Modelling mussel growth in ecosystems with low suspended matter
loads using a Dynamic Energy Budget approach
P. Duarte a,b,, M.J. Fernández-Reiriz c, U. Labarta c
a University Fernando Pessoa, CIAGEB, 349 Praça 9 de Abril, 4249-004 Porto,
Portugal
b Interdisciplinary Centre for Marine and Environmental Research—CIIMAR, Rua dos
Bragas, 289, 4050-123 Porto, Portugal
c Consejo Superior de Investigaciones Científicas. Instituto de Investigaciones Marinas,
Eduardo Cabello 6, 36208 Vigo, Spain
Keywords: Mussel Growth, Modeling, Individual Based Models, DEB, Low Seston,
Galician Rias
abstract
The environmental and the economic importance of shellfish stimulated a great deal of
studies on their physiology over the last decades, with many attempts to model their
growth. The first models developed to simulate bivalve growth were predominantly
based on the Scope For Growth (SFG) paradigm. In the last years there has been a shift
towards the Dynamic Energy Budget (DEB) paradigm. The general objective of this
work is contributing to the evaluation of different approaches to simulate bivalve
growth in low seston waters by: (i) implementing a model to simulate mussel growth in
low suspended matter ecosystems based on the DEB theory (Kooijman, S.A.L.M.,
2000. Dynamic and energy mass budgets in biological systems, Cambridge University
Press); (ii) comparing and discussing different approaches to simulate feeding
processes, in the light of recently published works both on experimental physiology and
physiology modeling; (iii) comparing and discussing results obtained with a model
based on EMMY (Scholten and Smaal, 1998). The model implemented allowed to
successfully simulate mussel feeding and shell length growth in two different Galician
Rias. Obtained results together with literature data suggest that modeling of bivalve
feeding should incorporate physiologic feed-backs related with food digestibility. In
spite of considerable advances in bivalve modeling a number of issues is yet to be
resolved, with emphasis on the way food sources are represented and feeding processes
formulated.
1. Introduction
Bivalve filter-feeders form the basis of many aquaculture systems and fisheries
worldwide. However, the exploitation of this important resource has a number of
problems, that have a major importance on shellfish production and that are, at least to
some degree, physiologically related. For example, carrying capacity limitations (Dame
and Prins, 1998), large summer mortalities and species invasions (Van der Veer and
Alluno-Bruscia, 2006).
The culture of bivalve filter-feeders is probably one of the most environmentally benign
aquaculture production systems, since shellfish are near the base of the food web
(Crawford et al., 2003) and depend only on natural food items (phytoplankton and
organic detritus). Both the quantity and the quality of these food items are important for
bivalve growth (Bayne, 1993; Hawkins et al., 1998). However, even these culture
systems may have a relevant ecological footprint, depending on the location, farm
dimension and stocking densities (Black, 2001; Folke et al., 1998; World Bank, 2006).
The environmental and the economic importance of shellfish stimulated a great deal of
studies on their physiology over the last decades (e.g. Bayne, 1998), with many attempts
to model their growth (e.g. Bacher et al. (1991), Raillard (1991), Pouvreau et al. (2006)
and Bourlès et al. (2009), for the oyster Crassostrea gigas, Solidoro et al. (2000), for the
Manila clam Tapes phillipinarum, Hawkins et al. (2002), for the Chinese scallop
Chlamys farreri, Rueda et al. (2005), for the cockle Cerastoderma edule, Van Haren and
Kooijman (1993), Scholten and Smaal (1998) and Rosland et al. (2009), for the blue
mussel Mytilus edulis). These physiology models may be broadly divided in Scope for
Growth (SFG) and Dynamic Energy Budget Models (DEB) (Duarte et al., 2010). The
former are based on an energy balance, where energy available for growth and
reproduction is calculated as the difference between energy absorption and maintenance
costs. DEB models describe the rates of energy absorption and utilization as a function
of the organism and the environment (Van der Meer, 2006). Over the last years, the
DEB approach developed by Kooijman (2000) has been increasingly employed in
bivalve modeling (e.g. the DEBIB project (Van der Veer and Alluno-Bruscia, 2006)).
According to the last authors, one of the objectives of the DEBIB project was to
introduce a framework for the analysis of the functioning of bivalve species,
considering the limits of available growth models, such as, being species or site-specific
and to complex in the representation of some processes. It is therefore important to
apply DEB models to a wide range of species and environmental conditions, to get
some insight into their generality and to help understanding the variability in parameter
values among species in terms of their ecology and phylogeny (Van der Meer, 2006).
Studies on bivalve feeding and growth are probably more frequent in ecosystems with
high suspended matter loads than in low seston environments such as many coastal
areas and fjord like ecosystems (Rosland et al., 2009), in spite of the considerable
number of studies carried out in Galician Rias (e.g. Labarta, 2004). One of the critical
issues in bivalve physiology modeling is feeding that may be separated in several steps:
water pumping, filtration, pre-ingestive rejection/ pseudofaeces production and
ingestion of living and non-living organic and inorganic matter. The complexity of the
feeding process is expected to be lower in low seston environments, such as the
Galician Rias, where selective processes may be less important, since available seston is
mostly organic and pseudofaeces are not produced (Duarte et al., 2010; FernándezReiriz et al., 2007; Filgueira et al., 2009; Filgueira et al., 2010). Under similar
conditions, Rosland et al. (2009) applied the DEB approach of Kooijman (2000) to
model the blue mussel (M. edulis), reared in low seston environments in Norway.
According to these authors, model simulations matched fairly well observations with
some limitations to simulate long-term starvation. Recently, Saraiva et al. (2011)
extended the DEB model of Kooijman (2000) with amechanistic module for clearance,
filtration and pseudofaeces production.
In a previous work, Duarte et al. (2010) applied a DEB approach based on the EMMY
model by Scholten and Smaal (1998) to simulate the growth of the mussel Mytilus
galloprovincialis in a low seston environment in Galicia (Northeast Spain)—Ria de
Ares-Betanzos. EMMY was referred as the most sophisticated mussel physiology model
by Beadman et al. (2002).
The general objective of this work is contributing to the evaluation of different
approaches to simulate bivalve growth in low seston waters considering that, ideally, a
model should: (i) allow accurate estimates of bivalve growth; (ii) be based on well
known and demonstrated physiologic mechanisms; (iii) depend on a relatively small
number of easily measurable parameters.
Accordingly, the specific objectives of this work are to: (i) implement a model to
simulate mussel growth in low suspended matter ecosystems based on the DEB theory
(Kooijman, 2000); (ii) compare and discuss different approaches to simulate feeding
processes, in the light of recently published works both on experimental physiology and
physiology modeling; (iii) compare and discuss results obtained with a model based on
EMMY (Scholten and Smaal, 1998).
2. Methodology
The physiological model described below is based on the DEB theory developed by
Kooijman (2000). Model setup and simulations were made as similar as possible to
those presented in Duarte et al. (2010) to allow a comparison between the model
presented by those authors, based on the EMMY approach (Scholten and Smaal, 1998),
and the present one.
The model was implemented with EcoDynamo—an object oriented modeling software
(for details see Pereira et al. (2006)). This model may be run in a “state variable” or an
“individual based model” (IBM) mode sensu Grimm (1999) and Grimm et al. (1999). In
the first case, an average mussel is simulated with a particular parameter set. In the
second case, a population of n mussels is simulated with each individual having its
specific parameter set. Under the IBM mode, it is necessary to define ranges for each
parameter. In the present work, this definition was based on literature and experimental
data obtained by the authors and the specific parameter values for each mussel were
generated randomly, within the mentioned ranges. The IBM mode has some interesting
advantages discussed in Duarte et al. (2010): (i) running the model for a large number of
mussels allows selection of parameter sets that produce the best fit between predicted
and observed mussel growth; (ii) from (i) it follows that model results may be used to
select parameter ranges that lead to growth predictions within ranges observed in nature,
to be used in a “state-variable” model.
2.1. Ecophysiology DEB model
In the present work, DEB symbols and notations described in Kooijman (2000) are
applied, where square brackets [] denote quantities expressed per unit of the structural
volume, while braces {} denote quantities expressed per unit surface area of the
structural volume. All rates, i.e. dimension per time, have dots above. In the DEB model
described by that author and implemented for several bivalve species by e.g. Van der
Veer et al. (2006) and Rosland et al. (2009), there are two state variables: reserve
density [E] and structural body volume (V). Eqs. (1) and (2) below describe how these
variables change over time. For details see the authors cited above. The first term on the
right side of Eq. (1) corresponds to energy absorption from food and the second term
corresponds to energy utilization from the reserve pool. The first term on the right side
of Eq. (2) corresponds to growth of structural body volume, whereas the second
corresponds to maintenance costs.
d[E] PA
= −c[E] = {PAm}fV−1/3−c[E]
dt
V
dV K PAm [ E ]V 2 / 3 /[ E M ]  [ PM ]V
=
dt
[ EG ]  K [ E ]
(1)
(2)
Where,1
[E]
Reserve density [JL− 3]
PA
Assimilation rate [JT− 1]
C
Proportionality coefficient that sets the rate at which the reserve density drops
when no assimilation occurs [T− 1];
V
Structural body volume [L3];
Κ
Fraction of the energy utilized from the reserves that is spent on growth and
somatic maintenance;
{PAm} Maximum surface-area-specific assimilation rate [JT− 1 L− 2];
[Em]
Maximum reserve density [JL− 3];
[PM]
Maintenance costs [JT− 1 L− 3];
[EG]
Energetic costs to synthesize a unit of structural body volume [JL− 3].
