Growth models for farmed post-smolt to adult salmonids: a systematic review for Atlantic salmon aquaculture under warming and salmon-lice pressure

Abstract

Rising sea surface temperatures and salmon lice (Lepeophtheirus salmonis) are interacting environmental and health pressures that can affect growth, condition, survival, treatment needs, and production outcomes in farmed Atlantic salmon (Salmo salar). This systematic review evaluated growth models used in farmed salmonid aquaculture to identify frameworks suitable for quantifying the combined effects of temperature and salmon lice burden during the post-smolt to adult production phase. We initially screened salmonid growth-model studies broadly, including farmed and wild systems, but excluded wild salmonid models from the final synthesis because their ecological objectives, feeding assumptions, data structures, and outputs were poorly aligned with farm-level aquaculture scenario modeling. The retained farmed-salmonid models included empirical index and phenomenological models, bioenergetic models, and nutritional models. Empirical approaches such as Thermal-unit Growth Coefficient and logistic growth models require relatively few inputs and are practical for farm-level scenario analysis, but their transferability depends on local calibration and validation. Mechanistic bioenergetic and nutritional models provide greater biological realism and can represent stressor effects more explicitly, but require substantially more parameters and higher-resolution data. Explicit coupling of salmon growth with salmon-lice dynamics remains rare. For scenario-oriented assessment of warming and salmon lice in Atlantic salmon aquaculture, the most practical near-term framework is a validated, temperature-driven farmed-salmon growth model that is locally calibrated with production and environmental data and coupled modularly to a lice-dynamics or infestation-pressure component.

1 Introduction

Atlantic salmon (Salmo salar) ranks among the ten most produced and valuable marine fish globally within the aquaculture sector (FAO, 2020). Since 2000, global production of farmed Atlantic salmon has remained stable at around 2 million metric tons (MMT) (Asche et al., 2019), with Norway dominating the global market, producing 1,517,516 MMT in 2023 (Directorate of Fisheries, 2024). However, cage farming operations are increasingly challenged globally by rising climate-driven sea surface temperatures (SST) (Calado et al., 2021) causing higher fish mortality (Staurnes et al., 2001; Ytrestøyl et al., 2020; Montes et al., 2018; León-Muñoz et al., 2018), fish welfare issues (Bowers et al., 2000; Grave et al., 2004; Hamre et al., 2009), higher operational costs (Nofima, 2024), loss of revenue (Calado et al., 2021), and spillback effects to the environment (Torrissen et al., 2013; Vollset et al., 2018). Climate projections indicate an increase of 1 to 3 °C in global SST over the next century (Pörtner et al., 2019), with a higher increase in SST expected to happen at higher latitudes (You et al., 2021; Hanssen-Bauer et al., 2009). Higher SSTs are linked to more frequent harmful algal blooms (Trainer et al., 2020), jellyfish blooms (Clinton et al., 2021), and enhanced parasite transmission (Karvonen et al., 2010; Sandvik et al., 2021) all of which can have substantial economic impacts due to losses in farmed salmon production (Torrissen et al., 2013; Vollset et al., 2018).

Since the inception of Atlantic salmon farming in Sunnmøre, mid-Norway, in the late 1960s, the industry has faced recurring challenges from a pathogenic marine parasite, the salmon louse (Lepeophtheirus salmonis) (Costello, 2006; Torrissen et al., 2013). In Norway alone, salmon lice prevention and treatment costs are estimated at €610 million (Nofima, 2024). In addition to exerting the greatest economic impact among all parasites affecting aquaculture, salmon lice also detrimentally affect the welfare of farmed Atlantic salmon (Bowers et al., 2000; Grave et al., 2004; Hamre et al., 2009) and they impact surrounding fish communities (Torrissen et al., 2013; Vollset et al., 2018) including wild populations of Atlantic salmon, seatrout (Salmo trutta), Arctic char (Salvelinus alpinus) and Atlantic cod (Gadus morhua), through spillback effects (Strøm et al., 2025; Torrissen et al., 2013; Vollset et al., 2018; Bøhn et al., 2024; Strøm et al., 2022). Rising SST is expected to intensify this challenge because salmon lice development, larval production, and copepodite infectivity are temperature-dependent; warmer conditions shorten development time from non-infective nauplii to infective copepodites and can substantially increase infection pressure from aquaculture sites (Samsing et al., 2016; Hamre et al., 2019; Sandvik et al., 2021). This has direct implications for both production regulation and fish growth. In Norway, the traffic-light system regulates production capacity in salmonid aquaculture according to the estimated mortality risk imposed by salmon lice on migrating wild salmon smolts; production areas classified as red may have permitted production capacity reduced by 6%, meaning that high lice pressure can limit industry expansion or force biomass reductions (Ministry of Climate and Environment, 2024). At the fish level, lice attachment and feeding cause epithelial damage, osmotic imbalance, stress responses, immune activation, reduced condition, and increased mortality risk, all of which can reduce feed intake and divert energy away from somatic growth (Fjelldal et al., 2022; Fjelldal et al., 2020). Lice management can further suppress growth because delousing commonly involves fasting, crowding, pumping, handling, freshwater, chemical, thermal, or mechanical exposure; non-medicinal treatments are associated with stress, physical injury, reduced appetite, increased mortality, and short-term biomass loss (Overton et al., 2019; Walde et al., 2022).

