Modelling growth performance and feeding behaviour of Atlantic salmon (Salmo salar L.) in commercial-size aquaculture net pens: Model details and validation through full-scale experiments.

We have developed a mathematical model which estimates the growth performance of Atlantic salmon in aquaculture production units. The model consists of sub-models estimating the behaviour and energetics of the fish, the distribution of feed pellets, and the abiotic conditions in the water column. A field experiment where three full-scale cages stocked with 120,000 salmon each (initial mean weight 72.1  ± SD 2.8 g) were monitored over six months was used to validate the model. The model was set up to simulate fish growth for all the three cages using the feeding regimes and observed environmental data as input, and simulation results were compared with the experimental data. Experimental fish achieved end weights of 878, 849 and 739 g in the three cages respectively. However, the fish contracted Pancreas Disease (PD) midway through the experiment, a factor which is expected to impair growth and increase mortality rate. The model was found able to predict growth rates for the initial period when the fish appeared to be healthy. Since the effects of PD on fish performance are not modelled, growth rates were overestimated during the most severe disease period. This work illustrates how models can be powerful tools for predicting the performance of salmon in commercial production, and also imply their potential for predicting differences between commercial scale and smaller experimental scales. Furthermore, such models could be tools for early detection of disease outbreaks, as seen in the deviations between model and observations caused by the PD outbreak. A model could potentially also give indications on how the growth performance of the fish will suffer during such outbreaks. STATEMENT OF RELEVANCE: We believe that our manuscript is relevant for the aquaculture industry as it examines the growth performance of salmon in a fish farm in detail at a scale, both in terms of number of fish and in terms of duration, that is higher than usual for such studies. In addition, the fish contracted a disease (PD) midway through the experiment, thus resulting in a detailed dataset containing information on how PD affects salmon growth, which can serve as a foundation to understanding disease effects better. Furthermore, the manuscript describes an integrated mathematical model that is able to predict fish behaviour, growth and energetics of salmon in response to commercial production conditions, including a dynamic model of the distribution of feed pellets in the production volume. To our knowledge, there exist no models aspiring to estimate such a broad spectre of the dynamics in commercial aquaculture production cages. We believe this model could serve as a future tool to predict the dynamics in commercial aquaculture net pens, and that it could represent a building block that can be utilised in a future development of knowledge-driven decision-support tools for the salmon industry.

Introduction

The finfish aquaculture industry currently follows a development where individual production units (i.e. net-cages or tanks) increase in physical size and fish holding capacity. Cages with circumferences of 157 m and depths down to 50 m are today common in the salmon industry (Jensen et al., 2010), and even larger cages with circumferences up to 200 m are seeing increased usage. According to present Norwegian regulations, each cage may be stocked with up to 200,000 individual fish and 25 kg fish m− 3. Although this has increased the production capacity of individual cages, the number of cages at each farm site is generally not reduced, meaning that the average fish farm is now producing larger amounts of fish than before. These trends indicate that the industry is experiencing a drive toward economies of scale, giving reduced production costs and increased production efficiency. In the wake of the industrial development, the amount of research targeting cultured fish has increased, typically aiming to improve production efficiency (e.g. Aas et al., 2006), reduce environmental impacts (e.g. Bendiksen et al., 2011) and ensure fish welfare (e.g. Oppedal et al., 2011b). Much of this research involves experimentation using lab facilities that feature experimental units of significantly smaller physical scales than commercial production volumes. There are several reasons for this disparity in physical scale. First, for ethical reasons, one always seeks to use as few individuals as possible in animal experiments. Second, it is both economically and practically more manageable to maintain smaller units in research experiments. Third, the production environment and the fish population are easier to monitor and control in small volumes as opposed to large volumes.

Several studies within other fields of research have identified that the physical (or geographical) scale of a study may have a notable impact on the results (e.g. Uchic and Dimiduk, 2005, Schweiger et al., 2005, Haileslassie et al., 2007). It is thus important to examine whether results obtained from fish in a lab-scale experiment are representative of a commercial farming situation. Earlier studies have found that the growth of Atlantic salmon may be affected by factors such as tank size and current speed (Boeuf and Gaignon, 1989), and fish density (Refstie and Kittelsen, 1976), which are all relevant elements when considering scaling effects. (Espmark et al., in press) focused on assessing this question more directly by conducting an experiment where a set of land based tanks of different geometric sizes (0.9, 3, 103 and 190 m 3) were stocked with Atlantic salmon smolts from a common genetic strain and cohort. The main aim of that study was to investigate whether there were differences in fish performance (i.e. growth and mortality) between the different tank sizes when all other factors (e.g. temperature, light, feeding regime) were kept similar. Coordinating, conducting and managing such studies is a comprehensive and difficult task, and requires that there are several laboratory facilities available for simultaneous stocking with a specific batch of fish, which is often not the case. A numerical model able to predict variations in the performance of fish reared at different physical scales would therefore represent an attractive tool for future investigations into the relationship between physical scale and fish performance. Such models would be complementary to real experiments, and also provide the ability to predict scale dependent effects on fish beyond what is practical to investigate through experiments.

In mathematical modelling, mathematical language is used to describe the dynamics of a specific system, often through the use of differential equations. Mathematical models are today employed within most scientific and industrial disciplines, and their use for describing biological phenomena and systems is increasing in popularity. This tendency is also present in research on finfish aquaculture, and models portraying e.g. the population dynamics in a start-feeding tank for cod (e.g. Alver et al., 2005), the metabolism and growth of adult salmon (e.g. Olsen and Balchen, 1992, Bar et al., 2007, Dumas et al., 2010) and the behaviour of salmon in sea-cages (e.g. Føre et al., 2009) exist today. A numerical model describing how physical scale affects fish performance would need a detailed representation of the fish population, covering aspects of both behaviour and energetics. Furthermore, the model would need an environmental component able to produce realistic estimates of how the environment is modified when altering the physical scale. This would be most important for factors that are known to have a notable effect on fish growth and survival, such as temperature and feed.