In DEB models, fluxes are, usually, expressed in energy units. In the present work, state
variables and fluxes are also expressed in carbon units and, where appropriate, in
nitrogen units. This was done for two reasons: (i) comparability with other modeling
studies; (ii) possibility of coupling a DEB model with an ecosystem model where book
keeping calculations generally require quantifying carbon and nitrogen fluxes.
Some of the critical issues in bivalve modeling are water pumping, filtration, preingestive rejection/pseudofaeces production and ingestion of living and non-living
organic and inorganic matter. In bivalves, estimates of maximum ingestion and
assimilation rates are difficult to determine due to the complicated food intake
mechanisms and the dependence on seston load and quality (e.g. Bayne, 1993, 1998;
Bayne et al., 1993; Hawkins et al., 1999; Van der Meer, 2006). At low food
concentrations (total suspended matter (TPM) <3mg L−1), pseudofaeces are not
produced and filtration rate (FR), which is the product of clearance rate (CR) and food
concentration, equals ingestion rate (JX) (Rosland et al., 2009). In the DEB model of
Kooijman (2000), it is assumed that JX is related to food density though a Hollings type
II curve (Eq. (3)).
Jx = {JXm}
X
V2/3={JXm}fV2/3
Xk  X
(3)
Where,
Jx
Ingestion rate [JT−1];
{JXm}
Maximal ingestion rate per unit area of body surface [JT−1 L−2];
X
food concentration;
Xk
half saturation constant.
In the present work, CR of a standard 60 mm mussel is first calculated and then
recalculated as a function of V2/3 (a proxy for body surface area) in accordance with Eq.
(3). Details on CR standardization are given below. CR for a standard mussel is
calculated in two different ways, following Duarte et al. (2010):
(i) As a function of total particulate matter and the ratio between particulate organic
matter (POM) and TPM, below a chlorophyll (Chl) threshold of 1.18mg Chl L−1,
following experimental results of Filgueira et al. (2009, 2010), and a constant CR value
(3.9 L h−1mussel−1) is assumed above the mentioned threshold (Table 1, Eq. (4)). The
previous authors found a parabolic relationship between CR and TPM above the Chl
threshold. However, this relationship was not considered in this work neither in Duarte
et al. (2010) due to its relatively low R2 of 0.56 and due to the uncertainty of CR being
comparable to the variability explained by the parabolic function.
(ii) As a function of gut volume (GV), gut passage time (GPT) and food concentration,
following the model of Willows (1992) (Table 1, Eqs. (5)–(7)) and EMMY (Scholten
and Smaal, 1999).
Filtration rate is calculated from the product of total particulate matter (TPM) and CR
(Table 1, Eq. (8)).
In the present model, there are two different ways of calculating ingestion rate
(represented by IR in Duarte et al. (2010)): (i) Equate it with FR (product of CR and
food concentration), assuming no pseudofaeces (PF) in accordance with Rosland et al.
(2009), when simulating mussel growth in low seston waters (Table 1, Eq. (9)); (ii)
Following Scholten and Smaal (1999), with ingestion rate depending on GV and GPT
(Table 1, Eqs. (10) and (11)). It is important to note that IRmax is used in Eq. (11)
instead of {JXm} for consistency with Duarte et al. (2010) and because units are not the
same. In the model, it is assumed that phytoplankton and detritus are ingested according
to their proportions in TPM.
Absorption is calculated from ingested food and absorption efficiency (AE), following
Fernández-Reiriz et al. (2007) (Table 1, Eq. (12)). However, absorption is limited by
{PAm} for consistency with Eqs. (1) and (2) above (Table 1, Eq. (13)). According to
Kooijman (2000), assimilation rate denotes the free energy fixed into reserves, i.e., food
intake minus energy lost in faeces and in losses related with digestion, and it is
calculated from Eq. (13) (Table 1). In the present work, PA was equated with absorption
rate (AR), rather than assimilation rate, since it does not include energy losses related
with maintenance and growth, for consistency with previous works (e.g. Hawkins et al.,
2002). By analogy, {PAm} is assumed as a maximum absorption rate. In fact, following
Kooijman (2000), assimilated energy enters into a reserve pool that is used at a rate
calculated by the second term of Eq. (1). A fraction κ of this used energy is spent on
maintenance plus growth.
In the present model, both food ingestion and maintenance costs may be limited by
temperature using the Van't Hoff-Arrhenius equation (cf.—Van der Meer, 2006), with
two parameters: Arrhenius temperature (TA) and a Reference Temperature (T1). In
Table 2, model parameter meaning, values and units are synthesized. Whenever ranges
were available they were considered for model calibration.
In the DEB approach described in Kooijman (2000), physiologic rates are scaled to the
surface area of the organism, expressed as V2/3 and alometric coefficients are not used.
Therefore, it was necessary to recalculate CR of a standard mussel on a surface area
basis. This was done using data from Filgueira et al. (2008), where CR is allometrically
related with shell length (L). Therefore, CR for any mussel is calculated from:
 V  2/3
CR = CRsa. 

 Vsa 
(14)
Where,
CRsa stands for clearance rate per unit of body surface [L3T−1 L−2] of a 60 mm length
mussel with a volume Vsa.
In the model, it is important to relate body volume with meat dry weight and with shell
length, for the sake of comparison between model results and available data:
V = (δ.LShell)3
(15)
Where,
LShell
Shell length (mm).
This equation relates body volume with body length (L) through a shape factor (δ). For
a first estimate of δ dry flesh mass measurements from experimental data described
below (cf.—2.2) were converted to wet flesh mass by a dry-to-wet-mass conversion
factor of 5 following Rosland et al. (2009). Afterwards, estimated wet mass was used to
substitute structural volume V (cm3) in Eq. (15), assuming a body density of 1 g cm−3
according to Rosland et al. (2009). The shape factor was estimated by plotting V1/3
against L, and determining the slope of a linear regression that was forced to pass
through the origin, following other works (e.g. Rosland et al., 2009) and using
experimental mussel growth data described below (cf.—2.2)—a value of 0.294 was
obtained for δ (r2=0.894). However, since observed flesh mass of mussels grown in a
natural cycle includes gonads, structure and reserves (i.e. not only structure) this value
is not an accurate estimate of δ and it was used only as a starting estimate in model
simulations (see below).
Vsa may be calculated from Eq. (15) as c.a. 5.5 cm3 for δ=0.294 and, knowing that CR
of a 60 mm (CR60) mussel is c.a. 3.9 L h−1 (Filgueira et al., 2009), CRsa may be
calculated dividing CR60 by V raised to 2/3, i.e., a proxy of body surface, obtaining
1.25 L h−1 cm−2. In Duarte et al. (2010), CR was calculated from an allometric
relationship with shell length (in fact there is a printing error in Eq. (6), Table 1 of
Duarte et al. (2010), where all the right hand side of the equation should be raised to b,
the allometric coefficient for feeding):
 LShell  b
CR = CR60 

 LSt 
(16)
Where,
LSt
Shell length of a standard mussel (60 mm); b—Allometric coefficient for
feeding.
In Fig. 1, a comparison between CR estimated from Eq. (14) and from Eq. (16), with
three allometric coefficients in the range reported in the literature (Filgueira et al., 2008)
is shown. Both equations show similar results, especially for the highest allometric
coefficient.
In the model, V is used to derive shell length from Eq. (15). V and E are used to
calculate meat dry weight by: (i) converting structural volume to wet and then to dry
weight (following a similar reasoning as described above to estimate body volume); (ii)
converting reserves energy to wet weight using a conversion factor of c.a. 1900 J cm−3
and (iii) adding estimated structural and reserve weights . Shell length is allowed to
increase only. Under a reduction in V, shell length remains constant. Dry shell weight
(DSW) is calculated from an empirical relationship with shell length (Eq. (17)),
obtained from the experimental growth data described below. DSW is necessary for the
calculation of mussel condition indexes (CI).
DSW = 0.00002LShell3:053
(17)
A simple approach was adopted for reproduction, as described in Duarte et al. (2010),
by imposing a storage loss at a predefined time (e.g. Julian day 120). This loss was
estimated as c.a. 60% of storage tissue (Labarta, unpublished). This simplification was
assumed because it was difficult to determine reproduction moments due to its quasi
continuous nature over spring–summer seasons (Villalba, 1995). Moreover, the absence
of observational data regarding reproductive tissue prevented any comparison with
model prediction of the reproductive buffer used in the DEB theory of Kooijman
(2000).
2.2. Field data for model forcing and calibration
Observations on mussel growth—shell length, meat and shell dry weight—and on raft
cultivation ropes, are those described in Fernández-Reiriz et al. (2007) and Duarte et al.
(2010). The former data was obtained in Ria de Arousa and the latter was obtained in
Ria de Ares-Betanzos—two low seston ecosystems in Galicia (NW Spain) (Fig. 2).
