The experimental ponds used in the present study were located in Zhoushan City, Zhejiang Province, China (24°35′N, 112°7′E). The size of the two polyculture ponds was 1.33 ha, with an average water depth of 1.2 m during the study period. The stocking density of P. trituberculatus, P. japonicus, and S. constricta is shown in Table 1. The experiment lasted 240 days from June 2020 to January 2021.

An ecosystem consists of several interrelated functional groups in the Ecopath model, each consisting of a species or many related species. During model construction, all functional groups should cover the energy flow of the ecosystem. The energy of each functional group needs to be balanced between the input and output, i.e., production – predation mortality – harvesting – net migration – biomass accumulation = 0.

The complete ecosystem model is represented by a linear system of joint cubic equations describing n biological functional groups:

where, B_n is the biomass of group n, (PB)n is the production biomass ratio of group n, EE_n is the ecotrophic efficiency of group n, B_n is the biomass of predator n, (QB)n is the consumption biomass ratio of predator n, DC_nn is the contribution of prey n in the diet of predator n, Y_n is the yield of fisheries, E_n is the migration of group n, and BA_n is the biomass accumulation of n during the study period.

The PP and PPS integrated pond aquaculture ecosystems comprised 14 and 15 functional groups, respectively. In addition to aquaculture animals, both ecosystems contained 12 identical functional groups: benthos, macrozooplankton, microzooplankton, benthic bacteria, bacterioplankton, micro-phytoplankton, nano-phytoplankton, pico-phytoplankton, crab feed, shrimp feed, detritus in the sediment, and detritus in water.

The two main inputs to the Ecopath model were biomass (B), production/biomass (P/B), and consumption/biomass (Q/B) (Table 2). Three replicate ponds were set up for both types of aquaculture ponds, and the survey data was compared to ensure the credibility of the model input data, and finally one of the replicate ponds was randomly selected to construct the ecosystem model. The biomass of all functional groups was determined by performing measurements every month, except for the biomass of P. trituberculatu, P. japonicus, and S. constricta, which was calculated from initial and harvesting weights. The P/B values of the aquaculture animals were calculated as the average value of the initial and harvesting weights. The P/B value of each phytoplankton group was obtained from experiments using the light and dark bottle oxygen method (Diana et al., 1991). The production of bacterioplankton was obtained according to Schwaerter et al. (1988). The P/B value of benthic bacteria was calculated from the measured respiration and P/Q value, which was 0.30 (Winberg, 1972). The Q/B values of P. trituberculatu, P. japonicus, and S. constricta were calculated from the feeding rates (Qi et al., 2010; Yang et al., 2010; He et al., 2017). The Q/B value of bacterioplankton was calculated based on field experiments (Williams, 1981). The Q/B value of benthic bacteria was calculated by measuring sediment respiration (Hagrave, 1972). The P/B and Q/B values of zooplankton were obtained from reported references (Feng et al., 2017). The amounts of crab and shrimp feed were recorded and entered into the system as the “detritus” group (Zhou et al., 2015).

The food composition of the consumers in the two integrated pond aquaculture ecosystems is shown in Table 3. The diets of P. trituberculatus, P. japonicus, S. constricta, benthos (Jin, 2010), macrozooplankton, and microzooplankton (Li and Lin, 1995) were analyzed using carbon stable-isotope analysis based on the related references (Craig, 1957; Anderson et al., 2007). The food composition of bacterioplankton and benthic bacteria was derived from available results of previous studies on shrimp ponds (Zhou, 2015).

The assimilation efficiency (AE) of consumers is highly variable (Blanchard et al., 2002). Here the proportion of unassimilated food (1 - AE) was 0.4 for zooplankton and 0.2 for most of other consumers (Feng et al., 2018).

Since the Ecopath model has to ensure the conservation of matter and energy among the functional groups, ecotrophic efficiency (EE) ≤ 1 is primarily used as the basic constraint during model debugging (Christensen and Pauly, 1992a). If the EE of a functional group in the output parameters is greater than 1, the food composition, P/B, or Q/B values need to be adjusted repeatedly until the output parameters are in a reasonable range. The P/Q value was maintained in the range of 0.1–0.3 to ensure that EE ≤ 1 (the P/Q value of some fast-growing animals may be greater than 0.3). The reliability and accuracy of the basic input data are the main factors affecting the quality of Ecopath models. Ecopath models are typically evaluated using the pedigree index (P), which refers to the quality and uncertainty of the input parameters. The higher the P value, the more credible the model is and the closer it is to actual ecosystem conditions. The Ecopath model balancing and the P are described in detail by Christensen et al. (2005).