In this study, we developed a mathematical model framework for estimating the behaviour and growth performance of Atlantic salmon populations reared in aquaculture production units. We did not include mortality in our model, as it is difficult to derive models which provide a mechanistic relationship between culture conditions and the survivability of the fish. The framework was built around the integration of three separate models portraying fish energetics (Marafioti et al., 2012), fish behaviour (Føre et al., 2009, Føre et al., 2013) and pellet distribution in a sea-cage (Alver et al., 2004, Alver et al., 2016), respectively. Our study also included a six month long large scale experiment where fish growth was monitored in three industrial size sea-cages, each stocked with approximately 120,000 individual fish. The data from this experiment was used to validate the model. To our knowledge there exist no commercial modelling frameworks able to capture all elements necessary to conduct such numerical studies today.

Materials and methods

The model description provided in this manuscript adheres to the ODD (Overview, Design concepts and Details) protocol for describing individual-based (or agent-based) models as recommended by Grimm et al. (2006). Since the model framework is built up around a core of three models previously described in literature, much of the core functionality is described in the “Submodels” segment. Necessary features that were not covered by these models, such as the coupling between the feed and fish behaviour models, were implemented directly into the framework.

State variables and scales

Our model is individual-based, thus the basic entities are individual fish which respond to a dynamic environment and the presence of other individuals. The energetic and behavioural dynamics of each fish is modelled explicitly, and the individuals are equipped with a set of specific state variables (Table 1) describing their spatial movement (3D position and orientation r, 3D swimming velocity vector ), their size (dry weight BW, body length BL, structural volume V) and their feeding dynamics (gut contents G, energy reserves E). In addition, the fish were provided with an auxiliary state variable (Behavioural mode) which specifies their present motivation to feed (see Føre et al., 2009, for more details on the Behavioural mode variable).

Table 1

Main state variables for fish. ’-’ denotes dimensionless.

Description	Symbol	Unit
Position and orientation	r	m, radians
Swimming velocity vector	r˙	m s− 1
Behavioural mode	Mode	–
Body length	BL	m
Dry body weight	BW	g
Structural volume	V	cm3
Reserves	E	J
Gut contents	G	g

The environmental model was designed to simulate the factors in aquaculture production environments known to affect fish performance and behaviour, and includes representations of the cage/tank structure, water temperature, light intensity and feed distribution. With the exception of the cage/tank structure, which is formulated as a set of static parameters bounding the spatial movement of the fish, all environmental factors may vary along all three spatial axes and with time.

When simulating, spatial and temporal scales and resolutions of environmental datasets primarily depended on the total duration of the simulation and the physical scale (i.e. size) of the simulated production unit. In addition, the spatial and temporal sampling frequencies of any experimentally obtained data series used as inputs to the simulation influenced the resolutions and scales of the datasets derived from these measurements. For simulations including datasets with different spatial resolutions, the dataset with the highest spatial resolution was first identified. The other datasets were then conformed to this resolution by using interpolation and extrapolation so that spatial variations in all environmental datasets were on the same level of detail. A 3D grid of cells was then generated based on the common spatial resolution, with each cell relating to distinct data values in all datasets. The only dataset not subjected to this conformation was feed distribution, which maintained a separate spatial 3D grid as a realistic representation of pellet distribution may require a higher spatial resolution than other factors (e.g. temperature, light). Interaction between fish and environment was thus more efficient as the fish then only needed to relate to two spatial cell structures to access all environmental datasets rather than using separate cell structures for each environmental factor.

When a fish requested the environmental conditions at its present location, it conveyed its position to the environmental model, which then used the position to find out which cell in the 3D structures the fish resided within. The values returned to the fish were obtained by interpolating in space (3D trilinear interpolation) between the present cell and adjacent cells, and interpolation in time (linear interpolation). This ensured that the environmental factors facing the fish were continuous and smooth in time and space, and prevented spikes or jumps in their values which might in turn elicit unrealistic responses from the fish.

To capture how the salmon interacted with the environment with sufficient resolution, the behavioural and environmental submodels were simulated and updated using a fixed timestep of 1 s. However, in cases where the spatial resolution of feed distribution was high (i.e. small cell sizes in the 3D grid structure for feed), the pellet distribution model had to be simulated using timesteps < 1 s to ensure that the mass balance and dynamics within the feed distribution were maintained. Dynamics of the energetic states of fish tend to vary more slowly than behaviour, thus a larger timestep was allowed in the energetic model than in the behavioural model. Since the main aim of this model was to evaluate growth performance over time, we set no upper limit to the duration of simulations.

Process overview and scheduling

The equation system defining a population of individual fish interacting with a dynamic environment will contain a set of complex and non-linear equations that is difficult or impossible to solve analytically. Hence, we solved our model using numerical modelling techniques, in which solutions are found through simulations in the time domain. The main processes occurring within the individuals in our model were growth, feeding (behaviour and assimilation) and movement, while the main environmental processes were to update the present environmental state and compute the pellet distribution within the production unit. For each numerical iteration of the model, these processes were executed in a fixed sequence starting with the update of the environmental states (Fig. 1). The model then iterated through all individual fish which executed their respective tasks, starting by submitting their current position to the environmental model. Based on this position, the environmental model computed local environmental conditions and supplied these back to the fish. The fish computed its behavioural response toward these conditions, resulting in an updated position and swimming speed. If the fish decided to ingest feed, it sent a request for feed intake to the environmental model. The environmental model then evaluated whether there was sufficient feed in the vicinity of the fish to cover the requested amount. If there was sufficient feed, the environmental model returned the amount originally requested by the fish. Otherwise, a feed intake reduced in accordance to local feed concentration was returned to the fish, thus ensuring that feed intake does not exceed the total amount available. Finally, the energetic response was computed based on feed intake, swimming activity and environmental conditions, and used to update the gut contents, energetic state and size of the fish. In cases where the timestep used in the energetic model was greater than that applied in the behavioural calculations, responses from energetic processes remained constant during iterations which did not entail an energetic timestep.

