# From farm to food systems: Developing aquaculture models to explore their role in food systems

Anne-Jo van Riel, Marit A. J. Nederlof, Ollie van Hal, Geert F. Wiegertjes,

Imke J. M. de Boer, Killian Thibaud Chary

► To cite this version:

Anne-Jo van Riel, Marit A. J. Nederlof, Ollie van Hal, Geert F. Wiegertjes, Imke J. M. de Boer, et al.. From farm to food systems: Developing aquaculture models to explore their role in food systems. Ecological Modelling, 2026, 515, pp.111504. 10.1016/j.ecolmodel.2026.111504. hal-05508477

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Short communication

# From farm to food systems: developing aquaculture models to explore their role in food systems

A.J. van Riel<sup>a,b,*</sup> <sup>●</sup>, M.A.J. Nederlof<sup>a</sup>, O. van Hal<sup>b</sup>, G.F. Wiegertjes<sup>a</sup>, I.J.M. de Boer<sup>b</sup>, K. Chary<sup>a,c,d</sup>

## ARTICLE INFO

### Keywords:

- Circularity

- Bioenergetic model

- Life-cycle growth performance

- Aquatic foods

- Fish farming

## ABSTRACT

As a vital food source worldwide, aquaculture is set to play an essential role in future food systems. To explore potential configurations for feeding a growing population within planetary limits, agro-ecological food system and resource allocation models can offer valuable insights. So far, the potential of aquaculture in such modelling studies have focused on a few species. Understanding the large diversity of aquaculture species and farming practices, however, is key to determine their contribution to future food systems. With limited empirical data on aquaculture production systems across different environmental conditions and intensities, bioenergetic models could be used to predict growth, serving as an input for food system modelling. In this study, we first selected Atlantic salmon, European seabass, and common carp to represent the variety of finfish aquaculture in Europe. We characterised key production systems for these species using contrasting yet realistic management practices and created coastal water temperature clusters for Europe. For each aquaculture system, we first simulated life-cycle growth performance using a dynamic energy budget (DEB) model, and then predicted nutrient requirements and feed intake using feed compound data. The temperature clusters we defined were found to overlap with existing Atlantic salmon and European seabass aquaculture locations. When compared to empirical farm data, the DEB model accurately predicted harvest times for the various systems and species. Incorporating these aquaculture systems in food system or resource allocation models can enhance our understanding of aquaculture's role in future food systems in Europe.

## 1. Introduction

While food systems are vital for feeding the growing world population, they also exceed several planetary boundaries, such as climate change, freshwater depletion, and nutrient overloads in aquatic and terrestrial ecosystems (Campbell et al., 2017). Agro-ecological food system and resource allocation models can be used to investigate alternative food system configurations that can feed an ever-increasing human population, while reducing environmental impact.

In recent years, several of these models have been developed for Europe, with a focus on crops and livestock (Frehner et al., 2022; Karlsson and Röös, 2019; Van Hal et al., 2019; Van Selm et al., 2022;

Van Zanten et al., 2023). The livestock systems included in these models reflect common practice, based on data from literature and databases regarding growth, nutrient requirements and rearing practices. Livestock systems previously implemented are dairy cattle, beef cattle, pigs, broiler chickens and laying hens. So far, however, the potential of aquaculture systems in future food systems is little studied. To the best of our knowledge, only two species have been explored, namely Atlantic salmon and Nile tilapia (Karlsson and Röös, 2019; Van Hal et al., 2023). Tilapia, although not commonly cultured in Europe, was selected in the study of Hal et al. (2023) as a proxy for an omnivorous fish species. While Van Hal et al. (2023) explored livestock with multiple productivity levels, the two aquaculture systems in their study were simplified,

<footnote><sup>a</sup> Aquaculture biology and Fisheries ecology group, Wageningen University & Research, Wageningen, the Netherlands</footnote>

<footnote><sup>b</sup> Animal Production Systems group, Wageningen University & Research, Wageningen, the Netherlands</footnote>

<footnote><sup>c</sup> ISEM, Univ Montpellier, CNRS, IRD, CIRAD, Montpellier, France</footnote>

<footnote><sup>d</sup> CIRAD, UMR ISEM, Montpellier, France</footnote>
using uniform management practices and production performances across Europe. To better understand the role of aquatic production in food systems, a better representation of aquaculture species and farming systems is required. This is particularly relevant because aquatic foods are rich in many essential nutrients and are associated with lower risks of non-communicable diseases compared to red meat (Golden et al., 2021). From a resource-use perspective, aquaculture systems and species also largely differ in their ability to recycle feed into food and generate lower emissions and impacts on land and water than many terrestrial meats (Chary et al., 2023; Gephart et al., 2021).