The carrying capacity assessment of the integrated pond aquaculture ecosystems was established according to existing studies on the carrying capacity assessment of bivalve aquaculture ecosystems based on the Ecopath model (Jiang and Gibbs, 2005; Byron et al., 2011a; Kluger et al., 2016). In this study, P. trituberculatus and P. japonicus were the artificial feeding animals, and thus the carrying capacity was estimated for both current and adequate feeding levels. The carrying capacity estimation of the integrated pond aquaculture ecosystems was similar to that of bivalve aquaculture ecosystems. We continuously increased the biomass of one of the three species (P. trituberculatus, P. japonicus, and S. constricta) (0.01 g/m² each time) until any of the functional groups in the system was unbalanced. The resulting biomass of the cultured organism was recorded as the carrying capacity at current feeding levels. Since the biomass of cultured organisms eventually reaches the carrying capacity, the amount of crab and shrimp feed may be the limiting factor. Therefore, as the biomass of cultured organisms increased, the amount of feed was also increased until any of the functional groups was unbalanced (EE > 1), except for the feed functional group. The resulting biomass of cultured organisms was recorded at adequate feeding levels. The ratio of the biomass and the carrying capacity of cultured organisms is multiplied by current stocking density to obain the stocking density at which the biomass reach the carrying capacity.

The EE values and effective trophic level of the functional groups in the two integrated pond aquaculture ecosystems are listed in Table 2. Ecotrophic efficiency refers to the efficiency of production transfer from one trophic level of the food web to the next (a range of 0–1) affected by fishing and predation pressures. The P. trituberculatus, P. japonicus, and S. constricta showed high EE values in their respective systems. The EE values of P. trituberculatus and P. japonicus were 0.962 and 0.954 in both systems, and that of S. constricta was 0.952 in the PPS system. The EE values of micro-phytoplankton, nano-phytoplankton, pico-phytoplankton, and bacterioplankton were 0.019, 0.023, 0.023, and 0.067 in the PP system and 0.418, 0.407, 0.311, and 0.310 in the PPS system, respectively. The EE value of the microzooplankton in the PP system (0.261) was lower than that in the PPS system (0.831). The EE values of crab feed in the PP and PPS systems were 0.582 and 0.638, respectively, and those of the shrimp feed were 0.482 and 0.533. The EE values of benthic bacteria in the two systems were 0.630 and 0.575, and those of bacterioplankton were 0.261 and 0.288, respectively. The EE values for each functional group were less than 1, which was within the range required by the Ecopath model. The effective trophic level is the trophic level at which each organism feeds in proportion to the predator’s food composition (Odum, 1971). In the two integrated pond aquaculture ecosystems, the highest effective trophic level was benthos with 2.650. The effective trophic levels of P. trituberculatus and P. japonicus were 2.065 and 2.027 in the PP system, and those of P. trituberculatus, P. japonicus, and S. constricta were 2.057, 2.018, and 2.010 in the PPS system. The effective trophic levels of the other functional groups were equal in the two systems.

The energy flows between the trophic levels in the two integrated pond aquaculture ecosystems are shown in Figure 1. The energy flows occurred mainly within four trophic levels. The total biomass of the primary producers in the PP system was 14.30 g/m², and the primary production was 2623.79 g/m²/240 days, of which 55.95 g/m²/240 days flowed to trophic level II and 2568.84 g/m²/240 days flowed to detritus, with 2.13 and 97.87% of the energy flowing to trophic level II and the detritus. The total biomass of the primary producers in the PPS system was 14.80 g/m², and the primary production was 2781.48 g/m²/240 days, of which 1052.16 g/m²/240 days flowed to trophic level II, and 1729.32 g/m²/240 days flowed to detritus, with 37.83 and 62.17% of the energy flowing to trophic level II and detritus. The total energy of the detritus group was 2900.89 and 2372.98 g/m²/240 days, with 931.02 and 1505.35 g/m²/240 days flowing to trophic level II, respectively. In the two integrated pond aquaculture ecosystems, the system energy circulation was mainly distributed in trophic levels I and II. In addition, the transfer efficiency of trophic level II was 17.16% from primary producers and 17.63% from detritus in the PP system and 7.02 and 13.41% in the PPS system, respectively.