Fig. 1

Sequence diagram explaining the sequence of events occurring in the time step from t to t for a single individual. Vertical black lines represent the time lines of the three main sub-models, solid arrows denote exchange of information between sub-models while dashed arrows mark processes occurring internally within a sub-model.

Design concepts

Sensory abilities of fish

The simulated fish were able to detect the water temperature, feed concentration and light intensity at their present position, and could sense the presence and location of other fish that were nearby. Since light intensity, pellets and other fish are detected through visual perception or the lateral line organ, the fish were also programmed to be able to gauge the spatial gradient in these factors. Sensing of temperature however, requires corporeal contact between the fish and the water and it is thus unlikely that a fish is able to acquire a full overview of thermal gradients in the water volume. We therefore limited the fish to remembering their position in the previous timestep and the temperature sensed at that position, rather than providing them with more extensive information on the spatial gradient.

Interaction and emergence

Individual fish interacted through two basic behavioural rules programming the fish to exhibit either avoidance or alignment in response to neighbouring individuals based on the distances to these neighbours. Given a sufficiently high density of fish in the production unit, this has been shown to lead to an emergent behavioural trait where the population (or part of the population) starts exhibiting circular swimming patterns tracing the inner perimeter of the production unit. This trait is more thoroughly explained and discussed in Føre et al. (2009).

In our model, the feed intake depended strongly on the maximum gut capacity of the fish, which in turn increased with the size of the fish. Furthermore, the maximum movement speed of the modelled fish was set to be an expression depending on the body length of the fish (Føre et al., 2009). These two model features may together lead to the emergence of an effect in which larger fish are better able to capture and consume feed than the smaller individuals due to their higher feed intake capacity and larger mobility. This could in turn result in monopolization of a limited resource (in this case feed), which is not uncommon in animal populations (Weir and Grant, 2004) and as such is not unrealistic. However, if this effect is too strong, a consequence may be that the size variation in the simulated population becomes disproportionally large.

Submodels

Since the details of three of the models used to build this framework (i.e. salmon energetics, pellet distribution and salmon behaviour) have previously been published, only the most essential and eventual new properties in these will be covered in this section. The integration between the three models will also be addressed, and Table 2 contains a list of auxiliary variables used to realise the interconnection between the models with regards to feeding.

Table 2

Auxiliary variables related to feed delivery and feeding.

Description	Symbol	Unit
Temperature sensed by fish	Tw	∘ C
Max gut volume	Vmax	g
Ingested feed	p˙_I	g
Feed contents in cell i in list of cells that are within Dmax	ci	g
Feed contents in cell i , j , k in feed distribution grid	ci , j , k	g
Total amount of feed in cage	cT	g
Requested feed intake	wreq	#pellets
Actual feed intake	wfm	#pellets
Probability of detecting feed	pd	–
Probability of capturing feed	pc	–
Probability of experiencing hunger	pa	–

Energetic model

To model fish energetics we used a Dynamic Energy Budget (DEB) model adapted to Atlantic salmon as presented by Marafioti et al. (2012). DEB model theory is based on a set of assumptions on how organisms of all types (e.g. animals, plants, bacteria) acquire, store and utilise energy (Kooijman, 2000, van der Meer, 2006), and how energy fluxes scale according to the growth of organisms and between species of different sizes. Although more advanced formulations of the DEB model must be applied to model plants and animals with particular requirements, the simplest model formulation with a single structure and a single reserve is suitable for most species and sizes. Differences between species can be expressed through a small number of parameter values and structural adaptations to represent the life cycles of the species. A widespread selection of aquatic species have been portrayed using DEB models, including fish (e.g. Pecquerie et al., 2009), bivalves (e.g. van der Veer et al., 2006, Rosland et al., 2009, Handå et al., 2011) and zooplankton (e.g. Alver et al., 2006, Peeters et al., 2010). The main principles and structures of DEB models are outlined by Kooijman (2000).

Our DEB model for Atlantic salmon applied the same model structure as in Alver et al. (2007) to simulate cod larvae energetics, omitting the reproductive elements of the generic DEB model format. The following equations give the dynamics for the three DEB model states G (gut contents in g), E (energy reserves in J) and V (structural volume in cm3):whereandand and T represent the feed ingested and the temperature experienced by the fish, respectively. Ingested energy in the G compartment is assimilated into the energy reserves E. Reserves are mobilized to cover maintenance () and growth giving an increase in the structural volume V.

The parameter values of the DEB model have been tuned for farmed Atlantic salmon (Table 3). Most parameters, notably [E], κ, k and [p], have values fairly close to those used by Alver et al. (2007) for cod larvae, while the parameter has a significantly higher value. The temperature dependence parameters used in Eq. (5) give the highest metabolic rates at 15  C, and decreasing rates above and below.

Table 3

DEB parameters used in energetic model.

Description	Symbol	Value
Gut evacuation parameter 1	a1	0.45
Gut evacuation parameter 2	a2	0.76
Volume specific cost of growth	[EG]	1900 J cm − 3
Assimilated fraction of ingested feed	kas	0.75
Energy partitioning parameter	κ	0.8
Volume specific maintenance rate	p˙_M	120 J cm − 3
Energy conductance	v˙	0.21 cm d − 1
Temperature dependence parameter 1	T1	285 K
Temperature dependence parameter 2	TA	7000 K
Temperature dependence parameter 3	TAL	10,000 K
Temperature dependence parameter 4	TAH	30,000 K
Temperature dependence parameter 5	TH	289 K
Temperature dependence parameter 6	TL	283 K

Pellet distribution

The model presented by Alver et al. (2004) simulated the distribution patterns of feed pellets in Atlantic salmon cages based on feed consumption by the fish, water current, pellet sinking rates and the size and location of the feed dispersal area on the water surface. This model was originally developed as a 2D-application, only considering the distribution along one horizontal axis and the vertical axis. Alver et al. (2004) found the model able to realistically estimate feed waste from sea-cages by validating model output with experimental data from Talbot et al. (1999).

