Yingbin WANG, Wei ZHANG

School of Fisheries, Zhejiang Ocean University, Zhoushan 316022, China

Abstract Marine ranching can be regarded as a type of artif icial f ishery, and its construction aims at the sustainable utilisation of f ishery resources. Therefore, the sustainable yield level of target species in marine ranching has become one of the concerns of stakeholders. The enhancement surplus production model proposed by Wang (2021) based on the traditional surplus production model can be used to assess the sustainable utilisation of settled species in marine ranches. However, when the target species has the characteristics of migration inside and outside marine ranches, its sustainability assessment will be aff ected.Based on the movement range and resource density levels of enhancement species inside and outside marine ranches, we built a biomass change model that is suitable for enhancement species with migration characteristics inside and outside marine ranches (migration enhancement biomass model). Moreover, we simulated the eff ects of factors, such as the ratio of the movement range and the ratio of resource density within and outside marine ranches and the f ishing strategy for the enhancement species in marine ranches,on the estimation of maximum sustainable yield (MSY). Results show that the large movement range of enhancement species outside marine ranches was associated with the obvious advantage of the proposed migration enhancement model over the traditional enhancement production model. A small diff erence in the densities of enhancement species inside and outside marine ranches was highly benef icial for improving the accuracy of MSY estimation. The migration enhancement biomass model proposed in this study provides an idea for estimating the MSY of an enhancement species that migrates inside and outside marine ranches.Researchers can adjust the parameters of the model in accordance with the actual situation of resource distribution and changes to improve the scientif icity of f ishery stock assessment.

Keyword: marine ranching; stock enhancement and releasing; migration; production model; maximum sustainable yield (MSY)

1 INTRODUCTION

In the second half of the 20thcentury, China’s off shore capture f isheries developed rapidly. As a result, China has become the largest f ishery producer and aquatic product trading country in the world. At the same time, overf ishing and the deterioration of the f ishing ground environment have resulted in the degradation of the off shore f ishery resources in China(Zhang et al., 2003). Following some countries and regions with developed f isheries, in recent years,China has also started the research and development of technologies for artif icial habitat construction,aquatic biology behavioral control, and environmental monitoring, and has established a stock enhancement and aquaculture industry that can sustainably supply high-quality aquatic products. One of the successful forms of such a technology is the construction of marine ranches (Zhang et al., 2003).

Marine ranching refers to the f ishery mode that can increase the conservation of f ishery resources,improve the marine ecological environment, and achieve the sustainable utilisation of f ishery resources.These can be achieved by constructing or repairing sites required for reproduction, growth or feeding in specif ic sea areas through placing artif icial reefs and releasing based on the principles of the marine ecosystem (General Offi ce of Shandong Provincial People’s Government, 2019). Through human intervention, f ishery resources in marine ranches can be concentrated and utilised sustainably, which is one of the goals of marine ranch construction and management and is a concern of managers and resource scientists.

Marine ranching activities can be traced back to more than a century ago (Liao, 1997; Liao et al.,2003). Ever since, stock enhancement has been attempted at some level in over 25 countries worldwide (Bartley, 1999) with more than 100 species(f ish, crustaceans, molluscs, and other invertebrates)(Liao, 1999; Fushimi, 2001). In-depth studies on marine ranching were conducted in the early 21st century and focused on juvenile releasing techniques(Fushimi, 2001; Junio-Meñez et al., 2002; Yamamoto and Morioka, 2002), released species health management (Buchmann et al., 2001), tagging methods (Brennan et al., 2002a, b), and ecological and genetic diversity (Tseng et al., 2001; Miller and Walters, 2004). Scholars in China have also carried out considerable research on the assessment of the conservation and enhancement eff ects of marine ranching resources. In Zhangzi Island, the investigation and evaluation of f ishery resources in marine ranches and the comparison of species within and outside reef areas have shown that artif icial reefs have a good conservation eff ect on f ishery resources(Wang et al., 2018). The evaluation of the conservation eff ect on f ishery resources in marine ranches in Xiangshan Port illustrates that the species richness,total biomass, and abundance increased after artif icial reefs were installed (Wang et al., 2019b). The results of the assessment of the f ishery resource enhancement eff ect of marine ranching in Zhelin Bay in the eastern Guangdong Province depict that f ishery habitats have improved and the catch per unit of eff ort (CPUE) has increased (Wang et al., 2019a). Recent reports have proposed strategies for the principles and techniques of the conservation of resources in marine ranches in China (Zhang et al., 2020). Although these studies have focused on the sustainable utilisation of f ishery resources in marine ranching, they do not involve the quantitative analysis of the development and management of important species, which is one of the issues of concern of the experts in this f ield.

