A total of 273 wild black seabream A. schlegelii were collected from the wharf landings of fishermen who used gillnets, fishing tackle, or trawls in the sea near the Zhanjiang estuary, in June, July, and September of 2020 to April 2021. The fish samples were taken back to the laboratory for biological analysis, the standard length (L) and body mass (W) of the black sea bream were measured, and the stages of gonadal maturity were determined (Holden and Raitt, 1974). The length was accurate to 1 mm, and the body mass was accurate to 0.1 g.

Estimation of the increase in body mass of released fish was based on biological data from black sea bream collected in the field. Simulation of the number and biomass of released stocks were based on the relationship between stocking density and mortality rates. To optimize the stocking effects of constant total quantity of released fish, we simulated five stocking scenarios with the months as the interval unit (Table 1). For simplicity of calculation, we assumed that the total number of fish released is 50,400, and the stocking times is 1, 2, 3, 4, and 7, respectively, in scenarios I, II, III, IV, and V, and then simulated the stocking effect in a maximum 6-month period and six more months after release. Density-dependent theory in ecology usually maintains a linear, inverse relationship between the population mortality and population density (Roughgarden, 1971; Herrando-Pérez et al., 2012; Lee and Strauss, 2016). Therefore, differences in stock density during a single release may lead to varied mortality rates. Combined with the total number of fish released and their estimated natural mortality rates, the changes of the number of released fish stocks and their corresponding weight in each period could be simulated. Refer to the Ricker model to predict exponential yield (Ricker, 1975). Finally, the total biomass (weight/quantity) of the released fish was accumulated, and the effects of the stocking scenarios were evaluated.

The model assumes the following:

1) The mortality rate of released fish is restricted only by density. Although studies have shown that the mortality rate of released fish in wild conditions can vary with age and size (Lorenzen, 2000), in this study, the release interval of different batches was relatively short (months), and therefore, the effect of the size difference between the batches of released fish on mortality was ignored.

A total of 273 black sea bream samples were collected in this study. The standard length (SL) range was 74–406 mm, and the average was 235.65 SL. The dominant body-length groups were 129–148 mm (12.09%) and 259–277 mm (10.62%) (Figure 2).

The gonadal stages of the black seabream were evaluated and a coefficient of sexual maturity was calculated for fish in the sea area near the Zhanjiang estuary. The breeding period of the fish was from December to March of the next year. Among the 273 fish sampled, 131 females, 88 males, and six hermaphrodites were visually identifiable as the gonad differentiation was obvious. Monthly variation in the stages of gonadal development denoting males and females is shown in Figure 3. Gonads in stages IV and V appeared from December to March.

The relationship between the body length and body mass showed a more-or-less equivalent increase in black sea bream in this sea area. The annual body mass relationship of black sea bream was W = 5.092 × 10^–5 L ^2.906 (R ² = 0.971) (Table 2). Comparing the body length and weight parameters in different seasons, the condition factor a was winter > spring > autumn > summer. The power index b is summer > autumn > winter > spring (Table 2). The b value in summer is greater than 3, reflecting positive allometric growth; the b value in autumn and winter is less than 3, indicating negative allometric growth.

The von Bertalanffy growth parameters were obtained by the ELEFAN I method using the time-series and body length frequency data of black sea bream (Figure 4) as follows: asymptotic body length L _∞ = 54.39 cm, growth rate K = 0.15, and t ₀ = −0.967.

Changes in the number and biomass of black sea bream (Table 3; Figures 5, 6) indicated that dividing the release of black seabream into two batches was best. Five kinds of release scenarios were simulated (Figure 7), with each releasing a total of 50,400 juvenile black sea bream but at different intervals. The survival and biomass of the twice release strategies (dividing the total quantity of released fish into two batches) in December accounted for 15.81% of the total release, and the remaining strategies decreased with more release events. A one-time release strategy had the worst effect because of the high mortality rate of released stocks, and the remaining amount is 1.78 and 10.57%. Trends in the biomass and the quantity of released juvenile fish were similar. Because the individual’s natural growth rate is lower than the rate of natural mortality, all release curves showed a downward trend. One release–effect curve decreased monthly after a maximum in the first month, and the other release–effect curves exhibited peaks because of multiple release events. After the last releasing (in July), the stocks and biomass of the juvenile fish under the different release scenarios decreased at different rates because of no further supplement to the existing stocks.

