A Bayesian Approach to Carrying Capacity Estimate: The Case of Greek Coastal Cage Aquaculture

Abstract

The estimation of the carrying capacity (CC) is a fundamental process in integrated environmental management, policy making, and decision making. Aquaculture carrying capacity has been studied since the 1960s to allow estimation of the production limits of aquaculture projects and, hence, their maximum economic performance within sustainable limits for the local environment. One major drawback of these approaches is that they can provide CC estimates after a fish farm is installed and operates in a certain location (ex post approaches). This paper approaches the estimation of CC using a Bayesian/CHAID model of profiling information on the environmental quality, geomorphology, and human activities on the adjacent coastal area (land side) using as an indicator the trophic state of the marine area in terms of chlorophyll-a concentration (upper mesotrophic). This way, having the above information for a certain site, it is possible to calculate the maximum annual production of a cage fish farm so that the trophic state of the area will not exceed the environmental goal of the upper mesotrophic level. We examined the effects of 27 different physical, chemical, social and geomorphological parameters on CC (in fish biomass terms). CC was found to be correlated by particulate nitrogen (PN), silicates (Si-SiO₄), salinity, and suspended particulate matter (SPM). The overall relationship found is: Biomass_{at CC level} = +473.762[Chl-a] − 6856.64[PN] + 9.302[Salinity] − 473.5[Si-SiO₄] + 341.864[SPM] − 207.046. The analysis performed allowed us to estimate the maximum levels for each factor to maintain a eutrophication status up to the upper mesotrophic level: particulate nitrogen < 0.018 mg/L, silicates < 0.137 mg/L, salinity > 38 PSU and SPM > 0.815 mg/L. Finally, the current fish farm licensing legislation in Greece concerning the CC estimation algorithm is discussed.

1. Introduction

Carrying capacity is a fundamental property of the coastal environment and an important piece of information for integrated coastal zone management plans using the ecosystem approach [1,2]. In simple terms, CC is a measure of the maximum sustainable pressure that a specific environment (based on its characteristics and geomorphology) can receive from a human activity (such as the case of aquaculture) before it loses its full resilience capabilities or the particular activity becomes a limiting factor. The term has been used to conceptualize several aspects of environmental pressure such as the population CC described by Malthus [3], without using the term carrying capacity, and others: for example, water resources CC, tourism CC, ecological CC, social CC and urban CC [4,5], all the way to the population CC of Earth [6]. For historic purposes, the term CC was first used in a report to represent the maximum load of a merchant ship by the Secretary of State to the Senate in 1845 [1]. The CC level can be considered as the balance point between economic development, environmental protection and environmental sustainable exploitation [1].

The effects of aquaculture on the marine ecosystems has been the focus of a large number of EU funded projects such as AQCESS, BIOFAQ, MedVeg, ECASA, SAMI, MERAMED, OrAQUA, AQUAMED, AQUASPACE, MARIBE, DIVERSIFY and MEDAID, to name a few [7]. There is a consensus regarding the effects of aquaculture regarding the loading of the marine environment with nitrogen and phosphorous nutrients organic waste from excretory products and feed losses, sedimentation of organic matter, reduced dissolved oxygen concentration consumed for the aerobic decomposition of the organic matter and excessive growth of certain organisms such as phytoplankton and benthic assemblages, even though such cases are scarce due to the dispersion of the nutrients with currents and waves and the oligotrophic nature of the East Mediterranean basins (including Greek seas). In addition, cage fish farms act as fish aggregation devices attracting wild fish population of coastal species creating a conflict with small scale fisheries. Finally, some ecosystem effects have also been recognized, especially the possibility of interaction of escapees (sea bass and seabream) with the wild populations and potential genetic interference with local strains [7].

Carrying capacity is the maximum level of environmental pressure exerted by human activities without the permanent natural and physical deterioration of an area’s ability to continue to provide ecosystem services qualitatively and quantitatively. Carrying capacity is a multidimensional concept, since its estimate is based on environmental (natural capital, biodiversity, water quality), physical (infrastructure, number of farms allowed, effects on other local infrastructure) and psychological (social, perceptual) impacts [8]. Carrying capacity depends on the local conditions and site characteristics, and thus, CC levels cannot be estimated for large areas [9].

Aquaculture has shown a fast development over the last 30 years. In 2014, the global annual production from aquaculture was higher than the annual production of capture fisheries in 2014 [1], thus becoming an important source for animal protein for human consumption [10]. Early on during aquaculture development, concerns regarding its environmental impact on the coastal zone were raised. Recently, the social acceptability of aquaculture has been re-examined as an important aspect in aquaculture development and investments [11] and a very important management indicator for the establishment of aquaculture allocated zones (AZA; [12]). Considering the importance of aquaculture for human nutrition and economy at a global scale, the improvement of the estimation of CC, especially before the installation and operation of a fish farm, is valuable for the proper licensing of the farms in terms of maximum annual production per site.