Assessing both the direct and indirect effects of increasing SST on farmed Atlantic salmon is essential (Brugère and De Young, 2015; Seggel and De Young, 2016; Galappaththi et al., 2018) to understand since this species is a significant contributor to commercial aquaculture (Asche et al., 2019; FAO, 2020) providing food to 172 countries (FAO, 2022). It is also important to assess the impacts of increasing SST to make proper climate change adaptation (CCA) strategies for the industry. According to the IPCC (2022) CCA strategies require adjustments “to actual or expected climate and its effects, in order to moderate harm or exploit beneficial opportunities”. Because mitigation strategies are also needed in order to maintain current warming trajectories compatible with a habitable planet (IPCC, 2022), CCA strategies directed at the Atlantic salmon aquaculture industry should therefor aim to (i) maintain or enhance the viability and welfare of farmed Atlantic salmon during increasing SST and increased pressures by other biotic and abiotic stressors (Calado et al., 2021; Qviller et al., 2024), and (ii) lower environmental pressure of farmed Atlantic salmon by reducing spillback effects and the need for salmon lice treatments (Krkosek et al., 2024; Balstad et al., 2025). Temperature has a direct and non-linear effect on Atlantic salmon growth because feeding, digestion, metabolism, oxygen demand, and feed conversion are all temperature-dependent (Thyholdt, 2014, Handeland et al., 2008, Oppedal et al., 2011). Growth generally follows a thermal performance curve, where performance increases toward an optimum but declines when temperatures become too low or too high. For post-smolts and adult Atlantic salmon in seawater, optimal growth is commonly reported around 13 to 14 °C, although the optimum varies with fish size, life stage, acclimation history, and production conditions (Handeland et al., 2008; Hevrøy et al., 2012; Hevrøy et al., 2013). At elevated temperatures, particularly around 18 to 19 °C, Atlantic salmon may show reduced appetite, poorer feed utilization, depletion of energy stores, and downregulation of muscle-growth pathways, leading to reduced somatic growth despite higher metabolic demand (Hevrøy et al., 2013; Hevrøy et al., 2012; Kullgren et al., 2013). At very low temperatures, feeding and growth are also reduced, and exposure close to the lower thermal limit can cause physiological stress and mortality risk (Vadboncoeur et al., 2023). Although acute thermal endpoints such as critical thermal maximum (CTmax) and chronic incremental thermal maximum (ITmax) are useful indicators of upper thermal tolerance, they should not be interpreted as optimal production temperatures; growth impairment and welfare costs occur well below lethal thresholds (Anttila et al., 2013; Gamperl et al., 2022; Ignatz et al., 2023).

There are several methods of assessing the effects of increasing SST on farmed Atlantic salmon, such as reviewing scientific and gray literature (Crozier and Siegel, 2023; Maulu et al., 2021; Predragovic et al., 2023), interviewing stakeholders (Tiller et al., 2014), scenario building (Couture et al., 2021), and simulations (Zhang et al., 2024; Føre et al., 2016). Computer-based simulations are particularly valuable because they can link SST increases to salmon growth responses and predict how factors such as higher parasite loads may affect yield, fish health, and the environment (Azevedo et al., 2025; Myksvoll et al., 2018). Growth models are one type of simulation-based approaches, offering quantitative insights into how fish weight, body composition, and growth rates evolve in response to temperature, diet, parasite load and other environmental conditions (Bar et al., 2007; Zhang et al., 2020).

Given the key role that growth models play in understanding and predicting how post-smolt to adult Atlantic salmon will respond to both climate-induced temperature changes and biological stressors (e.g., salmon lice infestations), this review aims to identify which farmed-salmonid growth-models frameworks are most suitable for coupling with salmon-lice dynamics to assess temperature-driven effects on growth and production outcomes in farmed post-smolt to adult Atlantic salmon. We initially explored growth models from both wild and farmed salmonids because salmonid models share several physiological and temperature-dependent growth principles. However, wild salmonid models were excluded from the final synthesis because they are generally designed for ecological or population-dynamic questions rather than farm-level production forecasting, and because their assumptions regarding food availability, density, mortality, and management interventions differ substantially from aquaculture systems.