In a recent study, the feed model was expanded to portray pellet distributions in 3D, while specific features such as pellet sinking rates and horizontal spread factors were validated and adjusted through a series of small-scale experiments (Alver et al., 2016). The 3D model was also equipped with a new representation of surface distribution of pellets, as the approach used in the original 2D version (Alver et al., 2004) was considered unsuitable for 3D applications. Oehme et al. (2012) conducted a study of the horizontal pellet spreading patterns produced by pneumatic rotor spreaders, the main findings of which were that these patterns were non-uniform with respect to spreader orientation and that the distribution depends on spreader type, spreader nozzle orientation and pneumatic airspeed. To accommodate these features in the 3D model, Alver et al. (2016) implemented a new module which emulated pellet surface distribution patterns based on the results from Oehme et al. (2012). The functionality of these new features were verified by comparing outputs from the 3D model with the dataset used to validate the original 2D version of the model (Talbot et al., 1999). With the exception of the fish model, all model aspects presented by Alver et al. (2016) were implemented in the present framework.

To integrate the pellet model with the fish model, we needed a scheme for transferring pellets from the spatial feed distribution to the individual fish. A direct implementation, where the amount removed from the water column matches the amount of pellets a fish attempts to ingest could lead to negative feed concentrations if local feed availability is lower than the requested amount. We therefore designed a scheme for pellet extraction that ensured that the amount of feed a fish may ingest is limited by the amount of feed within a certain distance (Dmax) from the current position of the fish. When a fish attempts to ingest an amount of pellets (w), this amount is evaluated against the feed available in the cells (c , i ∈ (0, . . ., imax)) in the pellet distribution grid that are within Dmax m from the cell presently occupied by the fish (i.e. the cell with index i = 0). Each request for pellets elicits the pellet model to iterate through these cells, starting with the present cell (i = 0), then the second closest cell (i = 1), and onwards until the most remote cell (i = imax) is evaluated. Feed amounts are removed from all evaluated cells (c) and aggregated into a sum that represents the actual amount of feed ingested by the fish (w). In case w equals the amount of feed requested by the fish (w), the evaluation loop breaks and w = w is reported back to the fish, meaning that the requested amount of feed was available in the vicinity of the fish and has been extracted from the pellet distribution. Otherwise, the sum of feed in all cells within Dmax m from the present cell is returned to the fish as a measure of the maximum ingestable amount of feed close to the fish (i.e. ). Algorithm 1 explains this procedure in pseudo-code.

Scheme for collecting pellets from adjacent cells.

Fish behaviour

In Føre et al. (2009), an Individual Based Model (IBM) of Atlantic salmon behaviour in response to culture conditions typically experienced in salmon sea-cages was presented. The fish were programmed to respond to temperature and light intensity, the cage structure, feed and the other fish within the cage. Based on comparisons with observation data, this model was proven able to replicate the vertical distribution dynamics of a salmon population when exposed to varying temperature and natural light levels (Føre et al., 2009). Further, the modelled fish displayed circular swimming patterns in response to their confinement to the cage and the other individuals which resembled schooling behaviours typically displayed by salmon in marine sea-cages (Oppedal et al., 2011a). This model was later expanded to also accommodate behavioural responses toward submerged light sources, enabling predictions of how submerged artificial lights could be used to steer the swimming depth of Atlantic salmon (Føre et al., 2013).

Since the energetic model features a state for gut contents (G), we excluded the simplified model for gut contents used as a proxy for energetic dynamics in the earlier versions of the model (Føre et al., 2009, Føre et al., 2013). Furthermore, the wet weight dependent expression for Gmax used in the original model was exchanged by an expression depending on structural volume (V) based on the assumption that energy reserves do not influence gut capacity (Eq. (6)). This expression was derived by gradual adjustment of the proportional constant until the model returned realistic feed intake rates in a small idealised simulation case.

G and Gmax were then used to derive the relative gut fullness which can be used as an input to computing appetite. However, initial simulations revealed that the expression for the likelihood of experiencing hunger, or appetite, of the fish (p) which was adapted from Olsen and Balchen (1992) in the original model, produced too low appetite values, particularly when simulations were run over longer time spans. A simpler expression which ensured a higher appetite for intermediate degrees of relative gut fullness was therefore derived:

As the integrated pellet model provided a detailed description of the feed distribution within the cage volume, we supplied each fish with the feed concentration and gradient (i.e. the spatial direction in which pellet concentration increases most) at their present position, and the total amount of feed in the cage. These values were used to derive modified expressions for the probabilities of detecting (p) and capturing (p) pellets as presented by Føre et al. (2009):

The variable c represents the total amount of feed in the cage at the present time, while c represents the feed concentration in the feed distribution cell (i.e. cell with indexes i, j and k in the feed distribution grid) currently occupied by the fish. Although it is unrealistic to assume that each individual fish has a tally on the total amount of feed in the cage at all times, the expression in Eq. (8) simulates that the fish has increased likelihood of detecting the presence of feed when the total amount increases. As in the original model, p, p and p controlled the value of the Behavioural mode variable, which largely governs the feeding behaviour of the fish (Føre et al., 2009).

Since the pellet distribution model provided the fish with local gradients in feed, we altered the feeding response such that the fish followed the gradient rather than orienting directly toward the feed dispersal area as used in Føre et al. (2009). This may be a more realistic approach as the fish will then aim toward areas where feed concentration increases, thus improving their chance of capturing pellets, while it also increases the similarity of the simulated feeding behaviour with foraging behaviours of other animals (Godin, 2002). In turn, this will also lead to larger individual variations in behavioural patterns during feeding.

