Helena Lopes Galasso
email: helenagalasso@gmail.com

Sébastien Lefebvre

Catherine Aliaume

Bastien Sadoul

Myriam D Callier
email: myriam.callier@ifremer.fr

Using the Dynamic Energy Budget theory to evaluate the bioremediation potential of the polychaete Hediste diversicolor in an integrated multi-trophic aquaculture system

Keywords: DEB, deposit feeders, fish waste, metabolism, ragworm, semelparous, bioenergetics

Integrated Multi-Trophic Aquaculture (IMTA) systems have been designed to optimize nutrient and energy use, to decrease waste, and to diversify fish-farm production.

Recently, the development of detritivorous aquaculture has been encouraged, as detrivores can consume organic particulate matter, reducing benthic eutrophication and the environmental footprint of aquaculture. To this end, the polychaete Hediste diversicolor is a promising species due to its broad feeding behaviour and its resistance in a wide range of environments. In this study, an existing Dynamic Energy Budget (DEB) model of H. diversicolor was used to predict the ragworm's metabolic processes in various environmental conditions and to estimate its bioremediation capacity in an aquaculture context. First, the scaled functional response (f) was calibrated in a 98-day growth experiment with two types of food (Fish faeces and Fish feed). Then, we further validated the model using data on the ammonia excretion and oxygen consumption of individuals fed with fish faeces at four different temperatures using the previously calibrated f. Overall, we found that the DEB model was able to correctly predict the experimental data (0.51<MRE<0.80). Lastly, different environmental scenarios of seawater temperatures and assimilation rates were compared. The bioremediation potential of H. diversicolor was estimated based on cumulated assimilation rates, which could represent 75-289 kg of fish waste year -1 for a 100 m 2 ragworm farm (3700 ind. m - 2 ). These findings suggest that the DEB model is a promising tool for further IMTA development and management.

Introduction

Fed aquaculture can impact ecosystems through the release of organic matter and dissolved nutrients (Hargrave, 2005). One way to minimize aquaculture waste is to develop Integrated Multi-Trophic Aquaculture (IMTA), in which organisms of different trophic levels are co-cultured on the same farm [START_REF] Chopin | Open-water integrated multi-trophic aquaculture: environmental biomitigation and economic diversification of fed aquaculture by extractive aquaculture[END_REF]. This type of aquaculture can include fed species (e.g. finfish or shrimp) as well as extractive species such as algae that can feed on dissolved inorganic waste generated by the fed species [START_REF] Abreu | IMTA with Gracilaria vermiculophylla: Productivity and nutrient removal performance of the seaweed in a land-based pilot scale system[END_REF][START_REF] Erler | Biological remediation of aquaculture waste: a combined finfish, artificial substrate treatment system[END_REF] or filter-feeders and detritivores that can feed on generated organic waste [START_REF] Jiang | Growth and food sources of Pacific oyster Crassostrea gigas integrated culture with Sea bass Lateolabrax[END_REF][START_REF] Neori | Integrated aquaculture: rationale, evolution and state of the art emphasizing seaweed biofiltration in modern mariculture[END_REF]. In open water, particulate organic matter fluxes (faeces and uneaten feed) are mainly vertical [START_REF] Filgueira | Vertical particle fluxes dominate integrated multi-trophic aquaculture (IMTA) sites: implications for shellfish -finfish synergy[END_REF] and may accumulate on the bottom sediment both within the farm site and close to it, inducing benthic eutrophication (Hargrave, 2005). The quantity and biochemical composition of the nutrients and organic matter released depends on the cultured species, the farm size, the feed composition, and the rearing conditions [START_REF] Brigolin | Modelling the biomass yield and the impact of seabream mariculture in the Adriatic and Tyrrhenian Seas (Italy)[END_REF].

Using detritivore species in IMTA may improve the mineralization of organic matter through bioturbation processes [START_REF] Hedman | Particle reworking and solute transport by the sediment-living polychaetes Marenzelleria neglecta and Hediste diversicolor[END_REF] and feeding [START_REF] Cammen | The significance of microbial carbon in the nutrition of the deposit feeding Polychaete Nereis succinea[END_REF], thus preventing benthic eutrophication. The bioremediation potential of several detritivorous species has been evaluated, including fish [START_REF] Katz | Gray mullets ameliorate organically enriched sediments below a fish farm in the oligotrophic Gulf of Aqaba (Red Sea)[END_REF][START_REF] Porter | Preliminary assessment of grey mullet (Mugil cephalus) as a forager of organically enriched sediments below marine fish farms[END_REF], sea cucumbers [START_REF] Cubillo | Role of deposit feeders in integrated multi-trophic aquaculture -A model analysis[END_REF][START_REF] Macdonald | Consumption and remediation of European Seabass (Dicentrarchus labrax) waste by the sea cucumber Holothuria forskali[END_REF][START_REF] Nelson | The absorption efficiency of the suspension-feeding sea cucumber, Cucumaria frondosa, and its potential as an extractive integrated multi-trophic aquaculture (IMTA) species[END_REF]Paltzat et al., 2008;[START_REF] Chary | Integrated multi-trophic aquaculture of red drum (Sciaenops ocellatus) and sea cucumber (Holothuria scabra): Assessing bioremediation and life-cycle impacts[END_REF], sea urchins [START_REF] Cook | Enhanced production of the sea urchin Paracentrotus lividus in integrated open-water cultivation with Atlantic salmon Salmo salar[END_REF][START_REF] Orr | Ingestion rate, absorption efficiency, oxygen consumption, and fecal production in green sea urchins (Strongylocentrotus droebachiensis) fed waste from sablefish (Anoplopoma fimbria) culture[END_REF] and polychaetes [START_REF] Fang | Applicability of Perinereis aibuhitensis Grube for fish waste removal from fish cages in Sanggou Bay[END_REF][START_REF] Marques | New species for the biomitigation of a super-intensive marine fish farm effluent: Combined use of polychaete-assisted sand filters and halophyte aquaponics[END_REF]. Among polychaetes, Hediste (Nereis) diversicolor (O. F. Müller, 1776) has been widely studied [START_REF] Gillet | Response of Nereis diversicolor population (Polychaeta, Nereididae) to the pollution impact -Authie and Seine estuaries (France)[END_REF][START_REF] Mermillod-Blondin | Influence of bioturbation by three benthic infaunal species on microbial communities and biogeochemical processes in marine sediment[END_REF]. Similar to other Nereididae, this species plays an important ecological role by constructing burrows in sediment to create galleries.