A review of growth models for post-smolt to adult farmed salmonids aimed at identifying the framework best suited to simulate increasing salmon-lice pressure under rising SST has, to our knowledge, not previously been undertaken. However, existing reviews have addressed adjacent topics more broadly, including fish growth reporting and growth-function selection in aquaculture (Hopkins, 1992; Lugert et al., 2016), modeling of growth and body composition in fish nutrition (Dumas et al., 2010), farm-scale aquaculture modeling across species and production systems (Chary et al., 2022), and salmonid-focused feeding and bioenergetic production models (Cho and Bureau, 1998; Cho, 1992).

2 Method

We followed the Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guidelines (Page et al., 2021) to structure the literature search and screening process (see Figure 1). Our primary database was Web of Science, complemented by Oria. Two initial searches targeted only Atlantic salmon references using variations of “Atlantic salmon” AND “growth model*,”. This returned 190 papers but yielded only 9 papers in Web of Science and 3 in Oria after screening, since most of the literature was about Atlantic salmon in the parr life stage. To capture a broader range of potentially applicable salmonid growth-modeling approaches, the search was expanded to include “salmon”, “trout”, “charr”, and “salmonid” in combination with “growth model*”, “Thermal Growth Coefficient”, “TGC”, “Ewos Growth Index”, “EGI”, “logistic growth model*”, “bioenergetic model*”, “Dynamic Energy Budget”, “DEB”, “Net Energy Balance”, “NEB”, and “nutritional model*” (see Table 1). Although we attempted to focus only on Atlantic salmon, including other salmonids (other salmon, trout, and charr) allowed us to capture a more diverse range of modeling approaches that could also apply to Atlantic salmon. These non-Atlantic salmon studies were not treated as direct parameter sources for Atlantic salmon. Some of the included studies also looked at non salmonid species. For these studies, the non-salmonid species were left out of this review.

Figure 1

The broader search produced 712 papers (Table 1), which were screened by title and abstract, with methods sections consulted when necessary. During screening, we assessed whether each study was relevant to the review objective: identifying growth-model frameworks suitable for farmed Atlantic salmon scenario analysis under rising temperature and salmon lice pressure. Wild salmonid studies were recorded during screening but excluded from the final synthesis because they generally addressed ecological growth, survival, migration, density dependence, or population processes in natural systems rather than aquaculture production outcomes. These models often assume natural prey limitation and conservation-oriented endpoints, whereas farmed Atlantic salmon models typically assume controlled feeding, husbandry interventions, production biomass, mortality, treatment timing, and harvest outcomes. After excluding 689 papers that did not meet the inclusion criteria, 23 farmed salmonid studies were retained (see Figure 1).

These studies were classified by production system, country, type of growth model (individual, cohort, farm), has the growth model used other biotic stressors (parasites, bacteria, or virus), has the growth model estimated mortality, and has the growth model calculated revenue and/or cost. This step was necessary to assess which growth models would align the most with our aim. They were further categorized as empirical or mechanistic models and assigned to sub-model categories: index models, phenomenological models, bioenergetic models, and nutritional models. For each study, we extracted information on model name, required input variables, data availability, validation status, and reported fit or performance. These classifications were used to evaluate which model frameworks best aligned with the aim of coupling temperature-dependent salmon growth with salmon lice pressure in future scenario analyses. After reviewer evaluation, one additional targeted citation-search record was added because it directly coupled a temperature-dependent Atlantic salmon growth model with sea-lice control and economic outcomes. This study was not retrieved by the original database search but met the revised relevance criterion for model-coupling evidence and was therefore included as a supplementary farmed-salmon model record (Liu and vanhauwaer Bjelland, 2014).

Graphical visualization of Figure 2 was done using Rstudio (Posit team, 2025) and the Tidyverse package (Wickham et al., 2019).

Figure 2

3 Results

3.1 Characteristics of included studies

The final synthesis included 24 temperature-dependent studies of farmed salmonid growth models (see Table 2). Atlantic salmon and rainbow trout (Oncorhynchus mykiss) were the dominant species, with additional salmonids represented in broader reviews or multi-species modeling studies, including Chinook salmon (Oncorhynchus tshawytscha), coho salmon (Oncorhynchus kisutch), brown trout (Salmo trutta), and brook trout (Salvelinus fontinalis). Atlantic salmon studies mainly concerned marine net-pen, sea-cage, offshore-cage, or closed-containment systems from Norway, Ireland, Scotland/UK, Canada, Chile, China, and broader European datasets, whereas rainbow trout studies were mainly based on freshwater tank, raceway, or land-based systems in Canada, Italy, Estonia, and Japan.

