An R package for simulating growth and organic wastage in aquaculture farms in response to environmental conditions and husbandry practices
An R package for simulating growth and organic wastage in aquaculture farms in response to environmental conditions and husbandry practices
Damiano Baldan 0 1
Erika Maria Diletta Porporato 1
Roberto Pastres 0 1
Daniele Brigolin 0 1
0 Bluefarm S.r.l., Venezia Marghera, Italy, 2 Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice , Venezia Mestre , Italy
1 Editor: Juan A. Añel, Universidade de Vigo , SPAIN
A new R software package, RAC, is presented. RAC allows to simulate the rearing cycle of 4 species, finfish and shellfish, highly important in terms of production in the Mediterranean Sea. The package works both at the scale of the individual and of the farmed population. Mathematical models included in RAC were all validated in previous works, and account for growth and metabolism, based on input data characterizing the forcing functionsÐwater temperature, and food quality/quantity. The package provides a demo dataset of forcings for each species, as well as a typical set of husbandry parameters for Mediterranean conditions. The present work illustrates RAC main features, and its current capabilities/limitations. Three test cases are presented as a proof of concept of RAC applicability, and to demonstrate its potential for integrating different open products nowadays provided by remote sensing and operational oceanography.
Data Availability Statement: All RAC files are
available from the CRAN repository
(https://cran.rproject.org/package=RAC). For installation select
the repositories CRAN, then type: install.packages
(ªRAC ª, dependencies = TRUE).
Funding: DBr, EMDP and RP are researchers
employed at the Department of Environmental
Sciences, Informatics and Statistics, University of
Venice (DAIS). The study was partly financed by
DAIS, as an individual research grant to DBr, within
the IRIDE project "ADvances in Aquaculture
MOdels: state of the art and perspectives
Virtual technologies are increasingly perceived as a resource for aquaculture science-based
]. The selection of sites/areas plays a key role in supporting the sustainable
development of this industry within the framework of the Ecosystem Approach to Aquaculture
]. With this respect, identification of Allocated Zones for Aquaculture (AZAs), the
selection of individual sites, and the design of Aquaculture Management Areas (AMAs) are
three complex, and inter-related issues [
]. This task is further complicated by the forecasted
long-term trends in environmental parameters, induced by climate changes, which will need
to be included in the planning, in order to attempt a sound adaptive management of these
]. To face these challenges, nowadays, aquaculture models can largely benefit
from the information provided by remote sensing and operational oceanography [
Current efforts are devoted at implementing existing aquaculture models in accessible formats,
available to users with different programming expertise. This is expected to help promoting
the use of models in aquaculture, and improve the reproducibility of results [
(ADAMO). Bluefarm S.r.l., a DAIS spin-off
company of which DBr and RP are co-founders
and shareholders, provided support in the form of
salary for the author DBa. There was no additional
external funding received for this study. The
specific roles of these authors are articulated in the
`author contributions' section. The funders had no
role in study design, data collection and analysis,
decision to publish, or preparation of the
Competing interests: Three authors (DB, RP and
DBr) are affiliated with Bluefarm S.r.l. DBr, EMDP
and RP are researchers employed at the
Department of Environmental Sciences,
Informatics and Statistics, University of Venice
(DAIS). DBr and RP are shareholders and DBa is
employed by Bluefarm S.r.l. There are no patents,
products in development or marketed products to
declare. This does not alter our adherence to all the
PLOS ONE policies on sharing data and materials,
as detailed online in the guide for authors.
Here we describe the new R software package RAC (R package for AquaCulture), which
focuses on 4 species, finfish and shellfish, highly important in terms of production in the
Mediterranean Sea [
]. RAC simulates the rearing cycle of the European seabass (Dicentrarchus
labrax), Gilthead seabream (Sparus aurata), Manila clam (Ruditapes philippinarum) and
Mediterranean mussel (Mytilus galloprovincialis), both at the individual and the population level.
These mathematical models account for growth and metabolism of the individual, based on
input data characterizing the forcing functionsÐwater temperature, and food quality and
quantity. For finfish, seabass and seabream, food availability is represented by the feed
provided by the farmer, while shellfish models require a characterization of quantity and quality
of the suspended organic matter. The package provides a demo dataset of forcings for each
species, as well as a typical set of husbandry parameters for Mediterranean conditions, in order
to allow the user to run a default simulation. The present work illustrates the main features of
RAC and delineates its current capabilities in terms of predicting growth and environmental
interactions of aquaculture. RAC outputs represent a baseline which could be integrated with
environmental spatial data, economic-social criteria and policy issues, in order to support the
decision makers in the identification of suitable area for aquaculture activities and for the
implementation of an EAA [
]. Three test cases were carried out in the Adriatic Sea (Italy) as
a proof of concept of RAC applicability: a) individual model runs for each of the 4 species:
seabass, seabream, clam and mussel; b) evaluation of site suitability for mussel aquaculture; c)
evaluation of the response of seabream growth and organic waste release to climate-induced
changes in water temperature.