Ria de Arousa data were obtained in two different growth experiments: one between the
27th of November 1995 and the 3rd of July 1996 and another between the 28th of
January and the 8th of July 1998, covering the first stage of mussel cultivation from
seeding to thinning out (50–60 mm), with mussels harvested along the seashore and
with mussels harvested from collector ropes placed inside the Ria. In total, 16
cultivation ropes (12 m) were used, with a seed density of 19 kg per rope (1.6 kg m−1 of
rope or 2600 mussels m−1 of rope).
Ria de Ares-Betanzos data were obtained during two different growth experiments at
Lorbé (Fig. 2): one between the 1st of April 2004 till the 18th of May 2005 (hereafter
referred as Experiment 1), with mussels harvested along the seashore, and another
between the 10th of June 2004 and the 19th of May 2005 (hereafter referred as
Experiment 2), with mussels harvested from collector ropes placed inside the Ria. M.
galloprovincialis were collected monthly from each rope, at 3–4 m depth, using two
replicates of 200–300 mussels.
Water quality characteristics—water temperature, TPM, POM and Chl concentration—
used to force the model are depicted in Fig. 3, regarding Ria de Arousa simulations.
More details may be found in Fernández- Reiriz et al. (2007). Concerning Ria de AresBetanzos simulations, forcing function data were the same presented in Fig. 1 of Duarte
et al. (2010).
TPM and POM concentration were determined gravimetrically (in triplicate) following
the methodology described by Filgueira et al. (2006). Chl was extracted using acetone
(90%) and quantified by means of the equation of Jeffrey and Welschmeyer (1997) for
natural seawater. A detailed explanation of the methods is provided in Peteiro (2009).
Shell length, meat dry weight and condition index were calculated according to the
methodology described in Peteiro et al. (2006).
2.3. Model simulations
Model simulations were analogous with those described in Duarte et al. (2010) for the
sake of comparability, except that simulations were run without (as in the previous
authors) and with temperature limitation. The IBM described above was run for a
virtual population of 10,000 mussels with parameter values and ranges depicted in
Table 2. Each mussel had a different parameter set, where each parameter value was
randomly assigned from its range (when available). Model results were analyzed and
compared with observations, to define those parameter sets that produced the best fit
between the former and the latter for calibration purposes.
A synthesis of model simulations is presented in Table 3. Eight separate calibration
model runs—Simulations 1a, b, c and d and Simulations 2a, b, c and d—were
performed for each time period corresponding to Experiments 1 and 2 carried out in Ria
de Ares Betanzos (cf.—2.2). The former four were compared with data from
Experiment 1 and the latter four with data from Experiment 2. In Simulations 1a, 1c, 2a
and 2c, CR was calculated from Eq. (5), whereas in Simulations 1b, 1d, 2b and 2d, CR
was calculated from Eq. (4) (Table 1). Simulations 1c, 1d, 2c and 2d included
temperature limitation though a Van't Hoff- Arrhenius equation (cf.—2.1). Therefore,
model simulations were designed to contrast two different methods of calculating CR
and to check the potential importance of temperature limitation. Furthermore,
Simulations 1a, 1b, 2a and 2b are comparable with simulations 1a, 1b, 2a and 2b,
presented in Duarte et al. (2010). IR was calculated from Eq. (9). Initial conditions for
Simulations 1a, b, c and d were a structural body volume (V) of 0.09 cm3 and a reserve
density [E] of 2190 J cm−3. For Simulations 2a, b, c and d initial V was 0.18 cm3 and
initial [E] was the same used for the previous simulations. Initial conditions were
defined to match mussel characteristics at the beginning of Experiments 1 and 2 (cf.—
2.2). After the model was calibrated for mussels collected along the shore (Simulations
1) and in collector ropes (Simulations 2), parameters obtained with Simulations 1a, 1b,
1c and 1d were used to run the model to simulate Experiment 2, as a first validation
step. Afterwards, the model was run with growth and water quality data from Ria de
Arousa obtained in 1995–96 and 1998 (cf.—2.2). Parameters calibrated with
Simulations 1a, 1b, 1c and 1d were used to simulate the growth trials in Ria de Arousa
(cf.—2.2). For the 95–96 period, available data included meat dry weight, shell length
and also CR and OIR, presented in Table 2 of Babarro et al. (2000a). Therefore,
comparisons between model and observations were made not only for meat weight and
shell length but also for those physiologic rates, whenever available. To make model
predicted physiologic rates comparable to those of the previous authors, predicted
values were standardized to the same shell lengths considered by Babarro et al. (2000a)
and using the same allometric coefficient of those authors—1.85.
No attempts were made to calibrate the model for the 95–96 or the 98 data. The
rationale was that of relying on a parameter set calibrated for another ecosystem and
check whether it is capable of reproducing physiology and growth on another, yet
similar, ecosystem. A good model performance would give some confidence on model
applicability for clear water ecosystems.
Preliminary tests have shown that reproduction has a negligible effect on Simulation 1
and 2 results. Therefore, it was “switched off” in these simulations.
Water temperature, TPM, POM and Chl data were linearly interpolated and used to
force the model. These data were reloaded when simulation time was larger than the
sampling period. Model outputs include a file with mussel parameter sets, physiologic
rates and growth variables such as meat weight, shell dry weigh and shell length.
Obtained results for the virtual population were thereafter used to: (i) evaluate the
“best” parameter sets—those that lead to closest predictions on mussel growth between
model and observations; (ii) compare predicted with observed mussel growth
variability. A sensitivity analysis was carried out with model parameters from
Simulations 1a–d. Several simulations were run, changing one parameter at a time by
±10% and comparing obtained results, in terms of meat weight and shell length with a
standard simulation.
3. Results
Figs. 4 and 5 show observed and predicted mussel dry meat weight and shell length for
Simulations 1 and 2 mussels (cf.—2.3) that exhibited the best fits to observed data
(lower mean square deviation—MS). Corresponding parameter values are shown in
Table 2. Both observed and predicted results point out to an increase in meat weight and
shell length from 0.02 g and c.a. 16mm, till c.a. 1.4 g and 60mm, respectively. In all
simulations, shell length predictions compare better with observed data than meat dry
weight predictions. These compare relatively well with observations during the first 200
days of simulation, in the case of Simulations 1a, 1c and 1d, and during the first 150
days, in the case of Simulations 2a and 2c. Meat dry weight is expected to be much
more variable than shell length as a result of variability in food availability and quality,
as well as reproduction cycles. Comparing Figs. 5 and 8 presented in Duarte et al.
(2010) with Figs. 4 and 5 of the present work, it is apparent that the EMMY approach
followed in the former led to model predictions of comparable quality with those
presented in this paper. However, the EMMY approach required 5 state variables and 29
parameters whereas, in the present model implementation based on the DEB theory of
Kooijman, only 2 state variables ([E] and V cf.—Eqs. (1) and (2), other variables are
derived from these as explained above, cf.—2.1 Ecophysiology DEB model) and
between 15 and 21 parameters were needed, depending on the simulations—those
without temperature limitation and using Eq. (4) for CR calculation required 15
parameters whereas, those using Eq. (5) for CR calculation, and including temperature
limitation, required 21 parameters (cf.—Table 2).
In Figs. 4 and 5 it is apparent a reduction in meat weight in September for simulations
1b and 2d, in the first figure, and for simulations 2b and 2d, in the second figure. This is
due to the effect of changing CR calculation when Chl is below the threshold presented
in Table 1, Eq. (1) (Lim1=1.18 μg L−1). A small decrease in Chl below the mentioned
threshold may lead to a CR reduction (Filgueira et al., 2010). From the same figures, is
it apparent that including temperature limitation did not lead to any significant
improvement in model performance.
Fig. 6 shows measured shell length and meat dry weight in Experiment 2 and predicted
values using parameters calibrated in Simulations 1 (cf.—2.3). As it may be seen, shell
length predictions are within the range of observations for all but Simulation 1d
calibrated parameters. Meat dry weight predictions are relatively poor, except for
overall meat weigh increase in Simulations 1a and 1b.
Measured and predicted clearance and organic ingestion rates for the Ria de Arousa data
obtained between the 27th of November 1995 and the 3rd of July 1996 (cf.—2.2 and 2.3
and Babarro et al. (2000a)) are depicted in Fig. 7. Simulations were run using model
parameters calibrated with mussels harvested from rocky intertidal areas (Experiment 1
and Simulations 1a and 1b, cf.—2.3 and Table 3). There is a good agreement between
observations and simulations with Simulation 1a calibrated parameters. Similar results
were obtained with Simulations 1c and 1d (not shown)—a good agreement between
observations and predictions for the former and a poorer agreement for the latter.
Fig. 8 shows measured and predicted shell lengths and meat dry weights for the Ria de
Arousa data obtained between the 27th of November 1995 and the 3rd of July 1996
(cf.—2.2 and 2.3). Model parameters were those calibrated with mussels harvested from
rocky intertidal areas (Experiment 1 and Simulations 1, cf.—2.3 and Table 3). There is a
good agreement between model and observations regarding shell length but not so good
in what concerns meat dry weight. Simulations tend to overestimate meat dry weight
during a large part of the simulated period. However, there is a good agreement between
observed and predicted total meat weight increase when Simulation 1a and 1c
parameters are used.
