A Dynamic Energy Budget model for the macroalga Ulva lactuca

Ecological Modelling 418 (2020) 108922

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A Dynamic Energy Budget model for the macroalga Ulva lactuca a,b,c,

Romain Lavaud a b c

b

a

b

*, Ramón Filgueira , André Nadeau , Laura Steeves , Thomas Guyondet

a

T

Fisheries and Oceans Canada, Gulf Fisheries Centre, Moncton, NB, Canada Marine Affairs Program, Dalhousie University, Halifax, NS, Canada Institut des Sciences de la Mer, Université du Québec à Rimouski, QC, Canada

ARTICLE INFO

ABSTRACT

Keywords: Sea lettuce Nutrients Photosynthesis Eutrophication Estuary Synthesizing units

Macroalgal blooms in eutrophic coastal waters around the globe constitute a rising issue for ecosystems and economic activities. Sometimes leading to anoxic events, a better understanding of its growth dynamics is necessary to develop mitigation strategies and inform policies on nutrient runoff management. The development of a Dynamic Energy Budget (DEB) model for the sea lettuce, Ulva lactuca, provides a generic mechanistic description of energy and matter fluxes within the macroalgae and between macroalgae and the environment. Forcing variables consist of seawater temperature, light intensity, and seawater concentrations of dissolved carbon and nitrogen. The model includes a self-shading module for light reduction under heavy biomass and simulation outputs consist of (but are not limited to) total algae biomass, nutrient uptake (carbon and nitrogen), photosynthetic rate, and state of nutrient reserve. Model parameters were estimated using data-sets from the literature and laboratory experiments, then validated using an independent field study in two estuaries with contrasting nutrient loads that feed into Malpeque Bay, PEI (Canada). The validation step yielded accurate temporal predictions of sea lettuce biomass in both of these estuaries. These results indicate that the present mechanistic modelling approach for predicting sea lettuce dynamics captures salient patterns along a spectrum of nutrient loading and could therefore be of use for managing across diverse ecological conditions, which is particularly relevant for a widespread species like Ulva lactuca.

1. Introduction Blooms of opportunistic macroalgae are a growing concern in the context of climate change and coastal eutrophication. Blooms of sea lettuce, Ulva spp., are a prime example of one of the consequences of the increase of nutrient inputs from land all around the world (Smetacek and Zingone, 2013). On Prince Edward Island (PEI, Eastern Canada), where 40% of the land is cleared for agricultural use, nutrient runoff is the root cause of eutrophication and subsequent sea lettuce blooms in near-shore marine areas (Crane and Ramsay, 2012), leading to recurrent anoxia events (Coffin et al., 2018a). The green macroalga, Ulva lactuca, is naturally found in many bays and estuaries often freefloating in the water column and sometimes producing very dense mats at the water’s surface. Despite the increase in nitrogen loads, flora shifts from a greater proportion of phytoplankton to macroalgae may be more common in eutrophic waters (Wang et al., 2012; Wallace and Gobler, 2015). A recent study by Filgueira et al. (2015) suggested that a reduction in phytoplankton biomass from competition for nutrients with the sea lettuce and consumption by farmed and natural mollusks may limit the capacity of new aquafarms in some areas emphasizing the

⁎

necessity to include opportunistic macroalgae in models aiming at quantifying ecosystem dynamics. Modelling studies of primary producers in aquatic environments are mostly restricted to unicellular microalgae, i.e. phytoplankton. The emerging interest in macroalgae in light of the prevalence of eutrophication and their importance as a resource has recently prompted modelling studies (Hadley et al., 2015; Seghetta et al., 2016) in order to assess the threat they may represent for coastal ecosystems health and some industries (e.g. fish and shellfish aquaculture, tourism). These models can take different forms, ranging from empirical models using simple analytic formulae (Duarte and Ferreira, 1997; Huisman et al., 2002), to more complex numerical models (Broch and Slagstad, 2012) and generally all consider the two crucial controls of algal growth: light and nutrients. Empirically-based approaches play an important role in algae modelling (de los Santos et al., 2009; Anderson et al., 2010; McGillicuddy, 2010; Hadley et al., 2015), providing a link between conceptual and dynamic modelling. Such models can be coupled to other modules in box models, formalizing the interactions between the environment and organisms in more mechanistic frameworks, which can yield insights into physiological processes (Ren et al., 2012) and

Corresponding author at: Institut des Sciences de la Mer, Université du Québec à Rimouski, QC, Canada. E-mail address: [email protected] (R. Lavaud).

https://doi.org/10.1016/j.ecolmodel.2019.108922 Received 7 August 2019; Received in revised form 13 December 2019; Accepted 15 December 2019 Available online 17 January 2020 0304-3800/ Crown Copyright © 2020 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

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systemic properties and behavior (Roiha et al., 2010; Perrot et al., 2014). This may lead to a better understanding of ecosystem dynamics and functioning, however, empirical approaches lack predictive capacity and generalization to be applied to other species, locations, and times. One framework, the Dynamic Energy Budget (DEB) theory, may address this weakness. DEB provides a comprehensive description of the metabolic organization of individuals that allows the modelling of energy and mass fluxes between the environment and the organism and within the organism (Kooijman, 2010). DEB theory is generalist as it sets a series of common assumptions and parameters for all life forms, yet flexible in its implementation in order to simulate their diversity. A key feature of the theory is the use of generalized enzymes, the Synthesizing Units (SUs), to stoichiometrically operate the transformation of substrates (e.g. light, food, reserve compounds) into product (e.g. reserve molecules, heat, feces). Various studies have successfully developed DEB models for phytoplankton species to predict photosynthesis and growth rates (Papadakis et al., 2005; Lorena et al., 2010; Livanou et al., 2019), biocalcification (Muller and Nisbet, 2014), phytoplankton-zooplankton interaction (Poggiale et al., 2010). One study on macroalgae by Broch and Slagstad (2012) integrated some concepts of the DEB theory and successfully predicted the seasonal growth and composition of kelp. Further development of this type of modelling could be ideal to accurately assess and quantify the potential impact of opportunistic macroalgae on complex ecosystems such as coastal bays and estuaries. In this paper we present the first comprehensive DEB model for a macroalgal species. We describe the development of the model for the sea lettuce, Ulva lactuca, its calibration using literature and experimental data, and its application to a field study conducted in Malpeque Bay, PEI, Canada. This work represents an important advancement for the modelling of coastal ecosystems. It allows the quantification of the potential impact of sea lettuce on the nutrient dynamics in such complex and ever-changing systems.