Most models operated at the individual or fish-group/cohort level and used temperature as a direct growth driver, thermal-unit or degree-day term, or input to feed intake, bioenergetic, nutrient-demand, or dynamic energy budget calculations. These included growth-index or thermal-growth-coefficient models (Aunsmo et al., 2014; Dempsey et al., 2023; Dumas et al., 2007b, Thorarensen and Farrell, 2011), feed-intake or nutritional models (Azevedo et al., 2025; Cho and Bureau, 1998; Dumas et al., 2007a; Glencross et al., 2024, Glencross et al., 2022, Hua et al., 2009; Hua and Bureau, 2012), and individual-based or dynamic energy budget models for trout or salmon systems (Stavrakidis-Zachou et al., 2025; Takahashi et al., 2026; Zhang et al., 2024, van Riel et al., 2026). Some studies extended beyond individual growth to cohort, farm, or integrated production frameworks, including regional salmon growth functions, digital twins, climate-impact models, farm-scale reviews, and integrated multi-trophic aquaculture models (Chary et al., 2022; Cubillo et al., 2021; Ferreira et al., 2021; Kotta et al., 2023; Krupandan et al., 2025; Lamprianidou et al., 2015; Lima et al., 2023; Thyholdt, 2014).

The retained studies varied strongly in output. Most estimated body weight, growth rate, feed intake, feed conversion, nutrient deposition, body composition, or biomass development. Fewer models included mortality, economic output, waste production, environmental effects, or pathogen-related processes. Mortality or cost/revenue outputs were mainly present in broader bioenergetic, farm-scale, climate-impact, or pathogen-integrated frameworks (Chary et al., 2022; Cho and Bureau, 1998; Cubillo et al., 2021; Ferreira et al., 2021; Krupandan et al., 2025; van Riel et al., 2026).

3.2 Main model classes in included studies

The retained studies were first separated into empirical and mechanistic models, and then organized into three main model classes: index and phenomenological models, bioenergetic models, and nutritional models (see Table 3). Index and phenomenological models were generally empirical, relatively low-cost, and suitable for benchmarking, field validation, or temperature-scenario testing. This group included Thermal-unit Growth Coefficient models, Ewos Growth Index, and logistic growth functions (Aunsmo et al., 2014; Dumas et al., 2007b; Dempsey et al., 2023; Thorarensen and Farrell, 2011; Thyholdt, 2014). Bioenergetic models were more mechanistic and used energy-balance, Net Energy Balance, or Dynamic Energy Budget principles to link growth with feed intake, metabolism, environmental forcing, waste output, or disease modules (Cho and Bureau, 1998; Ferreira et al., 2021; Cubillo et al., 2021; Kotta et al., 2023; Takahashi et al., 2026; Zhang et al., 2024). Nutritional models focused more specifically on nutrient intake, digestibility, retention, body composition, feed formulation, and product quality (Hua et al., 2009; Hua and Bureau, 2012; Glencross et al., 2024; Glencross et al., 2022; Stavrakidis-Zachou et al., 2025).

Model performance varied by model class and validation context. Empirical models often showed strong fit within controlled experiments or region-specific production datasets, but their performance was sensitive to fish size, temperature range, photoperiod, life stage, and calibration region (Aunsmo et al., 2014; Dumas et al., 2007b; Thyholdt, 2014). Mechanistic, bioenergetic, and nutritional models required more detailed parameterization, but could predict a broader range of outputs, including feed conversion, nutrient deposition, waste production, harvest timing, product quality, environmental effects, mortality, and economic consequences (Hua and Bureau, 2012; Glencross et al., 2024; Krupandan et al., 2025). Thus, empirical models were generally more practical for farm-level biomass forecasting and scenario testing, whereas mechanistic models were more useful when the aim was to represent feed use, metabolism, environmental loading, or production losses in greater biological detail.