Their bioturbation and ventilation activities promote nutrient fluxes between water and sediment, favouring the oxygenation of the sediment [START_REF] Michaud | The functional group approach to bioturbation: II. The effects of the Macoma balthica community on fluxes of nutrients and dissolved organic carbon across the sediment-water interface[END_REF] and enhancing organic matter mineralization and nutrient recycling [START_REF] Heilskov | Effects of benthic fauna on organic matter mineralization in fish-farm sediments: importance of size and abundance[END_REF]. Additionally, H. diversicolor can cope with a large range of environmental conditions, in terms of variation in organic matter loading, temperature and salinity [START_REF] Kristensen | Ventilation and oxygen uptake by three species of Nereis (Annelida: Polychaeta). II. Effects of temperature and salinity changes[END_REF][START_REF] Ozoh | Growth and production of California sea cucumbers (Parastichopus californicus Stimpson) co-cultured with suspended Pacific oysters (Crassostrea gigas Thunberg)[END_REF]. Moreover, its feeding behaviour is diversified: it is considered a detritivore, carnivore, herbivore, suspension feeder and even an optional filter feeder [START_REF] Nielsen | Feeding, growth and respiration in the polychaetes Nereis diversicolor (facultative filter feeder) and N. virens (omnivorous) -a comparative study[END_REF][START_REF] Riisgård | Filter-feeding in the polychaete Nereis diversicolor: a review[END_REF]. More recently, the biomitigation activity of this species has been explored [START_REF] Cubillo | Role of deposit feeders in integrated multi-trophic aquaculture -A model analysis[END_REF][START_REF] Marques | New species for the biomitigation of a super-intensive marine fish farm effluent: Combined use of polychaete-assisted sand filters and halophyte aquaponics[END_REF][START_REF] Papaspyrou | The influence of infaunal (Nereis diversicolor) abundance on degradation of organic matter in sandy sediments[END_REF], and studies have demonstrated that individuals can grow significantly when fed on fish waste [START_REF] Bischoff | The fatty acid composition of Nereis diversicolor cultured in an integrated recirculated system: Possible implications for aquaculture[END_REF][START_REF] Wang | Growth and nutritional composition of the polychaete Hediste diversicolor (OF Muller, 1776) cultivated on waste from land-based salmon smolt aquaculture[END_REF]. [START_REF] Cubillo | Role of deposit feeders in integrated multi-trophic aquaculture -A model analysis[END_REF] and [START_REF] Marques | New species for the biomitigation of a super-intensive marine fish farm effluent: Combined use of polychaete-assisted sand filters and halophyte aquaponics[END_REF] have also shown that H. diversicolor could assimilate particulate organic matter from fish farms, confirming its potential for IMTA. However, these studies were carried out under specific temperature and salinity conditions, making predicting the bioremediation capacity in other environmental conditions difficult. In this context, mechanistic models can be useful tools as they can simulate physiological and ecological processes under a large range of environmental conditions. Starting from empirical results in a limited number of environmental conditions, this modelling framework allows these results to be extrapolated in order to predict the metabolic responses of individuals in other environmental conditions [START_REF] Reid | Performance measures and models for open-water integrated multi-trophic aquaculture[END_REF]. Bioenergetic models are based on the fluxes and conservation of energy in physiological processes, in which energy available for somatic growth is estimated as a result of feeding and excretion [START_REF] Brett | Physiological Energetics. Vol. VIII-Bioenergetics and Growth[END_REF]. The model chosen in this study was the Dynamic Energy Budget (DEB) model [START_REF] Kooijman | Dynamic Energy Budget theory for metabolic organisation[END_REF], which is based on the use of energy by an organism for physiological processes such as food assimilation, growth, maintenance and reproduction. This model has been demonstrated to correctly model the lifecycle of a wide range of species, from bacteria to large mammals. The framework provided by the DEB theory allows the quantification of processes of interest for aquaculture (such as growth and feeding efficiency) and of increasing interest for IMTA (such as the bioremediation capacity of extractive species) [START_REF] Reid | Performance measures and models for open-water integrated multi-trophic aquaculture[END_REF][START_REF] Chary | Integrated multi-trophic aquaculture of red drum (Sciaenops ocellatus) and sea cucumber (Holothuria scabra): Assessing bioremediation and life-cycle impacts[END_REF]. The associated DEB parameters for more than 2000 modelled species to date are available on the online platform Add-my-Pet (AmP) (www.bio.vu.nl/thb/deb/deblab/add_my_pet). Of these species, 7 are polychaetes, with the recent additions of Arenicola marina [START_REF] De Cubber | Annelid polychaetes experience metabolic acceleration as other Lophotrochozoans: Inferences on the life cycle of Arenicola marina with a Dynamic Energy Budget model[END_REF] and Hediste diversicolor [START_REF] Lefebvre | AmP Hediste diversicolor[END_REF]. These DEB model parameters for H. diversicolor can now be used to predict metabolic processes under different environmental conditions.