Fig. 1. Diagram of the Ulva DEB model. State variables are presented in grey boxes. Arrows indicate fluxes corresponding to the equations of the Ulva DEB model (see text for details). The carbon assimilation sub-model in which light and CO2 are used by Synthesizing Units (SUi) to produce carbohydrates describes the photosynthetic processes taking place in the chloroplasts of algal cells.

with MEC and MEN the respective mass of carbon and nitrogen reserves. Nutrients are first transformed into reserves through dedicated assimilation SUs (Fig. 1). Each reserve is mobilized independently and first allocated to a dedicated maintenance SU. Finally, the remaining reserve fluxes are combined in a single growth SU to produce structure. Because the dynamics of each reserve can be different, the growth SU can receive more of one type of substrate. This results in the rejection of a certain quantity of this substrate, a fraction of which is fed back to its reserve, while the other is excreted. When mobilized reserves are not sufficient to cover maintenance costs, structural mass is broken down to fulfill the required maintenance cost. Sea lettuce thalli are constituted of two cell layers separated by an intercellular volume, which can be considered negligible. As a results surface area and volume vary linearly, which qualifies sea lettuce as a V1-morph as specified in the DEB terminology, i.e. organisms with a surface area proportional to volume. This simplifies all model equations as compared to models for isomorphs. In the life cycle of sea lettuce both sexual and asexual reproduction occurs. Due to a lack of data on these mechanisms and for simplicity, the model in its current form does not account for reproductive processes. We now detail the equations of the model, which is based on the models previously developed for microalgae by Papadakis et al. (2005), Lorena et al. (2010), and more recently Livanou et al. (2019).

2. Material and methods 2.1. The Ulva DEB model 2.1.1. General concepts The DEB theory is governed by assumptions allowing a sound description of the metabolic organization in compatibility with physics and evolutionary laws. The strong homeostasis hypothesis (Kooijman, 2010) is a core assumption in DEB theory stating that the structure V and the reserve(s) E do not change in chemical composition and thermodynamic properties. A stable internal chemical composition means that organisms have a higher control over their own metabolism because the rate of chemical reactions depends on the chemical composition of the surrounding environment (Sousa et al., 2008). When assimilation pathways are essentially independent, such as in algae and other autotrophs, the constant chemical composition of reserves can only be ensured if there are different reserves for each assimilation pathway (Kooijman, 2010). We considered here two substrates: carbon and nitrogen, each with a corresponding assimilation pathway and reserve. Other nutrients such as phosphorus could be added, with similar dynamics as that of nitrogen but many studies showed that nitrogen prevails as the main limiting substrate for sea lettuce (Teichberg et al., 2010 and references within). Synthesizing Units (SUs), defined as conceptual enzymes in DEB theory (Kooijman, 2010), were used to perform all transformations of one or several substrate molecules into one or several product molecules. These mechanistic transformations were defined at the individual level for nutrient uptake as it is the appropriate level of organization for this process (Poggiale et al., 2010). These uptake formulations were then included in a DEB population model, which dynamics were represented by three state variables: structure MV (molV), nitrogen reserve density m EN = MEN / MV (molN molV–1), and carbon reserve density m EC = MEC /MV (molC molV–1);

2.1.2. Assimilation of nutrients The different forms of nitrogen taken up from the environment by macroalgae primarily consist of nitrate, ammonium, urea, and amino acids (Tyler et al., 2005; Giordano and Raven, 2014); however, nitrate is the major source (Kennison et al., 2011). Nitrogen uptake is operated by active transporter proteins in the cell membrane and is usually transformed to be assimilated into reserve as glutamate, although it may also be temporarily stored as nitrate, amino acids, or proteins prior to assimilation (Giordano and Raven, 2014). The incorporation of nitrogen into reserve is described in the model by a Michaelis-Menten relationship: 2

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jEN A = jEN Am

[N ] [N ] + KN

and yCO2 C the stoichiometric coefficients that denote the yield of C per compound NADPH and CO2, respectively. During the photolysis reaction of photosynthesis 4 mol of NADPH and 1 mol of dioxygen are produced (2H2O + 4 NADP+ + light → O2 + 4 NADPH). Therefore, the rate of oxygen production jO2 (gO2 g–1 h–1) can be computed from jL (Eq. (2)) as:

(1)

with jEN Am the maximum volume-specific assimilation rate (in molN molV–1 h–1), [N] the concentration of dissolved nitrogen in the environment (in molN L–1), and KN the half saturation constant (in molN L–1). Throughout this study rates such as jEN Am are expressed per C-mol of structure. The assimilation of carbon through photosynthesis is more complex, requiring two substrates: photons and CO2. Three ‘photosynthetic’ SUs are used to model the different steps of photosynthesis (Fig. 1). A first SU in the chloroplasts captures the photon flux through the photosystems (PS) and utilizes this energy to produce NADPH (this represents the light-dependent reaction of photosynthesis which also produces ATP); a second SU handles the uptake of CO2; and a third SU utilizes the products of the first two to assimilate carbon as carbohydrates into the reserve (this represents the Calvin-Benson cycle). As in Papadakis et al. (2005), we considered simple dynamics for the capture of photons (denoted γ) by the first photosynthetic SU, with no photorespiration. The relaxation rate of products by the first photosynthetic SU at steady state is denoted jL (in molγ molV–1 h–1) and is given by:

jL = L

L bL dPS

1+

L

L bL

jO2 =

with yLO2 the yield of O2 per photon (molO2 molγ ), W the total biomass (in g) and wO2 the molar weight of a molecule of dioxygen (in g mol–1). 2.1.3. Reserve dynamics Each reserve is then mobilized to fuel maintenance requirements, the remainder being allocated to growth. According to DEB theory, reserve densities m Ei , i = [N, C], follow first-order dynamics, which means that for a reserve Ei , the structure-specific mobilized flux equals:

jEi C = m Ei (k Ei

–1

–2

r=

–1

where L is the light intensity (in E m h or molγ m h ), L is the specific photon arrival cross section (m2 molPS–1), bL is the binding rate of photons to free SUs (dimensionless), dPS is the quantity of PS per unit of structural mass MV (in molPS molV–1), and kL is the dissociation rate (in molγ molPS–1 h–1). The unit of jL is not straightforward but it can be expressed in molNADPH molV–1 h–1 using a conversion factor of 0.2 as 5 mol of photons are required per mole of NADPH (Lika and Papadakis, 2009). Sea lettuce relies on different mechanisms for photosynthetic carbon uptake, the predominance of which depends on seawater chemistry (e.g. pH, temperature). Although the availability of free CO2 can be limited, direct diffusion may account for more than 50% at low pH (Axelsson et al., 1995). Some plants and algae, including sea lettuce, have developed mechanisms to utilize and concentrate HCO3– as an indirect source of carbon at higher pH (Axelsson et al., 1995). The uptake of carbon by sea lettuce may thus rely on a combination of direct CO2 diffusion, transport of HCO3– through membrane channels, and the intra- and extra-cellular/surface-bound dehydration of HCO3– in CO2 by the carbonic anhydrase. For simplicity, we consider that the second photosynthetic SU utilizes either source of carbon to deliver CO2 to the next SU. This can also be described through a Michaelis-Menten relationship:

jCO2 = jCO2 m

[CO2 ] [CO2] + K C

1 1 1 + ' + ' jEC Am j CO2 jL

1 dMV MV dt

jEMi i = min(jEi C , jEi M )

jEi G = jEi C

jEMi i

(9)

to the growth SU where they are all merged stoichiometrically to synthesize one C-mole of structure. Reserves are treated complementarily and in parallel in the growth SU, which leads to a specific growth flux given by:

jEi G

jVG =

(3)

1

(8)

2.1.4. Growth, maintenance and rejection Each reserve therefore sends a structure-specific flux:

i

j' L + j'CO2

(7)

which relates to the dilution by growth. Mobilized reserves are first used for maintenance, which in DEB theory refers to the turnover of structure, maintenance of cellular gradients, and maturity level maintenance, among others. The costs of maintenance are proportional to the structural volume and for a reserve Ei they amount to a constant structure-specific maintenance flux jEi M . The flux from mobilized reserve to maintenance is given by:

yEi V

1

jEi G i

yEi V

1

1

(10)

with yEi V the yield coefficient of the i-th reserve to structure, i.e. the number of moles of reserve Ei required to synthesize one C-mole of structure. Since nutrients are taken up independently, one structurespecific flux from reserve jEi G can limit the synthesis of structure. In that case, the non-limiting flux will occupy the respective SU’s binding site without being promptly processed (Lorena et al., 2010). As binding sites for the non-limiting substrate all become occupied, further arriving flux will be rejected by the growth SU at a specific rate:

with jCO2 m the maximum volume-specific uptake rate of CO2 (in molCO2 molV–1 h–1), [CO2] the concentration of carbon dioxide in the environment (in molCO2 L–1), and KC the half saturation constant (in molCO2 L–1). The products released by the first two photosynthetic SUs, i.e. NADPH on one hand and CO2 on the other hand are treated as complementary substrates in the third photosynthetic SU and processed in parallel (Lorena et al., 2010). It corresponds to the transformation of CO2 into carbohydrates during the Calvin–Benson cycle and results in a specific assimilation flux of carbon given by:

jEC A =

(6)

r)

with k Ei the turnover rate of the i-th reserve and r the net specific growth rate:

(2) –2

(5) –1

1

kL

MV j y wO W L LO2 2

jEi R =jEi G

yEi V jVG

(11)

which corresponds to the difference between the available flux for growth and the flux actually used for growth. The rejected fluxes are fed back to their respective reserve with a probability Ei , the rest being excreted in the environment. This excretion mechanism ensures that non-limiting reserves do not accumulate indefinitely. If the mobilized flux for a given reserve is not enough to cover maintenance costs, i.e. jEi M > jEi C , structure can be broken down to fill the deficit at a rate:

1

(4)

where jEC Am is the maximum volume-specific C assimilation rate (in molC molV–1 h–1) and j L = jL / yLC and j CO2 = jCO2 / yCO2 C are the specific arrival rates of NADPH and CO2 to the SU, respectively, with yLC 3

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jVMi = (jEi M

jEMi i ) yEi V

1

2.2.2. Starvation experiment data In April 2017, sea lettuce thalli were collected in Basin Head, Prince Edward Island (46°23′07.0″ N, 62°07′13.8″ W) and transported to the Dalhousie University Aquatron wetlabs in Halifax, NS, where they were placed in submerged mesh baskets in 12 tanks held at constant temperature (9 °C) matching in situ conditions at the time of collection. Tanks were covered to ensure complete darkness in order to block photosynthesis and therefore carbon assimilation. Over a period of 2 weeks and at a rate of 1 °C per day, temperature was gradually decreased to 4 °C in three random tanks and increased to 10, 16, and 22 °C in the other tanks (3 tanks per condition). Measurements of dry weight (gDW), carbon (C) and nitrogen (N) tissue content (in %DW) and seawater C and N concentration (mol L–1) were collected when the algae were brought to the lab and every 3–4 weeks after that, for 75 days. Three small mesh boxes containing an initial standardized weight of 3 gDW of sea lettuce were sampled from each tank throughout the experiment to monitor weight loss. At each sampling date, algae samples of about 20 g wet weight were collected in triplicate from each tank, dried, ground and kept frozen (−20 °C) until C and N tissue content quantification, later performed with a vario MICRO cube elemental analyzer (Elementar). Seawater nitrogen concentration (NO3 and NO2) was determined from 3 ml samples collected in triplicate from each tank, stored at −20 °C before being analyzed with an AutoAnalyser HR III (Seal Analytica).

(12)

The sum of the maintenance fluxes from structure amounts to jVM = i jVMi . Therefore the net specific growth rate may be written as r =jVG jVM and it is important to notice that it can be negative. Because r is implicit (c.f. Eq. (6)), we need to estimate its value at each time step. To do so, we used the sgr2.m function from the alga entry of the DEBtool package – an online collection of scripts freely available (https://www.bio.vu.nl/thb/deb/deblab/debtool/DEBtool_M/manual/ index.html) to estimate the specific growth rate for a two-reserve DEB model using a Newton-Raphson method with continuation. Finally, at the exception of the photon binding rate (bL , Lorena et al., 2010), all rates are corrected for the effect of temperature, as assumed in the DEB theory, using an Arrhenius correction factor calculated as: cT = exp

TA Tref

+ exp

TA T

TAH TH

1 + exp TAH Tref

TAL Tref

1 + exp

TAL TL TAL T

TAL TL

+ exp

TAH TH

TAH T

1

(13) with TA the Arrhenius temperature, Tref the reference temperature, TL and TH the lower and upper boundaries of the temperature tolerance range, and TAL and TAH the Arrhenius temperatures outside these boundaries (all expressed in Kelvin).