Explicit integration of biotic stressors was much more limited. Most retained growth models did not represent parasites, bacteria, or viruses as dynamic drivers of growth, feed intake, mortality, or treatment timing. The few examples were mainly research or decision-support frameworks rather than routine operational growth models. Ferreira et al. (2021) applied a farm-scale production framework across salmon-farming contexts including Norway, Scotland, Canada, Chile, the USA, and Ireland, linking deterministic growth and production with stochastic host–pathogen dynamics, mortality, feed conversion, environmental effects, and economic loss; however, the salmon application concerned viral disease rather than salmon lice. Chary et al. (2022) showed that disease components can be included in broader farm-scale aquaculture models, but generally as mortality, production-loss, or management modules rather than as fully coupled pathogen-population models. Liu and vanhauwaer Bjelland (2014) was the closest salmon-lice example and was specific to Norwegian salmon farming, coupling a Thermal-unit Growth Coefficient-based salmon growth model with empirical lice and treatment profiles, treatment costs, growth delay, added mortality, production loss, and profit. Overall, the retained literature shows that disease or parasite effects can be linked to growth through mortality, treatment timing, growth penalties, and economic loss, but no retained model dynamically coupled Atlantic salmon growth to a mechanistic salmon-lice population model. Such a framework would require an explicit lice or infestation-pressure module representing temperature-dependent development, larval production or infection pressure, attachment, and treatment thresholds, together with a stress-effect function translating lice burden and delousing events into reduced growth, appetite suppression, mortality, or delayed harvest.

3.2.1 Index and phenomenological models

Index and phenomenological models describe growth statistically without explicitly modeling the underlying physiological energy or nutrient fluxes. The main examples in the retained studies were the Thermal-unit Growth Coefficient, Ewos Growth Index, and logistic growth functions (Aunsmo et al., 2014; Cho and Bureau, 1998; Dempsey et al., 2023; Dumas et al., 2007a, 2007; Lamprianidou et al., 2015; Thorarensen and Farrell, 2011; Thyholdt, 2014). These models usually require few inputs, such as temperature or degree-days, initial and final body weight, growth duration, and sometimes photoperiod or simple allometric exponents. This makes them operationally useful because such variables are routinely available from farm production records.

Aunsmo et al. (2014) provided the most direct field validation of index models for Atlantic salmon farming. Using Norwegian commercial production data, they evaluated the Thermal-unit Growth Coefficient and Ewos Growth Index and showed that both were influenced by harvest weight, mean temperature, and day length. Reported fit was moderate, with R² = 0.73 for the Thermal-unit Growth Coefficient and R² = 0.56 for the Ewos Growth Index. Although Ewos Growth Index had lower statistical fit, it was considered more robust overall because it accounted for both biotic and abiotic factors. This highlights a key issue for index models: high simplicity, but potential bias when applied across variable environmental settings.

The Thermal-unit Growth Coefficient was the most frequently used index model. Cho and Bureau (1998) used it as part of a broader bioenergetic feeding framework, where the coefficient helped estimate production, feed requirement, waste output, and water-quality consequences. Dumas et al. (2007b) tested the assumption that one Thermal-unit Growth Coefficient exponent applies across the rainbow trout life cycle and found that the conventional cube-root formulation fitted intermediate-sized fish better than very small or large fish. This suggests that the model can require life-stage-specific adjustment. Dempsey et al. (2023) applied the same model to Atlantic salmon in Atlantic Canada to estimate the stocking weight needed to reach 5.5 kg under different growing-season lengths. The model was practical for temperature-scenario analysis, but output depended strongly on assumed growth coefficients, available degree-days, and thermal thresholds.

Phenomenological models were also represented by Thyholdt (2014), who developed regional logistic growth functions for Norwegian farmed salmon. The models fitted monthly regional biomass and temperature data well, with R² values above 0.95. Importantly, temperature effects differed by region: higher sea temperature increased growth in Northern and Central Norway but reduced growth in Southern Norway. This is directly relevant for climate-change applications because warming may improve growth in colder areas while reducing performance in regions already closer to upper thermal limits.

3.2.2 Bioenergetic models

Bioenergetic models represent growth through energy intake, metabolic expenditure, and allocation to somatic growth, storage, reproduction, or waste. Compared with index models, they require more detailed information, including feed intake, energy density, digestibility, body composition, temperature-dependent metabolism, oxygen demand, excretion, and environmental forcing. In the retained studies, this group included classical bioenergetic models, Dynamic Energy Budget models, Net Energy Balance models, feed-intake models, farm-scale production models, and integrated production–environment–pathogen frameworks (Azevedo et al., 2025; Chary et al., 2022; Cho and Bureau, 1998; Cubillo et al., 2021; Ferreira et al., 2021; Kotta et al., 2023; Krupandan et al., 2025; Takahashi et al., 2026; van Riel et al., 2026; Zhang et al., 2024).

Cho and Bureau (1998) developed bioenergetic models and the Fish-PrFEQ software to estimate production, feeding ration, nutrient retention, waste output, oxygen demand, and effluent water quality in salmonid aquaculture. This framework extended growth modeling beyond biomass prediction and made it relevant for feed management and environmental loading. However, this came with higher input requirements, including growth coefficients, temperature, carcass energy content, digestibility coefficients, retention efficiencies, and waste coefficients.