Measured and predicted shell lengths with data obtained between the 28th of January
and the 8th of July 1998 (cf.—2.2 and 2.3) are depicted in Fig. 9. Simulations were run
using model parameters calibrated with mussels harvested from rocky intertidal areas
(Experiment 1 and Simulations 1, cf.—2.3 and Table 3). There is a good agreement
between predicted and observed data for all but Simulation 1d parameters.
Fig. 10 shows predicted mussel shell length, CI and Reserve Density [E] for a period of
c.a. three years, with parameters calibrated from Simulation 1a and depicted in Table 3.
Obtained results suggest that [E] is at its minimum at the end of winter–beginning of
spring. This is the period when TPM reaches higher values (cf.—Fig. 2 of Duarte et al.
(2010)) and food quality, measured as the POM/TPM ratio, is at its minimum. Similar
results were obtained for the ratio between storage and somatic tissues—a surrogate of
reserve density—by Duarte et al. (2010). At the end of this simulation mussel length
was near 90 mm. Peteiro et al. (2006) fitted a Gompertz model to several mussel
populations in Ria de Ares-Betanzos, finding Y∞ values between 70.3 and 81.1 mm.
Model predicted CIs (Fig. 10) are within the range of those obtained by Duarte et al.
(2010)—from c.a. 15 till 22%. Maximum values compare well with observations, where
maximal values were 32 and 19% (not shown) in Experiment 1 and Experiment 2 (cf.—
2.2), respectively. In the EMMY approach used in Duarte et al. (2010), energy
allocation to the shell is calculated explicitly (cf. Table 3 of the cited authors), whereas
in the DEB approach presented here, shell length and dry shell weight are calculated
from empirical relationships (Eqs. (15) and (17)). Combining these two equations, Eq.
(18) is obtained:
DSW = 0.00002
V 1.018
 3.053
(18)
In this equation, V is raised to an exponent close to one. Therefore, DSW increases at
approximately the same rate of V.
Results from the model sensitivity analysis are presented in Table 4, showing that all
model simulations are more sensitive to parameters κ (Fraction of the energy utilized
from the reserves that is spent on growth and somatic maintenance), δ (Shape
coefficient), {PAm} (Maximum surface-area-specific assimilation rate) and [PM]
(Volume-specific maintenance costs). Model sensitivity to the remaining parameters is
between one and three orders of magnitude lower. It is also noteworthy that model
sensitivity is larger for meat dry weight than for shell length predictions. One of the
results presented in Table 4 is counterintuitive—the negative effect of an increase in
{PAm} on meat dry weight regarding Simulation 1d. The effect of increasing this
parameter was always positive on structural body volume (not shown). Therefore, this
apparently contradictory result is explained by a decrease on reserve density. This
decrease may be justified with Eq. (19) of the DEB theory for reserve utilization being
proportional {PAm} (see Kooijman, 2000):
Pc =
 PAm [ EG ]V 2 / 3

[E ]

 [ PM ]V 

[ EG ]  K [ E ] 
[EM ]

(19)
The obtained result does not mean that any increase in {PAm} leads to a reserve
decrease. However, this may happen depending on the values of the remaining
parameters and their interplay in the DEB equations.
4. Discussion
Galician Rias are low seston environments with TPM usually less than 3mg L−1 and Chl
usually less than 5 μg L−1 (Figueiras et al., 2002). Low seston environments occur under
natural oligotrophic conditions and may also take place where high bivalve densities
cause seston depletion as in some culture conditions (Blanco et al., 1996; Rosland et al.,
2009; Strohmeier et al., 2008).
According to Rosland et al. (2009) the Hollings type II function (Eq. (3)) allowed a
good fit between simulated and observed ingestion rates for Chl values below 1 μg Chl
a L−1, but underestimated ingestion rates at higher concentrations. The complex
relationship between bivalve feeding, food concentration and quality (Filgueira et al.,
2009, 2010; Hawkins et al., 2002) were the main reasons why the EMMY type model
presented in Duarte et al. (2010) and the model presented herein, had specific
formulations for feeding (cf.—2.1). Food quality may be viewed in terms of the organic
content of TPM and also in terms of the digestibility of suspended organics (Filgueira et
al., 2010). The abovementioned complexity may be hardly explained with a simple
asymptotic function of the type shown in Eq. (3). Filgueira et al. (2010) found out that
the Chl contents of ingested food has an important effect on the CR response to TPM
that may be explained by the higher digestibility of phytoplankton cells used in their
experimental work, in comparison to organic detritus.
It is important to emphasize that a lot of work has been devoted to simulate bivalve
feeding. Some authors consider that CR is maximal and constant up to certain TPM
limits, above which it exhibits a strong decrease (Raillard and Ménesguen, 1994;
Raillard et al., 1993; Smaal, 1997; Winter, 1973; Winter, 1978). Other authors
demonstrated that CR changes as a function of seston concentration and quality (e.g.
Bayne, 1993; Bayne, 1998; Bayne et al., 1993; Filgueira et al., 2009, 2010; Hawkins et
al., 1999). Jørgensen (1990, 1996) stated that these changes depend on the physical
environment and not on physiological regulation whereas, Bayne (1993) suggested that
such changes are also physiologically controlled. Riisgård (2001) and Riisgård et al.
(2003) considered that valve closure is a mechanistic response of physiological
regulation. Furthermore, according to some authors (e.g. Bayne, 1993 and Ward and
Shumway, 2004), bivalve suspension feeders may selectively ingest and/or digest
different food items whilst making adjustments to maximize the utilization of
chlorophyll rich particles (Hawkins et al., 1999; Hawkins et al., 2001). Apart from the
importance of food quality, other aspects may also play some role in feeding rates such
as gut fullness (Willows, 1992) and digestion rate (Kooijman, 2006).
The paper of Saraiva et al. (2011) extends the standard DEB model with a mechanistic
module for clearance and filtration, in accordance with DEB theory. These authors
based mussel feeding behavior in the Synthesizing Units (SUs) concept. Their equation
for CR predicts a continuous decrease of this process with substrate concentration in
spite of the fact that several authors suggest that CR is constant until a TPM
concentration threshold (e.g. Bougrier et al., 1995; Deslous-Paoli et al., 1992) as
recognized by Saraiva et al. (2011). Saraiva et al. (2011) calculate clearance and
ingestion rates solely as a function of food concentration and quality, not being
influenced by gut fullness. However, the model of Willows (1992) and the EMMY
model (Scholten and Smaal, 1998), include the mentioned feedbacks. Saraiva et al.
(2011) compared their clearance rate estimates with experimental data from several
authors. A good agreement was found in most cases. However, important deviations
were found between predicted CR and observations under low TPM. These authors
justify these deviations based on the lack of detailed information on the experimental
setup. Another possible explanation could be that some of the assumptions of their
approach are not completely fulfilled under low TPM loads.
Detailed laboratory studies on mussel feeding were conducted by Filgueira et al. (2006,
2008, 2009 and 2010) under the environmental conditions found in Galician Rias,
concerning food concentration and quality. According to these authors, M.
galloprovincialis CR is stable under a wide range of conditions, exhibiting a more
complex behaviour when the organic content of TPM has a low digestibility. This low
digestibility is reflected by a low chlorophyll concentration, when plant detritus is a
large proportion of POM. Under these conditions, clearance rate decreases with the
organic content of TPM (cf.—Table 1, Eq. (4), where food quality (Q1) is a negative
linear term). Those authors suggest that clearance rate may be limited by a physiologic
feedback that is most likely due to food digestibility than to gut fullness. Therefore, the
usage of Eq. (5)—where CR is assumed has constant except when limited by gut
fullness—and 6—where gut passage time is calculated—is justified to account for CR
stability and the negative feedbacks from gut fullness as a function of digestibility of
food items. Both Eqs. (5) and (6) are mechanistic. However, Eq. (7) is empirical and
based on allometric coefficients. Therefore, it constitutes a sort of a violation to the
mechanistic principles of DEB theory. The major drawback of Eq. (7) is the fact that gut
volume is calculated from meat weight that may change as a function of reserve density.
However, this equation may be substituted by a mechanistic counterpart, once a
relationship is established between gut volume and structural body volume of the
studied species. Interestingly, the best model performance, considering all data sets, was
obtained with Simulation 1a and 1c calibrated parameters, predicting accurately CR and
OIR as well as mussel growth for the 95–96 data sets that were not used in the
calibration (cf.—Figs. 7–9). This does not prove that the usage of Eqs. (5)–(7) for CR
calculation is the best option but it provides some evidence in its favor.
Considering the arguments and results presented in the previous two paragraphs, it may
be hypothesized that at low TPM values, mussel CR is stable except when food
digestibility provides a negative feedback to CR. Therefore, a realistic model should
include these feedbacks in the form of Eqs. (5)–(7) or in other comparable form.
The equation for ingestion rate used by Saraiva et al. (2011), implies that filtration rate
is always larger than ingestion rate (cf.—Table 2 of Saraiva et al. (2011)), the difference
corresponding to pseudofaeces production. Therefore, this equation may be appropriate
for environments with relatively high suspended matter loads but hardly appropriate for
low suspended matter environments such as those found in Galician Rias, where
pseudofaeces are not produced (Fernández-Reiriz et al., 2007). This is the reason why in
the present work ingestion rate is equated with filtration rate.