Model validation

The experiments conducted by Espmark et al. (in press) illustrated how differences in physical scale (i.e. geometric size) or scaling histories will affect Atlantic salmon performance in indoor tank facilities. To evaluate how well the tank based results compared with commercial production, these findings had to be compared with corresponding data achieved at industrial scales. A full-scale experiment was therefore conducted at a farming site (Korsneset, 63° N, 08° E, SalMar ASA) included in the SINTEF ACE experimental infrastructure system between March and October 2012. The experiment featured three cages (hereafter labelled cages 1, 2 and 3), each containing 120,000 individual salmon (average starting weights 72.1 g  ± SD 2.8 g), and the experimental period was considered to start the day the fish were released into the cages. Growth output from this experiment was used to validate our model framework.

Experimental setup at SINTEF ACE

To reduce any effects due to genetic differences between fish, the cages were populated with smolts from the same production facility and the exact same genetic strain and cohort as those used by Espmark et al. (in press). Further, the environmental settings in the tanks used by Espmark et al. (in press) were based on real-time environmental data from the field study at SINTEF ACE, such that the production conditions would be as equal as possible in the different physical scales. The physical scales of the cages were within the typical ranges used in modern fish farms in Norway today, with circumferences of 120 m, depths of 12 m and a volume of 16.815 m 3. During the experiment, the feeding schedule was monitored by the feeding software system at the farm, registering the duration and amount of feed delivered for each feeding period. To ensure a good basis on which to evaluate fish performance, it was essential to also monitor oxygen, which is known to be of critical importance for salmon growth (Oppedal et al., 2011b), and temperature and light, which are known to affect both behaviour (Oppedal et al., 2011a) and growth (Solbakken et al., 1994, Oppedal et al., 2003, Handeland et al., 2008). Oxygen was therefore measured every 5th minute at 3, 7 and 10 m depth, while temperature and light were logged every 10th minute at ten depths between 0.5 and 15 m depth. Fish sizes were sampled regularly during the experimental period through manual samplings in association with sea-lice counting (120 individuals per sample). Two cages (cages 2 and 3) were also equipped with VAKI biomass frames (www.vaki.is) which allowed a more continuous monitoring of the biomass. At the final experimental day, 160 fish were retrieved from each cage and measured to obtain a more accurate final estimate on fish size. This number was found sufficient to cover the variance in sample locations and representativity.

Simulation setup

Three simulations were set up using the numerical model framework, each representing one of the cages in the full-scale experiments. Environmental data and feeding schedules for each of the cages were used as inputs to the simulations, and the fish size distributions registered when stocking the cages in the experiment were used to initialise the virtual fish populations. Since environmental data and variations (i.e. in temperature, light, oxygen) were only monitored along the vertical axis, the resulting datasets only varied with depth and not horizontally. These datasets where hence assigned a 1 D grid structure with a resolution of 0.5 m (i.e. 1 × 1 × 29 grid cells). The feed distribution model was set up with a cell size of 2 × 2 × 2 m, which resulted in the cage volume being covered by 20 × 20 × 6 grid cells. To allow the fish to search for feed in the closest set of neighbouring cells, the parameter Dmax was set to be 2 m during simulations. Feed pellets were set up with a weight of 0.03 g and a sinking speed of 0.05 ms− 1, and were delivered to the cages using a spreader pattern resulting from setting up the feeder model in Alver et al. (2016) with an angle of 90° and airspeed of 30 ms− 1. Conducting a full individual-based simulation of these scenarios would be difficult in terms of required computation power considering the high number of individuals in the experimental cages and the long duration of the experimental period. Consequently, simulations of all three cages used in the trial were set up using 10,000 individual fish, thus resulting in a simulated population equal to 8% of the population kept in the experimental cages. Due to this restriction, the amount of pellets delivered to the cages during feeding was set to 8% of the amount used in the experiments, thus ensuring that the amount of feed per fish was kept equal to that applied in the experiments.

Results

Full-scale experiment in sea-cages

The observed mean individual weights in the experimental cages increased throughout the experimental period, with end weights based on the final sample of 160 individuals in the cages reaching 878, 849 and 739 g respectively (Fig. 2). Growth curves for the two cages equipped with VAKI frames (cages 2 and 3) were more detailed and varied than the growth curve for cage 1. Cumulative mortality during the experiment was somewhat high, with mortality rates of 9% for cage 1, 6.5% for cage 2 and 7.5% for cage 3. In late June/early July 2012, an outbreak of Pancreas disease (PD) was registered at the ACE location. Although PD is known to have adverse effects on the survival and growth of salmon (McVicar, 1987), and thus was likely to have impacted fish performance in the last months of the study, this disease is common within the salmon industry and was suspected or observed at 137 salmonid sites in Norway in 2012 (Anon., 2012). The experiment was therefore continued despite the disease outbreak.

Fig. 2

Observed growth for cages 1 (solid line), 2 (dashed line) and 3 (dotted line) at the ACE Aquaculture Engineering experimental site. The grey area in the figure denotes the time period when PD was identified at the site. Black circles denote the final weighing at the end of the experimental period.

Environmental data revealed that temperature ranged between 4.8 °C and 19.1 °C throughout the experimental period, with a total mean value of 11.5 ° C (Fig. 3). The first months of the experiment (May–July) featured generally lower temperatures (min: 4.8 °C, max: 17.7 °C, mean:10.1 °C) than the remainder (August–October) of the period (min: 8.7 ° C, max: 19.1 °C, mean: 12.9 °C). Whereas there was a slight vertical gradient in temperature during the first months, featuring differences between temperatures at the surface and the bottom of up to 4 °C, there was little vertical variation in the water column during the final months of the experiment (Fig. 3). Dissolved oxygen levels were found to mainly range between 70% and 100% through the experimental period, with the highest saturations being more frequent early in the experimental period, and lower values being more common toward the end.