Azevedo et al. (2025) developed a reference feed-intake model for Atlantic salmon based on body weight and temperature. Although simpler than full bioenergetic models, it is relevant because feed intake is a central driver of growth, feed conversion, and stress responses. The reported mean absolute percentage error was approximately 28–31%, showing useful but imperfect predictive performance. This likely reflects unmodelled effects of oxygen, feeding frequency, fish behavior, appetite variation, and husbandry conditions. For salmon-lice modeling, such a model could provide a baseline feeding expectation against which lice-induced appetite reduction or treatment effects could be imposed.

Several bioenergetic models were integrated into larger farm-scale or environmental frameworks. Ferreira et al. (2021) combined deterministic growth models with stochastic host–pathogen dynamics and environmental modules in the Aquaculture, Biosecurity and Carrying Capacity framework. Although their salmon case used infectious hematopoietic necrosis virus rather than salmon lice, the framework is methodologically relevant because it linked pathogen timing with yield, mortality, feed conversion, environmental effects, and economic loss. Cubillo et al. (2021) used bioenergetic and production models to simulate climate-change effects on aquaculture productivity, with reported farm-scale production errors of about 7.6–8.7%. Krupandan et al. (2025) linked salmon growth and nutrient-waste outputs with hydrodynamic transport and kelp growth in an integrated multi-trophic aquaculture system, reporting a final body-weight error of 9.87%.

Dynamic Energy Budget models were used in several studies to simulate growth under temperature and environmental forcing (Chary et al., 2022; Kotta et al., 2023; Takahashi et al., 2026; van Riel et al., 2026; Zhang et al., 2024). Reported performance varied because some studies used these models mainly for scenario analysis rather than formal validation. Takahashi et al. (2026) reported good agreement early in the rearing period but increasing error over time, with final body-mass error of about 22.7%. Zhang et al. (2024) validated a Dynamic Energy Budget model for Atlantic salmon site-selection in the Yellow Sea and showed strong agreement between observed and simulated weight. van Riel et al. (2026) used Dynamic Energy Budget models to estimate harvest timing across European aquaculture systems, with harvest times around 17.3 to 22.4 months depending on system and temperature cluster.

3.2.3 Nutritional models

Nutritional models are semi-mechanistic or mechanistic models that focus on how feed composition, digestibility, and nutrient partitioning determine growth, body composition, feed efficiency, and waste production. They are closely related to bioenergetic models but are more feed-centric. Typical inputs include dietary protein, lipid, energy, amino acids or fatty acids, apparent digestibility coefficients, retention efficiencies, body protein and lipid content, and temperature-dependent growth or maintenance terms. In the retained studies, this group included nutrient-based growth models, integrated growth and nutrient-utilization models, factorial nutrient-demand models, nutritional bioenergetic models, and fatty-acid dilution models (Dumas et al., 2007a; Glencross et al., 2024; Glencross et al., 2022; Hua et al., 2009; Hua and Bureau, 2012; Stavrakidis-Zachou et al., 2025).

Hua et al. (2009) adapted a non-ruminant nutrient-based growth model to rainbow trout. The model represented the use of energy-yielding nutrients for protein and lipid deposition, but performance was imperfect. It underestimated growth rate by 37% and protein deposition by 15%, while overestimating lipid deposition by 13%. This showed that nutrient-partitioning rules from terrestrial monogastric models cannot be transferred directly to salmonids without substantial reparameterization.

Hua and Bureau (2012) developed a more robust integrated growth and nutrient-utilization model for salmonids. The model combined bioenergetic and nutrient-utilization components and was used to evaluate plant-protein replacement in salmonid feeds. It achieved stronger predictive performance, with reported R² values of 0.91–0.96 between observed and predicted growth responses. This demonstrates the value of nutritional models for comparing feeding trials where diet composition, digestible nutrient supply, and nutrient adequacy differ among studies.

Dumas et al. (2007a) supported nutritional model development by quantifying rainbow trout body composition and nutrient deposition across life stages. This type of information is important because biomass gain is not compositionally constant; protein, lipid, water, and ash deposition change with body size and life stage. Glencross et al. (2022) developed a factorial nutrient-demand model for Chinook salmon, while Glencross et al. (2024) extended nutritional modeling to Atlantic salmon product quality by coupling nutrient-demand modeling with fatty-acid dilution. The latter model showed very high predictive performance for some fatty-acid outputs, with R² > 0.998, although total lipid prediction was less accurate. Stavrakidis-Zachou et al. (2025) developed a nutritional bioenergetic model for rainbow trout and reported low mean relative error for growth prediction.

