A proxy for carrying capacity of Mediterranean aquaculture

In developing a holistic and innovative approach to determining the carrying capacity in marine finfish aqua- culture, we carried out a modified Delphi exercise in which we asked industry experts to identify the factors influencing the production levels of the activity under different scenarios. We disseminated and discussed three rounds of questionnaires in sectoral roundtables and workshops with experts, culminating in the development of a simple formula that adapts production levels to the physical, ecological, social and economic conditions of the activity on the Spanish Mediterranean coast. We used this formula to approach the carrying capacity of the system. Based on the developed model and its theoretical application, we estimated the carrying capacity for floating cages on the Spanish Mediterranean coast at 117,162 t — about 1.5 times the current granted production level of 79,440 t. We therefore concluded that, subject to the execution of an in-situ validation of the model, the production level of floating nurseries on the Spanish Mediterranean coast could be increased by up to 47.5%.


Introduction
Over the last decades, worldwide, open sea fish farming has experienced an almost exponential growth (FAO, 2020) due to the high demand for fish products for human consumption (Ruiz-Zarzuela et al., 2009) and the decline of natural fish communities due to overfishing (FAO, 2020). The evolution and development of European Union fish farming, however, has not followed the same trend, with production stagnating since 2000 (APROMAR, 2022). This may be attributed mainly to the limited availability of suitable areas for aquaculture (Sanchez-Jerez et al., 2016) due to the confluence of uses of maritime space (UICN (Unión Internacional para la Conservación de la Naturaleza y de los Recursos Naturales), 2009) and the consequent conflicts for space with other sectors-such as fisheries and tourism (Neofitou et al., 2019). The planning and management of aquaculture sites will therefore play a key role in their successful sustainable development (Borg et al., 2011). Aquaculture management should thus consider the selection of allowable zones for aquaculture development (AZAs; Sanchez-Jerez et al., 2016), considering simultaneously their carrying capacity (FOESA (Fundación Observatorio Español de Acuicultura), 2013; Macias et al., 2019;Weitzman and Filgueira, 2020;Weitzman et al., 2021;).
Evaluation of the carrying capacity will facilitate the establishment of upper limits of aquaculture production, environmental limits and social acceptability of aquaculture (Ross et al., 2013).
Surprisingly, carrying capacity has not, to date, been used as one of the most relevant concepts-environmentally, socially and economically-in decision-making on the location of facilities (OESA (Observatorio español de acuicultura), 2019) or in their subsequent environmental management (Cranford et al., 2012; OESA (Observatorio español de acuicultura), 2019; Fernández-Ávila et al., 2020;Weitzman and Filgueira, 2020). In fact, only the Greek fish farming industry has implemented a new regulatory system based on the physical and ecological carrying capacity of the activity on the eastern Mediterranean coast (Karakassis et al., 2013). The regulation describes how to calculate the total production (starting from 150 t/ha) that should be allowed in different scenarios (Karakassis et al., 2013). Thus, it is an intuitive estimation model that calculates a proxy for the maximum allowable production level based on several factors (Macias et al., 2019;Yigit et al., 2021).
Despite this interesting methodological approach as a proxy for the calculation of carrying capacity on the eastern Mediterranean coast, the regulation does not take into account social and economic aspects of the activity, both of which have been identified as major challenges for the sustainable development of aquaculture (Weitzman and Filgueira, 2020). Here, we aim to bolster a framework for the estimation of carrying capacity in marine finfish aquaculture in a more holistic and innovative way, following the proposed concept of carrying capacity (McKindsey et al., 2006), and offering the possibility of incorporating new environmental factors that may be of interest on the other side of the Mediterranean. We therefore developed a methodology for adapting production levels of fish farming to the physical, ecological, social and economic conditions of the aquaculture sector in the western Mediterranean, specifically off the Spanish Mediterranean coast.