The aim of this study was to analyze the mitigation potential of deposit-feeding H.

diversicolor in co-cultivation with finfish. The objectives were (1) to validate the DEB model using new datasets obtained through laboratory experiments on growth rates and ammonia excretion, as well as data on oxygen consumption published independently of the calibration procedure, (2) to evaluate the effects of seawater temperatures (5°C to 25°C) and assimilation rates (from ad libitum to half an ad libitum ration) on some life history traits of H. diversicolor, and (3) to quantify the bioremediation potential of H. diversicolor in different aquaculture contexts.

Material and methods

The DEB theory and the lifecycle of H. diversicolor

A general presentation of the DEB theory and its mathematical formulation is presented in 'Supplementary material' (see S1). To perform the DEB simulations for H. diversicolor, we used the available parameters in the AmP database [START_REF] Lefebvre | AmP Hediste diversicolor[END_REF] (Table 1), using an abj-model. Essentially, the DEB theory is based on the assumption that assimilated energy first enters a reserve compartment (E). A fixed fraction (κ) of the energy flux coming from the reserve is then utilized, first for somatic maintenance costs and the remaining part for growth of the structural volume (V). The other fraction (1-κ) is spent on maturation (EH) in juveniles or on reproduction (ER) in adults, after having paid the maturity maintenance costs (Figure 1). Acquisition processes (i.e. ingestion and assimilation) are linked to the organism's surface area, while somatic maintenance is proportional to its volume. In contrast to the standard version of the DEB model (std), the abj-model considers a metabolic acceleration between birth and metamorphosis (see S1). Consequently, we scaled maximum surface-specific assimilation (

) and energy conductance ( ) to the organism 's structural length between birth and metamorphosis, following [START_REF] Kooijman | Scenarios for acceleration in fish development and the role of metamorphosis[END_REF]. Finally, as it is a semelparous species, H. diversicolor dies after its first reproduction [START_REF] Olive | Gametogenic cycle and population structure of Nereis (Hediste) diversicolor and Nereis (Nereis) pelagica from north-east England[END_REF]. Therefore, the maximum structural length Lm was the structural length of the animal that attains first reproduction. In DEB theory, authors refer to this reproductive strategy as 'suicide reproduction' [START_REF] Kooijman | Dynamic Energy Budget theory for metabolic organisation[END_REF].

The DEB model describes changes in the energy content of four state variables (E, V, EH and ER for adults), which cannot be measured directly. The volumetric structural length (L=V 1/3 ) can be approximated by the shape-corrected physical (observable) length (δM Lw). In this study, the length (cm) of the first three segments (L3: the combined length of the prostomium, peristomium and the first setiger) was used as the physical length, as this is more reliable than the total length in polychaetes. Wet weight (WW) was calculated as the sum of the wet mass of the structure and the wet mass of the reserve (see S1 stage (from 0 to 22 days), the polychaete offspring were fed with microalgae (Chlorella sp.), which were cultured at the experimental station and can be ingested (this was confirmed by microscopic observation of the gut content). Before the beginning of the growth experiment, juveniles (from 22 to 113 days), were fed with fish faeces and raised at temperatures ranging between 15°C and 18°C. This food was chosen because fish farm waste is mainly composed of fish faeces and a varying proportion of uneaten fish feed [START_REF] Galasso | The potential of near infrared spectroscopy (NIRS) to measure the chemical composition of aquaculture solid waste[END_REF].

Growth rates.

The growth experiment was conducted on individuals when they reached 113 days of age; the experiment lasted 98 days (February-April 2017). Two types of feed were tested: faeces from farmed European seabass Dicentrarchus labrax (Fish faeces) and commercial fish feed (Fish feed). The collection and preparation of these are detailed in [START_REF] Galasso | The potential of near infrared spectroscopy (NIRS) to measure the chemical composition of aquaculture solid waste[END_REF]. The fish faeces were composed of 72% organic matter (OM) (including 3% total organic nitrogen [TON] and 7% total lipids

[TL]), and 28% ash. The commercial fish feed was composed of 87% OM (including 7% TON and 12% TL) and 12% ash. Polychaetes were fed ad libitum (based on the observation of leftover food in the tank) from 48 mg feed.ind -1 .d -1 to 85 mg.ind -1 .d -1

(from the beginning to the end of the experiment). The 113 ± 1 day-old individuals (days post-fertilization) at the start of the growth experiment measured on average 1.16 ± 0.24 mm L3. Each treatment was performed in small tanks (4 L) in triplicate (6 tanks; 18 polychaetes per tank; total of 108 worms). The water temperature was maintained at 17 ± 1°C and at a salinity of 18 ± 1 psu (temperature and salinity conditions favourable to Hediste growth) [START_REF] Olivier | Juvenile growth of the polychaete Nereis virens feeding on a range of marine vascular and macroalgal plant sources[END_REF][START_REF] Batista | Production of the ragworm Nereis diversicolor (O. F. Müller, 1776), fed with a diet for gilthead seabream Sparus auratus L., 1758: survival, growth, feed utilization and oogenesis[END_REF]. The worms were reared without sediment, but plastic tubes (Ø = 4 mm; several lengths) were added to provide refuge to reduce stress (adapted from [START_REF] Nesto | Evaluation of different procedures for fertilization and larvae production in Hediste diversicolor[END_REF]. The tanks were continuously aerated to maintain oxygen concentration close to saturation for the given temperature [START_REF] Galasso | Body size and temperature effects on standard metabolic rate for determining metabolic scope for activity of the polychaete Hediste (Nereis) diversicolor[END_REF]. Individual wet weight was measured on days 177 and 211, and individual L3 length on days 113, 144, 177 and 211. The worms were weighed individually after a fasting period of 24 h to empty their digestive tract. They were then carefully taken from the water using a dip net, cleaned with seawater and dried on paper towels before being weighed on an analytical balance with a precision of 0.001 g.