The first objective of this work was to implement a model to simulate mussel growth in
low suspended matter ecosystems using the DEB theory of Kooijman (2000). Whilst
this has been done before for similar species (cf.—1) and for clear water ecosystems
(e.g. Rosland et al., 2009), there are still a number of questions that deserve further
research in several aspects of bivalve physiology modeling as suggested by the
discussion above.
The results presented herein show that the first objective of this work was
accomplished: the model is suitable to predict mussel growth in terms of shell length for
a period of over one year. Regarding meat weight, the model does not perform so well.
However, it predicts relatively well meat weight for a period of several months in some
cases, while in others it predicts reasonably well total meat weight increase. It is
possible that some inaccuracies in interpolated forcing data may produce much larger
differences in meat weight than on shell length, given the higher variability of meat
weight as a result of reserve dynamics and reproduction cycles.
The model implemented by Rosland et al. (2009) for a low seston environment
simulated fairly well some datasets, in terms of shell length and meat weight evolution,
whilst some were not so well represented. Similarly to the present work, shell length
appeared to be better simulated than meat weight. Other mussel growth studies with the
DEB model of Kooijman (2000) and EMMY successfully simulated mussel shell length
evolution in environments with high suspended matter loads (e.g. Scholten and Smaal,
1999; Van Haren and Kooijman, 1993).
While it is expectable some variability in model parameters among mussel populations
living under different conditions (for an example of the influence of particulate matter
on feeding parameters see Kooijman (2006)), it is encouraging to find out that the same
parameter set may explain feeding behavior and growth of mussels from different
habitats or even ecosystems. According to Rosland et al. (2009), the fact that model
simulations of mussels from different places or experimental treatments were validated
with a common basic parameter set, demonstrates the robustness and generality of the
model. Results shown in Fig. 6 suggest that, to some degree, this was true for mussels
harvested along the shore and harvested in collector ropes (cf.—2.2 and 2.3) in spite of
their physiologic differences discussed by several authors (e.g. Babarro et al., 2000a;
Babarro et al., 2000b; Babarro et al., 2003a; Babarro et al., 2003b; Duarte et al., 2010;
Labarta et al., 1997 and Pérez-Camacho et al., 1995). Results depicted in Figs. 7–9
show that model estimates with parameters adjusted for mussels from Ria de AresBetanzos allow simulating accurately mussel clearance and ingestions rates as well as
shell growth for mussels from another ecosystem—Ria de Arousa.
One critical issue in bivalve physiology modeling is the way food is represented.
Rosland et al. (2009) discuss the possible limitations of using Chl as a proxy for food.
These limitations may be related, among other things, to the importance of other food
sources, the variability of the Carbon:Chl ratio and the digestibility of different algal
cells. In a recent work, Bourlès et al. (2009), using a DEB model for the Pacific oyster
(C. gigas), found out that phytoplankton expressed in cell number per liter explains the
greater part of observed oyster growth. According to Rosland et al. (2009), future work
should aim at establishing better food proxies and improving the model formulations of
the processes involved in food ingestion and assimilation. Some mussel growth and
environmental data obtained in Galician Rias (unpublished) suggest that particle volume
may be a good proxy for food. In selecting such proxies, it is important to choose those
that may be monitored continuously or that may be easily correlated with the former.
In spite of the differences between the EMMY and the DEB approach of Kooijman
(2000) followed in the present work, both models performed similarly. The former
depends on more parameters since it is based on more empirical formulations than the
later. Another disadvantage of the former was the need to impose an asymptotic mussel
shell length to prevent unrealistically large shells in long term simulations. This was not
Fig. 10), presumably, because the area/volume ratio of the organisms decrease as they
grow bigger, reducing food intake in relation to maintenance costs. Rosland et al.
(2009) mentioned that the current DEB model does not allow energy extraction from the
structural tissue. However, Eq. (2) may produce negative changes in structural body
volume, when energy in reserves is low for maintenance needs. Another advantage of
the DEB model is that growth depends directly on reserves and not on absorbed food
whereas, in the EMMY model, when scope for growth is negative growth does not
occur and reserves are used only for maintenance. Whilst this may be realistic at some
temporal scales it may be hardly the case at small temporal scales, when organisms have
a good condition index.
5. Conclusions
In this work, an IBM model of mussel growth based on the DEB theory of Kooijman
(2000) was implemented for ecosystems with a low concentration of high quality seston
and compared with a previous model based on EMMY. The model was designed for
flexibility and generality, allowing the usage of different formulations for feeding
processes. Model runs were carried out with a large number of mussels and randomly
assigned physiologic parameter values. These values and respective ranges were taken
from the literature and experimental data obtained with M. galloprovincialis. Obtained
results allowed selecting parameter sets that produced the best fit between model and
observations following the same methodology of the previous work with the EMMY
approach. Model sensitivity analysis and the study of parameter variability together
with model predicted growth, allowed determining those parameters that explain more
growth variability and that should be experimentally assessed more accurately for
improving model performance. Model performance is similar to that obtained
previously with the EMMY approach and encouraging, suggesting that it is possible to
reproduce reasonably well mussel growth. In spite of considerable advances in bivalve
modeling a number of issues is yet to be resolved, with emphasis on the way food
sources are represented and feeding processes formulated. Obtained results together
with literature data suggest that modeling of bivalve feeding and growth should
incorporate physiologic feed-backs related with food digestibility.
Acknowledgements
This study was supported by the contract-project PROINSA Mussel Farm, codes CSIC
20061089 and 0704101100001, and Xunta de Galicia PGIDIT06RMA018E and
PGIDIT09MMA038E. We wish to thank L. G. Peteiro, H. Regueiro, M. García, B.
González, L. Nieto and O. Fernández-Rosende for technical assistance, PROINSA
mussel farm and their employees and also M.J. Guerreiro for her help with English
writing.
References
Babarro, J.M.F., Fernández-Reiriz, M.J., Labarta, U., 2000a. Feeding behavior of seed
mussel Mytilus galloprovincialis: environmental parameters and seed origin. Journal
of Shellfish Research 19, 195–201.
Babarro, J.M.F., Fernández-Reiriz, M.J., Labarta, U., 2000b. Metabolism of the mussel
Mytilus galloprovincialis from two origins in the Ria de Arousa. Journal of the Marine
Biological Association of the United Kingdom 80, 856–872.
Babarro, J.M.F., Labarta, U., Fernández-Reiriz, M.J., 2003a. Growth patterns in
biomass and size structure of Mytilus galloprovincialis cultivated in the Ría de Arousa
(north–west Spain). Journal of the Marine Biological Association of the United
Kingdom 83, 151–158.
Babarro, J.M.F., Fernández-Reiriz, M.J., Labarta, U., 2003b. In situ absorption
efficiency processes for the cultured mussel Mytilus galloprovincialis in Ría de
Arousa (north–west Spain). Journal of the Marine Biological Association of the
United Kingdom 83, 1059–1064.
Bacher, C., Héral, M., Deslous-Paoli, J.-M., Razet, D., 1991. Modèle énergétique
uniboite de la croissance des huîtres (Crassostrea gigas) dans le bassin de MarennesOléron. Canadian Journal of Fisheries and Aquatic Sciences 48, 391–404.
Bayne, B.L., 1993. Feeding physiology of bivalves: time-dependence and compensation
for changes in food availability. Bivalve Filter Feeders in Estuarine and Coastal
Ecosystem Processes. : In: Dame, R.F. (Ed.), NATO ASI Ser., Vol. G 33. SpringerVerlag, pp. 1–24.
Bayne, B.L., 1998. The physiology of suspension feeding by bivalve molluscs: an
introduction to the Plymouth “TROPHEE” workshop. Journal of Experimental Marine
Biology and Ecology 219, 1–19.
Bayne, B.L., Widdows, J., 1978. The physiological ecology of two populations of
Mytilus edulis L. Oecologia 37, 137–162.
Bayne, B.L., Iglesias, J.I.P., Hawkins, A.J.S., Navarro, E., Héral, M., Deslous-Paoli, J.M., 1993. Feeding behaviour of the mussel, Mytilus edulis L.: responses to variations
in quantity and organic content of the seston. Journal of the Marine Biological
Association of the United Kingdom 73, 813–829.
Beadman, H.A., Willows, R.I., Kaiser, M.J., 2002. Potential applications of mussel
modelling. Helgoland Marine Research 56, 76–85.Black, K.D., 2001. Sustainability of
aquaculture. In: Black, K.D. (Ed.), Environmental Impacts of Aquaculture. Sheffield
Academic Press, pp. 199–212.
Blanco, J., Zapata, M., Moroño, A., 1996. Some aspects of the water flow through
mussel rafts. Scientia Marina 60, 275–282.
Bougrier, S., Geairon, P., Deslous-Paoli, J.M., Bacher, C., Jonquieres, G., 1995.
Allometric relationship and effects of temperature on clearance rate and oxygen
consumption rates of Crassostrea gigas (Thumberg). Aquaculture 134, 143–154.
Bourlès, Y., Alunno-Bruscia, M., Pouvreau, S., Tollu, G., Leguay, D., Arnaud, C.,
Goulletquer, P., Kooijman, S.A.L.M., 2009. Modelling growth and reproduction of
the Pacific oyster Crassostrea gigas: advances in the oyster-DEB model through
application to a coastal pond. Journal of Sea Research 62, 62–71.