In Europe, aquaculture production, excluding seaweeds, reached 3.5 million tonnes in 2022, accounting for 3.7 % of all fish and shellfish raised in aquaculture worldwide (FAO, 2024b). The production volume is mainly composed of salmonids (67 %), molluscs (16 %), carps and other cyprinids (7 %), and other coastal fish (6 %) (FAO, 2024b). These species are produced in various production systems, with open-water cages systems being most common for marine species and ponds for freshwater species (Hough, 2022). As water temperature is not controlled in these systems, it varies across time and space, so species are farmed based on their temperature preferences across different European subregions, leading to varying growth performances. Other major factors influencing farm productivity are intensification levels, determined by feeding management and stocking density, among others. Given the limited empirical data on growth, across various environmental and management conditions, bioenergetic models could help predict growth under various conditions, providing crucial input for food system modelling studies.

Many models have been developed to simulate fish growth and farm performances but not all are suitable for food system modelling (Chary et al., 2022). Growth models vary from simple empirical approaches (Thermal growth curve, von Bertalanffy) to more complex mechanistic models, such as dynamic energy budget (DEB) models. Bioenergetic approaches, such as DEB, can account for the effect of water temperature or feed availability on fish metabolism. DEB theory uses differential equations to describe flows of assimilation and use of energy from food for an organism's maintenance, reproduction and development as a function of food availability and the organisms' temperature (Kooijman, 2009). These models are thus useful to simulate individual fish performances in dynamic environments. A key advantage is DEB's generic nature, grounded in physiological principles that are common to all species, making it applicable across species and contexts.

This study aims to develop an approach for modelling the life-cycle production of representative finfish aquaculture systems, facilitating their future inclusion in European food systems models. To this aim, we select representative fish species for European aquaculture, accounting for diversity in production areas, trophic levels, and farming systems. We define key aquaculture systems for Atlantic salmon, European seabass and common carp, incorporating diverse and realistic management practices, and create regional water temperature clusters for Europe. We then simulate growth performance for each system with DEB models and, predict nutrient requirements and feed intake, using feed compound data, over the entire life cycle, which are essential inputs for food systems modelling.

## 2. Materials & method

### 2.1. Selection of aquaculture species and systems

We selected three representative finfish species for aquaculture in Europe based on current production volumes, diversity in production area (optimal temperature range), natural trophic level and production system (cage and pond). We focused on finfish species that receive compound feed, so called fed-species, to evaluate the contribution of fish to upcycle biomass in food systems. Therefore, we exclude non-fed species such as bivalves and seaweeds in this study. High trophic level marine fish species make up the majority of aquaculture in Europe (Riel

et al., 2023). For this reason, we selected Atlantic salmon and European seabass. These two marine species represent the two most produced carnivorous species reared in sea cages, with contrasting temperature preferences that result in opposite geographical production areas - Atlantic salmon in northern Europe and European seabass in the south (FAO, 2024b). We selected common carp, the most produced pond species in Europe (Hough, 2022), to represent a freshwater omnivorous species that can be farmed in freshwater ponds. Each aquaculture species was modelled according to multiple productivity levels.

For Atlantic salmon and European seabass, we modelled species performance in two temperature clusters to account for temperature variations in European coastal waters. For each species, one cluster represented conditions close to their optimal temperature (optimal cluster), while the other cluster fell within their tolerance range but was outside optimal temperature conditions (sub-optimal cluster). Growth, and therefore years until harvest, varied depending on the cluster where the grow-out occurred. We assumed the fish were stocked into the cages throughout the year (Fernández Sánchez et al., 2022; Mowi, 2024). We simulated stocking in January and July and used the average growth estimates from these two simulations. Atlantic salmon and European seabass were assumed to be farmed in intensive systems and fed compound feed only. Assumed stocking and harvest weight derived from literature, can be found in Table 1.