Specific growth rate was calculated as = × 100, where and is the wet weight (g) at the beginning and the end of the experiment respectively, and t is the experiment duration (d) [START_REF] Hopkins | Reporting Fish Growth: A Review of the Basics[END_REF]. A Two-way Anova was performed to test the effect of food type (fixed factor, n= 2, Fish feed and Fish faeces) and tank (random factor, n=3) on WW and L3 at each biometry data. In total, 54 individuals were measured per food type.

Oxygen consumption.

The oxygen consumption rates of the ragworms were recorded as a proxy of the minimal metabolic rate (the standard metabolic rate) at four temperatures (11°C, 17°C, 22°C and 27°C). The oxygen consumption could be considered a proxy of the minimal metabolic rate as it was measured on individuals that had fasted for 24 h in the dark. A detailed description of the experiments and results are presented in [START_REF] Galasso | Body size and temperature effects on standard metabolic rate for determining metabolic scope for activity of the polychaete Hediste (Nereis) diversicolor[END_REF]. The individuals ranged from 0.02 to 0.57 g WW, and

1.40 to 3.64 mm L3. The polychaetes were acclimatized for 10 days and fed ad libitum with seabass Dicentrarchus labrax faeces, then acclimatized for 7 days at the experimental temperature conditions. The incubation times were chosen to prevent oxygen saturation from dropping below 80%. Consequently, incubation times varied from 4 h (for the aquariums at 22°C and 27°C) to 5 h (for those at 11°C and 17°C). The results were expressed in µmol/h.

Ammonia excretion.

An ammonia excretion experiment was performed simultaneously with oxygen consumption measurements. Water samples (50 mL) were taken at the beginning of the experiment ( ) (filtered seawater was used to fill the individual chambers) and at the end of incubation ( ), and immediately frozen at -20°C for further ammonium analyses (N-NH4). The ammonium concentrations were measured using Seal AA3 analytical autoanalyser standard methods [START_REF] Aminot | Dosage automatique des nutriments dans les eaux marines[END_REF] with fluorometric detection (from JASCO, FP-2020plus, France).

Ammonia excretion rates were determined following the equation used by Galasso et al.

(2018) for oxygen. N-NH4 was transformed to N-NH3 using the conversion factor 1.22 (based on molar mass).

Comparison between predicted and observed data

Simulations were then carried out to compare the output of the model to data from laboratory experiments on growth performance, oxygen consumption ( ) and ammonia excretion ( ). In DEB theory, and are weighted sums of three basic fluxes: assimilation ( ), dissipation ( ) and growth ( ! ) (see S1 for details and equations).

First, optimizations of scaled functional response (f) were performed to evaluate the assimilation rate of the polychaetes. This was performed using the cma_es function from the cmaes package in R (Trautman et al., 2011) run to minimize the mean relative error (MRE) between predicted and observed data. First an f value was obtained for the period prior to the growth experiment (until 113 days of age), and then an f value was fitted for each feeding condition (fish faeces or fish feed) in the growth experiment. The last L3 length was not used in the fitting process because of high size-specific mortality related to reproduction. As individuals become green at maturity (Dales, 1950), we used this criteria to remove these individuals from the group and from the dataset. Water temperatures during the different experiments were included in the model.

Second, since the oxygen consumption and ammonia excretion experiment was performed using individuals fed on faeces, the f fitted using the growth experiment on individuals fed faeces was used for simulating these variables. In addition, as the polychaetes used in the respiration and excretion experiment were collected in the wild, the age and life histories of these individuals were unknown. The scaling with the length and weight was therefore obtained using the DEB model run for individuals with identical life histories (but different ages). Therefore, all the observed differences in lengths within this experiment were linked to differences in age. Finally, since the experiment was performed on polychaetes that had been starved for 24 h, we assumed that the oxygen consumption and ammonia excretion associated to energy assimilation was null ( = 0).

2.4.

IMTA scenarios: temperature and assimilation rates 2.4.1 Effects of temperature and assimilation rate variations. We evaluated the effects of two key factors that may affect growth: temperature and assimilation rates. As temperature is the main factor in metabolism changes, especially in ectotherms [START_REF] Wieser | Effects of Temperature on Ectothermic Organisms: Ecological Implications and Mechanisms of Compensation[END_REF], the effect of a large range of temperatures from 5°C to 25°C (in 5°C increments), with fixed optimal feeding conditions (scaled functional response, f=1), was tested. This range was selected based on temperature variations observed in H. diversicolor habitats [START_REF] Scaps | A review of the biology, ecology and potential use of the common ragworm Hediste diversicolor (O. F. Müller) (Annelida: Polychaeta)[END_REF] and temperatures that are recorded in European aquaculture production from Norway to Mediterranean Sea (ex. [START_REF] Brigolin | Modelling biogeochemical fluxes across a Mediterranean fish cage farm[END_REF][START_REF] Wang | Embryonic and larval development in the semelparous Nereid polychaete Hediste diversicolor (OF Muller, 1776) in Norway: Challenges and perspectives[END_REF].

Assimilation rates were also tested, with f ranging from 0.5 to 1 (half ration of ad libitum to full ad libitum) (in 0.1 increments), at a constant 20°C temperature.

The gonadosomatic index (GSI) is the ratio between gonad mass and total body mass.

Using DEB theory, GSI is estimated as the ratio between the reproduction buffer wet mass and the wet weight of the animal (see S1). The GSI could therefore be estimated for each age in the growth experiment. In parallel, survival was recorded during the growth experiment. It was assumed to be mostly related to the spawning event (and the associated death) of the animals. We posited that spawning was triggered above a certain GSI threshold. The survival curve was fitted over time using a sigmoid function with the nls function in R (3.6.2) and Rstudio (1.2.5033). This enabled us to create a link between the estimated GSI and survival. The curve was fitted with a polynomial curve (of degree 5) using the poly function in R in order to obtain links between survival and any GSI. Only the results from the growth experiment using faeces were used for these estimations, since faeces are intended to be the most important food source in a well-designed IMTA system. A GSI of 3% was chosen for the bioremediation simulations since survival was high until this threshold (>90%).