Study approach
Achieving consensus among several experts or practioners is challenging, and current techniques have been developed to seek agreements and establish criteria that facilitate decision-making (Fernández-Á vila et al., 2020). One of these techniques is the Delphi study (Dalkey and Helmer, 1963) which has been used not only in aquatic environmental impact assessments (Zuboy, 1981;Green et al., 1990;Mohorjy and Aburizaiza, 1997;Clark and Richards, 2002;Taylor and Ryder, 2003) but also in aquaculture planning and management (Karakassis et al., 2013;Díaz et al., 2015;Weitzman et al., 2021). A systematic and interactive survey technique, it is based on independent input from a group of experts on a specific problem which they address based on general group agreement (Mohorjy and Aburizaiza, 1997;Fernández-Á vila et al., 2020). Here, we used a modification of the traditional Delphi methodology to find a consensus on the estimation of carrying capacity based on basal production and certain other factors. Main differences with the traditional Delphi methodology were the inclusion of a prospective round (Round 1; Fig. 1) of interviews/questionnaires to identify most suitable sustainability indicators that may be further discussed for inclusion in subsequent rounds (Rounds 2 and 3; Fig. 1). These latter were face-to-face workshops rather than traditional individual questionnaires that avoid direct contact between experts (Dalkey and Helmer, 1963). Given the wide range of knowledge that is needed to build up a holistic carrying capacity model, the in-person consensus workshops allowed different stakeholders to give a more informed response to questions on technical-productive, environmental, social and economic factors ranges and weights to be included in the model.

Selection of expert participants
We first formed a network of contacts to elaborate a preliminary list of the potential Delphi expert panel. We used a mixed scanning method of identification which included word-of-mouth communications with existing contacts, bibliographical references from 62 studies and 10 face-to-face and virtual/telephonic meetings with producers, research centres and public administration. To ensure a balance of interests, the final contacts network included 21 experts distributed between the private, academic and government sectors. Private sector experts were professionals involved in the offshore fish farming sector, comprising mainly producers on the Spanish Mediterranean coast. We included both key personnel from relevant government ministries and agencies working for, or with, governance and/or public administration agencies and the academic community from both universities and research institutions.

Delphi exercise
This study used a modified Delphi approach (Hasson and Keeney, 2011) where the wording of the questions evolved over three rounds in response to the results and expert comments (Fig. 1).
In the first round, we conducted semi-structured interviews where experts were asked to show the most representative sustainability indicators in the carrying capacity models and their degree of importance on a scale of 1 to 10, with 1 being unrepresentative and 10 being highly representative. We divided these indicators into categories of carrying capacity for which the indicator was useful (technical-productive, environmental, social and economic). During this first round we developed a preliminary questionnaire of sustainability indicators that could be included the model. The second round had two clear objectives: i to reach a consensus on the value of basal production and the factors to be considered in the model for estimating carrying capacity, and ii to establish their corresponding ranges and weighting values. To this end, we held three face-to-face working groups with different representatives from each sector. At each of the roundtables, these representatives discussed the preliminary questionnaire, reassessing the degree of importance of the sustainability indicators and determining the value of the baseline production. Each working group presented its results and the Delphi panel of experts-after a consensus analysis looking at the average score of the rounds-selected the value of the basal production and the factors involved in an increase or decrease in basal production. In addition, we also proposed five ranges and five weighting values for each of the factors and they were discussed at each of the tables after their selection. Thus, the second round ended with a model proposal for an estimating carrying capacity. The need for testing the model led us to carry out 29 simulations in real activity environments. Because we detected inconsistencies and difficulties in the data collection, the technical team of the project convened the Delphi expert panel in a third    Table 2 Preliminary model for the estimation of the carrying capacity for floating cages.
Carrying capacity = BP * V T1 * V T2 * V T3 * V A1 * V A2 * V A3 * V S1 * V E1 Basal production allowed ( round. During this round our objective was to present the results of the validation and to propose possible alternatives in terms of factor changes, ranges and weighting values. At its conclusion re-adjustments led to a final model after reaching a consensus analysis of the alternatives presented.