Crawford, C.M., Macleod, C.K.A., Mitchell, I.M., 2003. Effects of shellfish farming on
the benthic environment. Aquaculture 224, 117–140.
Dame, R.F., Prins, T.C., 1998. Bivalve carrying capacity in coastal ecosystems. Aquatic
Ecology 31, 409–421.
Deslous-Paoli, J.M., Lannou, A.M., Geairon, P., Bougrier, S., Raillard, O., Héral, M.,
1992. The effects of food behaviour of Crassostrea gigas (Molluscs bivalvia) on
natural particulate matter biosedimentation. Hydrobiologia 231, 85–91.
Duarte, P., Fernández-Reiriz, M.J., Filgueira, R.A., Labarta, U., 2010. Modelling
mussel growth in ecosystems with low suspended matter loads. Journal of Sea
Research 64, 273–286.
Fernández-Reiriz, M.J., Duarte, P., Labarta, U., 2007. Modelos de comportamiento
alimentario del mejillón de las Rias de Galicia. In: Figueras, A. (Ed.), Biología y
Cultivo del Mejillón (Mytilus galloprovincialis) en Galicia, Consejo Superior de
Investigaciones Científicas, pp. 195–223.
Figueiras, F.G., Labarta, U., Fernández-Reiriz, M.J., 2002. Coastal upwelling, primary
production and mussel growth in the Rias Baixas of Galicia. Hydrobiologia 484, 121–
131.
Filgueira, R.F., Labarta, U., Fernández-Reiriz, M.J., 2006. Flow-through chamber
method for clearance rate measurements in bivalves. Design and validation of
individual chambers and mesocosm. Limnology and Oceanography Methods 4, 284–
292.
Filgueira, R., Labarta, U., Fernández-Reiriz, M.J., 2008. Effect of condition index on
allometric relationships of clearance rate in Mytilus galloprovincialis Lamarck, 1819.
Revista de Biología Marina y Oceanografía 43, 391–398.
Filgueira, R., Fernández-Reiriz, M.J., Labarta, U., 2009. Clearance rate of the mussel
Mytilus galloprovincialis. I. Response to extreme chlorophyll ranges. Ciencias
Marinas 35, 405–417.
Filgueira, R., Fernández-Reiriz, M.J., Labarta, U., 2010. Clearance rate of the mussel
Mytilus galloprovincialis. II. Response to uncorrelated variables (quantity, quality and
chlorophyll content) of the seston. Ciencias Marinas 36, 15–28.
Folke, C., Kautsky,N., Berg, H., Jansson, Å., Troell, M., 1998. The ecological footprint
concept for sustainable seafood production—a review. Ecological Applications 8, 63–
71.
Grimm, V., 1999. Ten years of individual-based modelling in ecology: what have we
learned and what could we learn in the future? Ecological Modelling 115, 129–148.
Grimm, V., Wyszomirski, T., Aikman, D., Uchmanski, J., 1999. Individual-based
modelling and ecological theory: synthesis of a workshop. Ecological Modelling 115,
275–282.
Hawkins, A.J.S., Bayne, B.L., Bougrier, S., Héral, M., Iglesias, J.I.P., Navarro, E.,
Smith, R.F.M., Urrutia, M.B., 1998. Some general relationships in comparing the
feeding physiology of suspension-feeding bivalve molluscs. Journal of Experimental
Marine Biology and Ecology 219, 87–103.
Hawkins, A.J.S., James, M.R., Hickman, R.W., Hatton, S., Weather head, M.,
1999.Modelling of suspension-feeding and growth in the green-lipped Perna
canaliculus exposed to natural and experimental variations of seston availability in the
Marlborough Sounds, New Zealand. Marine Ecology Progress Series 191, 217–232.
Hawkins, A.J.S., Fang, J.G., Pascoe, P.L., Zhang, J.H., Zhang, X.L., Zhu, M.Y., 2001.
Modelling short-term responsive adjustments in particle clearance rate among bivalve
suspension-feeders: separate unimodal models of seston volume and composition in
the scallop Chlamys farreri. Journal of Experimental Marine Biology and Ecology
261, 61–73.
Hawkins, A.J.S., Duarte, P., Fang, J.G., Pascoe, P.L., Zhang, J.H., Zhang, X.L., Zhu,
M.Y., 2002. A functional model of responsive suspension-feeding and growth in
bivalve shellfish, configured and validated for the scallop Chlamys farreri during
culture in China. Journal of Experimental Marine Biology and Ecology 281, 13–40.
Iglesias, J.I.P., Pérez-Camacho, A., Navarro, E., Labarta, U., Beiras, R., Hawkins,
A.J.S., Widdows, J., 1996. Microgeographic variability in feeding, absorption, and
condition of mussels (Mytilus galloprovincialis LMK): a transplant experiment.
Journal of Shellfish Research 15, 673–680.
Jeffrey, S.W., Welschmeyer, N.A., 1997. Spectrophotometric and fluorometric
equations in common use in oceanography. In: Jeffrey, S.W., Montura, R.F.C.,
Wright, S.W. (Eds.), Phytoplankton pigments in oceanography, pp. 597–615.
Jørgensen, C.B., 1990. Bivalve Filter Feeding: Hydrodynamics, Bioenergetics,
Physiology and Ecology. Olsen & Olsen. Jørgensen, C.B., 1996. Bivalve filter feeding
revisited. Marine Ecology Progress Series 142, 287–302.
Jørgensen, S.E., Nielsen, S., Jørgensen, L., 1991. Handbook of Ecological Parameters
and Ecotoxicology. Elsevier. Kooijman, S.A.L.M., 2000. Dynamic and Energy Mass
Budgets in Biological Systems. Cambridge University Press. Kooijman, S.A.L.M.,
2006. Pseudo-faeces production in bivalves. Journal of Sea Research 53, 103–106.
Labarta, U. (Ed.), 2004. Bateeiros, mar, mejillón. Una perspectiva bioeconómica. CIEF.
Fundación Caixagalicia, Santiago, pp. 49–77.
Labarta, L., Fernández-Reiriz, M.J., Babarro, J.M.F., 1997. Differences in physiological
energetics between intertidal and raft cultivated mussels Mytilus galloprovincialis.
Marine Ecology Progress Series 152, 167–173.
Navarro, E., Iglesias, J.I.P., Pérez-Camacho, A., Labarta, U., Beiras, R., 1991. The
physiological energetics of mussels (Mytilus galloprovincialis Lmk) from different
cultivation rafts in the Ría de Arosa (Galicia, N.W. Spain). Aquaculture 94, 197–212.
Pereira, A., Duarte, P., Norro, A., 2006. Different modelling tools of aquatic
ecosystems: a proposal for a unified approach. Ecological Informatics 1, 407–421.
Pérez-Camacho, A.P., Labarta,U., Beiras, R., 1995. Growth of mussels (Mytilus
galloprovincialis) on cultivation rafts: influence of seed source, cultivation site and
phytoplankton availability. Aquaculture 138, 349–362.
Peteiro, L.G., 2009. Patrones de asentamiento y reclutamiento de Mytilus
galloprovincialis en la Ría de Ares-Betanzos e implicaciones para su cultivo en batea,
PhDthesis, Coruña University, 2009.
Peteiro, L.G., Babarro, J.M.F., Labarta, U., Fernández-Reiriz, M.J., 2006. Growth of
Mytilus galloprovincialis after the Prestige oil spill. ICES Journal of Marine Science
63, 1005–1013.
Pouvreau, S., Bourles, Y., Lefebvre, S., Gangnery, A., Alunno-Bruscia, M., 2006.
Application of a dynamic energy budget model to the Pacific oyster, C. gigas, reared
under various environmental conditions. Journal of Sea Research 56, 156–167.
Raillard, O., 1991. Etude des interactions entre les processus physiques et biologiques
intervenant dans la production de l'huître japonaise Crassostrea gigas du basin de
Marennes-Oléron: essais de modélisation, Thèse doct. Océanographie, Univ. Paris VI.
Raillard, O., Ménesguen, A., 1994. An ecosystem box model for estimating the carrying
capacity of a macrotidal shellfish system. Marine Ecology Progress Series 115, 117–
130.
Raillard, O., Deslous-Paoli, J.-M., Héral, M., Razet, D., 1993. Modélisation du
comportment nutritionnel et de la croissance de l'huître japonaise Crassostrea gigas.
Oceanologica Acta 16, 73–82.
Riisgård, H.U., 2001. On measurement of filtration rates in bivalves—the stony road to
reliable data: review and interpretation. Marine Ecology Progress Series 211, 275–
291.
Riisgård, H.U., Kittner, C., Seerup, D., 2003. Regulation of opening state and filtration
rate in fiter-feeding bivalves (Cardiumedule, Mytilus edulis, Mya arenaria) in
response to low algal concentration. Journal of Experimental Marine Biology and
Ecology 284, 105–127.
Rosland, R., Strand, Ø., Alunno-Bruscia, M., Bacher, C., Strohmeier, T., 2009.
Applying Dynamic Energy Budget (DEB) theory to simulate growth and bioenergetics of blue mussels under low seston conditions. Journal of Sea Research 62,
49–61.