In carp pond aquaculture, we assumed three intensity levels that reflect current practices: intensive, semi-intensive, and extensive farming (Woynarovich, 2011). In pond aquaculture, food can be available in the form of natural food web and compound feed. The higher the system's intensity, the greater the contribution of compound feed to fish growth compared to natural food from the pond, and the higher the stocking density (Table 2). In practice, as compound feeds and production intensity are reduced, overall food availability in the pond decreases, and natural food becomes a larger portion of the carp's diet (Woynarovich, 2011). To maintain carp growth, stocking densities are reduced at lower intensity levels. Because of the reduction in stocking density, semi-intensive and extensive systems can still achieve

<caption>Table 1</caption>

Characterization of the finfish aquaculture production systems selected for this study, based on stocking density, stocking weight and harvesting weights of aquaculture species at different intensity levels and temperature clusters. Stocking density expressed as kg harvested fish per hectare. Five EU coastal waters clusters were defined based on homogeneous water temperature: North (NO), North-middle (NM), Middle (MI), South-middle (SM), South (SO). For each species, one cluster represents near optimal conditions (optimal), while the other represented sub-optimal but tolerable conditions (sub-optimal).

<table><thead><tr><th>Species</th><th>Temperature cluster</th><th>Intensity level</th><th>Stocking weight (g)</th><th>Harvest weight (g)</th><th>Stocking density</th></tr></thead><tbody><tr><td>Atlantic Salmon</td><td>NM (optimal) &amp; NO (sub-optimal)</td><td>Intensive</td><td>100<sup>a</sup></td><td>5500<sup>d</sup></td><td>16<sup>e</sup> (kg/m<sup>3</sup>)</td></tr><tr><td>European seabass</td><td>SO (optimal) &amp; SW (sub-optimal)</td><td>Intensive</td><td>4<sup>b</sup></td><td>500<sup>b</sup></td><td>15<sup>f</sup> (kg/m<sup>3</sup>)</td></tr><tr><td rowspan="3">Common Carp</td><td>-</td><td>Intensive</td><td>2<sup>c</sup></td><td>1200<sup>c</sup></td><td>0.16<sup>e</sup> (kg/m<sup>2</sup>)</td></tr><tr><td>-</td><td>Semi-intensive</td><td>2<sup>c</sup></td><td>1800<sup>c</sup></td><td>0.12<sup>e</sup> (kg/m<sup>2</sup>)</td></tr><tr><td>-</td><td>Extensive</td><td>2<sup>c</sup></td><td>1800<sup>c</sup></td><td>0.07<sup>e</sup> (kg/m<sup>2</sup>)</td></tr></tbody></table>

<footnote>a (Aunsmo et al., 2014);</footnote>

<footnote>b (García et al., 2016);</footnote>

<footnote>c (Woynarovich, 2011);</footnote>

<footnote>d (Van Hal et al., 2023);</footnote>

<footnote>e (Folkedal et al., 2012);</footnote>

<footnote>f (EFSA, 2008).</footnote>
<caption>**Table 2**</caption>

Feed conversion ratios (FCR), diet proportions, assimilation efficiency (κ<sub>X</sub>) and food density (X) of aquaculture species at different intensity levels and temperature clusters. Five EU coastal waters clusters were defined based on homogeneous water temperature: North (NO), North-middle (NM), Middle (MI), South-middle (SM), South (SO). One cluster represents near optimal conditions (optimal), while the other represented sub-optimal but tolerable conditions (sub-optimal).

<table><thead><tr><th rowspan="2">Species</th><th rowspan="2">Temperature cluster</th><th rowspan="2">Intensity level</th><th colspan="3">FCR</th><th rowspan="2">κ<sub>X</sub></th><th rowspan="2">X (j/cm<sup>2</sup>)</th></tr><tr><th>Feed</th><th>Natural food</th><th>Natural food in diet (proportion)</th></tr></thead><tbody><tr><td>Atlantic salmon</td><td>NM (optimal) &amp; NO (sub-optimal)</td><td>Intensive</td><td>1.2<sup>a</sup></td><td>-</td><td>-</td><td>0.32</td><td>100</td></tr><tr><td>European seabass</td><td>SO (optimal) &amp; SW (sub-optimal)</td><td>Intensive</td><td>1.9<sup>b</sup></td><td>-</td><td>-</td><td>0.42</td><td>100</td></tr><tr><td rowspan="3">Common carp</td><td>-</td><td>Intensive</td><td>1.8<sup>c</sup></td><td>0.3<sup>d</sup></td><td>0.2<sup>e</sup></td><td>0.05</td><td>100</td></tr><tr><td>-</td><td>Semi-intensive</td><td>2.5<sup>d</sup></td><td>0.4<sup>d</sup></td><td>0.4<sup>c</sup></td><td>0.03</td><td>0.65</td></tr><tr><td>-</td><td>Extensive</td><td>-</td><td>0.7<sup>d</sup></td><td>1<sup>c</sup></td><td>-</td><td>0.65</td></tr></tbody></table>

comparable growth rates to each other (Woynarovich, 2011). In the three types of systems, the carp were stocked in May and harvested in Autumn to reflect current practice (Woynarovich, 2011).