The values of the main energy flow parameters and characteristic parameters of the Ecopath model for the two integrated pond aquaculture ecosystems are shown in Table 4. The total system throughput (TST) was 8461.70 g/m²/240 days and 9665.06 g/m²/240 days in the PP and PPS systems, respectively. In the PP and PPS systems, total consumption accounted for 12.52 and 27.24%, total respiration (TR) accounted for 6.43 and 17.64%, total output accounted for 34.28 and 32.78%, and total flow to detritus accounted for 45.38 and 34.26% of the TST, respectively. The values of the energy flow parameters, such as total system flow, total consumption, TR, total productivity, and total primary production (TPP), were higher in the PPS system than the PP system, and the value of total flow to detritus was higher in the PP system than the PPS system. The TPP/TB and TPP/TR ratios describe the activity, extent, and potential of ecosystem development. The TPP/TB values of the PP and PPS systems were 33.969 and 20.903, respectively. The TPP/TR value of the PP system (4.824) was higher than that of the PPS system (1.632). The connectance index (CI) and system omnivory index (SOI) are correlated with ecosystem complexity, indicating whether the food chain is web-like or linear (Odum, 1971; Christensen et al., 2000). The CI values of the PP and PPS systems were 0.350 and 0.339, and the SOI values were 0.040 and 0.041, respectively. Finn’s cycling index (FCI) is the ratio of the amount of material or energy flowing into the debris in the system required to re-enter the system circulation to the total system flow. It characterizes the maturity, stability, and degree of external disturbance of the system. Finn’s mean path length (FML) is the average length of each cycle flowing through the food chain in the system. The FCI values of the PP and PPS systems were 27.217 and 3.933%, and the FML were 2.375 and 2.598, respectively.

The estimation results of the carrying capacity of P. trituberculatus, P. japonicus, and S. constricta in the two integrated pond aquaculture ecosystems are shown in Figure 2. At the current feeding level, the carrying capacities of P. trituberculatus and P. japonicus were 65.15 and 47.62 g/m² in the PP ecosystem, and those of P. trituberculatus, P. japonicus, and S. constricta were 64.96, 48.06, and 100.79 g/m² in the PPS ecosystem, respectively. After the biomass of P. trituberculatus and P. japonicus in the two ecosystems exceeded the carrying capacity, the first imbalanced functional group was the feed group, indicating that the biomass of crab and shrimp could be increased by increasing the amount of aquatic animal feed. At adequate feeding levels, the carrying capacities of P. trituberculatus and P. japonicus were 83.76 and 48.52 g/m² in the PP ecosystem and 81.82 and 53.44 g/m² in the PPS ecosystem, respectively. After the biomass of each aquaculture animal in the two ecosystems exceeded the carrying capacity, the first imbalanced functional group was the microzooplankton. When the biomass of the cultured organisms reached the carrying capacity at adequate feeding levels, the minimum amounts of crab and shrimp feed were 451.67 and 595.66 g/m²/240 days in the PP system and 442.94 and 648.58 g/m²/240 days in the PPS system. The results showed that when the biomass of the cultured organisms reached the carrying capacity, the stocking density of P. trituberculatus and P. japonicus in the PP system was increased to 13.16 and 4.21 kg/ha, and the stocking density of P. trituberculatus, P. japonicus, and S. constricta in the PPS system was increased to 11.92, 3.73, and 78.13 kg/ha in the current aquaculture environment with artificial feeding. After increasing the feeding amount to ensure that the feed was not a limiting factor, the stocking densities of P. trituberculatus and P. japonicus in the PP system were increased to 16.92 and 4.29 kg/ha and those were increased to 15.01 and 4.15 kg/ha in the PPS system, respectively.

The Ecopath pedigree indices of the PP and PPS systems were 0.556 and 0.561, respectively. The indices were in the upper levels compared to those of 50 ecosystems and 393 Ecopath models evaluated by Morissette et al. (2006) (0.164–0.676).