2.2.3. Parameter calibration All simulations and the parameter calibration were performed in Matlab R2018b. Parameters of the Arrhenius relationship were estimated via non-linear regression. We used the values given by Lorena et al. (2010) as initial values for the other parameters. All experimental data-sets were used at the same time to manually calibrate the model parameters. The goodness of fit of the model to observed data was evaluated through root mean square error (RMSE) for each data-set. A normalized RMSE (NRMSE) was determined to assess the overall quality of the estimated parameters by calculating the average of each data-set’s normalized RMSE, as given by:

2.1.5. Model dynamics The dynamics of the state variables are given by the following differential equations:

d m E = jEi A dt i d MV = rMV dt

jEi C +

Ei jEi R

rm Ei (14)

Total biomass is given by:

(

)

W = wV + m EN * w EN + m EC * w EC MV

(15)

n

with wV and w Ei the molar weight for structure and reserve i (in g mol–1), respectively. The N:C ratio in the whole organism was computed as:

nNV * MV + MEN nNV + m EN Ntotal = = Ctotal MV + MEC 1 + m EC

NRMSE=

W

Wshading

(16)

(18)

2.3. Model validation The parameters for the Ulva DEB model were validated against an in-situ monitoring data-set of sea lettuce biomass over an entire growing season. Model performance was evaluated through type 2 linear regressions between observed and simulated data. Algae were collected in two estuaries that feed into Malpeque Bay, Prince Edward Island, Canada between 18 May and 02 November 2017 (Fig. 2). These two locations were selected for their known contrasted nutrient load and sea lettuce abundance. Barbara Weit (∼0.71 km2), located southeast of the bay receives high nitrogen inputs and usually shows high sea lettuce biomasses. The Tyne Valley estuary (∼1.44 km2), located at the north-west of the bay, has limited nutrient runoffs and usually shows scarcer sea lettuce presence. We will refer to these systems as the “high N estuary” and “low N estuary”, respectively. In the high N estuary, seven cross-estuary transects and three water sampling points were determined from the up-river to the bay and their GPS coordinates recorded. In the low N estuary, 18 transects were established also with three sampling points each. Every two weeks we collected sea lettuce from each sampling point from a shallow vessel using oyster tongs

1

with Wshading the biomass threshold for self-shading effect and species specific coefficient.

RMSEi (max[pij ] min[pij ])

with pij the set of predictions for the dependant variable of data set n. Notice that, as explained by Marques et al. (2019), including more data from the literature in the parameter estimation is likely to increase variation in environmental conditions and so in parameter values, resulting in increased NRMSE.

The density of macroalgae in the environment reduces the quantity of light that penetrates in the water, leading to self-shading. This effect was implemented in the model as a correction factor to light intensity based on a logistic function of biomass:

cL = 1 + exp

1 n i=1

(17) a

2.2. Model calibration 2.2.1. Calibration data Model parameters were calibrated using experimental data-sets from the literature (Table 1), including nitrogen uptake rate (Runcie et al., 2003; Gordillo et al., 2001), photosynthetic production rate (Rivers and Peckol, 1995; Riccardi and Solidoro, 1996), growth rate (Steffensen, 1976; Fortes and Lüning, 1980; Gordillo et al., 2001; Tremblay-Gratton et al., 2018), and C and N contents (Gordillo et al., 2001; Figueroa et al., 2009; Tremblay-Gratton et al., 2018) as well as data from a starvation experiment collected specifically for this study and described hereafter. 4

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Table 1 Experimental data used to calibrate the DEB parameters. Reference Runcie et al. (2003)

Data N uptake (μmol

gDW–1

–1

h ) –1

–1

Rivers and Peckol (1995)

Photosynthetic production rate (mgO2 g

Riccardi and Solidoro (1996)

Photosynthetic production rate (mgO2 g–1 h–1)

Steffensen (1976)*

Specific growth rate (d–1)

Fortes and Lüning (1980)*

Specific growth rate (d–1)

Gordillo et al. (2001)

Growth rate (%DW d–1) C:N ratio (mol mol–1)

Tremblay-Gratton et al. (2018) N and C proportion (%DW) Growth rate (%WW d–1)

Figueroa et al. (2009)

N and C proportion (mg g–1)

This study

Dry weight (gDW) N:C ratio (mol mol–1)

h )

Experimental conditions

Duration

T° =25 °C [N] = from 0 to 50 μmol L–1 T° = 5, 15, and 25 °C I = range from 0 to 1400 μE m–2 h–1 T° = 10, 20, and 30 °C I = range from 0 to 70 μE m–2 h–1 T° =27 °C I = range from 0 to 1100 μE m–2 h–1 T° = from 5 to 30 °C [C] = not specified [N] = not specified I = assumingly constant at 75 μE m–2 h–1 T° = from 0 to 25 °C [C] = not specified [N] = not specified I = 16:8 LD regime (70 μE m–2 h–1) T° =25 °C [C] = normal (20 μmol L–1) and CO2 enriched (300 μmol L–1) [N] = low (250 μmol L–1) and high (5000 μmol L–1) I = constant at 117 μE m–2 h–1 for 6 d, then circadian with max at 150 μE m–2 h–1 T° = 5 and 10 °C [C] = assumingly current (10 μmol L–1) [N] = low, medium, high (2865, 3570, and 4284 μmol L–1 respectively) I = circadian rhythm with max at 100 μE m–2 h–1 T° =22 °C [C] = assumingly current (10 μmol L–1) [N] = low (5.3 μmol L–1) and high (332 μmol L–1) I = circadian rhythm with max at 1650 μE m–2 h–1 T° = 4, 10, 16, and 22 °C [C] = current (10 μmol L–1) [N] = constant (∼15 μmol L–1) I = dark (0 μE m–2 h–1)

Discrete measurements Discrete measurements Discrete measurements

7 days

7 days

12 days

10 days

20 days

75 days

*only used in the estimation of Arrhenius parameters (see Fig. 4).