Bioremediation capacity.

To estimate the bioremediation capacity of polychaete to consume fish solid wastes, total assimilated energy was estimated over a ragworm production cycle (from birth to harvest) in several scenarios (at 20°C with f=0.5 or f=1, and at 5°C and 25°C with f=1). In aquaculture, a good compromise between reaching commercial weight and survival rates has to be found. For each scenario, simulations were either stopped when the GSI reached 3%, or when individual reached 0.5 g WW (minimum polychaete market size, [START_REF] Nesto | Effects of diet and density on growth, survival and gametogenesis of Hediste diversicolor (O. F. Müller, 1776) (Nereididae, Polychaeta)[END_REF]. Total assimilated energy (J) was then transformed into grams of dry weight (g DW) of faeces considering that the energy content of one g (DW) of fish faeces was 10.4 kJ. We based our estimation on the average composition of seabass faeces: proteins (14%), lipids (4.6%), carbohydrates (12.8%), fibre (40.6%), and ash (28%) [START_REF] Galasso | The potential of near infrared spectroscopy (NIRS) to measure the chemical composition of aquaculture solid waste[END_REF], and the associated respective energy contents of 23.6 kJ.g -1 , 36.2 kJ.g -1 , 17.2 kJ.g -1 , 8 kJ.g -1 and 0 kJ.g -1 [START_REF] Brigolin | Modelling biogeochemical fluxes across a Mediterranean fish cage farm[END_REF][START_REF] Chary | Integrated multi-trophic aquaculture of red drum (Sciaenops ocellatus) and sea cucumber (Holothuria scabra): Assessing bioremediation and life-cycle impacts[END_REF]. Based on information provided in another study [START_REF] Scaps | A review of the biology, ecology and potential use of the common ragworm Hediste diversicolor (O. F. Müller) (Annelida: Polychaeta)[END_REF], we considered a population density of 3700 ind.m -2 and estimated the bioremediation capacity of a ragworm farm per m 2 for a year-round production, considering the life expectancy of the ragworms and the control of H. diversicolor reproduction [START_REF] Wang | Embryonic and larval development in the semelparous Nereid polychaete Hediste diversicolor (OF Muller, 1776) in Norway: Challenges and perspectives[END_REF].

Results and discussion

The results from our simulations obtained for H. diversicolor using DEB theory provided a good fit with new empirical data on growth, oxygen consumption and excretion in aquaculture conditions. This new empirical data set was not used for the optimization of the parameters available online [START_REF] Lefebvre | AmP Hediste diversicolor[END_REF], and therefore we applied it in order to independently validate the parameter set.

3.1 Growth rates and food quality. The effect of the two food types, Fish faeces and Fish feed, on the growth rates of Hediste diversicolor are presented in Table 2. After 98 days of the experiment, polychaetes fed with Fish faeces had a slightly (NS) higher final weight (0.41 ± 0.17 g) and length (L3 = 0.30 ± 0.05 cm) than those fed with Fish feed (WW= 0.36 ± 0.15 g and L3= 0.28 ± 0.06 cm). Significant difference between treatment was only observed on day 177 (two-way Anova test, see Table 2). Individual growth rates (from day 113 to 177) were 0.03 mm L3.d -1 and 5 mg WW.d -1 (3.8% SGR) for faeces, and 0.02 mm L3.d -1 and 4.2 mg WW.d -1 (3.5% SGR) for feed. We used the DEB model as an explanatory tool to estimate scaled functional response (f) levels in our growth experiment. f were estimated at 0.6 and 0.5, for Fish faeces and Fish feed respectively, resulting in slightly higher growth rates for H. diversicolor feed with Fish faeces. The DEB simulation fit well with observed length data in the growth experiment (Figure 2), with an MRE of 0.11. In results obtained in other studies, a high variation in growth rates has been observed in relation to food quality. For example, in similar conditions of temperature and salinity (25 psu, 18°C) and for comparable initial weights (50 mg WW), lower growth rates (2.1 mg WW.d -1 , 1.8% SGR) were measured for H.

diversicolor fed with macroalgae [START_REF] Olivier | Juvenile growth of the polychaete Nereis virens feeding on a range of marine vascular and macroalgal plant sources[END_REF]. [START_REF] Meziane | Growth of Nereis diversicolor (L.) juveniles fed with detritus of halophytes[END_REF] obtained even lower growth rates (0.5 to 2.8 mg WW.d -1 , 0.3% to 1.9% SGR) for ragworms fed with halophyte detritus in similar environmental conditions (15 psu, 21°C). However, Fidalgo e Costa et al. (2000) measured growth rates of 14 mg WW. d -1

(5.5% SGR) feeding H. diversicolor with a post-larval shrimp diet (15 psu and 20°C).

High growth rates (6% to 12% d -1 SGR) were also recorded in [START_REF] Nesto | Effects of diet and density on growth, survival and gametogenesis of Hediste diversicolor (O. F. Müller, 1776) (Nereididae, Polychaeta)[END_REF], who tested three different sources of food, including Larviva-Biomar® and a seaweed (Sargassum muticum, a low-protein food) in H. diversicolor cultures. In fact, this last study was used in the parameter estimation procedure for H. diversicolor [START_REF] Lefebvre | AmP Hediste diversicolor[END_REF], Add-my-Pet), considering a maximal functional response for the best food source (f =1). [START_REF] Wang | Growth and nutritional composition of the polychaete Hediste diversicolor (OF Muller, 1776) cultivated on waste from land-based salmon smolt aquaculture[END_REF] observed that H. diversicolor reared on fish feed (0.025 d -1 SGR) grew significantly faster than worms grown on the other diets, including smolt waste (0.012 d -1 SGR). The difference between their growth rates and the rates measured in our study may originate from varying food quality and other different experimental conditions, i.e. presence/absence of sediment. Indeed, in our experiment, food was provided ad libitum, suggesting that f=1. The fitted f values of 0.5 and 0.6 obtained in our study probably result from a lower digestibility of fish waste compared to other food sources (see [START_REF] Lefebvre | Pacific oyster (Crassostrea gigas) feeding responses to a fish-farm effluent[END_REF]. Further experiments could be performed to investigate these hypotheses. Nevertheless, our results showed that despite differences in food quality, growth rates were in the range of other studies. More importantly, although fish waste does not lead to the best SGR compared to other studies, our results indicate that it is a suitable food type for the development, growth and reproduction of H. diversicolor in the context of IMTA.