In this study, the effects of different scenarios were compared based on growth parameters and the estimated mortality rate. The stocking effect of twice release strategy is the best among the five releasing strategies (Figure 7). In a practical fish stocking program, in order to achieve the effect of population replenishment, the number of released fish is usually very large (Tang, 2019), and the preferable released strategy needs to be optimized on species accordingly. The simulation model of Yamashita et al. (2017) of an optimum stocking density of juvenile flounder Paralichthys olivaceus showed that the most important factors were prey density and the number of wild juvenile flounder. If the population size is relatively high in a certain sea area, the natural regulation within the population would lead to a slower growth rate of the fish and an increase in mortality (Liu et al., 1994). In the stocking practice, multiple release sites can be selected in the target stocking sea area to reduce the drastic increase of mortality rate due to overhigh stocking density.

Studies have shown that the survival rate of released marine fish varied with seasons (Mckinnell and Lundqvist, 2000). Most of the release work of black seabream in the northern SCS has begun in summer, and is expected to be finished in autumn every year. However, insufficient attention is paid to the actual effects of both the stocking interval and the quantity of fish released in a single event, with fish being released once to many times every year (Liang et al., 2010; Liu et al., 2019). Zhou (2004) summarized the releases of black seabream in the Xiangshan estuary from 1992 to 1994, which were mainly released from June to October, and the recapture rate was about 4.4%–6.05%. In all, the total released quantity of black sea bream subsequently increased year by year, with good economic benefits. However, few quantitative studies on costs and benefits of stock enhancement have been reported, with some qualitative reports. The recapture rate of black seabream in Daya bay in November 2014 was 7.76%, exceeding that record in June 2015 (3.66%) and July 2016 (2.49%), but that the better recapture effect in November was mainly due to the larger size of the released stocks (Liu et al., 2019). Xu et al. (2008) suggested that to avoid the phenomenon of black sea bream being caught immediately after stocking, releases are more appropriate in the closed fishing season, generally in summer and autumn—a time when the development of the released fish corresponds with the natural population. Based on the body length–weight relationship in this study, the b value was higher in summer, following the closed season for fishing in the SCS, which begins in May (Lin and Cheng, 2009). Therefore, June to October would be more appropriate for the release of black sea bream in Zhanjiang estuary waters. The swimming and disperse ability of black sea bream after release is strong, and the number of recaptures appears to be highest at 3–5 months after release, and decrease sharply thereafter (Liu et al., 2019). In combination with the optimal release season (June–October), the optimum release interval of black sea bream in the Zhanjiang estuary waters would be 5 months, with the fish first released in June, and again in October.

In this study, the release interval and natural mortality were considered to be the two most important factors on stocking effects. As for the release interval, a longer release cycle was expected to be better stocking results. The release interval constituted the biggest difference between the release strategies. Short intervals would amount to a more continuous release of the juvenile fish into the natural water, with each release event involving a relatively small number. However, shortened time intervals and insufficient dispersal of the previous batch of released fish allows for greater intraspecific competition among successive batches, with implications for survival. According to the density-dependent theory (Lorenzen and Enberg, 2002), increases in population density of the released fish lead to higher mortality in certain waters (Liu et al., 1994). With repeated releases, the increase in population density of the released fish leads to an overall high mortality rate, and thus the natural mortality for early released fish is high. In contrast, although secondary releases may involve a large number of fish, there will be less interaction owing to the longer interval, because half of them are released later, with a short period of natural morality, resulting in a larger number of final survivors. Using a yield-per-recruit model, Xu (2015) simulated a release and management strategy of Chinese white prawn Penaeus chinensis, and proposed that a postponed release time somewhat could achieve greater fishing yields. Therefore, appropriately extending the time interval between two releases but within the appropriate release period can reduce the impact of natural mortality on the released fish biomass.