(oyster fishing tools consisting of two 4 m-long rakes attached like scissor blades) with a fixed raking area of 1 m2. Algae were carefully sorted and separated from other material (e.g. wood, aquatic fauna, inorganic material), rinsed with seawater to clean mud or sand, and excess water was removed using a large spin-drier. Samples were weighed, put in bags, and stored at −20 °C for further dry weight, ash weight and C and N content analysis. Surface temperature was recorded with a YSI probe and water samples were collected in triplicates at three locations in each estuary (upstream, midstream, and downstream) to determine nutrient concentration in the seawater (Fig. 2b,c). As the macroalgae were collected at more stations than water samples, biomass data were clustered over three sub-estuary areas, each centred on the position of the corresponding water sampling location (up-, mid-, and downstream). Analysis of C and N tissue content was conducted with a vario MICRO cube elemental analyzer (Elementar) and nitrogen concentration (NO3 and NO2) in seawater samples was quantified with an AutoAnalyzer HR III (Seal Analytica). Carbon dioxide concentration was assumed to remain constant over the study period at a value of 0.0001 mol L–1 (corresponding to a pCO2 of 350 μatm). Solar radiation data (in kWh m–2 d–1) from the University of Prince Edward Island Climate Lab (downloaded from: http://projects.upei.ca/climate/ research/) were used to compute light intensity (in μE m–2 h–1) throughout the monitoring period, using a correction factor of 0.3 to account for light absorption in seawater. Processes naturally occurring in the field such as drifting, grazing, and decomposition by bacteria can become important in late summer in Malpeque Bay, resulting in significant biomass losses, independently from the nutrient availability (Hammann and Zimmer, 2014; Coffin et al., 2017). Based on such field observations, we choose to account for these various processes through a stress function, s, meant to increase the lysis of structure through time. This function was defined as:

s = f (t , jl , rl, tl ) = jl * (1 + exp [ rl * (t

tl )])

1

(19)

where t is the time of the simulation (in hours) and the three parameters jl =0.0006 h–1, rl = 0.01 and tl =2000 h are calibrated constants of the function, corresponding to the maximum lysis rate, the logistic growth rate and the activation point in time respectively. The term s was then added to the sum of fluxes from structure to maintenance, now amounting to:

jVM =

i

jVMi + s

(20)

3. Results 3.1. Model calibration The parameters of the Ulva DEB model were estimated using seven independent studies (Table 2). The RMSE was satisfactory for most data-sets (Fig. 3). Growth rates predicted at 5 and 10 °C in the study from Tremblay-Gratton et al. (2018) were underestimated although the RMSE of 0.37 can still be considered satisfactory for growth data (Fig. 3d). Carbon content in the study by Figueroa et al. (2009) was overestimated (Fig. 3h), however, the observed drop through time is not expected nor well explained by the authors. All predictions of dry weight and N:C ratios for the starvation experiment were within the standard deviation of observations (Fig. 3f,i). The NRMSE obtained for this set of parameters was 10.81; this relatively high value was mostly driven by the overestimation in Figueroa et al. (2009) data-set. Excluding these data from the procedure yielded a NRMSE of 0.64, which can be considered to be very good. The starvation experiment, during which macroalgae were kept in the dark for 10 weeks, allowed the calibration of the specific 5

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average sea lettuce biomass in both systems. Contrarily, the model was not able to capture the observed short-term dynamics, but it is important to note the high variability in observations, suggesting a high spatial variability in terms of sea lettuce biomass. Despite this variability, a comparison of observed versus simulated data indicated an overall good accuracy of the model with an adjusted R-squared of 0.92 (p < 0.001, Fig. 6b) for the low N estuary and an adjusted R-squared of 0.78 (p < 0.001, Fig. 6a) for the high N estuary. The model seemed to perform better in the low N estuary as indicated by the NRMSE of 0.11 for the low N estuary and 0.14 for the high N estuary. As expected, the level of N concentration in the high N estuary (Table 3) did not limit the growth of sea lettuce, as evidenced by the stable reserve N (Fig. 7a). Self-shading temporarily reduced C reserve in late July-early August, but the N:C ratio remained stable (Fig. 7c). Contrarily, the highly variable N reserve (Fig. 7d) and N:C ratio (Fig. 7f) in sea lettuce growing in the low N estuary show that nitrogen was the limiting substrate. 4. Discussion With increasing concerns of the impact of macroalgal blooms on the resilience and durability of ecosystems, progress in understanding and predicting their development and impact is crucial to developing successful ecosystem management policies. The model presented in this study is the first comprehensive DEB model ever developed for a macroalgal species. Using the concept of synthesizing units to implement the assimilation of energy through photosynthesis and its allocation to the different metabolic functions, this model represents a key advancement in the theory and in the field of coastal ecological modelling. It provides a mechanistic understanding of nutrient uptake and utilization that was calibrated on a series of literature data-sets and validated in a natural environment. In this section we first discuss the nitrogen assimilation module, then the carbon assimilation module and finally the validation of the model in Malpeque Bay. 4.1. Nitrogen assimilation The main interest in modelling opportunistic macroalgae such as sea lettuce lies in the possibility to predict and quantify their rapid growth capacities and the potential impacts on their surrounding environment. In the context of climate change and increasing human activities in the coastal zone, macroalgal blooms have increased in recent decades due to the rise of temperatures and nutrient runoffs (Xing et al., 2015). Therefore, a key part of the modelling process lies in the assimilation of nutrients. The parameters of the Ulva DEB model linked to the uptake of nitrogen can be compared to previously reported values in the literature. Cohen and Neori (1991) measured maximum assimilation rates of nitrogen between 50 and 390 μmol g–1 h–1, Fujita, 1985reported values between 138 and 252 μmol g–1 h–1, and Runcie et al. (2003) observed rates ranging from 116 to 450 μmol g–1 h–1. These figures compare well with our estimate of 140 μmol g–1 h–1 (or 4.5 mmol molV–1 h–1). The range of measured values in the literature corresponds to different acclimation conditions (i.e. limiting or sufficient nitrogen concentration in the water) or different substrates (e.g. nitrate, ammonium), showing how the uptake capacity of sea lettuce may vary with their internal state and in response to environmental conditions. Half-saturation coefficients such as KN, which is key to determine the nitrogen assimilation rate, generally depend on the characteristics of the environment and consequently are highly variable across studies (Solidoro et al., 1997). Incidentally, this parameter is often used to calibrate the energy input of DEB models (Rosland et al., 2009; Alunno-Bruscia et al., 2011). Perrot et al. (2014) in their growth model for sea lettuce proliferation on the Atlantic coast of France also relied on this physiological plasticity to calibrate the maximum nitrogen uptake rate (40–200 μmol gDW–1 h–1) as well as the half-saturation coefficient (5–50 μmol L–1) according to seasonal changes and site-specific conditions. Because our two study