Results and discussion
During the first round, recognising the importance of appropriate selection of baseline production and carrying capacity estimators, the experts identified a total of 36 sustainability indicators classified according to their appropriate carrying capacity categories (technical--productive, environmental, social and economic) and their degree of importance (Appendix I). After the first round of the 36 indicators, 14 were excluded from the study, since they usually appear in environmental monitoring programmes; and 21 indicators were grouped into 7 factors each containing three very similar indicators. In addition, the experts also identified 3 new indicators of sustainability (Appendix II), culminating in a total of 11 factors as possible estimators of carrying capacity (Table 1). After a consensus analysis by the Delphi expert panel, the second round ended with a model proposal based on a baseline production and 8 factors estimating carrying capacity, together with their respective ranges and weighting values (Table 2).

Preliminary carrying capacity model
First, the Delphi expert panel proposed a model built on basal production and applied different factors-representing different types of carrying capacities-to the model. In the second round, in the absence of a homogeneous, licensed production scheme in terms of concessions authorising cultivation, the experts determined a basal production value of 50 t per hectare of concession. They established this value based on a previously proposed model (Karakassis et al., 2013) and the production data from the annual report on the evolution of the aquaculture sector in Spain and Europe (APROMAR, 2018)-as a precautionary measure, allowing for a maximum of 20% variation. The Delphi expert panel ensured that this value generally represented that of standard, commercially productive companies implementing environmental monitoring plans (APROMAR, 2018).
Second, the application of factors used in estimating carrying capacity shows how basal production is modulated. The expert panel considered that, under same environmental conditions, the carrying capacity is mostly driven by operational management of aquaculture facilities. Therefore, they selected three technical-productive and three environmental factors to include in the model. Additionally, and to achieve a holistic approach, one each of economic and social factors were selected.

Selection of factors
For the consensus selection of the model factors, for each of the carrying capacity categories the Delphi expert panel identified tipping points. For the technical-productive factors, the Delphi expert panel considered mainly those factors that had a more direct effect on the seabed, based on suggestions, opinions and technical documentation presented in the workshops (Aguado-Giménez et al., 2012). Experts identified this category as that most affected by aquaculture activity, and therefore one of the most important when determining the carrying capacity of the system. They therefore selected the food conversion rate, which expresses the efficiency of the animal in relation to the amount of feed required to achieve the final biomass of the culture (Abdel-Tawwab et al., 2015), and thus indirectly assesses the uneaten feed that is lost (Islam, 2005). Other selected factors were related to the hydrology of the Table 3 Results of the preliminary model for validation, carried out by the technical team of the project where BP is the basal production in t/ha and V is the weighting value for each of the factors.
facility as it impacted the prevention of pathologies-in particular, the distance between facilities and the space arrangement of the concession; the experts defined both as factors that influence the concentration of the remains of the activity (faeces and food) on the seabed (Dosdat et al., 1996). In relation to environmental factors and considering the benthos as a relevant ecological compartment and source of organic enrichment (Dosdat et al., 1996), the Delphi expert panel included in the model the depth below the floating cages and the current velocity in the production area, as both are closely related to the capacity to spread the nutrients and solids generated by the activity (Borja, 2002). The greater the depth and the higher the current velocity, the greater the volume of particulate debris that can be dispersed, thereby reducing both the impacts of the farming activity on both the seabed and the spread of diseases (Dosdat et al., 1996;Bostock et al., 2010;Holmer, 2010;Price et al., 2015;APROMAR, 2018). In addition, the panel also included distance to priority habitats which, although there is no clear legislation in this regard, was identified by experts as an important indicator that could potentially alter adjacent priority habitats such as seagrass meadows (Herrera-Paz et al., 2015), maerl beds (EC (European Community), 1992; Ruiz et al., 2001;Sanz-Lázaro et al., 2011) and gorgonian beds, all included in Annex I of the Habitats Directive 92/43/EEC of the Council of 21 March 1992 (EC (European Community), 1992).
Regarding social factors, the experts included the employment provided, citing the increase in social acceptability accompanying demonstrable socio-economic benefits, the assessment of impacts on the environment and open communication with communities that are kept informed about the management requirements to be met by the companies (Carvalho, 1998;Wilson, 2001;Whitmarsh and Palmieri, 2009). Thus, the experts established the employment provided as an indicator of social carrying capacity, reflecting the acceptance by society of the activity thanks to the generation of new jobs in the area. As regards economic factors, to the panel included investment in R&D as an indicator of economic carrying capacity despite its lower score in the rounds, as legal security of the concession was initially established as a determining factor due to the industry perception that it is necessary to a certain degree. This factor thus reflects the willingness of companies and administrations to contribute to the improvement of current farming systems by increasing their efficiency through participation in R&D projects.