Suicide reproduction and GSI.

It is important to anticipate reproduction, especially when it is associated to death, as is the case for semelparous species. In ragworm aquaculture, harvesting would have to be performed just before reproduction when worms have reached minimum market size (0.5 g WW, [START_REF] Nesto | Effects of diet and density on growth, survival and gametogenesis of Hediste diversicolor (O. F. Müller, 1776) (Nereididae, Polychaeta)[END_REF]. In our study, observations of the first mortalities attributed to suicide reproduction were made on day 144 (mean survival of 94%). On day 211, mortality reached 43% for individuals fed fish faeces and 52% for individuals fed fish feed. Using DEB simulation, we were able to attribute a GSI to these individuals (Figure 3). We used a GSI of 3% as a threshold for harvesting the individuals during the bioremediation simulations. Indeed, under a GSI of 3%, a survival rate above 90% was estimated (Figure 3). This threshold was estimated from our growth experiment only. Further studies in which GSI is measured on live animals are therefore needed to confirm this threshold. Environmental factors may greatly influence reproduction, including temperature and photoperiod variations [START_REF] Scaps | A review of the biology, ecology and potential use of the common ragworm Hediste diversicolor (O. F. Müller) (Annelida: Polychaeta)[END_REF][START_REF] Nesto | Evaluation of different procedures for fertilization and larvae production in Hediste diversicolor[END_REF]. In a natural environment, [START_REF] Olive | Gametogenic cycle and population structure of Nereis (Hediste) diversicolor and Nereis (Nereis) pelagica from north-east England[END_REF] observed the first appearance of developed oocytes in H. diversicolor coelom after 18 months. In our study, polychaetes started to reproduce after 5 months, which may indicate that aquaculture conditions with a stable temperature and stable feed input were more favourable to ragworms than natural conditions. Maturation around 4 months under control environment has been observed previously [START_REF] Nesto | Effects of diet and density on growth, survival and gametogenesis of Hediste diversicolor (O. F. Müller, 1776) (Nereididae, Polychaeta)[END_REF]. The DEB framework allows simulations to be performed in an environment in which food and temperature vary over time, and therefore estimations of in situ age at death (i.e. reproduction) could be performed in the wild as long as temperatures and food conditions are available.

Oxygen consumption and ammonia excretion rates.

The results showed that oxygen consumption (metabolic rate) and ammonia excretion rates increased with body size (WW and L3) and temperature (Figures 4 and5). The DEB outputs for oxygen consumption and ammonia excretion at different temperatures correctly fit observed data despite the wide variability in oxygen consumption, ranging from 0.09 to 2.35 μmol.h -1 (Figure 4) [START_REF] Galasso | Body size and temperature effects on standard metabolic rate for determining metabolic scope for activity of the polychaete Hediste (Nereis) diversicolor[END_REF], and ammonia excretion, ranging from 4.10 -6 to 0.58 µmol.h -1 (Figure 5). The fit between the oxygen consumption data and the predictions was better than for the ammonia excretion data, with respective MREs of 0.51 and 0.80. It appeared that the ammonia results were underestimated by the model.

The ammonia results were more scattered than the oxygen consumption rate results. The incubation times was short to keep a good oxygen saturation and concentrations were close to the detection limit. A longer incubation period and no previous starvation may have provided less variable data. In marine species, an increase in ammonia excretion with increased temperature is well known, including for invertebrates [START_REF] Chen | Effects of temperature and salinity on oxygen consumption and ammonia excretion of juvenile Penaeus japonicus Bate[END_REF]. In contrast to fish, very little is known regarding the ammonia excretion mechanism and the participating excretory organs in marine invertebrates, especially in polychaetes (Thiel et al., 2017). Thus, our study provides valuable data on this topic, which will need further quantitative data in order to properly characterize nutrient fluxes in IMTAs.

Bioremediation potential.