Fig. 2. Map of the study areas in Malpeque Bay (Prince Edward Island, Canada) with position of macroalgae and water sampling points. a) Location of the two studied estuaries in the bay; b) sampling points in the low N estuary; c) sampling points in the high N estuary. Sea lettuce was collected at each point symbolized by a circle and results were clustered into up- (black), mid- (grey), and downstream (white) sub-estuary areas centred on the position of the water sampling points indicated by stars.

maintenance costs for nitrogen and carbon. The green coloration of sea lettuce thalli started to fade past day 45 in the warmest condition (22 °C) and a complete degradation of the smallest algal sheets was observed in all conditions but the coldest (4 °C) at the last sampling of the experiment. The Arrhenius parameters, estimated from three data-sets (Rivers and Peckol, 1995; Steffensen, 1976; and Fortes and Lüning, 1980), resulted in a temperature correction function with an adjusted R–squared of 0.831 (nonlinear regression model, p–value = 9.13 10–10; Fig. 4). 3.2. Model validation Overall sea lettuce biomass was remarkably lower in the low N estuary (Fig. 5d,e,f) compared to the high N estuary (Fig. 5a,b,c), with a maximum biomass of 279 g m–2 in July 2017 in the low N estuary compared to a value of 1355 g m–2 in August 2017 in the high N estuary, both recorded midstream. The model was able to simulate the 6

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Table 2 Parameters of the Ulva DEB model. Notation is adapted from Kooijman (2010). Description

Symbol

Value

Unit

Reference temperature

Tref TA TL TH TAL TAH dPS

293

K

0.15

molγ molPS–1 h–1

Arrhenius temperature Lower boundary threshold temperature Upper boundary threshold temperature Arrhenius temperature at the lower boundary Arrhenius temperature at the upper boundary Density of photosynthetic units Specific photon arrival cross section Binding rate of photons to free SUs

bL

4323 278.8 296.5 60306 68642 0.36 1 0.2

kL KN KC jEN Am

4 10–5 1 10–5 0.0045

L

Dissociation rate of photosynthetic products

Half saturation constant of N uptake Half saturation constant of C uptake Maximum volume-specific assimilation rate of nitrogen Maximum volume-specific uptake rate of CO2

jCO2 m

Maximum volume-specific assimilation rate of carbon

jEC Am

Yield of C reserve per photon Yield of C reserve per CO2

yLC yCO2 C

Yield of structure on N reserve

yEN V

Yield of O2 per photon

yLO2

Yield of structure on C reserve

yEC V

Specific maintenance costs requiring N

jEN M

Specific maintenance costs requiring C

jEC M

N reserve turnover

k EN

C reserve turnover

k EC

Elemental coefficient of N in structure Fraction of rejected flux from growth SU incorporated back into N reserve

nNV EN

Fraction of rejected flux from growth SU incorporated back into C reserve

EC

Biomass threshold for self-shading effect Self-shading constant Molar weight of structure Molar weight of N reserve

Wshad

Molar weight of O2

w O2

wV w EN w EC

Molar weight of C reserve

sites were relatively close to each other we kept a fixed value for KN that was estimated at 40 μmol L–1. Despite the large variation in nutrient loads between and within the two systems, the model seemed to reproduce accurately the observed biomass in each location. We did not distinguish between the different forms of dissolved nitrogen (nitrate, ammonium, nitrite, or urea) and rather considered a general pool of nitrogen used to fuel the metabolism. However, studies have shown that sea lettuce preferentially assimilate ammonium over nitrate (e.g. Wang et al., 2014). Urea and amino acids can also constitute up to 90% of total macroalgal nitrogen uptake when dissolved inorganic nitrogen availability is low (Tyler et al., 2005). We also considered nitrogen alone, but other elements such as phosphorus (Tremblay-Gratton et al., 2018) may be included in further developments. The comparison of experimental results highlights the fact that as coastal waters increasingly undergo nutrient enrichment, blooms of algae will increase, and that the limiting element supporting the growth, initially nitrogen, may shift to phosphorus in those waters subject to the highest nitrogen loadings (Teichberg et al., 2010). Measurements of phosphorus (ortho-phosphate) concentration conducted on the same water samples collected in this study showed a better covariation with sea lettuce biomass along the estuary gradient (p = 4.546 10–9, adjusted R-squared = 0.4769) than nitrogen nitrite-nitrate (p = 9.235 10–4, adjusted R-squared = 0.1764; unpublished results). This may suggest that phosphorus is of greater importance to sea lettuce growth and model accuracy in natural conditions might benefit from the addition of this other substrate. Filgueira et al. (2015) evoked the possibility that phytoplankton productivity might not be limited by nitrogen, since turbidity and the adsorption of phosphorous to the ironrich soils of PEI may cause light and phosphorous to be limiting factors. However, N:P ratios in the high N (0.59) and in the low N (10.53)