Several tools have been used and approaches adopted for the estimation of CC for a given location. However, the first step is common and involves the determination and setting of the specific goals, objectives, and priorities in environmental management. Usually, these take the form of one or more indicators, which should not be exceeded by the fish farming operation. Based on the indicator(s), suitable and relevant information are collected either from in situ field studies or the literature fed into predictive models or empirical studies which all lead to the estimation of CC. Models can be simple calculated sustainability indicators [13,14], mathematical production models/scope for growth models/energy budget models/nutrient budget models [15,16] and spatial tools based on single or multi-criteria GIS applications [17]. In relation to social acceptability, stakeholder involvement tools are usually applied besides the above [18,19,20]. The main drawback of these approaches is that CC can be evaluated after the installation and operation of a fish farm by evaluating indicators or collecting model data within a cyclical process based on the standard sequence of policy application, effect evaluation, reconsideration and adaptation. This approach may provide significant results for sustainable aquaculture, but it is not suitable to provide a stable operational and financial environment for business. In some cases, the models which are used or proposed for the estimation of the relationship between the use of resources and production are linear (for example, see [21]), while it is obvious that within a certain balanced existing biological–geological–economic–social system (as any coastal area is), this relationship should be non-linear with a maximum at the CC value [22] following a Verhulst logistic or Malthusian curve [23,24]. It is true that such equations are highly simplistic and much more of heuristic than practical value, since only a few populations follow a logistic growth [24] and, furthermore, lack the effect of societal behaviour on population dynamics. However, such models include the K parameter, which is the upper limit (equal to the CC) of development enhancing the mathematical stability of the modelling process.

This paper focuses on the elaboration of a novel approach in CC estimation for coastal cage aquaculture development based on Bayesian methodology, using physical and chemical quality of seawater and sediment data, information on local land use from specific aquaculture sites (urban areas, etc.) and the data on the geomorphology of the coastal area (openness, protected/unprotected site, depth, etc.). The deliverable of this work is an application programmed in the Orange data mining platform [25] which enables the ex ante identification of the environmental issues related to the establishment and operation of a coastal fish farm. The basis of our approach is to use the above data in a Bayesian/CHAID with the objective being to identify the most important environmental parameters which affect eutrophication of cage aquaculture sites. In addition, we aim to estimate the minimum or maximum values of these parameters so that the eutrophication of the area due to the operation of a cage farm, will not exceed the upper mesotrophic level (in terms of chlorophyll-a concentration).

2. Materials and Methods

2.1. Data Type and Origin

Eight marine cage farm sites in Greece were selected for the collection of physicochemical and geomorphological data coded S01 to S09 (Figure 1). Please note that information from S03 was not used, since this is a coastal shellfish culture farm. All fish farms are coastal cage farms producing mainly European sea bass and gilthead seabream. In addition, specific information per farm such as licensed production, species, and production scheme were collected through face-to-face interviews and questionnaires (

Table 1. Fish farm location, configuration and production characteristics.

Code	Geographical Location (Decimal Degrees)	Number of Cages	Annual Licensed Production (t)
S01	38.9164 N; 22.9175 E	64	2200
S02	38.8469 N; 22.7139 E	126	1270
S04	38.6508 N; 23.1042 E	34	200
S05	38.5628 N; 23.3231 E	64	390
S06	38.3628 N; 24.0467 E	57	750
S07	38.0800 N; 24.2817 E	75	575
S08	38.3375 N; 22.6792 E	32	150
S09	38.3378 N; 22.3850 E	43	379

).

Water samples from each fish farm were collected monthly during the period 2015–2016 (March 2015–May 2016) at 1 m below the surface and 1 m above the bottom, using 8-l Nisskin samplers. Seawater samples were taken below the cages from one or two locations, depending on the size of the area covered by the farm cages. The average values were used. Vertical profiles of salinity and temperature were acquired at every station using a SEABIRD-19 CTD. Seawater samples were analysed for determining suspended particulate matter (SPM), total organic carbon (TOC), particulate organic carbon (POC), particulate organic nitrogen (PON), particulate organic phosphorus (POP), dissolved oxygen (DO), dissolved inorganic nitrogen (DIN = ammonium (NH₄⁺) +nitrates (NO₃⁻) +nitrites (NO₂⁻)), soluble reactive phosphorus (PO₄⁻³), total nitrogen (TN), total phosphorus (TP) and chlorophyll-a (chl-a). For determining dissolved oxygen (DO), samples were first taken from the sampling bottle with the recommended precautions to prevent any biological activity and gas exchanges with the atmosphere and ‘fixed’ immediately after collection, on board with the Winkler method according to [26]. Seawater samples were collected in 100 mL polyethylene bottles ‘aged’ with HCl 10% and rinsed 3 times with distilled water and 3 times with the filtered sample. Seawater samples from each depth were collected in triplicate. The samples for determining nutrients were filtered through membrane Millipore filters 0.45 μm immediately after the sampling. Then, the filtered seawater samples were kept deep-frozen (−20 °C) until their analysis according to the ELOT EN ISO/IEC 17025 procedure using a SEAL III autoanalyzer according to standard methods for silicates, nitrates, nitrites, and phosphates and a UV/VIS spectrophotometer for ammonium. Samples for determination of total nitrogen (TN) and total phosphorus (TP) were collected in 50 mL Pyrex bottles. The samples were kept continuously under deep freeze (−20 °C) in the dark until their analysis in the lab, according to the oxidation method [27]. Water samples for TOC analysis were collected in pre-combusted (480 °C, 12 h) glass ampoules, acidified with 2.5 M HCl to pH~2, and flame-sealed immediately on board. TOC analysis was carried out in the laboratory following the catalytic oxidation method using a SHIMADZU TOC-5000 [28]. Seawater samples for the particulate organic carbon (POC), particulate organic nitrogen (PN) (1–2 L for each parameter) and the particulate phosphorus (PP; 0.2–0.3 L) determination were filtered through Whatman filters pre-combusted at 450 °C. Filters were stored in Petri dishes and kept continuously under deep freeze (−20 °C) in the dark until their analysis in the lab. POC and PN were measured on an EA 1108 CHN Fisons Instruments CHN analyser [29]. PP was determined using a persulfate wet-oxidation method and finally measured using a SEAL III nutrient autoanalyzer [27]. The samples for determining chl-a concentration (1.5 L for each depth), were filtered through Whatman GF/F filters (Ø47 mm and pore opening 0.45 μm) and kept continuously under deep freeze (−20 °C) in the dark until their analysis in the lab using a TURNER 00 AU-10 fluorometer [30].