We found that growth rates increased with increasing temperatures (Figure 6) and scaled functional response (f, Figure 7). For the bioremediation estimation, simulations were stopped when GSI reached 3% or 0.5 g WW, considered as the minimum market size. The results from selected scenarios are shown in Table 3. At 20°C, an increased assimilation rate (higher f) reduced the time to reach the GSI threshold (99 days with f=0.5 vs 79 days with f=1). At this stage, ragworms weighed only 0.2 g at f=0.5 compared to 0.6 g when f=1. At the maximum assimilation rate (f=1), increased temperature (5°C vs 25°C) decreased the time to reach a GSI of 3% (163 days at 5°C vs 64 days at 25°C), but had no effect on the final wet weight (0.6 g). Similar observations were made when simulations were stopped at a wet weight of 0.5 g. It should be noted that at 20°C with f=0.5, the minimum market size of 0.5 g was reached in 128 days, but with a GSI of 3.9%. In a bioremediation perspective, the potential of H. diversicolor was estimated based on cumulated assimilation rates (ṗA). Assuming an energy content of 10.4 kJ.g -1 DW of seabass faeces, and based on the high density of H. diversicolor (3700 ind. m -2 ) reported in nature [START_REF] Scaps | A review of the biology, ecology and potential use of the common ragworm Hediste diversicolor (O. F. Müller) (Annelida: Polychaeta)[END_REF], we estimated a bioremediation capacity ranging from 0.23 to 0.87 g faeces DW ind -1 year -1 , eq of 755 to 2887 g faeces DW m -2 year -1 (Table 3). This could represent 75-289 kg for a 100 m 2 ragworm farm, equivalent to a 2-9 % reduction in the waste produced by a 20T seabass farm (160 kg of DW faeces per ton of seabass production, based on assimilation coefficients in [START_REF] Brigolin | Modelling biogeochemical fluxes across a Mediterranean fish cage farm[END_REF]. This study therefore confirms the potential of H. diversicolor in IMTA systems, in particular associated with fish farms, as has been shown in previous studies [START_REF] Batista | Production of the ragworm Nereis diversicolor (O. F. Müller, 1776), fed with a diet for gilthead seabream Sparus auratus L., 1758: survival, growth, feed utilization and oogenesis[END_REF][START_REF] Bischoff | The fatty acid composition of Nereis diversicolor cultured in an integrated recirculated system: Possible implications for aquaculture[END_REF][START_REF] Cubillo | Role of deposit feeders in integrated multi-trophic aquaculture -A model analysis[END_REF][START_REF] Marques | New species for the biomitigation of a super-intensive marine fish farm effluent: Combined use of polychaete-assisted sand filters and halophyte aquaponics[END_REF]. Comparisons of bioremediation capacity to other studies are, however, difficult as most of previous studies are site specific or based on specific scenario. The quantity of faeces produced by a marine fish farms depends on numerous factors (species, conversion ratio, temperature, farm management, etc) and can vary from 160 kg of DW faeces per ton of seabass production [START_REF] Brigolin | Modelling biogeochemical fluxes across a Mediterranean fish cage farm[END_REF] to 224 Kg of DW faeces per ton of salmon production (see review by [START_REF] Van Rijn | Waste treatment in recirculating aquaculture systems[END_REF]. [START_REF] Wang | Growth and nutritional composition of the polychaete Hediste diversicolor (OF Muller, 1776) cultivated on waste from land-based salmon smolt aquaculture[END_REF] estimated that 1 Kg of fish released 250 g of faeces and 30 g of uneaten feed and could produce 800 g of H. diversicolor. Considering the feed conversion ratio (g dry faeces used/g polychaete biomass produced) of 3.55 given by the authors, we could estimate a bioremediation capacity of 23 g of fish faeces, eq 9.2 % of faeces reduction (ragworm density was not provided in this study). Chary et al.

(2020) compared studies using mathematical models to examine uptake of solid organic matter or nutrients in IMTA systems by other detritivores. Conclusions were quite contrasted [START_REF] Chary | Integrated multi-trophic aquaculture of red drum (Sciaenops ocellatus) and sea cucumber (Holothuria scabra): Assessing bioremediation and life-cycle impacts[END_REF]. [START_REF] Cubillo | Role of deposit feeders in integrated multi-trophic aquaculture -A model analysis[END_REF] and [START_REF] Ren | An ecosystem model for optimising production in integrated multitrophic aquaculture systems[END_REF] predicted that bottom culture of sea cucumbers could remove more than 70% of the benthic particulate organic carbon (C) from Atlantic salmon (Salmo salar) farm units. These two studies did not consider rearing constraints (limit of density) for the extractive species.

Including such considerations in models can help predict more realistic production design and bioremediation potentials from extractive species. When considering current density rearing practices, [START_REF] Watanabe | Estimation of energy budget of sea cucumber, Holothuria scabra, in integrated multi-trophic aquaculture[END_REF] calculated that 4.3% of total particulate nitrogen from milkfish (Chanos chanos) culture could be removed by seacumber detritivore species. In the present study, the bioremediation potential was expressed per individual and per m -2 , and for a large range of temperature, to allow future comparisons. The DEB model allows simulations to be performed that may be useful to predict life history traits in different environmental conditions, as well as to anticipate harvest before reproduction.

Conclusion.

Our results suggest that fish waste could constitute the exclusive source of food for the polychaete Hediste diversicolor. We were able to obtain these results using a DEB model that accurately predicted the species' metabolic processes. Further studies could build on these results by including certain environmental factors, such as water salinity, photoperiod, as well as other water temperature variations that may trigger reproduction. These findings suggest that DEB modelling is a promising tool for IMTA development. The method could help fish producers manage the use of H. diversicolor to complement their primary production and could also assist environmental policy by utilizing the bioremediation potential of H. diversicolor when associated to fish production. 3. Effects of temperature and scaled functional response (f=0.5, f=0.6 and f=1 at 20°C; 5°C and 25°C with f=1) on H. diversicolor L3 length (cm), wet weight (WW g) and total assimilated energy (Assim in J) and faeces assimilation (g DW). Total assimilated energy was estimated over ragworm production cycle (see [START_REF] Wang | Embryonic and larval development in the semelparous Nereid polychaete Hediste diversicolor (OF Muller, 1776) in Norway: Challenges and perspectives[END_REF] for production cycle description). A production cycle was stopped when GSI reached 3%, or when WW reached 0.5 g WW (minimum polychaete market weight). The bioremediation capacity of one individual was estimated by transforming the assimilated energy in fish faeces by assuming (based on the literature) that 1 g of fish faeces represents 10.4 kJ. A population density of 3700 ind.m -2 [START_REF] Scaps | A review of the biology, ecology and potential use of the common ragworm Hediste diversicolor (O. F. Müller) (Annelida: Polychaeta)[END_REF]

  the ERA-Net COFASP (Strengthening Cooperation in European Research on Sustainable Exploitation of Marine Resources in Seafood Chains) project (IMTA-Effect project) with funding from the French National Research Agency (ANR-15-COFA-0001-06). It was also supported by the Brazilian government's 'Science Without Borders' programme (CAPES PhD scholarship n°13.773-13-5 awarded to HG) and the European Maritime and Fisheries Fund (EPURVAL2 project) (postdoctoral grant awarded to BS).