Density-dependent mortality is a key consideration in the optimization of a release strategy, as the natural mortality importantly acts on the released fish. The natural mortality rates of fish populations vary greatly at different life stages and are difficult to estimate accurately (Zhan, 1995). Some research believed that the rates of natural mortality were underestimated for released fish. The release strategy simulation by Xu (2015) deployed a constant mortality rate and assumed that the natural mortality coefficient did not conform to actual changes in the parameter, and this could affect the strategy optimization results. Lindholm (2001) studied the response of cod Gadus morhua larvae to changes in sea-bottom habitat based on three types of response curves depicting mortality and population density, and found that the relationship between survival rate and density of the cod was similar regardless of the type of curve. The purpose of the present study was to optimize the releasing strategy for stocking black seabream, and thus only change in one type of mortality rate was selected. There is an obvious upper limit in a mortality curve. In the case of a large quantity of released fish, the mortality rate increased, but this change did not affect the increasing trend of the amount after releasing. Therefore, although the quantity of released fish stocked in two events (scenario II in Table 1) is still high, the mortality rate will not be significantly higher than that with the other release strategies. In addition, factors affect the mortality rate of released fish, and will exert stocking effects even in circumstances of unknown mortality of released fish, but it will affect the actual stocking effects. Thus, simulation results can still provide a reference for the optimization of the release strategies.

The results indicate that the growth of black seabream is better in waters of the Zhanjiang estuary area than in Daya bay because of the value of parameter a (Eq. 1) was higher for fish in the Zhanjiang estuary (4.37 × 10^–5), compared with that for those in Daya bay (1.55 × 10^–5) (Chen et al., 2019). Seasonal variation in a revealed the trend winter > spring > fall > summer. In general, the highest value of a reflects the stage of gonad maturity (Zhan, 1995). The gonad with maturity stage IV or V in the black seabream was observed mainly from December to March of the next year, when the inflated gonad occupied three quarters or more of the body cavity.

The values of the growth parameters reflect the impacts of environmental changes on life conditions of fish (Froese and Pauly, 2021). The a value of the stocks correspondingly varied with the different life stages of the black seabream. The growth index b (2.906) indicates the growth of fish expressed as isauxesis for length and body mass. The value of b was close to that for the black seabream in Daya bay (Chen et al., 2019) and in Taiwanese waters (Chu et al., 2011). Seasonal variations in b revealed the descending trend from summer, fall, winter, to spring in order. The higher b value in summer was possibly attributable to the rapid growth in body mass and faster development of gonads (Zhan, 1995; Chen et al., 2019). This research found a lower b value in winter compared with that in summer and fall, which was possibly caused by a shortage of food and the high energy costs in the winter. Furthermore, higher seasonal fishing pressure may lead to allometric growth as well as a decrease in the quantity of bait fish (Stergiou and Moutopoulos, 2001).

Male-to-female sex change in black seabream is possibly related to the body shape (Todd et al., 2016). The black seabream is male in the first 2 years (Lee et al., 2001). The popular theory for explaining the gynandromorphy is the size-advantage hypothesis (Munday et al., 2006; Kazancıoğlu and Alonzo, 2010), which hypothesizes that the sex change of fish stocks is adaptive with the total reproductivity of the whole population, and that the body shape determines the direction of the sex change. Under this assumption, males that change to females gain more individual advantages, such as a bigger body shape and higher fecundity, which are beneficial for survival of the whole population (Gemmell et al., 2019). It is imperative to take a systematic consideration, incorporating the reproductive characteristics into the optimization of stocking practice, to attain the desired stocking goals.