Geomorphological features of each farm location were measured using online satellite products such as Google Map, Google Earth, and ETOPO-1 online [31] and cartographic techniques using onscreen tools such as angle and distance callipers [32]. The main parameters are summarised and explained in

Table A1. Annual average physical and chemical data at the fish farm locations.

Station	Statistic	EUTR Scale	Temp (5 m)	Sal (5 m)	DO	Depth (m)	Watershed, km²	Inhabitants, No	Effective Fetch, km	Coastal Area, km²	Max Depth, m	Section Area, km²	Exposure	Tp, Days	N-NO3, mg/L	N-NO2, mg/L	N-NH4, mg/L	Si-SiO4, mg/L	P-PO4, mg/L	TN, mg/L	TP, mg/L	POC, mg/L	PN, mg/L	PP, mg/L	Chl-a, mg/m3	SPM, mg/L
S01	Mean	3.000	19.14	36.92	7.32	45	88.9	0	2.0	0.66	60	0.177	26.818	0.112	0.012	0.002	0.007	0.086	0.001	0.109	0.006	0.140	0.017	0.002	0.471	0.741
	St. Dev.	0.739	4.86	0.75	0.60										0.013	0.001	0.003	0.047	0.001	0.028	0.002	0.039	0.005	0.000	0.175	0.293
	Min	2	13.05	35.85	6.45										0.005	0.001	0.004	0.040	0.000	0.080	0.004	0.082	0.007	0.001	0.202	0.435
	Max	4	27.05	37.68	8.31										0.052	0.004	0.013	0.209	0.005	0.167	0.011	0.216	0.025	0.002	0.792	1.295
S02	Mean	3.500	18.77	36.60	7.26	20	1907.2	17,814	34.0	87.30	50	0.330	0.378	6.614	0.005	0.002	0.011	0.117	0.001	0.125	0.009	0.201	0.027	0.003	0.891	1.151
	St. Dev.	0.905	4.95	0.44	0.69										0.002	0.002	0.003	0.053	0.000	0.019	0.003	0.038	0.008	0.001	0.648	0.323
	Min	2	12.68	36.08	6.06										0.002	0.000	0.006	0.045	0.000	0.109	0.006	0.136	0.019	0.002	0.261	0.723
	Max	5	26.59	37.27	8.11										0.009	0.005	0.018	0.228	0.002	0.172	0.016	0.258	0.047	0.005	2.619	1.600
S04	Mean	3.167	19.29	37.08	7.42	15	14.7	1070	53.6	46.60	50	0.417	0.895	2.794	0.007	0.001	0.011	0.119	0.001	0.122	0.007	0.209	0.029	0.002	0.545	1.109
	St. Dev.	0.718	5.52	0.25	0.65										0.002	0.001	0.003	0.062	0.000	0.015	0.001	0.042	0.007	0.001	0.175	0.195
	Min	2	12.44	36.76	6.46										0.004	0.000	0.007	0.065	0.000	0.103	0.005	0.165	0.021	0.002	0.297	0.845
	Max	4	27.59	37.65	8.39										0.010	0.003	0.017	0.266	0.001	0.161	0.010	0.304	0.048	0.004	0.921	1.538
S05	Mean	2.667	19.38	37.03	7.10	58	15.6	883	36.9	27.70	77	0.600	2.167	1.777	0.024	0.003	0.021	0.165	0.003	0.148	0.009	0.162	0.025	0.003	0.444	0.635
	St. Dev.	0.778	5.25	0.12	0.64										0.006	0.002	0.009	0.058	0.001	0.017	0.003	0.087	0.008	0.001	0.226	0.248
	Min	2	12.45	36.87	6.23										0.018	0.001	0.005	0.101	0.002	0.128	0.005	0.000	0.012	0.001	0.134	0.285
	Max	4	27.53	37.24	8.23										0.040	0.009	0.041	0.312	0.006	0.184	0.014	0.294	0.034	0.005	1.012	1.165
S06	Mean	2.667	19.04	38.21	7.23	38	44.0	4827	42.3	36.40	62	0.465	1.277	2.427	0.008	0.001	0.015	0.066	0.001	0.110	0.006	0.180	0.021	0.002	0.453	0.756
	St. Dev.	0.888	4.45	0.29	0.76										0.007	0.001	0.008	0.044	0.000	0.023	0.001	0.039	0.004	0.001	0.322	0.318
	Min	2	13.01	37.88	6.13										0.001	0.000	0.005	0.024	0.000	0.072	0.004	0.129	0.016	0.001	0.144	0.440
	Max	4	25.37	38.95	8.28										0.027	0.005	0.033	0.184	0.002	0.157	0.009	0.254	0.030	0.004	1.321	1.445
S07	Mean	1.917	18.89	38.11	7.55	40	6.6	0	95.2	30.40	84	0.712	2.343	1.792	0.005	0.001	0.009	0.041	0.001	0.088	0.004	0.133	0.015	0.001	0.232	0.633
	St. Dev.	0.289	3.94	0.57	0.80										0.003	0.001	0.003	0.009	0.000	0.015	0.002	0.032	0.004	0.001	0.079	0.385
	Min	1	14.18	37.09	6.42										0.002	0.000	0.003	0.031	0.000	0.065	0.002	0.083	0.009	0.001	0.097	0.200
	Max	2	24.61	38.84	8.96										0.011	0.002	0.015	0.063	0.002	0.106	0.008	0.202	0.024	0.004	0.366	1.310
S08	Mean	2.083	19.77	38.80	7.16	40	3.4	2984	70.6	48.90	100	0.945	1.933	2.587	0.006	0.001	0.011	0.040	0.001	0.093	0.005	0.138	0.018	0.002	0.294	0.463
	St. Dev.	0.669	4.34	0.40	0.48										0.004	0.001	0.008	0.015	0.000	0.016	0.002	0.047	0.007	0.001	0.141	0.106
	Min	1	14.15	38.01	6.26										0.002	0.000	0.003	0.018	0.000	0.064	0.002	0.075	0.010	0.001	0.068	0.175
	Max	4	26.08	39.23	8.04										0.017	0.003	0.035	0.074	0.002	0.133	0.008	0.246	0.030	0.003	0.669	0.600
S09	Mean	2.417	19.66	38.86	7.21	36	4.5	7758	26.4	134.00	200	3.140	2.343	4.268	0.013	0.001	0.018	0.054	0.002	0.120	0.008	0.166	0.020	0.002	0.422	0.601
	St. Dev.	0.669	4.73	0.18	0.73										0.006	0.001	0.013	0.021	0.001	0.031	0.003	0.049	0.007	0.001	0.225	0.167
	Min	2	13.96	38.44	5.82										0.006	0.000	0.003	0.024	0.000	0.073	0.004	0.108	0.011	0.002	0.233	0.260
	Max	4	26.98	39.07	8.30										0.025	0.003	0.046	0.107	0.004	0.187	0.015	0.277	0.034	0.003	1.080	0.805