Figure 1 .

 1 Figure1. DEB representation of allocation rule (κ rule) and energy fluxes in an organism. Ingested energy is either assimilated or lost by defecation. Then part of the energy mobilized from the reserve (κ) is allocated for somatic maintenance and growth, and the remaining energy is spent for maturity and its associated maintenance. Once sexual maturity is reached, the energy available for maturity is used for the production of gametes (modified from[START_REF] Kooijman | Dynamic Energy Budget theory for metabolic organisation[END_REF].

Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .

 234567 Figure 2. Hediste diversicolor. Comparison of DEB simulation (line) and growth data (a) L3 length (cm) and (b) wet weight (WW) (g) for polychaetes fed with Fish faeces and Fish feed. After optimization, f=0.5 for Fish feed and f=0.6 for Fish faeces. Before the experiment (dashed line), f was estimated to be 0.4. Individual WW was measured on days 177 and 211, and individual L3 length on days 113, 144, 177 and 211. The values obtained during the last biometry (211 days post-fertilization) were not included in the optimization due to high suicide reproduction. MRE = 0.11 for L3 length values. a)

  coupling coefficient for the growth flux

. H. diversicolor growth performance in controlled environments 2.2.1. Sampling.

	WW calculation because it was considered negligible most of the time (GSI<3%, see
	below).
	2.2H. diversicolor individuals were collected in the wild in Arnel
	Lagoon, on the French Mediterranean coast. The experiments were conducted in the
	Ifremer marine aquaculture experimental station (Palavas-les-Flots, France). For the
	oxygen and excretion experiments, individuals were acclimatized for 10 days (see
	details below). For the growth experiment, in vitro reproduction was carried out in
	October 2016 in order to begin with individuals of the same age. During the early larvae
	). The wet mass of the reproductive buffer was not included in the

Table 1 .

 1 DEB abj-model parameters estimated for the polychaete Hediste diversicolor(Lefebvre, 2019, Add-my-Pet database).

	Parameters	Value	Unit	Description
	#	0.53073	Cm	Maximum volumetric length
		14.3197	J cm -2 d -1	Maximum surface-specific assimilation rate
	$	0.01123	cm d -1	Energy conductance (velocity)
	g	2.761754	-	Energy investment ratio
	% &	0.002	d -1	Maturity maintenance rate coefficient
	% '	0.007663691	d -1	Somatic maintenance rate
	(	0.96018	-	Allocation fraction to soma
	( )	0.95	-	Reproduction efficiency
	* ' +	25.91	J cm -3 d -1	Volume specific somatic maintenance rate
	*, ! +	3380.46	J cm -3	Volume specific costs of structure
	, -.	0.0003164	J	Energy maturity at birth
	, -/	0.7665	J	Energy maturity at metamorphosis
	, -0	7.883	J	Energy maturity at puberty
	1 2	4877.15	K	Arrhenius temperature
	1 34	293.15	K	Reference temperature
	5	0.440695	-	Contribution of reserve to body weight or physical volume
	δM	2.3579	-	Shape coefficient for L3 length

Table 2 .

 2 Growth performance of Hediste diversicolor fed with fish faeces and commercial fish feed over time (age in days), and associated means of L3 length (cm), wet weight (WW g) and survival: n = number of observations and SD = standard deviation. Statistical analysis was performed with food type as fixed factor and tank as random factor (* when p< 0.05).

	Age (days) Food type n L3 ± SD (cm) WW ± SD (g) Survival (%)
	113	Fish faeces 54 0.11 ± 0.02 Fish feed 54 0.12 ± 0.02
	144	Fish faeces 50 0.21 ± 0.05 Fish feed 52 0.18 ± 0.05		93 96
	177	Fish faeces 45 0.30 ± 0.05* Fish feed 42 0.27 ± 0.05*	0.35 ± 0.16 0.30 ± 0.18	83 78
	211	Fish faeces 31 0.30 ± 0.05 Fish feed 26 0.28 ± 0.06	0.41 ± 0.17 0.36 ± 0.15	57 48

Table

  was chosen to estimate the bioremediation capacity of a ragworm farm per m 2 and year.

	T	f age	L3	WW GSI Surv	Assim (per ind.)	Bioremediation
	(°C)	days	cm	g	%	%	J cycle -1 J yr -1 g (DW) yr -1	g (DW) m -2 yr -1	kg (DW) 100m -2 yr -1
	up to 3% GSI
	20 0.5 99 0.24	0.2	3.0	90	641 2370	0.23	755	75
	20 1 79 0.31	0.6	3.0	90	1603 7443	0.72	2370	237
	5	1 163 0.31	0.6	3.0	90	1596 3572	0.34	1137	114
	25 1 64 0.31	0.6	3.0	90	1600 9067	0.87	2887	289
	up to 0.5 g WW
	20 0.5 128 0.32	0.5	3.9	67	1536 4390	0.42	1039	104
	20 1 75 0.30	0.5	2.9	90	1363 6598	0.63	2122	212
	5	1 155 0.30	0.5	2.9	90	1355 3187	0.31	1025	103
	25 1 62 0.30	0.5	2.9	90	1362 8020	0.77	2579	258

Acknowledgements

The authors would like to thank Luca Florean, Osvaldo Makowiecky and Alexandre Dousset for their valuable help reviewing life history traits and in the laboratory, Thibault Geoffroy and Sébastien Triplet for their participation in the experimental work, and Marion Richard for her great help planning and conducting the oxygen consumption experiments. We thank two anonymous reviewers for their constructive comments, which helped us to improve the manuscript. We also thank Elise Bradbury for careful revision of the English. The study was carried out within the framework of