Selection of ranges and weighting values
While the selection of the model factors was guided by the considerations described above, the experts also called on their personal suggestions, opinions and experiences to agree on the ranges and weighting values. In considering what increases in production from the 50 t/ha threshold could be allowed to produce similar effects when a facility's assimilation rate was high, its spatial organisation adequate and its location in deeper sites, away from both priority habitats and facilities, with high current velocity and with feasible social and economic impacts, the experts established optimal, partial and adverse scenarios for basal production (Table 2).

Readjustment of the model
The project's technical team then analysed the model, detecting inconsistencies and difficulties in data collection and observing a high restrictive power in 72.4% of the facilities analysed (Table 3). After informing of this limitations, the experts considered the option of modifying some of the model's factors; changing their multiplier values and numerical range; or even substituting factors where applicability was complex. Round 3 thus ended with a final readjustment to three of  its factors-space arrangement of the concession, distance to priority habitats and depth (Table 4)-and the replacement of two of them-food conversion rate and investment in R&D (Table 5).

Readjustment of the factors
Some of the factors of the model were difficult to implement in real situations of the activity, and the technical team of the project had some reservations regarding real reference values of the facilities; the Delphi expert panel therefore proposed a readjustment in the ranges of the factors space arrangement of the concession and the depth below the floating cages. First, they split the lowest multiplier value for space arrangement of the concession (<1) into two ranges, <0.5 and 0.5-1, as they considered these values to be the only ones with the power to decrease the carrying capacity of the system, and second, they established an a priori appropriate depth of 30-40 m. Furthermore, based on the premise that all aquaculture facilities should be located in an area which has been considered a suitable site for aquaculture, the Delphi expert panel proposed a change in the ranges and weighting values for distance to priority habitats, thereby decreasing the model's restriction on the effects that the activity may have on adjacent habitats. The experts considered a distance of 1 nm to a priority habitat for conservation to be a considerable distance at which the effects of the activity on the seabed would no longer be detected (Pérez et al., 2008). In this case, they set 1.2 nm as the distance at which the activity would not affect the seabed of priority habitats for conservation.

Substitution of factors
In view of the difficulty in applying certain factors of the model and, consequently, its possible rejection by the administrations as a viable system for regulating aquaculture, the Delphi expert panel proposed a series of alternatives for the change in the food conversion rate and investment in R&D factors (Table 5). First, they proposed three alternatives as the most representative in terms of the most realistic way to determine the amount of organic matter discharged into the environment, and two to encompass the economic aspects of the activity. For the first factor (food conversion rate), the alternatives they proposed were based on the amount of feed provided, either by tonnes of feed produced, by cost-value of sale or by year-area of concession; and for the second one (investment in R&D), alternatives were based on unit cost of production and the price of first sale. Among all the alternatives, the Delphi panel of experts selected the tonnes of feed supplied per year per hectare of concession (tonnes feed per hectare) and the amount of money it costs to produce one kilogram of fish in each facility (unit cost of production), for their generalist behaviour in representing the reality of the nutrient input to the environment and for their easy applicability and more direct implication in the economic aspects.