K K K K K molPS molV–1 m2 molPS–1 –

0.006

molN L–1 molC L–1 molN molV–1 h–1

molCO2 molV–1 h–1 molC molV–1 h–1

0.006 10 1

molγ molC–1 molCO2 molC–1

0.08

molN molV–1

molO2 molγ–1

0.125 1.25

6.7 10–4 –4

1.6 10

molC molV–1

molN molV–1 h–1 molC molV

0.04

h–1

0.08 0.1

– –

0.02

0.8

1000 100 27.51 17 30 32

–1

h–1

h–1

–

g g g g

m–2 m–2 mol–1 mol–1

g mol–1 g mol–1

estuaries are both well below the Redfield ratio of 16 which points towards a limitation by N. More data is therefore warranted to determine the actual limiting nutrient for primary producers in this environment. It is important to note that the addition of another substrate for growth in the model would require another state variable and six additional parameters, greatly increasing its complexity. This trade-off between simplicity of the model and accuracy is a recurrent issue in numerical modelling and the final decision usually depends on the purpose of the study. In the present case, there is limited value to adding more parameters given that the contrasted average total nutrient load in the studied estuaries (Table 3) undoubtedly explains the difference in growth potential of sea lettuce in these locations. 4.2. Carbon assimilation Previous DEB models for microalgae characterized carbon fixation through photosynthesis in more or less complex ways using the concept of synthesizing units (Papadakis et al., 2005), some of them including photoinhibition (Lorena et al., 2010) or photorespiration (Kooijman et al., 2010). Sea lettuce does not seem to be subject to photoinhibition, especially in high-latitude ecosystems (Rivers and Peckol, 1995). Selfshading, however, has been identified as a common cause for rapid collapse of macroalgal blooms (Carpenter, 1990; Perrot et al., 2014). In our model this process is key to the simulation of biomass dynamics in the estuaries of Malpeque Bay. Without this component, sea lettuce biomass would increase infinitely, especially in the high N estuary where N is not limiting. In DEB theory algae are classified as “supply” organisms, as opposed to a “demand” type. They are extremely flexible in terms of growth and shrinkage (growth rate can in fact be negative), which depend on feeding conditions. Demand systems, conversely, 7

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Fig. 3. Simulations of experimental data from the literature as part of the calibration of model parameters. Experimental data used to calibrate the DEB parameters. a) Oxygen production rate as a function of light intensity at 10 (black, observed: circles, modelled: curve), 20 (blue), and 30 °C (red) from Riccardi and Solidoro (1996); b) Oxygen production rate as a function of light intensity at 5 (black, observed: circles, modelled: curve), 15 (blue), and 25 °C (red) from Rivers and Peckol (1995); c) Nitrogen uptake rate (observed: circles, modelled: curve) as a function of nitrogen concentration from Runcie et al. (2003); d) Growth rate (observed: full bar, modelled: empty bar) as a function of temperature from Tremblay-Gratton et al. (2018) and e) as a function of nitrogen concentration from Gordillo et al. (2001); g) Nitrogen and carbon proportions from Tremblay-Gratton et al. (2018) and h) from Figueroa et al. (2009) ; f) Dry weight and i) N:C ratio during starvation experiment at 4 (black, observed: circles, modelled: curve), 10 (blue), 16 (green), and 22 °C (red) (this study). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

depend on processes that use energy such as maintenance and growth, which requires energy intake of matching size (Kooijman, 2010). The limitation of growth through the self-shading function is therefore an indirect process. Perrot et al. (2014) also noted the strong influence of self-shading in the limitation of total production and reported observations of its effect at a biomass threshold of 1 kg m–2, the same as in our model (Table 2). Yet, conflicting findings exist in the literature: some studies found that stocking densities of 1 kg m–2 resulted in better growth compared to macroalgae grown at 3 kg m–2 (Msuya, 2008), while other reports indicated that nitrogen uptake rate was insensitive to algal stocking density in the range of 1–6 kg m–2 (Cohen and Neori, 1991). The threshold biomass used in the self-shading correction factor in the model (1000 g m–2) falls in line with the values reported in these two studies. Discrete measurements of light extinction under sea lettuce mats in Malpeque Bay carried out with a LICOR LI-193 Spherical Underwater Quantum Sensor in September 2017 during the validation study indicated that photon penetration can drop rapidly immediately under these floating mats. However it is complicated to estimate these effects in situ as sea lettuce in these estuaries is free-floating in the water and subject to displacement by currents and wind. Water turbidity may also be relevant at some times of the year following intense precipitations and may be considered to attenuate light intensity.

Fig. 4. Temperature correction function (red line) calculated from the Arrhenius equation (eq. 13) fitted to data from [1] Steffensen (1976) (circles), [2] Fortes and Lüning (1980) (squares), and Rivers and Peckol (1995) (triangles). Adjusted R–squared = 0.831 (p = 9.13 10–10). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 8

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Fig. 5. Observed (circles) and modeled (lines) sea lettuce biomass (in g m–2) collected in the a), d) upstream, b), e) midstream, and c), f) downstream parts of a high N estuary (left panels) and a low N estuary (right panels) in Malpeque Bay (PEI, Canada). The shaded area represents the standard deviation around observed points.

Concentration of chlorophyll-a varies in time and with environmental conditions such as light intensity and nutrient concentrations (Bischof et al., 2002; Figueroa et al., 2009). In this model the density of photosynthetic units (dPS ) was kept constant for simplicity but more precise predictions might require taking into account this physiological plasticity (Faugeras et al., 2004). Indeed, the capacity of macroalgae to adjust the concentration/sensitivity of photoreceptors might mitigate the effects of self-shading up to a certain point. Lorena et al. (2010) discussed these implications for a microalgae DEB model and suggested to consider an additional structure if one was to model photoacclimation.

the bottom (sand or mud mostly). Thalli may thus drift freely in the water column forced by wind and currents and accumulate in areas such as the head of estuaries or small embayments. Drifting may have two consequences on modelled sea lettuce dynamics: i) the underestimation of sea lettuce biomass at the peak of production in JulyAugust, when precipitation is low and river flow is reduced leading to a rather “stagnant” system where sea lettuce accumulates on the sides of the estuaries and ii) the overestimation of biomass at the end of the growing season in September-October, when sea lettuce becomes more subject to drifting, possibly due to increased river flow and wind. Coupling to a spatialized hydrodynamic model in which wind and current dispersal effects are accounted for would address these issues. The addition of the stress function to the model must temper our confidence in the validation process and more robust validation is therefore necessary, which could be obtained with the use of observed data at the individual scale through mesocosm experiments. In coastal and estuarine systems, the importance of macroalgae in nutrient cycling is well known (Hanisak, 1993; Human et al., 2015; Lanari et al., 2017). However, data on the rate of decomposition of sea lettuce thalli are rare (Hanisak, 1993). It is commonly accepted that

4.3. Model validation and ecological implications As this model was calibrated using experimental data, processes such as grazing or drifting were included after the calibration of model parameters through a stress function aiming at reducing sea lettuce biomass. Although sea lettuce can attach to various substrates (rock, wood, metal, shells) via a small disc holdfast, it is mostly found drifting in the water column in the studied area, likely due to the soft nature of 9