## 2.2. Water temperature

Potential production zones for marine species in European coastal waters were defined based on water temperature. Daily surface water temperature for European coastal water (22 km radius from the coast) was extracted from Copernicus for the period 2015–2020 (Copernicus, 2023). The Baltic Sea was excluded because brackish water is unsuitable to produce both Atlantic salmon and European seabass. We used Ward’s linkage as a form of hierarchical cluster analysis to distinguish production zones based on daily water temperature. Growth was only simulated for the zones in which species are currently produced, i.e., the clusters around Norway and the UK for salmon and the clusters from France to Greece for European seabass (FAO, 2024a).

Water temperature for pond aquaculture was simulated with a temperature curve model from Seginer & Halachmi (2008) (Eq. (1)) applied to Central Europe where most pond aquaculture is located and water temperatures are relatively homogeneous over the region. We used the same temperature time series for the three productivity levels.

$$T_n = T_m - T_a \times \sin\left(2\pi \frac{n + \phi_T}{365}\right) \quad (1)$$

Where T<sub>m</sub> is the mean water temperature over the year, T<sub>a</sub> the amplitude of the variation, n is time (days), and φ<sub>T</sub> the phase shift.

## 2.3. Fish growth and nutrient requirements modelling

To best represent animal production in food systems (modelling) approach, the entire life cycle of the animal should be considered. Accounting for the entire life cycle of a farmed fish requires data on individual growth and related nutrient requirements per life stage as well as data on population level, such as mortality and reproduction. First, production (e.g. growth, duration per life stage) was estimated for an individual fish at each life cycle stage based on water temperatures and feeding levels using DEB models, as explained in more detail below (Fig. 1). Second, the resources (e.g. nutrients, energy) needed to produce a single harvested fish were calculated based on the number of non-producing animals (e.g. larvae, fry, and broodstock) needed to harvest a single producing animal (Atlantic salmon, European seabass or common carp) using species-specific mortality and fecundity data (Table S1 and S2).

Individual fish growth and energy requirements were estimated with

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Data requirement and framework to estimate life cycle requirements for fish species. DEB: Dynamic energy budget.</figcaption></figure>

<footnote>a (Aas et al., 2022);</footnote>

<footnote>b (García et al., 2019);</footnote>

<footnote>c (Suprayudi et al., 2022);</footnote>

<footnote>d (Roy et al., 2020);</footnote>

<footnote>e personal communication K. Roy.</footnote>
DEB models. DEB models quantify the rates of energy ingestion, assimilation and use, as a function of food availability and the organism's temperature (Van Der Meer, 2006). More details about DEB models can be found in Kooijman (2009).

We used the NicheMapR package (Kearney and Porter, 2017) to solve DEB equations. DEB parameters for European seabass and common carp were retrieved from the Add-my-pet database (AmP, 2024; B. Kooijman and Souloumiac, 2018; Lika et al., 2018). For Atlantic salmon, more recent parameters from Lika et al. (2020) were used.

In NicheMapR, food availability is represented with the variable of food density (X), which is the energy available per surface area. In cage and intensive pond systems, fish were assumed to be fed to satiation. Therefore, food density was set to a value that does not limit fish growth (100 J/cm²). In extensive and semi-intensive pond systems, food density was assumed to be a factor limiting the growth and was set to reflect the expected time at harvest weight (Stanivuk et al., 2024) resulting in a food density of 0.65 J/cm² in both systems (Table 2).

NicheMapR outputs include fish body weight, and assimilated energy ($p_A$) at each time step (days) of the simulated period. In the DEB theory, assimilation efficiency ($\kappa_X$), is the ratio of assimilated energy ($p_A$) to ingested energy. Therefore, we estimated feed intake by dividing the $p_A$ by the digestible energy of the feed (gross energy content of the feed multiplied by $\kappa_X$). Gross energy content of the feed was based on commercial feed composition and assumed to be species- and life stage-specific (IAFFD, 2024).