.

The trophic (eutrophication) state of each location was estimated using a 5-rank scale based on the concentration of chlorophyll-a [33,34]. Each location was assigned with a rank between 1 and 5: 1, oligotrophic; 2, lower mesotrophic; 3, upper mesotrophic; 4, lower eutrophic; 5, upper eutrophic. Sites ranked below 3 were acceptable, while sites ranked higher than 3 were unacceptable [35,36].

In total, we analysed 3 physical parameters (temperature, salinity, and dissolved oxygen), 15 chemical parameters and their derivatives (nitrogen, phosphorus, silicates organic carbon, and particulate matter), 8 morphological parameters (depth, watershed, fetch, openness, coastal area, exposure and water retention time), 1 farm operational parameter (biomass), and 1 social parameter (local inhabitants).

2.2. Software Platform and Statistical Analysis

The model was set in Orange data mining platform version 3.26.0 (free access at https://orange.biolab.si/; accessed on 15 September 2020) using embedded functions [25]. Spearman and Pearson correlations were conducted to examine relationships between the physical, chemical, and geomorphological parameters of the sites and reveal relationships that would be interesting for CC estimation relationships between parameters. Before selecting the correlation test, all parameters were tested for normality using the Shapiro–Wilk test. When all parameters show normality, the Pearson test was used. When all parameters or some parameters do not show normality, the Spearman test was used. Correlation values above 0.7 or below −0.7 were considered significant relevant correlations while values between −0.1 and +0.1 were considered as neutral relevant correlations or no relevant correlations. Canonical correspondence analysis (CCA) was also used to examine clustering relationships between sites based on the environmental parameters and geomorphological factors. Comparison of means was conducted with ANOVA tests and multiple range tests for further analysis of means groupings. Proposed equations were based on the multiple linear regression models and optimum model selection was carried out using the Akaike information criterion (AIC).

3. Results

3.1. Physical and Chemical Quality

The average annual physical and chemical quality data per site are summarised in

Table 2. Geomorphological description of the farm locations.

Feature	Parameter Description and Measurement	Units	Reference or Origin of Data
Cage Depth	The average depth under the farm cages	m	Merchant marine maps, Hellenic Seas; GARMIN plotter files
Watershed area	The land area surrounding the coastal area with such a slope that all runoffs lead to the coastal area	km2	Google online maps; Greek Military Geological Survey Maps at 1:50,000
Inhabitants	The number of permanent inhabitants in the case that a settlement, village, or town is within the micro-watershed area	number, number/ km2	Latest Greek National Population Survey 2011
Effective Fetch	The distance between the fish farm and the opposite land which limits the exposure of the farm site. The distance along the axis of the main effects of the sea (waves)	km	[32]
Coastal Area	The sea area of the gulf or bay into which the fish farm is located	km2	[32]
Maximum Depth	The maximum depth of the coastal area, in middle	m	Merchant marine maps, Hellenic Seas; GARMIN plotter files
Section Area	The vertical area of the opening separating the coastal area and the open sea	km2	[32]
Exposure	It is the ‘openness’ feature of the Coastal Area and is estimated as the ratio: [(Coastal Area)/(Section Area)] × 100	%	[32]
Retention time	The estimated time required to renew the water of the coastal area: Tp = 0.5 × (Area volume/Section area) based on the assumptions that the coastal area is small (1–100 km2) and the tides at the site are insignificant (in Greece normally 0–20 cm)	days	[32]

. The fact that the data include combinations of physical, chemical, and morphological data leading to eutrophication states between 1 and 5 (the full eutrophication scale used) indicates that the data are representative of the rest of the analyses to be conducted. Based on average values, the Redfield ratio was found to range between 15.8 and 22.9. This is in accordance with the original ratio of 16:1 (proposed by Redfield) as well as the recently revised ratio of 22:1 [37].