Software characteristics and capabilities
RAC simulates the rearing cycle of the four farmed species, both at the individual and the
population level. The package is based on a set of models independently validated in previous
studies. RAC is released as open-source and can be freely downloaded from its website, https://
cran.r-project.org/package=RAC. This section will briefly introduce the models (sections
Individual model and Population up-scaling), therefore focusing on input/output information
flow (section Inputs and outputs), the package structure (section Package structure), and the
instructions required for running it (section Instructions).
The growth of the individual is simulated by solving the following general energy balance
· w is the wet weight [g]
· t is time [d]
· A is the anabolic rate [J d-1]
· C is the catabolic rate [J d-1]
· ε [J g-1] represents the energy density of body tissues.
The weight increment is therefore described as the difference between the anabolism and
the catabolism. Formulations and parameters are reported in the Supporting Information
(Tables in S1 and S2 Files). These terms are species-specific and are described in detail in
Brigolin et al. [
] (Mediterranean mussel), in which Eq (1) is modified in order to account for
reproduction, Solidoro et al. [
] (Manila clam), Brigolin et al. [
] (gilthead seabream),
Brigolin et al. [
] (European seabass).
According to the methodology used by Bacher and Gangnery [
], the individual model was
up-scaled to the population level by means of a set of Monte Carlo simulations, which were
used for estimating the size structure of the population (see [
]). Such differences were
accounted for by assigning a different initial weight and maximum clearance rate to each
shellfish specimen, and a different initial weight and ingestion rate to each finfish specimen, in
order to reflect the variability in individual phenotypes, as well as the differences in the
localization of specimens within the farm (for shellfish). Individuals in the population have a fixed
mortality rate, forced to be discontinuous by stocking and harvesting of animals in the farm.
Inputs and outputs
RAC inputs and outputs, summarized in Tables 1 and 2, are species specific. Finfish are forced
by the time series of water temperature (ÊC), feed availability (g d-1), and feed composition
(relative %), this latter one characterized in terms of proteins, lipids and carbohydrates, and not
dependent on time. Mussels are forced by daily time series of water temperature (ÊC),
chlorophyll-a concentration (μg l-1), Particulate Organic Carbon concentration (POC, mg C l-1),
Particulate Organic Matter concentration (POM, mg C l-1), Total Suspended Matter concentration
(TSM, mg C l-1) and the POC characterization in terms of C/P and N/P molar ratios (-). The
Clam model is forced by the water temperature (ÊC) and the chlorophyll-a concentration (μg l-1).
RAC simulations generate two main classes of outputs: i) vector outputs, providing a time
series of the number of individuals in the farmed population; ii) matrix outputs, with the mean
and the standard deviation of each model state variable, as well as metabolic processes, which
are estimated over the distribution of simulated individuals. These output variables, which are
different for the 4 models, are summarized in Table 2. Finfish models compute the weight of
the individual (g), the ingestion rate (g d-1), temperature response functions [±], metabolic
rates (anabolism and catabolism, J d-1), faeces produced (in terms of proteins, lipids and
carbohydrates, g d-1 for individuals or kg d-1 for population), uneaten feed (in terms of proteins,
lipids and carbohydrates, g d-1 for individuals or kg d-1 for population), O2 consumption (g d-1
for individuals or kg d-1 for population) and ammonia production (gN d-1 for individuals or
kgN d-1 for population). Mussel model computes the somatic and gonadic dry weight of the
individual (g), the wet weight of soft tissues (g), and the total weight including the shell (g), the
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Feeding rate + Feed composition
W, weight; L, length; Exc, excretion; Wst, Waste produced; T fun, Temperature response function; MR, Metabolic rates; Pf, Pseudofaeces; CNP, C:N:P composition; O2,
O2 consumed; NH4, NH4 produced; N, Number of individuals.
length (cm), faeces and pseudofaeces produced (in terms of C, N and P; g d-1 for individuals or
kg d-1 for population), metabolic rates (anabolism and catabolism J d-1), CNP content of
animal tissues (g), temperature limitation function, O2 consumption (g d-1 for individuals or kg
d-1 for population) and ammonia production (gN d-1 for individuals or kgN d-1 for
population). Clam model outputs include the wet weight of the individual (g), temperature limitation
function, metabolic rates (J d-1), and shell length (mm). The number of individuals is also
provided as an output. Finally, the number of days needed to reach the commercial size from the
beginning of the integration period is reported for all the models.