Fig. 3

Water temperatures during the entire experimental period. Different colours denote different temperatures.

Feed delivery was monitored throughout the experiment, and the cumulative feed delivery to each of the three cages followed similar trajectories from the start of the experiment until the disease outbreak, indicating that similar feeding strategies were applied to the cages (Fig. 4). In the last half of the experiment, feed delivery varied more between the cages and was less regular than prior to the arrival of PD, resulting in less smooth curve shapes for cumulative feed delivery (Fig. 4).

Fig. 4

Cumulative feed delivery to cages 1 (solid line), 2 (dashed line) and 3 (dotted line) at the ACE Aquaculture Engineering experimental site. The grey area in the figure denotes the time period when PD was identified at the site.

Simulation outputs in the form of individual dry weights were converted to wet weight values and averaged to yield a grounds for comparison with the experimental results from the full-scale experiments (Fig. 5, Fig. 6, Fig. 7). Correspondence was best for the first half of the experiment for all cages, after which the model overestimated growth rates for about a month. Near the end of the trial, the experimental data showed a higher growth rate than the simulations in all cages, thus leading to lower deviations between model output and observations in the last stages of the experiments.

Fig. 5

Comparison between observed mean weight from cage 1 at ACE and the corresponding model estimate. Black circles denote weight measurements in the experiment, while the solid black line marks the model estimate. The vertical grey dashed line marks the approximate onset of Pancreas disease in the cages.

Fig. 6

Comparison between observed mean weight from cage 2 at ACE and the corresponding model estimate. Black circles denote weight measurements in the experiment, while the solid black line marks the model estimate. The vertical grey dashed line marks the approximate onset of Pancreas disease in the cages.

Fig. 7

Comparison between observed mean weight from cage 3 at ACE and the corresponding model estimate. Black circles denote weight measurements in the experiment, while the solid black line marks the model estimate. The vertical grey dashed line marks the approximate onset of Pancreas disease in the cages.

This trend is also apparent when reviewing the SGR values of all cages through the experimental period. In the period prior to the disease outbreak (Table 4), estimated SGRs were higher than observed SGRs, indicating too high growth rates in the modelled fish. During the remainder of the experimental period, the simulated fish grew less or similarly to the real fish, resulting in SGRs that were slightly lower than or equal to those observed (Table 5). The SGR values for the whole experimental period were comparable with observed values (Table 6), which is in accordance with the similarities in end weight.

Table 4

Estimated and observed SGR values for the first half of the experimental period (90 d).

Cage number	Model estimate of SGR (%)	Observed SGR (%)
1	1.52	1.08
2	1.63	1.19
3	1.65	1.28

Table 5

Estimated and observed SGR values for the second half of the experimental period (102 d).

Cage number	Model estimate of SGR (%)	Observed SGR (%)
1	1.50	1.51
2	1.16	1.40
3	1.32	1.32

Table 6

Estimated and observed SGR values for the whole experimental period.

Cage number	Model estimate of SGR (%)	Observed SGR (%)
1	1.51	1.33
2	1.37	1.30
3	1.46	1.30

Discussion

Compared with the parallel land-based experiment at Sunndalsøra presented by Espmark et al. (in press), the end weights in the cages compared well with results from the 3 m3 tanks, while being higher and lower than the end weights in the 0.9 m3 and 103 m3 tanks respectively.

The effects of the disease outbreak probably perturbed the results from the cages. Several clinical studies have investigated the effects of PD on salmonids, and in addition to increased mortalities there are clear indications that the disease may severely weaken fish growth (McVicar, 1987, McLoughlin et al., 2002, McLoughlin and Graham, 2007). Furthermore, toward the end of the experimental period, the fish displayed elevated growth rates, which is consistent with compensatory growth. Since compensatory growth typically occurs in fish after periods of nutrition deprivation (Metcalfe and Monaghan, 2001) it is likely that the compensatory growth seen in the cages occurred in response to a preceding period of reduced appetite due to PD.

Temperatures in the cages were in a range that is generally considered favourable for salmon growth, especially toward the end of the experiment (Koskela et al., 1997, Handeland et al., 2008). Furthermore, since the vertical temperature gradient was generally weak throughout the period, it is unlikely that a few individuals or groups of individuals were able to monopolize the most preferable temperatures by suppressing the other fish. It is thus possible that all fish were able to assume positions where they were exposed to preferable temperatures, hence achieving similar thermal effects on growth through the experiment. Oxygen saturation was in the range 70%–100% throughout the entire experiment, which has been found to be levels where O2 is unlikely to act as a limiting factor on salmon growth (Remen et al., 2012).

After being similar prior to the disease outbreak, feed delivery patterns varied much between the cages after the onset of the PD infection. One of the first signs of a PD outbreak in Atlantic salmon is that feed intake drastically drops, probably due to a loss in appetite (McLoughlin et al., 2002). To counteract excessive feed loss in such situations, salmon farmers reduce the feed delivery to the cages in a period after the outbreak. When fish health seems to have improved, indicating that the most virulent period of the disease has passed, the farmers may start feeding again, and then typically with increased feed amounts to allow compensatory growth. This experiment applied such a feeding strategy, with cumulative feed delivered (Fig. 8) increasing more slowly between the end of July and the beginning of September than from September onwards. Based on veterinary observations (SINTEF ACE, pers. comm.), the PD outbreak in cage 1 was more severe than in the other cages. This is also reflected in that cage 1 experienced higher gross mortality than cages 2 and 3. Interestingly, cage 1 was also the cage that received the largest cumulative amount of feed, at between 15 and 20% more feed than the other two cages.

Fig. 8

Plot of fish growth in cage 2 as estimated by the model (solid line) and the cumulative delivery of feed to cage 2 in tonnes (dashed line). The vertical grey dashed line marks the approximate onset of Pancreas disease in the cages.