The surplus production model (SPM) is one of the most important f ishery stock assessment models used for estimating the annual sustainable catch of the objective species (Punt, 2003). When both the habitat water and f ishing water for the target species are limited to the marine ranch, the traditional SPM can be used to estimate the maximum sustainable yield(MSY) of the species in it. However, after the implementation of stock enhancement, the MSY of the enhancement species cannot be eff ectively estimated using the traditional SPM. Wang (2021)proposed an enhancement SPM for the estimation of the MSY for enhancement species settled in marine ranches. However, this enhancement SPM is unsuitable for species that migrate inside and outside marine ranches; such migratory behaviour is highly common for f ish living in the sea areas of marine ranches. The migration of f ish inside and outside marine ranches will aff ect the assessment results of MSY, especially when the living area outside a marine ranch is large. At the same time, the implementation of stock enhancement also increases the complexity of the stock assessment. In this research, a new model for describing the biomass change of the enhancement species migrating inside and outside marine ranches was proposed based on the enhancement SPM, which can be used to estimate the MSY of the species that is released to marine ranch but migrate inside and outside of it. The comparison between the proposed model and the enhancement SPM were also made.

2 MATERIAL AND METHOD

2.1 Model

Wang (2021) established a discrete nonequilibrium SPM for enhancement species based on the logistic biomass growth model (here, we call this model the enhancement model). The general form of biomass changes, which is the theoretical basis of the model, is

whereBtis the biomass in yeart,ris the intrinsic rate of growth,eis the eff ective enhancement rate,Stis the enhancement biomass in yeart,Kis the carrying capacity andCtrepresents the catch in yeart. This model can be used to estimate the MSY of the species settled in a marine ranch under the inf luence of stock enhancement. Given that, the movement range of this species usually does not exceed the boundary of the marine ranch, and the living area of the species is consistent with their f ishing seas. In this way, the estimated MSY for such a species will be highly accurate. However, in addition to settled species,species with strong swimming capability will be released into the marine ranch. The movement range of these species is not limited within the marine ranch.For example, the movement range of some f ish may exceed several times the area of the ranch. Equation 1 will not be a good choice for the estimation of the MSY of such a species.

When the movement range of the enhancement species exceeds the boundary of a marine ranch, the individuals inside and outside the marine ranch can be treated separately. Suppose that the movement ranges inside and outside the marine ranch areAinandAout,respectively, and the ratio of the resource density inside and outside the marine ranch is equal toτ(usuallyτ>1 considering the eff ect of f ish collection due to the construction of artif icial habitats in the marine ranch). Based on Eq.1, the changes in the biomass inside and outside the marine ranch can be expressed by using the following equations:

By adding Eqs.2 & 3 together, we can obtain Eq.5,which is suitable for the biomass change of enhancement species with the characteristics of migration inside and outside marine ranches(migration enhancement biomass model):

The parametersr,q,K,Bt(whentis the initial year)andeare estimated by using the observation error method, and then MSY can be calculated.

where CPUEtis the catch per unit of eff ort in yeart;Etis the f ishing eff ort in yeart;qis catchability;εtrepresents the error and follows a normal distributionN(0,σ2), the parameterσcame from the actual observations data in the past few years, and was equal to 10%. After obtaining the parameter values, the MSY of the enhancement species in a marine ranch can be calculated by using the following equation:

The specif ic derivation of Eq.6 can be found in Wang (2021).