4 Discussion

This review was revised around a narrower question: which temperature-dependent growth model classes are most useful for modeling post-smolt to adult farmed Atlantic salmon under increasing temperature and salmon-lice pressure. The retained literature shows that no single model class is optimal for all purposes. Instead, the most appropriate framework depends on the intended output. Simple index and phenomenological models are best suited for biomass forecasting and scenario testing, bioenergetic models are better suited when feed use, metabolism, waste, or environmental forcing must be represented, and nutritional models are most useful when feed composition, nutrient retention, body composition, or product quality are central endpoints (Cho and Bureau, 1998; Chary et al., 2022; Glencross et al., 2024).

For the specific objective of coupling salmon growth with warming and salmon-lice pressure, a parsimonious temperature-driven growth model is the most practical starting point. Thermal-unit Growth Coefficient models and related phenomenological formulations require few inputs, such as initial weight, temperature or degree-days, growth duration, and harvest weight, and these variables are routinely available in commercial salmon farming. Aunsmo et al. (2014) showed that both Thermal-unit Growth Coefficient and Ewos Growth Index can be applied to Norwegian Atlantic salmon production data, although both were influenced by harvest weight, mean temperature, and day length. Dempsey et al. (2023) further showed how Thermal-unit Growth Coefficient models can be used for scenario analysis by estimating stocking weights needed to reach harvest size under different temperature regimes in Atlantic Canada. Similarly, Thyholdt (2014) demonstrated that regional logistic growth functions can describe Norwegian salmon biomass development and that temperature effects differ regionally, with positive effects in Northern and Central Norway but negative effects in Southern Norway. These studies are directly relevant to climate applications because they show both the usefulness and the limitations of temperature-driven empirical models.

However, the high apparent fit of empirical models should not be interpreted as general predictive robustness. Several retained studies showed that empirical growth indices are sensitive to fish size, photoperiod, life stage, and calibration context (Aunsmo et al., 2014; Dumas et al., 2007b; Thyholdt, 2014). Dumas et al. (2007b), for example, showed that the conventional cube-root Thermal-unit Growth Coefficient formulation fitted intermediate-sized rainbow trout better than very small or large fish, indicating that allometric assumptions may need life-stage-specific adjustment. This is important for post-smolt modeling because growth from transfer to harvest covers a large body-size range. For scenario modeling, empirical models should therefore be calibrated and validated against production data from the relevant region, temperature range, smolt size, and management regime before being used for projections.

Bioenergetic and Dynamic Energy Budget models offer greater biological resolution but at higher data cost. Cho and Bureau (1998) extended growth modeling toward feed allocation, oxygen demand, nitrogen and phosphorus excretion, and water-quality consequences. Dynamic Energy Budget models were used to simulate growth under environmental forcing in several retained studies, including rainbow trout and Atlantic salmon applications (Kotta et al., 2023, Takahashi et al., 2026, van Riel et al., 2026, Zhang et al., 2024). Zhang et al. (2024), for example, used a Dynamic Energy Budget framework to map suitable Atlantic salmon farming areas in the Yellow Sea under current and future warming scenarios, while van Riel et al. (2026) used Dynamic Energy Budget models to estimate harvest timing across European aquaculture systems. These models are valuable where the aim is to evaluate environmental suitability, harvest timing, metabolic constraints, or system-level production. For a lice-coupled farm model, however, their additional complexity is only justified if the required data and parameters are available and if outputs beyond biomass, mortality, or treatment timing are needed.

Nutritional models provide a different type of mechanistic detail. They are most relevant when feed composition, digestibility, protein and lipid deposition, fatty-acid composition, or harvest quality are part of the modeling objective. Hua et al. (2009) showed that a nutrient-based growth model adapted from terrestrial monogastric models did not transfer directly to rainbow trout, underestimating growth and protein deposition while overestimating lipid deposition. In contrast, Hua and Bureau (2012) developed a more robust integrated growth and nutrient-utilization model for salmonids, with stronger agreement between predicted and observed growth responses. Glencross et al. (2022) and Glencross et al. (2024) further demonstrated how nutrient-demand and fatty-acid dilution models can predict dietary requirements and product-quality traits. These models are useful for feed-formulation and harvest-quality questions, but they are not necessarily required for a first-generation salmon-lice and warming model unless appetite suppression, compensatory feeding, feed conversion, or product quality are explicit endpoints.