Although body weight estimates resulted in reasonably good predictions, the DEB model underestimated $p_A$, resulting in unrealistic feed conversion ratio. Therefore, we adjusted the $\kappa_X$ based on the expected economic feed conversion ratio (eFCR) found in literature for each species (Table 2) corrected by the mortality to estimate feed intake plus feed losses (Section S1). To estimate compound feed intake in carp, we subtracted the share of natural food based on proportions of natural food in stomach contents and FCRs of natural food and compound feed (Table 2). The FCR of common carp derived from Roy et al. (2020) was reported on dry matter basis and we adjusted it for the natural foods moisture content of 89 % and compound feed of 10 % (Ovie and Ovie, 2006). Nutrient requirements in terms of digestible methionine, digestible lysine, eicosapentaenoic acid (EPA), and docosahexaenoic acid (DHA) for the fish were based on the estimated feed intake and the life stage and nutrient composition of species-specific compound feed (IAFFD, 2024). Although three life stages (egg, juvenile, adult) are used in the DEB models, nutrient composition of aquaculture feeds varies

over more life stages. Therefore, we expanded the number of life stages based on the changes in feed composition.

### 3. Results and discussion

In this short communication, we developed a methodology to simulate the performances of representative finfish species in various European production areas, providing a basis to explore the role of aquaculture in future food systems. To this end, we modelled aquaculture systems for Atlantic salmon, European seabass with multiple temperature clusters and common carp with multiple productivity levels. We combined DEB models and commercial feed data to predict growth performances, production cycle and nutrient requirements for contrasting temperatures (locations) and management practices.

#### 3.1. Aquaculture production in temperature clusters

To reflect different possible locations of aquaculture production sites, we defined five coastal temperature clusters characterized by homogeneous water temperature (Fig. 2). Temperature clusters North (NO) and North-Middle (NM) are in line with current aquaculture production sites for Atlantic salmon. In the United Kingdom, Atlantic salmon aquaculture overlaps almost completely with cluster NO, while there is very limited salmon aquaculture in cluster NM (Jennings et al., 2016). In Norway, most Atlantic salmon aquaculture occurs in either cluster NO or cluster NM (Oliveira et al., 2021), whereas in Iceland, aquaculture of Atlantic salmon is dominant in cluster NO (FAO, 2024a). Temperature clusters South (SO) and South-Middle (SM) are in line with current aquaculture production sites for European seabass. Most European seabass aquaculture is located around Italy and Greece (cluster SO), with fewer farms on the east of Spain (cluster SM) (Gianluca et al., 2018). Overall, in our study, cluster Middle (MI) was not included in the growth models because it falls out of the preferred temperature range of both European seabass and Atlantic salmon. Apart from temperature, various environmental parameters, such as pH, salinity, turbidity, play an important role in identifying suitable sites for aquaculture (Aguilar-Manjarrez et al., 2017). However, temperature appears to be an important and straightforward determinant when assessing coastal regions for aquaculture production in Europe.

When applying these aquaculture species and systems in food system models, the selected species can be used as proxy for other aquaculture species with similar growth, nutrient composition and trophic level.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Temperature clusters based on average daily temperature in EU 27 + Norway and UK. a. cluster areas of the coastal zones b. average temperature changes over the year of the surface water of each cluster. Each cluster is named according to its geographic region: North (NO), North-middle (NM), Middle (MI), South-middle (SM), South (SO).</figcaption></figure>
Atlantic salmon has similar characteristics (e.g. trophic level, temperature and nutrient requirements) to other salmonids produced in aquaculture and can be used as a proxy for rainbow trout. In the same way, European seabass can be used as a proxy for seabream and common carp for other Cyprinus species. Further developments of aquaculture in food system models could also focus on including non-fed, low trophic level aquaculture, such as bivalves and seaweeds, which can be produced in the MI region, among others.

## 3.2. Evaluation of growth predictions

To evaluate modelled growth predictions for the Atlantic salmon and European seabass in the different temperature clusters, we compared the duration that the fish spend in sea cages (harvest time) to empirical farm data in each temperature cluster.

Based on the DEB model, the harvest time of Atlantic salmon takes 22.4 months when reared in the cluster NO and 17.3 months when reared in the cluster NM to reach harvest weight of 5.5 (kg) (Fig. 3). This is in line with growth reported by the biggest Norwegian salmon company, ranging from 12–24 months (Mowi, 2024). According to our simulations, European seabass cultivated in temperature cluster SO, needs around 16.5 months to reach a harvest weight of 400 (g) and in cluster SM around 23.3 months, which is comparable to the 18–24 months reported by EUMOFA (2019). The slightly lower harvest time simulated in temperature cluster SO compared to the harvest time reported by EUMOFA (2019), can partly be explained by the higher stocking weight used in our simulation (4 g vs. 2 g in EUMOFA). Thus, the DEB model predicted the harvest time reasonably well for Atlantic salmon and European seabass systems, indicating that the growth predictions are realistic. As expected, harvest time was shorter in temperature clusters with the optimal temperature range.