The general workflow of RAC is schematically described in Fig 1. SKELETON function creates
a folder structure at a user defined path and pastes to the structure pre-formatted input files,
which can be modified by the user. The subsequent execution of this function overwrites all
the files, if present. DATA-LOADER function loads the input data located in the folders to the
workspace, interpolating them, in order to fill those parts of the data series that are unequally
spaced, thus meeting the requirements of the main script. PRE-PROCESSOR function
converts the forcing units (e.g.: computes detritus + zooplankton C concentration as the difference
between the POC concentration and phytoplanktonic C concentration). Additionally, the
preprocessor function plots the interpolated forcing values, saving them into the previously
created folder structure. The pre-processor can be executed by the main script as many times as
required in order to satisfy the user requirements. Subsequently, MAIN function calls all the
functions that are required to solve the balance and to save the results. The RK-SOLVER
function implements the 4th order Runge-Kutta scheme for the solution of the bioenergetics
balance. Equations describing limitation terms, and anabolic and metabolic rates are contained in
the EQUATIONS function, called by the RK-SOLVER function. Outputs of the RK-SOLVER
are processed by the POSTPROCESSOR function that plots and saves them in files. The
population script contains also the LOOP function that runs the Monte Carlo simulation and
computes the statistics of the simulated outputs. Finally, the POPULATION function solves the
population equation, based on mortality rate parameters and on husbandry practices.
RAC package requires the subsequent execution of three instructions from the R console.
The first instruction creates a directory structure at the path specified by the string variable
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Fig 1. General workflow of RAC package. Arrows show the information flow. The grey boxes indicate the functions called
directly by the user.
ªuserpathº. This instruction populates the directory with a ready to use dataset of forcings and
parameters, which can be subsequently modified by the user. The second instruction loads the list
of model forcings into the R workspace contained at the user defined path. The third instruction
runs the model with the loaded forcings and saves the textual and graphic results into the
directories specified by the string ªuserpathº. In order to select the species to model, and the level of
hierarchical organization (individual or population), two parts of the string need to be specified by the
user, while the third part reports the function of interest. In the first part of the string, the user
indicates the species (Bream, Bass, Mussel, Clam), while in the second part indicates ª_ind_º or
ª_pop_º, in order to run the individual or the population model respectively.
As an example, in order to run the Gilthead seabream individual model, the following
instructions need to be specified:
forcings <–Bream_ind_dataloader (userpath)
Output <–Bream_ind_main (userpath, forcings)
On the other hand, running the Mussel population model will require the following
forcings <–Mussel_pop_dataloader (userpath)
Output <–Mussel_pop_main (userpath, forcings)
In order to demonstrate the applicability of RAC, and the resources potentially provided by
operational oceanography and remote sensing data for running the model, the following set of
simulations was performed:
1. individual models were run for the 4 species, using as input present environmental data,
taken from the sites marked in Fig 2 - model predictions included growth trajectories, and
organic matter waste;
2. mussel individual model was run repeatedly over a spatial domain which represents a
portion of sea localized in a highly productive coastal area, in the Northern Adriatic Sea,
Emilia-Romagna regionÐmodel runs were used to estimate the growth performance of the
mussel over this area, which was quantified as days required by the mussel for reaching the
length of 5 and 7 cm;
3. water temperature time series for 2049±2050, predicted by climate models, were used to
run the seabream population model at a site located in the southern Adriatic Sea, Puglia
region (see Fig 2). These simulations were aimed at comparing growth, uneaten feed and
faeces release expected under different scenarios of global warming. In order to upscale the
individual to population model, a number of 5000 runs, each representing one individual
with different initial weight, 80 ± 8 g, and ingestion rate, 0.09 ± 0.018 g food g fish-m day-1,
were run via Monte Carlo simulation. This number of model runs was empirically found to
be the minimum needed to stabilize the results [
]. Farm characteristics and husbandry
parameters are resumed in Table 3, and were assigned on the basis of the papers by Solidoro
et al. [
], Pastres et al. [
] and Brigolin et al. [
]. Environmental forcings provided
to the models are also resumed in Table 3, and details on data sources and processing are
provided in the following section.
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Fig 2. Case study sites and species. M. galloprovincialis and R. philippinarum, and finfish, S. aurata and D. labrax. The shapefile of Italian boundaries was downloaded
from DIVA-GIS dataset (freely available at http://www.diva-gis.org/Data) and the layout was made in QGIS version 2.18.5.
