Models are important tools to address sustainability challenges associated with developing aquaculture at farm, regional and global scales. Farm‐scale models (FSMs), which are integrated mathematical models developed to simulate farm operations, can quantify energy, mass or economic input flows and predict a variety of outputs such as fish biomass, waste and by‐products. The variety of farming systems, equations available to build the models, and objectives of applications and intended users has resulted in the publication of wide range of FSMs. We performed a narrative review of 36 fish FSMs published from 1985–2021 to address several questions: Can the main characteristics of these models be defined? How do the farming system studied and the objectives of the study influence model development? What are the main modelling techniques available to simulate the main processes of a fish farm, and what are their advantages and disadvantages? How can FSMs help address sustainability challenges of aquaculture? This review discusses advances, limitations and future lines of research related to FSMs to help select existing models, or develop new ones, that are suitable for their intended use and users. The article is structured according to the main steps of the modelling process: (i) definition of scope and objectives; (ii) process formulation and model selection at individual, cohort and farm levels; (iii) implementation and evaluation; and (iv) applications (e.g. precision fish farming, IMTA modelling, supporting spatial management, life cycle assessment). At each step, recommendations are provided and research needs are stated.

This work focuses on the selection of new areas for shellfish farming along the coast of the Northern Adriatic Sea (Italy). Shellfish site suitability was assessed by means of a methodology based on Spatial Multi-Criteria Evaluation (SMCE), which provided the framework to combine mathematical models and operational oceanography products. Intermediate level criteria considered in the analysis included optimal growth conditions, environmental interactions, and socio-economic evaluation (e.g. organic carbon deposition; distance to harbour). Results showed that the whole coastal area comprised within 0 and 3 nm is highly suitable for farming of mussel, while the area comprised between 3 and 12 nm is divided between a highly suitable northern part, and a less suitable southern one. Seven different scenarios of development of shellfish aquaculture industry were explored. The introduction of a new species, and the assessment of the exposure to storm events are specific aspects taken into account in development scenarios. Results show that the degree of suitability for shellfish aquaculture in this area would not change dramatically with the introduction of oyster farming. Furthermore, results highlight that: (i) the growth potential in this area is high; (ii) the space with suitability index >0.5 increases when prioritizing the optimal growth condition criteria, and (iii) the socio-economic is the most restrictive Intermediate Level Criteria. Results were discussed by deriving general lessons concerning the use of SMCE in aquaculture space allocation, from the specific application in the Northern Adriatic Sea. Challenges and opportunities related to the proposed methodological framework, with particular reference to the use of resources provided by remote sensing and operational oceanography by means of mathematical models, were also discussed. Results can support a science-based identification of allocated zones for aquaculture in order to avoid conflicts, and promote sustainable aquaculture in the Mediterranean Sea, where the space for these activities is becoming increasingly limited.

An integrated approach is described for modelling interactions between off-shore fish cages and biogeochemical fluxes of carbon (C), nitrogen (N) and phosphorus (P). Two individual- based population dynamic models for European seabass Dicentrarchus labrax and gilthead seabream Sparus aurata were coupled with a Lagrangian deposition and a benthic degradation model. The individual models explicitly take into account the effects of water temperature and feed availability on fish growth. The integrated model was tested at a Mediterranean fish farm where a comprehensive set of in situ environmental and husbandry data was available. Tests were performed to compare the predicted and observed total organic carbon (TOC) concentrations in surface sediment under and near fish cages. At a local scale, the model output simulated the spatial\ud distribution of 4 biogeochemical indicators, namely: TOC concentrations, C fluxes towards the seabed and C:N and C:P ratios. These allowed the most impacted areas and more extended areas of intermediate organic enrichment to be identified. The model was also used for estimating the\ud mass balance of C, N and P, in order to determine the potential cumulative effects of multiple fish farms in the same area. The C, N and P fluxes among feed, fish and environment were calculated for each fish species over 24 mo of farm activity. The results showed that the amount of dissolved N directly released into the water column in inorganic form (ammonia/urea) was comparable to that deposited on the seafloor in particulate form as uneaten feed and faeces. A larger fraction of\ud P (about 65%) was released as faeces. Results from the integrated model yielded useful information for assessing the sustainability of an area for aquaculture activities that could be used to provide a scientific rationale for fish farm development in new areas