The model estimated that common carp in an intensive system reaches the harvest weight of 1.2 kg in October in the second year (i.e. 17 months) of production (Fig. 4), as commonly observed in real farms (Woynarovich, 2011). To reflect common practice in semi-intensive and extensive carp pond production, we simulated growth with limited food availability. This resulted in a harvest time of 28 months to reach 1.8 kg fish in September of the third year.

## 3.3. Nutrient requirements and feed intake

In food system models, data on growth performances, nutrient requirements and feed intake per harvested animal are required to

estimate how many animals can be produced with the available (and limited) feed resources in a region. Therefore, in the perspective of including aquaculture systems in food system models, we estimated the performance and related nutrient requirements for aquaculture species under different temperature clusters and productivity levels (Table 3).

The nutrient requirement in Table 3 is expressed per fish over the life cycle. When accounting for the nutrient requirements to harvest a single producing animal, the contribution of broodstock stage is marginal due to the high number of offspring in fish (Table S1 & S2). For example, one Atlantic salmon female of 6 kg can produce around 11,400 eggs. When accounting for mortality in the early life stages and growth-out phase, it is estimated that one female can produce around 2276 market-size animals. So, for one producing Atlantic salmon, 0.0044 broodstock females are required. In comparison, in livestock, the contribution of the broodstock stage to the total nutrient requirement is much higher (Van Hal et al., 2019).

The data generated in this study for the three fish species indicate differences among species and systems in terms of nutrient requirements. As shown in Table 3, Atlantic salmon and European seabass require feeds with higher levels of digestible methionine and lysine compared to common carp. In the pond systems, nutrient requirements from compound feeds decrease with decreasing production intensity. These differences in feed quality requirements among fish species and systems can be used to reflect the variety of aquaculture in food system models.

## 3.4. Avenues for further research

In this study, we used existing DEB models and data to simulate fish growth and feed intake. Calibration of a DEB model for a species is a data-intensive process, requiring species-specific empirical data on the entire life cycle (Kooijman et al., 2008). Parameters from a large variety of species can be extracted from literature or databases, such as the Add-My-Pet database (AmP, 2024). In our study, the predictions from the DEB models initially resulted in much lower assimilated energy and feed intake than usually assumed in commercial aquaculture settings. Similar issues were reported by Stavrakidis-Zachou et al. (2019) on the seabass DEB model. Furthermore, a more general review of models applied to aquaculture showed that bioenergetic modelling approaches (including DEB) often conclude that feeding rations commonly distributed in finfish aquaculture provide much more energy in the feed than needed to meet fish requirements (Chary et al., 2022). This mismatch, if confirmed, can be due to the complexity of predicting feed intake in fish,

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Growth curves using dynamic energy budget (DEB) model under the different temperature clusters: a. Atlantic salmon, b. European seabass. Each cluster is named according to its geographic region: North (NO), North-middle (NM), South-middle (SM), South (SO).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 4. Growth curve of common carp using dynamic energy budget (DEB) models with average pond temperature and two food availability levels representing intensive and semi-intensive + extensive systems. Average daily pond temperature is representative of Hungary and was based on Orság et al. (2023).</figcaption></figure>

<caption>**Table 3**</caption>

Growth and nutrient requirements during the entire life cycle of Atlantic salmon, European seabass and common carp at different intensity levels and temperature clusters. Five EU coastal waters clusters were defined based on homogeneous water temperature: North (NO), North-middle (NM), Middle (MI), South-middle (SM), South (SO). One cluster represents near optimal conditions (optimal), while the other represented sub-optimal but tolerable conditions (sub-optimal).