Rueda, J.L., Smaal, A.C., Scholten, H., 2005. A growth model of the cockle
(Cerastoderma edule L.) tested in the Oosterschelde estuary (The Netherlands).
Journal of Sea Research 54, 276–298.
Saraiva, S., van der Meer, J., Kooijman, S.A.L.M., Sousa, T., 2011. Modelling feeding
processes in bivalves: a mechanistic approach. Ecological Modelling 222, 514–523.
Scholten, H., Smaal, A.C., 1998. Responses of Mytilus edulis L. to varying food
concentrations: testing EMMY, an ecophysiological model. Journal of Experimental
Marine Biology and Ecology 219, 217–239.
Scholten, H., Smaal, A.C., 1999. The ecophysiological response of mussels (Mytilus
edulis) in mesocosms to a range of inorganic nutrient loads: simulations with the
model EMMY. Aquatic Ecology 33, 83–100.
Slobodkin, L.B., Richman, S., 1961. Calories/gm in species of animals. Nature 191,
299. Smaal, A.C., 1997. Food supply and demand of bivalve suspension-feeders in a
tidal system, Thesis of A.C.Smaal, Rijksuniversiteit Groningen.
Soletchnik, P., Goulletquer, P., Héral, M., Razet, D., Geairon, P., 1996. Evaluation du
bilan énergétique de l'huître creuse, Crassostrea gigas, en baie de Marennes-Oléron
(France). Aquatic Living Resources 9, 65–73.
Solidoro, C., Pastres, R., Melaku Canu, D., Pellizato, M., Rossi, R., 2000. Modelling the
growth of Tapes phillipinarum in Northern Adriatic lagoons. Marine Ecology
Progress Series 199, 137–148.
Strohmeier, T., Duinker, A., Strand, Ø., Aure, J., 2008. Temporal and spatial variation
in food availability and meat ratio in a long line mussel farm (Mytilus edulis).
Aquaculture 276, 83–90.
Van der Meer, J., 2006. An introduction to dynamic energy budget (DEB) models with
emphasis on parameter estimation. Journal of Sea Research 56, 85–102.
Van der Veer, H.W., Alluno-Bruscia, M., 2006. The DEBIB project: Dynamic Energy
Budgets in Bivalves. Journal of Sea Research 56, 81–84.
Van der Veer, H.W., Cardoso, J.F.M.F., Van der Meer, J., 2006. The estimation of DEB
parameters for various Northeast Atlantic bivalve species. Journal of Sea Research 56,
107–124.
Van Haren, R.J.F., Kooijman, S.A.L.M., 1993. Application of a dynamic energy budget
model to Mytilus edulis (L.). Netherlands Journal of Sea Research 31, 119–133.
Villalba, A., 1995. Game to genic cycle of cultured mussel, Mytilus galloprovincialis, in
the bays of Galicia (N.W. Spain). Aquaculture 130, 269–277.
Ward, J.E., Shumway, S.E., 2004. Separating the grain from the chaff: particle selection
in suspension- and deposit-feeding bivalves. Journal of Experimental Marine Biology
and Ecology 300, 83–130.
Willows, R.I., 1992. Optimal digestive investment: a model for filter feeders
experiencing variable diets. Limnology and Oceanography 37, 829–847.
Winter, J.E., 1973. The filtration rate of Mytilus edulis and its dependence on algal
concentration measured by continuous automatic recording apparatus. Marine Biology
22, 317–328.
Winter, J.E., 1978. Fundamental knowledge of suspension-feeding in lamellibranchiate
bivalves, with special reference to artificial aquaculture systems. Aquaculture 13, 1–
33.
World Bank, 2006. Aquaculture: Changing the Face of the Waters Meeting the Promise
and Challenge of Sustainable Aquaculture. The World Bank, Washington.
Table 1. Model rate equations. There are three different options to calculate CR and two different options to calculate IR. PF rejection
corresponds to the difference between FR and IR, when Eq. (10) is used to calculate IR.
Process
Equation
Equation
number
Units
Feeding and absorption
If Chl < Lim1 then CR60 = max[7.51.TPM− 3.01.TPM2− 6.86.Q1 + 2.26, 0] else
Clearance rate CR60 = const
4
Lh− 1
5
Gut passage
time
Gut volume
Filtration rate
GV = Agc. MeatDryWeightBgc
FR = CR. TPM
Ingestion rate
Maximal
IRmax = (GV. SpFoodMass)/GPT
ingestion rate
Absorption
efficiency
Absorption rate
6
h
7
8
9
10
mm3
mg h− 1
11
12
dimensionless
13
mg h− 1
Eqs. (4) and (5), from Filgueira et al., 2010 and Willows, 1992, respectively, and Eqs. (6) and (7) from Scholten and Smaal (1999) where,
CR60—Clearance rate of a 60 mm mussel; Lim1—Chlorophyll threshold (1.18 μg L− 1); Q1—POM/TPM; GV—Gut volume calculated
allometrically as a function of body weight as in Scholten and Smaal (1999)(mm3); VTPM—TPM in volume units (mm3/L); GPT—Gut Passage
Time (h); GPTmin and GPTmax (minimal and maximal gut passage times); PHYORG and DETORG—Phytoplankton and detritus organics
(mg L− 1) in TPM; α and β—Digestibility coefficients (0–1); Agc and Bgc—Allometric coefficients.Eq. (9) from Rosland et al. (2009), Eqs. (10)
and (11) from Scholten and Smaal (1999) and Eq. (12) from Fernández-Reiriz et al. (2007). In Eq. (13) FoodEnergy (Food energy contents) is in
J g− 1. It is calculated from the quantity of ingested food assuming a conversion ratio of 23.5 J mg− 1 (Slobodkin and Richman, 1961).
Table 2. Initial model parameter values and ranges and calibrated parameters from two simulations with 10,000 mussels: one between the 1st of
April 2004 till the 31st of March 2005 (Simulations 1a, 1b, 1c, 1d) and another between the 10th of June 2004 and the 19th of May 2005
(Simulations 2a, 2b, 2c and 2d). *—parameters not used in the simulation, **—parameters not used for calibration (cf.—2.3 Model simulations).
Parameter
Value
or
Units
range
Clearance rate of a
standard 60 mm mussel 3.9
(CR60) (Eqs. (4)–(5))
Carbon fraction of food
0.4
items (CDWFood)
Nitrogen fraction of
0.04
food items (NDWFood)
Reference
Calibrated parameters in
simulations
Calibrated parameters in
simulations
1a
Filgueira et al.,
2009, Navarro et
L h− 1
al., 1991,
**
−1
mussel
Iglesias et al.,
1996 and Labarta
et al., 1997
Average
conversion for
natural algal
g C g− 1 food
blooms within **
DW
nearshore waters
(Soletchnik et
al., 1996)
From nitrogen
g N g− 1 food
carbon ratios
**
DW
reported in
1b
1c
1d
2a
2b
2c
2d
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
Parameter
Value
or
Units
range
Reference
Calibrated parameters in
simulations
Calibrated parameters in
simulations
1a
1b
1c
1d
2a
2b
2c
2d
13.2
*
12.4
*
18.6
*
12.9
*
Jørgensen et al.
(1991)
Parameter for the
allometric relationship
between gut volume
and meat dry weight
(Agc)
Allometric coefficient
for the relationship
between gut volume
and meat dry weight
(Bgc)
Phytoplankton
digestibility α
12–20 mm3 g− 1
Scholten and
Smaal (1999)
0.4–
0.7
Dimensionless
0.63
*
0.63
*
0.62
*
0.59
*
1
Dimensionless
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
1.0
*
1.0
*
1.2
*
1.9
*
9.3
*
10.6
*
10.3
*
8.3
*
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
Detritus digestibility β 0.6
Dimensionless
GPTmin
1–2
h
GPTmax
2–12
h
SpFoodMass
1
mg mm− 3
Phytoplankton
energetic contents
23.5
J mg− 1
Bayne and
Widdows (1978)
Scholten and
Smaal (1999)
Scholten and
Smaal (1998)
Scholten and
Smaal (1999)
Slobodkin and
Richman (1961)
Parameter
Calibrated parameters in
simulations
Calibrated parameters in
simulations
1a
1b
1c
1d
2a
2b
2c
2d
J mg− 1
A similar
energetic
contents was
assumed for
detritus and
phytoplankton
organics
**
**
**
**
**
**
**
**
60
mm
–
**
**
**
**
**
**
**
**
33–
420
J cm− 2 d− 1
98.0
89.6
102.2 390.7 142.3 399.7 131.9 299.3
Value
or
Units
range
Reference
(PHYenergeticcontents)
Detritus energetic
contents
23.5
(DETenergeticcontents)
Length of a standard
mussel
Maximum surfacearea-specific
assimilation rate
Maximum reserve
density—[Em]
Energetic growth costs
per unit of growth in
structural body
volume—[EG]
Shape coefficient—δ
2085–
J cm− 3
2295
1900
J cm− 3
0.175–
0.381
Fraction of the energy
0.45–
utilized from the
Dimensionless
0.8
reserves that is spent on
Lower and upper 2159.2 2087.5 2094.0 2163.1 2245.6 2273.4 2285.4 2094.8
values from Van
der Veer et al.