The most consistent gap across the retained studies was the limited integration of explicit biotic stressors. Most temperature-dependent growth models did not represent parasites, bacteria, or viruses as dynamic drivers of growth, feed intake, mortality, or treatment timing. Ferreira et al. (2021) was the clearest exception, because the Aquaculture, Biosecurity and Carrying Capacity framework linked deterministic growth models with stochastic host–pathogen dynamics, mortality, feed conversion, environmental effects, and economic consequences. However, the salmon case focused on infectious hematopoietic necrosis virus rather than salmon lice. Chary et al. (2022) also showed that farm-scale aquaculture models can include disease, economic, and environmental modules, but such integration remains uncommon in growth-focused salmonid models. Thus, the main limitation in the current literature is not the absence of temperature-dependent growth models, but the lack of models that connect growth with parasite pressure and health-management decisions.

Liu and vanhauwaer Bjelland (2014) is therefore important as a targeted supplementary study. It provides a proof-of-concept for coupling a Thermal-unit Growth Coefficient salmon growth model with sea-lice control decisions and economic outcomes. In that framework, fish weight was predicted from accumulated temperature and initial body size, while sea-lice treatment timing was represented through an empirical lice and treatment profile rather than a mechanistic lice population model. Treatment events were then linked to direct costs, growth delay, mortality, production loss, and profit. This is highly aligned with the objective of the present review, but it also illustrates the remaining methodological gap: the lice component needs to be replaced or extended with a mechanistic salmon-lice population or infestation-pressure model if the purpose is to simulate future warming, seasonality, and parasite dynamics more explicitly.

The inclusion of rainbow trout and Chinook salmon studies should be interpreted as evidence for transferable model structures, input requirements, and validation practices, rather than as direct parameter evidence for Atlantic salmon. Rainbow trout studies contributed useful information on Thermal-unit Growth Coefficient assumptions, size-dependent growth scaling, nutrient deposition, nutrient utilization, and nutritional bioenergetics (Dumas et al., 2007a, 2007; Hua et al., 2009; Hua and Bureau, 2012; Stavrakidis-Zachou et al., 2025; Takahashi et al., 2026). While Glencross et al. (2022) provided relevant nutrient-demand modeling concepts for Chinook salmon. These approaches are conceptually useful because many salmonid growth models share common structural elements, including temperature-dependent growth, body-size scaling, feed intake, nutrient allocation, and energy or mass-balance assumptions. However, their parameters should not be transferred directly to Atlantic salmon. Empirical models would require re-estimation of growth coefficients or thermal-response functions using Atlantic salmon production data covering the relevant body-size range, temperature regime, photoperiod, and management conditions. Bioenergetic and nutritional models would require more extensive Atlantic salmon-specific parameterization for feed intake, maintenance metabolism, digestibility, nutrient retention, body composition, oxygen demand, and waste outputs. The limited use of some rainbow trout or Chinook salmon formulations in Atlantic salmon aquaculture therefore likely reflects the burden of species-specific calibration and validation, together with restricted access to commercial feed, growth, mortality, and environmental data, rather than a lack of conceptual relevance. Accordingly, non-Atlantic salmon studies are useful for identifying model architectures and validation strategies, but Atlantic salmon applications should be recalibrated and validated with region-specific farm data.

5 Conclusion

This review shows that temperature-dependent farmed salmonid growth models range from simple empirical indices to data-intensive bioenergetic and nutritional frameworks, with each model class suited to different objectives. Index and phenomenological models, such as Thermal-unit Growth Coefficient, Ewos Growth Index, and logistic growth functions, are practical for farm-scale scenario testing because they require few inputs and can be parameterized with routine production data, but their transferability depends on local calibration and validation because performance can be affected by fish size, life stage, temperature, photoperiod, and regional production conditions (Aunsmo et al., 2014; Dempsey et al., 2023; Dumas et al., 2007b; Thyholdt, 2014). Bioenergetic and nutritional models provide greater biological resolution and can represent feed intake, nutrient deposition, waste output, oxygen demand, product quality, and environmental effects, but require substantially more detailed parameterization (Cho and Bureau, 1998; Hua and Bureau, 2012; Glencross et al., 2024; Krupandan et al., 2025). The clearest gap is the limited integration of explicit biotic stressors, particularly salmon lice, into temperature-dependent growth models. Ferreira et al. (2021) demonstrated how pathogen dynamics can be linked with production, mortality, feed conversion, environmental effects, and economic consequences, while Liu and vanhauwaer Bjelland (2014) provided a useful proof-of-concept by coupling salmon growth with sea-lice treatment decisions and economic losses, although without a mechanistic lice-population component. Overall, a model for combined warming and salmon-lice scenarios should use a validated, temperature-driven Atlantic salmon growth model as the core, calibrated with region-specific production data, and couple it to explicit lice, treatment, mortality, and economic modules; more complex bioenergetic or nutritional components should be added only when feed intake, waste output, nutrient retention, oxygen demand, or product-quality endpoints are central to the research question.

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