Present time data (2015±2016). The SST and Chlorophyll-a (Chl-a) data were extracted
from the CopernicusÐMarine Environment Monitoring Service (http://marine.copernicus.
eu/). For the purposes of this study, satellite data level 4 with a spatial resolution of 0.008 (SST)
and 0.013 degrees (Chl-a) (~1 Km), from 01/03/2015 to 30/09/2016 were downloaded. As
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CNRM CM5 RCP 45 and 85 (Future)
previously described, the shellfish models require TSM, POC and POM concentrations as
forcing variables but, since satellite TSM, POC and POM were not available for the study area,
these values were imposed on the basis of existing data collected at mussel farms in the area
RAC spatial application. The area selected for running the model is located in the North
Adriatic Sea, along the coastline of Emilia-Romagna region, where mussel farming represents
an important activity (21.6 103 metric tons in 2013, 33.6% of the national production [
and aquaculture zoning and site-selection in the continental shelf comprised between 3 and 12
nm recently received increasing attention [
]. Model application in this area allowed to derive
an indicator of potential growth, selected on the basis of its capability to be easily
communicated to stakeholders, which is the number of days required to reach the minimum size
required by the law for commercializationÐ5 cm shell length for mussels. In this work, we
have also evaluated the days required to reach 7cm, as this represents the ideal commercial
target size to be achieved.
In order to apply the model, environmental data were extracted from NetCDF (Network
Common Data Form) datasets, and converted in data matrices (spatial coordinates + daily
values). Hence, the forcing variables time series at each grid cell were used as input for the RAC
model functions. RAC outputs were stored in a matrix, and associated to the cell spatial
coordinates. Two maps of the number of days required to reach both sizes for commercialization
were finally created, and the complete set of RAC daily outputs were stored in NetCDF files. R
code to run the individual mussel model over a spatial domain is reported in S1 Appendix.
Future climate scenarios (2049±2050). Time series of future SST data were downloaded
from the CEDA ESGF data node (https://esgf-index1.ceda.ac.uk/projects/esgf-ceda/) taking
advantage of the results obtained within the EURO-CORDEX initiative ([
Regional Climate Downscaling Experiment). This Regional Climate Model is based on the
IPCC Fifth Assessment Report (AR5) CMIP5 (Coupled Model Intercomparison Project). In
order to highlight the effects of future temperature changes, we have chosen two
Representative Concentration Pathways (RCP [
]) scenarios, 4.5 and 8.5 with a spatial resolution of 0.11
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Fig 3. Current individual model outputs of shellfish, M. galloprovincialis and R. philippinarum, and finfish, S. aurata and D. labrax. On the left panels the
individual growth in terms of length (cm and mm) for the shellfish (a and b) and of weight (g) for the finfish (d and e). On the right panel the organic waste produced by
M. galloprovincialis (c) in terms of faeces and pseudofaeces (g d-1) and the quantity of uneaten feed (g d-1), in terms of protein, lipids and carbohydrates, produced by S.
degrees (EUR-11; ~12.5 km). We have selected the climatic models ran by the Centre National
de Recherches MeÂteÂorologiques Coupled Global Climate Model, version 5 (CNR-CM5) for the
2049±2050 time period.
Potential uses and discussion
Individual model outputs
Fig 3A and 3B show the growth in length for the shellfish species (mussel and clam), while Fig
3D and 3E show the growth in weight for the finfish species (seabream and seabass). For all the
species, the individual growth predicted by the models under the effect of environmental
forcings provided by operational oceanography products is in good agreement with the results
obtained in previous studies in which model validation was carried out [
3C and 3F show the model output in terms of organic waste, which is represented by faeces
and pseudofaeces produced per individual mussel (g d-1), and the sum of faeces produced and
uneaten feed per individual seabream (g d-1). For mussels, predicted values are in agreement
with the measurements performed in eastern Canada [
], with faeces ranging between 29.1
and 44.4 mg ind.-1 d-1, and for seabream simulations agree with the results published for the
Southern Adriatic Sea [
], with values reaching 1.8 g ind-1 d-1.