<table><thead><tr><th rowspan="2">Species</th><th rowspan="2">Temperature cluster</th><th rowspan="2">Intensity level</th><th rowspan="2">Life stage</th><th rowspan="2">Duration (days)</th><th rowspan="2">Body weight gain (g)</th><th rowspan="2">Feed intake (g/d)</th><th rowspan="2">DE (MJ)</th><th colspan="3">Nutrient requirement (g)</th></tr><tr><th>DMet</th><th>DLys</th><th>EPA + DHA</th></tr></thead><tbody><tr><td rowspan="10">European seabass</td><td rowspan="3">SM (sub-optimal)</td><td rowspan="3">High</td><td>Larvae</td><td>198</td><td>4.97</td><td>0.02</td><td>0.09</td><td>0.06</td><td>0.12</td><td>0.06</td></tr><tr><td>Fry</td><td>210</td><td>44.53</td><td>0.27</td><td>1.02</td><td>0.61</td><td>1.27</td><td>0.57</td></tr><tr><td>Grower</td><td>582</td><td>447.61</td><td>1.35</td><td>14.2</td><td>8.06</td><td>16.49</td><td>7.18</td></tr><tr><td rowspan="5">SO (optimal)</td><td rowspan="5">High</td><td>Broodstock</td><td>503</td><td>1094.41</td><td>3.03</td><td>27.93</td><td>15.38</td><td>31.38</td><td>13.86</td></tr><tr><td>Larvae</td><td>194</td><td>4.89</td><td>0.02</td><td>0.09</td><td>0.05</td><td>0.11</td><td>0.05</td></tr><tr><td>Fry</td><td>133</td><td>44.18</td><td>0.43</td><td>1.03</td><td>0.61</td><td>1.27</td><td>0.57</td></tr><tr><td>Grower</td><td>437</td><td>447.11</td><td>1.80</td><td>14.26</td><td>8.1</td><td>16.56</td><td>7.2</td></tr><tr><td>Broodstock</td><td>479</td><td>1094.93</td><td>3.17</td><td>27.87</td><td>15.35</td><td>31.32</td><td>13.84</td></tr><tr><td rowspan="10">Atlantic salmon</td><td rowspan="5">NO (sub-optimal)</td><td rowspan="5">High</td><td>Larvae</td><td>130</td><td>18.91</td><td>0.06</td><td>0.16</td><td>0.08</td><td>0.26</td><td>0.12</td></tr><tr><td>Fry</td><td>30</td><td>29.92</td><td>0.42</td><td>0.25</td><td>0.12</td><td>0.39</td><td>0.15</td></tr><tr><td>Smolt</td><td>90</td><td>194.11</td><td>1.43</td><td>2.54</td><td>1.2</td><td>3.8</td><td>1.33</td></tr><tr><td>Grower</td><td>691</td><td>5212.77</td><td>6.87</td><td>99.58</td><td>40.24</td><td>125.04</td><td>45.1</td></tr><tr><td>Broodstock</td><td>32</td><td>421.57</td><td>14.30</td><td>8.99</td><td>4.44</td><td>14.14</td><td>11.44</td></tr><tr><td rowspan="5">NM (optimal)</td><td rowspan="5">High</td><td>Larvae</td><td>130</td><td>18.91</td><td>0.06</td><td>0.16</td><td>0.08</td><td>0.26</td><td>0.12</td></tr><tr><td>Fry</td><td>30</td><td>29.92</td><td>0.42</td><td>0.25</td><td>0.12</td><td>0.39</td><td>0.15</td></tr><tr><td>Smolt</td><td>75</td><td>193.64</td><td>1.66</td><td>2.44</td><td>1.16</td><td>3.65</td><td>1.28</td></tr><tr><td>Grower</td><td>539</td><td>5200.19</td><td>8.81</td><td>99.62</td><td>40.25</td><td>125.1</td><td>45.12</td></tr><tr><td>Broodstock</td><td>32</td><td>508.1</td><td>17.32</td><td>10.88</td><td>5.38</td><td>17.12</td><td>13.85</td></tr><tr><td rowspan="10">Common carp</td><td rowspan="5">-</td><td rowspan="5">Mid</td><td>Larvae</td><td>72</td><td>4.96</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.00</td></tr><tr><td>Fry</td><td>70</td><td>43.45</td><td>0.12</td><td>0.11</td><td>0.07</td><td>0.17</td><td>0.01</td></tr><tr><td>Grower</td><td>756</td><td>1737.62</td><td>1.86</td><td>18.23</td><td>10.23</td><td>23.83</td><td>0.80</td></tr><tr><td>Broodstock</td><td>312</td><td>1184.78</td><td>4.71</td><td>19.23</td><td>11.89</td><td>28.78</td><td>1.91</td></tr><tr><td>Larvae</td><td>65</td><td>4.82</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.02</td><td>0.00</td></tr><tr><td rowspan="5">-</td><td rowspan="5">High</td><td>Fry</td><td>61</td><td>44.52</td><td>0.18</td><td>0.15</td><td>0.10</td><td>0.24</td><td>0.02</td></tr><tr><td>Grower</td><td>437</td><td>1135.47</td><td>2.47</td><td>15.09</td><td>9.02</td><td>21.17</td><td>0.85</td></tr><tr><td>Broodstock</td><td>329</td><td>1780.35</td><td>7.42</td><td>35.38</td><td>21.97</td><td>52.74</td><td>3.66</td></tr></tbody></table>