3.2. Geomorphological Characteristics of Farming Sites

The selection of representative fish farming sites enabled us to obtain a high range of data covering most cases in Greece (

Table 3. Summary of the geomorphological features of the sites.

Feature Description	SE01	SE02	SE04	SE05	SE06	SE07	SE08	SE09	Mean	St. Dev
Average Biomass, t	361.9	1110.5	198.0	86.7	893.2	657.1	126.7	241.4	459.4	382.9
Cage Depth, m	45	20	15	58	38	40	40	36	36.5	13.6
Watershed, km2	88.9	1907.2	14.7	15.6	44.0	6.6	3.4	4.5	260.6	666.0
Local human population (inhabitants) within the watershed, in total number and inhabitants/km2	0	17,814	1070	883	4827	0	2984	7758	4417	6042
	0	9	73	57	110	0	878	1724	356	626
Effective fetch, km	2.0	34.0	53.6	36.9	42.3	95.2	70.6	26.4	45.1	28.4
Coastal Area, km2	0.7	87.3	46.6	27.7	36.4	30.4	48.9	134.0	51.5	41.3
Maximum Depth, m	60	50	50	77	62	84	100	200	85.4	49.5
Section Area, km2	0.2	0.3	0.4	0.6	0.5	0.7	0.9	3.1	0.8	1.0
Exposure, %	26.8	0.4	0.9	2.2	1.3	2.3	1.9	2.3	4.8	8.9
Retention time, days	0.1	6.6	2.8	1.8	2.4	1.8	2.6	4.3	2.8	1.9

). The fish biomass cultured during the study period ranged between 87 and 1110 t of fish. Commonly, Greek fish farms are licensed for an annual production of between 200 and 500 t, but licenses for an annual production of over 1000 t exist, though in limited cases. From experience in site selection for coastal cage fish farms, the depth under the cages usually should not exceed 50 m, since its placement and maintenance by divers are very complicated and expensive. In addition, to provide optimum water exchange through and under the farm nets, minimum depth cannot be less than 20 m (as a rule of thumb, double the maximum net height).

3.3. Correlations

Spearman correlation analysis showed a few significant relationships between parameters (p-value denotes the probability that the correlation is 0):

• Salinity was strongly related to Section Area (0.857; p = 0.0089) indicating that the inflow of open seawater affects salinity in the farm location
• Si-SiO₄ is strongly related to Total N (value = 0.88; p = 0.0078). This relationship seems to be owed to their importance for the algal growth and, hence, chl-a concentration [38].
• Total N is strongly related to Total P (value = 0.93; p = 0.0017), Particulate N (value = 0.88; p = 0.009) and Particulate P (value 0.98; p = 0.0002). The direct relationship of Total N with other forms of N (here the particulate N) can be expected as Total N includes all N forms in the water. On the other hand, a strong relationship between Total N and forms of P can be explained through the Redfield ratio and their direct relationship to chl-a [39].
• Total P is strongly related to Particulate P (value = 0.95; p = 0.001).

3.4. Site Profiling and Carrying Capacity Component Estimates

The relationship between the annual state of eutrophication and chl-a concentration shows clearly that the cultivated fish biomass is not a pressure that results in the deterioration of the eutrophication state. This holds for farm S02, which holds on average the largest biomass of the rest. However, much smaller farms such as S01 and S04 have similar chl-a concentrations as other farms with good eutrophication status such as S05, 6, and 9. The smaller farms, i.e., S07 and 8, show good eutrophication status and exhibit the smaller biomass (Figure 2).

Following this, we analysed the relationship between the monthly state of eutrophication per farm with all physical, chemical, morphological, farm and social parameters to obtain a general view of which parameters are important pressures that govern the state of eutrophication (Figure 3). Data show that important factors in the case of the eutrophic state are mostly geomorphological and social (watershed, coastal area, human population, and organic P) while the mesotrophic (and below) state is mostly related to section, nutrients, and retention time. The graph in Figure 3 shows that all eutrophic status is correlated with the farms with high biomass.

The application of the Bayesian–CHAID algorithm based on the monthly data of all parameters measured allowed the identification of the important parameters which allow for a good eutrophication state and their maximum values above which the eutrophication state changes to bad (i.e., lower or upper eutrophic environment) (Figure 4). These are biomass, particulate nitrogen, salinity, silicates, and suspended particulate matter (SPM) (Figure 4).