Space suitability for mussel farming: Time to reach the market size
As one can see in Fig 4A mussels, seeded at 2.5 cm, reach the minimum size for
commercialization, 5 cm, in a period comprised between two months and eight months and half. As visible
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Fig 4. RAC spatial application: Output of M. galloprovincialis. In these maps are represented the number of days necessary to reach the commercial size of 5 cm (a)
and 7 cm (b). The shapefile of Italian boundaries was downloaded from DIVA-GIS dataset (freely available at http://www.diva-gis.org/Data) and the layout was made in
QGIS version 2.18.5.
in Fig 4B, mussels reach in the northern area the size of 7 cm in approximately 8 months,
while in the south-eastern area this size is not achieved within the simulated period of 10
months. Results suggest that the northern part of this area is more suitable compared to the
southern one. Indeed, this portion of sea, being under the direct influence of the Po river
plume, is highly rich in nutrients, and sustains an elevated primary productivity [
Climate change effects on growth and organic waste load
Fig 5A shows the forecasted effects of water temperature change on seabream growth,
including variability in weight trajectories among individuals belonging to the same farmed
population. Growth performance differs during the warm season, with the highest values in
correspondence to the more ªoptimisticº scenario, RPC4.5, with respect to RCP8.5. A similar
trend for RCP 4.5 and 8.5 is detectable both for faeces, Fig 5B, and uneaten feed, Fig 5C,
quantified in terms of proteins, lipids and carbohydrates. It is worth remarking here that the high
variability associated to these outputs (standard deviation within the population is shown in
grey) poses limitation to the overall significance of differences detected under the two
scenarios. The rapid decrease of uneaten feed and faeces, reaching 0 in December, are due to the
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Fig 5. Future population model outputs of S. aurata simulated at Bisceglie (Southern Adriatic Sea) under RCP 4.5
and 8.5 temperature scenarios. a) mean growth and ± standard deviation (g); b) the uneaten feed in terms of protein,
lipids and carbohydrates (Kg d-1); c) faeces produced in terms of protein, lipids and carbohydrates (Kg d-1).
pause in feeding during winter months, which is present in current days husbandry practices.
These husbandry practices may be subjected to substantial variations in the future. To this
regard, we remark model results could help in identifying the most appropriate practices,
based on the expected environmental changes, and effectively contribute to the planning of
sound adaptation strategies for aquaculture.
Conclusion and next steps
This paper provides a synthetic overview of design and applicability of the RAC package. The
reasonableness of RAC estimations was confirmed by the agreement between the results obtained in
test cases performed within the present work with previous studies in which models were
validated. Runs carried out demonstrate the potential of RAC for integrating different open products
nowadays provided by remote sensing and operational oceanography. This goes in the direction
of overcoming limitations imposed by data scarcity, recognized as a major obstacle to the
application of virtual technologies for aquaculture [
]. Indeed, this tool represents a resource for
simulating the rearing cycle of different species, finfish and shellfish, under different scenarios of change
of future climate conditions. This has the potential to support a science-based design of
aquaculture areas, e.g. integrating the outputs obtained from this tool with site selection criteria (i.e.:
depth, significant wave height, distance to harbour, etc. . .) in a multi-criteria evaluation process
], and contribute to an effective implementation of maritime spatial planning [
]. RAC outputs
can guide the implementation of site selection and management, for instance integrating the
results with deposition models [
], in order to achieve the sustainable development of
aquaculture activities. Future efforts will focus on RAC maintenance and improvement, in response to
user feedbacks. One upcoming update will be the integration of a new routine for automating the
runs performed in spatial explicit mode, starting from input rasters of environmental data. A
further planned update will be embedding in the package a deposition module [
S1 File. Model equations. Table A. Model state variables, forcings, and functional
relationships of M. galloprovincialis±as in Brigolin et al. (2009).
Table B. Functional expressions used in the individual growth models of D. labrax and S.
aurata±as in Brigolin et al. (2010; 2014).
Table C. Model state variables, forcings, and functional relationships of R. philippinarumÐas
in Solidoro et al. (2000).
S2 File. Model parameters. Table A. Parameters used in the Mytilus galloprovincialis growth
Table B. Parameters used in the Sparus aurata (SA) and Dicentrarchus labrax (DL) growth
Table C. Parameters used in the Ruditapes philippinarum growth model.
S1 Appendix. R code to run the individual mussel model spatially explicit.
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Conceptualization: Roberto Pastres, Daniele Brigolin.
Data curation: Damiano Baldan, Daniele Brigolin.
Formal analysis: Erika Maria Diletta Porporato, Daniele Brigolin.
Funding acquisition: Roberto Pastres, Daniele Brigolin.
Methodology: Daniele Brigolin.
Software: Damiano Baldan, Erika Maria Diletta Porporato, Daniele Brigolin.
Writing ± original draft: Damiano Baldan, Erika Maria Diletta Porporato, Daniele Brigolin.
Writing ± review & editing: Damiano Baldan, Erika Maria Diletta Porporato, Roberto Pastres,
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