The similarity between simulation results and observed growth development in the early stages of the experimental period before PD affected the sea cages indicates that our model featured the main mechanisms and effects required to estimate the performance of healthy Atlantic salmon in production facilities. Data on environmental conditions and feed input to the cages from the experiment were used directly as model input, meaning that the simulated fish were exposed to similar external influences as the experimental fish. Similarities between model output and observed growth thus suggests that the feed intake of the fish was realistically represented in the model.

When environmental conditions are kept within ranges that do not significantly impair fish growth, model output will strongly correlate with feed input to the cage. This is best illustrated by comparing the trajectories for simulated mean individual fish size in cage 2 and the cumulative feed delivery to that cage (Fig. 8). The feeding regime is visible through the estimated growth curve, which follows a smooth almost exponential curve (indicating high feed intake and efficient growth) until the disease outbreak. After this point, the growth curve of the simulated fish was more jagged, indicating more erratic growth coinciding with a more uneven delivery of feed to the cage in the final half of the experimental period.

The rapidly increasing gap in simulated and observed wet weight after the onset of PD implies higher growth rates in the model than in the observed fish. Since the model contains no representation of the effects of disease on mortality and growth, such a deviation is to be expected. Deviations between model output and observed values were highest for cage 1, which also harmonises with the observation that this cage appeared to be more strongly affected by the disease than cages 2 and 3. Representations of disease and compensatory growth are beyond the scope of the present model, but it could provide a useful framework for investigating hypotheses about such effects.

The appetite of salmon is known to vary with season (Oppedal et al., 2011a), and it is likely that some of these variations are explained by variations in temperature (Koskela et al., 1997, Handeland et al., 2008). In our model, temperature and appetite are only indirectly linked. Gut fullness controls appetite while being influenced by temperature through the gut evacuation rate. This association could be too weak to reproduce seasonal appetite variations, and may thus have contributed to the SGRs estimated by the model being higher than the observations early in the experiment and lower or equal to observations near the end of the experiment. Temperature increased with time through the experimental period, and a more direct connection between thermal conditions and feed intake could thus have led to a better match between model output and observations.

Another factor that may have led to the overestimated SGRs early in the period is that the model did not take into account that the fish were transferred from a well boat into the three cages at experimental startup. It is not uncommon for salmon to display stress responses after having been handled, which may in turn lead to reduced feed intake and growth in the first days or weeks after transfer before the fish fully adapt to their new surroundings (Ashley, 2007).

Most measurements made prior to the onset of PD in the experiments were obtained through manual sampling (120 fish) using dip nets and casting nets, whereas the majority of the data points occurring after the disease outbreak were obtained using biomass frames (VAKI). In addition, the final samplings of average fish weight were conducted using a higher number of fish (134–170), probably making the estimate in this sampling more accurate than in the other manual samples. Changes in primary sampling technique during an experiment may introduce a bias to the observed dataset, as different methods may sample different sub-groups in the population. Due to the large variations in size in salmon populations of such scales as those used in the present experiment, it is difficult to determine which method is likely to produce the most representative sub-samples. However, the two methods were also frequently used within the same sub segments of the experimental period, during which they returned comparable estimates of mean weight. This suggests that sampling technique did not introduce a significant bias on the observed dataset.

To reduce the computational load of the simulations, we simulated a population that numbered 10,000 individual fish, i.e. about 8% of the population size used per cage in the experiments (120,000 fish). The matching reduction of feeding rate to 8% of original values should prevent consequences for the feed intake of the fish, as the amount of feed per individual was the same as in the experiments. A reduction in population size could also impact behavioural responses, as each individual fish would then have more space for movement, and be less affected by neighbouring individuals due to a lower general fish density. Although this could essentially affect the ability of the fish in capturing and ingesting pellets, feeding schedules applied at fish farms are designed with the aim of ensuring that sufficient feed is delivered to all fish in the population. As long as the amount is scaled according to population size, the feeding schedule should thus reduce this uncertainty by keeping the likelihood of capturing pellets comparable for each individual irrespective of population size.

To ensure that the number of individuals included in a simulation would not have a large influence on fish performance we conducted a series of brief hypothetical simulations where only the number of individuals was varied. All other features of the simulation (e.g. feed amount per fish, production unit size, environmental conditions) were kept similar to isolate the effects of population size. These simulations showed that as long as the number of individuals was kept at more than approximately 500 fish, the model would perform quite consistently on predicting the performance of the fish.

Application areas and further work

The disease situation illustrates a typical challenge in conducting field experiments where external factors may unpredictably impact your experiment. Diseases count among the main challenges in the salmon industry today, and the direct economical costs of e.g. PD outbreaks may be considerable (Aunsmo et al., 2010). In containing frequent samples of fish size, environmental conditions and feeding, the datasets obtained in the experiments outlined in this study could represent a valuable asset in deriving more knowledge on how PD affects farmed Atlantic salmon. Additionally, a predictive model such as the one presented in this manuscript could be subjected to a simulated environment based on the conditions and production settings observed and used at a site experiencing an outbreak. As the model simulates healthy fish, deviations between model output and experimental data during the disease period could then be seen as a measure of how PD affects fish growth. This would reduce eventual uncertainties arising due to masking effects caused by variations in culture conditions and management routines between farms, but would also require that the most essential environmental factors (e.g. oxygen, temperature) are monitored with sufficiently high spatial and temporal resolution. Such virtual assessments of lost production due to disease could ultimately end up with a grounds on which it is possible to develop mathematical models for simulating disease pathology.