Final model
After the substitution of unsuitable factors, and modification of some ranges and weighting values of the model (Table 6), and applying it to real operational conditions, we found that the results showed an acceptable restriction (Table 7). Taking the production granted by the administration as the potential annual production value of each concession, we found 24.1% of the concessions to be below the estimate of the carrying capacity (same as with the preliminary model), 24.1% to be around the maximun carrying capacity (13.8% with the preliminary model) and 51.7% to exceed the carrying capacity calculated by the model (62.1% with the preliminary model). All in all, and subject to the execution of an in-situ validation of the model, the Spanish Mediterranean aquaculture production may be sustainably increased by 47.5% (from 79,440 to 117,162 t/year). However, marine fish production in Spain is far from reaching even the granted production (79,440 t), being in 2021 close to 40,000 t (APROMAR, 2022). The latter suggests that carrying capacity should be addressed in terms of holding capacity (i.e. maximum biomass that can be held in a facility at a given time) rather than the annual production, although both values should be closely connected, their values might be significantly different.

Conclusions
Despite the great effort of the scientific community to implement the concept of 'carrying capacity' in aquaculture planning and management (Weitzman and Filgueira, 2020;Weitzman et al., 2021), its application remains complex. Several recent studies have established carrying capacity as a potentially important tool in the assessment of the ecological, productive and social sustainability of aquaculture (McKindsey et al., 2006;Weitzman et al., 2021), yet the lack of interdisciplinary and integrated frameworks to assess carrying capacity in a holistic way remains (Guyondet et al., 2010;Weitzman et al., 2021) based not only on bivalve culture-which is well studied (Inglis et al., 2000;Filgueira et al., 2020)-but also on finfish culture (Karakassis et al., 2013). Ours is thus the first study to generate consensus on the need to address carrying capacity in a holistic and innovative way (McKindsey et al., 2006;Weitzman et al., 2021) by developing simple and effective models. Our model does not explicitly consider conflict with other users, the latter being globally identified as a constrain in the spatial expansion of marine aquaculture (Galparsoro et al., 2020). Therefore, it seems clear that Table 7 Results of the final model, where BP is the basal production in t/ha and V is the weighting value for each of the factors.

Farm
Hectares it must be coupled with a maritime spatial planning strategy that identifies suitable areas for aquaculture in which the model will address maximum holding capacity. Modelling by consensus methodologies, involving all stakeholders of the activity, is one of the fundamental pillars in the sustainable development of an activity, of necessity considering a wide variety of perceptions as a relevant part of marine aquaculture management and planning (Robertson et al., 2002;Foley et al., 2005;Mazur and Curtis, 2008;Chu et al., 2010;Ross et al., 2013). Insufficient involvement of stakeholders could lead to resource mismanagement and the emergence of social conflicts (Kaiser and Stead, 2002;Shindler et al., 2002;Buanes et al., 2004). Thus, the development of aquaculture management models should be based on the estimation of carrying capacity through effective stakeholder participation, where both present and future conditions of the activity are assessed through simple sustainability indicators encompassing all aspects of the activity (McKindsey et al., 2006). Simple models have been shown to be as accurate as complex models requiring much more information (Sakamoto, 1966) and they will be adopted as a final regulatory system only if they are feasible. In applying the Delphi technique in our study, we have achieved consensus on the development of a simple model for the estimation of carrying capacity for open sea fish farming in floating fisheries off the Spanish Mediterranean coast based on physical, environmental, social and economic factors. The incorporation of social and economic aspects in the model renders it holistic and innovative, as no previous study to date has included all the components of the activity in the same model. Most studies have focused only on the productive and ecological aspects of the activity, ignoring the socio-economic aspects due to their possible subjectivity and dependence on the environment in which the activity takes place (Guyondet et al., 2010). This model is therefore an example of how the carrying capacity could be incorporated in the planning and management of marine aquaculture. The need to develop an in-situ validation of the model after observing an acceptable level of constraint in its theoretical application will inform future projects.