The results show that the CC model in terms of biomass is related to the following factors: organic phosphorous, salinity, and silicates. We have also added chlorophyll-a concentration and the environmental state based on the used eutrophication state with values 1–5 as:

Biomass = f(chl-a, particulate Nitrogen, Salinity, Silicates, SPM)

We have calculated the above relationship based on a multiple linear regression model as follows, setting the eutrophication state value at 3, which is the maximum:

Biomass = +473.762 × Chl-a − 6856.64 × PN + 9.302 × S − 473.5 × Si-SiO₄ + 341.864 × SPM-69.015 × Scale = 473.762 × Chl-a − 6856.64 × PN + 9.302 × S − 473.5 × Si-SiO₄ + 341.864 × SPM-207.046

r² = 0.67, std. error of estimate = ±359.9 t.

For a better mathematical correlation, the same model was estimated using log₁₀-transformed raw data:

logBiomass = +0.056 × logChl-a − 0.366 × logPN + 1.001 × logS − 0.246 × logSi-SiO₄ + 0.658 × logSPM − 0.153, r² = 0.977

A similar form of the model was also estimated to facilitate ease of use, using a semi-log model where all variables are in log₁₀ form and biomass in raw form (t):

Biomass = −50.2518 × logScale + 314.808 × logChl-a − 243.877 × logPN + 63.576 × logS − 153.288 × logSi-SiO₄ + 489.655 × logSPM = +314.808 × logChl-a − 243.877 × logPN + 63.576 × logS − 153.288 × logSi-SiO₄ + 489.655 × logSPM-23.976 = r² = 0.655, std. error of estimate = ±378.8 t.

The normality test per parameter showed that a hypothesis of normality cannot be rejected (p values > 0.05;

Table 4. Pearson moment correlation table between the selected factors (p values show normality probability).

	Biomass (p = 0.1709)	Chl-a (p = 0.1717)	PN (p = 0.4225)	Salinity (p = 0.2153)	Si-SiO4 (p = 0.3749)	SPM (p = 0.1398)
Biomass		0.3548	0.0505	n.s.	n.s.	0.3336
		n.s.	0.6252	0.0972	0.5802	n.s.
Chl-a			0.3696	−0.2891	0.2110	0.4642
			n.s.	n.s.	n.s.	n.s.
PN				−0.4161	0.3901	0.4746
				n.s.	n.s.	n.s.
S					−0.3973	−0.4413
					n.s.	n.s.
Si-SiO4						n.s.
						0.2453
SPM

Values stated in the table are significantly different from 0 at p = 0.05 level. The upper value is the Pearson moment correlation coefficient, and the lower value is the probability of non-zero correlations at 95% confidence level; n.s., not significant.

), and therefore, the Pearson correlation test was used. The correlations between the selected factors are summarised in Table 4. The results show that all pairwise correlations are statistically significant (p values < 0.05) except the pairs between biomass and particulate nitrogen, salinity, and silicates and the SPM–silicate pair.

4. Discussion

4.1. General Comments

Modern coastal aquaculture development goal has been the increase in production based on the principles of sustainability and the holistic ecosystem approach to management of both the farms and the surrounding coastal zone. Initially, there were only a few design principles for the proper design of a cage farm in terms of production and the proper location of the cages based on the sea depth and the local hydrology (currents, waves), and local weather, all of which can be characterized as ‘short-sighted’ and of ‘short-term’ value [40]. Along the way, based on experiences around the world, more principles were considered, such as the minimization of the environmental impact of the production and the social acceptance of the farms close to the coastal zone, to account for environmentally induced problems (diseases, high mortalities, etc.) and the generation of conflicts between users [40]. Moreover, all recent EU (and others) policies, directives, and regulations consider the CC as one of the important tools which can serve as the upper limit of any human economic activity (MSFD, MSP, Water Directive, etc.).

Within the ecosystem approach to coastal management, CC is an important concept that describes the maximum production capacity of any given fish farm in any given coastal location, so that certain environmental, social, financial, and ecological goals and legislation and policy objectives are met. Carrying capacity is a customized toolbox that includes all the relevant methods and instrumentation required for the estimation of the impact of a fish farm on the particular rules and goals set for a given coastal location and for this reason CC is of local importance [9]. In Greece, following a Ministerial Decision (121570/1866/2009) based on the results of an ad hoc funded project [21], the CC of a fish farm (maximum allowed annual licensed production tonnage) is estimated based on the following formula:

$$\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{Pr}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}, \mathrm{t}/\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}=\left[150+8\left(\mathrm{E}-1\right)\right]\cdot {\mathrm{f}}_{\mathrm{A}}\cdot {\mathrm{f}}_{\mathrm{B}}\cdot {\mathrm{f}}_{\mathrm{C}}$$

where E is the leased sea area of the farm (licensed acreage calculated in hectares), f_A is the distance from the coast factor (values between 1 and 2 for distances <100 m to >1000 m), f_B is the depth at the middle of the farm leased area (values between 0.9 and −2 for depths between <20 m to >60 m), and f_C is a factor based on the morphology of the coastal area (exposed, open or closed gulf with values between 1 and 2.5 for closed/protected areas, open areas, exposed areas, and highly exposed areas).

At a glance, this oversimplified approach may serve as a tool to cover the need for CC estimation and provide a basic production value for the needs of fish farm licensing, especially in the absence of other more reliable methods. However, it fails to incorporate into the calculations equally important factors such as the current/wave directions, the type of the sediment and the bioaccumulation potential of the area, and all land-originating processes which contribute to the amounts of materials and pollutants towards the particular coastal zone. However, the most important issue with this approach is the fact that the model does answer the main question, “Which aspect of the environment is preserved by setting the maximum production of a fish farm based on this model?” In other words, “How will the environment deteriorate if a fish farm will produce more fish than the equation estimates?” According to [41], to estimate the CC of a given area, the relationship between the production of the farm and a certain impact needs to be established.