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much lower than those estimated for the phytoplankton species Thalassiosira weissflogii: 1.2 10–2 molN molV–1 h–1 and 5.4 10–2 molC g–1 h–1 (Lorena et al., 2010). However, because the starvation experiment was conducted in controlled conditions, excluding grazers and bacterial degradation, the measured rate of decomposition (as weight loss) should be regarded as a minimum estimation compared to the rapid degradation sometimes observed in the wild (Lenzi et al., 2015). Reports of excessive nutrient runoff leading to blooms of primary producers in coastal areas around the world are accumulating (Glibert, 2016; Liu et al., 2016). The aftermath of such productivity can lead to hypoxia or anoxia which may result in die-off of fauna and other ecological consequences (Giordani et al., 1996; Coffin et al., 2018a, b). While better practices in nutrient runoff management remain paramount to limit the effects of coastal eutrophication, there is growing interest in developing commercial usages of sea lettuce for example as part of integrated aquaculture frameworks (Hadley et al., 2015), animal feed (Bansemer et al., 2016), bio-fuels (Barbot et al., 2016), or in biochemical applications (e.g. crop fertilizer), which might help mitigating these effects. Because the development of macroalgae in estuaries effectively traps catchment-derived nutrients, the export of nitrogen to deeper and more open waters can be reduced (Woodland et al., 2015; Xiao et al., 2017). On Prince Edward Island, a pilot study investigating the feasibility of a removal program of sea lettuce in local bays highlighted the technical difficulty and high cost of such an enterprise, especially considering that the macroalgal populations can double in size in just a few days (Crane and Ramsay, 2012). The current model constitutes a tool that may be useful in some of these applications, especially regarding nutrient cycling and growth predictions. 5. Conclusions In this study we presented the first comprehensive DEB model for a macroalgal species, a mechanistic model that we successfully validated in field conditions. While model improvements are always possible, the agreement between model predictions and observed data in the field is remarkable, especially considering that the parameter values of the Ulva DEB model did not result from any statistical optimization procedure. Further validation should be conducted by testing the applicability of the model to other locations. The inclusion of other nutrient sources, such as phosphorus, may help capture more variability in sea lettuce biomass and should be tested in Malpeque Bay as well as in other locations depending on the characteristics of these new environments. Another important validation step is the application of this model to other macroalgal species, which is being addressed in an ongoing study on the sugar kelp Saccharina latissima in Narraganset

Fig. 6. Regression plots of observed versus simulated sea lettuce biomass (in gDW m–2) in the upstream (white circles), midstream (grey squares), and downstream (black triangles) of a) a high N estuary (R2 = 0.78, p < 0.001) and b) a low N estuary (R2 = 0.92, p < 0.001) in Malpeque Bay (PEI, Canada).

opportunistic algae developed physiological strategies through evolution allowing them to grow and reproduce quickly and resist stress (Lenzi et al., 2015). Low maintenance costs result in more energy allocated to the building of structure, and the low value of maintenance parameters in our model ( jEN M = 6.7 10–4 molN molV–1 h–1, jEC M = 1.6 10–4 molC molV –1 h–1) reflect this characteristic. These values are

Table 3 Average, maximum, and minimum environmental conditions at the locations sampled during the monitoring in Malpeque Bay from 18 May 2017 to 02 November 2017. Standard deviations are indicated in brackets. High N estuary

Low N estuary

Parameter

Upstream

Midstream

Downstream

Upstream

Midstream

Downstream

Surface temperature (°C) max min Salinity

18.2 (4.5) 23.7 9.8 20.95 (1.37) 22.44 19.35 84.66 (81.99) 268.50 14.50 98.12 (52.60) 232.25 27.00 237.27 (103.29) 358.11 77.38

18.0 (4.6) 22.3 8.7 23.01 (1.07) 24.83 21.22 46.19 (56.05) 222.01 2.10 66.14 (26.96) 122.60 33.00

17.7 (4.5) 21.6 8.9 25.27 (0.26) 25.52 24.77 8.17 (6.65) 20.49 0.90 25.23 (13.25) 52.75 7.00

18.4 (4.4) 22.7 10.9 23.41 (1.73) 25.43 20.59 5.21 (3.43) 11.16 0.11 0.31 (0.27) 1.00 0.05

18.1 (3.7) 22.1 11.7 25.74 (0.57) 26.47 24.67 0.41 (0.51) 1.55 0.06 0.40 (0.36) 1.38 0.05

17.9 (3.6) 22.0 11.8 26.18 (0.26) 26.63 25.77 0.16 (0.16) 0.69 0.04 0.41 (0.35) 1.28 0.02

Nitrogen (mmol L–1) (NO3, NO2) Phosphorus (mmol L–1) light intensity (μE m–2 h–1) (same for all locations)

10

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Fig. 7. Modeled dynamics of N reserve (a,d), C reserve (b,e), and N:C ratio (c,f) of sea lettuce in upstream (dotted line), midstream (grey line), and downstream (dark line) parts of a high N estuary (left panels) and a low N estuary (right panels) in Malpeque Bay (PEI, Canada).

Bay, Rhode Island, USA (collaboration with A. Humphries, University of Rhode Island). Further refinement of these models will serve to prove the benefit of using mechanistic models such as those based on DEB theory. Because sea lettuce develops in shallow embayments and estuaries, its impact on nutrient cycling is direct. The quantification of this impact through a process-based model offers an opportunity to better understand and predict the dynamics of coastal systems. Potential interactions with the phytoplankton community and impacts on shellfish production in Malpeque Bay have been hypothesized by Filgueira et al. (2015). These questions are currently being investigated using the present DEB model within the modelling framework designed by these authors (Lavaud et al., in prep.). Such approaches combining physiological processes at the individual level, population dynamics, and inter-specific interactions at the scale of the ecosystem are hoped to help us predict the impacts of future changes on these systems, which ultimately inform estuarine planning and management.

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. Acknowledgements The authors would like to thank two anonymous reviewers for their careful and valuable reviews. We also want to thank the technical staff of the Aquatron facility in Dalhousie University for their help in running the starvation experiment. We thank Mike Coffin, Jeff Barrell, and Celeste Venolia for useful discussions and comments which greatly improved the manuscript. This project was funded through the Program for Aquaculture Regulatory Research projectPARR-2015-G-11 and a NSERC Discovery Grant to RF.

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