DE:Digestible Energy, DMet: Digestible methionine, DLys:Digestible lysine, EPA: eicosapentaenoic acid and DHA: docosahexaenoic acid.

notably due to many factors involved (Sun et al., 2016). More research is therefore needed to better understand and model feed intake in fish, but this goes beyond the scope of this study. In this study, we aimed to estimate realistic feed use in commercial aquaculture systems. Therefore, we adapted the assimilation efficiency parameters to increase feed intake and obtain realistic eFCR for commercial conditions. This resulted in assimilation efficiency values that have little biological meaning. Our feed intake estimates are therefore close to rations usually distributed on fish farms, but the assimilation efficiency parameters provided here should not be reused for other purposes.

This study focused on sea cage and pond systems. These are the dominant systems used in Europe for the species studied. However, other production systems can also be used (e.g. recirculating aquaculture systems, raceway systems) with variable technology and management practices, hence resulting in different farming performances. Other dominant aquaculture species in Europe include non-fed species, such as bivalves and seaweeds. Incorporating non-fed species into food system models could provide insights into their capacity to recycle nutrients from the water. These other systems and species could also be modelled with our DEB-based approach in future research.
### 3.5. Application in food systems

By integrating our developed systems in food systems studies, we can explore how aquaculture systems, in addition to livestock, can contribute to future food systems. In a companion paper (van Riel et al., unpublished), we aim to integrate the models developed in the present study into resource allocation models, such as those from Van Selm et al. (2022) and Van Hal et al. (2019). These models can estimate the optimal number of animals and animals' mix to meet a human population nutrient requirement, based on the available feed resources in a region (e.g. leftovers from the food system).

To date, the resource allocation model of Van Hal et al. (2019) only includes Nile Tilapia and Atlantic salmon as representatives for aquaculture species. By including more species, we can represent aquaculture in Europe in a more realistic way. Furthermore, including different simulations that account for different water temperature regimes will allow to account for regional variation in production performances. This approach could be extended to incorporate simulations in future water temperature regimes affected by climate change.

Including a greater diversity of aquaculture species and systems in resource allocation models will allow to explore the role of each system and species in up-cycling food system by-products. We expect that Atlantic salmon and European seabass will be preferred for upgrading high-value animal by-products because they are both carnivorous species. Since both species have similar dietary preferences, but Atlantic salmon has a lower feed conversion ratio, we expect Atlantic salmon to be preferred for production. On the other hand, we expect that common carp systems will be selected to utilize low-quality by-products with a preference for lower intensity level systems.

The integration of the new aquaculture species in resource allocation models will also allow to explore the effects of the differences in nutrient richness between fish species and between livestock in general. Previous results from the model from Van Hal et al. (2019), indicated that farmed fish are essential to provide essential fatty acids (EPA & DHA) for human nutrition. In this regard, we expect the addition of common carp to alter the results. Common carp, in contrast to carnivores, can synthesize essential fatty acids from non-essential fatty acids and are therefore more efficient in producing these nutrients (Tocher et al., 2003). However, the large differences in essential fatty acids content of salmon and carps will also be considered and will influence the optimal animal mix in the food system.

Finally, resource allocation models allow to estimate environmental impact for different food system scenarios in terms of greenhouse gas emissions (e.g. Van Selm et al., 2024; Van Zanten et al., 2023). On average, fish species have lower greenhouse gas emissions than most terrestrial animal species (Gephart et al., 2021; Poore and Nemecek, 2018). Incorporating the new aquaculture systems and species in the resource allocation model will allow to clarify the environmental impact mitigation potential of diets including varying proportions of aquatic foods, and will provide insight on the environmental effect of, for example, replacing red meat with fish.

In summary, representing aquaculture in food systems models will provide insight into what can be used as aquaculture feed, how much aquaculture can be produced, environmental impacts related to this production and what nutrients aquaculture can supply to human nutrition. Overall, this will provide a better understanding of the contribution of aquaculture in future food systems.

### CRediT authorship contribution statement

A.J. van Riel: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Project administration, Methodology, Formal analysis, Data curation, Conceptualization. M.A.J. Nederlof: Writing – review & editing, Writing – original draft, Supervision, Methodology, Conceptualization. O. van Hal: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. G.F.

Wiegertjes: Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Conceptualization. I.J.M. de Boer: Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Conceptualization. K. Chary: Writing – review & editing, Writing – original draft, Supervision, Methodology, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Anne-Jo van Riel reports financial support was provided by Wageningen University & Research. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ecolmodel.2026.111504.

### Data availability

Data will be made available on request.

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