2.2 Simulation analyses

In the simulation analyses, 20 scenarios were assumed to compare the impacts of diff erent factors on the enhancement model and migration model (Table 1). Three impact factors were considered, including(1) the living area of the enhancement species, (2) the diff erence of resource densities inside and outside marine ranch, and (3) the f ishing strategy in marine ranch. For the f irst factor, the living area of enhancement species excluding the marine ranch (Aout)was used; for the second factor, the ratio of resource density inside and outside marine ranch (Din/Dout) was used; for the third factor, we assumed four changetrends of catch in the marine ranch, namely annual catch continuously decrease, annual catch continuously increase, annual catch increase f irst then decrease, and annual catch decrease f irst then increase (Table 1). For each scenario, Eq.1 (enhancement model) and Eq.5(representing the new model, which we call the migration model) were used to estimate MSY to analyse the diff erences between the two models. The MSY estimation was repeated 1 000 times.

Table 1 Simulation scenarios of the enhancement species and f ishing strategy

3 RESULT

3.1 Models and curves

Compared with the enhancement model (Eq.1), the migration model (Eq.5) proposed in this research has two more variables, i.e., the movement ranges inside and outside the marine ranch (AinandAout). At the same time, the original initial biomassB0is replaced by the initial biomass inside and outside the marine ranch, i.e.B(in)0,B(out)0andB0=B(in)0+B(out)0.

Fig.1 Schematic of the biomass change trend for the migration enhancement biomass model

Fig.2 Schematic of the sustainable yield for the migration enhancement biomass model

The curves of the migration model are similar to those of the enhancement model. The growth curves for the total biomass and the biomass inside and outside the marine ranch are all S-shaped (Fig.1). The relationship between continuous yield and biomass is parabolic and is aff ected by stock enhancement.Consistent with the report by Wang (2021), yield is still present even when the biomass is zero (Fig.2).

3.2 Simulation analyses

Under diff erent simulation scenarios, the MSY is underestimated by the enhancement model (Table 2).The size of the movement range outside the marine ranch has great eff ect on the enhancement model. As the movement range outside the marine ranch increases, the absolute value of the relative estimation error (REE) of the estimated MSY also increases. For the migration model, it is not sensitive to the movement range outside the marine. Diff erent f ishing strategies have diff erent eff ects on the MSY estimation. Generally, when the catch continuously increases, the MSYs are underestimated, and for other three f ishing strategies the MSYs are overestimated.When the catch decreases f irst and then increases, theerror of the estimated MSY is relatively small. When the catch continuously increases, the estimated MSY diff ers greatly from the true value. When the proportion of movement range outside the marine ranch increases, the MSY estimated by using the migration model is more accurate than that estimated by using the enhancement model.Given the construction of marine ranches, the density of the enhancement species inside marine ranches will be higher than that outside. When the biomass density ratio of the enhancement species inside a marine ranch to that outside increases from 2꞉1 to 3꞉1, the error of the estimated MSY increases(Tables 2 & 3). The distribution of 1 000 MSY values of the enhancement species estimated using the migration model indicates its advantages when the resource density of the target sepcies in the marine ranch is high and the living area outside the ranch is large (Supplementary Figs.S1 & S2).

Table 2 REE of MSY under diff erent movement ranges of enhancement species and f ishing strategies in marine ranches