Water velocities are known to impact the growth of salmon in general (Jorgensen and Jobling, 1993, Davison, 1997, Thorarensen and Farrell, 2011), and Boeuf and Gaignon (1989) found that fish grew faster in tanks with strong flow fields than when current speeds were low. Furthermore, the water velocity patterns arising in a tank will have a great impact on how the feed pellets will be distributed after having been released by surface feeders. These observations imply that water flow needs to be taken into account when investigating scale dependent differences in fish performance. One of the main priorities in terms of future expansion of our model is to include support for simulating the water velocity fields in indoor tanks, and how the fish respond behaviourally to these. Indoor tanks have significantly smaller internal volumes than sea-cages, meaning that the pellet distribution and environmental models would need to use 3D grids with smaller cells to provide sufficiently high spatial resolution. Smaller cell sizes require a shorter time step or a more advanced numerical scheme to ensure accuracy in solving the model equations, both for the pellet distribution and environmental models.

Enabling simulation of salmon rearing processes in tanks will also allow validating the model against the results presented by Espmark et al. (in press). If this validation is successful, the model can then be used as a foundation for developing a “virtual laboratory”, with which it is possible to conduct simulated scaling experiments using tanks of arbitrary physical scales. Such simulations could in turn allow us to evaluate how results obtained in laboratory scales need to be adjusted to be representative for other physical scales, and ultimately for full scale production in sea-cages.

Conducting comprehensive experiments such as the scaling experiment presented jointly between this manuscript and Espmark et al. (in press) requires significant planning to ensure desired experimental outputs and sufficient scientific quality. Using a mathematical model it is possible to simulate how different experimental designs would perform, and then shape the experiment according to the desired performance. With virtual experiments being substantially less expensive, labour intensive and time consuming than physical experiments, the model could thus serve to increase the efficiency and precision of experimental planning, and possibly directly reduce experimental costs.

Feed costs represent about 50% of the total production cost of salmon from eggs to meat (Directorate of Fisheries, Norway, 2011). In Alver et al. (2016) the pellet distribution model included in the present framework was validated against observed data, implying that the model produces realistic estimates of pellet distribution in cages. When fish growth, as estimated by the model, closely resembles growth rates observed in a fish population, it is thus likely that the feed wastage predicted by the model is similar to the actual feed waste from the cage. The feed distribution model can be set up to maintain a cumulative tally of how much feed is ingested by the fish, and hence how much feed is lost to the environment. A new area of usage for our model could thus be to represent a tool for estimating feed waste from commercial fish cages. The most straight-forward way of doing this would be to conduct the analyses post-production, when all data from the production process are available as input for the model. Alternatively, the model could be run as an online application which is provided all relevant and available data from the production process in real-time. This would require more detailed data from the process than what is commonly observed at commercial fish farms, but would also result in an online monitoring tool able to estimate both feed loss and fish growth. Furthermore, estimated feed consumption and feed spills could be used as a direct input to the process of dynamically adjusting feed delivery to cages, which is a central part of the daily management routines used in modern salmon farming. With regards to estimating feed consumption and waste, it is nonetheless important to note that in commercial scale settings such as this, it is impossible to measure how much of the feed delivered to the cage ends up being eaten by the fish, and how much ends up as feed waste. This further means that a direct validation of the feed intake of the fish will be impossible, which could make model estimates of gross feed intake and feed waste less reliable. However, since feed conversion ratios (FCR) for salmon production tend to lie between 1.0 and 1.3 during normal production, most of the feed delivered to salmon cages is ingested by the fish and converted into fish meat when the fish are growing efficiently. The growth in the periods prior to and after the most intense disease period in this experiment was similar to growth levels expected for fish of this size, with SGR rates of between 1.5 and 2%. Since the feeding schedule to the cages is set up with respect to the mean fish size and biomass in the cage, this implies that the fish were exhibiting FCRs close to 1.0, meaning that the fish consumed most of the feed delivered to the cage. In directly using the feed delivery rates from the experiments as input, the model estimate of feed consumption could thus be assumed to be realistic for these periods.

Our model, in being individual-based, could also represent a tool for directly studying individual effects in cages, such as SGR and thermal growth coefficients (TGC). Using a similar method as in the case study in Føre et al. (2013) and by evaluating individual expressions for SGR and TGC, the model could be used to estimate how different operational treatments would impact these. This could prove useful both when planning and setting up scientific experiments, and from an industrial perspective when designing operational routines at a farm.

The DEB-model formulation contains several variables that are difficult to observe in vivo, such as reserves size vs. structural volume and daily individual feed intake in % of wet weight. Although such variables are difficult to validate through experiments, they can be used to produce novel knowledge on fish energetics and feeding physiology by applying elements of Model-Based Estimation (MBE). When using MBE, primary model outputs are continuously compared with corresponding observations in an experiment or a physical system, and as long as the model estimates are close to observed values, one can assume that the other features of the underlying model will also exhibit realistic dynamics. By comparing estimated fish weights with observed weights it is thus possible to obtain reliable information on unobservable system properties which could be useful in a production situation, such as daily individual feed intake. This could in turn increase our knowledge on the underlying mechanisms behind salmon growth in aquaculture.

Conclusion

In this study, we modelled salmon growth performance in aquaculture production units by integrating a set of existing and previously validated models describing different aspects of the production process. Further, we conducted an experiment featuring three full-scale sea-cages, each stocked with 120,000 salmon, during which fish size development in the cages was continuously monitored. This experiment was associated with a land-based study on the effects of physical scale on salmon performance (Espmark et al., in press). Although the fish included in the experiment were afflicted by disease (PD) during the trial, experimental outputs from this study were compared with outputs from the numerical model, and validated that the model was able to predict the growth of healthy salmon.

The basic premise of Precision Livestock Farming (PLF) is to use principles, technologies and concepts from process engineering to manage livestock production (Wathes et al., 2008). In producing detailed and individual based data on the fish, mathematical models such as the one presented here could represent building blocks in a future process of adapting concepts from PLF to aquaculture production of fish. The potential of PLF methods in improving animal welfare and production efficiency within terrestrial farming is evaluated as very high (Banhazi et al., 2012), and there is no reason why we should not expect a similar potential when applying these methods to aquaculture production of fish.