We believe that any CC model should include factors related to the pressures (in this case the biomass of fish cultivated), the determining factors (such as the morphology of the area, land and sea effects, etc.), and the environmental goal following the full operation of the farm (for example, eutrophication thereafter to be below z mg/m³ in terms of chlorophyll-a or NOx below y mg/L level or similar). As Stigebrandt [41] correctly states, Carrying capacity is defined as the maximum biomass of a farmed species that can be supported without violating the maximum acceptable impacts to the farmed stock and its environment. Maximum acceptable impacts on the farmed stock and the environment are expressed by standards for water quality in the farm and the surrounding environment. Environmental quality standards are established in a political process [41,42]”. According to this definition, it is clear that CC estimation needs to consider the acceptable impacts on the environment set as standards of water quality, all of which are missing from the aforementioned approach. Similar approaches have been used for other sectors such as tourism [42]. Taking as an example a study conducted on the Aegean coast of Turkey [43], which follows exactly the aforementioned study [21], it was estimated that the annual production of the area can increase from the current level of 11,800 t/year to 27,694 t/year, stating that “Based on the results of the present study, the total production capacity of fish farms in the allocated potential aquaculture site off the Cittaslow town-Sigacik is below acceptable limits according to physical carrying capacity estimations for the study area. [43] (p. 9758)”, while at the same time they add that “long-term monitoring with biological investigation of the water column and bottom sediments is encouraged. [43] (p. 9758)”, obviously understanding that this approach is a proxy that does not provide any information on the state of the environment after the increase in production and indicating that this approach is of extremely limited value since, according to the authors, any change in the production needs to be followed by further studies and monitoring, thus adding to the management cost of a given coastal area, to prove that the change in production is below or equal to CC or we have an overshoot status [22].

4.2. The Model

Using a Bayesian approach to estimate a model for the estimation of the CC of a given coastal area for cage fish farming, we succeeded in including, within one formula, factors related to the environmental goal (i.e., the eutrophication level related to chl-a concentration, and keeping the environment always equal or below high mesotrophic state) as well as statistically important factors related to natural pressures on the coastal area. There are more complicated and, possibly, more accurate approaches such as the use of the models ECOPATH [19], CORMIX, DEPOMOD, WASP, TRISULA, MOM, and GIS-based Multicriteria Analysis [44], but one of the aims of this approach is to create a model which can be used by anyone with different levels of education or expertise (for example, public administrators).

The results showed that the CC of the studied fish farm areas (measured as the maximum cultivated biomass so that the eutrophication level remains always at the upper mesotrophic level or below), is affected by the following parameters (ranked from most important to least important): particulate nitrogen, salinity, silicates and suspended particulate matter. According to the model estimated, the CC, in terms of maximum fish biomass cultivated, is positively affected by SPM, chl-a and salinity, while it is negatively affected by particulate nitrogen and silicates. It was expected that chlorophyll-a relation with biomass would be negative, i.e., the coefficient of chl-a in the equation should be a minus. We consider that this irregularity in the proposed model occurred because the range of raw data included much better than bad eutrophication states (75 cases versus 21 cases, overall, the data set, respectively) and only a few states 4 or 5 (i.e., lower and upper eutrophic: 20 cases and 1 case, respectively, out a data set of 96). The analysis of elasticities based on the log–log model we estimated shows that the effect of chlorophyll on biomass, even as positive as it seems, does not contribute to the dramatic increase in the biomass CC. For any 1% increase in chlorophyll-a concentration, CC increases only by 0.06%, which is negligible, and therefore, a plus or minus sign has no practical effect. Based on the log–log model, the most influential parameter to increase CC is salinity (1:1 change). On the contrary, the most influential parameter that limits the increase in biomass CC estimate is particulate nitrogen (1:0.37) [45].

4.3. Importance of Parameters

Particulate nitrogen (PN) is one of the two forms of nitrogen in aquatic ecosystems; the other being dissolved nitrogen (DN). It is the form of nitrogen that occurs in plankton, microorganisms, and detritus. Most of the available PN originates in inland waters as a result of the human production of food and energy [46] and is transferred to the coastal zones through natural processes such as erosion and storms [46,47] through a complex relationship of runoff, precipitation, and watershed slope, using the suspended solids as a vector [46]. The concept that phosphorous is a limiting factor for the freshwater systems was generalized for the estuarine and coastal areas, but evidence has shown that coastal eutrophication is affected by both nitrogen and phosphorous [48,49], with nitrogen being the more important factor of the two and phosphorous being a limiting factor [49]. Moreover, it has been theorized that P is a secondary limiting factor, the first being light, especially in the deeper parts of coastal waters [50]. The N/P ratio of each sampling station (Figure 4) shows that all stations show statistically similar values of N/P ratio both between them and between the stations and the theoretical Redfield ration of N/P = 16:1, indicating a rather N and P replete state (no stress) [51]. Figure 5 shows that even though there exists this statistical similarity among stations, the overall eutrophication state is different (station 2 is ranked as exhibiting a bad environmental state).