4 DISCUSSION

The structure of the migration model proposed in this study is similar to that of the enhancement model.However, because it is not only aff ected by stock enhancement but also by the biomass and migration of the enhancement species inside and outside marine ranches, the migration model is more complex than the enhancement model. The enhancement model contains f ive parameters (r,K,B t,q, ande), whereas the migration model contains one more parameter than the enhancement model (that is,Btis divided intoB[in]tandB[out]t) because it treats the inside and outside areas of marine ranches as independent sea areas. In addition,when using the migration model, we should providethe preliminary estimate of the movement range of the enhancement species and the area of the marine ranch.Although its parameters have been increased, the migration model can address the changes in the biomass inside and outside marine ranches separately in one model. If the enhancement species move inside and outside marine ranches, a recruitment mechanism will form between these two areas. When f ishing occurs within a marine ranch, the unf ished stock outside the marine ranch will be recruited into the marine ranch;this trend maintains the ratio of resource densities inside and outside the marine ranch at the initial level.Although a recruitment trend for the enhancement species inside and outside the marine ranch is observed,it is not as regular as the trend described above because the movement of the enhancement species exhibits randomness. Equation 5 provides a way to estimate the MSY of the enhancement species that migrates inside and outside marine ranches.

Table 3 REE of MSY for diff erent f ishing strategies obtained by using the migration model when the ratio of biomass density of enhancement species inside and outside marine ranches is 3∶1

In fact, the ratio of the biomasses of the enhancement species and the ratio of the carrying capacity (K) inside and outside marine ranches in Eqs.2, 3, & 5 can be set in accordance with the specif ic situation. In this study,the ratio is set based on the movement range areas of the enhancement species inside and outside marine ranches, whose resource densities are used as the weight coeffi cients. In practical applications, the researcher should provide initial estimates of the ratios of the area and resource density of the enhancement species inside and outside marine ranches in line with actual conditions through surveys or historical data.

As inferred from the simulation analysis results of the enhancement model and migration model, when f ishing only occurs within the marine ranch, and the living area of the enhancement species does not exceed the boundaries of the marine ranch, the enhancement model and migration model are exactly the same. Thus, both models can be used to estimate the MSY of the enhancement species. As the movement range of enhancement species outside the marine ranch increases, the advantages of the migration model become increasingly obvious(Table 2 and Supplementary Fig.S1).

There are few reports on the estimation of MSY of enhancement species in marine ranch, and only Wang(2021) proposed an enhancement SPM for the estimation of the MSY for enhancement species settled in marine ranches. In the current study, we compared the results of enhancement model and migration model when dealing with the situation that enhancement species can migrate inside and outside the marine ranch. The results showed that the migration model is more suitable for the enhancement species that migrate inside and outside the marine ranch than the enhancement model. When theAout=0,the estimated MSY of the two models are exactly the same. WhenAout>0, the enhancement model only considers the enhancement individuals inside the marine ranch, and does not deal with those outside the marine ranch. When the movement range of the enhancement species outside marine ranch becomes large, the consistency between the f ishing area inside the marine ranch and the living area of the enhancement species becomes poor. Using the enhancement model is equivalent to estimating the biomass in the entire movement range based on only the catch data in the marine ranch, indicating that the representativeness of the f ishing information is very low. Thus, it may underestimate the MSY. The improvement of the proposed migration model over the enhancement model is that it extends the scope of application beyond marine ranch by introducing the ratio of the resource density (τ) and treating the individuals inside and outside the marine ranch separately (Eqs.2, 3, &5). Therefore, the estimated MSYs of migration model are better than those of enhancement model when the proportion of movement range outside the marine ranch increases (Table 2).

Although the migration model is appropriate to the migration characteristics of the enhancement species inside and outside marine ranch, it has a tendency to overestimate the results, especially when the movement range of enhancement species outside the marine ranch increases. There may be many reasons for the overestimation. First, given that the enhancement species can move freely inside and outside marine ranches, the MSY of the enhancement species in a marine ranch and the MSY in the entire living area should be similar, i.e., the resources that are reduced because of capture in the marine ranch can be recruited from outside the ranch. Therefore,the catchability coeffi cient (q) is the critical parameter for stock assessment for a large-scale sea area based on the catch data in marine ranches.qrepresents the proportion of the biomass of the target species to the total biomass in a certain sea area caught by one unit of eff ort. In theory, as long as the value ofqcan be accurately determined, a viable MSY can be estimated.However, when f ishing only occurs in marine ranch,and at the same time the resource density in the marine ranch is higher than that outside,qis prone to be overestimated, which will lead to the overestimation of MSY. Second, the parameter value ofemay also be overestimated since the survival rate of the enhancement species maybe high benef it from the recruitment from outside the marine ranch and the protective eff ects of artif icial reefs, etc. Third, the division of carrying capacity (K) and enhancement biomass (S) inside and outside marine ranch is based on the resource density and area (Eqs.2 & 3), which is a mathematical approach we had to use since the f ield monitoring data was unavailable. Fourth, the recruitment biomass (Bsupp) lacks a specif ic calculation formula, which may also be a source of error in overestimating MSY. All of the above issues are needed to be studied in depth in future research.

