows the Droop equation with a higher apparent q 0 , the Droop model predicts that q N is an increasing function of the growth rate under P-limitation. Conversely a model that would only integrate the inhibiting effect of the internal quota would describe a decreasing trend of the N-saturated quota with growth rate as it was previously observed for the P-saturating quota under N-limiting conditions (see equation 11). Therefore if our model was neglecting the limiting effect of q P on N-uptake it would fail to fit the physiological boundaries correctly (indeed, an equation similar to [START_REF] Droop | Vitamin B12 and marine ecology. IV. the kinetics of uptake growth and inhibition in Monochrysis lutheri[END_REF] would have been obtained, leading to a decrease of q N with respect to μ). The asymmetrical functions of N (structural) and P (functional) and particularly the energetic role of P at the acquisition level were therefore critical in our modelling approach. Thus although P is quantitatively low in the acquisition machinery it appears to play a major role in the uptake of NO 3 .

Finally it can also be observed from figure 2 that the capacity of N-luxury consumption decreases with growth rate as for P-luxury consumption. Moreover the capacity of N-luxury consumption has often been reported to be lower than that of P [START_REF] Elrifi | Steady-state luxury consumption and the concept of optimum nutrient ratios: a study with phosphate and nitrate limited selenastrum minutum (chlorophyceae)[END_REF][START_REF] Terry | Nitrate and phosphate uptake interactions in a marine prymnesiophyte[END_REF] and the model succeeded in describing this difference.

Model prediction inside the physiological limit boundaries

In the case where more balanced N:P input ratio were used (i.e. ratio close to the Redfield ratio) one may suspect different kinetics for the non-limiting quota as they may not reach saturation. Indeed simulations of the model show different trends for the two non-limiting quota depending on the growth rate ranges under consideration. Under conditions where P is limiting and in the range of low growth rates, the non-limiting q N exhibits an increasing trend with growth rate until the physiological limit boundary is reached. From the model theory it can be assumed that at low growth rates where P is highly limiting growth the limited available energy (ATP) highly constrains N transport even if ambient N concentration is high. For higher growth rates the limiting control of P on N-uptake is decreased and q N can build-up to the limit boundary where the inhibition of NO 3 -uptake by the N-internal quota prevails. Kinetics of the non-limiting q P are roughly similar to that observed for q N . It can also be noticed that in situations where P-is sublimiting (figure 1b) the non-limiting q P exhibits a very similar kinetic to that of the limiting q P but with a slightly higher apparent q P0 . This Droop-like kinetic of the non limiting quota was already assumed by [START_REF] Droop | The nutrient status of algal cells in continuous culture[END_REF] and experimentally observed by [START_REF] Goldman | Steady-state growth and chemical composition of the marine chlorophyte dunaliella tertiolecta in nitrogen-limited continuous cultures[END_REF] under N:P ratios close to the critical ratio. Figure 3 shows simulation results for the kinetic of q N : q P versus growth rate under different input N:P ratio ranging from 1 to 100. At low growth rates q N : q P remains equivalent to the input ratio as long as the input ratio falls within the physiological limit boundaries and none of the two nutrients is limiting. As growth rates increases q N : q P remains constant until the physiological boundaries are reached and uptake inhibition by the internal quota takes place. Further increase in growth rate results in alteration of the q N : q P ratio driven by the physiological limit boundaries of the quota as we described above under extreme N:P input ratios.

Conclusion

We proposed a new modelling approach that focus on the N-P colimitation concept. Our Droop-based model suggests that the interaction between N and P should be considered at the acquisition rather than at the assembly level. Indeed we feel that the Droop function between growth rate and quota remains unaffected by the N-P interaction while the N-quota construction is tightly tied to the P-status of the cell. The combination of the uptakelimiting effect of P through energy availability needed by NO 3 porters and the concept of uptake-inhibition by the internal quota allowed the model to reproduce the experimental data of the few studies dealing with the two nutrients and particularly under extreme N:P input ratios. We therefore suggest that regarding the colimitation concept, N and P would better be considered as dependent nutrients rather than operationally independent ones. As several authors already pointed out [START_REF] Klausmeier | A model of flexible uptake of two essential resources[END_REF][START_REF] Flynn | The importance of the form of the quota curve and control of non-limiting nutrient transport in phytoplankton models[END_REF][START_REF] Leonardos | Elemental and biochemical composition of rhodomonas reticulata (cryptophyta) in relation to light and nitrate-to-phosphate supply ratios[END_REF] there is a critical need of new experimental data considering N and P under different conditions of input ratios and growth rates.

Figure 1 :

 1 Figure 1: Comparison of experimental results for the nitrogen quota (a and b) and the phosphorus quota (c and d) obtained at steady state with Selenastrum minutum under nitrogen limitation (a and c), and phosphorus limitation (b and d).

Figure 2 :

 2 Figure 2: Model simulation of N-quota (a ) and P-quota (b ) versus growth rate under different N:P input ratio ranging from 1 to 100.

Figure 3 :

 3 Figure 3: Model simulation of the cell-N:P versus growth rate under different N:P input ratio ranging from 1 to 100.

Table 1 :

 1 Parameter values used for model of N-P colimitation with Selenastrum minutum

		-3	molP. molC -1
	q NL q PL ρ N max ρ P max K S N K S P	0.22 0.06 9.6 4 10 -2 0.22 10 -6 molN.L -1 molN. molC -1 molP. molC -1 molN.molC -1 .day -1 molP.molC -1 .day -1 0.06 10 -6 molP.L -1

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Acknowledgements: This paper presents research results supported by the ANR-06-BIOE-014 Shamash project.