Salinity, together with temperature, has been reported that governs phytoplankton communities (hence chl-a and eutrophication), especially in diatom and cyanophyte-dominated communities [52]. Salinity in general within the Greek territorial waters is high (above 38 PSU; average for the period 1990–2005), except for a small area in the North Aegean Sea, due to the existence of large rivers in that region [53]. Its importance as a pressure factor for eutrophication is that it is usually highly variable along the coastal zone and especially close to estuaries and deltas, which are common sites for aquaculture development. Going back to the issue of which nutrient between N and P is the limiting for the coastal environment, it is known that high salinity values increase P availability in coastal waters and consequently increase the importance of N for primary production, making N the limiting nutrient. The raw data indicate that the studied fish farm areas exhibit relatively high salinity values between 36.6 and 38.9 PSU (ANOVA test, p < 0.0001, a = 95%, d.f. = 2.93, value range = 37.695 ± 0.904 PSU; normality test Shapiro–Wilk p = 0.2153). In addition, we did not find a statistical difference between the salinity values between stations characterized as BAD and GOOD (Tukey one-sided and Dunnet two-sided multiple range tests; p = 0.465), though the p-value indicates a modest qualitative effect in favour of the GOOD sites. This shows that the farm sites which conform to the environmental goal set in this study exhibit qualitatively lower salinity than the other nonconforming sites (average annual salinity values of 36.8 ± 0.2 and 28.3 ± 0.6 PSU, respectively). Apart from this effect, [54] reported that elevated salinity values are related to high pH (as high as +10%) and low dissolved oxygen values (as lower as −30%) in marine waters, which can affect nitrification–denitrification cycles and the chemical environment of the site, contributing indirectly to improving eutrophication status by hindering phytoplankton growth. This also indicates that high salinity sites are preferable for the selection of the installation of fish farms for euryhaline species (such as sea bass and seabream in Greece), so that the N/P ration lowers towards the standard 16:1 value and the assimilation of N is reduced; hence, eutrophication capacity lowers [52]. Finally, it should be noted that experiments on algal growth under variable concentrations of SPM, N and P nutrients under different salinities have shown that salinity is mainly affecting the survival of the plankton species. In particular, low salinities cause the increase of mortality of plankton species, depending on their salinity resistance [55].

Silicates (Si-SIO₄) are major nutrients for siliceous primary producers (diatoms), which can become limiting factors in oligotrophic areas such as the Greek seas (similar to the rest of the Mediterranean Sea, with values starting from 1–3 μM in the west and reaching 0.003 μM in the Levantine basin) [56]. Most of the silicon inputs (up to 80% on a global scale) in the marine environment come from continental discharges, from both surface water (rivers mostly) and groundwater [56], though recently, it has been shown that beach weathering contributes to Si [57]. Due to the reduction in the river outflows in the Mediterranean basin by 20% between 1960 and 2000, silicate concentration and availability have been reduced significantly [58]. However, at a microscale such as the fish farm area, silicates may exhibit a tidal-dependent fluctuation [59] which, however, cannot be justified for Greece, since tides are less than 20 cm in height in all territorial waters. Demand for Si by primary producers is limited only to diatoms that require Si as much as N and P. A study in a Mediterranean coastal ecosystem showed that salinity affects the concentration of silicates, and in particular, high salinities correspond to low silicate concentrations [56]. This, combined with the high filtration of silicates along the sediments surrounding the underground discharges, results in a concentration of Si in the coastal waters which is less than 3.5% of the initial concentration in the groundwater (freshwater), and following a cycle of subterranean mixing, it can reach the inner shelf at even lower concentrations of 2.2% [56,60]. The Bayesian–CHAID model resulted in the inclusion of silicates in the group of important parameters, obviously due to its relation to salinity and its classification as a limiting factor, as well as since together with N and P, in the various forms that the model predicted, they are the three essential nutrients for phytoplankton and chl-a values along the coastal zone. The main difference between Si, N, and P is that N and P are regenerated based on the ocean’s biological activity, while Si is regenerated through geophysical processes (dissolution of dead diatoms, sinking, and mixing) [61,62].

Suspended particulate matter (SPM) is a term used to describe nano to sand-size particles that are suspended in the water column of both fresh and marine aquatic systems and is an important prerequisite for the description and prediction of the ecological conditions of water (also in the EU Water Directive 2000/60). Suspended particulate matter is a heterogeneous mix comprising lithogenic [63] and organic materials as parts of flocs [64]. It is the primary cause of increased turbidity (linear relationship [63]) and light attenuation for the primary production. The presence of SPM in the coastal water inhibits the growth of plankton and, hence, maintains the eutrophication state at lower levels. SPM, as a factor, is considered the most potent driver for plankton growth and eutrophication compared with N and P nutrient enrichment, due to its direct effect on light availability for photosynthesis [55,65]. A simultaneous increase in SPM and high nutrient enrichment in coastal waters shows that plankton species (depending on their resilience to low light conditions) may survive without growth and, hence, eutrophication is limited [66]. In addition, the origin of SPM connects the current CC model with the adjacent land and the land-originating effluents.

The application of the model to the current farm sites shows that from the 8 farms studied, only S01 should maintain their level of annual production to achieve the environmental goal of a eutrophication level up to 3 (upper mesotrophic). Of the rest, farms S02, S06, and S07 should reduce their average production, while farms S04, S05, S08, and S09 can easily increase their average production and almost double it (Figure 5). Again, at this point, we should remind the reader that the above-proposed changes in average annual production are related only to the environmental management goal of maintaining the farm site at a eutrophication level of 3 (below or equal to upper mesotrophic) at all times.