Funding sources
We carried out this project with the collaboration of Fundación Biodiversidad, the Ministerio para la Transición Ecológica y el Reto Demográfico and through the Pleamar Programme, and were cofinanced by FEMP.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request. "Environmental Innovation Measures for the Development and Establishment of Protocols for Carrying Capacity for Aquaculture Sustainability (MIMECCA)"; "Marine Aquaculture Carrying Capacity Applied Models (MACCAM)"; "GLObal change Resilience in Aquaculture-2 (GLORiA 2 )," supported by the Biodiversity Foundation of the Spanish Ministry for the Ecological Transition and Demographic Challenge, through the Pleamar Program and co-financed by the European Maritime and Fisheries Fund (EMFF). It is also part of the LIFE IP INTE-MARES Project "Integrated, innovative and participatory management of the Natura 2000 Network in the Spanish marine environment". This study forms part of the ThinkInAzul programme and was supported by MCIN with funding from European Union NextGenerationEU (PRTR-C17⋅I1) and by Generalitat Valenciana (THINKINAZUL/2021/044-TOWARDS).

Appendix I. Relevance of the sustainability indicators identified in Round 1
Sustainability indicator Mean level of importance Round 1 Number of professional associations 6.83 National training in aquaculture 7.00 Existence of a national aquaculture strategy 7.00 Annual marine fish aquaculture production at national level 7.50 Quantity of fish produced for domestic markets and apparent consumption 3.33 Price of fish compared to the minimum wage 4.33 Percentage of farmers with specialised and certified training in aquaculture 7.67 Number of hours per month currently worked by aquaculture workers 6.00 Economic Market-oriented aquaculture (in-company market strategy) 7 Diversification of goods and services 6.66 Sales price development 5.83 Evolution of total aquaculture production value 6.0 Existence of quality certification systems 6.33 Cost of feed /kg fish produced (and % of total) 6.17 Cost of fry /kg (and % of total cost/kg) 5.83 Investment in aquaculture R&D 6.33 Legal security of the concession 7.33 Duration of an authorisation/concession 6.83 Number of domestic hatcheries (and % imported) 4.17 Existence of a national support mechanism for aquaculture 5

Appendix II. Relevance of the sustainability indicators identified in Round 2
Sustainability indicator Mean level of importance Round 1 Mean level of importance Round 2

Technical and Production
Food conversion rate 7.5 8.5 Percentage of space used (%) new 10 Volume of water occupied per kg of product (Kg/m 3 ) 6.5 Distance between facilities new 8.5 Implementing an Environmental Monitoring Plan (EMP) 7.65 excluded Compliance with code of good practice 6.83 excluded Existence of a well-defined aquaculture environmental policy, programme and/or strategy.
6.33 excluded Distance to the coast 6.50 excluded Carbon footprint index 5.67 excluded

Environmental
Distance to priority habitats new 10 Depth 8.5 9 Microbiological indicators 5.67 8 Oxygen saturation 5.83 Existence of common criteria for site selection 7.33 7 Current velocity 8.67

Social
Sustainability or staff turnover rate 6.67 10 Quantity and quality of employment 7.17 Communication effort 7.17 7.11 Employee-management relations 7.33 Number of professional associations 6.83 National training in aquaculture 7.00 excluded Existence of a national aquaculture strategy 7.00 excluded Annual marine fish aquaculture production at national level 7.50 excluded Quantity of fish produced for domestic markets and apparent consumption 3.33 excluded Price of fish compared to the minimum wage 4.33 excluded Percentage of farmers with specialised and certified training in aquaculture 7.67 excluded Number of hours per month currently worked by aquaculture workers 6.00 excluded

Economic
Market-oriented aquaculture (in-company market strategy) 7 8 Diversification of goods and services 6.66 Sales price development 5.83 Evolution of total aquaculture production value 6.0 Existence of quality certification systems 6.33 Cost of feed /kg fish produced (and % of total) 6.17 Cost of fry /kg (and % of total cost/kg) 5.83 Investment in aquaculture R&D 6.33 Legal security of the concession 7.33 9 Duration of an authorisation/concession 6.83 (continued on next page)