The diff erence in the resource density of the enhancement species inside and outside marine ranches can also aff ect the MSY estimation results.Great diff erences provide poor estimation results. A large diff erence in density means that the homogeneity of resource distribution inside and outside a marine ranch is poor, which inevitably aff ects the randomness of the migration of the enhancement species inside and outside the marine ranch. When f ishing occurs in the marine ranch, ensuring that the ratio of resource densities inside and outside the marine ranch remains at the original level becomes diffi cult even though resources may be recruited into the marine ranch from the outside. If the resource densities inside and outside the marine ranch are similar, maintaining the consistency of the resource density through resource migration, which can also improve the accuracy of the estimation of MSY, is easy.

In 1998, Hannesson proposed a biomass variation model based on the migration characteristics of f ish inside and outside marine reserves (Hannesson, 1998).A parameter of the migration rate of the stock in the marine reserve is introduced into this model.Subsequently, some scholars applied the concept of migration rate in the study of the sustainable yield of f ishery resources in protected marine areas (and sea areas where f ishing operations cannot be performed due to special reasons) (Pincin and Wilberg, 2012;Shibata et al., 2015; Paul et al., 2018). In contrast to marine protected areas, marine ranches are artif icial f ishing grounds (Shandong Provincial Oceanic and Fishery Department, 2017) and are a service provided for the sustainable utilisation of f ishery resources.Therefore, f ishing operations occur within marine ranches. However, f ishing behaviour is usually restricted in marine ranches and is forbidden in surrounding sea areas to protect resources from being overexploited. The concept of migration rate can also be applied in the study of the dynamics of f ishery resources inside and outside marine ranches. However,determining the actual migration rate of the target species is diffi cult. Techniques, such as marking or underwater observation, can be used for the estimation of migration rate, and their results are usually subject to large errors. Therefore, we did not use the parameter of migration rate in the current study but instead added variables representing the areas and the original biomasses inside and outside a marine ranch to the model. These variables can be obtained through routine surveys and are easy to acquire.

In the current study, a migration enhancement biomass model for an enhancement species is proposed based on the movement ranges and density ratios of the target species inside and outside marine ranches. It provides an idea of estimating the MSY of the target species for similar situations. The application of this model is not limited to marine ranch. The model can be used to estimate the MSY of an enhancement species when the sea area for its f ishing operation is inconsistent with its living area. Moreover, the accuracy of the results estimated by this model is higher than that of the results estimated by the enhancement model. The parameters in the model can be adjusted in accordance with the actual situation to meet the characteristics of resource migration and distribution, thereby improving the accuracy of stock assessment.

5 CONCLUSION

The migration enhancement biomass model proposed in this study can be used to estimate the MSY of the enhancement species with migration characteristics inside and outside marine ranches. The MSY is prone to be overestimated, and movement range ratios and biomass density inside and outside marine ranches are two important parameters that can aff ect the accuracy of the estimation results. The proposed model also provides an idea for estimating the MSY of species with inconsistent living and f ishing areas.

6 DATA AVAILABILITY STATEMENT

The data that support the f indings of this study are available from the corresponding author upon reasonable request.

7 ACKNOWLEDGMENT

We are grateful for all scientif ic staff and crew for their assistance with data collection during all the surveys.