(2006) and this **
**
**
**
**
**
**
**
work in the case
of the shape
coefficient
0.2477 0.2298 0.2474 0.2948 0.2479 0.2752 0.2510 0.2670
0.78
0.75
0.74
0.46
0.56
0.46
0.72
0.47
Parameter
growth and somatic
maintenance—κ
Volume-specific
maintenance costs—
Arrhenius
temperature—TA
Value
or
Units
range
23–
32.3
J cm− 3 d− 1
5800–
7022
°k
Reference
temperature—T1
288.6
Reference
Calibrated parameters in
simulations
Calibrated parameters in
simulations
1a
2a
1b
1c
1d
2b
2c
2d
26.49 25.67 26.35 29.80 25.47 30.17 29.93 32.18
Upper value
from Van der
Veer et al.
(2006) and lower *
value from
Rosland et al.
(2009)
Experimental
conditions of
**
Filgueira et al.
(2009)
*
5871.1 6811.9 *
*
5975.6 6026.7
**
**
**
**
**
**
**
Table 3. Model simulations (cf.—2.3).
Simulations
Ria de Ares-Betanzos
Simulated
experiment
(cf.—2.2 Field
data for model
forcing and
calibration)
1a
1b
1c
1 Mussels
harvested in
intertidal areas
1d
2a
2b
2 Mussels
harvested in
collector ropes
Ria de Arousa
Simulated
Comparable
experiment
Clearance
Temperature simulations in
(cf.—2.2 Field
rate
Simulations
limitation
Duarte et al.
data for model
calculation
(2010)
forcing and
calibration)
Eq. (5)
Simulation
(cf.—
No
1a
1a
Table 1)
parameters
Eq. (4)
Simulation
(cf.—
No
1b
1b
Table 1)
parameters Mussels
harvested in
Eq. (5)
Simulation intertidal areas
(cf.—
Yes
–
1c
Table 1)
parameters
Eq. (4)
Simulation
(cf.—
Yes
–
1d
Table 1)
parameters
Eq. (5)
Simulation
(cf.—
No
2a
1a
Mussels
Table 1)
parameters harvested in
Eq. (4)
Simulation collector ropes
No
2b
(cf.—
1b
Clearance
Temperature
rate
limitation
calculation
Eq. (5)
(cf.—
Table 1)
Eq. (4)
(cf.—
Table 1)
Eq. (5)
(cf.—
Table 1)
Eq. (4)
(cf.—
Table 1)
Eq. (5)
(cf.—
Table 1)
Eq. (4)
(cf.—
No
No
Yes
Yes
No
No
Simulations
Ria de Ares-Betanzos
Simulated
experiment
(cf.—2.2 Field
data for model
forcing and
calibration)
2c
2d
Ria de Arousa
Simulated
Comparable
experiment
Clearance
Temperature simulations in
(cf.—2.2 Field
rate
Simulations
limitation
Duarte et al.
data for model
calculation
(2010)
forcing and
calibration)
Table 1)
parameters
Eq. (5)
Simulation
(cf.—
Yes
–
1c
Table 1)
parameters
Eq. (4)
Simulation
(cf.—
Yes
–
1d
Table 1)
parameters
Clearance
Temperature
rate
limitation
calculation
Table 1)
Eq. (5)
(cf.—
Table 1)
Eq. (4)
(cf.—
Table 1)
Yes
Yes
Table 4. Sensitivity analysis as % variation in final meat dry weight and shell length predicted by the model after changing each
calibrated model parameter by ± 10%. For the meaning and calibrated values of each parameter refer to Table 2. For Simulation setups
refer to section Model simulations (see text).
Mussels harvested along
the seashore—Simulation
1a
Meat weight
Agc + 10%
5.47
Agc− 10%
− 5.71
Bgc + 10%
1.57
Bgc− 10%
− 1.45
GPTmin + 10% − 0.15
GPTmin− 10% 0.15
GPTmax + 10% − 5.04
GPTmax− 10% 5.90
κ+ 10%
23.46
κ− 10%
− 21.14
ShapeCoeff
− 0.01
δ+ 10%
ShapeCoeff
0.00
δ− 10%
Em + 10%
1.67
Em− 10%
− 1.91
+ 10%
22.73
Mussels harvested along
Mussels harvested along the
the seashore—Simulation
seashore—Simulation 1b
1c
Mussels harvested along the
seashore—Simulation 1d
Shell length
1.79
− 1.94
0.52
− 0.49
− 0.05
0.05
− 1.71
1.92
7.45
− 7.76
Meat weight
*
*
*
*
*
*
*
*
24.00
− 21.54
Shell length
*
*
*
*
*
*
*
*
7.55
− 7.87
Meat weight
5.56
− 5.92
1.00
− 0.93
− 0.16
0.16
− 5.24
5.99
23.69
− 21.25
Shell length
1.84
− 2.03
0.34
− 0.32
− 0.06
0.05
− 1.80
1.98
7.53
− 7.81
Meat weight
*
*
*
*
*
*
*
*
30.05
− 25.29
Shell length
*
*
*
*
*
*
*
*
8.60
− 8.58
− 9.09
− 6.88
− 10.91
− 1.10
− 9.43
− 43.66
− 22.44
11.11
6.41
13.12
0.00
11.11
87.85
33.32
− 0.95
0.96
7.04
− 0.05
− 0.12
25.74
− 1.51
1.56
8.09
1.73
− 1.89
22.03
− 0.88
0.94
6.81
1.60
− 1.62
− 1.47
− 0.55
0.56
0.51
− 10%
PM + 10%
PM− 10%
TA + 10%
TA− 10%
Mussels harvested along
the seashore—Simulation
1a
Mussels harvested along
Mussels harvested along the
the seashore—Simulation
seashore—Simulation 1b
1c
Mussels harvested along the
seashore—Simulation 1d
Meat weight
− 20.12
− 15.31
18.63
*
*
Meat weight
− 22.41
− 15.13
18.32
*
*
Meat weight
1.71
− 19.97
26.31
0.65
− 0.62
Shell length
− 7.20
− 5.50
6.00
*
*
Shell length
− 8.24
− 5.39
5.85
*
*
Meat weight
− 20.02
− 15.39
18.76
0.21
− 0.26
Shell length
− 7.14
− 5.53
6.04
0.08
− 0.10
Shell length
− 0.66
− 5.02
7.56
0.31
− 0.30
Fig. 1. A comparison between clearance rate estimated from Eq. (14) and from Eq. (16), with three allometric coefficients (b) in the range
reported in the literature (see text).
Fig. 2. Ria de Ares-Betanzos and Ria de Arosa (upper and lower panels, respectively, with the geographical coordinates of the lower right and
upper left limits of both panels shown according, to the WGS84 datum). The asterisks show the places where growth experiments took place (see
text).
Fig. 3. Ria deArousa Forcing function data formodel simulations covering the periods 27th of November 1995–3rd of July 1996 and 28th of
January–8th of July 1998. (see text).
Fig. 4. Simulations 1a, b, c and d. Measured shell lengths±1 standard deviation error bars (upper panel) and meat dry weights (lower panel) and
predicted values (for individuals exhibiting best fit between model and observations). Measured data from the 1st of April 2004 till the 18th of
May 2005 for the Lorbé station (Experiment 1, cf.—2.3).
Fig. 5. Simulations 2a, b, c and d. Measured shell lengths ±1 standard deviation error bars (upper panel) and meat dry weights (lower panel) and
predicted (for individuals exhibiting best fit between model and observations). Measured data from the 10th of June 2004 till the 19th of May
2005 for the Lorbé station (Experiment 2, cf.—2.3).
Fig. 6. Measured shell length ±1 standard deviation error bars (upper panel) and meat dry weights (lower panel) and predicted values. Measured
data from the 10th of June 2004 till the 19th of May 2005 for the Lorbé station (Experiment 2, cf.—2.3). Model parameters were those calibrated
with mussels harvested from rocky intertidal areas (Experiment 1 and Simulations 1, cf.—2.3 and Table 3).
Fig. 7. Measured and predicted clearance and organic ingestion rates for the Ria de Arousa data obtained between the 27th of November 1995
and the 3rd of July 1996 (cf.—2.2 and 2.3 and Babarro et al. (2000a)). Model parameters were those calibrated with mussels harvested from
rocky intertidal areas (Experiment 1 and Simulations 1a—upper panel—and 1b—lower panel, cf.—2.3 and Table 3).
Fig. 8. Measured and predicted shell lengths and meat dry weights for the Ria de Arousa data obtained between the 27th of November 1995 and
the 3rd of July 1996 (cf.—2.2 and 2.3). Model parameters were those calibrated with mussels harvested from rocky intertidal areas (Experiment 1
and Simulations 1, cf.—2.3 and Table 3).
Fig. 9. Measured and predicted shell lengths for the Ria de Arousa data obtained between the 28th of January and the 8th of July 1998 (cf.—2.2
and 2.3).Model parameters were those calibrated with mussels harvested from rocky intertidal areas (Experiment 1 and Simulations 1, cf.—2.3
and Table 3).
Fig. 10. Shell length, condition index (CI) and Reserve Density [E] predicted by the model for a mussel for a period of 32 months, with
parameters calibrated from Simulation 1a and depicted in Table 2. Arrows show simulated gamete release (see text).